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I've retranscribed a piece of music whose original transcription was made around 1800 during Napoleon's Egypt expedition. The original transcriber describes the following tuning, for the Arabic Rast mode in D:

D E F+1/3 G A B C+1/3

This tuning system differs from the currently practiced 24-tet quarter-tone Arabic system (standardized in 1932 at a famous music conference in Cairo), in that it uses third-tones instead. However, the 4th and 5th tones still respect the 4:3 and 3:2 intervals.

My question is, what would be the name of this tuning in our current music theory?

Fwiw, here's my transcription: https://musescore.com/infojunkie/ya-labesyn

  • I don't suppose there's another name for this. Much like 12-edo is only an approximation for western scales (which are in principle just-intonated), 24-edo is only a system that can be used to render an approximation of maqams in their original intent. Quite possibly, these ¹⁄₃-raised minor third's are pretty much the “true” Rast scale, and what's called modern Rast is a worse approximation. But, I know very little about Arabic music. – leftaroundabout Feb 6 '17 at 1:02
  • To be sure, what is this now – F+33ct (¹⁄₆ tone up from F) or F+67ct (¹⁄₃ tone up)? The latter would seem to make more sense thinking of 7-limit just intonation, but it would not resemble the 24-edo Rast scale. – leftaroundabout Feb 6 '17 at 1:10
  • You could try fitting it to a documented scale via huygens-fokker.org/scala but 4:3, 3:2 isn't much to go on... what are the exact intervals used as the base, for comparison? – thrig Feb 6 '17 at 17:06
  • Thanks for the comments and sorry for the late reply. According to Wikipedia, 12-TET was already used by the 19th century, so the regular base tones apply, except for F and C which are raised 1/3 of a TONE, not 1/3 of a semitone. – infojunkie Mar 10 '17 at 5:41
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The nearest scales AFAIK are 4th (plagal) Byzantine Liturgical modes. It would be only off by ~15-20 cents on the F and C. Also the Arabic Segah (Dudon) is pretty near (off by 17 cents).

You will find them in "The Mathematical Theory of Tone Systems" by Ján Haluška.

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