1803edo: Difference between revisions
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== Theory == | == Theory == | ||
{{harmonics in equal|1803|columns=10}} | {{harmonics in equal|1803|columns=10}} | ||
It is consistent on the 2.3.7.13.17.19.23.29 subgroup, that is no 5-s, no 11-s 29-limit. | |||
In the 2.19.23.29 subgroup, 1803edo tempers out 2476099/2475904, and supports the corresponding rank 3 temperament eliminating this comma. In the 13 limit, 1803edo tempers out 2080/2079 and 4225/4224. In the 7-limit, it tempers out 420175/419904. | In the 2.19.23.29 subgroup, 1803edo tempers out 2476099/2475904, and supports the corresponding rank 3 temperament eliminating this comma. In the 13 limit, 1803edo tempers out 2080/2079 and 4225/4224. In the 7-limit, it tempers out 420175/419904. | ||
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Since 1803 years is equal to 94076 weeks, it produces a cycle where 94076 mod 1803 = 320 years are leap, and using the maximal evenness method of finding rank two temperaments, the associated rank two temperament is 320 & 1803, which if it had a name would be ''hectosaros leap week''. The generator for such a temperament is 524\1803, a neutral third. | Since 1803 years is equal to 94076 weeks, it produces a cycle where 94076 mod 1803 = 320 years are leap, and using the maximal evenness method of finding rank two temperaments, the associated rank two temperament is 320 & 1803, which if it had a name would be ''hectosaros leap week''. The generator for such a temperament is 524\1803, a neutral third. | ||
Since 320edo is consistent in the 19-limit, hectosaros leap week temperament is defined for the 2.3.7.13.17.19 subgroup. The resulting comma basis is 10081799/10077696, 39337984/39328497, 10754912/10744731, and 480024727/480020256. In addition, the generator is mapped to 6144/3757, which rounds to 524\1803, and is therefore consistent. | |||
A simple scale such a temperament it produces is [[3L 4s]], which is also described in the Solar Calendar Leap Rules page as 231 293 231 293 231 293 231. In addition, if one were to rearrange the steps (or raise the 4th degree by 62\1803) so they instead produce 231 293 '''293 231''' 231 293 231, the resulting scale is [[Maqam Sikah]]. | A simple scale such a temperament it produces is [[3L 4s]], which is also described in the Solar Calendar Leap Rules page as 231 293 231 293 231 293 231. In addition, if one were to rearrange the steps (or raise the 4th degree by 62\1803) so they instead produce 231 293 '''293 231''' 231 293 231, the resulting scale is [[Maqam Sikah]]. | ||
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Hectosaros Lunisolar is defined as 664 & 1803 and is generated by 1078\1803 interval measuring about 717 cents, which puts it in the far ultrapyth range, close to the sharp fifth of [[5edo]]. A simple scale would be an almost equipentatonic scale which results in very hard diatonic scale. | Hectosaros Lunisolar is defined as 664 & 1803 and is generated by 1078\1803 interval measuring about 717 cents, which puts it in the far ultrapyth range, close to the sharp fifth of [[5edo]]. A simple scale would be an almost equipentatonic scale which results in very hard diatonic scale. | ||
== Regular temperament properties == | |||
=== Rank-2 temperaments by generator === | |||
{| class="wikitable center-all left-5" | |||
!Periods | |||
per octave | |||
!Generator | |||
(reduced) | |||
!Cents | |||
(reduced) | |||
!Associated | |||
ratio | |||
!Temperaments | |||
|- | |||
|1 | |||
|524\1803 | |||
|348.752 | |||
|6144/3757 | |||
|[[Hectosaros leap week]] | |||
|} | |||
== Scales == | == Scales == | ||
* HectosarosLeapWeek[7], a MOS of type [[3L 4s]] (mosh) - 231 293 231 293 231 293 231 | * HectosarosLeapWeek[7], a MOS of type [[3L 4s]] (mosh) - 231 293 231 293 231 293 231 | ||
* Hectosaros Maqam Sikah, a MODMOS of type [[3L 4s]] (mosh) - 231 293 293 231 231 293 231 | * Hectosaros Maqam Sikah, a MODMOS of type [[3L 4s]] (mosh) - 231 293 293 231 231 293 231 | ||
== Links == | == Links == | ||
* Wikipedia Contributors, [[wikipedia:Saros (astronomy)|Saros (astronomy)]]. | * Wikipedia Contributors, [[wikipedia:Saros (astronomy)|Saros (astronomy)]]. | ||