How is the Santur (Santour / Santoor) usually tuned (in pure intonation)?

Question

From what I've read the Persian Santur is usually tuned to the Phyrgian mode, but what are the actual frequencies or ratios of the notes? How would I tune one by ear? e.g. a piano tuner might count beats.

I have found little information in English, but one video (How To Tune A Persian Santoor) shows:

D♯ 158.2 Hz +28 cents
F  349.2 Hz  +0 cents / 176.9 Hz +22 cents
G  784.1 Hz  +0 cents
A  438.7 Hz  -5 cents
A♯ 465.8 Hz  -1 cents / 233.6 Hz +4 cents
C  523.4 Hz  +0 cents / 262.2 Hz +4 cents
D  587.0 Hz  +0 cents / 146.6 Hz -2 cents

If we take just the cent values we can guess at the following ratios:

D    0 cents        1/1
E♭ 129 cents        probably 27/25, 133 cents
F  301-323 cents    6/5
G  501 cents        probably 4/3, 498 cents
A  696 cents        probably 3/2, 702 cents
B♭ 800-805 cents    probably 8/5, 814 cents
C  1001-1005 cents  could be 16/9 996 cents, or 9/5 1018 cents

Am I close here? What are the most commonly used ratios? Is there some intentional tempering? Is it different for e.g. Persian vs Indian music?

In an interview with Sourena Sefati he mentioned using quarter tones and I have heard this mentioned by Indian musicians as well. But I thought quarter tones would normally refer to 24-TET not pure intonation, so this adds to my confusion.

Answer 1

(I think I remember this, but I don't have a reference.) There are about 7 scales (western word) systems in use in Persian music. These are similar to the Arabic and Turkish tunings but not exactly the same (also close to the western scales). Two problems make things a bit complicated.

First, the "accidental" or "between" notes are not tuned the same by the same player from day to day. Some theory books suggest quarter-tone tuning and others suggest third-tone. One study I saw (but I cannot find) used electronic measurements on tunings and found that the tunings vary. In addition, piano music just uses half-steps for these notes. There seems to be a bit of variability.

Second, there need not be octave equivalence. This occurs with melodies that may range (for example) C-D-E-F-G-A-B-C-D-Eb. One could do the same in westen tuning.