10-form - Revision history

Vector at 02:53, 9 May 2026

2026-05-09T02:53:31Z

← Older revision		Revision as of 02:53, 9 May 2026
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	=== Hemipythagorean tuning ===		=== Hemipythagorean tuning ===
	The hemipythagorean decatonic halves each interval of the conventional pentatonic. It is notably used as the basis of the 10-form interval categorization scheme in Famana, and can be seen as a 3-limit scale produced without stacks of fifths. To construct the hemipythagorean decatonic, we take the fifth and fourth (the 10-form 4- and 6-steps) and their tritone complements (the 10-form 1- and 9-steps), and also the neutral third and sixth (the 10-form 3- and 7-steps) and their tritone complements (the 10-form 2- and 8-steps). The tritone and the unison/octave comprise the 5-step and the 0-/10-step respectively.		The hemipythagorean (or "diploid dicot") decatonic halves each interval of the conventional pentatonic. It is notably used as the basis of the 10-form interval categorization scheme in Famana, and can be seen as a 3-limit scale produced without stacks of fifths. To construct the hemipythagorean decatonic, we take the fifth and fourth (the 10-form 4- and 6-steps) and their tritone complements (the 10-form 1- and 9-steps), and also the neutral third and sixth (the 10-form 3- and 7-steps) and their tritone complements (the 10-form 2- and 8-steps). The tritone and the unison/octave comprise the 5-step and the 0-/10-step respectively.

	=== Blackdye ===		=== Blackdye ===

Vector at 02:53, 9 May 2026

2026-05-09T02:53:01Z

← Older revision		Revision as of 02:53, 9 May 2026
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	* Fundamental tetrad: 0-3-6-8\10, with inversions 0-3-5-7\10, 0-2-4-7\10, and 0-2-5-8\10		* Fundamental tetrad: 0-3-6-8\10, with inversions 0-3-5-7\10, 0-2-4-7\10, and 0-2-5-8\10

	== Notes about distinctions ==		=== Notes about distinctions ===
	The 9/7 interval, while considered a [[third]] by [[diatonic]] classification, is generally a kind of imperfect fourth here. The same goes for 7/6, which is classified as a [[latus]], rather than being a third as in diatonic.		The 9/7 interval, while considered a [[third]] by [[diatonic]] classification, is generally a kind of imperfect fourth here. The same goes for 7/6, which is classified as a [[latus]], rather than being a third as in diatonic.

	== Important scales ==		== Important scales ==

			=== Hemipythagorean tuning ===
			The hemipythagorean decatonic halves each interval of the conventional pentatonic. It is notably used as the basis of the 10-form interval categorization scheme in Famana, and can be seen as a 3-limit scale produced without stacks of fifths. To construct the hemipythagorean decatonic, we take the fifth and fourth (the 10-form 4- and 6-steps) and their tritone complements (the 10-form 1- and 9-steps), and also the neutral third and sixth (the 10-form 3- and 7-steps) and their tritone complements (the 10-form 2- and 8-steps). The tritone and the unison/octave comprise the 5-step and the 0-/10-step respectively.

	=== Blackdye ===		=== Blackdye ===
	[[File:Blackdye.png\|thumb\|520x520px\|Blackdye constructed from zarlino]]		[[File:Blackdye.png\|thumb\|520x520px\|Blackdye constructed from zarlino]]

Overthink: /* Notes about distinctions */ improve writing

2026-04-06T04:29:55Z

Notes about distinctions: improve writing

← Older revision		Revision as of 04:29, 6 April 2026
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	== Notes about distinctions ==		== Notes about distinctions ==
	9/7, while ~~conventionally~~ a [[third]], is generally a kind of imperfect fourth here. ~~Same~~ goes for 7/6 ~~and being~~ a [[latus]], rather than a third.		The 9/7 interval, while considered a [[third]] by [[diatonic]] classification, is generally a kind of imperfect fourth here. The same goes for 7/6, which is classified as a [[latus]], rather than being a third as in diatonic.

	== Important scales ==		== Important scales ==

Vector: Added function names for degrees, a combination of Western convention and Aura's "varicant" function for the unilatus and antilatus

2026-04-04T03:32:54Z

Added function names for degrees, a combination of Western convention and Aura's "varicant" function for the unilatus and antilatus

← Older revision		Revision as of 03:32, 4 April 2026
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	!Note names<br>([[User:Overthink\|Overthink]])		!Note names<br>([[User:Overthink\|Overthink]])
	!Notable just intervals		!Notable just intervals
			!Function
	\|-		\|-
	\|0		\|0
Line 24:		Line 25:
	\|C		\|C
	\|1/1		\|1/1
			\|tonic
	\|-		\|-
	\|1		\|1
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	\|R		\|R
	\|16/15, 10/9		\|16/15, 10/9
			\|supertonic
	\|-		\|-
	\|2		\|2
Line 44:		Line 47:
	\|D		\|D
	\|8/7, 7/6		\|8/7, 7/6
			\|contravaricant
	\|-		\|-
	\|3		\|3
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	\|E		\|E
	\|6/5, 5/4		\|6/5, 5/4
			\|mediant
	\|-		\|-
	\|4		\|4
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	\|F		\|F
	\|9/7, 4/3		\|9/7, 4/3
			\|subdominant
	\|-		\|-
	\|5		\|5
Line 74:		Line 80:
	\|T		\|T
	\|7/5, 10/7, 11/8, 16/11		\|7/5, 10/7, 11/8, 16/11
			\|antitonic
	\|-		\|-
	\|6		\|6
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	\|G		\|G
	\|3/2, 14/9		\|3/2, 14/9
			\|dominant
	\|-		\|-
	\|7		\|7
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	\|A		\|A
	\|5/3, 8/5		\|5/3, 8/5
			\|submediant
	\|-		\|-
	\|8		\|8
Line 104:		Line 113:
	\|S		\|S
	\|7/4, 12/7		\|7/4, 12/7
			\|varicant
	\|-		\|-
	\|9		\|9
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	\|B		\|B
	\|15/8, 9/5		\|15/8, 9/5
			\|subtonic
	\|-		\|-
	\|10		\|10
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	\|C		\|C
	\|2/1		\|2/1
			\|tonic
	\|}		\|}

Overthink: /* Pentawood */ + semaphore

2026-03-21T03:38:49Z

Pentawood: + semaphore

← Older revision		Revision as of 03:38, 21 March 2026
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	=== Pentawood ===		=== Pentawood ===
	Blackwood[10], or pentawood, has the notable feature of every note of the scale having either a major or a minor chord built on it, which not even [[mosdiatonic]] has (as mosdiatonic has a diminished chord). However, this is at the cost of the fifth necessarily being tuned rather sharply. The scale has only two modes, which may be considered major and minor, and as a 1\5-octave scale lacks a single chain of identical intervals capable of describing it. It can be compared to Diaschismic[10]; instead of linking the third and antilatus, it makes the antilatus a perfect interval, with no distinctions available within the MOS form of the scale. Pentawood includes the structure of [[Archy]] ~~temperament~~.		Blackwood[10], or pentawood, has the notable feature of every note of the scale having either a major or a minor chord built on it, which not even [[mosdiatonic]] has (as mosdiatonic has a diminished chord). However, this is at the cost of the fifth necessarily being tuned rather sharply. The scale has only two modes, which may be considered major and minor, and as a 1\5-octave scale lacks a single chain of identical intervals capable of describing it. It can be compared to Diaschismic[10]; instead of linking the third and antilatus, it makes the antilatus a perfect interval, with no distinctions available within the MOS form of the scale. Pentawood includes the structure of the [[Archy]] and [[Semaphore]] temperaments.

	Additionally, pentawood is a tempering of the aforementioned blackdye.		Additionally, pentawood is a tempering of the aforementioned blackdye.

Overthink: /* Chords */ + semiquartal triad

2026-03-21T03:37:43Z

Chords: + semiquartal triad

← Older revision		Revision as of 03:37, 21 March 2026
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	10-form harmony can be constructed out of:		10-form harmony can be constructed out of:
	* Fundamental triad: 0-3-6\10, with inversions 0-3-7\10 and 0-4-7\10		* Fundamental triad: 0-3-6\10, with inversions 0-3-7\10 and 0-4-7\10
			* Semiquartal triad: 0-2-4\10, with inversions 0-2-8\10 and 0-6-8\10
	* Fundamental tetrad: 0-3-6-8\10, with inversions 0-3-5-7\10, 0-2-4-7\10, and 0-2-5-8\10		* Fundamental tetrad: 0-3-6-8\10, with inversions 0-3-5-7\10, 0-2-4-7\10, and 0-2-5-8\10

Overthink: /* Interval regions */ add my proposed note names

2026-03-21T03:36:27Z

Interval regions: add my proposed note names

← Older revision		Revision as of 03:36, 21 March 2026
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	!10edo		!10edo
	!Region		!Region
	!Names (Tellurian)		!Names<br>(Tellurian)
	!Names (Diatonic)		!Names<br>(Diatonic)
	!Names (Hybrid)		!Names<br>(Hybrid)
	!Solfege ([[User:Vector\|Vector]])		!Solfege<br>([[User:Vector\|Vector]])
			!Note names<br>([[User:Overthink\|Overthink]])
	!Notable just intervals		!Notable just intervals
	\|-		\|-
Line 21:		Line 22:
	\|unison		\|unison
	\|do		\|do
			\|C
	\|1/1		\|1/1
	\|-		\|-
Line 30:		Line 32:
	\|second		\|second
	\|re		\|re
			\|R
	\|16/15, 10/9		\|16/15, 10/9
	\|-		\|-
Line 39:		Line 42:
	\|unilatus		\|unilatus
	\|na		\|na
			\|D
	\|8/7, 7/6		\|8/7, 7/6
	\|-		\|-
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	\|third		\|third
	\|mi		\|mi
			\|E
	\|6/5, 5/4		\|6/5, 5/4
	\|-		\|-
Line 57:		Line 62:
	\|fourth		\|fourth
	\|fa		\|fa
			\|F
	\|9/7, 4/3		\|9/7, 4/3
	\|-		\|-
Line 66:		Line 72:
	\|median		\|median
	\|zi		\|zi
			\|T
	\|7/5, 10/7, 11/8, 16/11		\|7/5, 10/7, 11/8, 16/11
	\|-		\|-
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	\|fifth		\|fifth
	\|so		\|so
			\|G
	\|3/2, 14/9		\|3/2, 14/9
	\|-		\|-
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	\|sixth		\|sixth
	\|la		\|la
			\|A
	\|5/3, 8/5		\|5/3, 8/5
	\|-		\|-
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	\|antilatus		\|antilatus
	\|be		\|be
			\|S
	\|7/4, 12/7		\|7/4, 12/7
	\|-		\|-
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	\|seventh		\|seventh
	\|ti		\|ti
			\|B
	\|15/8, 9/5		\|15/8, 9/5
	\|-		\|-
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	\|octave		\|octave
	\|do		\|do
			\|C
	\|2/1		\|2/1
	\|}		\|}

Overthink: /* Equidecatonic MOSes */ Why the blank column?

2026-03-21T03:31:32Z

Equidecatonic MOSes: Why the blank column?

← Older revision		Revision as of 03:31, 21 March 2026
Line 1,071:		Line 1,071:
	!EDO		!EDO
	!Temperament		!Temperament
	!
	\|-		\|-
	\|9L 1s		\|9L 1s
	\|29		\|29
	\|Negri		\|Negri
	\|
	\|-		\|-
	\|8L 2s		\|8L 2s
	\|28		\|28
	\|Semibuzzard		\|Semibuzzard
	\|
	\|-		\|-
	\|7L 3s		\|7L 3s
	\|27		\|27
	\|Beatles (27 & 37)		\|Beatles (27 & 37)
	\|
	\|-		\|-
	\|6L 4s		\|6L 4s
	\|26		\|26
	\|Lemba		\|Lemba
	\|
	\|-		\|-
	\|5L 5s		\|5L 5s
	\|25		\|25
	\|Blackwood		\|Blackwood
	\|
	\|-		\|-
	\|4L 6s		\|4L 6s
	\|24		\|24
	\|''(TODO: find representative temperament)''		\|''(TODO: find representative temperament)''
	\|
	\|-		\|-
	\|3L 7s		\|3L 7s
	\|23		\|23
	\|Magic		\|Magic
	\|
	\|-		\|-
	\|2L 8s		\|2L 8s
	\|22		\|22
	\|Pajara		\|Pajara
	\|
	\|-		\|-
	\|1L 9s		\|1L 9s
	\|21		\|21
	\|Miracle		\|Miracle
	\|
	\|}		\|}

Overthink: /* Taric */ note octokaidecal

2026-03-21T03:30:21Z

Taric: note octokaidecal

← Older revision		Revision as of 03:30, 21 March 2026
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	=== Taric ===		=== Taric ===
	[[Taric]] reverses the small and large steps of jaric. Its period is 1\2 like jaric, but its generator is an [[oneirotonic]] fifth rather than a mosdiatonic one.		[[Taric]] reverses the small and large steps of jaric. Its period is 1\2 like jaric, but its generator is an [[oneirotonic]] fifth rather than a mosdiatonic one. It corresponds to [[Octokaidecal]], which can be considered what is to Pajara as [[Mavila]] is to [[Meantone]].

	Taric is particularly notable since its major tetrad (0-400-733-1000 in 18edo) is close to +1+1+1 [[DR]] in certain tunings.		Taric is particularly notable since its major tetrad (0-400-733-1000 in 18edo) is close to +1+1+1 [[DR]] in certain tunings.

Overthink: /* Interval regions */ link userpage

2026-03-21T03:28:16Z

Interval regions: link userpage

← Older revision		Revision as of 03:28, 21 March 2026
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	!Names (Diatonic)		!Names (Diatonic)
	!Names (Hybrid)		!Names (Hybrid)
	!Solfege (Vector)		!Solfege ([[User:Vector\|Vector]])
	!Notable just intervals		!Notable just intervals
	\|-		\|-