Pinetone: Difference between revisions

Line 1,855:

In the Pinetone chromatic with sharps, which contains the Pinetone major-harmonic octatonic as the naturals plus G♯, the Ultharian dark major mode can be expressed as D E F G G♯ A B C. The Pinetone diminished mode on D, the dark major diminished, is therefore D E F G G♯ A♯ B C♯. In the Pinetone chromatic with flats, which contains the Pinetone minor-harmonic octatonic as the naturals plus A♭, the Mnarian middle major mode can be expressed as D E F G A♭ A B C. The Pinetone diminished mode on D, the middle major diminished, is therefore D E♭ F G♭ A♭ A B C.

We know that this scale tempers to Porcupine[8]; tempering M=s instead leads to LsLsLsLs, i.e., Diminished[8]; and finally tempering L=s leads to LsLLLsLs, a ~~mod~~ of Father[8]. Like the Pinetone chromatic and diatonic scale, this scale is an SN scale, and is therefor achiral. We may name this scale perhaps the Porcupine-Diminished scale, or we may include it in the Pinetone system as the Pinetone diminished scale, or the Pinetone diminished octatonic

We know that this scale tempers to Porcupine[8]; tempering M=s instead leads to LsLsLsLs, i.e., Diminished[8]; and finally tempering L=s leads to LsLLLsLs, a MODMOS of Father[8]. Like the Pinetone chromatic and diatonic scale, this scale is an SN scale, and is therefor achiral. We may name this scale perhaps the Porcupine-Diminished scale, or we may include it in the Pinetone system as the Pinetone diminished scale, or the Pinetone diminished octatonic

Every other step of any mode of the Pinetone diminished scale gives an inversion of the 5-limit diminished tetrad; therefore every second step of the Pinetone diminished scales only comes in two different sizes, as opposed to the four different sizes of every second step of the Pinetone harmonic octatonics. Although the Pinetone diminished is simpler in this way, the Pinetone major and minor-harmonic octatonic provides more major and minor triads respectively (this is why I have named them the Pinetone major and minor-harmonic octatonics).

@@ Line 1,855: / Line 1,855: @@
 In the Pinetone chromatic with sharps, which contains the Pinetone major-harmonic octatonic as the naturals plus G♯, the Ultharian dark major mode can be expressed as D E F G G♯ A B C. The Pinetone diminished mode on D, the dark major diminished, is therefore D E F G G♯ A♯ B C♯. In the Pinetone chromatic with flats, which contains the Pinetone minor-harmonic octatonic as the naturals plus A♭, the Mnarian middle major mode can be expressed as D E F G A♭ A B C. The Pinetone diminished mode on D, the middle major diminished, is therefore D E♭ F G♭ A♭ A B C.
-We know that this scale tempers to Porcupine[8]; tempering M=s instead leads to LsLsLsLs, i.e., Diminished[8]; and finally tempering L=s leads to LsLLLsLs, a mod of Father[8]. Like the Pinetone chromatic and diatonic scale, this scale is an SN scale, and is therefor achiral. We may name this scale perhaps the Porcupine-Diminished scale, or we may include it in the Pinetone system as the Pinetone diminished scale, or the Pinetone diminished octatonic
+We know that this scale tempers to Porcupine[8]; tempering M=s instead leads to LsLsLsLs, i.e., Diminished[8]; and finally tempering L=s leads to LsLLLsLs, a MODMOS of Father[8]. Like the Pinetone chromatic and diatonic scale, this scale is an SN scale, and is therefor achiral. We may name this scale perhaps the Porcupine-Diminished scale, or we may include it in the Pinetone system as the Pinetone diminished scale, or the Pinetone diminished octatonic
 Every other step of any mode of the Pinetone diminished scale gives an inversion of the 5-limit diminished tetrad; therefore every second step of the Pinetone diminished scales only comes in two different sizes, as opposed to the four different sizes of every second step of the Pinetone harmonic octatonics. Although the Pinetone diminished is simpler in this way, the Pinetone major and minor-harmonic octatonic provides more major and minor triads respectively (this is why I have named them the Pinetone major and minor-harmonic octatonics).