10edo: Difference between revisions
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== Intervals == | == Intervals == | ||
{| class="wikitable right-1 right-2 center-7 center-8" | {| class="wikitable right-1 right-2 center-7 center-8" | ||
|- | |||
! Degree | ! Degree | ||
! Cents | ! Cents | ||
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! Additional ratios <br> of 3, 5 and 9<ref>adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-edo intervals</ref> | ! Additional ratios <br> of 3, 5 and 9<ref>adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-edo intervals</ref> | ||
! Interval names | ! Interval names | ||
! colspan="3" | [[Ups and downs notation]] | ! colspan="3" | [[Ups and downs notation]]<br />([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and m2) | ||
([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and m2) | |||
! Audio | ! Audio | ||
|- | |- | ||
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This notation is a subset of the notations for EDOs [[20edo#Sagittal notation|20]] and [[30edo#Sagittal notation|30]] and a superset of the notation for [[5edo#Sagittal notation|5-EDO]]. | This notation is a subset of the notations for EDOs [[20edo#Sagittal notation|20]] and [[30edo#Sagittal notation|30]] and a superset of the notation for [[5edo#Sagittal notation|5-EDO]]. | ||
====Evo and Revo flavors==== | ==== Evo and Revo flavors ==== | ||
<imagemap> | <imagemap> | ||
File:10-EDO_Sagittal.svg | File:10-EDO_Sagittal.svg | ||
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</imagemap> | </imagemap> | ||
====Evo-SZ flavor==== | ==== Evo-SZ flavor ==== | ||
<imagemap> | <imagemap> | ||
File:10-EDO_Evo-SZ_Sagittal.svg | File:10-EDO_Evo-SZ_Sagittal.svg | ||
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== 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]] | ! rowspan="2" | [[Comma list]] | ||
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|- | |- | ||
! [[Harmonic limit|Prime<br>limit]] | ! [[Harmonic limit|Prime<br>limit]] | ||
! [[Ratio]]<ref> | ! [[Ratio]]<ref>{{rd}}</ref> | ||
! [[Monzo]] | ! [[Monzo]] | ||
! [[Cent]]s | ! [[Cent]]s | ||
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== 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 | |||
! | |||
|- | |- | ||
|[[26zpi]] | ! ZPI | ||
|10.0084563372591 | ! Steps per octave | ||
|119.898609691954 | ! Step size (cents) | ||
|4.477141 | ! Height | ||
|1.082282 | ! Integral | ||
|14.181485 | ! Gap | ||
|10edo | ! EDO | ||
|1198.98609691954 | ! Octave (cents) | ||
|8 | ! Consistent | ||
|5 | ! Distinct | ||
|- | |||
| [[26zpi]] | |||
| 10.0084563372591 | |||
| 119.898609691954 | |||
| 4.477141 | |||
| 1.082282 | |||
| 14.181485 | |||
| 10edo | |||
| 1198.98609691954 | |||
| 8 | |||
| 5 | |||
|} | |} | ||
== Scales == | == Scales == | ||
=== MOS scales === | === MOS scales === | ||
* Decimal/Lemba[6] [[4L 2s]] (period = 5\10, gen = 2\10): 2 2 1 2 2 1 | * Decimal/Lemba[6] [[4L 2s]] (period = 5\10, gen = 2\10): 2 2 1 2 2 1 | ||
* Dicot[7] [[3L 4s]] (gen = 3\10): 1 2 1 2 1 2 1 | * Dicot[7] [[3L 4s]] (gen = 3\10): 1 2 1 2 1 2 1 | ||
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=== Other scales === | === Other scales === | ||
* [[The Pinetone System#Pinetone pentatonic|Pinetone major pentatonic]] (subset of Dicot[7]): 2 1 3 1 3 | * [[The Pinetone System#Pinetone pentatonic|Pinetone major pentatonic]] (subset of Dicot[7]): 2 1 3 1 3 | ||
* [[The Pinetone System#Pinetone pentatonic|Pinetone minor pentatonic]] (subset of Dicot[7]): 3 1 2 3 1 | * [[The Pinetone System#Pinetone pentatonic|Pinetone minor pentatonic]] (subset of Dicot[7]): 3 1 2 3 1 | ||
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{{Main| 10edo/Music }} | {{Main| 10edo/Music }} | ||
{{Catrel|10edo tracks}} | {{Catrel|10edo tracks}} | ||
== Notes == | |||
<references group="note" /> | |||
[[Category:Macrotonal]] | [[Category:Macrotonal]] | ||
{{todo|add lumatone mapping}} | {{todo|add lumatone mapping}} | ||