Topic: Mathieu and shrutis
2 scales
| File | Description | Notes | Period (ยข) |
|---|---|---|---|
| indiang | Shruti/Mathieu's Magic Mode scale in 94-et (garibaldi) temperament | 22 | 1200.0 |
| indians | Shruti/Mathieu's Magic Mode scale in 289-equal (schismic) temperament | 22 | 1200.0 |
Thread (3 messages)
From: Gene Ward Smith (2004-07-11) Subject: 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
From: Kraig Grady (2004-07-11) Subject: Re: [tuning] Mathieu and shrutis 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
From: Haresh BAKSHI (2004-07-14) Subject: Re: Mathieu and shrutis --- In [email protected], "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.