Some Georgian Tuning info found

Here's a quote:

In general, in music with true three-part polyphonic independence and
a small melodic range, fifths will be more important than octaves.
The fifth will replace the octave as the unit of structural stability
and pitch equivalence, and the scale will repeat at the fifth instead
of the octave. We can usefully speak of such music as being built
around the "quintave" rather than the octave. In a scale based on the
quintave, furthermore, the tendency will be to subdivide the fifth
not into whole and half steps but into four intervals more nearly
equal in size, blurring or erasing the sense of major and minor.
Those intervals produce a lowered second, a near-neutral third, and a
raised fourth--which, when projected by a fifth, results in a raised
eighth degree, a wide octave. The effects of this tendency vary by
region in proportion to the tradition of true three-part polyphony,
but some form of quintave tuning is common to almost all Georgian
music.

from here http://argosoft.com/kavkasia/album2/intro.htm

That sounds very interesting. I have some recordings of other
Georgian music, is there a program I could use to analyze the
frequencies of the scales?

todd

Can anyone make sense of this? Suppposedly it is the ratios for a
Georgian tuning found here
http://users.bestweb.net/~notr/kartuli/tuning.txt

Svan:

sm2 ln(3**7/125)*12/ln(2) = 49.547439 -> +2242
M2
sm3 ln(3**5/25)* 12/ln(2) = 39.371476 -> +1521
sM3 2*ln(5/9) * 12/ln(2) = -20.351926 -> -1441
sP4 ln(27/5) * 12/ln(2) = 29.195513 -> + 801
s+4 3*ln(5/9) * 12/ln(2) = -30.527889 -> -2162
s-5 ln(9**5/5**4)*12/ln(2)= 78.742952 -> +3043
P5
sm6 ln(9**4/125)*12/ln(2) = 68.566989 -> +2322
M6
sm7 ln(9**3/25)* 12/ln(2) = 58.391026 -> +1602
sM7 ln(25/27)* 12/ln(2) = -1.332376 -> -1361
sP8 ln(81/5) * 12/ln(2) = 48.215063 -> + 881

--- In MakeMicroMusic@y..., "booeyschewy" <booeyschewy@y...> wrote:
> Here's a quote:
>
> In general, in music with true three-part polyphonic independence
and
> a small melodic range, fifths will be more important than octaves.
> The fifth will replace the octave as the unit of structural
stability
> and pitch equivalence, and the scale will repeat at the fifth
instead
> of the octave. We can usefully speak of such music as being built
> around the "quintave" rather than the octave. In a scale based on
the
> quintave, furthermore, the tendency will be to subdivide the fifth
> not into whole and half steps but into four intervals more nearly
> equal in size, blurring or erasing the sense of major and minor.
> Those intervals produce a lowered second, a near-neutral third, and
a
> raised fourth--which, when projected by a fifth, results in a
raised
> eighth degree, a wide octave. The effects of this tendency vary by
> region in proportion to the tradition of true three-part polyphony,
> but some form of quintave tuning is common to almost all Georgian
> music.
>
> from here http://argosoft.com/kavkasia/album2/intro.htm
>
> That sounds very interesting.

yes, i was able to evoke the sounds of some of the more unusual
georgian choral pieces i've heard with such a "stretched 7-equal"
tuning. thanks for that.

--- In MakeMicroMusic@y..., "booeyschewy" <booeyschewy@y...> wrote:

> Can anyone make sense of this? Suppposedly it is the ratios for a
> Georgian tuning found here
> http://users.bestweb.net/~notr/kartuli/tuning.txt
>
>
> Svan:
>
> sm2 ln(3**7/125)*12/ln(2) = 49.547439 -> +2242
> M2
> sm3 ln(3**5/25)* 12/ln(2) = 39.371476 -> +1521
> sM3 2*ln(5/9) * 12/ln(2) = -20.351926 -> -1441
> sP4 ln(27/5) * 12/ln(2) = 29.195513 -> + 801
> s+4 3*ln(5/9) * 12/ln(2) = -30.527889 -> -2162
> s-5 ln(9**5/5**4)*12/ln(2)= 78.742952 -> +3043
> P5
> sm6 ln(9**4/125)*12/ln(2) = 68.566989 -> +2322
> M6
> sm7 ln(9**3/25)* 12/ln(2) = 58.391026 -> +1602
> sM7 ln(25/27)* 12/ln(2) = -1.332376 -> -1361
> sP8 ln(81/5) * 12/ln(2) = 48.215063 -> + 881

the (seemingly contrived) ratios being posited here are

2187/2000 (154.74 cents)
243/200 (337.15 cents)
100/81 (364.81 cents)
27/20 (519.55 cents)
1000/729 (547.21 cents)
59049/40000 (674.30 cents)
P5 no deviation from 700 cents given
6561/4000 (856.70 cents)
M6 no deviation from 900 cents given
729/400 (1039.10 cents)
50/27 (1066.76 cents)
81/40 (1221.5 cents)

the last column gives the deviations in MIDI pitch bend units from
the corresponding 12-equal pitch.