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→Intervals: split interval table (incomplete)
Line 22: Line 22:


== Intervals ==
== Intervals ==
{| class="wikitable center-all right-3 right-5"
Inconsistent intervals are in ''italics''.
{| class="wikitable right-1 right-2"
|-
! Steps
! Cents
! 43-odd-limit ratios*
! Additional ratios
|-
| 0
| 0.00
|
|
|-
| 1
| 57.14
|
|
|-
| 2
| 114.29
|
|
|-
| 3
| 171.43
|
|
|-
| 4
| 228.57
|
|
|-
| 5
| 285.71
|
|
|-
| 6
| 342.86
|
|
|-
| 7
| 400.00
|
|
|-
| 8
| 457.14
|
|
|-
| 9
| 514.29
|
|
|-
| 10
| 571.43
|
|
|-
| 11
| 628.57
|
|
|-
| 12
| 685.71
|
|
|-
| 13
| 742.86
|
|
|-
| 14
| 800.00
|
|
|-
| 15
| 857.14
|
|
|-
| 16
| 914.29
|
|
|-
| 17
| 971.43
|
|
|-
| 18
| 1028.57
|
|
|-
| 19
| 1085.71
|
|
|-
| 20
| 1142.86
|
|
|-
| 21
| 1200.00
|
|
|}
<nowiki/>*In the 2.15.7.33.39.23.29.31.43 subgroup
 
{| class="wikitable mw-collapsible mw-collapsed center-all right-3 right-5"
|-
|-
! [[Degree]]
! [[Degree]]
Line 29: Line 149:
! [[5L 3s]] octotonic<br>notation
! [[5L 3s]] octotonic<br>notation
! [[Extended-diatonic interval names|Extended-diatonic <br> interval name]]
! [[Extended-diatonic interval names|Extended-diatonic <br> interval name]]
! Approximate Ratios *1
|+ style="font-size: 105%; white-space: nowrap;" | Notation systems for 21edo
! Approximate Ratios *2
! Approximate Ratios *3
|-
|-
| 0
| 0
Line 40: Line 158:
| C
| C
| Unison
| Unison
| 1/1
| 1/1
| 1/1
|-
|-
| 1
| 1
Line 51: Line 166:
| C#
| C#
| Subminor 2nd
| Subminor 2nd
| 28/27, 30/29
| 35/34, 36/35
| 64/63
|-
|-
| 2
| 2
Line 62: Line 174:
| Db
| Db
| Minor 2nd
| Minor 2nd
| 16/15, 15/14, 29/27
| 18/17
| 16/15, 25/24
|-
|-
| 3
| 3
Line 73: Line 182:
| D
| D
| Submajor 2nd
| Submajor 2nd
| 10/9, 32/29
| 10/9,11/10
| 9/8, 11/10
|-
|-
| 4
| 4
Line 84: Line 190:
| D#
| D#
| Supermajor 2nd
| Supermajor 2nd
| 8/7
| 8/7
| 8/7, 10/9
|-
|-
| 5
| 5
Line 95: Line 198:
| Eb
| Eb
| Subminor 3rd
| Subminor 3rd
| 27/23, 32/27
| 13/11, 20/17
| 6/5, 7/6
|-
|-
| 6
| 6
Line 106: Line 206:
| E
| E
| Neutral 3rd
| Neutral 3rd
| 28/23
| 11/9
| 16/13
|-
|-
| 7
| 7
Line 117: Line 214:
| E#/Fb
| E#/Fb
| Major 3rd
| Major 3rd
| 29/23
| 44/35
| 5/4, 9/7, 11/9, 14/11
|-
|-
| 8
| 8
Line 128: Line 222:
| F
| F
| Third-fourth ([[naiadic]])
| Third-fourth ([[naiadic]])
| 30/23
| 13/10, 17/13, 22/17
| 13/10
|-
|-
| 9
| 9
Line 139: Line 230:
| F#
| F#
| Acute 4th
| Acute 4th
| 161/120, 256/189
| 35/26
| 4/3, 18/13
|-
|-
| 10
| 10
Line 150: Line 238:
| Gb
| Gb
| Narrow tritone
| Narrow tritone
| 32/23
| 18/13
| 7/5, 11/8
|-
|-
| 11
| 11
Line 161: Line 246:
| G
| G
| Wide tritone
| Wide tritone
| 23/16
| 13/9
| 10/7, 16/11
|-
|-
| 12
| 12
Line 172: Line 254:
| G#
| G#
| Grave 5th
| Grave 5th
| 189/128, 240/161
| 52/35
| 3/2, 13/9
|-
|-
| 13
| 13
Line 183: Line 262:
| Hb
| Hb
| Fifth-sixth ([[cocytic]])
| Fifth-sixth ([[cocytic]])
| 23/15
| 17/11, 20/13, 26/17
| 20/13
|-
|-
| 14
| 14
Line 194: Line 270:
| H
| H
| Minor 6th
| Minor 6th
| 46/29
| 35/22
| 8/5, 11/7, 14/9, 18/11
|-
|-
| 15
| 15
Line 205: Line 278:
| H#/Ab
| H#/Ab
| Neutral 6th
| Neutral 6th
| 23/14
| 18/11
| 13/8
|-
|-
| 16
| 16
Line 216: Line 286:
| A
| A
| Supermajor 6th
| Supermajor 6th
| 27/16, 46/27
| 17/10, 22/13
| 5/3, 12/7
|-
|-
| 17
| 17
Line 227: Line 294:
| A#
| A#
| Subminor 7th
| Subminor 7th
| 7/4
| 7/4
| 7/4, 9/5
|-
|-
| 18
| 18
Line 238: Line 302:
| Bb
| Bb
| Supraminor 7th
| Supraminor 7th
| 29/16, 9/5
| 9/5, 20/11
| 16/9, 20/11
|-
|-
| 19
| 19
Line 249: Line 310:
| B
| B
| Major 7th
| Major 7th
| 15/8
| 17/9
| 15/8, 48/25
|-
|-
| 20
| 20
Line 260: Line 318:
| B#/Cb
| B#/Cb
| Supermajor 7th
| Supermajor 7th
| 27/14, 29/15
| 35/18, 68/35
| 63/32
|-
|-
| 21
| 21
Line 271: Line 326:
| C
| C
| Octave
| Octave
| 2/1
| 2/1
| 2/1
|}
|}
&lowast;1: based on treating 21edo as a 2.7.15.23.27.29 subgroup temperament
&lowast;2: based on treating 21edo as a 2.9/5.11/5.13/5.17/5.35/5 subgroup temperament
&lowast;3: based on treating 21edo as 13-limit laconic temperament
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