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Please note, this is under heave revision and will be for about another week. Much material (for instance octave species) needs to be cross referenced and so on and on.
This is an attempt to free up the mode article from too much information about the Greek modes, at the same time as giving them a proper place for discussion within the system. Please comment ! Mwasheim ( talk) 16:32, 17 November 2009 (UTC)
Just to ward of premature editing, Aristoxenos is preceeded by other classifications (a synthetic one which weighs Pythagoras and Archytas much more so, because of the mathematics) but this is a transient state. To avoid the error of subsuming all ancient Greek systems in Aristoxenos, we MUST show other forms of classification, but I'm sorting out which can reliably be referenced. As a starting point I've used Chalmers first, since his account covers that which is more readily subject to empirical study (ie. the numerical ratios and intervals which Aristoxenos eschewed, in part if not whole). But, just as the observation which is often made of Aristoxenos that he accorded more importance to musical practice and tuning by ear can apparently (Stanford) be applied to Archytas, Aristoxenos synthesis arguably has to be placed in a more prominent position, once we have the apparatus as a whole. Mwasheim ( talk) 23:42, 23 November 2009 (UTC)
Robert Erickson
A harmonia is fundamentally a tuning (Grove Dictionary) the word may include the meaning of "scale". A definition which is true to its meaning through Plato, and the sense in which the term will be used in this paper is: an ordered array of tones. See also Musical Thought in Ancient Greece, Edward A. Lippman, New York, 1964, Ch.I.
This needs to be further elaborated. The whole Mode / Tonoi / Pitch Class / Scale discussion goes awry in this regard. And it seems to be the 'turning point' of much of the polemic. The relationship of the polemic to the practice... oh, my. In so far as we are able to 'see through' Plato's polemic (or see it for that matter?!) it's a matter of worth some effort IF as Erickson (or John Chalmers, Irving Wilson, et. al.) efforts to produce actual music using the available evidence leads us to a 'more accurate' representation of the music that 4th century Greeks actually heard. On the other hand, Chalmer's emphasizes the 'purely' generative which also has it's merits. But that's ALL outside of the scope of the wikipedia but for the part which actually explains the fragments we have. Mwasheim ( talk) 22:05, 12 January 2010 (UTC)
This sentence is confusing:
To bridge this inconsistency, the system allowed moving the Nete one step up permitting the construction of the synemmenon ('conjunct') tetrachord.
Is the "Nete" here the Nete of the Diezeugmenon? If so, then isn't it moved down one step (from E to D), not up? 24.242.253.206 ( talk) 20:52, 20 December 2019 (UTC)
A Later Addition: The whole discussion of the Greater and Lesser Perfect Systems is extremely confusing. It might be inconsistent, but I think the main problem is that it is too condensed--it leaves out things which are difficult if not impossible for readers to infer for themselves. I have tried to do just that; the result are below. I have done no consultation in primary sources--this is me trying to interpret the article-- so I am not going to insert it as an edit; I'm just putting it out to see if more deeply-informed people take it up. Here it is, starting from the first mention of the Greater Perfect System:
The Greater Perfect System (systema teleion meizon) was composed of four stacked tetrachords called the (from bottom to top) Hypaton, Meson, Diezeugmenon and Hyperbolaion tetrachords (see the right hand side of the diagram). Each of these tetrachords contains the two fixed notes that bound it. [This is unchanged. What follows diverges right away.]
The system is composed of two full octaves (a1 to a and a to A), with intervals 1-1-1/2-1-1-1/2-(1) going down in pitch. Each octave is composed of two like tetrachords (1-1-1/2 going down) connected by one common tone, the Synaphe; the lowest notes (the a and A) are added. At the position of the note Paramese (i.e. b, the lowest note in the Diezeugmenon tetrachord) the system encounters a boundary. The proper internal divisions of the lower full octave (a to A) must be retained. To retain the proper internal divisions of the tetrachords as well (see below for more detail), so that the tetrachord Meson not consist of three whole tone steps (b-a-g-f), the tetrachord Meson can begin not on that b but on the a exactly one octave below a1. The proper distribution of all the remaining notes, from a to A, immediately follows. However, the new interval b to a is not linked to the proper internal structure of any tetrachord. To remedy this, an interstitial b-flat, the Diazeuxis ('dividing') was introduced between the notes Paramése and Mese. The tetrachord Diezeugmenon is the 'divided'. This interstitial b-flat allowed moving the note Nete one step, to d1, permitting the construction of the synemmenon ('conjunct') tetrachord (see the far left of the diagram). By permitting both the b and the b-flat, all five tetrachords become interlocked with shared tones and the entire system is governed by the 1-1-1/2 interval tetrachord pattern.
The use of the synemmenon tetrachord with the b-flat also yielded an octave, d1-to-d, with the same arrangement of intervals as the original two full octaves. It thus effected a modulation of the system, hence the name systema metabolon, the modulating system, also the Lesser Perfect System. [and so on...] HHHEB3 ( talk) 21:48, 22 July 2020 (UTC)
The section "Aristoxenus's tonoi" shows the tone names assigned to a range from F to F, instead of A to A, without any explanation why. — Preceding unsigned comment added by 24.242.253.206 ( talk) 21:49, 20 December 2019 (UTC)
It might be worthwhile to include their original spellings. They are otherwise hard to find on the web.
The transliteration "nete" in the diagram is accented paroxytonically, but Wiktionary has the accent on the last syllable (νητή). Is the transliteration an error? 24.242.253.206 ( talk) 19:16, 31 December 2019 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||
|
Please note, this is under heave revision and will be for about another week. Much material (for instance octave species) needs to be cross referenced and so on and on.
This is an attempt to free up the mode article from too much information about the Greek modes, at the same time as giving them a proper place for discussion within the system. Please comment ! Mwasheim ( talk) 16:32, 17 November 2009 (UTC)
Just to ward of premature editing, Aristoxenos is preceeded by other classifications (a synthetic one which weighs Pythagoras and Archytas much more so, because of the mathematics) but this is a transient state. To avoid the error of subsuming all ancient Greek systems in Aristoxenos, we MUST show other forms of classification, but I'm sorting out which can reliably be referenced. As a starting point I've used Chalmers first, since his account covers that which is more readily subject to empirical study (ie. the numerical ratios and intervals which Aristoxenos eschewed, in part if not whole). But, just as the observation which is often made of Aristoxenos that he accorded more importance to musical practice and tuning by ear can apparently (Stanford) be applied to Archytas, Aristoxenos synthesis arguably has to be placed in a more prominent position, once we have the apparatus as a whole. Mwasheim ( talk) 23:42, 23 November 2009 (UTC)
Robert Erickson
A harmonia is fundamentally a tuning (Grove Dictionary) the word may include the meaning of "scale". A definition which is true to its meaning through Plato, and the sense in which the term will be used in this paper is: an ordered array of tones. See also Musical Thought in Ancient Greece, Edward A. Lippman, New York, 1964, Ch.I.
This needs to be further elaborated. The whole Mode / Tonoi / Pitch Class / Scale discussion goes awry in this regard. And it seems to be the 'turning point' of much of the polemic. The relationship of the polemic to the practice... oh, my. In so far as we are able to 'see through' Plato's polemic (or see it for that matter?!) it's a matter of worth some effort IF as Erickson (or John Chalmers, Irving Wilson, et. al.) efforts to produce actual music using the available evidence leads us to a 'more accurate' representation of the music that 4th century Greeks actually heard. On the other hand, Chalmer's emphasizes the 'purely' generative which also has it's merits. But that's ALL outside of the scope of the wikipedia but for the part which actually explains the fragments we have. Mwasheim ( talk) 22:05, 12 January 2010 (UTC)
This sentence is confusing:
To bridge this inconsistency, the system allowed moving the Nete one step up permitting the construction of the synemmenon ('conjunct') tetrachord.
Is the "Nete" here the Nete of the Diezeugmenon? If so, then isn't it moved down one step (from E to D), not up? 24.242.253.206 ( talk) 20:52, 20 December 2019 (UTC)
A Later Addition: The whole discussion of the Greater and Lesser Perfect Systems is extremely confusing. It might be inconsistent, but I think the main problem is that it is too condensed--it leaves out things which are difficult if not impossible for readers to infer for themselves. I have tried to do just that; the result are below. I have done no consultation in primary sources--this is me trying to interpret the article-- so I am not going to insert it as an edit; I'm just putting it out to see if more deeply-informed people take it up. Here it is, starting from the first mention of the Greater Perfect System:
The Greater Perfect System (systema teleion meizon) was composed of four stacked tetrachords called the (from bottom to top) Hypaton, Meson, Diezeugmenon and Hyperbolaion tetrachords (see the right hand side of the diagram). Each of these tetrachords contains the two fixed notes that bound it. [This is unchanged. What follows diverges right away.]
The system is composed of two full octaves (a1 to a and a to A), with intervals 1-1-1/2-1-1-1/2-(1) going down in pitch. Each octave is composed of two like tetrachords (1-1-1/2 going down) connected by one common tone, the Synaphe; the lowest notes (the a and A) are added. At the position of the note Paramese (i.e. b, the lowest note in the Diezeugmenon tetrachord) the system encounters a boundary. The proper internal divisions of the lower full octave (a to A) must be retained. To retain the proper internal divisions of the tetrachords as well (see below for more detail), so that the tetrachord Meson not consist of three whole tone steps (b-a-g-f), the tetrachord Meson can begin not on that b but on the a exactly one octave below a1. The proper distribution of all the remaining notes, from a to A, immediately follows. However, the new interval b to a is not linked to the proper internal structure of any tetrachord. To remedy this, an interstitial b-flat, the Diazeuxis ('dividing') was introduced between the notes Paramése and Mese. The tetrachord Diezeugmenon is the 'divided'. This interstitial b-flat allowed moving the note Nete one step, to d1, permitting the construction of the synemmenon ('conjunct') tetrachord (see the far left of the diagram). By permitting both the b and the b-flat, all five tetrachords become interlocked with shared tones and the entire system is governed by the 1-1-1/2 interval tetrachord pattern.
The use of the synemmenon tetrachord with the b-flat also yielded an octave, d1-to-d, with the same arrangement of intervals as the original two full octaves. It thus effected a modulation of the system, hence the name systema metabolon, the modulating system, also the Lesser Perfect System. [and so on...] HHHEB3 ( talk) 21:48, 22 July 2020 (UTC)
The section "Aristoxenus's tonoi" shows the tone names assigned to a range from F to F, instead of A to A, without any explanation why. — Preceding unsigned comment added by 24.242.253.206 ( talk) 21:49, 20 December 2019 (UTC)
It might be worthwhile to include their original spellings. They are otherwise hard to find on the web.
The transliteration "nete" in the diagram is accented paroxytonically, but Wiktionary has the accent on the last syllable (νητή). Is the transliteration an error? 24.242.253.206 ( talk) 19:16, 31 December 2019 (UTC)