60edo: Difference between revisions
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A step of 60edo is exactly 9 [[dexl]]s, or exactly 41 [[mina]]s. | A step of 60edo is exactly 9 [[dexl]]s, or exactly 41 [[mina]]s. | ||
== Intervals == | == Intervals == | ||
| Line 51: | Line 18: | ||
! Degrees | ! Degrees | ||
! Cents | ! Cents | ||
! Approximate ratios<br | ! Approximate ratios<br>in the 2.3.5.7.13.17 subgroup | ||
! Additional ratios<br | ! Additional ratios<br>of 11 (tending flat, 60e val) | ||
|- | |- | ||
| 0 | | 0 | ||
| Line 358: | Line 325: | ||
| 2/1 | | 2/1 | ||
| | | | ||
|} | |||
== Notation == | |||
=== Ups and downs notation === | |||
60edo can be notated using [[ups and downs notation]] using [[Helmholtz–Ellis]] accidentals: | |||
{{Sharpness-sharp5|60}} | |||
If arrows are taken to have their own layer of enharmonic spellings, then in some cases certain notes may be best spelled with three arrows. | |||
=== Sagittal notation === | |||
This notation is a superset of the notations for EDOs [[12edo#Sagittal notation|12]] and [[6edo#Sagittal notation|6]]. | |||
==== Evo flavor ==== | |||
<imagemap> | |||
File:60-EDO_Evo_Sagittal.svg | |||
desc none | |||
rect 80 0 300 50 [[Sagittal_notation]] | |||
rect 300 0 655 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] | |||
rect 20 80 190 106 [[45927/45056]] | |||
rect 190 80 310 106 [[46/45]] | |||
default [[File:60-EDO_Evo_Sagittal.svg]] | |||
</imagemap> | |||
==== Revo flavor ==== | |||
<imagemap> | |||
File:60-EDO_Revo_Sagittal.svg | |||
desc none | |||
rect 80 0 300 50 [[Sagittal_notation]] | |||
rect 300 0 628 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] | |||
rect 20 80 190 106 [[45927/45056]] | |||
rect 190 80 310 106 [[46/45]] | |||
default [[File:60-EDO_Revo_Sagittal.svg]] | |||
</imagemap> | |||
== 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 | |||
|- | |||
| [[301zpi]] | |||
| 59.9201656607655 | |||
| 20.0266469020418 | |||
| 7.046396 | |||
| 1.131000 | |||
| 15.932359 | |||
| 60edo | |||
| 1201.59881412251 | |||
| 10 | |||
| 10 | |||
|} | |} | ||
| Line 543: | Line 575: | ||
|} | |} | ||
<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 | ||
== Diagrams == | == Diagrams == | ||
| Line 587: | Line 587: | ||
== Nearby equal-step tunings == | == Nearby equal-step tunings == | ||
There are a few other useful [[equal-step tuning]]s which occur close to 60edo in step size: | There are a few other useful [[equal-step tuning]]s which occur close to 60edo in step size: | ||
; 207ed11, 168ed7 | ; 207ed11, 168ed7 | ||
| Line 598: | Line 597: | ||
{{Harmonics in equal|207|11|1|intervals=prime|columns=11|collapsed=1}} | {{Harmonics in equal|207|11|1|intervals=prime|columns=11|collapsed=1}} | ||
{{Harmonics in equal|168|7|1|intervals=prime|columns=11|collapsed=1}} | {{Harmonics in equal|168|7|1|intervals=prime|columns=11|collapsed=1}} | ||
; 139ed5 | ; 139ed5 | ||
| Line 608: | Line 606: | ||
It also causes the [[val]] for [[11/1]] to flip from 208 steps to 207 steps. | It also causes the [[val]] for [[11/1]] to flip from 208 steps to 207 steps. | ||
{{Harmonics in equal|139|5|1|intervals=prime|columns=11|collapsed=1}} | {{Harmonics in equal|139|5|1|intervals=prime|columns=11|collapsed=1}} | ||
; 301zpi | ; 301zpi | ||
| Line 620: | Line 617: | ||
301zpi is both [[consistent]] and [[distinctly consistent]] up to the 10-[[integer-limit]], which is unusually high for a two digit edo or three digit zpi. | 301zpi is both [[consistent]] and [[distinctly consistent]] up to the 10-[[integer-limit]], which is unusually high for a two digit edo or three digit zpi. | ||
{{Harmonics in equal|1|38083|37645|intervals=prime|columns=11|title= Approximation of prime harmonics in 301zpi|collapsed=1}} | {{Harmonics in equal|1|38083|37645|intervals=prime|columns=11|title= Approximation of prime harmonics in 301zpi|collapsed=1}} | ||
; 60edo | ; 60edo | ||
{{Harmonics in equal|60|2|1|intervals=prime|columns=11|collapsed=1}} | {{Harmonics in equal|60|2|1|intervals=prime|columns=11|collapsed=1}} | ||
; 255ed19 | ; 255ed19 | ||
| Line 634: | Line 629: | ||
It also causes the [[val]] for [[7/1]] to flip from 168 steps to 169. | It also causes the [[val]] for [[7/1]] to flip from 168 steps to 169. | ||
{{Harmonics in equal|255|19|1|intervals=prime|columns=11|collapsed=1}} | {{Harmonics in equal|255|19|1|intervals=prime|columns=11|collapsed=1}} | ||
; 208ed11 | ; 208ed11 | ||
| Line 644: | Line 638: | ||
It also causes the [[val]]s to flip for [[5/1]], [[7/1]] and [[17/1]]. | It also causes the [[val]]s to flip for [[5/1]], [[7/1]] and [[17/1]]. | ||
{{Harmonics in equal|208|11|1|intervals=prime|columns=11|collapsed=1}} | {{Harmonics in equal|208|11|1|intervals=prime|columns=11|collapsed=1}} | ||
; 272ed23 | ; 272ed23 | ||