Pinetone: Difference between revisions

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Additionally available in porcutone are a set of octatonic modes with their own Porcupine functional harmony, that combine [[Porcupine]][8] with the [[oneirotonic]] modes that are gaining popularity at the moment.

If you have a [[Lumatone]], you can use the standard Bosanquet mapping for 12edo. The white keys are the porcutone diatonic, a cross between the meantone diatonic scale and Porcupine[7], and then black keys give the porcutone pentatonic, which approximates the just intonation pentatonic scale 9/8 5/4 3/2 5/3 2/1. I've chosen to colour the G♯/Ab key pink, and the other chromatic keys blue, because I'm a proud trans woman and a big nerd. You can use any colours, but I find it helps to colour the G♯/A♭ key a different colour since that's the one chromatic key used along with the diatonic keys to make the porcutone octatonic.

If you have a [[Lumatone]], you can use the standard Bosanquet mapping for 12edo. The white keys are the porcutone diatonic, a cross between the meantone diatonic scale and Porcupine[7], and then black keys give the porcutone pentatonic, which approximates the just intonation pentatonic scale 9/8 5/4 3/2 5/3 2/1. I've chosen to colour the G♯/A♭ key pink, and the other chromatic keys blue, because I'm a proud trans woman and a big nerd. You can use any colours, but I find it helps to colour the G♯/A♭ key a different colour since that's the one chromatic key used along with the diatonic keys to make the porcutone octatonic.

== The porcutone diatonic ==

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Using the familiar Bosanquet 12-note keyboard mapping (the preset for 12edo), we set the porcutone diatonic scale to the white keys, starting on D. We than add, on F♯/G♭, the porcutone penatonic as a set of 5 chromatic keys. There are two options for the chromatic keys, either all sharps or all flats. All sharps makes the porcutone harmonic minor available, and all flats makes the porcutone harmonic major available. These scales will be discussed below. In either case, in the just tuning, the chromatic keys give the scale 9/8 5/4 3/2 5/3 2/1, starting from F♯/G♭, tuned to 100/81 (F♯) or 162/125 (G♭) from D. This scale has step pattern msLsL, with step signature and step mapping 2L 1m 2s = (6/5, 9/8, 10/9). The same scale is also available as G-A-B-D-E.

We are familiar with this scale as the just pentatonic. If we temper m and s together, we get Meantone[5]: ssLsL. If we temper m and L together instead we get a scale called Father[5], tempering out the diatonic semitone 16/15. This mode of Father[5] has step pattern LsLsL. Keep the connection to Father[5] in the back of your minds for now, we'll come back to it. The porcutone pentatonic is also a subset of the porcutone diatonic, since Meantone[5] is a subset of Meantone[7]. It is available as G-A-B-D-E. The scale F-G-A-C-D is a mode of the inverse of G-A-B-D-E. The porcutone pentatonic is [[Chirality|''chiral'']] (i.e., it is not symmetric, unlike the porcutone diatonic and procutone chromatic scales, which are ''achiral''). There is a pair of porcutone pentatonic scales, the right handed porcutone pentatonic, 9/8 5/4 3/2 5/3 2/1 in JI, it's mirror inverse the left handed porcutone pentatonic, 10/9 5/4 3/2 5/3 2/1 in JI, which tempers to ssLsL in Meantone, but to sLLsL in Father. F-G-A-C-D gives a left handed porcutone pentatonic, while G-A-B-D-E, F#-G#-A#-C#-D#, and Gb-Ab-Bb-Db-Eb are right handed porcutone pentatonics.

We are familiar with this scale as the just pentatonic. If we temper m and s together, we get Meantone[5]: ssLsL. If we temper m and L together instead we get a scale called Father[5], tempering out the diatonic semitone 16/15. This mode of Father[5] has step pattern LsLsL. Keep the connection to Father[5] in the back of your minds for now, we'll come back to it. The porcutone pentatonic is also a subset of the porcutone diatonic, since Meantone[5] is a subset of Meantone[7]. It is available as G-A-B-D-E. The scale F-G-A-C-D is a mode of the inverse of G-A-B-D-E. The porcutone pentatonic is [[Chirality|''chiral'']] (i.e., it is not symmetric, unlike the porcutone diatonic and procutone chromatic scales, which are ''achiral''). There is a pair of porcutone pentatonic scales, the right handed porcutone pentatonic, 9/8 5/4 3/2 5/3 2/1 in JI, it's mirror inverse the left handed porcutone pentatonic, 10/9 5/4 3/2 5/3 2/1 in JI, which tempers to ssLsL in Meantone, but to sLLsL in Father. F-G-A-C-D gives a left handed porcutone pentatonic, while G-A-B-D-E, F♯-G♯-A♯-C♯-D♯, and G♭-A♭-B♭-D♭-E♭ are right handed porcutone pentatonics.

Adding the right handed porcutone chromatic (on F♯/G♭) to the just porcutone chromatic, a 12-note mirror-symmetric scale with step signature and step mapping of 7L 1m 4s = (27/25, 25/24, 250/243) = (133.2376c, 70.6724c, 49.1661c), i.e., 7 large steps of what was the small step of the just porcutone diatonic, 1 medium step of the chromatic semitone 25/24, the distance between 6/5 and 5/4, and 4 small steps of 250/243, the porcupine comma, that separates 10/9 from 27/25. For the all sharps scale, we set mode -3 on D (for all flats we set mode 3 on D): 250/243 10/9 6/5 100/81 4/3 25/18 3/2 125/81 5/3 9/5 50/27 2/1, with step pattern sLLsLmLsLLsL.

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== Porcutone harmonic minor and harmonic major ==

Additionally, we have another set of [[Porcupine]][7] modes contained in the Porcutone octatonic: Replacing the G with the G# changes the mode of the Porcupine[7] scale represented, and replaces diatonic with harmonic minor modes for the [[Meantone]][7] scale represented, now a MODMOS.

Additionally, we have another set of [[Porcupine]][7] modes contained in the Porcutone octatonic: Replacing the G with the G♯ changes the mode of the Porcupine[7] scale represented, and replaces diatonic with harmonic minor modes for the [[Meantone]][7] scale represented, now a MODMOS.

We note that there are fewer consonant triads available in these scales than in the porcutone diatonic and octatonic scales, so they may be useful for melody only.

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On D we get the scale:

174.055 320.69 557.888 704.524 878.579 1025.214 1199.269 on the notes D E F G# A B C D

174.055 320.69 557.888 704.524 878.579 1025.214 1199.269 on the notes D E F G♯ A B C D

We get the following 7 modes of porcutone harmonic minor scale:

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* smsmmsL altered diminished magical seventh

Using an Ab instead, we get the scale:

Using an A♭ instead, we get the scale:

174.055 320.69 494.745 641.38 878.579 1025.214 1199.269

@@ Line 9: / Line 9: @@
 Additionally available in porcutone are a set of octatonic modes with their own Porcupine functional harmony, that combine [[Porcupine]][8] with the [[oneirotonic]] modes that are gaining popularity at the moment.
-If you have a [[Lumatone]], you can use the standard Bosanquet mapping for 12edo. The white keys are the porcutone diatonic, a cross between the meantone diatonic scale and Porcupine[7], and then black keys give the porcutone pentatonic, which approximates the just intonation pentatonic scale 9/8 5/4 3/2 5/3 2/1. I've chosen to colour the G♯/Ab key pink, and the other chromatic keys blue, because I'm a proud trans woman and a big nerd. You can use any colours, but I find it helps to colour the G♯/A♭ key a different colour since that's the one chromatic key used along with the diatonic keys to make the porcutone octatonic.
+If you have a [[Lumatone]], you can use the standard Bosanquet mapping for 12edo. The white keys are the porcutone diatonic, a cross between the meantone diatonic scale and Porcupine[7], and then black keys give the porcutone pentatonic, which approximates the just intonation pentatonic scale 9/8 5/4 3/2 5/3 2/1. I've chosen to colour the G♯/A♭ key pink, and the other chromatic keys blue, because I'm a proud trans woman and a big nerd. You can use any colours, but I find it helps to colour the G♯/A♭ key a different colour since that's the one chromatic key used along with the diatonic keys to make the porcutone octatonic.
 == The porcutone diatonic ==
@@ Line 539: / Line 539: @@
 Using the familiar Bosanquet 12-note keyboard mapping (the preset for 12edo), we set the porcutone diatonic scale to the white keys, starting on D. We than add, on F♯/G♭, the porcutone penatonic as a set of 5 chromatic keys. There are two options for the chromatic keys, either all sharps or all flats. All sharps makes the porcutone harmonic minor available, and all flats makes the porcutone harmonic major available. These scales will be discussed below. In either case, in the just tuning, the chromatic keys give the scale 9/8 5/4 3/2 5/3 2/1, starting from F♯/G♭, tuned to 100/81 (F♯) or 162/125 (G♭) from D. This scale has step pattern msLsL, with step signature and step mapping 2L 1m 2s = (6/5, 9/8, 10/9). The same scale is also available as G-A-B-D-E.
-We are familiar with this scale as the just pentatonic. If we temper m and s together, we get Meantone[5]: ssLsL. If we temper m and L together instead we get a scale called Father[5], tempering out the diatonic semitone 16/15. This mode of Father[5] has step pattern LsLsL. Keep the connection to Father[5] in the back of your minds for now, we'll come back to it. The porcutone pentatonic is also a subset of the porcutone diatonic, since Meantone[5] is a subset of Meantone[7]. It is available as G-A-B-D-E. The scale F-G-A-C-D is a mode of the inverse of G-A-B-D-E. The porcutone pentatonic is [[Chirality|''chiral'']] (i.e., it is not symmetric, unlike the porcutone diatonic and procutone chromatic scales, which are ''achiral''). There is a pair of porcutone pentatonic scales, the right handed porcutone pentatonic, 9/8 5/4 3/2 5/3 2/1 in JI, it's mirror inverse the left handed porcutone pentatonic, 10/9 5/4 3/2 5/3 2/1 in JI, which tempers to ssLsL in Meantone, but to sLLsL in Father. F-G-A-C-D gives a left handed porcutone pentatonic, while G-A-B-D-E, F#-G#-A#-C#-D#, and Gb-Ab-Bb-Db-Eb are right handed porcutone pentatonics.
+We are familiar with this scale as the just pentatonic. If we temper m and s together, we get Meantone[5]: ssLsL. If we temper m and L together instead we get a scale called Father[5], tempering out the diatonic semitone 16/15. This mode of Father[5] has step pattern LsLsL. Keep the connection to Father[5] in the back of your minds for now, we'll come back to it. The porcutone pentatonic is also a subset of the porcutone diatonic, since Meantone[5] is a subset of Meantone[7]. It is available as G-A-B-D-E. The scale F-G-A-C-D is a mode of the inverse of G-A-B-D-E. The porcutone pentatonic is [[Chirality|''chiral'']] (i.e., it is not symmetric, unlike the porcutone diatonic and procutone chromatic scales, which are ''achiral''). There is a pair of porcutone pentatonic scales, the right handed porcutone pentatonic, 9/8 5/4 3/2 5/3 2/1 in JI, it's mirror inverse the left handed porcutone pentatonic, 10/9 5/4 3/2 5/3 2/1 in JI, which tempers to ssLsL in Meantone, but to sLLsL in Father. F-G-A-C-D gives a left handed porcutone pentatonic, while G-A-B-D-E, F♯-G♯-A♯-C♯-D♯, and G♭-A♭-B♭-D♭-E♭ are right handed porcutone pentatonics.
 Adding the right handed porcutone chromatic (on F♯/G♭) to the just porcutone chromatic, a 12-note mirror-symmetric scale with step signature and step mapping of 7L 1m 4s = (27/25, 25/24, 250/243) = (133.2376c, 70.6724c, 49.1661c), i.e., 7 large steps of what was the small step of the just porcutone diatonic, 1 medium step of the chromatic semitone 25/24, the distance between 6/5 and 5/4, and 4 small steps of 250/243, the porcupine comma, that separates 10/9 from 27/25. For the all sharps scale, we set mode -3 on D (for all flats we set mode 3 on D): 250/243 10/9 6/5 100/81 4/3 25/18 3/2 125/81 5/3 9/5 50/27 2/1, with step pattern sLLsLmLsLLsL.
@@ Line 1,568: / Line 1,568: @@
 == Porcutone harmonic minor and harmonic major ==
-Additionally, we have another set of [[Porcupine]][7] modes contained in the Porcutone octatonic: Replacing the G with the G# changes the mode of the Porcupine[7] scale represented, and replaces diatonic with harmonic minor modes for the [[Meantone]][7] scale represented, now a MODMOS.
+Additionally, we have another set of [[Porcupine]][7] modes contained in the Porcutone octatonic: Replacing the G with the G♯ changes the mode of the Porcupine[7] scale represented, and replaces diatonic with harmonic minor modes for the [[Meantone]][7] scale represented, now a MODMOS.
 We note that there are fewer consonant triads available in these scales than in the porcutone diatonic and octatonic scales, so they may be useful for melody only.
@@ Line 1,574: / Line 1,574: @@
 On D we get the scale:
-.055 320.69 557.888 704.524 878.579 1025.214 1199.269 on the notes D E F G# A B C D
+.055 320.69 557.888 704.524 878.579 1025.214 1199.269 on the notes D E F G♯ A B C D
 We get the following 7 modes of porcutone harmonic minor scale:
@@ Line 1,586: / Line 1,586: @@
 * smsmmsL altered diminished magical seventh
-Using an Ab instead, we get the scale:
+Using an A♭ instead, we get the scale:
 .055 320.69 494.745 641.38 878.579 1025.214 1199.269