Rectified hebrew: Difference between revisions

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'''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 [[generator]]s.

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

Its name derives 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.

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.

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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.

~~===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.

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

=== Specific chords and intervals ===

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.

==~~Links~~==

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

== Interval chain ==

{| class="wikitable"

|+

! Generator<br>steps

! Interval<br>(2.5.7.13 subgroup)

|-

| 0

| [[1/1]]

|-

| 1

| [[26/25]]

|-

| 2

| [[14/13]]

|-

| 3

| [[28/25]]

|-

| 4

| [[65/56]]

|-

| 6

| [[5/4]]

|-

| 7

| [[13/10]]

|-

| 9

| [[7/5]]

|-

| 11

| [[98/65]]

|-

| 13

| [[13/8]]

|-

| 15

| [[7/4]]

|}

== External links ==

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

[[Category:Rectified hebrew| ]]

[[Category:Rank-2 temperaments]]

[[Category:Subgroup temperaments]]

[[Category:Hemimean clan]]

[[Category:Didacus]]

@@ 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 [[generator]]s.
-It comes from a calendar layout by the same name.
+Its name derives 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.
+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.
@@ Line 15: / Line 14: @@
 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===
-bbbbb 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.
+/168 amounts to 3 steps, which is the L step of the full 93L 37s rectified Hebrew scale.
+=== Specific chords and intervals ===
+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.
-==Links==
-*[http://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar]
+== Interval chain ==
+{| class="wikitable"
+|+
+! Generator<br>steps
+! Interval<br>(2.5.7.13 subgroup)
+|-
+| 0
+| [[1/1]]
+|-
+| 1
+| [[26/25]]
+|-
+| 2
+| [[14/13]]
+|-
+| 3
+| [[28/25]]
+|-
+| 4
+| [[65/56]]
+|-
+| 6
+| [[5/4]]
+|-
+| 7
+| [[13/10]]
+|-
+| 9
+| [[7/5]]
+|-
+| 11
+| [[98/65]]
+|-
+| 13
+| [[13/8]]
+|-
+| 15
+| [[7/4]]
+|}
+== External links ==
+* [http://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar]
+[[Category:Rectified hebrew| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
+[[Category:Subgroup temperaments]]
+[[Category:Hemimean clan]]
+[[Category:Didacus]]