68edo: Difference between revisions
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ArrowHead294 (talk | contribs) m Formatting + ups and downs notation |
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== Intervals == | == Intervals == | ||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
|- | |||
! Degrees | ! Degrees | ||
! Cents | ! Cents | ||
! Approximate | ! Approximate ratios | ||
|- | |- | ||
| 0 | | 0 | ||
| Line 301: | Line 302: | ||
== Notation == | == Notation == | ||
===Sagittal notation=== | === Sagittal notation === | ||
This notation uses the same sagittal sequence as [[75edo#Sagittal notation|75-EDO]]. | This notation uses the same sagittal sequence as [[75edo#Sagittal notation|75-EDO]]. | ||
==== Evo flavor ==== | |||
<imagemap> | <imagemap> | ||
File:68-EDO_Evo_Sagittal.svg | File:68-EDO_Evo_Sagittal.svg | ||
| Line 317: | Line 318: | ||
</imagemap> | </imagemap> | ||
====Revo flavor==== | ==== Revo flavor ==== | ||
<imagemap> | <imagemap> | ||
File:68-EDO_Revo_Sagittal.svg | File:68-EDO_Revo_Sagittal.svg | ||
| Line 331: | Line 331: | ||
</imagemap> | </imagemap> | ||
====Evo-SZ flavor==== | ==== Evo-SZ flavor ==== | ||
<imagemap> | <imagemap> | ||
File:68-EDO_Evo-SZ_Sagittal.svg | File:68-EDO_Evo-SZ_Sagittal.svg | ||
| Line 346: | Line 345: | ||
In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO. | In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO. | ||
=== Ups and downs notation === | |||
60edo can be notated using [[ups and downs notation]] using [[Helmholtz–Ellis]] accidentals: | |||
{{Sharpness-sharp8}} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
| Line 361: | Line 366: | ||
| 245/243, 2048/2025, 2401/2400 | | 245/243, 2048/2025, 2401/2400 | ||
| {{mapping| 68 108 158 191 }} | | {{mapping| 68 108 158 191 }} | ||
| | | −0.983 | ||
| 0.915 | | 0.915 | ||
| 5.19 | | 5.19 | ||
| Line 368: | Line 373: | ||
| 121/120, 176/175, 245/243, 1375/1372 | | 121/120, 176/175, 245/243, 1375/1372 | ||
| {{mapping| 68 108 158 191 235 }} | | {{mapping| 68 108 158 191 235 }} | ||
| | | −0.541 | ||
| 1.206 | | 1.206 | ||
| 6.84 | | 6.84 | ||
| Line 375: | Line 380: | ||
| 121/120, 176/175, 196/195, 245/243, 275/273 | | 121/120, 176/175, 196/195, 245/243, 275/273 | ||
| {{mapping| 68 108 158 191 235 252 }} | | {{mapping| 68 108 158 191 235 252 }} | ||
| | | −0.745 | ||
| 1.191 | | 1.191 | ||
| 6.75 | | 6.75 | ||
| Line 382: | Line 387: | ||
| 121/120, 136/135, 154/153, 176/175, 196/195, 275/273 | | 121/120, 136/135, 154/153, 176/175, 196/195, 275/273 | ||
| {{mapping| 68 108 158 191 235 252 278 }} | | {{mapping| 68 108 158 191 235 252 278 }} | ||
| | | −0.671 | ||
| 1.118 | | 1.118 | ||
| 6.34 | | 6.34 | ||
| Line 389: | Line 394: | ||
| 121/120, 136/135, 154/153, 190/189, 176/175, 196/195, 275/273 | | 121/120, 136/135, 154/153, 190/189, 176/175, 196/195, 275/273 | ||
| {{mapping| 68 108 158 191 235 252 278 289 }} | | {{mapping| 68 108 158 191 235 252 278 289 }} | ||
| | | −0.661 | ||
| 1.046 | | 1.046 | ||
| 5.93 | | 5.93 | ||
| Line 395: | Line 400: | ||
== Zeta properties == | == Zeta properties == | ||
===Zeta peak index=== | === Zeta peak index === | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | ! colspan="3" | Tuning | ||
! | ! colspan="3" | Strength | ||
! colspan="2" | Closest EDO | |||
! colspan="2" | Integer limit | |||
!EDO | |||
! | |||
|- | |- | ||
|[[354zpi]] | ! ZPI | ||
|68.0493056282519 | ! Steps per octave | ||
|17.6342725163943 | ! Step size (cents) | ||
|7.666604 | ! Height | ||
|1.254592 | ! Integral | ||
|17.034505 | ! Gap | ||
|68edo | ! EDO | ||
|1199.13053111481 | ! Octave (cents) | ||
|10 | ! Consistent | ||
|10 | ! Distinct | ||
|- | |||
| [[354zpi]] | |||
| 68.0493056282519 | |||
| 17.6342725163943 | |||
| 7.666604 | |||
| 1.254592 | |||
| 17.034505 | |||
| 68edo | |||
| 1199.13053111481 | |||
| 10 | |||
| 10 | |||
|} | |} | ||
== Scales == | == Scales == | ||
''See also [[34edo#Scales]] and [[17edo#Scales]].'' | ''See also [[34edo#Scales]] and [[17edo#Scales]].'' | ||