Keresés

Részletes keresés
Így működik

Bővebben az új keresőről

spiroslyra 2002. nov. 25. Creative Commons License 6592
The modern modes that are playable with the context of the well tempered 12 tone system are named using the ancient Greek appelations, and can be described as the diatonic (white key) sequences:

Ionian: C D E F G A B (C)
Dorian: D E F G A B C (D)
Phrygian: E F G A B C D (E)
Lydian: F G A B C D E (F)
Mixolydian: G A B C D E F (G)
Aeolian: A B C D E F G (A)
Locrian: B C D E F G A (B)

Here, the first tone of the sequence is the resting or tonic note, and the tone in parenthesis is the tone an octave above the first tone, and has double the frequency. Although this might look like a bit of meaningless but fancy footwork since we are talking about nothing more than cyclic permutations of the same set of tones, the distinctions should be seen in terms of sequence of Full tone (T) and semitone (S) intervals.

Ionian: T T S T T T S
Dorian: T S T T T S T
Phrygian: S T T T S T T
Lydian: T T T S T T S
Mixolydian: T T S T T S T
Aeolian: T S T T S T T
Locrian: S T T S T T T

It is the resting point combined with intervallic structure that gives a mode its auditory qualities.

One might think that these names were taken over directly from the Liturgical nomenclature for pretty much the same structures. One would be very wrong.

One would think that after having corrected the correspondences to the liturgical modes, that then the objects and names would be in accordance with those of the ancient Greeks. One would be even more wrong. So clearly these are assumptions definitely not to be made.

We are very fortunate to have some rather early theoretical writings by Greeks concerning music. The earliest is seemingly the "Harmonics" of Aristoxenus (ca. 330 BCE), and so we know what the theorists say. Understanding what they mean, however, is an entirely different matter, since written examples of any music to which the written theory may pertain is almost nonexistent. This ignorance of the reality of ancient Greek music goes so far that we are not quite sure what a Greek mode really was. We understand Greek music on the level of pitch tempering. Trying to understand or retrodict what the music was like is equivalent to predicting the "Variations and Double Fugue on a Theme of Bach", by Max Reger, merely from a knowledge of well tempering and possibly a bit about chords and classical chromatic harmonic cadential formulas. It can't be done.

For an interesting and thoughtful essay on the problem that is based in actual research, see The Ancient Musical Modes: What Were They?, together with more links there.

From the writings of Aristoxenus, one can deduce that the ancient Greeks used microtonal embellishments, probably not unlike those stylistic practices in modern Greek music, and indeed throughtout middle eastern cultures. These have no notational place in western scoring language.

To the Greeks, all thinking about anything serious was philosophy, and writings on music theory were therefore in that culture, philosophy. Ancient Greek philosophers were in one important respect no different that philosophers in any other culture or time: the writings were predominantly prescriptive and proscriptive. See Plato's "Republic", Hobbes "Leviathan" [shudder], or any other poison of choice. Whether or not the theories of Greek music were actually pay attention to in practice is at very least in question.

It is reasoably clear that all theorizing about music is fundamentally derived from Pythagoras who understood the intervallic concepts that we call the octave, fifth, and fourth. Greek music seems to have been automatically wedded to language either by recitation or by song, but most popularly involved also two instruments, the aulos and the kithara. For some other musical definitions Eric's Treasure Trove: music may be helpful.
http://graham.main.nc.us/~bhammel/MUSIC/Gmodes.html

spiroslyra 2002. nov. 25. Creative Commons License 6591
2.5 Ancient Greek Modes
The scale presented above has semitone intervals between C and B and also F and E. All the rest of the intervals are whole tones. A different scale pattern in terms of the position of tone and semitone intervals may thus be produced by traversing the scale from different starting points.
The ancient Greeks distinguished harmoniai which were scale patterns in the greater perfect system from tonoi which were the modes used in tuning and performance of a stringed instrument. Tonos meant to stretch or tension.

The seven possible harmoniai are given in the following table. [EB] Unspaced letters show semitone intervals.

E D CB A G FE Dorian
D CB A G FE D Phrygian
CB A G FE D C Lydian
B A G FE D CB Mixolydian
A G FE D CB A Hypodorian
G FE D CB A G F Hypophrygian
FE D CB A G F Hypolydian
Ancient Greek Modes

spiroslyra 2002. nov. 25. Creative Commons License 6590
Listen to Audio Samples: To hear a sample, click the song title below. Windows Media player is required.
1. Diatonon Genus, Major System: Dorios Harmonia Or Doristi 9. Chromatic Genus, Major System: Phrygios Harmonia Or Phrygisti
2. Diatonon Genus, Major System: Ypodorios Harmonia Or Ypodoristi 10. Chromatic Genus, Major System: Lydios (Lydian) Harmonia, Or Lydisti
3. Diatonon Genus, Major System: Phrygios Harmonia Or Phrygisti 11. Chromatic Genus, Major System: Hypophrygios Harmonia Or Hypophrygisti
4. Diatonon Genus, Major System: Hypophrygios Harmonia Or Hypophrygisti 12. Enharmonion Genus: Dorios Harmonia Or Doristi
5. Diatonon Genus, Major System: Lydios (Lydian) Harmonia, Or Lydisti 13. Enharmonion Genus, Minor System: Dorios Harmonia In Diatonon Genus
6. Diatonon Genus, Major System: Hypolydios Harmonia Or Hypolidisti 14. Enharmonion Genus, Examples Of Musical Documents: Athenaeus, Paian
7. Diatonon Genus, Major System: Mixolydios Harmonia Or Mixolydisti 15. Enharmonion Genus, Fragment Of A Dramatic Lament On The Death Of Ajax
8. Chromatic Genus, Major System: Dorios Harmonia Or Doristi 16. Enharmonion Genus, Fragment Of An Instrumental Melody

http://shopping.yahoo.com/shop?d=product&id=1921301774

spiroslyra 2002. nov. 25. Creative Commons License 6589

The measurement of
Aristoxenus's Divisions of the Tetrachord
© 1999 by Joe Monzo

[1.24.11-14]
Pyknon de legestho to ek duo diastematon synestekos ha syntethenta elatton diastema periexei tou deipomenou diastematos en toi dia tessaron.
Let us call _'pyknon'_ that which is composed of two intervals which, when put together, cover an interval smaller than that which makes up the remainder of the fourth [i.e., 'perfect 4th'].

[2.45.35] Tonos d' estin ho to dia pente [2.46.1] tou dia tessaron meixon;
The tone is that by which the fifth is greater than the fourth.

That is, (3/2)/(4/3) = 9/8 = ~203.910 cents. This is the standard Pythagorean definition of the 'tone'. Aristoxenus continues:

[1.21.24-30] Diaireistho d' eis treis diaireseis; meloideistho gar | autou to te hemisu kai to triton meros kai tetarton; ta de touton elattona diastemata panta esto ameloideta. Kaleistho de to men elachiston diesis enarmonios elachiste, to d' echomenon | diesis chromatike elachiste, to de megiston hemitonion.
It [the tone] is to be divided in three ways, since the half, the third, and the quarter of it should be considered melodic. All intervals smaller than these are to be treated as unmelodic. Let the smallest of them be called the _least enharmonic diesis_, the next the _least chromatic diesis_, and the greatest the _semitone_.

[2.46.3-8] Ton de tou tonou meron melodeitai to hemisi, ho kaleitai hemitonion, kai to triton meros, | ho kaleitai diesis chromatike elachiste, kai to tetarton, ho kaleitai diesis enarmonios elachiste; toutou d' elatton ouden melodeitai diastema.

Of the parts of the tone the following are melodic: the half, which is called the semitone, the third part, which is called the least chromatic diesis, and the quarter, which is called the least enharmonic diesis. No interval smaller than that is melodic.

[2.55.13-23] Ean men oun prostachthe pros to dothenti phthongo labein epi to bary to | diaphonon oion ditonon ... epi to oxy apo tou dothentos phthongou lepteon to dia tessaron, eit epi to bary to dia pente, eita palin epi to | oxy to dia tessaron, eit epi to bary to dia pente. kai houtos estai to ditonon apo tou lephthentos phthongou eilemmenon to epi to bary.
if we have the task of constructing from a given note a discord such as a ditone downwards ... we should construct from the given note a fourth upwards, from there a fifth downwards, then another fourth upwards, and then another fifth downwards. In this way the ditone downwards from the given note will have been constructed.

[2.55.24-26] ean d' epi tounantion prostachthe labein to diapho|non, enantios poieteon ten ton symphonon lepsin.
And if the task is to construct the discord in the opposite direction, the concords should be constructed the opposite way round.

[2.55.27-31] Gignetai de kai ean apo symphonou diastematos to diaphonon aphairethe dia symphonias kai to loipon dia symphonias eilemmenon; aphaireistho | gar to ditonon apo tou dia tessaron symphonias;
Further, if a discord is subtracted from a concordant interval by means of concords, the remainder will also have been found by means of concords. For instance, let the ditone be subtracted by means of concords from the for...

[2.55.31-56.12] delon de hoti hoi ten hyperochen periechontes he to dia tessaron hyperechei tou ditonou dia symphonias esontai pros allelous eilemmenou; hypar||chousi men gar hoi tou dia tessaron horoi symphonoi; apo de tou oxyterou auton lambanetai phthongos symphonos epi to oxy dia tessaron, apo de tou le|phthentos heteros epi to bary dia pente, (eita palin epi to oxy dia tessaron,) eit' apo toutou heteros epi to bary dia pente. kai peproke to teleutaion symphonon epi ton exyterou ton hyperochen horizonton, host' einai pha|neron, hoti, ean apo symphonou diaphonon aphairethe dia symphonias, estai kai to loipon dia symphonias eilemmenon.
It is clear that the notes bounding the remainder by which the fourth exceeds the ditone have also been constructed, by means of concords, in their relation to one another. The notes bounding the fourth are themselves concordant. From the higher of them we find a note concordant at a fourth above, from that note another a fifth below, then again one a fourth above, and then from that note another a fifth below. The last of these concordant intervals falls on the higher of the notes bounding the remainder in question: and it is thus clear that if a discord is subtracted from a concord by means of concords, the remainder will also have been found by means of concords.

[2.50.22...] Mia men [23]oun ton diaipeseon estin enarmonios, [24]en he to men pyknon, hemitonion esti; to [25]de loipon, ditonon.
One of these divisions [of the tetrachord] is enharmonic, in which the pyknon is a semitone and the remainder a ditone.

[1.23.12-22] Hoi men gar tei nun katechousei melopoiiai synetheis monon ontes eikotos ten ditonon lichanon exorizousi; | syntonoterais gar chrontai schedon hoi pleistoi ton nun. toutou d' aition to boulesthai glukainein aei, semeion d' hoti toutou stochazontai, malista men gar kai pleiston chronon en toi chromati dia|tribousin, hotan d' aphikontai pote eis ten harmonian, engus tou chromatos prosagousi synepispomenou tou ethous.

It is to be expected that those who are used only to the style of composition at present in vogue rule out the ditone _lichanos_, since most people nowadays use higher ones. The reason is their endless pursuit of sweetness: that this is their objective is shown by the fact that they spend most time and effort on the chromatic, whereas when they do occasionally come to the enharmonic they force it close to the chromatic, and the melody is correspondingly pulled out of shape.

[1.24.22-25] katholou gar barytatai men hai enarmonioi lichanoi esan, echomenai d' hai chromatikai, syn|tonotatai d' hai diatonoi. taken overall, the enharmonic _lichanoi_ are the lowest, the chromatic next, and the diatonic the highest.

[1.22.27-30] Lichanou men oun esti toniaios ho sympas topos en hoi kineitai, oute gar elatton aphistatai meses toniaiou diaste|matos oute meizon ditonou. The total range in which _lichanos_ moves is a tone, since it does not stand at less than the interval of a tone from _mese_, nor at a greater interval than a ditone.
[2.46.28-33] phainetai de syntonotate men einai lichanos he tonon apo meses apechousa, | poiei d' haute diatonon genos, barytate d' he ditonon, gignetai d' haute enarmonios; host' einai phaneron ek touton, hoti toniaios estin ho tes lichanou topos. It appears that the highest _lichanos_ is that which lies at a tone from _mese_, and creates the diatonic genus; and the lowest is that at a ditone from _mese_, which belongs to the enharmonic. Hence it is clear that the range of _lichanos_ is a tone.

[1.26.13-27] Noeteon gar apeirous ton arithmon tas lichanous; ohu gar | an steseis ten phonen tou apodedeigeenou lichanoi topou lichanos estai, diakenon d' ouden esti tou lichanoeidous topou oude toiouton hoion me dechesthai lichanon. Host' einai me peri mikrou ton | amphisbetesin; hoi men gar alloi diapherontai peri tou diastematos monon, hoion poteron ditonos estin he lichanos e syntonotera hos mias ouses enarmoniou; hemeis d' ou monon pleious en | hekastoi genei phamen einai lichanous mias alla kai prostithemen hoti apeiroi eisi ton arithmon. For it must be understood that the lichanoi are unlimited in number. Wherever you arrest the voice in the range that accommodates the _lichanos_ will be a _lichanos_, and no place in the lichanos range is empty or incapable of receiving a lichanos. Hence the present controversy is of no little importance. Other people argue only about the interval in question, for instance whether the lichanos stands at a ditone or is higher, as if there were only one enharmonic lichanos. But we not only say that there is more than one _lichanos_ in each genus, but also add that they are unlimited in number.
[1.26.24-27] hemeis d' ou monon pleious en | [25] hekastoi genei phamen einai lichanous mias alla kai prostithemen hoti apeiroi eisi ton arithmon. we not only say that there is more than one _lichanos_ in each genus, but also add that they are unlimited in number.
[1.26.14-18] ohu gar | an steseis ten phonen tou apodedeigeenou lichanoi topou lichanos estai, diakenon d' ouden esti tou lichanoeidous topou oude toiouton hoion me dechesthai lichanon. Wherever you arrest the voice in the range that accommodates the _lichanos_ will be a _lichanos_, and no place in the lichanos range is empty or incapable of receiving a lichanos.

The range of the _parhypatai_

[1.23.27-29] let the range of ... _parhypate_ [be agreed to be] the smallest diesis, since it never comes closer to _hypate_ than a diesis and is never more than half a tone away from it.
[1.23.27-29] let the range of ... _parhypate_ [be agreed to be] the smallest diesis [i.e., '1/4-tone'], since it never comes closer to _hypate_ than a diesis [i.e., (256/243)^(1/2) above _hypate_] and is never more than half a tone away from it [i.e., either (9/8)^(1/2) or 256/243 above _hypate_].

[2.52.5 ...] tettaron d' ouson parypaton, he [6] men enarmonios idia esti tes harmo-[7]nias; hai de treis koinai tou te diatonou, [8]kai tou chromatos. Of the four _parhypatai_, the enharmonic one is peculiar to the enharmonic genus, while the other three are common to the diatonic and chromatic.

Mathiesen illustrates distinctions in Aristoxenus's terminology at this point, which have been missed by most editors and translators:

[1.26.30-33, text from Mathiesen 1976, eliminating emendations] parypates de duo eisi topoi - ho men koinos tou te diatonou kai tou chromatos, ho d' heteros idios tes harmonias - ; koinonei gar duo gene ton parypaton. enarmonios men oun esti parypate pasa he barytera tes barytates chromatikos, ... [Mathiesen 1976, p 14, translating Aristoxenus 1.26.30-33] There are two positions for the parhypate, the one common to the diatonic and _color_, the other unique to the _Harmonia_, for the two genera share the parhypate. For every parhypate is _enharmonic_ which is lower than the lowest _chromatic_ [parhypate], ...

[2.51.32] Lichanoi men oun eisin hex. mia enarmo-[33]nios, treis chromatikai, kai duo diato-[34]noi. {parypatai de tettares,} hosai per ai [2.52.1] ton tetrachordon diaipeseis. parypatai [2] de duo{in} elattous. te gar hemitoniaia [3] chrometha pros te tas diatonous, kai [4] pros ten tou toniaiou chromatos diaipe- [5]sin. There are thus as many _lichanoi_ as there are divisions of the tetrachord [i.e., six], and two fewer _parhypatai_, since we use that which stands at a semitone both for the diatonic divisions and for that of the tonic chromatic.

1.24.15-25.11]

[1.24.15-25.11]
> [Meibom:]
15> Touton houtos horismenon, pros toi
16> baryteroi ton menonton phthongon eile-
17> phtho to elachiston. pyknon d' estai to
18> ek duo dieseon enarmonion kai chro-
19> matikon elachiston. esontai duo de li-
20> chanoi eilemmenai duo genon bary-
21> tatai. he men harmonias; he de, chro-
22> matos. katholou gar barytatai
23> men hai enarmonioi lichanoi esan.
24> echomenai de, hai chromatikai. syn-
25> tonotatai de, hai diatonoi. Meta tau-
26> ta triton eilephtho pyknon pros toi
27> autoi. tetarton eilephtho pyknon to-
28> niaion. pempton de pros toi autoi,
29> to ex hemitoniou kai hemioliou diastem-
30> matos synestekos systema eilephtho.
31> hekton de, ex hemitoniou kai tonou. Hai
32> men oun ta duo ta prota lephthen-
33> ta pykna horizousai lichanoi eiren-
34> tai; he de to triton pyknon horizousa
[25]
1> lichanos, chromatike men estin; kalei-
2> tai de to chroma, en hoi estin, hemiolion.
3> he de to tetarton pyknon horizousa li-
4> chanos, chromatike men estin; kaleitai
5> de to chroma, en hoi esti, toniaion. he de
6> to pempton lephthen systema horizousa
7> lichanos, ho meizon ede pyknou en.
8> epeideper isa esti ta duo toi heni, ba-
9> rytate diatonos estin. he de to hekton
10> lephthen systema horizousa lichanos,
11> syntonotate diatonos estin.

> [Macran:]
> Touton houtos horismenon pros toi baryteroi ton menonton
> phthongon eilephtho to elachiston pyknon; touto d' estai to ek
> duo dieseon autoi; touto de estai to ek duo dieseon> chromatikon elachiston.
> esontai de duo li|chanoi eilemmenai duo genon barytatai,
> he men harmonias he de chromatos. katholou gar barytatai men
> hai enarmonioi lichanoi esan, echomenai d' hai chromatikai,
> syn|tonotatai d' hai diatonoi. Meta tauta triton eilephtho
> pyknon pros toi autoi; tetarton eilephtho pyknon toniaion;
> pempton de pros toi autoi, to ex hemitoniou kai hemioliou
> diastem|matos synestekos systema eilephtho; hekton de to ex
> hemitoniou kai tonou. Hai men oun ta duo [ta] prota lephthenta
> pykna horizousai lichanoi eirentai; he de to triton pyknon
> horizousa || lichanos chromatike men estin, kaleitai de to
> chroma en hoi estin hemiolion. He de to tetarton pyknon horizousa
> lichanos chromatike men estin, kaleitai | de to chroma en hoi
> esti toniaion. he de to pempton lephthen systema horizousa
> lichanos, ho meizon ede pyknou en, epeideper isa esti ta duo
> toi heni, barytate diatonos estin. he de to hekton lephthen |
> systema horizousa lichanos syntonotate diatonos estin.
>
>> Given these definitions, let us take the smallest pyknon, placed
>> next to the lower of the fixed notes. This will be the one
>> composed of two enharmonic or two of the smallest chromatic
>> diesis. The two lichanoi thus specified will be the lowest in
>> each of the two genera, one in the enharmonic, the other in the
>> chromatic: for we have explained that, taken overall, the
>> enharmonic lichanoi are the lowest, the chromatic next, and the
>> diatonic the highest. After these, consider a third pyknon
>> placed next to the same note, and then a fourth one, which
>> is a tone: fifthly, from the same note take the systema composed
>> of a semitone and an interval one and a half times as great, and
>> sixthly, that composed of a semitone and a tone.
>> We have already spoken of the lichanoi bounding the first two
>> pykna listed. The one that bounds the third is chromatic, and
>> the chroma in which it is is called hemiolic. That bounding the
>> fourth pyknon is chromatic, and the chroma in which it is is
>> called tonic. The lichanos bounding the fifth systema mentioned,
>> which was specified as greater than a pyknon, since the two
>> intervals are equal to the one, is the lowest diatonic: that
>> which bounds the sixth systema mentioned is the highest diatonic.

[1.25.11-26.7]
[Meibom:]
[25]
11> .................. He men oun
12> barytate chromatike lichanos tes
13> enarmoniou barytates hektoi merei to-
14> nou oxytera estin. epeideper he chro-
15> matike diesis tes enarmoniou dieseos
16> dodekatemorioi tonou meizon esti. Dei
17> gar to tou autou tritemorion tou tetartou
18> merous dodekatemorioi hyperechein.
19> hai de duo chromatikai ton duo
20> enarmonion delon hos toi diplasioi.
21> touto de estin hektemorion elatton dia-
22> stema tou elachistou ton meloidoume-
23> non. Ta de toiauta ameloideta
24> estin. ameloideton gar legomen, ho me
25> tattetai kath' heauto en systemati. He de
26> barytate diatonos tes barytates
27> chromatikos hemitonioi kai dodekate-
28> morioi tonou oxytera estin. epi men gar
29> ten tou hemioliou chromatos lichanon
30> hemitonion en ep' autes. apo de tes hemio-
31> liou epi ten enarmonion, diesis. apo
32> de tes enarmoniou epi ten baryta-
33> ten chromatiken, hektemorion. apo de
34> tes barytates chromatikes epi ten hemiolion, dodekatemorion tonou. to
[26]
1> de tetartemorion ek trion dodeka-
2> temorion synkeitai. host' einai phane-
3> ron, hoti to eiremenon diastema estin
4> apo tes barytates diatonou, epi ten
5> barytaten chromatiken. he de syn-
6> tonotate diatonOS tes barytates
7> diatonou, diesei esti syntonotera.

[Macran:]
> He men oun barytate chromatike lichanos tes
> enarmoniou barytates hektoi merei tonou oxytera estin, epeideper
> he chro|matike diesis tes enarmoniou dieseos dodekatemorioi
> tonou meizon esti. Dei gar to tou autou tritemorion tou tetartou
> merous dodekatemorioi hyperechein, hai de duo chromatikai ton
> duo | enarmonion delon hos toi diplasioi. touto de estin
> hektemorion, elatton diastema tou elachistou ton meloidoumenon.
> Ta de toiauta ameloideta estin, ameloideton gar legomen ho me |
> tattetai kath' heauto en systemati. He de barytate diatonos
> tes barytates chromatikos hemitonioi kai dodekatemorioi tonou
> oxytera estin. epi men gar ten tou hemioliou chromatos lichanon |
> hemitonion en ap' autes, apo de tes hemioliou epi ten
> enarmonion diesis, apo de tes enarmoniou epi ten barytaten
> chromatiken hektemorion, apo de tes barytates chromatikes epi
> ten hemiolion dodekatemorion tonou. to || de tetartemorion
> ek trion dodekatemorion synkeitai, host' einai phaneron, hoti to
> eiremenon diastema estin apo tes barytates diatonou epi ten |
> barytaten chromatiken. He de syntonotate diatonos tes barytates
> diatonou diesei esti syntonotera.

>
>> Thus the lowest chromatic lichanos is higher than the lowest
>> enharmonic by a sixth part of a tone, since the chromatic diesis
>> is greater by a twelfth part of a tone than the enharmonic diesis.
>> A third part of anything must exceed a quarter of the same thing
>> by a twelfth part, and the two chromatic dieses must evidently
>> exceed the two enharmonic ones by twice that amount. This is
>> a sixth part, an interval smaller than the least of the melodic
>> intervals. Such intervals are unmelodic, since we call 'unmelodic'
>> any interval that is not placed in a systema in its own right.
>> The lowest diatonic lichanos is higher than the lowest chromatic
>> by a semitone and a twelfth part of a tone. We said that it is
>> a semitone from the lichanos of the hemiolic chromatic, and from
>> there to the enharmonic lichanos is a diesis: from the enharmonic
>> to the lowest chromatic lichanos is a sixth part of a tone, and
>> from the lowest chromatic to the hemiolic lichanos is a twelfth
>> part of a tone. Now a quarter is composed of three twelfth parts,
>> so that it is clear that from the lowest diatonic to the lowest
>> chromatic lichanos is the interval stated. The highest diatonic
>> lichanos is higher than the lowest diatonic by a diesis.

[25.11 ...] He men oun [12] barytate chromatike lichanos tes [13] enarmoniou barytates hektoi merei to-[14]nou oxytera estin. [25.11 ...]Thus the [12] lowest chromatic lichanos from [13] the lowest enharmonic a sixth part of a tone [14] is higher.
epeideper he chro-[15]matike diesis tes enarmoniou dieseos [16] dodekatemorioi tonou meizon esti. since the chromatic [15] diesis from the enharmonic diesis [16] by a twelfth part of a tone is greater.
Dei [17] gar to tou autou tritemorion tou tetartou [18] merous dodekatemorioi hyperechein. A [17] third part of anything from a quarter of the [18] same thing a twelfth-part must exceed.
[19] hai de duo chromatikai ton duo [20] enarmonion delon hos toi diplasioi. [19] and the two chromatics from the two [20] enharmonics evidently must double that.
[21] touto de estin hektemorion elatton dia-[22]stema tou elachistou ton meloidoume-[23]non. [21] This is a sixth part, an interval smaller [22] than the least of the melodic [23] ones.
Ta de toiauta ameloideta [24] estin. ameloideton gar legomen, ho me [25] tattetai kath' heauto en systemati. Such intervals are unmelodic, [24] since we call 'unmelodic' any [25] that is not placed in a systema.
He de [26] barytate diatonos tes barytates [27] chromatikos hemitonioi kai dodekate-[28]morioi tonou oxytera estin. The [26] lowest diatonic (lichanos) from the lowest [27] chromatic a semitone and a twelfth [28] part of a tone is higher.
epi men gar [29] ten tou hemioliou chromatos lichanon [30] hemitonion en ep' autes. We said that [29] from the hemiolic chromatic lichanos, [30] it is a semitone.
apo de tes hemio-[31]liou epi ten enarmonion, diesis. and from the hemiolic [31] to the enharmonic is a diesis.
apo [32] de tes enarmoniou epi ten baryta-[33]ten chromatiken, hektemorion. from [32] the enharmonic to the lowest [33] chromatic is a sixth part.
apo de [34] tes barytates chromatikes epi ten hemiolion, dodekatemorion tonou. from [34] the lowest chromatic to the hemiolic is a twelfth part of a tone.
to [26.1] de tetartemorion ek trion dodeka-[2]temorion synkeitai. Now [26.1] a quarter of three twelfth-[2]parts is composed.
host' einai phane-[3]ron, so that it is clear [3] that
hoti to eiremenon diastema estin [4] apo tes barytates diatonou, epi ten [5] barytaten chromatiken. it is the interval stated [4] from the lowest diatonic, to the [5] lowest chromatic.
he de syn-[6]tonotate diatonOS tes barytates [7] diatonou, diesei esti syntonotera. The tensest [6] diatonic (lichanos) from the lowest [7] diatonic is a diesis tenser.


> Ek touton de phaneroi gignontai hoi topoi ton lichanon hekastes;

[1.24.15-21] > Touton houtos horismenon pros toi baryteroi ton > menonton phthongon eilephtho to elachiston pyknon; touto > d' estai to ek duo dieseon (enarmonion elachiston; epeita > deuteron pros toi autoi; touto de estai to ek duo dieseon) > chromatikon elachiston. esontai de (hai) duo li|chanoi > eilemmenai duo genon barytatai, he men harmonias he de chromatos. > >> let us take the smallest pyknon, placed next to the lower >> of the fixed notes. This will be the one composed of two >> enharmonic or two of the smallest chromatic diesis. The two >> lichanoi thus specified will be the lowest in each of the >> two genera, one in the enharmonic, the other in the chromatic:

[2.50.23-24] > Mia men oun ton diaipeseon estin enarmonios en he > to men pyknon hemitonion esti to | de loipon ditonon. > >> One of these divisions is enharmonic, in which the _pyknon_ >> is a semitone and the remainder a ditone.

> [2.50.22 ...] Mia men [23] oun ton diaipeseon estin enarmonios, > [24] en he to men pyknon, hemitonion esti; > to [25] de loipon, ditonon. > >> One of these divisions [of the tetrachord] is enharmonic, in >> which the pyknon is a semitone and the remainder a ditone.

[1.24.15-21]
> let us take the ... _pyknon_ ... composed of ... two of
> the smallest chromatic dieses. The ... [_lichanos_] thus
> specified will be the lowest in ... the chromatic [genus].

[1.25.11-14]
> He men oun barytate chromatike lichanos tes enarmoniou
> barytates hektoi merei tonou oxytera estin,
>
>> the lowest chromatic _lichanos_ is higher than the lowest
>> enharmonic by a sixth part of a tone, ...

[1.25.32-33]
> apo de tes enarmoniou epi ten barytaten chromatiken hektemorion,
>
>> from the enharmonic to the lowest chromatic _lichanos_ is a
>> sixth part of a tone, ...

[1.25.14-16]
> epeideper he chro|matike diesis tes enarmoniou dieseos
> dodekatemorioi tonou meizon esti.
>
>> ... since the chromatic diesis is greater by a twelfth part of
>> a tone than the enharmonic diesis.

[2.51.4-8]
> [4...] Hoti d' esti [5] meizon to hemiolion pyknon
> tou malakou, [6] rhadion synidein.
> to men gar enarmo-[7]niou dieseos leipei tonos einai;
> to de, [8] chromatikos.
>
>> It is easy to see that the hemiolic pyknon
>> is greater than that of the soft chromatic,
>> for the former falls short of being a tone by an enharmonic diesis,
>> the latter by a chromatic diesis.

>> ... the ... _pyknon_ ... of the soft chromatic ... falls
>> short of being a tone ... by a chromatic diesis.

> [2.50.28] malakou men oun chromatos esti diai-[29]pesis,
> en he to men pyknon ek duo chro-[30]matikon dieseon elachiston synkei-[31]tai;
> to de loipon duo metrois metrei-[32]tai;
> hemitonioi men tris, chromatikei [33]de diesei hapax.
> hoste metreisthai trisin hemitoniois, kai tonou tritei merei hapax.
> [34]esti de ton chromatikon pyknon elachiston,
> kai lichanos haute barytate tou [2.51.1] genous toutou.
>
>> [2.50.28] The division of the soft chromatic is that
>> [29] in which the _pyknon_ consists of two of the [30] smallest chromatic dieses,
>> [31] and the remainder is measured by two units of measurement,
>> [32] by the semitone three times, and by the chromatic [33] diesis once [,
>> so that the sum of it amounts to three semitones and the third of a tone].
>> [34] It is the smallest of the chromatic _pykna_,
>> and this _lichanos_ is the lowest in [2.51.1] this genus.

[1.24.26]
> Meta tauta triton eilephtho pyknon pros toi autoi;
>
>> consider a third _pyknon_ placed next to the same note [_hypate_]...

[1.25.30-31]
> apo de tes hemioliou epi ten enarmonion diesis,
>
>> from the _lichanos_ of the hemiolic chromatic ... to the enharmonic
>> _lichanos_ is a diesis ...

> [2.51.1 ...] hemioliou de chromatos di-[2]aipesis estin,
> en he to te pyknon hemiolion [3] esti, tou [t'] enarmoniou,
> kai ton dieseon heka-[4]teras ton enarmonion.
>
>> [2.51.1 ...] The division of the hemiolic chromatic [2] is that
>> in which the _pyknon_ is one and a half times [3] that of the enharmonic,
>> and each of its dieses is [4] one and a half times the corresponding enharmonic diesis.

[2.51.4-7]
> the hemiolic _pyknon_ ... falls short of being a tone by
> an enharmonic diesis

[1.25.30-31]
> apo de tes hemioliou epi ten enarmonion diesis,
>
>> from the _lichanos_ of the hemiolic chromatic ... to the enharmonic
>> _lichanos_ is a diesis ...

[1.26.1-2]
> from the lowest chromatic to the hemiolic _lichanos_ is a twelfth part
> of a tone.

[1.24.27]
> tetarton eilephtho pyknon toniaion;
>
>> consider ... a fourth [_pyknon_, in the series of six],
>> which is a tone ...

[2.51.8-11]
> toniaiou de chromatos diaipesis estin en he to men pyknon
> ex hemi|tonion duo synkeitai to de loipon triemitonion estin.
>
>> The division of the tonic chromatic is that in which the
>> _pyknon_ consists of two semitones and the remainder is
>> three semitones.

[1.24.28-30]
> pempton de pros toi autoi, to ex hemitoniou kai hemioliou
> diastem|matos synestekos systema eilephtho;
>
>> fifthly, from the same note [_hypate_] take the _systema_ composed
>> of a semitone and an interval one and a half times as great, ...

[1.25.26-28]
> He de barytate diatonos tes barytates chromatikos hemitonioi
> kai dodekatemorioi tonou oxytera estin.
>
>> The lowest diatonic _lichanos_ is higher than the lowest chromatic
>> by a semitone and a twelfth part of a tone.

[1.25.26-30]
> He de barytate diatonos ... epi men gar ten tou hemioliou chromatos
> lichanon | hemitonion en ap' autes,
>
>> The lowest diatonic _lichanos_ ... is a semitone from the _lichanos_
>> of the hemiolic chromatic

> [2.51.11 ...] Mechri men oun tautes tes di-[12]aipeseos
> amphoteroi kinountai hoi phthon-[13]goi.
> meta tauta d' he men parypate me-[14]nei;
> dieleluthe gar ton hautes topon;
> he de [15] lichanos kineitai diesin enarmonion.
> kai [16] gignetai to lichanou kai hypates
> diaste-[17]ma ison toi lichanou kai meses.
> hoste me-[18]keti gignesthai pyknon en tautei tei diai-[19]pesei.
> symbainei d' hama payesthai to py-[20]knon,
> synistamenon en tei ton tetrachor-[21]don diairesei
> kai archesthai gignomenon to [22] diatonon genos.
>
>> [2.51.11 ...] Up to [the tonic chromatic] division,
>> [12] both the notes [_lichanos_ and _parhypate_] move,
>> [13] but after this _parhypate_ stays still,
>> [14] since it has travelled through its whole range,
>> while [15] _lichanos_ moves through an enharmonic diesis,
>> and [16] the interval between _lichanos_ and _hypate_
>> [17] becomes equal to that between _lichanos_ and _mese_,
>> so that [18] in this division the _pyknon_ no longer occurs.
>> [19] The _pyknon_ disappears [20] in the division of the tetrachord [21] simultaneously
>> with the first occurrence of the [22] diatonic genus.

> [2.51.24 ...] malakou men oun esti diatonou diai-[25]pesis,
> en he to men hypates kai parypa-[26]tes hemitoniaion esti;
> to de parypates kai [27] lichanou trion dieseon enarmonion;
> [28] to de lichanou kai meses, pente dieseon.
>
>> [2.51.24 ...] The division of the soft diatonic is that
>> [25] in which the interval between _hypate_ and _parhypate_ [26] is a semitone,
>> that between _parhypate_ and [27] _lichanos_ is three enharmonic dieses,
>> and [28] that between _lichanos_ and _mese_ is five dieses.

[1.24.31]
> hekton de to ex hemitoniou kai tonou.
>
>> sixthly, [consider] that [_systema_] composed of a semitone and a tone.

> [2.51.29] syntonou de,
> en he to men hypates kai pa-[30]rypates hemitoniaion;
> ton de loipon to-[31]niaion hekateron estin.
>
>> [2.51.29] [The division] of the tense diatonic is that
>> in which the interval between _hypate_ and [30] _parhypate_ is a semitone,
>> and each of the others [31] is a tone.

[Cleonides, section 7; Strunk 1950, p 39-40]
> The tone is assumed to be divided into twelve least parts,
> of which each one is called a twelfth-tone. The remaining
> intervals are also assumed to be divided in the same proportion,
> the semitone into six twelfths, the diesis equivalent to a
> quarter-tone into three twelfths, the diesis equivalent to a
> third-tone into four twelfths, the whole diatessaron into
> thirty twelfths.

[Cleonides, section 7; Strunk 1950, p 40]
> In terms of quantity, then, the enharmonic will be sung by 3, 3,
> and 24 twelfths, the soft chromatic by 4, 4, and 22, the hemiolic
> chromatic by 4&1/2, 4&1/2, and 21, the tonic chromatic by 6, 6,
> and 18, the soft diatonic by 6, 9, and 15, the syntonic diatonic
> by 6, 12, and 12.

1/12-tones

enharmonic 3, 3, 24
soft chromatic 4, 4, 22
hemiolic chromatic 4&1/2, 4&1/2, 21
tonic chromatic 6, 6, 18
soft diatonic 6, 9, 15
syntonic diatonic 6, 12, 12

spiroslyra 2002. nov. 25. Creative Commons License 6588
Budapest, Tűzoltó Múzeum

a világhírű, római kori (Kr. u. 228.), aquincumi víziorgona rekonstrukciója, 1996.

Munkánk során figyelembe vettük a régészeti leletek laboratóriumi vizsgálatokkal meghatározott anyagait. Így a különböző alkotórészeket abból az anyagból készítettük el, amiből kb. 1770-1800 évvel ezelőtt is készítették. A sípok és egyéb részek kivitelezésénél fontosnak tartottuk az antik megoldásokat. Ezért teljesen el kellett vonatkoztatnunk a mai orgonaépítésben alkalmazott technológiáktól. A régi leírásokat, ábrázolásokat, valamint a fizika törvényeit figyelembevéve rekonstruáltuk a víziorgonát.

Egyiptomi terrakotta

A farészeket és a díszítéseket apró, kézzel kovácsolt bronz szögekkel rögzítettük egymáshoz. A hiányzó, vagy hiányos sípok hosszát régi római mértékegységek segítségével számoltuk ki. A hangszer elkészítése közben többszáz kérdéssel találtuk szembe magunkat mind zeneileg, mind technikailag. Ezekre biztos választ valószínűleg csak az örökkévalóságban kaphatunk, mindazonáltal valljuk, hogy rekonstrukciónk az eddigiekhez képest a leghűebben tükrözi az egykori hangszert.

Az orgona története

Budapest III. kerületében, az Aquincumi Múzeumtól délre, az Elektromos Művek transzformátorháza alapjainak kiásásakor a munkások az egykori tűzoltószékház romjai között egy beomlott római-kori pincére bukkantak. Ennek kő és törmelék halmaza alatt találták meg az összetört bronz sípokat és az orgona alkatrészeit. A világhírű maradványokat Nagy Lajos, az Aquincumi Múzeum akkori régésze ásta ki 1931-ben.

Megtalálták az ajándékozás tényét megörökítő táblácskát is, aminek szövegéből kitűnik, hogy a hangszert 228-ban ajándékozta az aquincumi tűzoltótestületnek parancsnokuk Gaius Iulius Viatorinus.

Az orgona feliratos bronztáblája. (Értelmezése: Gaius Iulius Viatorinus, Aquincum colonia rangú város tanácsnoka, egykori aedilis (rendőrparancsnok féle) a tűzoltóság parancsnoka (praefectus collegii centonariorum) orgonát a saját pénzéből ajándékoz a fent megvezett társulatnak Modestus és Probus konzulsága idején (I. u. 228-ban).

Az orgona, ami a tűzoltószékház alápincézett helyiségében a tűzoltóparancsnok rendelkezésére állhatott - akkor zuhanhatott a pincébe, amikor ellenséges ostrom során i. sz. 250 körül - maga a székház is leégett. Fa és bőr részei a tűzben elégtek, illetve a hő hatására elszenesedtek, ólomba ágyazott alkatrészei egymásba olvadtak. Mivel a tűzvész után a pincét nem takarították ki, az orgona darabjai betemetődve megmaradtak, ezeket ugyan nem a legjobb állapotban sikerült kiemelni, ám a megmaradt részek alapján hitelesebb képet lehetett kialakítani a római kori orgonáról.

Az orgona maradványai

Nagy Lajos szerint az orgona maradványait olyan helyzetben találták, amely megfelelt eredeti állapotának, s mivel hanyatt esett, az a része került felülre, ami eredetileg a hallgatóság felé nézett. Ezért került először a hangszer előoldalára erősített - már említett ajándékozási táblácska - a régész kezébe. Az eredeti alkatrészek épebb darabjait megtisztításuk után mindjárt kiállították az Aquincumi Múzeumban a törmelékek pedig egy ládában várták sorsukat.

Az első orgonarekonstrukció

Nagy Lajos és Kalmár János tervei szerint a fellelt alkatrészek, sípok méreteinek és feltehető elrendezésének megfelelően 1935-ben a pécsi Angster-orgonagyár elkészítette a hordozható orgonarekonstrukciót, ami kovácsfújtatóra emlékeztető két kis bőrfújtatóval szólaltatható meg.
1959 őszén Ráfael Viktor, az Aquincumi Múzeum restaurátora - a háborús bombatámadásokat sértetlenül átvészelt kiállított részek, valamint 1944-ben a Bazilika pincéjébe biztonságba helyezett törmelék alkatrészek felhasználásával összeállította az eredeti alkatrészeket.
Ráfael mester sem víziorgonaként építette össze az egyetlen római-kori orgona eredeti alkatrészeit, hanem az Angster-féle rekonstrukciót tekintette mintának. Ugyanő készített 1956-ban a Tűzoltó Múzeum első állandó kiállítására egy meg nem szólaltatható orgonamakettet.

Második rekonstrukció

Werner Walcker-Mayer ludwigsburgi orgonaépítő mester 1969-ben új rekonstrukciót készített és 1970-ben arról egy részletes tanulmányt tett közzé. Jóllehet a víziorgona elv mellett érveket sorol fel, orgonáját mégsem víziorgonaként működteti.
Időközben a Központi Múzeológiai és Technológiai Osztály elvégezte az eredeti darabok újabb restaurálását és konzerválását. Ennek során "a tűz által meggörbült és összezsugorodott töredékeket gondos munkával kiegyengették. Az egyes kisebb hiányzó részeket megfelelő eljárással pótolták". 1973-ban a modern kiállítási elveknek megfelelő, jól szemléltethető módon plasztikra szerelték az eredeti alkatrészeket.

Az Aquincumi római-kori orgona hidraulusz (víziorgona)-ként történő rekonstrukciója és a fújtató működőképes modelljének megépítése

A Tűzoltó Múzeum kutatója - Minárovics János - 1987-től foglalkozik intenzívebben az aquincumi orgona víziorgona voltának bizonyításával.

Orgona rajza az utrechti Egyetemi Könyvtárban őrzött 9. századi zsoltároskönyvből.

A víziorgonákban az állandó légnyomást a légszabályozó vagy pnigeus (más néven szélharang, vagy légüst) biztosítja. A levegőt a henger alakú vagy légfújtatós pumpák juttatják a pnigeusba, amit általában harang alakú légtartályként ábrázolnak.

A pnigeus alsó peremén nyílások vannak, vagy térköztartókon ül a víztartályba helyezve. Ha levegőt pumpálnak a pnigeusba, a vízszint csökken a légtartályon belül és emelkedik azon kívül. Ha túl sok levegő kerül bele, akkor az a perem mentén távozik és átbuborékol a vízen, így a légnyomás állandó szinten marad.

Heron víziorgonájának szerkezete (Schmidt után)

A víz szerepe az, hogy biztosítsa a folyamatos levegőáramlást a pnigeusból a szélládába és onnan a sípokhoz. Minárovics megfigyelései alapján elkészített vízifújtatóval szólaltatható meg a cégünk által 1996-ban rekonstruált ókori hangszer.

http://www.orgona.hu/orgonaink/tuzolto_orgona_h.html


spiroslyra 2002. nov. 25. Creative Commons License 6587
"OUTE GAR EUKATAFRONITON ESTI TINI OS NOUN EHEI TO MATHIMA"
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Ozene(bona) :) XIX. Aristoxenos

Vegyunk ket diesist, enharmonikus elahistost. Ez a legkisebb pyknon. Ket chromatikus es ket enharmonikus diesis, a ket legmelyebb lihanos. A kovetkezo a chromatikus imiolius lichanos. Ezt koveti a tonikus chromatikus lichanos. Az otodik piknon a mely diatonikus, a hatodik a magas .

A legmelyebb chromatikus lichanos es a legmelyebb enharmonikus kulonbozik a tonus egy hatodaval.
....
----....4+4=8 malako chromatikus
...
---...3+3=6 enharmonikus
A chromatikus diesis egy dodekatimorionnal nagyobb az enharmonikusnal.
...
....
A mely diatonikus lichanos es a mely chromatikus kulonbsege egy fel es egy dodekatimorion tonus, 7/12.
......6
------.........9 6+9=15 malako diatonikus
....
----....4+4=8 malako chromatikus
...............15-8=7
........8
--------.......7
A mely, masneven lagy diatonikustol az chromatikus imiolion lihanosig a kulonbseg
imitonio egy fel tonus.
......6
------.........9+6=15-9=6 6/12=1/2 tonus
....*4,5
----*....*4,5 4,5+4,5=9 imiolio chromatikus
A tavolsag az imioliontol az enharmonikusig egy diesis.3/12 dodekatimorio, 1/4 tonus, enharmonikus diesis.
....*4,5
----*....*4,5 4,5+4,5=9 imiolio chromatikus
...
---...3+3=6 enharmonikus lichanos
.........9-6=3 3/12=1/4
......6
Az enharmonikustol a mely chromatikusig egy ektimorion .
...
---...3+3=6 enharmonikus lichanos
....
----....4+4=8 malako chromatikus
......6
........8-6=2 2/12=1/6 ektimorion
A legmelyebb chromatikustol az imiolionig
egy dodekatimorion. 1/12 tonus.
....
----....4+4=8 malako chromatikus
....*4,5
----*....*4,5 4,5+4,5=9 imiolio chromatikus
........8
.........9-8=1
A lichanosok terulete a mely diatonikustol a mely chromatikusig terjed.
......6
------............12 6+12=18 syndono diatonikus
......6
------.........9 6+9=15 malako diatonikus
......6
------......6 6+6=12 tonikus chromatikus
....*4,5
----*....*4,5 4,5+4,5=9 imiolio chromatikus
....
----....4+4=8 malako chromatikus
A syndonos diatonikus lichanos a mely diatonikusnal egy diesissel magasabb.3 moria, 3/12 , 1/4 enharmonikus elahistos diesis.
......6
------............12 6+12=18 syndono diatonikus
......6
------.........9 6+9=15 malako diatonikus
..................18-15=3
...............15

A suneheias termeszete hasonlit a szavaknak a betukbol valo osszetetelehez. Nem lehetseges nyolc egymast koveto diesis , nem megvalosithato harom diesis egymas utani leeneklese. Ha ket diesis fole emelkedik a hang, nem haladhat tovabbb, csak annyit, amennyi kiegesziti a tetrachordot. Az elahiston diesisnel nyocszor kisebb diasztema hasznalhatatlan. Leszallitva a dallamot ket diesis utan egy tonusnal kisebb diasztema ameloditos.

[Aristoxenos itt lezar egy fejezetet, es jo szokasa szerint, mielott tovabb haladna, vissza es egyben elore nez. E korbejaras okat most ne firtassuk, nemelyek arra gyanakszanak, hogy rankmaradt muve egy utolagos osszeallitas, tobb konyvebol osszerakva, ezzel magyarazhato a tobbszori nekifutas. De meglehet, hogy tudatos modszerrol van szo, az ismeretek fokozatos elmelyiteserol, az ismetlessel az emlekezet felfrissiteserol. Ha valojaban ezek elo eloadasok voltak, melyeket utolagosan jegyezetek le, ha ez igaz, akkor az idonkent felbukkano, vitazo, polemikus elu, kerdesekre valaszolo mondatok, nem stilaris jegyek, hanem az elobeszed jelei. Aristoxenos muve nem tobb szaz oldalnal, de ezt egy lendulettel elmondani, ugy hogy a hallgatosag, megha jaratos is a zeneben, felfogja, igen nehez. Mindenesetre ,vigasztalasunkra megjegyzi, hogy akinek esze van, annak megertheto ez a tudomany, persze ha ez jo emlekezettel is parosul. A lassu eszjarasuakat es nem jo memoriajuakat hol finomabban, hol goromban eltanacsolja. Magara vessen tehat az, aki mint en, csekely ertelemmel es veszkodo emlekezettel probalja kovetni...:)]

Katholou men oun noiteon ousan imin tin theorian peri melous pantos pos pote pefiken i foni epitinomeni kai aniemeni tithenai ta diastimata. fusikin gar di tina famen imeis tis fonin kinisin kineistai kai ouh os etihe diastima tithenai. Ka touton apodeixeis peirometha legein omologoumenas tois fainomenois , ou kathaper oi embrosten, oi men allotriologountes kai tin men aithisin ekklinontes os ousan ouk akribi, nitas de kataskebazontes logous te tinas arithmon einai kai tahi pros allila en ois to te oxi kai to baru gignetai, panton allotriotatous logous legontes kai enantiotatous tois fainomenois' oi d' apothespizontes ekasta aneu aitias kai apodeixeos oud' auta ta fainomena kalos exirithmikotes. Imeis d' arhas te peirometha labein fainomenas apasas tois empeirois mousikis kai ta ek touton sumbainonta apodeinunai. Esti di to men olon imin theoria peri melous pantos mousikou tou gignomenou en foni te kai organois. Anagetai d' i pragmateia eis duo, eis te tin akoin kai eis tin dianoian. ti men gar akoi krinomen ta ton diastimaton megethi, ti de dianoia theoroumen tas ton (fthongon) dynameis. Dei oun epethisthinai ekasta akribos krinein. ou gar estin osper epi ton diagrammaton eithistai leghesthai. esto touto eutheia grammi, - outo kai epi ton diastimaton eiponta apillaxthai [dei]. O men geometris ouden hritai ti tis aisthiseos dunamei, ou gar ethizei tin opsin oute to euthi outhe to periferes out' allo ouden ton touton oute fablos oute eu krinein, alla mallon o tektonkai o torneutis kai eterai tines ton tehnon peri tauta pragnateuontai. to de mousiko shedon estin. arhis ehousa taxin i tis aisthiseos akribeia, ou gar endehetai faulos aisthanomenon eu legein peri touton on midena tropon aisthanetai. Esthai de touto faneron ep autois tis pragmateias. Ou dei d' agnoin, oti i tis mousikis xinesis ama menontos tinos kai kinoumenou esti kai touto shedon dia pasis kai kata pan meros autis, os eipein aplos, diateinein. Eutheos gar tas ton genon diaforas aisthanometha tou men periehontos menontos , ton de meson kinoumenon' kai palin otan menontos tou megethous tode men kalomen upatin kai mesin, tode de paramesin kai nitin, menontos [gar] tou megethous otan tou autou megethous pleio shimata gignitai, kathaper tou te dia tessaron kai dia pente kai eteron' osautos de kai otan tou autou diastimatos pou men tithemenon metaboli gignitai, pou de mi. Palin en tois peri tous rithmous polla toiauth oromen gignomena' kai gar menontos tou logou kath' on dioristai ta geni ta megethi kineitai ton podon dia tin tis agogis dynamin, kai ton megethon menonton anomoioi gignountai oi podes' kai to auto megethos poda te dunatai kai suzigian dilon d' oti kai ai ton diareseon te kai shumaton peri menon ti megethos gignontai. katholou eopein i men ruthmopoiia pollas kai pantodapas kiniseis kineitai, oi de pdes ois sumainometha tous rutmous aplas te kai tas autas aei. Toiautin d' ehousis fusin tis mousikis anagkaion kai en tois peri to irmosmenon sunethisthinai tin dianoian kai tin aisthisin kalos krinein to te menon kai to kinoumenon. Aplos men oun eipein toiauti tis estin i armoniki klitheista epistimi oian dieliluthamen sumbebike d' autin diaireisthai eis epta meri. Os estin en men kai proton to diarisai ta geni kai poiisai faneraon, tinon pote menonton kai tinon kinoumenon ai diaforai autai gignontai. Touto gar oudeis popotai diorise tropon tina eikotos' ou gar epragmateuonto peri ton duo genon, alla peri autis tis armonias' ou min all' oi ge diatribontes peri ta organa diisthanonto men ekastou ton genon, auto de to pote arhetai ex armonias hroma ti gignesthai, oudeis oud epeblepse popot' auton. oute gar kata pasan hroan ekastou ton genon diisthanonto dia to mite pasis melopoiias empeiroi einai mite sueithisthai peri tas toiautas diaforas akribologeisthai' aut' auto pos touto katemathon oti topoi tines isan ton kinoumenon fthongon en tais ton genon diaforais. Di' as men oun aitias ouk in diarismena ta geni proteron, shedon eisin ai eirimenai' oti de dioristeon ei mellomen akolouthein tais gignomenais en tois melesi diaforais, faneron. Proton men oun ton meron esti to eirimenon' deuteron de to peri diastimaton eipein, midemian ton uparhouson autois diaforon eis dunamin paralimpanontas. Shedon de, os aplos eipein, ai pleious auton eisin atheoritoi. ou dei d' agnoin, oti kath' in an genometha ton eklimpanouson te kai atheoriton diaforon, kata tautin agnoisomen tas en tois melodoumenos tas en tois melodoumenois diaforas. Epei d' estin uk autarki ta diastimata pros tin ton ftoggon diagnosin- pan gar, os aplos eipein, diastimatos megethos pleionon tinon dunameon koinon estin- , triton an ti meros eii tis olis pragmeteias to peri ton fthongon eipein osoi t' eisi kai tini gnorizontai kai pateron taseis tines eisin, osper oi polloi upolambanousin, i dunameis kai auto touto ti pot' estin i dunamis. Ouden gar ton touton diaratai katharos upo ton ta toiauta pragmateuomenon. Tetarton d' an eii meros ta sustimata theorisai posa t' esti kai poi' atta kai pos ek te ton diastimaton kai fthoggon sunestikota. Oudeteron gar ton tropon tetheoritai to meros touto upo ton emprosthen' oute gar ei panta tropon ek ton diastimaton suntithetai ta sustimata kai midemia ton suntheseon para fusisn estin episkepseos tetuhiken ai diaforai pasai ton sustimaton up oudenos exirithmintai. Peri men gar emmelous i ekmelous aplos oudena logon pepointai oi pro imon, ton de sustimaton tas diaforas oi men olous ouk epeheiroun exarithmein- alla peri auton monon ton epta oktahordon a akaloun armonias tin episkepsin epoiounto-, oi d' epiheirisantes oudena tropon exirithmounto, kathaper oi peri Puthagoran ton Zakunthion ka Aginora ton Mitulinaion. Esti de toiauti i peri to emmeles te kai ekmeles taxis oia kai i peri ton grammaton sunthesin en to dialegesthai' ou gar panta tropon ek ton auton grammaton suntithemeni xillabi gignetai, alla pos men, pos d' oun.
Pemton d' esti ton meron to peri tous tonous ef on tithemena ta sustimata melodeitai. Peri on oudeis ouden eiriken, outai tina tropon lipteon outai pros ti blepontas ton arithmon auton apodoteon astin. alla pantelos eoike ti ton imeron agogi ton armonikon i peri ton tonon apodosis, oion otan Korinthioi men dekatin agosin Athinaioi de pemton eteroi de tines ogdoin. outo gar oi men ton armonikon legousi barutaton men ton upodorion ton tonon, imitonio de oxiteron touton ton mixolidion, touton d imitonion ton dorion, tou de dorion tono ton frigion, osautos de kai tou frugiou ton ludion etero tonou' eteroi de pros tois eirimenois ton upofrugion aulon prostitheasin epi to baru, oi de au pros tin ton aulon trupisisn blepontes treis men tous barutatous trisi diesesin ap' allilon horizousin, ton te upofrigion kai ton upodorion kai ton dorion, ton de frigion apo tou doriou tono, ton de ludion apo tou frugiou palin treis desesis afistasin' osautos de kai ton mixolydion tou lydiou. Ti d' esti pros o blepontes outo poieisthai tin diastasin ton tonon protethumintai, ouden eirikasin. Oti de estin i katapuknosis ekmelis kai panta tropon ahristos, faneron ep autis estai tis pragmateias.

Jegyzetek:
Eloszor meghatarozuk a nemeket, genos. A mozgo es allo hangokat, melyek megadjak a nemek jelleget. Masodszor szemugyre vesszuk a diasztemakat. Eztan megnezzuk, hogy mukodnek tasis es dynamis szerint. Negyedszerre megszamoljuk a szisztemakat, skalakat. Otodszorre sorjaztatjuk a tonusokat [Itt nem a diasztema alapegysegrol, a dia tesszaron es a dia pente kulonbsegerol, a tizenket dodekatimoriara,stb. osztott hangkozrol van szo, mint tonusrol, hanem mas jelentesben ertendo! Vigyazat, egybeeses!]- a hypodorius, a myxolidios, a dor, a phryg, a lyd, a hyperfrig hangsorok. A legalacsonyabb a hypodor, egy feltonussal magasabb a mixolid, egy fel tonussal a dor, egy tonusssal a phryg, egy tonussal a lyd. A phryg a dortol tonus, a lyd a phrigtol harom diesi tavolsagra van. Ugyanigy a mixolid a lydtol.



Előzmény: spiroslyra (6575)
spiroslyra 2002. nov. 22. Creative Commons License 6586
Melpomen
Ancient Greek Music of the 5th century BC

Conrad Steinmann/Luiz Alves da Silva/Massimo Cialfi

spiroslyra 2002. nov. 22. Creative Commons License 6585
Greek Mathematics and its Modern Heirs
Classical Roots of the Scientific Revolution
For over a thousand years--from the fifth century B.C. to the fifth century A.D.--Greek mathematicians maintained a splendid tradition of work in the exact sciences: mathematics, astronomy, and related fields. Though the early synthesis of Euclid and some of the supremely brilliant works of Archimedes were known in the medieval west, this tradition really survived elsewhere. In Byzantium, the capital of the Greek-speaking Eastern empire, the original Greek texts were copied and preserved. In the Islamic world, in locales that ranged from Spain to Persia, the texts were studied in Arabic translations and fundamental new work was done. The Vatican Library has one of the richest collections in the world of the products of this tradition, in all its languages and forms. Both the manuscripts that the Vatican collected and the work done on them in Rome proved vital to the recovery of ancient science--which, in turn, laid the foundation for the Scientific Revolution of the 16th and 17th centuries. In the Roman Renaissance, science and humanistic scholarship were not only not enemies; they were natural allies.

Euclid, Elements
In Greek, Ninth century

Euclid's "Elements," written about 300 B.C., a comprehensive treatise on geometry, proportions, and the theory of numbers, is the most long-lived of all mathematical works. This manuscript preserves an early version of the text. Shown here is Book I Proposition 47, the Pythagorean Theorem: the square on the hypotenuse of a right triangle is equal to the sum of the squares on the sides. This is a famous and important theorem that receives many notes in the manuscript.

Vat. gr. 190, vol. 1 fols. 38 verso - 39 recto math01 NS.01

Archimedes, Works
In Latin, Translated by Jacobus Cremonensis, ca. 1458

In the early 1450's, Pope Nicholas V commissioned Jacobus de Sancto Cassiano Cremonensis to make a new translation of Archimedes with the commentaries of Eutocius. This became the standard version and was finally printed in 1544. This early and very elegant manuscript may have been in the possession of Piero della Francesca before coming to the library of the Duke of Urbino. The pages displayed here show the beginning of Archimedes' "On Conoids and Spheroids" with highly ornate, and rather curious, illumination.

Urb. lat. 261 fol. 44 verso - 45 recto math02 NS.17

Piero della Francesca, De quinque corporibus regularibus
In Latin, 1480s

The early Renaissance artist Piero della Francesca developed a mathematically rigorous system of perspective on which he wrote the treatise "De prospectiva pingendi." His interest in mathematics increased as he grew older and late in his life he wrote two other treatises, a "Trattato d'abaco," on algebra and the measurement of polygons and polyhedra (solids), and "De quinque corporibus regularibus," on the five regular polyhedra, which survives only in this unique manuscript from the library of the Duke of Urbino. The figures are said to be by Piero himself. Shown here are the inscriptions of an icosahedron (a solid composed of twenty equilateral triangular faces) in a cube, and of a cube in an octahedron (a solid of eight equilateral triangular faces).

Urb. lat. 632 fols. 40 verso - 41 recto math03 NS.18

Euclid, Optics
In Latin, 1458

Euclid's "Optics" is the earliest surviving work on geometrical optics, and is generally found in Greek manuscripts along with elementary works on spherical astronomy. There were a number of medieval Latin translations, which became of new importance in the fifteenth century for the theory of linear perspective. This technique is beautifully illustrated here in the miniature of a street scene in this elegant manuscript from the library of the Duke of Urbino. It may once have been in the possession of Piero della Francesca, who wrote one of the principal treatises on perspective in painting.

Urb. lat. 1329 fol. 1 recto math04 NS.19

Archimedes, Works
In Latin, Translated by William of Moerbeke, ca. 1270

William of Moerbeke was the most prolific medieval translator of philosophical, medical, and scientific texts from Greek into Latin. This is the holograph of his translation of the greatest Greek mathematician, Archimedes, with the commentaries of Eutocius. The translations were made in 1269 at the papal court in Viterbo from two of the best Greek manuscripts of Archimedes, both of which have since disappeared. Shown here is a part of Eutocius's commentary on Archimedes' "On the Sphere and the Cylinder" in which he reviews solutions to the classical problem of the duplication of the cube, i.e. how to construct a cube twice the volume of a given cube.

Ottob. lat. 1850 fols. 36 verso - 37 recto math05 NS.52

There is an extra picture of Euclid's Elements behind the ancient door. This room has another display with
more Greek Mathematics.

You can also go back and through one of the two other ancient doors:
Ptolemy's Geography.
Greek Astronomy.
Or you can walk all the way back to the Main Hall.
http://www.ibiblio.org/expo/vatican.exhibit/exhibit/d-mathematics/Greek_math.html

spiroslyra 2002. nov. 22. Creative Commons License 6584
--------------------------------------------------------------------------------

Letter from Girolamo Mei to Vincenzo Galilei
8 May 1572

This copy of an important letter from the humanist Girolamo Mei to the Florentine musician Vincenzo Galilei, father of the great astronomer, concerns the nature of Greek music. The letter includes a discussion of the presumed power of Greek music to move the emotions; from these ideas Galilei and his colleagues in Florence developed a new musical aesthetic that led to the creation of opera and other baroque forms.

http://www.loc.gov/exhibits/vatican/music.html
--------------------------------------------------------------------------------

spiroslyra 2002. nov. 22. Creative Commons License 6583
--------------------------------------------------------------------------------

Ptolemy, Harmonics
In Latin
Late fifteenth century

Music was a mathematical science in its own right in the classical tradition. This copy of a Latin translation of Ptolemy's important theoretical work, Harmonics, was owned by the Italian music theorist Franchinus Gaffurius (ca. 1451-1522) and ends with a colophon in his own hand.

http://www.loc.gov/exhibits/vatican/music.html

spiroslyra 2002. nov. 22. Creative Commons License 6582
The Creation of Musical Scales, part II.
by Thomas Váczy Hightower.

Pythagoras
"The Greek philosopher Pythagoras (570 - 490 BC) spent 22 years in Egypt mainly with the high priest in Memfis, where he became initiated to their secret knowledge of Gods. When the Persians conquered Egypt, he was kept in captivity in Babylon for 16 years before he could return to Greek and begin his teaching.
I began to study the theory of the Pythagorean and their esoteric schools. Very little is known of them. Pythagoras demanded silence about the esoteric work. This historic school was founded in the Greek colony, Kroton, in southern Italy about 2500 years ago.

I realized after dozens of books about the matter what an outstanding role that school had for the creation of the western civilization. He created an entirely new concept. Any person - man or woman - who had a sincere wish for knowledge could enter the school stepwise, with a number of initiations. The tradition of priesthood monopoly of knowledge of God was broken.

Pythagoras' study of the moving string and his discovery of the harmonic progression of simple whole numbers was the first real scientific work and the creation of modern science. But his vision went far beyond present science in his deep understanding of the integration of the triad: A-science, B-work on being, C-love and study of God. Something modern science could learn from. Pythagoras' study of the moving string and his discovery of the harmonic progression of simple whole numbers was the first real scientific work and the creation of modern science. But his vision went far beyond present science in his deep understanding of the integration of the triad: A-science, B-work on being, C-love and study of God. Something modern science could learn from.
Nicomachus of Gerasa
Nicomachus the Pythagorean (second century B.C.) was the first who wrote about Pythagoras legendary encounter with "the harmonious blacksmith" and the weights of the 4 different hammers being 12, 9, 8 and 6, that determined the variation in the pitches Pythagoras heard. This story illustrate how the numerical proportions of the notes were discovered. His methodical measuring of the hammers and how the sound was produced and related (collecting data), then making experiments with strings, their tension and lengths (repeating the findings and, with mathematic, formulating them into a law), was the first example of the scientific method.
We will not dwell with the question about the force of the impact or the tension of the strings, which later was discovered as the square root of the force, but just stick to the proportion of weights and the pitches he heard, which led him to his discovery.
Pythagoras' experiments led to the combination of two tetra chords, two fourths, separated with a whole tone, 9/8, which constitute an octave. He changed the traditional unit in Greek music, the tetra chord, into the octave by an octachord.

In the time of Pythagoras the tradition was strongly based on the seven strings of the lyre, the heptachord. The Greeks considered the number 7 sacred and given by the god, Hermes, who handed down the art of lyre playing to Orpheus. The seven strings lyre was also related to the 7 planets among other things the ancients venerated.
The lyre often, but not always, consisted of 7 strings comprising two tetra chords each one spanning the most elementary concord, the fourth, both joint together on the note mese.
According to legend, a son of Apollo, Linos, invented the four stringed lyre with 3 intervals, a semi-tone, whole tone and a whole tone comprising a fourth;
the fourth, "the first and most elementary consonance" as Nicomathus calls it, and from which all the musical scales of ancient Greek music eventually developed.

Trepander of Antissa on Lesbos, born about 710 B.C., assumed a mythological status for his musically genius. His most lasting contributions was perhaps his transformation of the four stringed lyre to the instrument which became institutionalized by tradition to the heptachord.
Trepander did before Pythagoras extend the heptachord from its minor seventh limits to a full octave, but without having to add the forbidden eight string.
He removed the Bb string, the trite of the conjunct tetra chord, and add the octave string, E1 yielding a scale of E F G A C D E1.
This arrangement left a gap of a minor third between A and C, and seemed to have enhanced the Dorian character of Trepander's composition.

Harmonia
Only Pythagoras escaped censure for adding an eighth string to the ancient and venerated lyre because of his position as a great master and religious prophet. His purpose was to teach man the unifying principle and immutable laws of harmonia by appealing to his highest powers - the rational intellect and not to his untrustworthy and corruptible senses. Pythagoras altered the heptachord solely to engage man's intellect in proper "fitting together" - harmonia - of the mathematical proportions.

Plutarch (44-120) stats that for Pythagoras and his disciples, the word harmonia meant "octave" in the sense of an attunement which manifests within its limits both the proper fitting together of the concordant intervals, fourth and fifth, and the difference between them, the whole tone.
Moreover, Pythagoras proved that whatever can be said of one octave can be said of all octaves. For every octave no matter what pitch range it encompasses, repeats itself without variation throughout the entire pitch range in music. For that reason, Pythagoras considered it sufficient to limit the study of music to the octave.

This means that within the framework of any octave, no matter what its particular pitch range, there is a mathematically ordained place for the forth, the fifth, and for the whole tone. It is a mathematical matter to show, that all of the ratios involved in the structure of the octave are comprehended by the single construct, which is 12-9-8-6.
For the Pythagoreans, this construct came to constitute the essential paradigm - of unity from multiplicity.

The arithmetic- and harmonic mean
We see that 12:6 express the octave, 2:1; 9 is the arithmetic mean, which is equal to the half of the sum of the extremes, (12 + 6)/2 = 9.

Further, 8 is the harmonic mean of 12:6, being superior and inferior to the extremes by the same fraction.
Expressing this operation algebraically, the harmonic mean is 2ac/a+c, or in this series, 2*12*6/12+6 = 8.
Among the peculiar properties of the harmonic proportion is the fact, that the ratio of the greatest term to the middle is greater than the middle to the smallest term: 12:8 >8:6. It is this property that made the harmonic proportion appear contrary to the arithmetic proportion.
In terms of musical theory, these two proportions are basic for division of the octave since the fifth, 3/2, is the arithmetic mean of an octave and the fourth, 4/3, is the harmonic mean of an octave.

The semi tone
We have already seen that in the diatonic genus each tetra chord was divided into two full tones and one semi tone. A full tone derives from a fifth minus a fourth, 3/2 - 4/3 = 9/8. The semi tone will be 4/3 - (9/8 + 9/8), or 4/3 - 81/64 = 256/243.
This semi tone is called leimma, and is somewhat smaller than the half tone computed by dividing (for musical ratios dividing means the square root) the whole tone in half: (9/8)˝ = 3/2*2˝ .

The square root of 2 was for the Pythagoreans a chocking fact because their concept of rational numbers was scattered. (For me it represent the beauty of real science, because it revealed the flaws in the Pythagorean paradigm of numbers). Their own mathematic proved with the Pythagoreans doctrine of the right angle triangle, (the sum of the squares of the two smaller sides of a right-angled triangle is equal to the square of the hypotenuse), that in music as in geometry there are fractions, m/n, that are incommensurables such as square root 2, which can not be expressed with whole numbers or fractions, the body of rational numbers, but with irrationals numbers not yet developed.

This discovery was hold as a secret among the Pythagoreans and led to the separation of algebra and geometry for centuries until Descartes in the 17th century united them again.

For music it meant that there were no center of an octave, no halving of the whole tone, no perfect union of opposites, no "rationality" to the cosmos.

Philolaus
We have to bear in mind that Pythagoras himself left no written record of his work; it was and is against esoteric principles. Either did those few students, who survived the pogrom of Pythagoras. It is one in the next generation of Pythagoreans, Philolaus (ca.480- ? B.C.), who broke the precept of writing down the masters teaching. However, Philolaus' records are lost, so it is Nicomachus fragments of his writing, in his Manual of Harmonics, that actually is the only source the posterity has.

According to Philolaus, the whole tone, 9/8, was divided differently than the Pythagoreans by representing the whole tone with 27, the cube of 3, a number highly esteemed by the Pythagoreans. Philolaus divided the whole tone in two parts, calling the lesser part of 13 units a "diesis", and the greater part of 14 units, "apotome". Philolaus had in effect anticipated Plato's calculations in the Timaeus!

Timaeus by Plato
Plato (427-347 B.C.) gave in his work Timaeus a new meaning to the Pythagorean harmonic universe by - in a purely mathematical method - enclosing it within the mathematically fixed limits of four octaves and a major sixth. It was determined by the numbers forming two geometrical progressions of which the last term is the twenty seventh multiple of the first term:
27 = 1+2+3+4+8+9

The two geometric progressions in which the ratios between the terms is 2:1 and 3:1, respectively:
1-2-4-8 and 1-3-9-27. Combining this two progressions, Plato produced the seven-termed series: 1-2-3-4-8-9-27. The numbers in this series contains the octave, the octave and a fifth, the double octave, the triple octave, the fifth, the fourth and the whole tone. The entire compass from one to twenty-seventh multiple comprises therefore four octaves and a major sixth. In numerical terms it contains four octaves, 16:1 * 3:2 (a fifth) * 9:8 (a whole-tone) equals 27:1.
Plato then proceeded first to locate in each of the octaves the harmonic mean, the fourth, then the arithmetic mean, the fifth. By inserting the harmonic and the arithmetic means respectively between each of the terms in the two geometric progressions, Plato formulated mathematical everything Pythagoras had formulated by collecting acoustic data.

Plato did, however, independently of the Pythagoreans compute the semi tone in the fourth, which consist of two whole tones plus something which is less than the half of a whole tone, namely 256:243, the "leimma".
According to Flora Levin in her commentary of Nicromachus' "The Manual of Harmonics", Plato went further than Pythagoras by completing all the degrees in a diatonic scale:

1
9/8 81/64 4/3 3/2 27/16 243/128 2
E F# G# A B C# D# E'

Plato's calculations led to the inescapable fact of no center to the octave, no halving of the whole tone with rational numbers, no rationality of the cosmos. Nicomachus did his part of covering up the secret by misrepresenting Plato and putting off some of the shattering discoveries of irrational numbers to some future time.

The semi tones in the different modes
Pythagoras had practiced music long before he transformed the heptachord into an octachord that led him to discover the mathematical laws determining the basic structure of an octave. He had fully understood the therapeutic value of music in healing the body and soul. Most of all he knew the set of conditions for the melody. He recognized strongly that every tetra chord on which melody was based embodies the "natural" or physical musical progression of whole tone-whole tone-semi-tone.
He maintained the fundamental structure of both tetra chords in his scale and for musical reason he understood that this distribution of intervals had to be maintained for all melodic purposes with their configurations and inversions.
This was the foundation of the ancient Greek music, which further developed into the Greater Perfect system.

The confusion of systems
The Greek music has an inherent confusion of musical systems. A mix of the cyclic system of perfect fifths (Pythagorean tuning), and the modal system (tetrachords). We can only get a very faint idea of what ancient Greek music really was about because European theorists through time have made errors and misunderstandings.
In reality, the Arabs and the Turks happened to receive directly the inheritance of Greece. In many cases the works of Greek philosophers and mathematicians reached Europe through the Arabs. Most serious study on Greek music were written by Arabs scholars such as al-Färäbi in the tenth century and Avicenna a little later, while Westerners - Boethius in particular - already had made the most terrible mistakes.
It is the Arabs who maintained a musical practice in conformity with the ancient theory, so to get an idea of ancient Greek music, we should turn to the Arab music.

The Pythagorean Tuning
The musical scale, said to be created by Pythagoras, was a diatonic musical scale with the frequency rate as:

1, 9:8, 81:64, 4:3, 3:2, 27:16, 243:128, 2.

This scale is identical to the cyclic scale of fifths as the Chinese, if we take as tonic the F.
It has 5 major tones (9/8) and 2 semi tones, limma (256/243); the third, 81/64, is a cyntonic comma sharper than the harmonic third, 5/4.

Their scale was based on the three prime intervals: the octave, the perfect 5th and the perfect 4th. "Everything obeys a secret music of which the "Tetractys" is the numerical symbol"(Lebaisquais).

By generating 12 perfect fifths in the span of 7 octaves, 12 tones were produced and using the descending perfect 4th (the subdominant) to place the 12 tones within one octave, a 12 notes chromatic scale was made.

He discovered what later was called the Pythagorean comma, the discrepancy between twelve fifths and 7 octaves gives (3:2)12 > (2:1)7. Calculated through, it is: 129.74634 : 128 = 1.014. Or in cents: 23.5. See more about Pythagoras' Comma in part II.

Do not mistake Pythagoras' Comma for the syntonic comma, equal to 22 cents, which is derived from the difference between the major tone and the minor tone in the Just Diatonic Scale, or discrepancy between the Pythagorean third and the third in the harmonic series which is 5:4.

As far back as 2,500 years ago the Pythagorean figured out that it was impossible to derive a scale in which the intervals could fit precisely into an octave. The ancient Greeks explained this imperfection - the comma - as an example of the condition of mortal humans in an imperfect world.

This fundamental problem with the 3 prime ratios: 2:1, 3:2, 4:3, - which can be formulated in mathematical terms as interrelated prime numbers which have no common divisor except unity - has been compromised in a number of different temperaments of the diatonic scale up to out time.

The Greater Perfect System
In ancient Greek music several other modes were used based on the tetra chords with a span of the perfect fourth. Later two tetra chords were put together with a full tone in between so an octave was established. A number of different modes were used in practical music performance. The different placement of the two half tones made the different modes.

An account of ancient Greek contributions to musical tuning would not be complete without mentioning the later Greek scientist Ptolemy (2nd c. A.D.). He proposed an alternative musical tuning system which included the interval of the major third based on that between the 4th and 5th harmonics, 5 / 4. This system of tuning was ignored during the entire Medieval period and only re-surfaced with the development of polyphonic harmony."
http://home22.inet.tele.dk/hightower/scales2.htm

spiroslyra 2002. nov. 22. Creative Commons License 6581
GEOMETRIC CONSTRUCTIONS FOR THE MONOCHORD
[2.0] Geometric constructions required for a fastidious, "ideal" realization of Marchetto's tuning on the monochord had been known for about 2 millenia. E.g., Euclid VI,9 (Heath 1926/1956: v.2, 211-12) gave a formulation for dividing any line segment into any number of subsegments having equal lengths. This powerful construction would more than suffice for both Marchetto's dieses and the previously standard medieval tuning. However, both this earlier, Pythagorean tuning and Marchetto's innovative dieses could be constructed entirely by applying Euclid's well known construction (I,10) for bisecting any given line segment (Heath 1926/1956: v.1, 267-68: cf. Adkins 1980).
[2.1] Because the location of the mark for GGG (gamma- ut), the monochord's lowest note, was largely arbitrary (cf., however, [3.0-3.2], below), GGG's sounding length could be established indirectly at the outset by setting BB (a M3 above GGG) at 3 times any feasible length, x, where x = ~1/4 the length available:

(bridge) BB (bridge)
<----x--<---------------3x-------------

Merely by cutting off three consecutive segments of length x, BB's effective, sounding string-length (i.e., its distance from the rightmost bridge), would be 3x:

(bridge) BB (bridge)
<----x--<----x--<----x--<----x--

Bisecting BB's length once, b, a p8 above BB, would be at ( 1/2 ) * 3x = ( 3/2 ) x:

(bridge) BB b (bridge)
<--(2/2)x-><----(3/2)x--<----(3/2)x--
<-----------(5/2)x------<----(3/2)x--

Bisecting BB's length a second time, b1, a p15 above BB, would be at ( 1/4 ) * ( 3x ) = ( 1/2 ) * ( 3/2 ) x = ( 3/4 ) x , whereas EE, a p4 above BB (or a p5 below b, or a p12 below b1) would be at ( 3/4 ) * 3x = ( 3/2 ) * ( 3/2 ) x = ( 3/1 ) * ( 3/4 ) x = ( 9/4 ) x :

(bridge) BB EE b b1 (bridge)
<--(4/4)x-><(3/4)x><(3/4)x><(3/4)x><(3/4)x>
<----(7/4)x-----<--------(9/4)x------

And so forth, downward through the cycle of p5s, for A, D, G, C, F, and Bb.
[2.2] To add Marchetto's new, sharpened notes (e.g., C74), one need only bisect the whole tone above (D/E) twice, and cut off 1 of these 1/4s below the lower note (D):

|c| |c74| |d| |e|
9 8
36 32
36 35 34 33 32
37 36 32
81 74 72 70 68 66 64
9 8

Because the whole tone ( D/E ) would form the ratio 9/8 = 72/64, its 1/4s would be formed by marks for 70, 68, 66; the 1/4 below the lower note ( D = 72 ) would be at C74--and C, a whole tone below D, would be at 81.
[2.3] To construct all Marchetto's sharpened notes (F74, C74, G74, D74), one could begin the original tuning at f# ~1/2-way along the available string, rather than at BB (~1/4 from the bottom) and construct all other marks relative to this f#. BB's length would be 3/2 times f#'s; d74's would ( 37/36 ) * ( 9/8 ) greater; etc.:

|d| |d74| |e| (f#)
9 8
36 32
36 35 34 33 32
37 36 32
81 74 72 70 68 66 64
9 8

The Pythagorean F# (parenthesized) would be much (~ 42%) lower than Marchetto's new F74:

81 74 72
|f| (f#) |f74| |g|
<--42<--48
<------90----

[2.4] To divide a whole tone (e.g., A/B) into Marchetto's enharmonic semitone (A/Bb77) and diatonic semitone (Bb77/B), one would only have to bisect a whole tone above (B/C#, where C# would be a Pythagorean note not actually used by Marchetto) and cut off one of these 1/2s above the enharmonic semitone's lower note (A):

|a| |bb77| |b| (c#)
9 (8)
18 17 (16)
72 68 (64)
81 77 72

Because the whole tone above (B/C#) would be 9/8 = 72/64, its precise 1/2 (i.e., arithmetic mean) would be at 68. Since 72 - 68 = 4, the Bb77 could be marked readily at 77 = 81 - 4.
http://www.smt.ucsb.edu/mto/issues/mto.98.4.6/mto.98.4.6.rahn.html

http://www.smt.ucsb.edu/mto/issues/mto.98.4.6/mto.98.4.6.rahn.html#Section2

spiroslyra 2002. nov. 22. Creative Commons License 6580
Catiline's Ptera, Auli, Hydrauli, etc.

--------------------------------------------------------------------------------

The first two items are from The Story of the Organ by C.F. Abdy Williams, published in 1903 by Walter Scott Publishing and Charles Scribner's Sons. The third is from William Smith, A Dictionary of Greek and Roman Antiquities (New York, Harper, 1874).

--------------------------------------------------------------------------------

Appendix A.
Two small bronze instruments have been found at Pompeii (which was destroyed by the eruption of Vesuvius in A.D. 79) somewhat similar in appearance to the portative organs of the Middle Ages. They are now in the Naples Museum. The cases and pipes only remain, together with some fragments of bronze which may have had to do with regulating the supply of wind to the pipes. The blowing arrangements have disappeared entirely, as have the feet of the pipes, which were probably of wood. The cases are in three portions, the middle being ornamented with designs of three temples. The smaller instrument contains nine pipes; the larger, of which we give a diagram, eleven. The mathematical proportions of the pipes of the larger instrument give the following series of intervals: 1:middle-c 2:c-sharp 3:d 4:e 5:f 6:flattened a 7:sharpened a 8:b-flat 9:d 10:f 11:a, of which, if Nos. 6 and 7 form an enharmonic diesis, the series 6, 7, 8, 9, 10, 11 gives the Iastian mode described by Aristides Quintilianus. A writer of the twelfth or thirteenth century, called the Hagiopolite, whose tract is published by A.J.H. Vincent in his Notices des Mss. du Bibliotheque du Roi, 1847, says that the Iastian mode suits the pteron, which would appear to be a wing-shaped instrument from its name - for pteron means any wing-shaped thing. (The Germans call the grand piano Fluegel - i.e., "wing," from its shape.) The pteron is enumerated with the auloi and hydrauloi amonst wind instruments by Bellermann's "anonymus," (Anonymi de Musica, published by F. Bellermann, 1847) but he makes no further reference to it. It is possible that the two fragments in the Naples Museum are ptera, and that the pteron was a portative organ; it seems to be a connecting link between the bagpipe and the organ. Whether it was blown by the lungs or by some mechanical bellows cannot be ascertained; but it is not impossible that the excavations in progress at Pompeii, which have been rich in results of late, may in the near future throw more light on the matter.

Nero, just before his death, was much interested in a new kind of syrinx that had lately been invented, and wished to appear in public as a performer upon it. It may be this instrument that he had in view.

--------------------------------------------------------------------------------

Appendix B. The Rev. F.W. Galpin's Hydraulus
After a careful study of all known representations of the Hydraulus on contorniates, pictures in ancient manuscripts, and a well-preserved model in pottery found at Carthage in 1885, the Rev. F.W. Galpin has succeeded in constructing a complete working model of this instrument, by following in every detail the instructions given by Hero of Alexandria and Vitruvius. Two wooden levers are attached to two brass cylinders, the raising of which pumps air into a wind-chest. From the wind-chest a large pipe leads the wind to the top of a dome immersed in water, contained in the central vessel shown in the photograph, and in this lies the whole secret of the application of water. The principle is, as explained in Chapter I. [of the book for which this is the Appendix], the reverse of that of the fire-engine, in which the pressure of air confined in a dome causes water to flow in a continuous stream from the nozzle. In the hydraulus, the water endeavouring to rise in the dome (after being pressed down by the air which is pumped in) compresses the wind, and causes a fairly steady supply to reach the pipes. The "wind pressure" in Mr. Galpin's model is of the weight of 3 to 3 1/2 inches, being about that of the ordinary modern organ. By increasing the size of the tank, the depth of the water and the height of the dome, this pressure could be increased ad libitum, and the powerful sounds mentioned by ancient writers could be easily obtained by this means.

Above the wind-chest there are three channels running the length of the instrument, to which the wind is admitted by taps constructed on the ancient model, one of which can be seen in the photograph. Above the three channels are placed the three ranks of pipes, sounding the unison, octave, and superoctave, and the organ has therefore, in modern parlance, three "stops." To cause the pipes to sound, one or more of the taps are turned to admit wind to the required channel, and the keys, called by Vitruvius pinnae, are pressed by the fingers, as in the modern organ.

The keys, however, do not act on pallets, but push in regulae, or metal sliders, which have holes pierced in them, through which the wind passes to the pipes, on the same principle as in the sliders of modern organs. Vitruvius lays stress on the necessity of keeping the regulae well oiled, probably to relieve the touch and to help to prevent escape of wind. On removing the finger from a key the regula is brought back to its place by means of a spring, thus shutting off the wind from the pipes. Hero says that the springs should be of horn, but Vitruvius describes them as of metal, and Mr. Galpin has used metal springs similar to those found on ancient Roman brooches.

The nineteen keys give the following notes ... : d, e, f-flat, f, g, a, b-flat, b, c, d-flat, d, e-flat, e, f-flat, f, g, a-flat, a, b, which embrace the six modes mentioned by "Anonymus" as those used by players of the hydraulus, namely, the Hyperlydian, Hyper-Iastian, Lydian, Phrygian, Hypolydian, and Hypophrygian; the first, being an octave above the last, is played by using the octave "stop."

Mr. Galpin is to be congratulated on his success in having constructed the first working model of this interesting instrument. When one runs one's fingers at random over the keys, one is struck by the old-world effect produced by their modal arrangement and the slight unsteadiness of the wind, owing to the impossibility of keeping the water absolutely at a fixed point. This little unsteadiness, which would ruin modern harmonic music, gives a peculiar piquancy to the unison passages in the old modes, and seems to go far to account not only for the immense popularity enjoyed by the instrument before the advent of harmony, but also for its gradual disappearance when the growing use of harmonic progressions demanded some means of producing a more decided steadiness in the wind supply.

The labor of pumping wind into a large hydraulus must have been very great. It could never cease for a moment; the blower could not, as now, fill his bellows and rest for a little while till the "tell-tale" lets him know that he must resume his labours. Hence in the MS. pictures of hydrauli the players seem to be spending half their energies in urging the weary blowers, whose backs are bent double, to fresh exertions.

The instrument excited the keenest interest and admiration amongst the ancients on account of its ingenuity; while the bubbling of the hidden water (caused by over-blowing) is frequently alluded to, and was probably a great mystery to the uninitiated.

--------------------------------------------------------------------------------

Hydraula
an organist. According to an author quoted by Athenaeus [iv, 75 - compare Pliny H.N. vii, 38] the first organist was Ctesibius of Alexandrea, who lived about B.C 200. He evidently took the idea of his organ from the Syrinx or Pandean pipes, a musical instrument of the highest antiquity among the Greeks. His object being to employ a row of pipes of great size, and capable of emitting the most powerful as well as the softest sounds, he contrived the means of adapting keys with levers (agkoniskoi), and with perforated sliders (pomata) to open and shut the mouths of the pipes (glossokoma), a supply of wind being obtained, without intermission, by bellows, in which the pressure of water performed the same part which is fulfilled in the modern organ by a weight. On this account, the instrument invented by Ctesibius was called the water-organ (hydraulis[Athen. l.c.]; hydraulikon organon[Hero, Spirit. - Vitruv. x, 13 - Schneider ad loc. - Drieberg, die Pneum. Erfindungen der Griechen, p. 53-61 - Pliny. H.N., ix, 8 - Cic. Tusc. iii, 18]).Its pipes were partly of bronze (chalkeie aroura[Jul. Imp. in Brunck's Anal. ii, 403]; seges aena[Claud., De Mall. Theod. Cons. 316]), and partly of reed. The number of stops, and, consequently, of its rows of pipes, varied from one to eight[Vitruv. l.c.], so that Tertullian[De Anima, 14] describes it with reason as an exceedingly complicated instrument. It continued in use so late as the ninth century of our era: in the year 826, a water-organ was erected by a Venetian in the church of Aquis-granum, the modern Aix-la-Chapelle[Quix, Muenster Kirche in Aachen, p. 14].

The organ was well adapted to gratify the Roman people in the splendid entertainments provided for them by the emperors and other opulent persons. Nero was very curious about organs, both in regard to their musical effect and their mechanism[Sueton. Nero, 41, 54]. A contorniate coin of this emperor in the British Museum (see woodcut) shows an organ with a sprig of laurel on one side, and a man standing on the other, who may have been victorious in the exhibitions of the circus or the amphitheatre. It is probable that these medals were bestowed upon such victors, and that the organ was impressed upon them on account of its introduction on such occasions[Havercamp, De Num. contoniatis]. The general form of the organ is also clearly exhibited in a poem by Publilius Optatianus, describing the instrument, and composed of verses so constructed as to show both the lower part which contained the bellows, the wind-chest which lay upon it, and over this, the row of 26 pipes. These are represented by 26 lines, which increase in length each by one letter, until the last line is twice as long as the first[Wernsdorf, Poet. Lat. Min., v, ii, p 394-413].

--------------------------------------------------------------------------------
Return to Bellum Catilinae Home Page
http://users.ipa.net/~tanker/organs.htm

spiroslyra 2002. nov. 22. Creative Commons License 6579
YALE UNIVERSITY
BEINECKE RARE BOOK AND MANUSCRIPT LIBRARY
GENERAL COLLECTION OF RARE BOOKS AND MANUSCRIPTS
MEDIEVAL AND RENAISSANCE MANUSCRIPTS
--------------------------------------------------------------------------------

MS 271 Italy, s. XVI^^med
Aristides Quintilianus, De Musica (in Greek)

ff. 1r-216v[Greek].
[Greek].

R. P. Winnington-Ingram, ed., Aristides Quintilianus De musica
(Leipzig, 1963); T. J. Mathiesen, ed., Aristides Quintilianus: On Music
in Three Books (New Haven, 1983) p. 60.

Paper (watermarks buried in gutter), ff. i (paper) + 216 + i (paper), 196 x
148 (135 x 85) mm. Written in 13 long, well spaced lines, faintly ruled in
hard point; single vertical bounding lines do not extend into margins.
I-XVIII^^12. Catchwords perpendicular to text in lower margin of verso
along the inner bounding line.
Written by Camillus Venetus in neat Greek minuscule.
Heading and initial on f. 1r in red.
Binding: s. xx. Fairly limp vellum with a tight back. Bound in the same
manner and by the same binder as
MS 270.

Written in Northern Italy in the mid-16th century by a single scribe, who
was also responsible for Beinecke MSS 270 and 208. According to Karpozilos
(p. 68) the scribe was associated with or a student of Andreas Darmarius;
Knox attributes MSS 270 and 271 to Andreas Darmarius himself (Ziskind
Catalogue, pp. 44 and 53), as does de Meyier (p. 264, no. 7). However, a
close examination of the hand shows that all three manuscripts are the work of
Camillus Venetus (we thank P. Canart for this attribution). Library of the
Santa Iglesia del Pilar, Saragossa, Spain (Graux and Martin, p. 214, no. 621,
part II; Olivier, pp. 52-57). Purchased from C. A. Stonehill with funds from
the Jacob Ziskind Charitable Trust in 1957 (MS 3).

Bibliography: Faye and Bond, p. 48, no. 271.
Ziskind Catalogue, p. 44.
T. Mathiesen, "Towards a Corpus of Ancient Greek Music Theory: A New
Catalogue raisonne Planned for RISM," Fontes artis musicae 25, no. 2
(1978) pp. 129-32.

http://webtext.library.yale.edu/beinflat/pre1600.MS271.htm


spiroslyra 2002. nov. 22. Creative Commons License 6578
Oxyrhynchus Papyrus 1786:
Christian Hymn to the Trinity
Text
David Wardell: Oxyrhynchus Hymn


Translation
Paul Halsall: "The Earliest Christian Hymn: The Words"

BBC Musical Timeline: Oxyrhynchus Hymn


Original Music

Text Adaptations

Music Adaptations


Audio Files
Instrumental rendition of the melody from Stefan Hagel's Ancient Greek Music website at the Austrian Academy of Sciences

Paul Halsall: Real Audio version of Oxyrhynchus Hymn

Studies
Elvadine R. Veigel: "Article" (on early Christian organization and cultural accomplishments)


Bibliography
Mathiesen, Thomas J. _ A bibliography of sources for the study of ancient Greek music_, Hackensack, N.J., J. Boonin [1974].

Mathiesen, Thomas J. _Ancient Greek music theory : a catalogue raisonne of manuscripts_, Munchen : G. Henle Verlag, c1988.

West, M. L. (Martin Litchfield), _Ancient Greek music_, Oxford [England] : Clarendon Press ; New York : Oxford University Press, 1992.
http://webcampus3.stthomas.edu/jmjoncas/LiturgicalStudiesInternetLinks/ChristianWorship/Texts/Centuries/Texts_0200_0300CE/OxyrhynchusPapyrus1786.html

spiroslyra 2002. nov. 22. Creative Commons License 6577
Greek and Latin Music Theory

--------------------------------------------------------------------------------

Established in 1984 and published by the University of Nebraska Press, Greek and Latin Music Theory aims to establish truly critical texts for the many works of ancient, medieval, and (occasionally) renaissance music theory in Greek and Latin that do not presently exist in critical editions, accompanied by facing-page translations with annotations illuminating the content of the treatise. Each volume includes a major introductory essay discussing, as appropriate, the significance of the treatise to its theoretical tradition; the life of its author (or, for anonymous works, the probable authors); the design, sources, and theoretical premises of the treatise; the manuscripts used to establish the text and the actual establishment of the text itself; loci paralleli and quotations; and special considerations involved in the translation. The texts are based on a full collation of every relevant manuscript--insofar as possible--and the collation is reported in a critical apparatus at the bottom of each text page. The translations are intended to be readable, but at the same time, they attempt to preserve in large measure the consistency, variety, and subtlety of the original. Special care is given to the treatment of technical vocabulary, syntactic subtleties, and consistency of terminology. Finally, each volume includes indices verborum, nominum et rerum and--beginning with volume 10--a bibliography.

Ten volumes have been published to date:

Prosdocimo de' Beldomandi, Contrapunctus, a new critical text and translation by Jan Herlinger [1984], xii,109 p. $45

Oliver B. Ellsworth, ed. and trans., The Berkeley Manuscript: University of California Music Library, MS. 744, a new critical text and translation [1984], x,317 p. $55

Sextus Empiricus, Against the Musicians, a new critical text and translation by Denise Davidson Greaves [1986], x,213 p. OP

Prosdocimo de' Beldomandi, Proportiones and Monacordum, new critical texts and translations by Jan Herlinger [1987], x,182 p. $45

Gaspar Stoquerus, On Verbal Music, a new critical text and translation by Albert C. Rotola, S.J. [1988], xii,298 p. $50

Philip E. Schreur, ed. and trans., The Tractatus figurarum, a new critical text and translation [1989], xii,122 p. $30

Robertus de Handlo, Regule, and Johannes Hanboys, Summa, new critical texts and translations by Peter M. Lefferts [1991], x,403 p. $55

André Barbera, The Euclidean Division of the Canon: Greek and Latin Sources, new critical texts and translations [1991], xi,316 p. $50

Johannes Ciconia, Nova musica and De proportionibus, new critical texts and translation by Oliver B. Ellsworth [1993], x,532 p. $55

C. Matthew Balensuela, ed. and trans., Ars cantus mensurabilis mensurata per modos juris, a new critical text and translation [1994], xii,331 p. $50

Individual volumes are available through your bookstore or by direct order from the publisher; standing orders for the series carry a discount. For online ordering, click here; for further information, please contact:

The University of Nebraska Press
P.O. Box 880484
Lincoln, NE 68588-0484
Telephone: (800) 755-1105
FAX: (402) 472-6214
http://www.music.indiana.edu/chmtl/GLMT.html

spiroslyra 2002. nov. 22. Creative Commons License 6576

Thomas J. Mathiesen
Distinguished Professor and David H. Jacobs Chair in Music
School of Music, Indiana University, Bloomington

Professor Mathiesen is a musicologist specializing in the history of music and music theory in the ancient world and the Middle Ages. He is the founding editor of Greek and Latin Music Theory, a series of texts and translations of monuments of music theory (10 volumes to date), Director of the Center for the History of Music Theory and Literature , and Project Director of the Thesaurus Musicarum Latinarum , a five million-word database of music theory written in Latin from the third century C.E. through the seventeenth century, and Doctoral Dissertations in Musicology . In addition to these large projects, his individual conference papers and publications have concentrated on Greek codicology, organology, translations and editions of early Greek and Byzantine musical sources, the theory of textual criticism, bibliography, and the music for silent films. His most recent book, Apollo's Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages(1999), was honored with the Otto Kinkeldey Award of the American Musicological Society, the Wallace Berry Award of the Society for Music Theory, and a Deems Taylor Award from the American Society of Composers, Authors and Publishers.

Professor Mathiesen has been the research director for more than fifteen theses and dissertations and has regularly taught large undergraduate courses on the history of western music in addition to his smaller, more specialized offerings at the graduate level. Prior to his appointment at Indiana University, he served as an Associate Dean of Honors and General Education, in which capacity he expanded offerings in the fine arts and shared in the development of a series of "freshman seminars" on topics in western civilization.

Professor Mathiesen received his B.M. degree from Willamette University in 1968 and M.M. and D.M.A. degrees from the University of Southern California in 1970 and 1971. He joined the faculty at Indiana University in 1988.

Professor Mathiesen was elected a Fellow of the American Academy of Arts and Sciences in 2001. In addition, his work has been recognized and supported by fellowships and grants from the National Endowment for the Humanities (1985, 1992, and 1994), the Guggenheim Foundation (1990), the Répertoire International des Sources Musicales (1980), the American Council of Learned Societies (1977), and other institutions; and by various teaching awards.

Home: (812) 876-3592; Office: (812) 855-5471; Fax: (812) 856-5024; E-mail: mathiese@indiana.edu

spiroslyra 2002. nov. 22. Creative Commons License 6575
OST' EINAI MI PERI MIKROU TIN AMFISBITISIN"
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Ozene(bona) :) XVIII. Aristoxenos
Pyknosis:
A legmelyebb allo ftongustol kiindulva vegyunk ket diesist, enharmonikus elahistost. Ez a legkisebb pyknon.Vegyunk ket chromatikus es ket enharmonikus diesist, ezzel megmutattuk a ket legmelyebb lihanost. Az enharmonikus a melyebb. A kovetkezo a chromatikus imiolius lichanos. Ezt koveti a tonikus chromatikus lichanos. Az otodik piknon a mely diatonikus, a hatodik a magas diatonikus.

A legmelyebb chromatikus lichanos es a legmelyebb enharmonikus kulonbozik a tonus egy hatodaval. 2/12=1/6 a kulonbseg ket dodekatimorio.
....
----....4+4=8 malako chromatikus
...
---...3+3=6 enharmonikus
A chromatikus diesis egy dodekatimorionnal nagyobb az enharmonikusnal.
...
....
Ket chromatikus diesis es ket enharmonikus diesis kulonbsege ektimorion, 1/6 tonus.
A mely diatonikus lichanos es a mely chromatikus kulonbsege egy fel es egy dodekatimorion tonus, 7/12.
......6
------.........9 6+9=15 malako diatonikus
....
----....4+4=8 malako chromatikus
...............15-8=7
........8
--------.......7
A mely, masneven lagy diatonikustol az chromatikus imiolion lihanosig a kulonbseg
-Imitonio egy fel tonus.
......6
------.........9+6=15-9=6 6/12=1/2 tonus
....*4,5
----*....*4,5 4,5+4,5=9 imiolio chromatikus
A tavolsag az imioliontol az enharmonikusig egy diesis.3/12 dodekatimorio, 1/4 tonus, enharmonikus diesis.
....*4,5
----*....*4,5 4,5+4,5=9 imiolio chromatikus
...
---...3+3=6 enharmonikus lichanos
.........9-6=3 3/12=1/4
......6
Az enharmonikustol a mely chromatikusig egy ektimorion .
...
---...3+3=6 enharmonikus lichanos
....
----....4+4=8 malako chromatikus
......6
........8-6=2 2/12=1/6 ektimorion
A legmelyebb chromatikustol az imiolionig
egy dodekatimorion. 1/12 tonus.
....
----....4+4=8 malako chromatikus
....*4,5
----*....*4,5 4,5+4,5=9 imiolio chromatikus
........8
.........9-8=1
A lichanosok terulete a mely diatonikustol a mely chromatikusig terjed.
......6
------............12 6+12=18 syndono diatonikus
......6
------.........9 6+9=15 malako diatonikus
......6
------......6 6+6=12 tonikus chromatikus
....*4,5
----*....*4,5 4,5+4,5=9 imiolio chromatikus
....
----....4+4=8 malako chromatikus
A syndonos diatonikus lichanos a mely diatonikusnal egy diesissel magasabb.3 moria, 3/12 , 1/4 enharmonikus elahistos diesis.
......6
------............12 6+12=18 syndono diatonikus
......6
------.........9 6+9=15 malako diatonikus
..................18-15=3
...............15

Peri de syneheias kai tou exis akribos ou panu radion en arhi diorisai, tupo de peirateon uposiminai. Fainetai de touauti tis fussis einai tou cunehous en ti melodia oia kai en ti lexei peri tin ton grammaton sunthesin' kai gar en to dialegesthai i foni kath ekastin ton sullabon proton ti kai deuteron ton grammaton tithisi kai triton kai tettarton kai kata tous loipous arithmous osautos, ou pan meta pan, all esti touauti tis fusiki auxisis tis suntheseos. Praplisios de kai en to meldein eoiken i foni tithenai kata suneheian ta te diastimata kai tous fthoggous fusikin tina sunthesin diafilattousa, ou pan meta diastima melodousa out ison out anison. Zititeon de to sunehes ouh os oi armonikoi en tais ton diagrammaton katapuknosesin apodidonai peirontai, toutous apofenontes ton ftoggon exis allilon keisthai ois sumbebike to elahiston diastima diehein af' auton, ou gar oti [mi] dunaton dieseis okto kai eikosin exis melodisai ti foni estin, alla tin tritin diesin panta poiousa oux oia te esti prostithenai, al' epi men to oxi elahiston melodei to loipon tou dia tessaron, - ta do elatto panta exadinatei-touto d' estin itoi oktaplasion tis alahistis dieseos i mikrou tini pantelos kai ameloditon elatton, epi de to bari ton duo dieseon toniaiou elatton ou dunatai melodein.Ou prosekteon ei to sunehes ote men ex ison ote d' ex anison gignetai, alla pros tin tis melodias peirateon blepein katanoein te prothumoumenon ti meta ti pefiken i foni diastima tithenai kata melos. ei gar meta parupatin kai lihanon mi dunaton egguero melodisai ftoggon mesis, auti an eii meta tin lihanon, eitai diplasion eitai pollaplasion diastima orizei paripatis kai luhanou. Tina men oun tropon to te sunehes kai to exix dei zitein, shedon dilon ek ton eirimenon' pos de gignetai kai ti meta ti diastima tithetai te kai ou tithetai , en tois stoiheios deihthisetai.
Ipokeisto meta to puknon ito apuknon tithemenon ssustima epi me to oxi mi tithesthai elatton diastima tou leipomenon tis protis sumfonias, epi de to bari mi elaton toniaion' upokeisto de kai ton exis keimenon fthongon kata melos en ekasto genei itoi tous tetartous [ tois tetrasi] dia tettaron symfonein i tous pmptous [ tois dia pente] dia pente i amfoteros' o d' an ton fthoggon miden i touton sumbebikos, ekmeli touton einai pros tous ois asumfonos estin. Upokeisto de kai tettaron gignomenon diastimaton en to dia pente, duo men ison os epi to polu, ton to puknon katehondon, duo d' anison, tou te leipomenou tis protis sumfonias kai tis uperohis i to dia pente tou dia tessaron uperehei, enantios tithestai pros tois isois ta [de] anisa epi te to oxi kai to baru. Upokeistho d kai tous tois exis fthoggois sumfonountas dia tis autis sumfonias exis autois einai. Asuntheton de upokeistho en ekasto genei einai diastima kata melos o i foni melodousa mi dunatai diairein eis diastimata. Upokeistho de kai ton sumfonon ekaston mi diaireisthai eis asuntheta panta megethi. Agogi d' esto i dia ton exis fthoggon , esothen ton akron, [on] en ekaterothen asuntheton diastima' euteia d' i epi to auto.

A suneheias , (folyamatossag?) es az akolouthias (kovetes?) fogalmakat nem konnyu pontosan meghatarozni, de meg kell kiserelnunk nehany ideiglenes magyarazatot adni. A suneheias termeszte hasonlit a szavaknak a betukbol valo osszetetelehez. Letezik a szavak rendje, termeszetes menete. Hasonlo modon a hang es a melodia, a diasztemakat es a ftongusokat egy folyamatos sorba rendezi, egy termeszeti szabalyt kovetve, igy a dallamba egyetlen diasztema sem kerulhet veletlenul. Ezt a folytonossagot a vizsgalatunk soran nem a termeszetellenesen zsufolt diagrammaval kell keresni, mint ahogy azzal a Harmonikusok probalkoztak, az egymast koveto ftongusoknak a sorat abrazolva, a legkisebb diasztemat veve, es azzal epitkezve. Mert nem lehetseges az, hogy a hang nyolc egymast koveto diesist tegyen a dallamba, a gyakorlatban nem megvalosithato harom diesis egymas utani leeneklese. Ha ket diesis fole emelkedik a hang, nem haladhat tovabbb, csak annyit amennyi kiegesziti a tetrachordot. Teljesen lehetetlenseg kiserletezni, az elahiston diesisnel nyocszor kisebb diasztema hasznalhatatlan. Leszallitva a dallamot ket diesis utan egy tonusnal kisebb diasztema zeneietlen, ameloditos. Ha a parypatit es a lihanost a hang nem tudja melodizalni a kozephez kozeli ftongussal, akkor a kozep a lihanos utan talalhato.

Előzmény: spiroslyra (6562)
spiroslyra 2002. nov. 21. Creative Commons License 6574
Keszi Imre: BEVEZETÉS A ZENETÖRTÉNETBE •
Szabolcsi Bence könyve – Franklin
– Emberszagot érzek, – szólt izgatottan a hétfejű sárkány, belépvén palotája aranyszobájába, hol az elrabolt királykisasszony már elrejtette volt a megszabadítására érkezett királyfit. Mert az embernek valóban penetráns és nagyszerű illata van, minden burkon és rejteken átható. És ha a múlt század természettudományos formájú tanultságához a hétfejű sárkány hét orrának kifinomult szaglóérzéke kellett, hogy kiérezze az emberszagot, a mai szellemtudományok annál leplezetlenebbül árulják el a mögöttük álló embert. Szabolcsi Bence könyve voltaképpen nem más, mint egy ember számadása a belülről átélt tudományról. A tudományban van valami részegítő, különösen, ha olyan benső és szoros összefüggésben áll a művészettel, e másik és színesebb alkohollal, mint Szabolcsi Bence zenetudománya. Tudásnak és művészetnek csendes mámora lengi át e halkszavú könyv lapjait: egy nagyon finom és előkelő szellem emberszaga. Ember és tudás nem vívják e könyvben a megismerés párviadalát, nem állnak szembe egymással ellenfélként, de összeforrottak egy új és mágikus egységben, az antropomorf tudományban. Aki ezt a könyvet írta, az a muzsika megejtettje. Annak számára nem probléma többé a zene, melyet ki kell emelnie az élet sokrétű és zavaros dolgai közül, elkülönítenie és művé formálnia. Számára a zene a világ szimbóluma, mithosza, értelme. Háló, mely finom, de erős szálaival véglegesen és menthetetlenül befonja, de melynek négyzetei egyszersmind a világ geometriai és szabályos áttekintését biztosítják számára. Mindent a zenén keresztül lát meg, de mindent meglát a zenén keresztül.

Ez magyarázza a könyv hangját, tartalmát, beosztását is. Ez a könyv annyira szubjektív, világa annyira öntörvényű, hogy már szinte tárgyilagosan hat. Szabolcsi halkan beszél és nem lelkesedik. Az előttünk gőzölgő pecsenye elragadtatott felkiáltásokra ösztönözhet: amit megemésztettünk és vérünkké vált, nem lelkesít többé, de a mienk. Aki Forkellal együtt teremtette meg a maga számára zene és művelődés-történet kapcsolatait, Fetissel vizsgálta a fejlődés dinamikáját, Ambrosszal rendszerezett. W. K. Printztől kezdve Bückenig és Molnár Antalig renaissance-on, barokkon, rokokón, klasszicizmuson, romantikán, izmusokon és «neue Sachlichkeit»-on keresztül saját személyében élte végig a zenetudomány egész biogenézisét, az többet nem lehet a részletek és kiszakított adatok embere. Nem lehet hiányos akkor sem, ha vázlatos, mert minden mögött ott van a maga számára megfogott, mások előtt állandóan éreztetett egész. Szabolcsi könyve két részből áll. Először «Rendszerek és problémák» címen a fejlődő zenetudomány életét ismerteti, mintegy útként a második rész felé. Majd «Három fejezet a zenetörténelemből» a fejlődés eredménye, a Szabolcsi szemei előtt muzsikává varázslódó világ. Egyszólamú kultúrák, a többszólamúság születése, küzdelem a nagy formákért Európában, valóban csak három kiragadott fejezet a nagy egészből, de mint az eleven élet minden kiválasztott sejtje, a teljesség minden fényével sugároz. Az egyszólamú kultúrák ismerete betekintést nyujt nemcsak a népi zenék barbár tarkaságába, zenei térképébe Izlandtól a Tűzföldig, történelmébe az ógörög dallamtól a mai magyar népzenéig, de egyben megismertet a perifériákra kiszorított zenei élet, az ősi anyag megmaradásának titkaival is. A kezdődő többszólamúság világa egyszersmind a jogaival fellépő egyéniség követelményeinek megfogalmazása. A nagy formák európai művészete pedig a modern művészet centrális problémáját hordozza magával: a géniusz küzdelmét anyag, tömeg és legyőzendő idő nehézkedő erőivel.

Szabolcsi Bence könyvének egy különösen szép és fontos fejezete szól az alapmelódiákról. Különös sajátossága a keleti zenéknek az, hogy a főmelódiát nem kell és nem is szabad kitalálni. A muzsikus művészete az adott és állandó fődallam variálásából, szabad és mégis szertartásos feldolgozásából áll. A jávai patet, az indus raga, az arab makam, a zsidó niggun rendszere azonban mélyen beleölel az európai zenekultúrába is. A görög nomos, a bizánci epichéma, a középkori cantus firmus, a kezdődő újkor tánczenéjének basse-dance-szisztémája ott kísértenek a Bach, Händel chaconnejaiban, passacagliáiban, de Beethoven Eroica-variációiban is. A művésznek, tudósnak nem kitalálnia kell, de továbbépítenie. Az emberiség életén nagy, kollektív gyökérszálak futnak keresztül, ezekből fakad az egyén szépséges kivirágzása. Szabolcsi könyvének igaz értéke, hogy egyszerre utal gyökérre és virágra. Egy zenetörténet a sok közül, kíváló bevezetés az anyagba, bárki számára megközelíthető és élvezhető gyökér. De virág is: egy kíváló egyéniség, lelkiismeretes tudós és igaz, áhítatos művész teljes becsű megszólalása.
http://www.mek.iif.hu/porta/szint/human/szepirod/magyar/nyugat/html/index.html?23109.htm&23097.htm

spiroslyra 2002. nov. 21. Creative Commons License 6573
Zenetudomány az Interneten

British Forum for Ethnomusicology

Ethnomusicology Bibliographic Guide

Ethnomusicology Research Digest

Finn Zenetudományi Társaság

Liszt Ferenc Zeneakadémia

On-line MusicResource Databases

Royal Holloway University of London

Sibelius Academy

Society for Ethnomusicology
http://www.zti.hu/linkek.htm p

spiroslyra 2002. nov. 21. Creative Commons License 6572
MUV6172 Antik zenetörténet
kreditált kurzus Eredeti kód: KLF2420 Egyéb kreditált kód: ESZ2179; SZI2225
[EA] 2/2 Kárpáti András
A legfontosabb zeneelméleti és - esztétikai kérdések és a rendelkezésre álló forráscsoportok áttekintése.
TF: kollokvium
KMk: KMtt: 2000-2001/1 TSZ: LATT ETSZ: LATT
TSZ: LATT ÓH: Sz 10.30-12 B 220

spiroslyra 2002. nov. 21. Creative Commons License 6571

A MATHEMATICA NOTEBOOK ABOUT ANCIENT GREEK MUSIC AND
MATHEMATICS
Luigi Borzacchini and Domenico Minunni (Dept. of Mathematics, University of Bari, Italy)
REFERENCES
BORZACCHINI, L. (2001). Music, incommesurability and continuum: a cognitive approach. Not yet
published.
BURKERT, W. (1972) Lore and Science in ancient Pythagoreanism. Harvard Univ. Press, Cambridge Mass.
KNORR, W. R.(1975). Evolution of the euclidean Elements. Dordrecht, D.Reidel Pu. Co.
FASCICOLO, V.M. (2001). Simulazione della musica greca antica con il Mathematica. Tesi di laurea in
Informatica. Univ. di Bari.
SACHS, C. (1943). The rise of music in the ancient world. East and West. W.W.Norton and Co. New York
SACHS, C. (1962). The wellsprings of music. Martinus Nijhoff, L'Aia
SZABO, A. (1978). The beginnings of greek mathematics. Reidel Pu. Co., Dordrecht
van der WAERDEN, B. L. (1963). Science awakening. New York, Yohn Wiley.
WEST, M.L. (1992). Ancient greek music. Clarendon Press, Oxford.
REFERENCES
BORZACCHINI, L. (2001). Music, incommesurability and continuum: a cognitive approach. Not yet
published.
BURKERT, W. (1972) Lore and Science in ancient Pythagoreanism. Harvard Univ. Press, Cambridge Mass.
KNORR, W. R.(1975). Evolution of the euclidean Elements. Dordrecht, D.Reidel Pu. Co.
FASCICOLO, V.M. (2001). Simulazione della musica greca antica con il Mathematica. Tesi di laurea in
Informatica. Univ. di Bari.
SACHS, C. (1943). The rise of music in the ancient world. East and West. W.W.Norton and Co. New York
SACHS, C. (1962). The wellsprings of music. Martinus Nijhoff, L'Aia
SZABO, A. (1978). The beginnings of greek mathematics. Reidel Pu. Co., Dordrecht
van der WAERDEN, B. L. (1963). Science awakening. New York, Yohn Wiley.
WEST, M.L. (1992). Ancient greek music. Clarendon Press, Oxford.
http://math.unipa.it/~grim/SiBorzacchini.PDF
spiroslyra 2002. nov. 21. Creative Commons License 6570
Prof Sheds Light on Ancient Music of Yesteryear
Date: May 8, 2001
By: Marianne Kunnen-Jones
Phone: (513) 556-1826
Archive: Research News

The music of yesteryear takes on a whole new meaning - and millennium - through the research of a UC classics scholar and his web site.

William Johnson, assistant professor of classics, is providing modern ears with a rare opportunity to listen to melodies first heard in early imperial Rome. His web site on "Ancient Greek Music on Papyrus: Two New Fragments" (classics.uc.edu/music/) lets you hear audio renditions of two samples of ancient music.

Johnson's web site and two new journal articles are the result of five years of research into the two fragments of music from the second century A.D.

One article on the pair of fragments was just published in the Bulletin of the American Society of Papyrologists last week. Another was published earlier this year in the annual Journal of Hellenic Studies. According to Johnson, scholars know of only 30 melodies from ancient Greece and Rome. Five surviving pieces are preserved on stone inscriptions, and a few others have been passed down through the medieval and Christian tradition. But the rest of the surviving examples of music from antiquity take the form of scraps of paper -- papyri, or ancient waste paper.

Johnson's web site focuses on two scraps of papyri that represent what Johnson believes to be professional performance pieces. Although they're from the Roman era, they're written in ancient Greek, because Romans regarded their musical tradition as Greek, just like many other aspects of their culture. "The musical guilds were Greek and thought of themselves as Greek," the classical scholar explains.

With just a click of the computer mouse and the latest version of QuickTime 4 installed, Web surfers can hear an ancient vocal piece for baritone performed by Christopher Brunelle, assistant professor of classics at Vanderbilt University, and an instrumental fragment performed by former College-Conservatory of Music oboe student Kimberly Potter. Johnson decided the oboe was the closest modern equivalent to the ancient aulos, a double-reeded woodwind for which the piece may have been intended.

Both pieces came to Johnson's attention through curators of papyri collections at other universities. The first piece comes from a tattered piece of paper purchased by the Beinecke Manuscript and Rare Books Library at Yale University. Before its arrival at Yale, it had been purchased early in the 20th century by a collector from a dealer in Cairo, Egypt. The second scrap had been mistakenly catalogued for decades in the papyri collection at the University of Michigan until a curator recognized it as a possible musical piece and asked Johnson to look at it.

Johnson obliged, spending hours at both libraries examining the papyri under his microscope and studying photographs of each. He now jokes that he has spent more time looking through a microscope than his brother, a molecular biologist, has.

Johnson's classics expertise proved essential in understanding the musical fragments with their Greek text and notations. Without his knowledge of piano playing and reading music, however, he would not have been able to learn as much as he did about the historic tunes. "Compared to music today, both pieces sound a little odd," Johnson points out. "It's because they're based on a different musical structure than we use now. Rather than the octave, their underpinning is the tetrachord, or half-octave."

While scholars still can't say precisely what the melodies of ancient Greek poet Sappho or the choruses of Greek dramatist Sophocles may have sounded like, they do know more than you might think about ancient Western music, Johnson says. "We know quite a lot," he says. "We know a great deal about the rhythms of the music, since these are reflected in the metrical patterns of Greek verse. We know much about the musical system, that is, how the scales were conceived and the like. We can infer much about the instruments, using as evidence surviving fragments of ancient instruments, depictions on vases and wall paintings, literary descriptions and cross-cultural comparison." Yale University's Beinecke Library supported Johnson's work with the John D. and Rose H. Jackson Visiting Fellowship in 1997 to support his initial work on the Yale musical papyrus.
http://www.uc.edu/news/papyri.htm

spiroslyra 2002. nov. 21. Creative Commons License 6569
DOCTORAL DISSERTATIONS IN MUSICOLOGY-ONLINE

School of Music
Indiana University
Bloomington, IN 47405
ANTIQUITY

(An asterisk following the DDM code indicates a dissertation in progress)

--------------------------------------------------------------------------------

Hagel, Stefan.
Modulation in altgriechischer Musik.
Ph.D., Classical Philology, Wien, 1999. 155 p. illus., tbls., mus. exs., transcr., transl., append.
Research director: Georg Danek
DDM Code: 19scHagS; DA no.: RILM no.: UM no.:
Publication: Frankfurt am Main: Peter Lang, 2000. ISBN 3-631-36642-6.
Additional keywords: Aristoxenos, Aristoxenus, paian, paean, rhythm, scales, scale systems, harmonikoi, harmonicists, Mesomedes, Delphic paeans, Limenios, Plutarch, Bacchius

Puls, Kenneth A.
Musical Praise and Thanksgiving in the Old Testament: Word Studies on Hebrew Terms in the Old Testament Related to Praise and Thanksgiving in the Context of Music.
Ph.D., Church Music Ministry, Southwestern Baptist Theological Seminary, 1998. 2 vols., xi, 653 p. tbls., transcr., append., ind.
Research director: Bruce H. Leafblad
DDM Code: 10rePulK; DA no.: RILM no.: UM no.:
Additional keywords: psalms, Temple worship, Levites

Solomon, Jon.
Cleonides: Eisagoge armonike: Critical Edition, Translation, and Commentary.
Ph.D., Classics, University of North Carolina at Chapel Hill, 1980. 2 vols., viii, 389 p. illus., transl., bibliog.
DDM Code: 10trSolJ; DA no.: 41/08:3563; RILM no.: 80:4409dd; UM no.: 81-04424

Wegge, Glen T.
Musical References in the Neoplatonic Philosophy of Plotinus.
Ph.D., Theory, Indiana University, 1999. iv, 114 p. bibliog.
Research director: Lewis Rowell
DDM Code: 19phWegG; DA no.: 60/08:2846; RILM no.: UM no.: 99-42885
http://www.music.indiana.edu/ddm/Antiquity.html

spiroslyra 2002. nov. 21. Creative Commons License 6568
LITERATUR 16
Die Grunds¨ atze der Musiktheorie.
Zu Kontroversen und Positionen in der ersten H¨ alfte des 18. Jahrhunderts
Leif Frenzel
April 2001

Literatur
Quellen
[1] Aristoteles, Nikomachische Ethik. ¨ Ubersetzt von Franz Dirlmeier. Stutt-gart:
Reclam 1983.
[2] Jacob Adlung, Anleitung zu der musikalischen Gelahrtheit [. . . ]. Erfurt:
Jungnicol 1758 [AMG].
[3] Johann Josef Fux, Gradus ad Parnassum oder Anf¨ uhrung zur Re-gelm¨aßigen
Musicalischen Composition. Aus dem Lateinischen ins Teut-sche
¨ ubersetzt, mit Anmerckungen versehen und heraus gegeben von
Lorenz Christoph Mizler. [Leipzig 1742] Reprint Hildesheim, Z¨ urich,
New York: Olms 1984.
[4] Johann Mattheson, Das Beschuetzte Orchestre [. . . ]. Hamburg: Schiller
1717.
[5] Johann Mattheson, Das neu-Eroeffnete Orchestre [. . . ]. Hamburg:
Schiller 1713.
[6] Johann Mattheson, Der vollkomene Capellmeister. Studienausgabe im
Neusatz des Textes und der Noten. Hg. von Friederike Ramm. Kassel,
Basel, London, New York: B¨ arenreiter 1999 [VC; die in dieser Ausgabe
angegebene Originalpaginierung wird in Zitaten in eckigen Klammern
beigef¨ ugt].
[7] Johann Mattheson, Exemplarische Organisten-Probe, im Artikel vom
General-Bass [. . . ]. Hamburg: Schiller und Kissner 1719.
[8] Wolfgang Caspar Printz, Historische Beschreibung der edelen Sing- und
Klingkunst [. . . ]. Dresden: Johann Christoph Mieth 1690.
[9] Johann Gottfried Walther, Musicalisches Lexicon oder musikalische Bi-bliothek.
[1732] Faksimile-Nachdruck, hg. von Richard Schaal. Kassel,
Basel: B¨ arenreiter 1953 [WaltherL].
Forschungsliteratur
[10] Andrew Barker, “Music and perception. A study in Aristoxenus.” In:
Journal of Hellenic Studies 98 (1978), 9-16.
[11] George J. Buelow, Art. “Mattheson, Johann”. In: New Grove Dictio-nary
of Music and Musicians. Vol. 11. Ed. by Stanley Sadie. London,
New York: Macmillan 1980, 832-836.

LITERATUR 17
[12] George J. Buelow, Art. “Mizler von Kolof, Lorenz Christoph”. In: New
Grove Dictionary of Music and Musicians. Vol. 12. Ed. by Stanley Sa-die.
London, New York: Macmillan 1980, 372-373.
[13] Hellmut Federhofer, “Johann Joseph Fux und Johann Mattheson im
Urteil Lorenz Christoph Mizlers”. In: Speculum musicae artis. Festgabe
f¨ ur Heinrich Husmann. M¨ unchen: Fink 1970, 111-123.
[14] Hans Gunter Hoke, Art. “Mizler von Kolof, Lorenz Christoph”. In:
In: Die Musik in Geschichte und Gegenwart. Bd. 9. Hg. von Friedrich
Blume. Kassel, Basel, London, New York: B¨ arenreiter 1961, 388-392.
[15] C. von Jan, Art. “Aristoxenos (7)”. In: RE [Paulys Realencyclop¨adie
der Classischen Altertumswissenschaften] 3/II 1 (1895), 1057-1065.
[16] Peter Kivy, “Mattheson as philosopher of art”. In: The fine art of
repetition. Essays in the philosophy of music. Cambridge: cambridge
University Press 1993, 229-249.
[17] Richard Petzoldt, “Johann Mattheson. Zu seinem 250. Geburtstag am
28. September.” In: Die Musik XXIII (1931), 887-890.
[18] Roger Scruton, The Aesthetics of Music. Oxford: Oxford University
Press 1997.
[19] Hans Turnow, Art. “Mattheson, Johann”. In: In: Die Musik in Ge-schichte
und Gegenwart. Bd. 8. Hg. von Friedrich Blume. Kassel, Basel,
London, New York: B¨ arenreiter 1960, 1795-1815.
[20] Fritz Wehrli, Art. “Aristoxenos von Tarent”. In: Grundriss der Ge-schichte
der Philosophie. Begr¨ undet von Friedrich Ueberweg. Die Phi-losophie
der Antike, Bd. 3: ¨ Altere Akademie, Aristoteles - Peripatos.
Hg. von Hellmut Flashar. Basel, Stuttgart: Schwabe & Co. 1983, 540-
546.
[21] Fritz Wehrli, Art. “Aristoxenos (7)”. In: RE [Paulys Realencyclop¨adie
der Classischen Altertumswissenschaften] Suppl. 11 (1968), 336-343.
[22] R. P. Winnington-Ingram, Art. “Aristoxenus”. In: New Grove Dictio-nary
of Music and Musicians. Vol. 1. Ed. by Stanley Sadie. London,
New York: Macmillan 1980, 591-592.
http://www.leiffrenzel.de/Papers/found.pdf

spiroslyra 2002. nov. 21. Creative Commons License 6567
Summary
If you want to be a part of the Chorus (jury), you have to be qualified -- take the Quiz (also, on the right -- test and poll).

Questions
How to project their comments (laptops) on the screen, during the show? Who is in charge of screening it? The leader of the chorus.

Notes
Live public = chorus (for the cyber viewers). Who is the leader of the chorus? In academic regalia.

Next: Ideas
From ASTR List:

I have a copy of "Greek Tragedy" by H.D.F. Kitto originally published in 1939, revised in 1950. There are many references to the chorus under "New Tragedy," "Old Tragedy" and "Lyrical Tragedy" with additional sections on the chorus "as actor," "as lyrical body," "in Sophocles," "in Euripides" and "characterization of." There is a curious note that says "see also Ideal Spectator."

No one knows exactly how the Greek chorus performed. But thought-provoking guesses can be found in Pickard-Cambridge's classic works as well as Peter Arnott's _Greek Scenic Conventions in the Fifth Century BC_. Paul Nadler, Ph.D. Program in Educational Theatre, New York University

I recently taught an undergraduate seminar on classical Greek theatre, and found that the students were motivated by mystery to dig into outside secondary sources for recent developments in research. It's the opposite of a concise account, but it relieves some of the frustration of the "we don't know" mantra.
I would suggest looking at John Winkler's essay "The Ephebes Song: Tragoidia and Polis" in Nothing to Do with Dionysus (Princeton 1990). His own conjectures on what the chorus did are in part based on WHO the chorus members were, i.e. young men coming of age ( which meant impending military service, but also apparently involved some crossdressing rites of passage.) Check out Winkler's theory on why "goat song" became the word for tragedy.!
There is some evidence on dance in the context of religious festivals which helps us to understand the cultural meaning of dance and choral performance in Athens and other ancient Greek cultures, Look at Dance and Ritual Play ( Johns Hopkins, 1993) by Steven H. Lonsdale. Enjoy!


Dr. Charles B. Davis
Assistant Professor
Department of Theatre and Drama
University of Georgia
Fine Arts Building
Athens, Georgia,
30602 (USA)
Phone: (706) 542-2836
Fax: (706) 542-2080
Email: theatre@arches.uga.edu

There are also analyses on the notation of Greek music and how it might have actually sounded. A graduate student did a presentation on some of the latest theories over a year ago, but I can't find my notes. I did email her to ask. The sample she played sounded far more "musical" and a lot less "chanty" than I had thought it would. Anyway, there is an interesting web site on the extant music fragments: http://www.oeaw.ac.at/kal/agm/ The greeks used greek letters for the notation and the music here is hypothetically reconstructed using the frequency proportions devised by Pythagoras.
Unless I've missed a posting, I haven't seen anyone yet refer to Lillian B. Lawler's The Dance in Ancient Greece (Seattle: University of Washington Press, 1964). I read it some years ago and remember finding it very useful. Adrian Kiernander

W.B.Stanford's The Sound of Greek (University of California Press, 1967) is also quite interesting. It originally came with a phonograph record of Stanford replicating Greek intonation and rhythms as he conjectured them to be based on his reconstructions.

All of these suggestions about movement and pronunciation and music are intriguing and, in some cases, potentially exciting. But let's keep in mind that they are also completely conjectural. For instance, the message I happen to be replying to suggests a book and CD-ROM titled The Sound of Greek. The immediate question is, "What does the author mean by Greek?" At the time of what we usually mistakenly call "Greek Theatre", the peoples of what we now know as Greece spoke numerous tongues, some related to each other dialectically, others standing apart as separate languages. Each, of course, had its own particular system of pronunciation--and no one really knows what any of them sounded like.
I insist on these facts because even as late as my doctoral studies, professors were filling my mind and firing my imagination with false "facts" about theatre and its history. Thus, I have had to unlearn a good deal of what I learned. I cannot believe that I am the only one to have had this experience. Believe it or not, students will not maim or even disrespect you for admitting the truth of our ignorance about so many matters theatre-historical. Tom Pallen

In response to Dr. Pallen:

The conjectures on Greek poetry and music are usually based on snippets and quotes from "anthologies" from antiquity. Granted, their provenance is often doubtful, but beggars can't be choosers. I prefer to think that reconstructions, however hypothetical, are a means of greater creativity in our thinking about history. Not unlike the New Globe, whose accuracy will always be in doubt in some quarters, but whose galvanizing effect on the actors and audience are truly inspiring. Here's hoping we can get more than a handful of people to try some serious experimentation with Greeks in mind. Andy White

On the subject of how the music may have sounded, my personal favorite is Thomas J. Mathiesen's _Apollo's Lyre_, which goes into great detail about Greek musical practices, theatre included. G. Comotti and M. L. West have also published on the subject, and I believe a new anthology of ancient music (with notation) was recently published with West as co-editor.

The alphabet-notation system is interesting, not least because it takes the entire Greek alphabet to cover just one octave. Greek music was microtonal and required intensive training to perform -- it is likely that the Ephebes were drilled in microtonal scales just as they were drilled in swordsmanship. And the notation for higher and lower octaves, designated as Dr. Westlake says by letters twisted this way and that, seem to suggest the turnings of pegs on stringed instruments.

We may not have much in the way of sheet music, and reconstructions/recordings by impresarios like Christodoulos Halaris are always contingent on the state of knowledge at the time of recording -- his version of Euripides' _Orestes_ chorus, for instance, ignores microtonal intervals and is sung at a funereal pace that is not suggested by the meter of the lyrics. What I suggest is that you pick up a recording of Greek Orthodox chant, preferably monastic (from, say, the Mount Athos community) and listen to it as you leaf through Mathiesen. Orthodox chanters and composers claim descent from the dramatic composers of the Dionysia, and to some extent this may be true. (NB: A part of my dissertation will be devoted to parsing out the possible connections and disjunctures in the Greek musical tradition, notation and all.)

It may also interest your students to pick up the 2-volume set, _Greek Musical Writings_, edited by Andrew Barker. Both volumes provide a wealth of primary source material on the basic terminology and theories of Ancient Greek music, as well as contemporary reactions to specific composers' work. Pay special attention to Aristoxenus, a musician and pupil of Aristotle -- you'll find that Plato's much-ballyhooed theory of music in the _Republic_ was largely rejected and ignored by his protégés.

A modest proposal: given our expanding state of knowledge about the musical dimension of Greek drama, I think it's time we begin to call them composers, not "poets." The latter is merely transliteration, and although the former is Latin-based, it comes closer to the sense of the original Greek "maker."

Andy White
http://www.vtheatre.net/shows/hamlet/public.html

spiroslyra 2002. nov. 21. Creative Commons License 6566

ELECTRONIC ANTIQUITY:
COMMUNICATING THE CLASSICS

PHILOLOGY

Aristoxenus, Elementa Rhythmica. Edited by Lionel Pearson, in: Elementa Rhythmica. The Fragment of Book II and the Additional Evidence for Aristoxenean Rhythmic Theory. Translated by Lionel Pearson. Oxford: Clarendon Press, 1990
Barker, Andrew, ed. (1984). Greek Musical Writings, Volume I: The Musician and His Art. Cambridge Readings in the Literature of Music. Edited by John Stevens & Peter LeHuray. Cambridge: Cambridge University Press.
Barker, Andrew, ed. (1989). Greek Musical Writings, Volume II: Harmonic and Acoustic Theory. Cambridge Readings in the Literature of Music. Edited by John Stevens and Peter LeHuray. Cambridge: Cambridge University Press.
Benveniste, Emile. (1971). 'The Notion of 'Rhythm' in its Linguistic Expression', in: Problems in General Linguistics. Translated by Mary Elizabeth Meek. Coral Gables, Florida: University of Miami Press, pp. 281-289.
Heidegger, Martin. (1967). 'Vom Wesen und Begriff der phusis. Aristoteles' Physik B, 1', in: Wegmarken. Frankfurt am Main: Vittorio Klostermann, pp. 309-73.
Jaeger, Werner. (1936). Paideia. Die Formung des griechischen Menschen, erster Band. Second ed. Berlin and Leipzig: Walter De Gruyter & Co.
Leemans, E.A. (1948). 'Rythme en ruthmos'. L'Antiquite Classique, 17: 403-12.
Petersen, E. (1917). 'Rhythmus', in: Abhandlungen der koniglichen Gesellschaft der Wissenschaften zu Gottingen: philogisch-historische Klasse. Vol. xvi/5, Berlin: 1-104.
Seidel, Wilhelm. (1980). 'Rhythmus/Numerus', in: Handwoerterbuch der musikalischen Terminologie. Edited by Hans-Heinrich Eggebrecht. Wiesbaden: F. Steiner, 1972- , pp. 1- 36.

http://scholar.lib.vt.edu/ejournals/ElAnt/V1N4/morse.html

spiroslyra 2002. nov. 21. Creative Commons License 6565
Aristoxenus philosophus et musicus et Aristoxenica (Aristox.)
Wehrli, F., DSA 22, 1967.
Fr. = Fragmenta.
Pearson, L., Oxford 1990.
p. 28: Fr.Neap. = Fragmenta Neapolitana (olim Parisina) (cit. por n. de párr.).
p. 32: Fr.Temp. = Fragmentum de primo tempore (cit. por p.).
p. 20: Psell.Intr. = Michaelis Pselli introductio in Rhytmica (cit. por n. de párr.).
p. 2: Rhyth. = Elementa rythmica (cit. por n. de párr.).
p. 36: Rhyth.Ox. = Rhythmica (POxy.9 + 2687) (cit. por col. y lín. del pap.).
Da Rios, R., Roma 1954.
Harm. = Harmonica (cit. por p. y lín.).
Rossi, L.E., en Aristoxenica, Menandrea, Fragmenta philosophica, Florencia (STCPF 3) 1988.
p. 37: Harm.Ox. = Harmonica (POxy.667).
spiroslyra 2002. nov. 21. Creative Commons License 6564
Aristoxenus (364 BC?-304 BC?) [Library of Congress]

Great Books Biography [Malaspina]
Aristoxenus [Amazon Search Form]
Library of Congress Online Citations [LC]
COPAC UK Online Citations [COPAC]
Free Online Practice Exams [Grad Links]
Canadian Book Orders! [Chapters-Indigo]
Save on Textbooks! [Study Abroad]
Books from Amazon [Amazon]
Books from EBay! [Ebay]
Books from Amazon UK [Amazon UK]
Books from Chapters Canada [Chapters]
Amazon's 100 Hot CD's [Amazon]
Harmonika Stoicheia by Aristoxenus [Citations and Orders]
Aristoxenus: Elementa Rhythmica [Citations and Orders]
Musical Theory and Ancient Cosmology [Ernest G. McClain]
Intonational Injustice [Music Theory Online]
Greek and Liturgical Modes [Bill Hammel]

References to Aristoxenus in Perseus English Index

The Library of Congress >> Go to Library of Congress Authorities



DATABASE: Library of Congress Online Catalog

YOU SEARCHED: Subject Browse = Aristoxenus
SEARCH RESULTS: Displaying 1 through 25 of 25.


# Hits Headings (Select to View Titles) Type of Heading
[ 1 ] 5 Aristoxenus LC subject headings
2 0 Aristoxenus. Eléments harmoniques LC subject headings
[ 3 ] 1 Aristoxenus. Elements of rhythm LC subject headings
[ 4 ] 1 Aristoxenus. [from old catalog] LC subject headings
[ 5 ] 1 Aristoxenus. Harmonics LC subject headings
6 0 Aristoxenus. Rhythmika stoicheia LC subject headings
7 0 Aristoxenus. Traité d'harmonique LC subject headings

Resort results by: Full Title Main Author/Creator Date (Ascending) Date (Descending)
# Subject Heading Name: Main Author, Creator, etc. Full Title Date
[ 1 ] Aristoxenus Fritz, Kurt von, 1900- Pythagorean politics in southern Italy : an analysis of the sources / by Kurt von Fritz. 1977
ACCESS:
Jefferson or Adams Bldg General or Area Studies Reading Rms CALL NUMBER:
B199 .F7 1977

[ 2 ] Aristoxenus Fritz, Kurt von, 1900- Pythagorean politics in southern Italy; an analysis of the sources, by Kurt von Fritz. 1940
ACCESS:
Jefferson or Adams Bldg General or Area Studies Reading Rms CALL NUMBER:
B199 .F7

[ 3 ] Aristoxenus Laloy, Louis, 1874- Aristoxčne de Tarente et la musique de l'antiquité. 1904
ACCESS:
Performing Arts Reading Room (Madison, LM113) CALL NUMBER:
ML169.A7 L2

[ 4 ] Aristoxenus Laloy, Louis, 1874-1944. Aristoxčne de Tarente, disciple d'Aristote, et la musique de l'Antiquité / Louis Laloy. 1973
ACCESS:
Performing Arts Reading Room (Madison, LM113) CALL NUMBER:
ML169.A7 L2 1973

[ 5 ] Aristoxenus Mewaldt, Johannes, 1880- De Aristoxeni Pythagoricis sententiis et vita Pythagorica ... 1904
ACCESS:
Jefferson or Adams Bldg General or Area Studies Reading Rms
http://www.mala.bc.ca/~mcneil/aristoxenus1.htm

spiroslyra 2002. nov. 21. Creative Commons License 6563
Elnezest a duplazasert...:)