Pinetone: Difference between revisions

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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.

If we temper out the difference between the large and medium steps, we reduce the scale to Porcupine[8]. As we discussed above, Porcupine is generated by the interval 10/9~27/25. The table below introduces a set of functional mode names for Porcupine[8]. Along with the step pattern and mode number, the modes~~' '~~'[[UDP]]~~'' is~~ show in the table. ~~The~~ UDP ~~show~~ the number of generators in the direction the brighten the intervals of scale, followed the number of generators in the direction that darkens it, (followed by the number of periods per octave, if it is not one. In this case the scale repeats at the octave, so P = 1, and is not shown). Instead of building chords by stacking thirds (2-step intervals), in octatonic scales we can build major and minor triads by stacking 3-step intervals! Instead of diminished, we get modes with two large fourths making a quartal chord: Accordingly we call these modes 'quartal'. When we stack 3-step intervals of 8-note scales out minor triads come in first inversion, and our major triads come in second inversion, as the 3-step intervals of octatonic scales include 5/4 and 4/3. Hence the brightest modes are quartal, and the darkest are minor. The eighth note of Porcupine[8] is typically called 'H', and is equivalent to the note A♭ of Porcupine[7], but we will show the modes for G# as the eighth note as well, since we may use G# in our Porcutone chromatic and octatonic scales.

If we temper out the difference between the large and medium steps, we reduce the scale to Porcupine[8]. As we discussed above, Porcupine is generated by the interval 10/9~27/25. The table below introduces a set of functional mode names for Porcupine[8]. Along with the step pattern and mode number, the modes' [[UDP]] are show in the table. A mode's UDP shows the number of generators in the direction the brighten the intervals of scale, followed the number of generators in the direction that darkens it, (followed by the number of periods per octave, if it is not one. In this case the scale repeats at the octave, so P = 1, and is not shown). Instead of building chords by stacking thirds (2-step intervals), in octatonic scales we can build major and minor triads by stacking 3-step intervals! Instead of diminished, we get modes with two large fourths making a quartal chord: Accordingly we call these modes 'quartal'. When we stack 3-step intervals of 8-note scales out minor triads come in first inversion, and our major triads come in second inversion, as the 3-step intervals of octatonic scales include 5/4 and 4/3. Hence the brightest modes are quartal, and the darkest are minor. The eighth note of Porcupine[8] is typically called 'H', and is equivalent to the note A♭ of Porcupine[7], but we will show the modes for G# as the eighth note as well, since we may use G# in our Porcutone chromatic and octatonic scales.

The step signature and mapping of 5-limit Porcupine[8] is 7L 1s = (10/9~27/25, 25/24~81/80)

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 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.
-If we temper out the difference between the large and medium steps, we reduce the scale to Porcupine[8]. As we discussed above, Porcupine is generated by the interval 10/9~27/25. The table below introduces a set of functional mode names for Porcupine[8]. Along with the step pattern and mode number, the modes' ''[[UDP]]'' is show in the table. The UDP show the number of generators in the direction the brighten the intervals of scale, followed the number of generators in the direction that darkens it, (followed by the number of periods per octave, if it is not one. In this case the scale repeats at the octave, so P = 1, and is not shown). Instead of building chords by stacking thirds (2-step intervals), in octatonic scales we can build major and minor triads by stacking 3-step intervals! Instead of diminished, we get modes with two large fourths making a quartal chord: Accordingly we call these modes 'quartal'. When we stack 3-step intervals of 8-note scales out minor triads come in first inversion, and our major triads come in second inversion, as the 3-step intervals of octatonic scales include 5/4 and 4/3. Hence the brightest modes are quartal, and the darkest are minor. The eighth note of Porcupine[8] is typically called 'H', and is equivalent to the note A♭ of Porcupine[7], but we will show the modes for G# as the eighth note as well, since we may use G# in our Porcutone chromatic and octatonic scales.
+If we temper out the difference between the large and medium steps, we reduce the scale to Porcupine[8]. As we discussed above, Porcupine is generated by the interval 10/9~27/25. The table below introduces a set of functional mode names for Porcupine[8]. Along with the step pattern and mode number, the modes' [[UDP]] are show in the table. A mode's UDP shows the number of generators in the direction the brighten the intervals of scale, followed the number of generators in the direction that darkens it, (followed by the number of periods per octave, if it is not one. In this case the scale repeats at the octave, so P = 1, and is not shown). Instead of building chords by stacking thirds (2-step intervals), in octatonic scales we can build major and minor triads by stacking 3-step intervals! Instead of diminished, we get modes with two large fourths making a quartal chord: Accordingly we call these modes 'quartal'. When we stack 3-step intervals of 8-note scales out minor triads come in first inversion, and our major triads come in second inversion, as the 3-step intervals of octatonic scales include 5/4 and 4/3. Hence the brightest modes are quartal, and the darkest are minor. The eighth note of Porcupine[8] is typically called 'H', and is equivalent to the note A♭ of Porcupine[7], but we will show the modes for G# as the eighth note as well, since we may use G# in our Porcutone chromatic and octatonic scales.
 The step signature and mapping of 5-limit Porcupine[8] is 7L 1s = (10/9~27/25, 25/24~81/80)