94edo: Difference between revisions
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The list of 23-limit commas it tempers out is huge, but it's worth noting that it tempers out [[32805/32768]] and is thus a [[schismatic]] system, that it tempers out [[225/224]] and [[385/384]] and so is a [[marvel]] system, and that it also tempers out [[3125/3087]], [[4000/3969]], [[5120/5103]] and [[540/539]]. It provides the [[optimal patent val]] for the rank five temperament tempering out [[275/273]], and for a number of other temperaments, such as [[isis]]. | The list of 23-limit commas it tempers out is huge, but it's worth noting that it tempers out [[32805/32768]] and is thus a [[schismatic]] system, that it tempers out [[225/224]] and [[385/384]] and so is a [[marvel]] system, and that it also tempers out [[3125/3087]], [[4000/3969]], [[5120/5103]] and [[540/539]]. It provides the [[optimal patent val]] for the rank five temperament tempering out [[275/273]], and for a number of other temperaments, such as [[isis]]. | ||
=== Prime harmonics === | |||
{{Primes in edo|94|prec=2|columns=11}} | |||
== | == Intervals == | ||
{{main| Table of 94edo intervals }} | |||
== Regular temperament properties == | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! colspan="2" | | ! colspan="2" | | ||
| Line 67: | Line 66: | ||
94et has a lower relative error than any previous ETs in the 23-limit. The next ET that does better in this subgroup is 193. | 94et has a lower relative error than any previous ETs in the 23-limit. The next ET that does better in this subgroup is 193. | ||
== Rank | === Rank-2 temperaments === | ||
{| class="wikitable center-all right-3 left-5" | {| class="wikitable center-all right-3 left-5" | ||
| Line 139: | Line 138: | ||
Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for [[garibaldi temperament]], shows us how to extend it to the 23-limit. | Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for [[garibaldi temperament]], shows us how to extend it to the 23-limit. | ||
* 46&94 | * 46&94 {{multival| 8 30 -18 -4 -28 8 -24 2 … }} | ||
* 68&94 | * 68&94 {{multival| 20 28 2 -10 24 20 34 52 … }} | ||
* 53&94 | * 53&94 {{multival| 1 -8 -14 23 20 -46 -3 -35 … }} (one garibaldi) | ||
* 41&94 | * 41&94 {{multival| 1 -8 -14 23 20 48 -3 -35 … }} (another garibaldi, only differing in the mappings of 17 and 23) | ||
* 135&94 | * 135&94 {{multival| 1 -8 -14 23 20 48 -3 59 … }}(another garibaldi) | ||
* 130&94 | * 130&94 {{multival| 6 -48 10 -50 26 6 -18 -22 … }} (a pogo extension) | ||
* 58&94 | * 58&94 {{multival| 6 46 10 44 26 6 -18 -22 … }} (a supers extension) | ||
* 50&94 | * 50&94 {{multival| 24 -4 40 -12 10 24 22 6 … }} | ||
* 72&94 | * 72&94 {{multival| 12 -2 20 -6 52 12 -36 -44 … }} (a gizzard extension) | ||
* 80&94 | * 80&94 {{multival| 18 44 30 38 -16 18 40 28 … }} | ||
* 94 solo | * 94 solo {{multival| 12 -2 20 -6 -42 12 -36 -44 … }} (a rank one temperament!) | ||
Temperaments | Temperaments to which 94et can be detempered: | ||
* | * [[Satin]] (94&311) {{multival| 3 70 -42 69 -34 50 85 83 … }} | ||
* | * 94&422 {{multival| 8 124 -18 90 -28 102 164 96 … }} | ||
== Scales == | == Scales == | ||
* [[Garibaldi12]] | |||
* [[Garibaldi17]] | |||
Since 94edo has a step of 12.766 cents, it also allows one to use its MOS scales as circulating temperaments and is the first edo to allows one to use a Mohajira, Pajara or Miracle MOS scale a as circulating temperament{{clarify}}. | |||
Since 94edo has a step of 12.766 cents, it also allows one to use its MOS scales as circulating temperaments and is the first edo to allows one to use a Mohajira, Pajara or Miracle MOS scale a as circulating temperament. | |||
{| class="wikitable" | {| class="wikitable" | ||
|+Circulating temperaments in 94edo | |+Circulating temperaments in 94edo | ||