Pinetone: Difference between revisions

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Using the familiar Bosanquet 12-note keyboard mapping (the preset for 12edo), we set the Pinetone diatonic scale to the white keys, starting on D. We than add, on F♯/G♭, the Pinetone 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 Pinetone harmonic minor available, and all flats makes the Pinetone 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 Pinetone pentatonic is also a subset of the Pinetone 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 Pinetone pentatonic is [[Chirality|''chiral'']] (i.e., it is not symmetric, unlike the Pinetone diatonic and procutone chromatic scales, which are ''achiral''). There is a pair of Pinetone pentatonic scales, the right handed Pinetone pentatonic, 9/8 5/4 3/2 5/3 2/1 in JI, it's mirror inverse the left handed Pinetone 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~~ Pinetone pentatonic, while G-A-B-D-E, F♯-G♯-A♯-C♯-D♯, and G♭-A♭-B♭-D♭-E♭ are ~~right handed~~ Pinetone 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 Pinetone pentatonic is also a subset of the Pinetone 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 Pinetone pentatonic is [[Chirality|''chiral'']] (i.e., it is not symmetric, unlike the Pinetone diatonic and procutone chromatic scales, which are ''achiral''). There is a pair of Pinetone pentatonic scales, the right-handed Pinetone pentatonic, 9/8 5/4 3/2 5/3 2/1 in JI, it's mirror inverse the left-handed Pinetone pentatonic, 10/9 5/4 3/2 5/3 2/1 in JI, which tempers to ssLsL in Meantone, but to sLLsL in Father. Since 9/8 5/4 3/2 5/3 2/1 is familiar to us as the 5-limit major pentatonic, we could also call the right-handed Pinetone pentatonic the Pinetone major pentatonic; similarly, 6/5 4/3 3/2 9/5 2/1, a mode of the left-handed Pinetone pentatonic is familiar to us as the 5-limit minor pentatonic, we could also call the left-handed Pinetone pentatonic the Pinetone minor pentatonic. D-F-G-A-C gives the Pinetone minor pentatonic, while G-A-B-D-E, F♯-G♯-A♯-C♯-D♯, and G♭-A♭-B♭-D♭-E♭ are Pinetone major pentatonics.

=== Pinetone chromatic ===

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 Using the familiar Bosanquet 12-note keyboard mapping (the preset for 12edo), we set the Pinetone diatonic scale to the white keys, starting on D. We than add, on F♯/G♭, the Pinetone 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 Pinetone harmonic minor available, and all flats makes the Pinetone 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 Pinetone pentatonic is also a subset of the Pinetone 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 Pinetone pentatonic is [[Chirality|''chiral'']] (i.e., it is not symmetric, unlike the Pinetone diatonic and procutone chromatic scales, which are ''achiral''). There is a pair of Pinetone pentatonic scales, the right handed Pinetone pentatonic, 9/8 5/4 3/2 5/3 2/1 in JI, it's mirror inverse the left handed Pinetone 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 Pinetone pentatonic, while G-A-B-D-E, F♯-G♯-A♯-C♯-D♯, and G♭-A♭-B♭-D♭-E♭ are right handed Pinetone 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 Pinetone pentatonic is also a subset of the Pinetone 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 Pinetone pentatonic is [[Chirality|''chiral'']] (i.e., it is not symmetric, unlike the Pinetone diatonic and procutone chromatic scales, which are ''achiral''). There is a pair of Pinetone pentatonic scales, the right-handed Pinetone pentatonic, 9/8 5/4 3/2 5/3 2/1 in JI, it's mirror inverse the left-handed Pinetone pentatonic, 10/9 5/4 3/2 5/3 2/1 in JI, which tempers to ssLsL in Meantone, but to sLLsL in Father. Since 9/8 5/4 3/2 5/3 2/1 is familiar to us as the 5-limit major pentatonic, we could also call the right-handed Pinetone pentatonic the Pinetone major pentatonic; similarly, 6/5 4/3 3/2 9/5 2/1, a mode of the left-handed Pinetone pentatonic is familiar to us as the 5-limit minor pentatonic, we could also call the left-handed Pinetone pentatonic the Pinetone minor pentatonic. D-F-G-A-C gives the Pinetone minor pentatonic, while G-A-B-D-E, F♯-G♯-A♯-C♯-D♯, and G♭-A♭-B♭-D♭-E♭ are Pinetone major pentatonics.
 === Pinetone chromatic ===