Pinetone: Difference between revisions

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[http://x31eq.com/cgi-bin/rt.cgi?ets=7%261ce%264p&limit=2.3.5.11 7L 1m 4s = (27/25~12/11, 25/24~33/32, 250/243~55/54~121/120) = (146.63528c, 63.14327c, 27.41960c)].

Or we might tune to TE 2.3.5.11.13 Tetracot for

7L 1m 4s = (27/25~12/11~13/12, 25/24~33/32~27/26, 81/80~250/243~55/54~121/120~40/39) = (142.6653, 66.6782, 33.3391), which we note is very similar to 2.3.5.11.13 ptolemismic.

== Porcutone octatonic scales ==

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Or, from the porcutone chromatic with flats (mode 3), we add another porcutone diatonic scale, mode 0 starting on D♯, leading to the right-handed porcutone hyperchromatic scale, with step pattern, sLssLsLssLmsLssLsLs.

If 81/80 were additionally tempered out (tempering out the difference between the small step and the medium step), these scales would temper to Flattone[19], reflected in their layout on the lumatone. These scale comprises 7 large steps approximating 117/110 (the difference between the large and small steps of the porcutone chromatic), the medium step of the porcutone chromatic, approximating 25/24 ~~and~~ 33/32, and 11 small steps, the same as the small step of the pocutone chromatic, approximating 250/243, 55/54, 121/120, and 40/39.

If 81/80 were additionally tempered out (tempering out the difference between the small step and the medium step), these scales would temper to Flattone[19], reflected in their layout on the lumatone. These scale comprises 7 large steps approximating 117/110 (the difference between the large and small steps of the porcutone chromatic), the medium step of the porcutone chromatic, approximating 25/24, 33/32, and 27/26, and 11 small steps, the same as the small step of the pocutone chromatic, approximating 250/243, 55/54, 121/120, and 40/39.

We note that sLss, the interval from D to E♯, for example, is very near 9/8, and that sLsL, the interval from D to F♭, for an example, is very near 32/27. If we recognize these approximates, we additionally temper out 243/242, or 352/351, leading to Tetracot temperament, in which case the large step approximates 16/15. This also adds 81/80 to the list of intervals approximated by the small step. Adding an additional small step above G, for the left handed hyperchromatic, or below A, for the right handed hyperchromatic, would give us a MODMOS of Tetracot[20], splitting the one medium step into two small steps.

We note that sLss, the interval from D to E♯, for example, is very near 9/8, and that sLsL, the interval from D to F♭, for an example, is very near 32/27. If we recognize these approximates, we additionally temper out 243/242, or 352/351, leading to Tetracot temperament, in which case the large step approximates 16/15. This also adds 81/80 to the list of intervals approximated by the small step. Adding an additional small step above G, for the left handed hyperchromatic, or below A, for the right handed hyperchromatic, would give us a MODMOS of Tetracot[20], splitting the one medium step into two small steps (we note also that TE 2.3.5.11.13 ptolemismic tunes the medium step to 66.76626, which is almost exactly twice the size of its small step of 33.11646c).

In 2.3.5.11.13 Tetracot, the left handed porcutone hyperchromatic approximates the JI ratios 40/39 12/11 10/9 32/27 6/5 11/9 13/10 4/3 11/8 22/15 3/2 20/13 18/11 5/3 16/9 9/5 11/6 39/20 2/1, and the right handed porcutone hyperchromatic approximates the JI ratios 40/39 12/11 10/9 9/8 6/5 11/9 13/10 4/3 15/11 16/11 3/2 20/13 18/11 5/3 27/16 9/5 11/6 39/20 2/1.

@@ Line 826: / Line 826: @@
 [http://x31eq.com/cgi-bin/rt.cgi?ets=7%261ce%264p&limit=2.3.5.11 7L 1m 4s = (27/25~12/11, 25/24~33/32, 250/243~55/54~121/120) = (146.63528c, 63.14327c, 27.41960c)].
+Or we might tune to TE 2.3.5.11.13 Tetracot for
+L 1m 4s = (27/25~12/11~13/12, 25/24~33/32~27/26, 81/80~250/243~55/54~121/120~40/39) = (142.6653, 66.6782, 33.3391), which we note is very similar to 2.3.5.11.13 ptolemismic.
 == Porcutone octatonic scales ==
@@ Line 1,725: / Line 1,729: @@
 Or, from the porcutone chromatic with flats (mode 3), we add another porcutone diatonic scale, mode 0 starting on D♯, leading to the right-handed porcutone hyperchromatic scale, with step pattern, sLssLsLssLmsLssLsLs.
-If 81/80 were additionally tempered out (tempering out the difference between the small step and the medium step), these scales would temper to Flattone[19], reflected in their layout on the lumatone. These scale comprises 7 large steps approximating 117/110 (the difference between the large and small steps of the porcutone chromatic), the medium step of the porcutone chromatic, approximating 25/24 and 33/32, and 11 small steps, the same as the small step of the pocutone chromatic, approximating 250/243, 55/54, 121/120, and 40/39.
+If 81/80 were additionally tempered out (tempering out the difference between the small step and the medium step), these scales would temper to Flattone[19], reflected in their layout on the lumatone. These scale comprises 7 large steps approximating 117/110 (the difference between the large and small steps of the porcutone chromatic), the medium step of the porcutone chromatic, approximating 25/24, 33/32, and 27/26, and 11 small steps, the same as the small step of the pocutone chromatic, approximating 250/243, 55/54, 121/120, and 40/39.
-We note that sLss, the interval from D to E♯, for example, is very near 9/8, and that sLsL, the interval from D to F♭, for an example, is very near 32/27. If we recognize these approximates, we additionally temper out 243/242, or 352/351, leading to Tetracot temperament, in which case the large step approximates 16/15. This also adds 81/80 to the list of intervals approximated by the small step. Adding an additional small step above G, for the left handed hyperchromatic, or below A, for the right handed hyperchromatic, would give us a MODMOS of Tetracot[20], splitting the one medium step into two small steps.
+We note that sLss, the interval from D to E♯, for example, is very near 9/8, and that sLsL, the interval from D to F♭, for an example, is very near 32/27. If we recognize these approximates, we additionally temper out 243/242, or 352/351, leading to Tetracot temperament, in which case the large step approximates 16/15. This also adds 81/80 to the list of intervals approximated by the small step. Adding an additional small step above G, for the left handed hyperchromatic, or below A, for the right handed hyperchromatic, would give us a MODMOS of Tetracot[20], splitting the one medium step into two small steps (we note also that TE 2.3.5.11.13 ptolemismic tunes the medium step to 66.76626, which is almost exactly twice the size of its small step of 33.11646c).
 In 2.3.5.11.13 Tetracot, the left handed porcutone hyperchromatic approximates the JI ratios 40/39 12/11 10/9 32/27 6/5 11/9 13/10 4/3 11/8 22/15 3/2 20/13 18/11 5/3 16/9 9/5 11/6 39/20 2/1, and the right handed porcutone hyperchromatic approximates the JI ratios 40/39 12/11 10/9 9/8 6/5 11/9 13/10 4/3 15/11 16/11 3/2 20/13 18/11 5/3 27/16 9/5 11/6 39/20 2/1.