User:CompactStar/Ordinal interval notation - Revision history

CompactStar: Changed redirect target from /Lefts and rights notation/ to User:CompactStar/Lefts and rights notation

2024-01-02T03:31:54Z

Changed redirect target from /Lefts and rights notation/ to User:CompactStar/Lefts and rights notation

← Older revision		Revision as of 03:31, 2 January 2024
Line 1:		Line 1:
	#redirect [[/Lefts and rights notation/]]		#redirect [[User:CompactStar/Lefts and rights notation]]

CompactStar: It won't let me move it again.

2024-01-02T03:23:39Z

It won't let me move it again.

← Older revision		Revision as of 03:23, 2 January 2024
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	~~WIP (the reason this is in userspace)~~		#redirect [[/Lefts and rights notation/]]

	~~Ordinal interval notation is a notation for~~ [[~~just intonation]] in which all intervals are represented by a normal interval classification combined with an ordinal number.~~

	~~To get the classification for an interval, multiply the interval classes of the prime harmonics which it factors into, which are predefined as follows:~~
	~~{\|class="wikitable"~~
	\|-
	~~!Prime harmonic~~
	~~!colspan="2"\|Interval classification~~
	\|-
	~~\|[[2~~/~~1]]~~
	~~\|P8~~
	~~\|perfect octave~~
	\|-
	~~\|[[3/2]]~~
	~~\|P5~~
	~~\|perfect fifth~~
	\|-
	~~\|[[5/4]]~~
	~~\|M3~~
	~~\|major third~~
	\|-
	~~\|[[7/4]]~~
	~~\|m7~~
	~~\|minor seventh~~
	\|-
	~~\|[[11/8]]~~
	~~\|U4~~
	~~\|ultrafourth~~
	\|-
	~~\|[[13/8]]~~
	~~\|an6~~
	~~\|artoneutral sixth~~
	\|-
	~~\|[[17/16]]~~
	~~\|m2~~
	~~\|minor second~~
	\|-
	~~\|[[19/16]]~~
	~~\|m3~~
	~~\|minor third~~
	\|-
	~~\|[[23/16]]~~
	~~\|i5~~
	~~\|infrafifth~~
	\|-
	~~\|[[29/16]]~~
	~~\|m7~~
	~~\|minor seventh~~
	\|-
	~~\|[[31/16]]~~
	~~\|i8~~
	~~\|infraoctave~~
	\|-
	~~\|[[37/32]]~~
	~~\|UM2~~
	~~\|ultramajor second~~
	\|-
	~~\|[[41/32]]~~
	~~\|M3~~
	~~\|major third~~
	\|-
	~~\|[[47~~/32]]
	~~\|i5~~
	~~\|infrafifth~~
	\|}

CompactStar at 10:46, 1 January 2024

2024-01-01T10:46:46Z

← Older revision		Revision as of 10:46, 1 January 2024
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	\|-		\|-
	\|[[7/4]]		\|[[7/4]]
	\|~~im7~~		\|m7
	\|~~inframinor~~ seventh		\|minor seventh
	\|-		\|-
	\|[[11/8]]		\|[[11/8]]
Line 42:		Line 42:
	\|-		\|-
	\|[[23/16]]		\|[[23/16]]
	\|A4		\|i5
	\|~~augmented fourth~~		\|infrafifth
	\|-		\|-
	\|[[29/16]]		\|[[29/16]]
	\|~~an7~~		\|m7
	\|~~artoneutral~~ seventh		\|minor seventh
	\|-		\|-
	\|[[31/16]]		\|[[31/16]]
Line 64:		Line 64:
	\|i5		\|i5
	\|infrafifth		\|infrafifth
	\|-
	~~\|[[~~

	\|}		\|}

CompactStar at 09:13, 30 December 2023

2023-12-30T09:13:29Z

@@ Line 53: / Line 53: @@
 |infraoctave
 |-
+|[[37/32]]
 |}

CompactStar at 09:13, 30 December 2023

2023-12-30T09:13:24Z

@@ Line 53: / Line 53: @@
 |infraoctave
 |-
-|[[37/32]]
 |}

CompactStar at 09:12, 30 December 2023

2023-12-30T09:12:03Z

← Older revision		Revision as of 09:12, 30 December 2023
Line 22:		Line 22:
	\|-		\|-
	\|[[7/4]]		\|[[7/4]]
	\|m7		\|im7
	\|~~minor~~ seventh		\|inframinor seventh
	\|-		\|-
	\|[[11/8]]		\|[[11/8]]

CompactStar at 09:11, 30 December 2023

2023-12-30T09:11:58Z

← Older revision		Revision as of 09:11, 30 December 2023
Line 45:		Line 45:
	\|augmented fourth		\|augmented fourth
	\|-		\|-
	\|[[11/~~616~~]]		\|[[29/16]]
	\|an7		\|an7
	\|artoneutral seventh		\|artoneutral seventh
Line 53:		Line 53:
	\|infraoctave		\|infraoctave
	\|-		\|-
	\|		\|[[37/32]]
			\|UM2
			\|ultramajor second
			\|-
			\|[[41/32]]
			\|M3
			\|major third
			\|-
			\|[[47/32]]
			\|i5
			\|infrafifth
			\|-
			\|[[

	\|}		\|}

CompactStar: Quartertone-based names will be adopted, so neutral intervals are correctly expressed.

2023-12-30T08:54:27Z

Quartertone-based names will be adopted, so neutral intervals are correctly expressed.

← Older revision		Revision as of 08:54, 30 December 2023
Line 1:		Line 1:
	~~Indexed~~ interval notation is a notation for [[just intonation]] in which all intervals are represented by a normal interval classification combined with a ordinal number or index. An index of 1 is used for the simplest interval in an interval class (such as [[6/5]] for minor thirds), an index of 2 is used for the second-simplest, an index of 3 is used for the third-simplest, and so on.		WIP (the reason this is in userspace)

			Ordinal interval notation is a notation for [[just intonation]] in which all intervals are represented by a normal interval classification combined with an ordinal number.

	~~== Definition ==~~
	To get the classification for an interval, multiply the interval classes of the prime harmonics which it factors into, which are predefined as follows:		To get the classification for an interval, multiply the interval classes of the prime harmonics which it factors into, which are predefined as follows:
	{\|class="wikitable"		{\|class="wikitable"
Line 25:		Line 26:
	\|-		\|-
	\|[[11/8]]		\|[[11/8]]
	\|P4		\|U4
	\|~~perfect fourth~~		\|ultrafourth
	\|-		\|-
	\|[[13/8]]		\|[[13/8]]
	\|m6		\|an6
	\|~~minor~~ sixth		\|artoneutral sixth
	\|-		\|-
	\|[[17/16]]		\|[[17/16]]
Line 44:		Line 45:
	\|augmented fourth		\|augmented fourth
	\|-		\|-
	\|[[29/16]]		\|[[11/616]]
	\|m7		\|an7
	\|~~minor~~ seventh		\|artoneutral seventh
	\|-		\|-
	\|[[31/16]]		\|[[31/16]]
	\|P8		\|i8
	\|~~perfect octave~~		\|infraoctave
	\|-		\|-
	\|		\|
	\|}		\|}

CompactStar: CompactStar moved page User:CompactStar/Indexed interval notation to User:CompactStar/Ordinal interval notation

2023-12-30T08:50:04Z

CompactStar moved page User:CompactStar/Indexed interval notation to User:CompactStar/Ordinal interval notation

← Older revision	Revision as of 08:50, 30 December 2023
(No difference)

CompactStar at 08:49, 30 December 2023

2023-12-30T08:49:01Z

← Older revision		Revision as of 08:49, 30 December 2023
Line 1:		Line 1:
	~~'''Binary search~~ notation~~'''~~ is a notation for [[just intonation]] ~~devised~~ by [[~~User:CompactStar\|CompactStar~~]].		Indexed interval notation is a notation for [[just intonation]] in which all intervals are represented by a normal interval classification combined with a ordinal number or index. An index of 1 is used for the simplest interval in an interval class (such as [[6/5]] for minor thirds), an index of 2 is used for the second-simplest, an index of 3 is used for the third-simplest, and so on.

	~~Intervals are represented by a conventional interval category with a stack of lefts and rights (abbreviated as L and R) added before.~~ To get the ~~category of~~ an interval, multiply the ~~categories~~ of the prime harmonics which it factors into, which are predefined as follows:		== Definition ==
			To get the classification for an interval, multiply the interval classes of the prime harmonics which it factors into, which are predefined as follows:
	{\|class="wikitable"		{\|class="wikitable"
	\|-		\|-
	!Prime harmonic		!Prime harmonic
	!colspan="3"\|~~Notation~~		!colspan="2"\|Interval classification
	\|-		\|-
	\|[[2/1]]		\|[[2/1]]
	\|P8		\|P8
	\|perfect octave		\|perfect octave
	\|C
	\|-		\|-
	\|[[3/2]]		\|[[3/2]]
	\|P5		\|P5
	\|perfect ~~5th~~		\|perfect fifth
	\|G
	\|-		\|-
	\|[[5/4]]		\|[[5/4]]
	\|M3		\|M3
	\|major ~~3rd~~		\|major third
	\|E
	\|-		\|-
	\|[[7/4]]		\|[[7/4]]
	\|m7		\|m7
	\|minor ~~7th~~		\|minor seventh
	~~\|Bb~~
	\|-		\|-
	\|[[11/8]]		\|[[11/8]]
	\|P4		\|P4
	\|perfect ~~4th~~		\|perfect fourth
	\|F
	\|-		\|-
	\|[[13/8]]		\|[[13/8]]
	\|m6		\|m6
	\|minor ~~6th~~		\|minor sixth
	~~\|Ab~~
	\|-		\|-
	\|[[17/16]]		\|[[17/16]]
	\|m2		\|m2
	\|minor ~~2nd~~		\|minor second
	~~\|Db~~
	\|-		\|-
	\|[[19/16]]		\|[[19/16]]
	\|m3		\|m3
	\|minor ~~3rd~~		\|minor third
	~~\|Eb~~
	\|-		\|-
	\|[[23/16]]		\|[[23/16]]
	\|A4		\|A4
	\|augmented ~~4th~~		\|augmented fourth
	~~\|F#~~
	\|-		\|-
	\|[[29/16]]		\|[[29/16]]
	\|m7		\|m7
	\|minor ~~7th~~		\|minor seventh
	~~\|Bb~~
	\|-		\|-
	\|[[31/16]]		\|[[31/16]]
	\|P8		\|P8
	\|perfect octave		\|perfect octave
	\|C
	\|-		\|-
	\|~~[[37/32]]~~		\|
	~~\|M2~~
	~~\|major 2nd~~
	\|D
	\|-
	~~\|[[41/32]]~~
	~~\|M3~~
	~~\|major 3rd~~
	\|E
	\|-
	~~\|[[43/32]]~~
	~~\|P4~~
	~~\|perfect 4th~~
	\|F
	\|-
	~~\|[[47/32]]~~
	~~\|P5~~
	~~\|perfect 5th~~
	\|G
	\|-
	~~\|[[53/32]]~~
	~~\|M6~~
	~~\|major 6th~~
	\|A
	\|-
	~~\|[[61/32]]~~
	~~\|M7~~
	~~\|major 7th~~
	\|B
	\|-
	~~\|[[67/64]]~~
	~~\|m2~~
	~~\|minor 2nd~~
	~~\|Db~~
	\|-
	~~\|[[71/64]]~~
	~~\|M2~~
	~~\|major 2nd~~
	\|D
	\|-
	~~\|[[73/64]]~~
	~~\|M2~~
	~~\|major 2nd~~
	\|D
	\|-
	~~\|[[79/64]]~~
	~~\|M3~~
	~~\|major 3rd~~
	\|E
	\|-
	~~\|[[83/64]]~~
	~~\|P4~~
	~~\|perfect 4th~~
	\|F
	\|-
	~~\|[[89/64]]~~
	~~\|d5~~
	~~\|diminished 5th~~
	~~\|Gb~~
	\|-
	~~\|[[97/64]]~~
	~~\|P5~~
	~~\|perfect 5th~~
	\|G
	\|}		\|}
	The simplest (with respect to [[Tenney height]]) interval inside a category does not use any lefts or rights (or is "central"), for example [[6/5]] for minor 3rd. The simplest interval which is flatter than the central interval is left ([[7/6]] for minor 3rd), and the simplest interval which is sharper is right ([[11/9]] for minor 3rd). Then the simplest interval which is flatter than the left is leftleft, the simplest interval between left and central is leftright , the simplest interval which is between central and right is rightleft, and the simplest interval which is sharper than right is rightright. This process of bisection with lefts/rights can be continued infinitely to name all just intervals that are in a category. Interval arithmetic is preserved (e.g. M2 * M2 is always M3), however the lefts and rights do not combine like accidentals do.

← Older revision		Revision as of 03:23, 2 January 2024
Line 1:		Line 1:
	~~WIP (the reason this is in userspace)~~		#redirect [[/Lefts and rights notation/]]

	~~Ordinal interval notation is a notation for~~ [[~~just intonation]] in which all intervals are represented by a normal interval classification combined with an ordinal number.~~

	~~To get the classification for an interval, multiply the interval classes of the prime harmonics which it factors into, which are predefined as follows:~~
	~~{\|class="wikitable"~~
	\|-
	~~!Prime harmonic~~
	~~!colspan="2"\|Interval classification~~
	\|-
	~~\|[[2~~/~~1]]~~
	~~\|P8~~
	~~\|perfect octave~~
	\|-
	~~\|[[3/2]]~~
	~~\|P5~~
	~~\|perfect fifth~~
	\|-
	~~\|[[5/4]]~~
	~~\|M3~~
	~~\|major third~~
	\|-
	~~\|[[7/4]]~~
	~~\|m7~~
	~~\|minor seventh~~
	\|-
	~~\|[[11/8]]~~
	~~\|U4~~
	~~\|ultrafourth~~
	\|-
	~~\|[[13/8]]~~
	~~\|an6~~
	~~\|artoneutral sixth~~
	\|-
	~~\|[[17/16]]~~
	~~\|m2~~
	~~\|minor second~~
	\|-
	~~\|[[19/16]]~~
	~~\|m3~~
	~~\|minor third~~
	\|-
	~~\|[[23/16]]~~
	~~\|i5~~
	~~\|infrafifth~~
	\|-
	~~\|[[29/16]]~~
	~~\|m7~~
	~~\|minor seventh~~
	\|-
	~~\|[[31/16]]~~
	~~\|i8~~
	~~\|infraoctave~~
	\|-
	~~\|[[37/32]]~~
	~~\|UM2~~
	~~\|ultramajor second~~
	\|-
	~~\|[[41/32]]~~
	~~\|M3~~
	~~\|major third~~
	\|-
	~~\|[[47~~/32]]
	~~\|i5~~
	~~\|infrafifth~~
	\|}