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| === Relation to a calendar reform === | | === Relation to a calendar reform === |
| 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.
| | ''Main article: [[Rectified Hebrew]]'' |
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| 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.
| | 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. |
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| 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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| It's possible to use superpyth fifth of Rectified Hebrew fifth, 209\353, as a generator. In this case, 76 & 353 temperament is obtained. In the 2.5.7.13 subgroup, this results in the fifth being equal to 98/65 and the comma basis of 10985/10976, {{Monzo|-103 0 -38 51 0 13}}. | | It's possible to use superpyth fifth of Rectified Hebrew fifth, 209\353, as a generator. In this case, 76 & 353 temperament is obtained. In the 2.5.7.13 subgroup, this results in the fifth being equal to 98/65 and the comma basis of 10985/10976, {{Monzo|-103 0 -38 51 0 13}}. |
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| === Specific chords and intervals ===
| | 353edo also supports apparatus temperaments, and marvo and zarvo. |
| 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.
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| 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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| == Table of intervals == | | == Table of intervals == |