User:Rperlner: Difference between revisions

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In each case, I prefer the non-12EDO version.

A less well known example concerns music written using the Octatonic scale -- one of the better-known non-diatonic scales used in 12 EDO music. The standard treatment of this scale is as a MOS of the Rank-2 Diminished temperament, which tempers out the 7-limit commas 50/49, and 36/35. In this analysis, 12 EDO is pretty much optimal already. However, I have found that there is little downside to treating the Octatonic scale as a Rank-3 temperament that only tempers out 50/49 in the 7-limit (Jubilismic Temperament.) This allows the 6/5 and 7/6 minor thirds to be tuned differently, improving the fit to just intonation and the expressiveness of the system, Something similar is done with the Diatonic scale in Indian music, where 5-limit JI (effectively a rank 3 temperament) is used instead of Meantone temperament, rendering 9/8 and 10/9 as separate intervals. The downside of using 5-limit JI for diatonic music, in general, though, is that one is often faced with hard decisions regarding whether the D in C major, for example, should be rendered as being 9/8 or 10/9 relative to the tonic.

A less well known example of the benefits of alternate tunings concerns music written using the Octatonic scale -- one of the better-known non-diatonic scales used in 12 EDO music. The standard treatment of this scale is as a MOS of the Rank-2 Diminished temperament, which tempers out the 7-limit commas 50/49, and 36/35. In this analysis, 12 EDO is pretty much optimal already. However, I have found that there is little downside to treating the Octatonic scale as a Rank-3 temperament that only tempers out 50/49 in the 7-limit (Jubilismic Temperament.) This allows the 6/5 and 7/6 minor thirds to be tuned differently, improving the fit to just intonation and the expressiveness of the system, Something similar is done with the Diatonic scale in Indian music, where 5-limit JI (effectively a rank 3 temperament) is used instead of Meantone temperament, rendering 9/8 and 10/9 as separate intervals. The downside of using 5-limit JI for diatonic music, in general, though, is that one is often faced with hard decisions regarding whether the D in C major, for example, should be rendered as being 9/8 or 10/9 relative to the tonic.

There are no such difficult decisions in the Octatonic scale in a rank-3 Jubilismic temperament. If we render the semitone-wholetone Octatonic scale as

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 In each case, I prefer the non-12EDO version.
-A less well known example concerns music written using the Octatonic scale -- one of the better-known non-diatonic scales used in 12 EDO music. The standard treatment of this scale is as a MOS of the Rank-2 Diminished temperament, which tempers out the 7-limit commas 50/49, and 36/35. In this analysis, 12 EDO is pretty much optimal already. However, I have found that there is little downside to treating the Octatonic scale as a Rank-3 temperament that only tempers out 50/49 in the 7-limit (Jubilismic Temperament.) This allows the 6/5 and 7/6 minor thirds to be tuned differently, improving the fit to just intonation and the expressiveness of the system, Something similar is done with the Diatonic scale in Indian music, where 5-limit JI (effectively a rank 3 temperament) is used instead of Meantone temperament, rendering 9/8 and 10/9 as separate intervals. The downside of using 5-limit JI for diatonic music, in general, though, is that one is often faced with hard decisions regarding whether the D in C major, for example, should be rendered as being 9/8 or 10/9 relative to the tonic.
+A less well known example of the benefits of alternate tunings concerns music written using the Octatonic scale -- one of the better-known non-diatonic scales used in 12 EDO music. The standard treatment of this scale is as a MOS of the Rank-2 Diminished temperament, which tempers out the 7-limit commas 50/49, and 36/35. In this analysis, 12 EDO is pretty much optimal already. However, I have found that there is little downside to treating the Octatonic scale as a Rank-3 temperament that only tempers out 50/49 in the 7-limit (Jubilismic Temperament.) This allows the 6/5 and 7/6 minor thirds to be tuned differently, improving the fit to just intonation and the expressiveness of the system, Something similar is done with the Diatonic scale in Indian music, where 5-limit JI (effectively a rank 3 temperament) is used instead of Meantone temperament, rendering 9/8 and 10/9 as separate intervals. The downside of using 5-limit JI for diatonic music, in general, though, is that one is often faced with hard decisions regarding whether the D in C major, for example, should be rendered as being 9/8 or 10/9 relative to the tonic.
 There are no such difficult decisions in the Octatonic scale in a rank-3 Jubilismic temperament. If we render the semitone-wholetone Octatonic scale as