Pinetone: Difference between revisions
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'''Definition: Pinetone is a system of related rank-3 microtonal scales: pentatonic, diatonic, octatonic, chromatic, 15 and 19-note hyperchromatic.''' | '''Definition: Pinetone is a system of related rank-3 microtonal scales: pentatonic, diatonic, octatonic, chromatic, 15 and 19-note hyperchromatic.''' | ||
Are you interested in microtonal music with wild and wacky harmonies but want some familiarity to guide you? Heard about this Porcupine thing but not sure how to get 12 notes of it? Wish you had something like Porcupine but more accurate or with more interesting scales? Introducing | Are you interested in microtonal music with wild and wacky harmonies but want some familiarity to guide you? Heard about this Porcupine thing but not sure how to get 12 notes of it? Wish you had something like Porcupine but more accurate or with more interesting scales? Introducing Pinetone. The scales you know and love, with a new-age quirky spin. The perfect mix of consonant and dissonant harmonies, familiar and newfangled. Try it on your keyboard straight away (if you can retune your keyboard using Scala files, grab [[Porcutone chromatic (sharps)|this one]]! Copy the text into notepad and save as a .scl file). | ||
Pinetone combines [[Porcupine]] – arguably the best way to add the 11th harmonic to major and minor harmonies in a seven-note scale – with [[Meantone]] – the system underpinning most common practice music from the last several hundred years, so all the same scales (diatonic, harmonic minor, pentatonic, chromatic, etc.) are still available, just with a new Porcupine spin, and the 11th harmonic (and the 13th harmonic as well!). | |||
While there aren't as many consonant major and minor triads as we are used to, they are more consonant in Pinetone. | While there aren't as many consonant major and minor triads as we are used to, they are more consonant in Pinetone. | ||
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As opposed to in [[12edo]], each key is distinctly different in Pinetone scales, both a blessing and a curse. | As opposed to in [[12edo]], each key is distinctly different in Pinetone scales, both a blessing and a curse. | ||
Additionally available in | Additionally available in Pinetone are a set of octatonic modes with their own Porcupine-like functional harmony that combine [[Porcupine]][8] with the [[oneirotonic]] modes that are gaining popularity at the moment. Finally, Pinetone diminished scales combine Porcupine with the familiar diminished scale. | ||
If you have a [[Lumatone]], you can use the standard Bosanquet mapping for 12edo. The white keys are the Pinetone diatonic, a cross between the Meantone diatonic scale and Porcupine[7], and | If you have a [[Lumatone]], you can use the standard Bosanquet mapping for 12edo. The white keys are the Pinetone diatonic, a cross between the Meantone diatonic scale and Porcupine[7], and the black keys give the Pinetone 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 Pinetone octatonic. | ||
If you don't have a [[Lumatone]], no worries, you can set it up just fine on any keyboard! | If you don't have a [[Lumatone]], no worries, you can set it up just fine on any keyboard! | ||
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== Pinetone octatonic scales== | == Pinetone octatonic scales== | ||
The Porcupine comma is the small step of the Pinetone chromatic, so tempering the Pinetone chromatic scale to Porcupine leads from 7L 1m 4s = (27/25, 25/24, 250/243) to 7L 1s = (10/9~27/25, 25/24~81/80), which is Porcupine[8]! The Porcupine[7] scale has its large step between G and A, so the eighth note of Porcupine[8] is either G♯ or A♭, adding another small step of Porcupine[7] below A (for G♯) or above G (A♭). Mode -3 or mode 3 of the Pinetone chromatic scale, respectively, are set to D so that this is preserved in | The Porcupine comma is the small step of the Pinetone chromatic, so tempering the Pinetone chromatic scale to Porcupine leads from 7L 1m 4s = (27/25, 25/24, 250/243) to 7L 1s = (10/9~27/25, 25/24~81/80), which is Porcupine[8]! The Porcupine[7] scale has its large step between G and A, so the eighth note of Porcupine[8] is either G♯ or A♭, adding another small step of Porcupine[7] below A (for G♯) or above G (A♭). Mode -3 or mode 3 of the Pinetone chromatic scale, respectively, are set to D so that this is preserved in Pinetone. This leads to the Pinetone octatonic scales: D E F G G♯/A♭ A B C. In just intonation: 10/9 6/5 4/3 25/18 3/2 5/3 9/5 2/1 with G♯, or 10/9 6/5 4/3 36/25 3/2 5/3 9/5 2/1 with A♭. This scale has 4 large steps of 10/9, 3 medium steps of 27/25, and 1 small step of 25/24. It is not mirror-symmetric, or equivalentely, it is ''[[Chirality|chiral]]'' so it cannot be uniquely defined with a step signature like Meantone[7], Porcupine[7], Porcupine[8], Meantone[12], and the Pinetone diatonic (the Zarlino/Ptolemy just major scale is also not mirror symmetric). Scales that can be uniquely defined by a step signature are called ''step-nested scales''. More on that later. The Pinetone octatonic with G♯ is called the Pinetone major-harmonic octatonic, and the Pinetone octatonic with A♭ is called the Pinetone minor-harmonic octatonic. These names will make sense to the reader after further reading on these scales and the chords they contain, and on the Pintone diminished octatonic introduced below. The mirror inverse of any mode of the Pinetone major-harmonic octatonic is a mode of the Pinetone minor-harmonic octatonic (see [[chirality]]). This is true similarly of the familiar harmonic minor and harmonic major scales. | ||
On a keyboard with standard (Bosanquet or 12edo) mapping, the Pinetone 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 Pinetone octatonic is on the white and pink keys, while there's a Pinetone diatonic on the white keys and a Pinetone pentatonic on the blue and pink keys. | On a keyboard with standard (Bosanquet or 12edo) mapping, the Pinetone 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 Pinetone octatonic is on the white and pink keys, while there's a Pinetone diatonic on the white keys and a Pinetone pentatonic on the blue and pink keys. | ||
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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. | 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 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 | 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 Pinetone 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). | 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). | ||
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==Summary for xen-math nerds== | ==Summary for xen-math nerds== | ||
Pinetone scales are built via step nesting from the 5-limit minor seventh tetrad: 6/5 3/2 9/5 2/1. The bounds for its scales are the set of temperings of the rank-3 step-nested children of the 4-note SNS 6/5 3/2 9/5 2/1. Pinetone diminished scales are built via step-nesting from the 5-limit diminished tetrad: 6/5 36/25 5/3 2/1. The bounds for its scales are the set of temperings of the rank-3 step-nested children of the 4-note MOS scale 6/5 36/25 5/3 2/1. | |||
The Pinetone chromatic is a 12-note rank-3 [[Meantone]][12] x [[Ripple]][12] [[Fokker block]], a [[step-nested scale]] that also tempers to [[Porcupine]][8], comprising a diatonic [[Meantone]][7]-[[Porcupine]][7]-[[Dicot]][7] [[wakalix]] / 3-[[Step-nested scale|SNS]] on the white keys, and a pentatonic [[Meantone]][5]-[[Father]][5]-[[Bug]][5] [[wakalix]] on the 'black' keys. | The Pinetone chromatic is a 12-note rank-3 [[Meantone]][12] x [[Ripple]][12] [[Fokker block]], a [[step-nested scale]] that also tempers to [[Porcupine]][8], comprising a diatonic [[Meantone]][7]-[[Porcupine]][7]-[[Dicot]][7] [[wakalix]] / 3-[[Step-nested scale|SNS]] on the white keys, and a pentatonic [[Meantone]][5]-[[Father]][5]-[[Bug]][5] [[wakalix]] on the 'black' keys. | ||
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The Pinetone diatonic is a [[wakalix]] (pairwise well-formed scale) and a [[step-nested scale]]: A detempering of [[Meantone]][7] and [[Porcupine]][7], (and also of [[Dicot]][7]), a [[Fokker block]] with [[Unison vector|unison vectors]] of [[81/80]] and [[250/243]] (and [[25/24]]) comprising 1 large step of 9/8 (''L'' x ''L''), 3 medium steps of 10/9 (''L'' x ''s''), and 3 small steps of 27/25 (''s'' x ''s''). | The Pinetone diatonic is a [[wakalix]] (pairwise well-formed scale) and a [[step-nested scale]]: A detempering of [[Meantone]][7] and [[Porcupine]][7], (and also of [[Dicot]][7]), a [[Fokker block]] with [[Unison vector|unison vectors]] of [[81/80]] and [[250/243]] (and [[25/24]]) comprising 1 large step of 9/8 (''L'' x ''L''), 3 medium steps of 10/9 (''L'' x ''s''), and 3 small steps of 27/25 (''s'' x ''s''). | ||
The Pinetone | The Pinetone major and minor-harmonic octatonics are the 8-note rank-3 [[Porcupine]][8] x [[Father]][8] [[Fokker block|Fokker blocks]] with [[Unison vector|unison vectors]] of 250/243, 16/15, and 648/625; comprising 4 large steps of 10/9 (''L'' x ''L''), 3 medium steps of 27/25 (''L'' x ''s''), and one small step of 25/24 (''s'' x ''L''). | ||
The Pinetone diminished scale is a [[step-nested scale]] and a [[Porcupine]][8] x Diminished[8] [[Fokker block]] with [[Unison vector|unison vectors]] of 250/243, 648/625, and 16/15; comprising 4 large steps of 10/9 (''L'' x ''L''), 3 medium steps of 27/25 (''L'' x ''s''), and one small step of 25/24 (''s'' x ''s''). | |||
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