User:CompactStar/Lefts and rights notation - Revision history

CompactStar at 04:00, 2 January 2024

2024-01-02T04:00:15Z

← Older revision		Revision as of 04:00, 2 January 2024
Line 107:		Line 107:
	* The rightright (RR) interval is the simplest which is sharper than the right interval. For minor thirds: [[11/9]]		* The rightright (RR) interval is the simplest which is sharper than the right interval. For minor thirds: [[11/9]]
	And then using 3 lefts and rights:		And then using 3 lefts and rights:
	* The leftleftleft (LLL) interval is the simplest which is flatter than the leftleft interval. ~~(have not found the LLLm3 yet)~~		* The leftleftleft (LLL) interval is the simplest which is flatter than the leftleft interval.
	* The leftleftright (LLR) interval is the simplest which is between the leftleft interval and the left interval. ~~For minor thirds: [[43/37]]~~		* The leftleftright (LLR) interval is the simplest which is between the leftleft interval and the left interval.
	* The leftrightleft (LRL) interval is the simplest which is between the left interval and the leftright interval. For minor thirds: [[20/17]]		* The leftrightleft (LRL) interval is the simplest which is between the left interval and the leftright interval. For minor thirds: [[20/17]]
	* The leftrightright (LRR) interval is the simplest which is between the leftright interval and the Pythagorean interval. For minor thirds: [[77/65]]		* The leftrightright (LRR) interval is the simplest which is between the leftright interval and the Pythagorean interval. For minor thirds: [[77/65]]
	* The rightleftleft (RLL) interval is the simplest which is between the Pythagorean interval and the rightleft interval. For minor thirds: [[51/43]]		* The rightleftleft (RLL) interval is the simplest which is between the Pythagorean interval and the rightleft interval. For minor thirds: [[51/43]]
	* The rightleftright (RLR) interval is the simplest which is between the rightleft and the right interval. ~~For minor thirds: [[25/21]]~~		* The rightleftright (RLR) interval is the simplest which is between the rightleft and the right interval.
	* The rightrightleft (RRL) interval is the simplest which is between the right interval and the rightright interval. For minor thirds: [[17/14]]		* The rightrightleft (RRL) interval is the simplest which is between the right interval and the rightright interval. For minor thirds: [[17/14]]
	* The rightrightright (RRR) interval is the simplest which is sharper than the rightright interval. For minor thirds: [[17/14]]		* The rightrightright (RRR) interval is the simplest which is sharper than the rightright interval. For minor thirds: [[38/31]]

	And so on. This sort of binary search can be applied for an arbitrary number of lefts and rights to name all just intervals in a category.		And so on. This sort of binary search can be applied for an arbitrary number of lefts and rights to name all just intervals in a category.

CompactStar at 03:58, 2 January 2024

2024-01-02T03:58:25Z

← Older revision		Revision as of 03:58, 2 January 2024
Line 102:		Line 102:

	Pythagorean intervals do not use any lefts or rights. The left (L) interval in a given category is the simplest (with respect to [[Tenney height]]) interval which is flatter than the Pythagorean version. For example, the leftminor third is [[7/6]]. Similarly, the right (R) interval in a category is the simplest one that is sharper than the Pythagorean version (for minor thirds this is [[6/5]]). After this, the types split up into 4 using 2 lefts and rights:		Pythagorean intervals do not use any lefts or rights. The left (L) interval in a given category is the simplest (with respect to [[Tenney height]]) interval which is flatter than the Pythagorean version. For example, the leftminor third is [[7/6]]. Similarly, the right (R) interval in a category is the simplest one that is sharper than the Pythagorean version (for minor thirds this is [[6/5]]). After this, the types split up into 4 using 2 lefts and rights:
	* The leftleft (LL) interval is the simplest which is flatter than the left interval. For minor thirds: [[36/31]]		* The leftleft (LL) interval is the simplest which is flatter than the left interval. For minor thirds: [[43/37]]
	* The leftright (LR) interval is the simplest which is between the left interval and the Pythagorean interval. For minor thirds: [[13/11]]		* The leftright (LR) interval is the simplest which is between the left interval and the Pythagorean interval. For minor thirds: [[13/11]]
	* The rightleft (RL) interval is the simplest which is between the Pythagorean interval and the right interval. For minor thirds: [[19/16]]		* The rightleft (RL) interval is the simplest which is between the Pythagorean interval and the right interval. For minor thirds: [[19/16]]
	* The rightright (RR) interval is the simplest which is sharper than the right interval. For minor thirds: [[11/9]]		* The rightright (RR) interval is the simplest which is sharper than the right interval. For minor thirds: [[11/9]]
	And then using 3 lefts and rights:		And then using 3 lefts and rights:
			* The leftleftleft (LLL) interval is the simplest which is flatter than the leftleft interval. (have not found the LLLm3 yet)
			* The leftleftright (LLR) interval is the simplest which is between the leftleft interval and the left interval. For minor thirds: [[43/37]]
			* The leftrightleft (LRL) interval is the simplest which is between the left interval and the leftright interval. For minor thirds: [[20/17]]
			* The leftrightright (LRR) interval is the simplest which is between the leftright interval and the Pythagorean interval. For minor thirds: [[77/65]]
			* The rightleftleft (RLL) interval is the simplest which is between the Pythagorean interval and the rightleft interval. For minor thirds: [[51/43]]
			* The rightleftright (RLR) interval is the simplest which is between the rightleft and the right interval. For minor thirds: [[25/21]]
			* The rightrightleft (RRL) interval is the simplest which is between the right interval and the rightright interval. For minor thirds: [[17/14]]
			* The rightrightright (RRR) interval is the simplest which is sharper than the rightright interval. For minor thirds: [[17/14]]

			And so on. This sort of binary search can be applied for an arbitrary number of lefts and rights to name all just intervals in a category.

CompactStar at 03:48, 2 January 2024

2024-01-02T03:48:44Z

← Older revision		Revision as of 03:48, 2 January 2024
Line 8:		Line 8:
	\|-		\|-
	!Prime harmonic		!Prime harmonic
	!colspan="3"\|~~Notation~~		!colspan="3"\|Category
	\|-		\|-
	\|[[2/1]]		\|[[2/1]]
Line 100:		Line 100:
	\|B		\|B
	\|}		\|}

			Pythagorean intervals do not use any lefts or rights. The left (L) interval in a given category is the simplest (with respect to [[Tenney height]]) interval which is flatter than the Pythagorean version. For example, the leftminor third is [[7/6]]. Similarly, the right (R) interval in a category is the simplest one that is sharper than the Pythagorean version (for minor thirds this is [[6/5]]). After this, the types split up into 4 using 2 lefts and rights:
			* The leftleft (LL) interval is the simplest which is flatter than the left interval. For minor thirds: [[36/31]]
			* The leftright (LR) interval is the simplest which is between the left interval and the Pythagorean interval. For minor thirds: [[13/11]]
			* The rightleft (RL) interval is the simplest which is between the Pythagorean interval and the right interval. For minor thirds: [[19/16]]
			* The rightright (RR) interval is the simplest which is sharper than the right interval. For minor thirds: [[11/9]]
			And then using 3 lefts and rights:

CompactStar at 03:40, 2 January 2024

2024-01-02T03:40:25Z

@@ Line 1: / Line 1: @@
 WIP (the reason this is in userspace)
-Lefts and rights notation is a notation for [[just intonation]] developed by [[User:CompactStar|CompactStar]]. It is a combination of Pythagorean notation and a sequence of lefts (L) and rights (R) that are prepended to a Pythagorean classification based on a {{w|binary search}} to name all non-Pythagorean intervals.
+Lefts and rights notation is a notation for [[just intonation]] developed by [[User:CompactStar|CompactStar]]. It is a combination of Pythagorean notation and a sequence of lefts and rights which is based on a {{w|binary search}}.
-In order to map all intervals into 3-limit notation, each prime harmonic is mapped to
+== Definition ==

CompactStar at 03:30, 2 January 2024

2024-01-02T03:30:03Z

← Older revision		Revision as of 03:30, 2 January 2024
Line 1:		Line 1:
	WIP (the reason this is in userspace)		WIP (the reason this is in userspace)

	Lefts and rights notation is a notation for [[just intonation]] developed by [[User:CompactStar\|CompactStar]]. It is a combination of Pythagorean notation and a sequence of lefts (L) and rights (R) that are ~~added~~ to a Pythagorean classification based on a {{w\|binary search}} to name all non-Pythagorean intervals.		Lefts and rights notation is a notation for [[just intonation]] developed by [[User:CompactStar\|CompactStar]]. It is a combination of Pythagorean notation and a sequence of lefts (L) and rights (R) that are prepended to a Pythagorean classification based on a {{w\|binary search}} to name all non-Pythagorean intervals.

	In order to map all intervals into 3-limit notation, each prime harmonic is mapped to		In order to map all intervals into 3-limit notation, each prime harmonic is mapped to

CompactStar at 03:29, 2 January 2024

2024-01-02T03:29:54Z

@@ Line 1: / Line 1: @@
 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.
+Lefts and rights notation is a notation for [[just intonation]] developed by [[User:CompactStar|CompactStar]]. It is a combination of Pythagorean notation and a sequence of lefts (L) and rights (R) that are added to a Pythagorean classification based on a {{w|binary search}} to name all non-Pythagorean intervals.
-To get the classification for an interval, multiply the interval classes of the prime harmonics which it factors into, which are predefined as follows:
+In order to map all intervals into 3-limit notation, each prime harmonic is mapped to

CompactStar at 03:23, 2 January 2024

2024-01-02T03:23:43Z

← Older revision	Revision as of 03:23, 2 January 2024
Line 1:	Line 1:
		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.

		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: Blanked the page

2024-01-02T03:23:11Z

Blanked the page

← Older revision		Revision as of 03:23, 2 January 2024
Line 1:		Line 1:
	~~#REDIRECT [[User:CompactStar/Ordinal interval notation]]~~

CompactStar: Changed redirect target from User:CompactStar/Indexed interval notation to User:CompactStar/Ordinal interval notation

2023-12-30T08:50:31Z

Changed redirect target from User:CompactStar/Indexed interval notation to User:CompactStar/Ordinal interval notation

← Older revision		Revision as of 08:50, 30 December 2023
Line 1:		Line 1:
	#REDIRECT [[User:CompactStar/~~Indexed~~ interval notation]]		#REDIRECT [[User:CompactStar/Ordinal interval notation]]

CompactStar: CompactStar moved page User:CompactStar/Lefts and rights notation to User:CompactStar/Indexed interval notation over redirect: Can't decide between these two variants of it

2023-12-01T23:48:34Z

CompactStar moved page User:CompactStar/Lefts and rights notation to User:CompactStar/Indexed interval notation over redirect: Can't decide between these two variants of it

New page

#REDIRECT [[User:CompactStar/Indexed interval notation]]