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