intonation in a Tuvan song

I have a rough draft up of an analysis of the intonation in a Tuvan "Long
Song" at:

http://www.users.interport.net/~dante/crane.html

It does not feature the kind of harmonic singing that you expect from
Tuvans, but the intonation may be derived from the intervals within the
segment of the harmonic series that they do use in their overtone singing.

dante

Dante [TD209.1]

>I have a rough draft up of an analysis of the intonation in a Tuvan "Long
>Song" at:

>http://www.users.interport.net/~dante/crane.html

>It does not feature the kind of harmonic singing that you expect from
>Tuvans, but the intonation may be derived from the intervals within the
>segment of the harmonic series that they do use in their overtone singing.

I put the various frequencies sung into a program that I have that looks
for goodness of fit to being multiples or fractions of a single value.

The best fit was that all the frequencies are near fractions of 10920 Hz
which gives the following frequencies when divided by n

n 32 33 35 36 40 44 54
Freq 342 331 312 303 273 248 202

The presence of both 33 and 44 argues that the 11 ratio is definitely
real as all the others are normal numbers found in ratios. Apart from
the 342 these all agree very well with the average values in your chart.
Perhaps the singer could not reach 342?

The second best fit is for the frequencies being multiples of 9.177 Hz

n 37 36 34 33 30 27 22
Freq 340 330 312 303 275 248 202

I don't like this as much as the other one.

One of these days I will make the program consider fraction ratios also
such as 4/3, 3/2, 9/8 and so on, but at present it solves these by going
way outside the range to a common multiple or divisor. So the JI scale
would give 24 27 30 32 36 40 45 48 rather than 1 9/8 etc.

-- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
Cycles email list -- http://www.kcbbs.gen.nz/users/af/cyc.htm
Alexandria eGroup list -- http://www.kcbbs.gen.nz/users/af/alex.htm
Boundaries of Science http://www.kcbbs.gen.nz/users/af/scienceb.htm