Mathieu and shrutis

On page 220 of Harmonic Experience, Mathieu defines a mode in 12-equal
with 22 notes, in a way which really makes more sense if we convert it
into 5-limit JI, when it really does have 22 notes. If we do that, we
get a scale of 22 notes which Scala tells me is "indian.scl", the
Indian shruti scale.

If we look at tempering this, it makes a lot of sense to temper via
schismic, which adds a lot more 5-limit harmony to the mix. The scale
is 22-epimorphic, but the schisma is not a 22-et comma. However the
scale is decent enough, with three sizes of steps and a reasonable
degree of evenness, so I don't think we need to concern ourselves too
much over that. It just boils down to -10 to 11 on the chain of fifths.

We can add a little 9-limit harmony via the commas 225/224 and
5120/5103 of "garibaldi", or "simple septimal schismic" as I guess it
would be called in Keenan's system.

Below I give it tempered to 289-equal (5-limit poptimal) and 94-equal
(7 and 9 limit poptimal) for anyone wanting it; this may make more
sense for Indian (and most other kinds) of music than for what Mathieu
has in mind, though all three commas, 32805/32768, 225/224, 5120/5103,
are commas of 12-et.

! indians.scl
Shruti/Mathieu's Magic Mode scale in 289-equal (schismic) temperament
22
!
91.349481
112.110727
182.698962
203.460208
294.809689
315.570934
386.159170
406.920415
498.269896
519.031142
589.619377
610.380623
701.730104
793.079585
813.840830
884.429066
905.190311
996.539792
1017.301038
1087.889273
1108.650519
1200.000000

! indiang.scl
Shruti/Mathieu's Magic Mode scale in 94-et (garibaldi) temperament
22
!
89.361702
114.893617
178.723404
204.255319
293.617021
319.148936
382.978723
408.510638
497.872340
523.404255
587.234043
612.765957
702.127660
791.489362
817.021277
880.851064
906.382979
995.744681
1021.276596
1085.106383
1110.638298
1200.000000

Boomliter and Creel research also lead to this scale. When if you think
that the western scale come indirectly from this part of the world, should
be no surprise.

Gene Ward Smith wrote:

> On page 220 of Harmonic Experience, Mathieu defines a mode in 12-equal
> with 22 notes, in a way which really makes more sense if we convert it
> into 5-limit JI, when it really does have 22 notes. If we do that, we
> get a scale of 22 notes which Scala tells me is "indian.scl", the
> Indian shruti scale.
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>>>> On page 220 of Harmonic Experience, Mathieu defines a mode in 12-equal with 22 notes, in a way which really makes more sense if we convert it into 5-limit JI, when it really does have 22 notes. If we do that, we get a scale of 22 notes which Scala tells me is "indian.scl", the Indian shruti scale. >>>>

Very interesting post. As a beginner (I do not think I need to mention that I am a beginner -- everyone knows this by now), I have a question:

How do we convert into 5-limit JI?

Regards and thank you for your time,
Haresh.