Rectified hebrew: Difference between revisions
No edit summary |
Cleanup and +categories |
||
| Line 1: | Line 1: | ||
'''Rectified Hebrew''' is a 2.5.7.13 subgroup temperament | '''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. | ||
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). | 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. | ||
| 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. | 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. | ||
| Line 56: | Line 56: | ||
|} | |} | ||
== | == 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]] | |||