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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"
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).
|+[[Direct approximation]] (even if [[inconsistent]])
* 0-4-12 = D E A = Dsus2 = "D sus 2", or D F A = Dm = "D minor"
|-
* 0-5-12 = D ^F A = D^m = "D upminor"
! Interval, complement
* 0-6-12 = D ^^F A = D~ = "D mid"
! Error (abs, [[Cent|¢]])
* 0-7-12 = D vF# A = Dv = "D down" or "D downmajor"
|-
* 0-8-12 = D G A = Dsus4, or D F# A = D = "D" or "D major"
| [[16/13]] '''[[13/8]]'''
* 0-4-12-16 = D F A C = Dm7 = "D minor seven", or D F A B = Dm6 = "D minor six"
| 0.5276
* 0-5-12-16 = D ^F A C = D^m,7 = "D upminor add-seven", or D ^F A B = D^m,6 = "D upminor add-six"
|-
* 0-6-12-16 = D ^^F A C = D~,7 = "D mid add-seven", or D ^^F A B = D~,6 = "D mid add-six"
| [[15/14]] [[28/15]]
* 0-7-12-16 = D vF# A C = Dv,7 = "D down add-seven", or D vF# A B = Dv,6 = "D down add-six"
| 0.5571
* 0-8-12-16 = D F# A C = D7 = "D seven", or D F# A B = D6 = "D six"
|-
* 0-7-12-19 = D vF# A vC# = DvM7 = "D downmajor seven"
| [[10/9]] [[9/5]]
* 0-5-12-17 = D ^F A ^C = D^m7 = "D upminor-seven", or D ^F A ^B = D^m6 = "D upminor-six"
| 2.4037
 
|-
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.
| '''[[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 ==
== Notation ==
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{{Sagittal chart|Evo-SZ}}
{{Sagittal chart|Evo-SZ}}


== Chord names ==
== Approximation to JI ==
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).
=== Interval mappings ===
* 0-4-12 = D E A = Dsus2 = "D sus 2", or D F A = Dm = "D minor"
{{Q-odd-limit intervals|20}}
* 0-5-12 = D ^F A = D^m = "D upminor"
* 0-6-12 = D ^^F A = D~ = "D mid"
* 0-7-12 = D vF# A = Dv = "D down" or "D downmajor"
* 0-8-12 = D G A = Dsus4, or D F# A = D = "D" or "D major"
* 0-4-12-16 = D F A C = Dm7 = "D minor seven", or D F A B = Dm6 = "D minor six"
* 0-5-12-16 = D ^F A C = D^m,7 = "D upminor add-seven", or D ^F A B = D^m,6 = "D upminor add-six"
* 0-6-12-16 = D ^^F A C = D~,7 = "D mid add-seven", or D ^^F A B = D~,6 = "D mid add-six"
* 0-7-12-16 = D vF# A C = Dv,7 = "D down add-seven", or D vF# A B = Dv,6 = "D down add-six"
* 0-8-12-16 = D F# A C = D7 = "D seven", or D F# A B = D6 = "D six"
* 0-7-12-19 = D vF# A vC# = DvM7 = "D downmajor seven"
* 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.


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