Pinetone: Difference between revisions

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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, 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 ~~chromtic~~), 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, 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.

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 Tetracot[20].

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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, 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 chromtic), 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, 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.
 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 Tetracot[20].