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=21 Equal Divisions of the Tritave=
{{Infobox ET}}
{{ED intro}}


== Intervals ==
{| class="wikitable"
{| class="wikitable"
|-
|-
| | Degrees
! Degrees
| | Cents
! Cents
|hekts
! Hekts
| | Approximate Ratio
! Approximate Ratio
|-
|-
| colspan="3"| 0
| colspan="3" style="text-align: center;" | 0
| | [[1/1|1/1]]
| [[1/1|1/1]]
|-
|-
| | 1
| 1
| | 90.569
| 90.569
|61.905
| 61.905
| | [[21/20|21/20]], [[135/128|135/128]]
| [[21/20|21/20]], [[135/128|135/128]]
|-
|-
| | 2
| 2
| | 181.139
| 181.139
|123.81
| 123.81
| | [[10/9|10/9]]
| [[10/9|10/9]]
|-
|-
| | 3
| 3
| | 271.708
| 271.708
|185.714
| 185.714
| | [[7/6|7/6]]
| [[7/6|7/6]]
|-
|-
| | 4
| 4
| | 362.277
| 362.277
|247.619
| 247.619
| | [[16/13|16/13]]
| [[16/13|16/13]]
|-
|-
| | 5
| 5
| | 452.846
| 452.846
|309.524
| 309.524
| | [[13/10|13/10]]
| [[13/10|13/10]]
|-
|-
| | 6
| 6
| | 543.416
| 543.416
|371.429
| 371.429
| | [[15/11|15/11]], [[11/8|11/8]]
| [[15/11|15/11]], [[11/8|11/8]]
|-
|-
| | 7
| 7
| | 633.985
| 633.985
|433.333
| 433.333
| | [[13/9|13/9]]
| [[13/9|13/9]]
|-
|-
| | 8
| 8
| | 724.554
| 724.554
|495.238
| 495.238
| | 35/23
| 35/23
|-
|-
| | 9
| 9
| | 815.124
| 815.124
|557.143
| 557.143
| | [[8/5|8/5]]
| [[8/5|8/5]]
|-
|-
| | 10
| 10
| | 905.693
| 905.693
|619.048
| 619.048
| | 27/16
| 27/16
|-
|-
| | 11
| 11
| | 996.262
| 996.262
|680.952
| 680.952
| | 16/9
| 16/9
|-
|-
| | 12
| 12
| | 1086.831
| 1086.831
|742.857
| 742.857
| | [[15/8|15/8]]
| [[15/8|15/8]]
|-
|-
| | 13
| 13
| | 1177.401
| 1177.401
|804.762
| 804.762
| | 69/35
| 69/35
|-
|-
| | 14
| 14
| | 1267.97
| 1267.97
|866.667
| 866.667
| | 27/13
| 27/13
|-
|-
| | 15
| 15
| | 1358.539
| 1358.539
|928.571
| 928.571
| | 11/5 ([[11/10|11/10]] plus an octave), 24/11 (12/11 plus an octave)
| 11/5 ([[11/10|11/10]] plus an octave), 24/11 (12/11 plus an octave)
|-
|-
| | 16
| 16
| | 1449.109
| 1449.109
|990.476
| 990.476
| | 30/13 ([[15/13|15/13]] plus an octave)
| 30/13 ([[15/13|15/13]] plus an octave)
|-
|-
| | 17
| 17
| | 1539.678
| 1539.678
|1052.381
| 1052.381
| | 39/16
| 39/16
|-
|-
| | 18
| 18
| | 1630.247
| 1630.247
|1114.286
| 1114.286
| | 18/7 ([[9/7|9/7]] plus an octave)
| 18/7 ([[9/7|9/7]] plus an octave)
|-
|-
| | 19
| 19
| | 1720.816
| 1720.816
|1076.19
| 1076.19
| | 27/10
| 27/10
|-
|-
| | 20
| 20
| | 1811.386
| 1811.386
|1238.095
| 1238.095
| | 20/7, 128/45
| 20/7, 128/45
|-
|-
| | 21
| 21
| | 1901.955
| 1901.955
|1300
| 1300
| | 3/1
| 3/1
|}
|}


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21edt also contains a 4L5s MOS similar to [[BP|BP]], with a 4:1 ratio of large to small; quite exaggerated from the optimal 2:1. Although the 7/3 is a little off, the 4L+5s BP scale is pretty. However, one of the star scales in 21edt is the 3L+6s (ssLssLssL and modes thereof) which is very harmonically rich, the cornerstone of which is the approximate 9:13:19 chord (which is just the [[3edt|3edt]] essentially tempered chord).
21edt also contains a 4L5s MOS similar to [[BP|BP]], with a 4:1 ratio of large to small; quite exaggerated from the optimal 2:1. Although the 7/3 is a little off, the 4L+5s BP scale is pretty. However, one of the star scales in 21edt is the 3L+6s (ssLssLssL and modes thereof) which is very harmonically rich, the cornerstone of which is the approximate 9:13:19 chord (which is just the [[3edt|3edt]] essentially tempered chord).


Not the best approximations but all within 20 cents: it has 5th (+20c), 7th(-16c), 10th (+2c), 11th (+15c), 13th (-3c), 17th (-14c), 23rd (+6 c), and 37th (-2c) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.
== Harmonics==
[[Category:edt]]
Not the best approximations but all within 20 cents: it has 5th (+20¢), 7th (−16¢), 10th (+2¢), 11th (+15¢), 13th (−3¢), 17th (−14¢), 23rd (+6¢), and 37th (−2¢) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.
 
{{Harmonics in equal
| steps = 21
| num = 3
| denom = 1
| intervals = integer
}}
{{Harmonics in equal
| steps = 21
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = integer
}}
 
[[Category:tritave]]
[[Category:tritave]]
{{todo|expand|improve synopsis}}
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