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'''22edt''' is the '''equal division of the third harmonic''' ([[edt]]) into '''22 tones''', each 86.4525 [[cent]]s in size.
'''22edt''' is the '''equal division of the third harmonic''' ([[edt]]) into '''22 tones''', each 86.4525 [[cent]]s in size.


22edt has good approximations of the 7th, 11th, 19th and 20th harmonics, being better for its size in the 3.7.11 subgroup than even [[13edt]] is in 3.5.7. In this subgroup, it tempers out the commas [[1331/1323]] and [[387420489/386683451]], with the former comma allowing a hard [[5L 2s (3/1-equivalent)|5L 2s]] (macrodiatonic) scale generated by [[11/7]], two of which are equated to [[27/11]] and three of which are equated to [[9/7]] up a tritave. This [[9/7]] can also serve as the generator for a [[4L 5s (3/1-equivalent)|4L 5s]] (BPS enneatonic) scale, supporting [[Bohlen-Pierce-Stearns]] harmony by tempering out [[245/243]], although its representation of the 3.5.7 subgroup is less accurate than that of 13edt.
22edt has good approximations of the 7th, 11th, 19th and 20th harmonics, being better for its size in the 3.7.11 subgroup than even [[13edt]] is in 3.5.7. In this subgroup, it tempers out the commas [[1331/1323]] and [[387420489/386683451]], with the former comma allowing a hard [[5L 2s (3/1-equivalent)|5L 2s]] (macrodiatonic) scale generated by [[11/7]], two of which are equated to [[27/11]] and three of which are equated to [[9/7]] up a tritave. This [[9/7]] can also serve as the generator for a [[4L 5s (3/1-equivalent)|4L 5s]] (BPS Lambda) scale, supporting [[Bohlen-Pierce-Stearns]] harmony by tempering out [[245/243]], although its representation of the 3.5.7 subgroup is less accurate than that of 13edt.


Like [[11edt]], both the [[octave]] and [[small whole tone]] ([[10/9]]) are about 10c off (sharp and flat respectively) dissonant but recognizable. Akin to [[16edt]] with [[Blackwood]], admitting the octave induces an interpretation into a tritave-based version of [[Whitewood]] temperament.
Like [[11edt]], both the [[octave]] and [[small whole tone]] ([[10/9]]) are about 10c off (sharp and flat respectively) dissonant but recognizable. Akin to [[16edt]] with [[Blackwood]], admitting the octave induces an interpretation into a tritave-based version of [[Whitewood]] temperament.
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== Intervals ==
== Intervals ==


{| class="wikitable" style="text-align: right"
{| class="wikitable"
! Steps !! [[Cent]]s
!hekts
|-
|-
| 1 || 86.453
! | Degree
|59.091
! | Note (BPS-Lambda notation)
! | Note (Macrodiatonic notation)
! | Approximate 3.7.11 subgroup interval
! | cents value
! | hekts
|-
|-
| 2 || 172.905
| | 0
|118.182
| | E
| | E
| | 1/1
| | 0
| | 0
|-
|-
| 3 || 259.358
| | 1
|177.273
| | E# = Fb
| | F
| | 81/77, 363/343
| | 86.453
| | 59.091
|-
|-
| 4 || 345.81
| | 2
|236.364
| | F
| | Gb = Dx
| | 2673/2401, 6561/5929
| | 172.905
| | 118.182
|-
|-
| 5 || 432.263
| | 3
|295.4545
| | F#
| | E# = Abb
| | 343/297, 847/729
| | 259.358
| | 177.273
|-
|-
| 6 || 518.715
| | 4
|354.5455
| | Gb
| | F#
| | 11/9, 147/121
| | 345.810
| | 236.364
|-
|-
| 7 || 605.168
| | 5
|413.636
| | G
| | G
| | 9/7
| | 432.263
| | 295.455
|-
|-
| 8 || 691.620
| | 6
|472.727
| | G# = Hb
| | Ab = Ex
| | 729/539
| | 518.715
| | 354.545
|-
|-
| 9 || 778.073
| | 7
|531.818
| | H
| | Fx = Bbb
| | 343/243
| | 605.168
| | 413.636
|-
|-
| 10 || 864.525
| | 8
|590.909
| | H#
| | G#
| | 49/33, 121/81
| | 691.620
| | 472.727
|-
|-
| 11 || 950.978
| | 9
|650
| | Jb
| | A
| | 11/7
| | 778.073
| | 531.818
|-
|-
| 12 || 1037.430
| | 10
|709.091
| | J
| | Bb
| | 81/49
| | 864.525
| | 590.909
|-
|-
| 13 || 1123.883
| | 11
|768.182
| | J# = Ab
| | Cb = Gx
| | 3773/2187, 6561/3773
| | 950.978
| | 650.
|-
|-
| 14 || 1210.335
| | 12
|827.273
| | A
| | A# = Dbb
| | 49/27
| | 1037.430
| | 709.091
|-
|-
| 15 || 1296.788
| | 13
|886.364
| | A#
| | B
| | 21/11
| | 1123.883
| | 768.182
|-
|-
| 16 || 1383.24
| | 14
|945.4545
| | Bb
| | C
| | 99/49, 243/121
| | 1210.335
| | 827.273
|-
|-
| 17 || 1469.693
| | 15
|1004.5455
| | B
| | Db = Ax
| | 729/343
| | 1296.788
| | 886.364
|-
|-
| 18 || 1556.145
| | 16
|1063.636
| | B# = Cb
| | B# = Ebb
| | 539/243
| | 1383.240
| | 945.455
|-
|-
| 19 || 1642.598
| | 17
|1122.727
| | C
| | C#
| | 7/3
| | 1469.693
| | 1004.545
|-
|-
| 20 || 1729.05
| | 18
|1181.818
| | C#
| | D
| | 27/11, 121/49
| | 1556.145
| | 1063.636
|-
|-
| 21 || 1815.503
| | 19
|1240.909
| | Db
| | Eb
| | 891/343, 2187/847
| | 1642.598
| | 1122.727
|-
|-
| 22 || 1901.955
| | 20
|1300
| | D
| | Fb = Cx
| | 2401/891, 5929/2187
| | 1729.050
| | 1181.818
|-
| | 21
| | D# = Eb
| | D# = Gbb
| | 77/27, 343/121
| | 1815.503
| | 1240.909
|-
| | 22
| | E
| | E
| | 3/1
| | 1901.955
| | 1300.
|}
|}


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