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→Intervals: some note names in table; more notation is later
 
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== Intervals ==
== Intervals ==
Inconsistent intervals are in ''italics''.
Note names are given with 7edo as the naturals and arrows (written as ^ and v) for inflections up/down by one edostep. Inconsistent intervals are in ''italics''.
{| class="wikitable right-1 right-2"
 
{| class="wikitable center-1 right-2 right-3"
|-
|-
! Steps
! #
! Name
! Cents
! Cents
! Approximate Ratios*
! Approximate Ratios*
|-
|-
| 0
| 0
| C
| 0.00
| 0.00
| [[1/1]]
| [[1/1]]
|-
|-
| 1
| 1
| ^C
| 57.14
| 57.14
| [[21/20]]
| [[21/20]]
|-
|-
| 2
| 2
| vD
| 114.29
| 114.29
| [[14/13]], [[15/14]], [[16/15]]
| [[14/13]], [[15/14]], [[16/15]]
|-
|-
| 3
| 3
| D
| 171.43
| 171.43
| ''[[9/8]]'', ''[[13/12]]'', [[35/32]]
| ''[[9/8]]'', ''[[13/12]]'', [[35/32]]
|-
|-
| 4
| 4
| ^D
| 228.57
| 228.57
| [[8/7]], ''[[10/9]]''
| [[8/7]], ''[[10/9]]''
|-
|-
| 5
| 5
| vE
| 285.71
| 285.71
|''[[6/5]]'', [[7/6]]
|''[[6/5]]'', [[7/6]]
|-
|-
| 6
| 6
| E
| 342.86
| 342.86
| [[39/32]], [[128/105]], [[16/13]]
| [[39/32]], [[128/105]], [[16/13]]
|-
|-
| 7
| 7
| ^E
| 400.00
| 400.00
| [[5/4]], ''[[9/7]]''
| [[5/4]], ''[[9/7]]''
|-
|-
| 8
| 8
| vF
| 457.14
| 457.14
| [[13/10]], [[21/16]]
| [[13/10]], [[21/16]]
|-
|-
| 9
| 9
| F
| 514.29
| 514.29
| [[4/3]]
| [[4/3]]
|-
|-
| 10
| 10
| ^F
| 571.43
| 571.43
| [[7/5]]
| [[7/5]]
|-
|-
| 11
| 11
| vG
| 628.57
| 628.57
| [[10/7]]
| [[10/7]]
|-
|-
| 12
| 12
| G
| 685.71
| 685.71
| [[3/2]]
| [[3/2]]
|-
|-
| 13
| 13
| ^G
| 742.86
| 742.86
| [[20/13]], [[32/21]]
| [[20/13]], [[32/21]]
|-
|-
| 14
| 14
| vA
| 800.00
| 800.00
| [[8/5]], ''[[14/9]]''
| [[8/5]], ''[[14/9]]''
|-
|-
| 15
| 15
| A
| 857.14
| 857.14
| [[64/39]], [[128/105]], [[13/8]]
| [[64/39]], [[105/64]], [[13/8]]
|-
|-
| 16
| 16
| ^A
| 914.29
| 914.29
|''[[5/3]]'', [[12/7]]
|''[[5/3]]'', [[12/7]]
|-
|-
| 17
| 17
| vB
| 971.43
| 971.43
| [[7/4]], ''[[9/5]]''
| [[7/4]], ''[[9/5]]''
|-
|-
| 18
| 18
| B
| 1028.57
| 1028.57
| ''[[16/9]]'', ''[[24/13]]'', [[64/35]]
| ''[[16/9]]'', ''[[24/13]]'', [[64/35]]
|-
|-
| 19
| 19
| ^B
| 1085.71
| 1085.71
| [[13/7]], [[28/15]], [[15/8]]
| [[13/7]], [[28/15]], [[15/8]]
|-
|-
| 20
| 20
| vC
| 1142.86
| 1142.86
| [[40/21]]
| [[40/21]]
|-
|-
| 21
| 21
| C
| 1200.00
| 1200.00
| [[2/1]]
| [[2/1]]
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== Notation ==
== Notation ==
 
The following table gives a comparison of some notation systems for 21edo.
{| class="wikitable center-all right-3 right-5"
{| class="wikitable center-all right-3 right-5"
|-
|-
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! [[5L 3s]] octatonic<br>notation
! [[5L 3s]] octatonic<br>notation
! [[Extended-diatonic interval names|Extended-diatonic <br> interval name]]
! [[Extended-diatonic interval names|Extended-diatonic <br> interval name]]
|+ style="font-size: 105%; white-space: nowrap;" | Notation systems for 21edo
|+
|-
|-
| 0
| 0
Line 836: Line 860:
* [https://www.youtube.com/shorts/yLSIZxJnMh8 ''21edo waltz''] (2025)
* [https://www.youtube.com/shorts/yLSIZxJnMh8 ''21edo waltz''] (2025)
* [https://www.youtube.com/watch?v=1S4C-m_Dcno ''21edo improv''] (2026)
* [https://www.youtube.com/watch?v=1S4C-m_Dcno ''21edo improv''] (2026)
* [https://www.youtube.com/shorts/9a-nJ_Ml9z8 ''21edo groove''] (2026)


; [[Fabrizio Fiale]]
; [[Fabrizio Fiale]]
Line 861: Line 886:
; [[Claudi Meneghin]]
; [[Claudi Meneghin]]
* [http://soonlabel.com/xenharmonic/archives/2336 ''21-penny jingle''] {{dead link}}
* [http://soonlabel.com/xenharmonic/archives/2336 ''21-penny jingle''] {{dead link}}
* [https://www.youtube.com/watch?v=lpcqXD8tpXc ''Trio Sonata in 21edo for Organ (The Sewing Machine)'']
* [https://www.youtube.com/watch?v=lpcqXD8tpXc ''Trio Sonata in 21edo for Organ (The Sewing Machine)''] (2018)
* [https://www.youtube.com/watch?v=n0QA0ZQHPvk ''21edo Chacony, for two Harpsichords'']
* [https://www.youtube.com/watch?v=n0QA0ZQHPvk ''21edo Chacony, for two Harpsichords''] (2019)
* [https://www.youtube.com/watch?v=r0aKutu0gVg ''Twinkle Twinkle Little Star, with Shepard Effect''] (2023)
* [https://www.youtube.com/watch?v=r0aKutu0gVg ''Twinkle Twinkle Little Star, with Shepard Effect''] (2023)
* [https://www.youtube.com/watch?v=XlpAbSdy_sg ''Trio Sonata for Baroque Trio in 21 EDO''] (2026)


; [[Nick, The NRG]]
; [[Nick, The NRG]]
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; [[Stephen Weigel]]
; [[Stephen Weigel]]
* [https://soundcloud.com/overtoneshock/little-fugue-21-edo?in=overtoneshock/sets/xenharmonic-microtonal ''Iridescent Wenge Fugue''] (accepted to [https://www.seamusonline.org/ SEAMUS 2018] and [http://eabarndance.com/ Electroacoustic Barn Dance 2018])
* [https://soundcloud.com/overtoneshock/little-fugue-21-edo?in=overtoneshock/sets/xenharmonic-microtonal ''Iridescent Wenge Fugue''] (accepted to [https://www.seamusonline.org/ SEAMUS 2018] and [http://eabarndance.com/ Electroacoustic Barn Dance 2018])
* [https://xenharmonicgod.bandcamp.com/album/weigel-family-christmas-xenharmonic-chocolate ''WEIGEL FAMILY CHRISTMAS (xenharmonic chocolate)''], an album of xenharmonic Christmas covers, many are in 21 EDO
* [https://xenharmonicgod.bandcamp.com/album/weigel-family-christmas-xenharmonic-chocolate ''WEIGEL FAMILY CHRISTMAS (xenharmonic chocolate)'']{{dead link}}, an album of xenharmonic Christmas covers, many are in 21 EDO


; [[Randy Wells]]
; [[Randy Wells]]
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