Pinetone: Difference between revisions

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== Porcutone octatonic scales ==

The porcupine comma is the small step of the scale, so tempering the Porcutone chromatic scale to porcupine leads from 7L 1m 4s = (27/25, 25/24, 250/243) to 7L 1s = (10/9~27/25, 25/24~81/80), which is Porcupine[8]! The Porcupine[7] scale has its large step between G and A, so the eighth note of Porcupine[8] is either G♯ or A♭, adding another small step of Porcupine[7] below A (for G♯) or above G (A♭). Mode -3 or mode 3 of the Porcutone chromatic scale, respectively, are set to D so that this is preserved in The Porcutone System. This leads to the Porcutone octatonic scales: D E F G G♯/A♭ A B C. In Just intonation: 10/9 6/5 4/3 25/18 3/2 5/3 9/5 2/1 with G♯, or 10/9 6/5 4/3 36/25 3/2 5/3 9/5 2/1 with A♭. This scale has 4 large steps of 10/9, 3 medium steps of 27/25, and 1 small step of 25/24. It is not mirror-symmetric, or equivalentely, it is ''[[Chirality|chiral]]'' so it cannot be uniquely defined with a step signature like Meantone[7], Porcupine[7], Porcupine[8], Meantone[12], and the Porcutone diatonic (the ~~Zarlio~~/Ptolemy just major scale is also not mirror symmetric). Scales that can be uniquely defined by a step signature are called ''step-nested scales''. More on that later. The mirror inverse of any mode of the Porcutone octatonic with G♯ is a mode of the Porcutone octatonic with A♭. The Porcutone octatonic with G♯ is called the left handed porcupine octatonic, and the Porcutone octatonic with A♭ is called the right handed porcupine octatonic (see [[chirality]]).

The porcupine comma is the small step of the scale, so tempering the Porcutone chromatic scale to porcupine leads from 7L 1m 4s = (27/25, 25/24, 250/243) to 7L 1s = (10/9~27/25, 25/24~81/80), which is Porcupine[8]! The Porcupine[7] scale has its large step between G and A, so the eighth note of Porcupine[8] is either G♯ or A♭, adding another small step of Porcupine[7] below A (for G♯) or above G (A♭). Mode -3 or mode 3 of the Porcutone chromatic scale, respectively, are set to D so that this is preserved in The Porcutone System. This leads to the Porcutone octatonic scales: D E F G G♯/A♭ A B C. In Just intonation: 10/9 6/5 4/3 25/18 3/2 5/3 9/5 2/1 with G♯, or 10/9 6/5 4/3 36/25 3/2 5/3 9/5 2/1 with A♭. This scale has 4 large steps of 10/9, 3 medium steps of 27/25, and 1 small step of 25/24. It is not mirror-symmetric, or equivalentely, it is ''[[Chirality|chiral]]'' so it cannot be uniquely defined with a step signature like Meantone[7], Porcupine[7], Porcupine[8], Meantone[12], and the Porcutone diatonic (the Zarlino/Ptolemy just major scale is also not mirror symmetric). Scales that can be uniquely defined by a step signature are called ''step-nested scales''. More on that later. The mirror inverse of any mode of the Porcutone octatonic with G♯ is a mode of the Porcutone octatonic with A♭. The Porcutone octatonic with G♯ is called the left handed porcupine octatonic, and the Porcutone octatonic with A♭ is called the right handed porcupine octatonic (see [[chirality]]).

On a keyboard with standard (Bosanquet or 12edo) mapping, the Porcutone octatonic is the C Major bebop scale! On my [[Lumatone]] I chose to colour the G♯/A♭ pink, and the rest of the chromatic notes blue, so the Porcutone octatonic is on the white and pink keys, while there's a Porcutone diatonic on the white keys and a Porcutone pentatonic on the blue and pink keys.

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 == Porcutone octatonic scales ==
-The porcupine comma is the small step of the scale, so tempering the Porcutone chromatic scale to porcupine leads from 7L 1m 4s = (27/25, 25/24, 250/243) to 7L 1s = (10/9~27/25, 25/24~81/80), which is Porcupine[8]! The Porcupine[7] scale has its large step between G and A, so the eighth note of Porcupine[8] is either G♯ or A♭, adding another small step of Porcupine[7] below A (for G♯) or above G (A♭). Mode -3 or mode 3 of the Porcutone chromatic scale, respectively, are set to D so that this is preserved in The Porcutone System. This leads to the Porcutone octatonic scales: D E F G G♯/A♭ A B C. In Just intonation: 10/9 6/5 4/3 25/18 3/2 5/3 9/5 2/1 with G♯, or 10/9 6/5 4/3 36/25 3/2 5/3 9/5 2/1 with A♭. This scale has 4 large steps of 10/9, 3 medium steps of 27/25, and 1 small step of 25/24. It is not mirror-symmetric, or equivalentely, it is ''[[Chirality|chiral]]'' so it cannot be uniquely defined with a step signature like Meantone[7], Porcupine[7], Porcupine[8], Meantone[12], and the Porcutone diatonic (the Zarlio/Ptolemy just major scale is also not mirror symmetric). Scales that can be uniquely defined by a step signature are called ''step-nested scales''. More on that later. The mirror inverse of any mode of the Porcutone octatonic with G♯ is a mode of the Porcutone octatonic with A♭. The Porcutone octatonic with G♯ is called the left handed porcupine octatonic, and the Porcutone octatonic with A♭ is called the right handed porcupine octatonic (see [[chirality]]).
+The porcupine comma is the small step of the scale, so tempering the Porcutone chromatic scale to porcupine leads from 7L 1m 4s = (27/25, 25/24, 250/243) to 7L 1s = (10/9~27/25, 25/24~81/80), which is Porcupine[8]! The Porcupine[7] scale has its large step between G and A, so the eighth note of Porcupine[8] is either G♯ or A♭, adding another small step of Porcupine[7] below A (for G♯) or above G (A♭). Mode -3 or mode 3 of the Porcutone chromatic scale, respectively, are set to D so that this is preserved in The Porcutone System. This leads to the Porcutone octatonic scales: D E F G G♯/A♭ A B C. In Just intonation: 10/9 6/5 4/3 25/18 3/2 5/3 9/5 2/1 with G♯, or 10/9 6/5 4/3 36/25 3/2 5/3 9/5 2/1 with A♭. This scale has 4 large steps of 10/9, 3 medium steps of 27/25, and 1 small step of 25/24. It is not mirror-symmetric, or equivalentely, it is ''[[Chirality|chiral]]'' so it cannot be uniquely defined with a step signature like Meantone[7], Porcupine[7], Porcupine[8], Meantone[12], and the Porcutone diatonic (the Zarlino/Ptolemy just major scale is also not mirror symmetric). Scales that can be uniquely defined by a step signature are called ''step-nested scales''. More on that later. The mirror inverse of any mode of the Porcutone octatonic with G♯ is a mode of the Porcutone octatonic with A♭. The Porcutone octatonic with G♯ is called the left handed porcupine octatonic, and the Porcutone octatonic with A♭ is called the right handed porcupine octatonic (see [[chirality]]).
 On a keyboard with standard (Bosanquet or 12edo) mapping, the Porcutone octatonic is the C Major bebop scale! On my [[Lumatone]] I chose to colour the G♯/A♭ pink, and the rest of the chromatic notes blue, so the Porcutone octatonic is on the white and pink keys, while there's a Porcutone diatonic on the white keys and a Porcutone pentatonic on the blue and pink keys.