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
| −1.64
| 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
| −1.01
| 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
| −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
| −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
| −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


== Zeta properties ==
===Zeta peak index===
{| class="wikitable"
! 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
|}
== Scales ==
== Scales ==
* [[Supra7]]
* [[Supra7]]