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20edo: Difference between revisions

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{{interwiki
{{Interwiki
| en = 20edo
| de =
| de =
| en = 20edo
| es = 20 EDO
| es = 20 EDO
| ja = 20平均律
| ja = 20平均律
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{| class="wikitable center-all right-2"
{| class="wikitable center-all right-2"
|-
|-
![[Degree]]
! [[Degree]]
![[Cents]]
! [[Cents]]
! Approximate ratios
! Approximate ratios
! colspan="3" |[[Ups and downs notation]]
! colspan="3" |[[Ups and downs notation]]
![[2L 7s|Balzano]]<br>Notation
! [[2L 7s|Balzano]]<br>Notation
![[6L 1s|Archeotonic]]<br>notation
! [[6L 1s|Archeotonic]]<br>notation
! Nearest<br>harmonic
! Nearest<br>harmonic
|-
|-
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|}
|}


=== Selected 19-limit just intervals ===
=== Chord names in color notation ===
{| class="wikitable center-all"
|+[[Direct approximation]] (even if [[inconsistent]])
|-
! Interval, complement
! Error (abs, [[Cent|¢]])
|-
| [[16/13]] '''[[13/8]]'''
| 0.5276
|-
| [[15/14]] [[28/15]]
| 0.5571
|-
| [[10/9]] [[9/5]]
| 2.4037
|-
| '''[[19/16]]''' [[32/19]]
| 2.4869
|-
| [[14/11]] [[11/7]]
| 2.4920
|-
| [[19/13]] [[26/19]]
| 3.0146
|-
| [[15/11]] [[22/15]]
| 3.0492
|-
| [[15/13]] [[26/15]]
| 7.7410
|-
| [[16/15]] [[15/8]]
| 8.2687
|-
| [[14/13]] [[13/7]]
| 8.2982
|-
| [[8/7]] '''[[7/4]]'''
| 8.8259
|-
| [[13/11]] [[22/13]]
| 10.7902
|-
| '''[[11/8]]''' [[16/11]]
| 11.3179
|-
| [[11/9]] [[18/11]]
| 12.5920
|-
| [[11/10]] [[20/11]]
| 14.9957
|-
| '''[[17/16]]''' [[32/17]]
| 15.0445
|-
| [[9/7]] [[14/9]]
| 15.0840
|-
| [[6/5]] [[5/3]]
| 15.6412
|-
| [[7/5]] [[10/7]]
| 17.4878
|-
| '''[[3/2]]''' [[4/3]]
| 18.0449
|-
| [[13/12]] [[24/13]]
| 18.5726
|-
| [[9/8]] [[16/9]]
| 23.9100
|-
| '''[[5/4]]''' [[8/5]]
| 26.3137
|-
| [[7/6]] [[12/7]]
| 26.8709
|-
| [[12/11]] [[11/6]]
| 29.36294
|}
 
== Notation ==
=== Ups and downs notation ===
Like [[15edo]], every note has many names. D is also C# and Eb. The major 3rd is also a perfect 4th and a dim 5th. 20edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
{{Sharpness-sharp4a}}
 
[[Alternative symbols for ups and downs notation]] uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp4}}
 
=== Sagittal notation ===
This notation is a superset of the notations for edos [[10edo#Sagittal notation|10]] and [[5edo#Sagittal notation|5]].
 
==== Evo and Revo flavors ====
{{Sagittal chart|}}
 
==== Evo-SZ flavor ====
{{Sagittal chart|Evo-SZ}}
 
== Chord names ==
20edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13).
20edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13).
* 0-4-12 = D E A = Dsus2 = "D sus 2", or D F A = Dm = "D minor"
* 0-4-12 = D E A = Dsus2 = "D sus 2", or D F A = Dm = "D minor"
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* 0-5-12-17 = D ^F A ^C = D^m7 = "D upminor-seven", or D ^F A ^B = D^m6 = "D upminor-six"
* 0-5-12-17 = D ^F A ^C = D^m7 = "D upminor-seven", or D ^F A ^B = D^m6 = "D upminor-six"


For a more complete list, see [[Ups and downs notation#Chords and Chord Progressions|Ups and downs notation - Chords and Chord Progressions]]. Because many intervals have several names, many chords do too.
For a more complete list, see [[Kite's ups and downs notation #Chords and chord Progressions]]. Because many intervals have several names, many chords do too.
 
== Notation ==
Like [[15edo]], every note has many names. D is also C# and Eb. The major third is also a perfect fourth and a diminished fifth.
 
=== Stein–Zimmermann–Gould notation ===
[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
{{Sharpness-sharp4-szg}}
 
=== Kite's ups and downs notation ===
20edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
{{Sharpness-sharp4a}}
 
=== Sagittal notation ===
This notation is a superset of the notations for edos [[10edo #Sagittal notation|10]] and [[5edo #Sagittal notation|5]].
 
==== Evo and Revo flavors ====
{{Sagittal chart|}}
 
==== Evo-SZ flavor ====
{{Sagittal chart|Evo-SZ}}
 
== Approximation to JI ==
=== Interval mappings ===
{{Q-odd-limit intervals|20}}


== Regular temperament properties ==
== Regular temperament properties ==
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