Hi Paul,

I cannot even dream of beating you on the theoreticl part of it and I
have less than no support for the submitted scale. As I mentioned,
it's "as far as I have come up with, the only scientific article on
saz tuning..."

I can play bağlama sort of instruments poorly, depending on my
knowledge of Ud. I didn't ever measure a fret but I remember
occassionally moving some of them up or down for a better sounding
interval. The "standard" major/minor/just intervals are no problem.
However, I try to get 12/11 or 11/10 seconds (or 150~165 cents) which
are vital. I also try to get 5/4 instead of a ditone.

FWIW, I did some finger-position measurings on my Ud, which is a
fretless instrument, so more practical for legati and pitch
preciseness. For instance, 13/10 fourth came out from such
measurements rather than mathemetical calculations. (It's used to
form a Sabâ tetrachord/pentachord 10:11:12:13:15)

Best,
Ertugrul


--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> well, this is certainly 'theoretical', whether we consider it first
> hand or second hand. no one measures frets and comes up with a set
of
> ratios as those above, without incorporating (and revealing) their
> theoretical baggage . . . notice the long chains of perfect 3:2
> fifths, such as 16/9 - 4/3 - 1/1 - 3/2 - 9/8 - 27/16 - 81/64, then
> interrupted by the '17-comma' (?) 4131/4096 to begin another such
> chain: 32/17 - 24/17 - 18/17 - 27/17 - 81/68 -- with no prime
factor
> besides 2, 3, 11, or 17 coming into any of the ratios. were
> uncertainty values given for the measurements? if not, this can't
be
> considered an 'objective scientific measurement'.
>
> however, i'm willing to concede that this is an extremely close
(and
> numerically clever) approximation to the most common middle
eastern /
> arabic tuning, since according to ertugrul this accords in general
> with turkish practice.
>
> for future reference, the cents values of the above ratios are
>
> 98.95
> 150.64
> 203.91
> 302.86
> 354.55
> 407.82
> 498.04
> 597.00
> 648.68
> 701.96
> 800.91
> 852.59
> 905.87
> 996.09
> 1095.04
> 1146.73
> 1200.00
>
> correct? now, the unequal 17- and 24-tone systems you discredited
in
> your previous message -- are those the ones each derived as a
single
> chain of 3:2 fifths, coming, you might say, from 'Pythagorean'
> tendencies?