Rectified hebrew - Revision history

FloraC: - parent category

2025-04-28T14:37:18Z

- parent category

← Older revision		Revision as of 14:37, 28 April 2025
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	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
	!Generator		! Generator<br>steps
	steps		! Interval<br>(2.5.7.13 subgroup)
	!Interval
	(2.5.7.13 subgroup)
	\|-		\|-
	\|0		\| 0
	\|[[1/1]]		\| [[1/1]]
	\|-		\|-
	\|1		\| 1
	\|[[26/25]]		\| [[26/25]]
	\|-		\|-
	\|2		\| 2
	\|[[14/13]]		\| [[14/13]]
	\|-		\|-
	\|3		\| 3
	\|[[28/25]]		\| [[28/25]]
	\|-		\|-
	\|4		\| 4
	\|[[65/56]]		\| [[65/56]]
	\|-		\|-
	\|6		\| 6
	\|[[5/4]]		\| [[5/4]]
	\|-		\|-
	\|7		\| 7
	\|[[13/10]]		\| [[13/10]]
	\|-		\|-
	\|9		\| 9
	\|[[7/5]]		\| [[7/5]]
	\|-		\|-
	\|11		\| 11
	\|[[98/65]]		\| [[98/65]]
	\|-		\|-
	\|13		\| 13
	\|[[13/8]]		\| [[13/8]]
	\|-		\|-
	\|15		\| 15
	\|[[7/4]]		\| [[7/4]]
	\|}		\|}

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	* [http://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar]		* [http://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar]

	[[Category:~~Temperaments~~]]		[[Category:Rectified hebrew\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
			[[Category:Subgroup temperaments]]
	[[Category:Hemimean clan]]		[[Category:Hemimean clan]]
	[[Category:Didacus]]		[[Category:Didacus]]

Lériendil at 23:40, 19 April 2025

2025-04-19T23:40:42Z

← Older revision		Revision as of 23:40, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
			[[Category:Rank-2 temperaments]]
	[[Category:Hemimean clan]]		[[Category:Hemimean clan]]
	[[Category:Didacus]]		[[Category:Didacus]]

BudjarnLambeth: added links

2025-04-13T10:31:11Z

added links

← Older revision		Revision as of 10:31, 13 April 2025
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	'''Rectified Hebrew''' is a 2.5.7.13 subgroup temperament. Being a weak extension of [[didacus]], it is notable due to its ability to reach several simple intervals in just a few ~~generators~~.		'''Rectified Hebrew''' is a 2.5.7.13 [[subgroup]] temperament. Being a [[weak extension]] of [[didacus]], it is notable due to its ability to reach several simple intervals in just a few [[generator]]s.

	Its name derives from a calendar layout by the same name.		Its name derives from a calendar layout by the same name.

FloraC: FloraC moved page Rectified Hebrew to Rectified hebrew: All temperaments go lowercase

2023-06-29T05:47:11Z

FloraC moved page Rectified Hebrew to Rectified hebrew: All temperaments go lowercase

← Older revision	Revision as of 05:47, 29 June 2023
(No difference)

Eliora: /* Interval chain */

2022-11-13T02:36:52Z

Interval chain

← Older revision		Revision as of 02:36, 13 November 2022
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	\|-		\|-
	\|0		\|0
	\|1/1		\|[[1/1]]
	\|-		\|-
	\|1		\|1
	\|26/25		\|[[26/25]]
	\|-		\|-
	\|2		\|2
	\|14/13		\|[[14/13]]
			\|-
			\|3
			\|[[28/25]]
			\|-
			\|4
			\|[[65/56]]
	\|-		\|-
	\|6		\|6
	\|5/4		\|[[5/4]]
	\|-		\|-
	\|7		\|7
	\|13/10		\|[[13/10]]
	\|-		\|-
	\|9		\|9
	\|7/5		\|[[7/5]]
	\|-		\|-
	\|11		\|11
	\|98/65		\|[[98/65]]
	\|-		\|-
	\|13		\|13
	\|13/8		\|[[13/8]]
	\|-		\|-
	\|15		\|15
	\|7/4		\|[[7/4]]
	\|}		\|}

Eliora: /* Specific chords and intervals */

2022-10-06T15:43:37Z

Specific chords and intervals

← Older revision		Revision as of 15:43, 6 October 2022
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	In the original Hebrew calendar, years number 3, 6, 8, 11, 14, 17, and 19 within a 19-year pattern (makhzor (מחזור), plural:makhzorim) are leap. When converted to [[19edo]], this results in [[5L 2s]] mode, and simply the diatonic major scale. Following this logic, a temperament can be constructed for the Rectified Hebrew calendar (see below), containing 130 notes of the 353edo scale, which represents 353 years of the cycle. Hebrew[130] scale has 334\353 as its generator, which is a supermajor seventh, or alternately, 19\353, about a third-tone, since inverting the generator has no effect on the scale.		In the original Hebrew calendar, years number 3, 6, 8, 11, 14, 17, and 19 within a 19-year pattern (makhzor (מחזור), plural:makhzorim) are leap. When converted to [[19edo]], this results in [[5L 2s]] mode, and simply the diatonic major scale. Following this logic, a temperament can be constructed for the Rectified Hebrew calendar (see below), containing 130 notes of the 353edo scale, which represents 353 years of the cycle. Hebrew[130] scale has 334\353 as its generator, which is a supermajor seventh, or alternately, 19\353, about a third-tone, since inverting the generator has no effect on the scale.

	Rectified Hebrew temperament is a 13-limit extension of the didacus. In the 13-limit, the it tempers out [[3136/3125]], [[4394/4375]], [[10985/10976]], and [[1968512/1953125]]. 18L 1s of Rectified Hebrew gives 19edo a unique stretch: 6 generators correspond to [[5/4]], 13 correspond to [[13/8]], and 15 correspond to [[7/4]]. When measured relative to the generator~~<sup>[which?]</sup>~~, the error is less than 1 in 5000~~<!-- Why this measure? -->~~. 5 instances of 5/4 and two of 7/4 both amount to 30 generators (570 steps). Tempering of 4394/4375 means that a stack of three 13/10s (7 generators) is equated with 35/32, octave-reduced, and also splits 14/13 (2 generators) into two parts each corresponding to 26/25, the generator. Tempering of 10985/10976 means that a stack of three 14/13's are equated with 5/4.		Rectified Hebrew temperament is a 13-limit extension of the didacus. In the 13-limit, the it tempers out [[3136/3125]], [[4394/4375]], [[10985/10976]], and [[1968512/1953125]]. 18L 1s of Rectified Hebrew gives 19edo a unique stretch: 6 generators correspond to [[5/4]], 13 correspond to [[13/8]], and 15 correspond to [[7/4]]. When measured relative to the generator 19\353, the error is less than 1 in 5000. 5 instances of 5/4 and two of 7/4 both amount to 30 generators (570 steps). Tempering of 4394/4375 means that a stack of three 13/10s (7 generators) is equated with 35/32, octave-reduced, and also splits 14/13 (2 generators) into two parts each corresponding to 26/25, the generator. Tempering of 10985/10976 means that a stack of three 14/13's are equated with 5/4.

	The 11-step perfect fifth in this scale becomes 209\353, and it corresponds to 98/65, which is sharp of 3/2 by 196/195.		The 11-step perfect fifth in this scale becomes 209\353, and it corresponds to 98/65, which is sharp of 3/2 by 196/195.
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	The number 353 in this version of the Hebrew calendar must not be confused with the number of days in ''shanah chaserah'' (שנה חסרה)'','' the deficient year.		The number 353 in this version of the Hebrew calendar must not be confused with the number of days in ''shanah chaserah'' (שנה חסרה)'','' the deficient year.

			169/168 amounts to 3 steps, which is the L step of the full 93L 37s rectified Hebrew scale.

	=== Specific chords and intervals ===		=== Specific chords and intervals ===
	~~If we add~~ a ~~mapping for harmonic 3~~, the ~~353bbbbb val offers~~ the following ~~resolution sequence~~: 13/8 ~~D4/3~~ - D7 - T53, or in steps: 247-0-38-152 - 209-323-57-152 - 0-114-209, or 0-95-209. This has a very pleasant sound, with 13/8 acting as a "doubled resolvant" or "resolution into resolution". ~~169/168 amounts to 3 steps~~, ~~which is the L step~~ of the ~~full 93L 37s rectified Hebrew scale~~.		Rectified hebrew supports the tridecimal neutral seventh chords and a cadence invented by [[Eliora]].

			The tridecimal neutral seventh chord, noted as 13/8 N7, is represented in 353edo with steps 114 95 106, and its inversions respectively: 13/8 N65: 95 106 38, 13/8 N43: 106 38 114, 13/8 N42 (or 13/8 N2): 38 114 95. 114 steps is 6 generators, 95 steps is 5 generators, 38 steps is 2 generators, and 106 is closure of 13/8 against the octave, which consists of 5 generators with an octave residue to 19 generators.

			The tridecimal neutral cadence is the following: 13/8 N43 - D7 - T53, or in 353edo steps: 247-0-38-152 - 209-323-57-152 - 0-114-209, or 0-95-209. This has a very pleasant sound, with 13/8 acting as a "doubled resolvant" or "resolution into resolution".

			In regular temperament theory of 353edo, one can think of it as the 353bbbbb val, where 209\353 fifth represents 3/2.

			=== Miscellaneous properties ===
	Just as a large amount of [[12edo]] music can be played consistently in 19edo, it can also be played consistently in the 18L 1s subset of Rectified Hebrew.		Just as a large amount of [[12edo]] music can be played consistently in 19edo, it can also be played consistently in the 18L 1s subset of Rectified Hebrew.

FloraC: Cleanup and +categories

2022-10-06T05:42:38Z

Cleanup and +categories

← Older revision		Revision as of 05:42, 6 October 2022
Line 1:		Line 1:
	'''Rectified Hebrew''' is a 2.5.7.13 subgroup temperament~~, that while it is~~ a weak extension of didacus ~~from a formal perspective~~, is notable due to its ability to reach several ~~low-complexity~~ intervals in just ~~one circle of~~ generators.		'''Rectified Hebrew''' is a 2.5.7.13 subgroup temperament. Being a weak extension of [[didacus]], it is notable due to its ability to reach several simple intervals in just a few generators.

	~~It comes~~ from a calendar layout by the same name.		Its name derives from a calendar layout by the same name.

	== Theory ==		== Theory ==

	=== 353edo-specific theory ===		=== 353edo-specific theory ===
	In the original Hebrew calendar, years number 3, 6, 8, 11, 14, 17, and 19 within a 19-year pattern (makhzor (מחזור), plural:makhzorim) are leap. When converted to [[19edo]], this results in [[5L 2s]] mode, and simply the diatonic major scale. Following this logic, a temperament can be constructed for the Rectified Hebrew calendar (see below), containing 130 notes of the 353edo scale, which represents 353 years of the cycle. Hebrew[130] scale has 334\353 as its generator, which is a supermajor seventh, or alternately, 19\353, about a third-tone, since inverting the generator has no effect on the scale.		In the original Hebrew calendar, years number 3, 6, 8, 11, 14, 17, and 19 within a 19-year pattern (makhzor (מחזור), plural:makhzorim) are leap. When converted to [[19edo]], this results in [[5L 2s]] mode, and simply the diatonic major scale. Following this logic, a temperament can be constructed for the Rectified Hebrew calendar (see below), containing 130 notes of the 353edo scale, which represents 353 years of the cycle. Hebrew[130] scale has 334\353 as its generator, which is a supermajor seventh, or alternately, 19\353, about a third-tone, since inverting the generator has no effect on the scale.

	Rectified Hebrew temperament is a 13-limit extension of the didacus. In the 13-limit, the it tempers out [[3136/3125]], [[4394/4375]], [[10985/10976]], and [[1968512/1953125]]. 18L 1s of Rectified Hebrew gives 19edo a unique stretch: 6 generators correspond to [[5/4]], 13 correspond to [[13/8]], and 15 correspond to [[7/4]]. When measured relative to the generator, the error is less than 1 in 5000. 5 instances of 5/4 and two of 7/4 both amount to 30 generators (570 steps). ~~Temperance~~ of 4394/4375 means that a stack of three 13/10s (7 generators) is equated with 35/32, octave-reduced, and also splits 14/13 (2 generators) into two parts each corresponding to 26/25, the generator. ~~Temperance~~ of 10985/10976 means that three 14/~~13s~~ are equated with 5/4.		Rectified Hebrew temperament is a 13-limit extension of the didacus. In the 13-limit, the it tempers out [[3136/3125]], [[4394/4375]], [[10985/10976]], and [[1968512/1953125]]. 18L 1s of Rectified Hebrew gives 19edo a unique stretch: 6 generators correspond to [[5/4]], 13 correspond to [[13/8]], and 15 correspond to [[7/4]]. When measured relative to the generator<sup>[which?]</sup>, the error is less than 1 in 5000<!-- Why this measure? -->. 5 instances of 5/4 and two of 7/4 both amount to 30 generators (570 steps). Tempering of 4394/4375 means that a stack of three 13/10s (7 generators) is equated with 35/32, octave-reduced, and also splits 14/13 (2 generators) into two parts each corresponding to 26/25, the generator. Tempering of 10985/10976 means that a stack of three 14/13's are equated with 5/4.

	The 11-step perfect fifth in this scale becomes 209\353, and it corresponds to 98/65, which is sharp of 3/2 by 196/195.		The 11-step perfect fifth in this scale becomes 209\353, and it corresponds to 98/65, which is sharp of 3/2 by 196/195.
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	The number 353 in this version of the Hebrew calendar must not be confused with the number of days in ''shanah chaserah'' (שנה חסרה)'','' the deficient year.		The number 353 in this version of the Hebrew calendar must not be confused with the number of days in ''shanah chaserah'' (שנה חסרה)'','' the deficient year.
	===Specific chords and intervals===
	353bbbbb val offers the following resolution sequence:13/8 D4/3 - D7 - T53, or in steps: 247-0-38-152 - 209-323-57-152 - 0-114-209, or 0-95-209. This has a very pleasant sound, with 13/8 acting as a "doubled resolvant" or "resolution into resolution". 169/168 amounts to 3 steps, which is the L step of the full 93L 37s rectified Hebrew scale.		=== Specific chords and intervals ===
			If we add a mapping for harmonic 3, the 353bbbbb val offers the following resolution sequence: 13/8 D4/3 - D7 - T53, or in steps: 247-0-38-152 - 209-323-57-152 - 0-114-209, or 0-95-209. This has a very pleasant sound, with 13/8 acting as a "doubled resolvant" or "resolution into resolution". 169/168 amounts to 3 steps, which is the L step of the full 93L 37s rectified Hebrew scale.

	Just as a large amount of [[12edo]] music can be played consistently in 19edo, it can also be played consistently in the 18L 1s subset of Rectified Hebrew.		Just as a large amount of [[12edo]] music can be played consistently in 19edo, it can also be played consistently in the 18L 1s subset of Rectified Hebrew.
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	\|}		\|}

	==~~Links~~==		== External links ==
	*[http://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar]		* [http://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar]

			[[Category:Temperaments]]
			[[Category:Hemimean clan]]
			[[Category:Didacus]]

Eliora at 23:05, 5 October 2022

2022-10-05T23:05:44Z

@@ Line 19: / Line 19: @@
 Just as a large amount of [[12edo]] music can be played consistently in 19edo, it can also be played consistently in the 18L 1s subset of Rectified Hebrew.
 ==Links==
 *[http://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar]

Eliora: this needs to be on its own page rather than on 353edo's

2022-10-05T23:02:32Z

this needs to be on its own page rather than on 353edo's

New page

'''Rectified Hebrew''' is a 2.5.7.13 subgroup temperament, that while it is a weak extension of didacus from a formal perspective, is notable due to its ability to reach several low-complexity intervals in just one circle of generators.

It comes from a calendar layout by the same name.

== Theory ==

=== 353edo-specific theory ===
In the original Hebrew calendar, years number 3, 6, 8, 11, 14, 17, and 19 within a 19-year pattern (makhzor (מחזור), plural:makhzorim) are leap. When converted to [[19edo]], this results in [[5L 2s]] mode, and simply the diatonic major scale. Following this logic, a temperament can be constructed for the Rectified Hebrew calendar (see below), containing 130 notes of the 353edo scale, which represents 353 years of the cycle. Hebrew[130] scale has 334\353 as its generator, which is a supermajor seventh, or alternately, 19\353, about a third-tone, since inverting the generator has no effect on the scale.

Rectified Hebrew temperament is a 13-limit extension of the didacus. In the 13-limit, the it tempers out [[3136/3125]], [[4394/4375]], [[10985/10976]], and [[1968512/1953125]]. 18L 1s of Rectified Hebrew gives 19edo a unique stretch: 6 generators correspond to [[5/4]], 13 correspond to [[13/8]], and 15 correspond to [[7/4]]. When measured relative to the generator, the error is less than 1 in 5000. 5 instances of 5/4 and two of 7/4 both amount to 30 generators (570 steps). Temperance of 4394/4375 means that a stack of three 13/10s (7 generators) is equated with 35/32, octave-reduced, and also splits 14/13 (2 generators) into two parts each corresponding to 26/25, the generator. Temperance of 10985/10976 means that three 14/13s are equated with 5/4.

The 11-step perfect fifth in this scale becomes 209\353, and it corresponds to 98/65, which is sharp of 3/2 by 196/195.

In addition, every sub-pattern in a 19-note generator is actually a Hebrew makhzor, that is a mini-19edo on its own, until it is truncated to an 11-note pattern. Just as the original calendar reform consists of 18 makhzorim with 1 hendecaeteris, Hebrew[130] scale consists of a stack of naively 18 "major scales" finished with one 11-edo tetratonic.

The number 353 in this version of the Hebrew calendar must not be confused with the number of days in ''shanah chaserah'' (שנה חסרה)'','' the deficient year.
===Specific chords and intervals===
353bbbbb val offers the following resolution sequence:13/8 D4/3 - D7 - T53, or in steps: 247-0-38-152 - 209-323-57-152 - 0-114-209, or 0-95-209. This has a very pleasant sound, with 13/8 acting as a "doubled resolvant" or "resolution into resolution". 169/168 amounts to 3 steps, which is the L step of the full 93L 37s rectified Hebrew scale.

Just as a large amount of [[12edo]] music can be played consistently in 19edo, it can also be played consistently in the 18L 1s subset of Rectified Hebrew.
==Links==
*[http://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar]