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Brahms partsong JI

🔗Tom Dent <stringph@...>

10/28/2008 8:03:21 AM

This is a development of my idea that 171edo could be used as a good
approximation of 7-limit (and 17-containing) intervals, and
simultaneously as an adaptive almost-JI due to its almost exact
1/3-comma steps.

However, on consideration I think for Romantic repertoire one probably
needs the 16-19-24 minor chord, which is not all that well served by
this type of temperament. Hence I have gone over (or back) to JI using
7-, 17- or 19-containing intervals as necessary. Given the range of
fifths and tones available with fairly simple just ratios, temperament
is not strictly necessary.
The test piece was 'Waldesnacht':
http://choralwiki.net/wiki/index.php/Waldesnacht%2C_Op._62%2C_No._3_%28Johannes_Brahms%29

The notation is as follows: The default tuning of the root and fifth
of every common chord is Pythagorean with respect to the keynote D.
For major chords the default tuning of the third is 5/4 from the root.
Other chords and deviations from default will be specified
individually by giving the ratio relative to d=1/1 (up to octave
equivalence). Any other unspecified notes remain Pythagorean.

b.1 last 8th f#=5 c#=15
b.2 -
b.3 last quarter f#=5 b=5/3
b.4 first&last quarter c#=15 g=75/7
b.5 last quarter c=57
b.6 2nd&3rd quarter g=171 c=57, last quarter g=4/3 bb=76/3
b.7 2nd&3rd quarter f=19 last quarter c=57
b.8 f=6/5 b=42/25, 2nd half f#=63/50 d#=21/20
b.9 e=9 b=27 g#=45, 2nd half d=225/7
b.10 2nd half g=75/7
b.11 (g=75/7) f=19 c#=15
b.12 second half g=75/7
b.13 first half g=75/7 second half f#=5 g=4/3 b=375/224
b.14 b=375/224 e=28/25 c#=15 f#=5
b.15 c#=15 f#=5 b=5/3 e=10/9
b.16 e=9/8 c#=15 bb=51 g=75/7
b.17 -
b.18 2nd quarter f#=5 c=25/7 d#=21/5 3rd quarter g=171
b.19 first half b=1/19 f#=3/19 d#=5/19, second half b=5/3
b.20 c#=15 f#=5 g=75/7
b.21 c=25/7 d#=21/5 f#=5 (nb c-d#=147/125~20/17)
b.22 f#=5 d#=21/5 c=25/7 g=75/7 b=225/7 e=125/7
b.23 f#=5 c#=15 e=125/7 bb=19/3, second half b=5/3 g#=7/5
b.24 g=75/7
b.25 -

Of course there are many different possibilities, particularly for the
dim and aug intervals, but this ought to be a fair start.
Now the question is how (if at all) to synthesize it...
~~~T~~~

🔗Andreas Sparschuh <a_sparschuh@...>

10/28/2008 10:43:21 AM

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> This is a development of my idea that 171edo....

as known from:
http://tonalsoft.com/monzo/groven/groven.htm