Pinetone: Difference between revisions

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The following 13 notes are used in total for these scales: E♭, G♭, A♭ D, E, F, G, A, B, C, G♯, A♯, C♯

==Pinetone harmonic minor and harmonic major==

Additionally, we have another set of [[Porcupine]][7] modes contained in the Pinetone harmonic octatonics: 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 Pinetone diatonic and octatonic scales, so they may be useful for melody only.

On D we get the scale:

174.055 320.69 557.888 704.524 878.579 1025.214 1199.269 as the notes D E F G♯ A B C D, representing 10/9 6/5 25/18~11/8 3/2 5/3 9/5 2/1

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

*Lsmsmms Lydian ♯2 bright major starting on F

*mmsLsms Ionian ♯5 symmetric minor starting on C

*msLsmsm Ukranian dorian bright minor starting on D

*sLsmsmm Phyrgian dominant dark major starting on E

*msmmsLs harmonic minor dark diminished starting on A

*smmsLsm Locrian ♮6 bright diminished starting on B

*smsmmsL altered diminished magical seventh starting on G♯

Replacing the A with an A♭ instead, we get the modes of the Pinetone harmonic major scale. Starting on D we get the mode:

174.055 320.69 494.745 641.38 878.579 1025.214 1199.269 as the notes D E F G A♭ B C D, representing 10/9 6/5 4/3 36/25~13/9 5/3 9/5 2/1.

Which has modes:

*Lsmmsms Lydian Augmented ♯2 bright major starting on A♭

*msLsmms Lydian ♭3 bright minor starting on F

*sLsmmsm Mixolydian ♭2 dark major starting on G

*mmsmsLs harmonic major bright diminished starting on C

*msmsLsm Dorian ♭5 dark diminished starting on D

*smsLsmm Phrygian ♭4 symmetric minor starting on E

*smmsmsL Locrian magical ♭♭7 starting on B

We can see that this scale differs from the Pinetone diminished heptatonic by only a single note - 9/5 instead of 50/27.

The augmented step of the Pinetone harmonic minor and major scales is the same as of the Pinetone diminished heptatonic, representing 15/13 when 325/324 is tempered out (the difference between 100/99 and 144/143).

The Pintone harmonic minor and harmonic minor have step patterns msmmsLs, and mmsmsLs respectively, or, represented as MODMOS of detempered Meantone[7], LsLLsAs and LLsLsAs, the step patterns of the familiar harmonic minor and harmonic major scales.

====Pinetone diminished chromatic====

@@ Line 3,159: / Line 3,159: @@
 The following 13 notes are used in total for these scales: E♭, G♭, A♭ D, E, F, G, A, B, C, G♯, A♯, C♯
+==Pinetone harmonic minor and harmonic major==
+Additionally, we have another set of [[Porcupine]][7] modes contained in the Pinetone harmonic octatonics: 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 Pinetone diatonic and octatonic scales, so they may be useful for melody only.
+On D we get the scale:
+.055 320.69 557.888 704.524 878.579 1025.214 1199.269 as the notes D E F G♯ A B C D, representing 10/9 6/5 25/18~11/8 3/2 5/3 9/5 2/1
+We get the following 7 modes of Pinetone harmonic minor scale:
+*Lsmsmms Lydian ♯2 bright major starting on F
+*mmsLsms Ionian ♯5 symmetric minor starting on C
+*msLsmsm Ukranian dorian bright minor starting on D
+*sLsmsmm Phyrgian dominant dark major starting on E
+*msmmsLs harmonic minor dark diminished starting on A
+*smmsLsm Locrian ♮6 bright diminished starting on B
+*smsmmsL altered diminished magical seventh starting on G♯
+Replacing the A with an A♭ instead, we get the modes of the Pinetone harmonic major scale. Starting on D we get the mode:
+.055 320.69 494.745 641.38 878.579 1025.214 1199.269 as the notes D E F G A♭ B C D, representing 10/9 6/5 4/3 36/25~13/9 5/3 9/5 2/1.
+Which has modes:
+*Lsmmsms Lydian Augmented ♯2 bright major starting on A♭
+*msLsmms Lydian ♭3 bright minor starting on F
+*sLsmmsm Mixolydian ♭2 dark major starting on G
+*mmsmsLs harmonic major bright diminished starting on C
+*msmsLsm Dorian ♭5 dark diminished starting on D
+*smsLsmm Phrygian ♭4 symmetric minor starting on E
+*smmsmsL Locrian magical ♭♭7 starting on B
+We can see that this scale differs from the Pinetone diminished heptatonic by only a single note -  9/5 instead of 50/27.
+The augmented step of the Pinetone harmonic minor and major scales is the same as of the Pinetone diminished heptatonic, representing 15/13 when 325/324 is tempered out (the difference between 100/99 and 144/143).
+The Pintone harmonic minor and harmonic minor have step patterns msmmsLs, and mmsmsLs respectively, or, represented as MODMOS of detempered Meantone[7], LsLLsAs and LLsLsAs, the step patterns of the familiar harmonic minor and harmonic major scales.
 ====Pinetone diminished chromatic====