56edo: Difference between revisions
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{{Sharpness-sharp7}} | {{Sharpness-sharp7}} | ||
Here, a sharp raises by seven steps, and a flat lowers by seven steps, so single, double, and triple arrows can be used to fill in the gap. | Here, a sharp raises by seven steps, and a flat lowers by seven steps, so single, double, and triple arrows can be used to fill in the gap. | ||
== Approximation to JI == | |||
=== Zeta peak index === | |||
{| class="wikitable center-all" | |||
! colspan="3" | Tuning | |||
! colspan="3" | Strength | |||
! colspan="2" | Closest edo | |||
! colspan="2" | Integer limit | |||
|- | |||
! ZPI | |||
! Steps per octave | |||
! Step size (cents) | |||
! Height | |||
! Integral | |||
! Gap | |||
! Edo | |||
! Octave (cents) | |||
! Consistent | |||
! Distinct | |||
|- | |||
| [[276zpi]] | |||
| 56.0083399588546 | |||
| 21.4253805929895 | |||
| 6.063216 | |||
| 0.931117 | |||
| 14.804703 | |||
| 56edo | |||
| 1199.82131320741 | |||
| 8 | |||
| 8 | |||
|} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
Line 223: | Line 254: | ||
| {{monzo| 89 -56 }} | | {{monzo| 89 -56 }} | ||
| {{mapping| 56 89 }} | | {{mapping| 56 89 }} | ||
| | | −1.64 | ||
| 1.63 | | 1.63 | ||
| 7.64 | | 7.64 | ||
Line 230: | Line 261: | ||
| 2048/2025, 1953125/1889568 | | 2048/2025, 1953125/1889568 | ||
| {{mapping| 56 89 130 }} | | {{mapping| 56 89 130 }} | ||
| | | −1.01 | ||
| 1.61 | | 1.61 | ||
| 7.50 | | 7.50 | ||
Line 237: | Line 268: | ||
| 686/675, 875/864, 1029/1024 | | 686/675, 875/864, 1029/1024 | ||
| {{mapping| 56 89 130 157 }} | | {{mapping| 56 89 130 157 }} | ||
| | | −0.352 | ||
| 1.80 | | 1.80 | ||
| 8.38 | | 8.38 | ||
Line 244: | Line 275: | ||
| 100/99, 245/242, 385/384, 686/675 | | 100/99, 245/242, 385/384, 686/675 | ||
| {{mapping| 56 89 130 157 194 }} | | {{mapping| 56 89 130 157 194 }} | ||
| | | −0.618 | ||
| 1.69 | | 1.69 | ||
| 7.90 | | 7.90 | ||
Line 251: | Line 282: | ||
| 91/90, 100/99, 169/168, 245/242, 385/384 | | 91/90, 100/99, 169/168, 245/242, 385/384 | ||
| {{mapping| 56 89 130 157 194 207 }} | | {{mapping| 56 89 130 157 194 207 }} | ||
| | | −0.299 | ||
| 1.70 | | 1.70 | ||
| 7.95 | | 7.95 | ||
Line 322: | Line 353: | ||
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Scales == | == Scales == | ||
* [[Supra7]] | * [[Supra7]] |