Pinetone - Revision history

Lhearne: /* Additional heptatonic subsets of the Pinetone chromatic */

2026-01-19T11:48:52Z

Additional heptatonic subsets of the Pinetone chromatic

← Older revision		Revision as of 11:48, 19 January 2026
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	The scale D E F G A B C has step pattern MsMLMsM, which tempers to sssLsss under Porcupine (M=s) and LsLLLsL under Meantone (M=L).		The scale D E F G A B C has step pattern MsMLMsM, which tempers to sssLsss under Porcupine (M=s) and LsLLLsL under Meantone (M=L).

	Raising an F to an F♯ replaces ~6/5 with ~11/9, i.e., it raises the F by ~55/54, which is tempered out in [[Porcupine]], so the scale D E F♯ G A B C tempers to sssLsss under Porcupine as before, but to LLsLLsL under Meantone (Mixolydian mode rather than Dorian as before)~~, so will call the mode approximating the ratios 10/9 11/9~~ 4/3 3/~~2 5/3 9/5 2/1 Mixolydian symmetric minor~~, ~~and use~~ the ~~mode~~ to ~~name the scale as~~ a ~~whole~~.		Raising an F to an F♯ replaces ~6/5 with ~11/9, i.e., it raises the F by ~55/54, which is tempered out in [[Porcupine]], so the scale D E F♯ G A B C tempers to sssLsss under Porcupine as before, but to LLsLLsL under Meantone (Mixolydian mode rather than Dorian as before). The modes of this scale are detailed in Table 4.3. Similarly, lowering B to B♭ lowers by ~55/54, leading to the Duradian ♯5 shown in Table 4.4, which I consider to be a really beautiful minor mode.

	To calculate the mode numbers for Tables 4.3-4.5, the mode numbers of their temperings to Porcupine and to [[Meantone]] were added, ordered, and renumbered. When two modes are tied, small changes in tuning will affect their order. Given that Ptolemismic Porcupine is more accurate than Ptolemismic Meantone, the Porcupine mode number is weighted more heavily to determine the mode order in the event of any ties. Modes are named via the [[Tetracot]][7] [[MODMOS]] they temper to when [[243/242]] is tempered out (i.e., the difference between [[11/9]] and [[27/22]]), as in [[27edo]], [[34edo]], and [[41edo]]. Table 4.2 introduces the modes of Tetracot[7]. The Pinetone diatonic, therefore, is also a detempering of a Tetracot MODMOS, with generator chain equivalent to that of the double harmonic major scale (a MODMOS of the Meantone diatonic scale). Tetracot[7] mode names used the Archeotonic mode names [[6L 1s#Proposed names\|here]] as a basis, with the substitution of Azurian, Duradian, and Phyradian as Tetracot specific mode names from [https://www.youtube.com/watch?v=xYZwye9PWSo here].		To calculate the mode numbers for Tables 4.3-4.5, the mode numbers of their temperings to Porcupine and to [[Meantone]] were added, ordered, and renumbered. When two modes are tied, small changes in tuning will affect their order. Given that Ptolemismic Porcupine is more accurate than Ptolemismic Meantone, the Porcupine mode number is weighted more heavily to determine the mode order in the event of any ties. Modes are named via the [[Tetracot]][7] [[MODMOS]] they temper to when [[243/242]] is tempered out (i.e., the difference between [[11/9]] and [[27/22]]), as in [[27edo]], [[34edo]], and [[41edo]]. Table 4.2 introduces the modes of Tetracot[7]. The Pinetone diatonic, therefore, is also a detempering of a Tetracot MODMOS, with generator chain equivalent to that of the double harmonic major scale (a MODMOS of the Meantone diatonic scale). Tetracot[7] mode names used the Archeotonic mode names [[6L 1s#Proposed names\|here]] as a basis, with the substitution of Azurian, Duradian, and Phyradian as Tetracot specific mode names from [https://www.youtube.com/watch?v=xYZwye9PWSo here].
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	\|~ 10/9 6/5 4/3 22/15 44/27 16/9 2/1		\|~ 10/9 6/5 4/3 22/15 44/27 16/9 2/1
	\|}		\|}
	~~Similarly, lowering B to B♭ lowers by ~55/54, leading to the Aeolian symmetric minor shown in Table 4.2, which I consider to be a really beautiful minor minor mode.~~
	{\| class="wikitable"		{\| class="wikitable"
	\|+Table 4.4. Modes of the Ptolemismic Pinetone Duradian dark minor		\|+Table 4.4. Modes of the Ptolemismic Pinetone Duradian dark minor

Lhearne: /* Additional heptatonic subsets of the Pinetone chromatic */

2026-01-06T01:23:52Z

Additional heptatonic subsets of the Pinetone chromatic

← Older revision		Revision as of 01:23, 6 January 2026
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	{\| class="wikitable"		{\| class="wikitable"
	\|+Table 4.1.		\|+Table 4.1.
			! colspan="8" \|Scale (mode -3 subset)
	! colspan="8" \|Scale (mode 3 subset)		! colspan="8" \|Scale (mode 3 subset)
	~~! colspan="8" \|Scale (mode -3 subset)~~
	!JI ratios approximated		!JI ratios approximated
	!Step pattern		!Step pattern

Lhearne: /* Pinetone chromatic */

2026-01-06T00:30:20Z

Pinetone chromatic

← Older revision		Revision as of 00:30, 6 January 2026
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	The TE tuning in cents is: 146.636 174.055 320.690 467.326 494.745 641.381 704.524 851.159 878.579 1025.214 1171.849 1199.269		The TE tuning in cents is: 146.636 174.055 320.690 467.326 494.745 641.381 704.524 851.159 878.579 1025.214 1171.849 1199.269
	{\| class="wikitable"		{\| class="wikitable"
	\|+(2.3.5.11) [[~~SNS (2/1, 3/2, 6/5: 100/99)-12~~\|Ptolemismic Pinetone Chromatic]]		\|+(2.3.5.11) [[Ptolemismic Pinetone chromatic\|Ptolemismic Pinetone Chromatic]]
	!Mode number		!Mode number
	!Mode as simplest JI pre-image		!Mode as simplest JI pre-image

Lhearne: /* Pinetone harmonic diminished octatonic */

2026-01-05T01:57:38Z

Pinetone harmonic diminished octatonic

← Older revision		Revision as of 01:57, 5 January 2026
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	{\| class="wikitable"		{\| class="wikitable"
	\|+Table 9.1. Modes of the just Pinetone harmonic diminished		\|+Table 9.1. Modes of the just Pinetone harmonic diminished
	! Mode ~~(height order)~~		!Mode number
			! Mode name
	!Step pattern		!Step pattern
	!Oneirotonic step pattern		!Oneirotonic step pattern
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	! Comments		! Comments
	\|-		\|-
			\|4
	\|Hlanithian diminished		\|Hlanithian diminished
	\|AsLMLMLs		\|AsLMLMLs
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	\|		\|
	\|-		\|-
			\|3
	\|Mnarian diminished*		\|Mnarian diminished*
	\|LMLMLsAs		\|LMLMLsAs
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	\|		\|
	\|-		\|-
			\|2
	\|Celephaïsian diminished*		\|Celephaïsian diminished*
	\|LMLsAsLM		\|LMLsAsLM
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	\|		\|
	\|-		\|-
			\|1
	\|Sarnathian diminished<sup>†</sup>		\|Sarnathian diminished<sup>†</sup>
	\|MLMLsAsL		\|MLMLsAsL
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	\|10:12:15 on the root		\|10:12:15 on the root
	\|-		\|-
			\| -1
	\|Dylathian diminished*		\|Dylathian diminished*
	\|LsAsLMLM		\|LsAsLMLM
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	\|		\|
	\|-		\|-
			\| -2
	\|Kadathian diminished*<sup>††</sup>		\|Kadathian diminished*<sup>††</sup>
	\|MLsAsLML		\|MLsAsLML
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	\|root 4:5:6,10:12:15		\|root 4:5:6,10:12:15
	\|-		\|-
			\| -3
	\|Ultharian diminished*<sup>††</sup>		\|Ultharian diminished*<sup>††</sup>
	\|sAsLMLML		\|sAsLMLML
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	\|root 4:5:6,10:12:15		\|root 4:5:6,10:12:15
	\|-		\|-
			\| -4
	\|Illarnekian diminished*<sup>†</sup>		\|Illarnekian diminished*<sup>†</sup>
	\|sLMLMLsA		\|sLMLMLsA
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	{\| class="wikitable"		{\| class="wikitable"
	\|+Table 9.2. Modes of the Ptolemismic Pinetone harmonic diminished		\|+Table 9.2. Modes of the Ptolemismic Pinetone harmonic diminished
	! Mode ~~(height order)~~		!Mode number
			! Mode name
	!Step pattern		!Step pattern
	!Mode as simplest JI pre-image 5-limit JI		!Mode as simplest JI pre-image 5-limit JI
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	!Comments		!Comments
	\|-		\|-
			\|4
	\|Hlanithian diminished		\|Hlanithian diminished
	\|AsLMLMLs		\|AsLMLMLs
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	\|		\|
	\|-		\|-
			\|3
	\|Mnarian diminished*		\|Mnarian diminished*
	\|LMLMLsAs		\|LMLMLsAs
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	\|		\|
	\|-		\|-
			\|2
	\|Celephaïsian diminished*		\|Celephaïsian diminished*
	\|LMLsAsLM		\|LMLsAsLM
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	\|		\|
	\|-		\|-
			\|1
	\|Sarnathian diminished<sup>†</sup>		\|Sarnathian diminished<sup>†</sup>
	\|MLMLsAsL		\|MLMLsAsL
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	\|10:12:15 on the root		\|10:12:15 on the root
	\|-		\|-
			\| -1
	\|Dylathian diminished*		\|Dylathian diminished*
	\|LsAsLMLM		\|LsAsLMLM
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	\|		\|
	\|-		\|-
			\| -2
	\|Kadathian diminished*<sup>††</sup>		\|Kadathian diminished*<sup>††</sup>
	\|MLsAsLML		\|MLsAsLML
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	\|root 4:5:6,10:12:15		\|root 4:5:6,10:12:15
	\|-		\|-
			\| -3
	\|Ultharian diminished*<sup>††</sup>		\|Ultharian diminished*<sup>††</sup>
	\|sAsLMLML		\|sAsLMLML
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	\|root 4:5:6,10:12:15		\|root 4:5:6,10:12:15
	\|-		\|-
			\| -4
	\|Illarnekian diminished*<sup>†</sup>		\|Illarnekian diminished*<sup>†</sup>
	\|sLMLMLsA		\|sLMLMLsA
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	\|+		\|+
	Table 9.4. Intervals of modes of the Pinetone harmonic diminished		Table 9.4. Intervals of modes of the Pinetone harmonic diminished
	!Mode		!Mode (height order)
	!step		!step
	!2-step		!2-step

Lhearne: /* Pinetone-15 */

2026-01-04T11:39:51Z

Pinetone-15

← Older revision		Revision as of 11:39, 4 January 2026
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	Accordingly Pinetone-15 would temper to two step sizes in 19edo (Hanson), 22edo (Porcupine), 34edo (Hanson), and 27edo (Augmented). If we wish to keep the 3-step size structure, we can tune to 26edo or 41edo with (L, m, s) = (3, 2, 1), and (4, 3, 2) respectively.		Accordingly Pinetone-15 would temper to two step sizes in 19edo (Hanson), 22edo (Porcupine), 34edo (Hanson), and 27edo (Augmented). If we wish to keep the 3-step size structure, we can tune to 26edo or 41edo with (L, m, s) = (3, 2, 1), and (4, 3, 2) respectively.

	Tempering out the 325/324, the difference between 100/99 and 144/143 rather than both of 100/99 and 144/143 leads to a more accurate temperament that does not include the whole 2.3.5.11.13 subgroup., rather just the 2.3.5.13 subgroup. The simplest JI pre-image in this temperament would be 25/24 10/9 15/13 6/5 5/4 4/3 18/13 13/9 3/2 8/5 5/3 26/15 9/5 48/25 2/1, which differs only from the simplest pre-image of the scale under 2.3.5.11.13 Ptolemismic tempering by the inclusion of 18/13 rather than 11/8.		Tempering out the 325/324, the difference between 100/99 and 144/143 rather than both of 100/99 and 144/143 leads to a more accurate temperament that does not include the whole 2.3.5.11.13 subgroup., rather just the 2.3.5.13 subgroup. The simplest JI pre-image in this temperament would be 25/24 10/9 15/13 6/5 5/4 4/3 18/13 13/9 3/2 8/5 5/3 26/15 9/5 48/25 2/1, which differs only from the simplest pre-image of the scale under 2.3.5.11.13 Ptolemismic tempering by the inclusion of 18/13 rather than 11/8.

	2.3.5.13 325/324 may be ~~better~~ tuned to 46edo, with (L, m, s) = (4, 2, 1).		In this tuning the medium and small steps are within 1c of the same size. Tempering them together results in Cata temperament, an extension of Hanson. 2.3.5.13 325/324 may alternatively be tuned to 46edo, with (L, m, s) = (4, 2, 3), or as Cata[15] in 53edo, 72edo, or 87edo as (5, 3, 3), (7, 4, 4), or (8, 5, 5).

	Pinetone-15 may be represented with note names representing the corresponding Meantone notes as: D D♯ E E♯ F F♯ G G♯ A♭ A B♭ B C♭ C D♭ D, though we note that these notes do not necessarily correspond to the notes of the Pinetone chromatic or hyperchromatic of the same name.		Pinetone-15 may be represented with note names representing the corresponding Meantone notes as: D D♯ E E♯ F F♯ G G♯ A♭ A B♭ B C♭ C D♭ D, though we note that these notes do not necessarily correspond to the notes of the Pinetone chromatic or hyperchromatic of the same name.

Lhearne: /* Pinetone harmonic diminished octatonic */

2026-01-04T08:45:37Z

Pinetone harmonic diminished octatonic

← Older revision		Revision as of 08:45, 4 January 2026
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	\|12:15:20		\|12:15:20
	\|}		\|}
	<nowiki>*</nowiki> Non-bracketed JI ratios are those approximated in 2.3.5.11.13 Ptolemismic Pinetone; bracketed JI ratios are the 2.3.7 interval approximated by additionally tempering out 105/104 ~~or 245/243~~ as in Supermagic temperament. Alternatively, if the consonances of the triads are to be maximised, the scale could be tempered ~~to 2.3.5.~~7 ~~245/243 i.e., Sensamagic temperament~~.		<nowiki>*</nowiki> Non-bracketed JI ratios are those approximated in 2.3.5.11.13 Ptolemismic Pinetone; bracketed JI ratios are the 2.3.7 interval approximated by additionally tempering out 105/104 as in Supermagic temperament. Alternatively, if the consonances of the triads are to be maximised, the scale could be tempered 7-limit rather than 13-limit Supermagic.

	==Comma pump==		==Comma pump==

Lhearne: /* Pinetone-15 */

2026-01-04T05:53:07Z

Pinetone-15

← Older revision		Revision as of 05:53, 4 January 2026
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	tempering L = s (tempering out 250/243, the Porcupine comma) results in sLsLsLsLsLsLsLs, which is Porcupine[15].		tempering L = s (tempering out 250/243, the Porcupine comma) results in sLsLsLsLsLsLsLs, which is Porcupine[15].

	tempering out s would lead to ~~sLLsLsL~~, which is ~~Dicot~~[7];		tempering out s would lead to ssLsLssLsssL, which is a MODMOS of Diminished[12].

	tempering out m would lead to ~~ssLsLssLsssL~~, which is ~~a MODMOS of Diminished~~[12].		tempering out m would lead to sLLsLsL, which is Dicot[7];

	Tempering out 100/99 and 144/143 leads to the simplest pre-image: 25/24 10/9 15/13 6/5 5/4 4/3 11/8 13/9 3/2 8/5 5/3 26/15 9/5 48/25 2/1.		Tempering out 100/99 and 144/143 leads to the simplest pre-image: 25/24 10/9 15/13 6/5 5/4 4/3 11/8 13/9 3/2 8/5 5/3 26/15 9/5 48/25 2/1.

Lhearne: /* The Pinetone diatonic */

2026-01-04T04:28:34Z

The Pinetone diatonic

← Older revision		Revision as of 04:28, 4 January 2026
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	\|}		\|}
	{\| class="wikitable"		{\| class="wikitable"
	\|+Table 2.3. Modes of the just Pinetone diatonic		\|+Table 2.3. Modes of the [[SNS (2/1, 3/2, 6/5)-7\|just Pinetone diatonic]]
	!Mode number		!Mode number
	!Mode in JI		!Mode in JI
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	The modes of the Ptolemismic Pinetone diatonic are shown below in their simplest JI pre-image (the simplest JI ratios each interval above the tonic represents), and in cents, in an optimized tuning called [[TE tuning]].		The modes of the Ptolemismic Pinetone diatonic are shown below in their simplest JI pre-image (the simplest JI ratios each interval above the tonic represents), and in cents, in an optimized tuning called [[TE tuning]].
	{\| class="wikitable"		{\| class="wikitable"
	\|+Table 2.4. Modes of the Ptolemismic Pinetone diatonic		\|+Table 2.4. Modes of the [[SNS (2/1, 3/2, 6/5: 100/99)-7\|Ptolemismic Pinetone diatonic]]
	!Mode number		!Mode number
	!Pinetone diatonic mode		!Pinetone diatonic mode
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	The TE tuning in cents is: 146.636 174.055 320.690 467.326 494.745 641.381 704.524 851.159 878.579 1025.214 1171.849 1199.269		The TE tuning in cents is: 146.636 174.055 320.690 467.326 494.745 641.381 704.524 851.159 878.579 1025.214 1171.849 1199.269
	{\| class="wikitable"		{\| class="wikitable"
	\|+(2.3.5.11) Ptolemismic Pinetone Chromatic		\|+(2.3.5.11) [[SNS (2/1, 3/2, 6/5: 100/99)-12\|Ptolemismic Pinetone Chromatic]]
	!Mode number		!Mode number
	!Mode as simplest JI pre-image		!Mode as simplest JI pre-image

Lhearne: /* Introduction */

2026-01-03T06:45:57Z

Introduction

← Older revision		Revision as of 06:45, 3 January 2026
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	'''Definition: Pinetone is a system of related rank-3 microtonal scales: pentatonic, diatonic, octatonic, chromatic, and hyperchromatic.'''		'''Definition: Pinetone is a system of related rank-3 microtonal scales: pentatonic, diatonic, octatonic, chromatic, and 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 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 [[Pinetone chromatic (sharps)\|this one]]! Copy the text into notepad and save as a .scl file).		"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 [[Pinetone 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!).		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!).
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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 Pinetone are a two sets 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.		Additionally available in Pinetone are two sets 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 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. The white keys and the pink key together make a Pinetone octatonic scale - major-harmonic with G♯ and minor-harmonic for A♭. This is what I call the ''Pinetone System.''		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. The white keys and the pink key together make a Pinetone octatonic scale - major-harmonic with G♯ and minor-harmonic for A♭. This is what I call the ''Pinetone System.''

Lhearne: Added harmonic minor and major back in to intro

2025-12-25T22:59:49Z

Added harmonic minor and major back in to intro

← Older revision		Revision as of 22:59, 25 December 2025
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	* [[Pinetone#Pinetone pentatonic\|Pentatonic minor]]: 95695, B67B6 (subset of diatonic, harmonic diminished)		* [[Pinetone#Pinetone pentatonic\|Pentatonic minor]]: 95695, B67B6 (subset of diatonic, harmonic diminished)
	* [[Pinetone#Pinetone diatonic\|Diatonic]]: 5456545, 6567656 (subset of major and minor-harmonic octatonics)		* [[Pinetone#Pinetone diatonic\|Diatonic]]: 5456545, 6567656 (subset of major and minor-harmonic octatonics)
			* [[Pinetone#Pinetone harmonic minor and harmonic major\|Harmonic minor]]: 5455475, 6566585 (subset of major and minor-harmonic octatonic)
			* [[Pinetone#Pinetone harmonic minor and harmonic major\|Harmonic major]]: 5545474, 6656585 (subset of major and minor-harmonic octatonic)
	* [[Pinetone#Additional heptatonic subsets of the Pinetone chromatic\|Azurian bright minor]]: 5465455, 6576566 (subset of chromatic)		* [[Pinetone#Additional heptatonic subsets of the Pinetone chromatic\|Azurian bright minor]]: 5465455, 6576566 (subset of chromatic)
	* [[Pinetone#Additional heptatonic subsets of the Pinetone chromatic\|Duradian dark minor]]: 5456455, 6567566 (subset of chromatic)		* [[Pinetone#Additional heptatonic subsets of the Pinetone chromatic\|Duradian dark minor]]: 5456455, 6567566 (subset of chromatic)

← Older revision		Revision as of 22:59, 25 December 2025
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	* [[Pinetone#Pinetone pentatonic\|Pentatonic minor]]: 95695, B67B6 (subset of diatonic, harmonic diminished)		* [[Pinetone#Pinetone pentatonic\|Pentatonic minor]]: 95695, B67B6 (subset of diatonic, harmonic diminished)
	* [[Pinetone#Pinetone diatonic\|Diatonic]]: 5456545, 6567656 (subset of major and minor-harmonic octatonics)		* [[Pinetone#Pinetone diatonic\|Diatonic]]: 5456545, 6567656 (subset of major and minor-harmonic octatonics)
			* [[Pinetone#Pinetone harmonic minor and harmonic major\|Harmonic minor]]: 5455475, 6566585 (subset of major and minor-harmonic octatonic)
			* [[Pinetone#Pinetone harmonic minor and harmonic major\|Harmonic major]]: 5545474, 6656585 (subset of major and minor-harmonic octatonic)
	* [[Pinetone#Additional heptatonic subsets of the Pinetone chromatic\|Azurian bright minor]]: 5465455, 6576566 (subset of chromatic)		* [[Pinetone#Additional heptatonic subsets of the Pinetone chromatic\|Azurian bright minor]]: 5465455, 6576566 (subset of chromatic)
	* [[Pinetone#Additional heptatonic subsets of the Pinetone chromatic\|Duradian dark minor]]: 5456455, 6567566 (subset of chromatic)		* [[Pinetone#Additional heptatonic subsets of the Pinetone chromatic\|Duradian dark minor]]: 5456455, 6567566 (subset of chromatic)