Pinetone: Difference between revisions
→Pinetone octatonic scales: added pinetone harmonic diminished |
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2.3.5.13 325/324 may be better tuned to 46edo, with (L, m, s) = (4, 2, 1). | 2.3.5.13 325/324 may be better tuned to 46edo, with (L, m, s) = (4, 2, 1). | ||
=== | === Pinetone harmonic diminished === | ||
As a subset of Pinetone-15 we may find modified Pinetone octatonics built on MODMOS of Porcupine[8]. The Porcupine[8]'s 4M (''minimally modified MODMOS'') is useful given that it still comprises consonant 3-step triads on all notes, but with a more spread-out distribution, so that the triads of each type do not all occur adjacent to each other as in Porcupine[7] and Porcupine[8]. This scale may be found either by lowering G or raising B by a Porcupine[8] chroma, which represents 16/15, the large step of Pinetone-15. | As a subset of Pinetone-15 we may find modified Pinetone octatonics built on MODMOS of Porcupine[8]. The Porcupine[8]'s 4M (''minimally modified MODMOS'') is useful given that it still comprises consonant 3-step triads on all notes, but with a more spread-out distribution, so that the triads of each type do not all occur adjacent to each other as in Porcupine[7] and Porcupine[8]. This scale may be found either by lowering G or raising B by a Porcupine[8] chroma, which represents 16/15, the large step of Pinetone-15. | ||
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22122222 -> 13122222, 22131222, 22221312 i.e., s(Lsm)s(Ls)(ms)(Ls)(ms)(Ls) or (sL)(sm)(sL)(sm)(sL)s(msL)s, (sL)(sm)s(Lsm)s(Ls)(ms)(Ls) or (sL)(sm)(sL)s(msL)s(ms)(Ls), (sL)(sm)(sL)(sm)s(Lsm)s(Ls) or (sL)s(msL)s(ms)(Ls)(ms)(Ls), 6 modes of 2 scales. | 22122222 -> 13122222, 22131222, 22221312 i.e., s(Lsm)s(Ls)(ms)(Ls)(ms)(Ls) or (sL)(sm)(sL)(sm)(sL)s(msL)s, (sL)(sm)s(Lsm)s(Ls)(ms)(Ls) or (sL)(sm)(sL)s(msL)s(ms)(Ls), (sL)(sm)(sL)(sm)s(Lsm)s(Ls) or (sL)s(msL)s(ms)(Ls)(ms)(Ls), 6 modes of 2 scales. | ||
The first pair of modes temper to Diminished[8]. The scale has 1 augmented step of 52/45, 3 large steps of 10/9~11/10, 2 medium steps of 12/11~13/12, 2 small steps of 25/24~33/32~27/26. | The first pair of modes temper to Diminished[8] (m = 0), and to Father[8] (L=0). The scale has 1 augmented step of 52/45, 3 large steps of 10/9~11/10, 2 medium steps of 12/11~13/12, 2 small steps of 25/24~33/32~27/26. | ||
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|+Modes of the just Pinetone harmonic diminished | |+Modes of the just Pinetone harmonic diminished | ||