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→Intervals: cleanup and links (minor note: don't italicize ","); Remove "nearest just interval" (generally not preferred).
Line 26: Line 26:
! rowspan="2" | Steps
! rowspan="2" | Steps
! rowspan="2" | Cents
! rowspan="2" | Cents
! rowspan="2" | Approximate ratios (2.3.5.11)
! rowspan="2" | Ratios of the<br>[[2.3.5.11 subgroup]]
! colspan="2" |Intervals of 7
! colspan="2" | Intervals of 7
! colspan="3" rowspan="2" | [[Ups and downs notation]]
! colspan="3" rowspan="2" | [[Ups and downs notation]]
! colspan="3" rowspan="2" | [[Nearest just interval]] <br>(Ratio, cents, error)
|-
|-
!Patent val
! Patent val
!Superpyth (39d) val
! 39d val
|-
|-
| 0
| 0
| 0.0
| 0.0
| [[1/1]]
| colspan=3 | [[1/1]]
|
|
| P1
| P1
| perfect unison
| perfect unison
| D
| D
| 1/1
| 0.00
| None
|-
|-
| 1
| 1
| 30.8
| 30.8
| [[55/54]], [[81/80]]
| [[55/54]], [[81/80]]
|''28/27,'' 64/63
| ''[[28/27]]'', [[64/63]]
|''[[36/35]],'' [[50/49]]'', [[56/55]]''
| ''[[36/35]]'', [[50/49]], ''[[56/55]]''
| ^1, <br>vm2
| ^1, <br>vm2
| up unison, <br>downminor 2nd
| up unison, <br>downminor 2nd
| ^D, <br>vEb
| ^D, <br>vEb
| 57/56
| 30.64
| +0.1271
|-
|-
| 2
| 2
| 61.5
| 61.5
| [[33/32]]
| [[33/32]]
|''21/20,'' 36/35
| ''[[21/20]]'', [[36/35]]
|[[28/27]], ''[[49/48]]''
| [[28/27]], ''[[49/48]]''
| m2
| m2
| minor 2nd
| minor 2nd
| Eb
| Eb
| 29/28
| 60.75
| +0.7872
|-
|-
| 3
| 3
| 92.3
| 92.3
| ''[[16/15]]'', ''[[25/24]]''
| ''[[16/15]]'', ''[[25/24]]''
|''50/49''
| ''[[50/49]]''
|[[21/20]]
| [[21/20]]
| ^m2
| ^m2
| upminor 2nd
| upminor 2nd
| ^Eb
| ^Eb
| 39/37
| 91.14
| +1.1691
|-
|-
| 4
| 4
Line 86: Line 71:
|
|
|
|
|[[15/14]]
| [[15/14]]
| ^^m2
| ^^m2
| dupminor 2nd
| dupminor 2nd
| ^^Eb
| ^^Eb
| 44/41
| 122.26
| +0.8214
|-
|-
| 5
| 5
| 153.8
| 153.8
| [[11/10]], [[12/11]]
| [[11/10]], [[12/11]]
|''15/14''
| ''[[15/14]]''
|
|
| vvM2
| vvM2
| dudmajor 2nd
| dudmajor 2nd
| vvE
| vvE
| 35/32
| 155.14
| -1.2934
|-
|-
| 6
| 6
Line 114: Line 93:
| downmajor 2nd
| downmajor 2nd
| vE
| vE
| 10/9
| 182.40
| +2.2117
|-
|-
| 7
| 7
Line 122: Line 98:
| [[9/8]]
| [[9/8]]
|
|
|''[[8/7]]''
| ''[[8/7]]''
| M2
| M2
| major 2nd
| major 2nd
| E
| E
| 17/15
| 216.69
| -1.3021
|-
|-
| 8
| 8
| 246.2
| 246.2
|
|
|8/7, ''7/6''
| [[8/7]], ''[[7/6]]''
|[[81/70]]
| [[81/70]]
| ^M2, <br>vm3
| ^M2, <br>vm3
| upmajor 2nd, <br>downminor 3rd
| upmajor 2nd, <br>downminor 3rd
| ^E, <br>vF
| ^E, <br>vF
| 15/13
| 247.74
| -1.5873
|-
|-
| 9
| 9
| 276.9
| 276.9
|
|
|''81/70''
| ''[[81/70]]''
|[[7/6]]
| [[7/6]]
| m3
| m3
| minor 3rd
| minor 3rd
| F
| F
| 27/23
| 277.59
| -0.6676
|-
|-
| 10
| 10
Line 162: Line 129:
| upminor 3rd
| upminor 3rd
| ^F
| ^F
| 43/36
| 307.61
| +0.0846
|-
|-
| 11
| 11
Line 174: Line 138:
| dupminor 3rd
| dupminor 3rd
| ^^F
| ^^F
| 17/14
| 336.13
| +2.3320
|-
|-
| 12
| 12
Line 186: Line 147:
| dudmajor 3rd
| dudmajor 3rd
| vvF#
| vvF#
| 26/21
| 369.75
| -0.5160
|-
|-
| 13
| 13
| 400.0
| 400.0
| [[5/4]]
| [[5/4]]
|''14/11''
| ''[[14/11]]''
|
|
| vM3
| vM3
| downmajor 3rd
| downmajor 3rd
| vF#
| vF#
| 34/27
| 399.09
| +0.9096
|-
|-
| 14
| 14
| 430.8
| 430.8
|
|
|''35/27''
| ''[[35/27]]''
|[[9/7]], [[14/11]]
| [[9/7]], [[14/11]]
| M3
| M3
| major 3rd
| major 3rd
| F#
| F#
| 41/32
| 429.06
| +1.7068
|-
|-
| 15
| 15
| 461.5
| 461.5
|
|
|''9/7''
| ''[[9/7]]''
|[[35/27]]
| [[35/27]]
| v4
| v4
| down 4th
| down 4th
| vG
| vG
| 30/23
| 459.99
| +1.5441
|-
|-
| 16
| 16
Line 234: Line 183:
| perfect 4th
| perfect 4th
| G
| G
| 85/64
| 491.27
| +1.0386
|-
|-
| 17
| 17
Line 246: Line 192:
| up 4th
| up 4th
| ^G
| ^G
| 23/17
| 523.32
| -0.2420
|-
|-
| 18
| 18
| 553.8
| 553.8
| [[11/8]]
| [[11/8]]
|''7/5''
| ''[[7/5]]''
|
|
| ^^4
| ^^4
| dup 4th
| dup 4th
| ^^G
| ^^G
| 11/8
| 551.32
| +2.5283
|-
|-
| 19
| 19
Line 266: Line 206:
|
|
|
|
|[[7/5]]
| [[7/5]]
| vvA4, <br>^d5
| vvA4, <br>^d5
| dudaug 4th, <br>updim 5th
| dudaug 4th, <br>updim 5th
| vvG#, <br>^Ab
| vvG#, <br>^Ab
| 7/5
| 582.51
| +2.1032
|-
|-
| 20
| 20
Line 278: Line 215:
|
|
|
|
|[[10/7]]
| [[10/7]]
| vA4, <br>^^d5
| vA4, <br>^^d5
| downaug 4th, <br>dupdim 5th
| downaug 4th, <br>dupdim 5th
| vG#, <br>^^Ab
| vG#, <br>^^Ab
| 10/7
| 617.49
| -2.1032
|-
|-
| 21
| 21
| 646.2
| 646.2
| [[16/11]]
| [[16/11]]
|''10/7''
| ''[[10/7]]''
|
|
| vv5
| vv5
| dud 5th
| dud 5th
| vvA
| vvA
| 16/11
| 648.68
| -2.5283
|-
|-
| 22
| 22
Line 306: Line 237:
| down 5th
| down 5th
| vA
| vA
| 34/23
| 676.68
| +0.2420
|-
|-
| 23
| 23
Line 318: Line 246:
| perfect 5th
| perfect 5th
| A
| A
| 128/85
| 708.73
| -1.0386
|-
|-
| 24
| 24
| 738.5
| 738.5
|
|
|''14/9''
| ''[[14/9]]''
|[[54/35]]
| [[54/35]]
| ^5
| ^5
| up 5th
| up 5th
| A^
| A^
| 23/15
| 740.01
| -1.5441
|-
|-
| 25
| 25
| 769.2
| 769.2
|
|
|''54/35''
| ''[[54/35]]''
|[[11/7]], [[14/9]]
| [[11/7]], [[14/9]]
| m6
| m6
| minor 6th
| minor 6th
| Bb
| Bb
| 64/41
| 770.94
| -1.7068
|-
|-
| 26
| 26
| 800.0
| 800.0
| [[8/5]]
| [[8/5]]
|''11/7''
| ''[[11/7]]''
|
|
| ^m6
| ^m6
| upminor 6th
| upminor 6th
| ^Bb
| ^Bb
| 27/17
| 800.91
| -0.9096
|-
|-
| 27
| 27
Line 366: Line 282:
| dupminor 6th
| dupminor 6th
| ^^Bb
| ^^Bb
| 21/13
| 830.25
| +0.5160
|-
|-
| 28
| 28
Line 378: Line 291:
| dudmajor 6th
| dudmajor 6th
| vvB
| vvB
| 28/17
| 863.87
| -2.3320
|-
|-
| 29
| 29
Line 390: Line 300:
| downmajor 6th
| downmajor 6th
| vB
| vB
| 72/43
| 892.39
| -0.0846
|-
|-
| 30
| 30
| 923.1
| 923.1
|
|
|''140/81''
| ''[[140/81]]''
|[[12/7]]
| [[12/7]]
| M6
| M6
| major 6th
| major 6th
| B
| B
| 46/27
| 922.41
| +0.6676
|-
|-
| 31
| 31
| 953.8
| 953.8
|
|
|7/4, ''12/7''
| [[7/4]], ''[[12/7]]''
|[[140/81]]
| [[140/81]]
| ^M6, <br>vm7
| ^M6, <br>vm7
| upmajor 6th, <br>downminor 7th
| upmajor 6th, <br>downminor 7th
| ^B, <br>vC
| ^B, <br>vC
| 26/15
| 952.26
| +1.5873
|-
|-
| 32
| 32
Line 422: Line 323:
| [[16/9]]
| [[16/9]]
|
|
|''[[7/4]]''
| ''[[7/4]]''
| m7
| m7
| minor 7th
| minor 7th
| C
| C
| 30/17
| 983.31
| +1.3021
|-
|-
| 33
| 33
Line 438: Line 336:
| upminor 7th
| upminor 7th
| ^C
| ^C
| 9/5
| 1017.60
| -2.2117
|-
|-
| 34
| 34
| 1046.2
| 1046.2
| [[11/6]], [[20/11]]
| [[11/6]], [[20/11]]
|''28/15''
| ''[[28/15]]''
|
|
| ^^m7
| ^^m7
| dupminor 7th
| dupminor 7th
| ^^C
| ^^C
| 64/35
| 1044.86
| +1.2934
|-
|-
| 35
| 35
Line 458: Line 350:
|
|
|
|
|[[28/15]]
| [[28/15]]
| vvM7
| vvM7
| dudmajor 7th
| dudmajor 7th
| vvC#
| vvC#
| 41/22
| 1077.74
| -0.8214
|-
|-
| 36
| 36
| 1107.7
| 1107.7
| ''[[15/8]]'', ''[[48/25]]''
| ''[[15/8]]'', ''[[48/25]]''
|''49/25''
| ''[[49/25]]''
|[[40/21]]
| [[40/21]]
| vM7
| vM7
| downmajor 7th
| downmajor 7th
| vC#
| vC#
| 74/39
| 1108.86
| -1.1691
|-
|-
| 37
| 37
| 1138.5
| 1138.5
| [[64/33]]
| [[64/33]]
|35/18'', 40/21''
| [[35/18]], ''[[40/21]]''
|[[27/14]], ''[[96/49]]''
| [[27/14]], ''[[96/49]]''
| M7
| M7
| major 7th
| major 7th
| C#
| C#
| 56/29
| 1139.25
| -0.7872
|-
|-
| 38
| 38
| 1169.2
| 1169.2
| [[55/28]], [[108/55]], [[160/81]]
| [[108/55]], [[160/81]]
|63/32, ''27/14''
| [[63/32]], ''[[27/14]]''
|''[[35/18]], [[49/25]]''
| ''[[35/18]]'', [[49/25]]
| ^M7, <br>v8
| ^M7, <br>v8
| upmajor 7th, <br>down 8ve
| upmajor 7th, <br>down 8ve
| ^C#, <br>vD
| ^C#, <br>vD
| 112/57
| 1169.36
| -0.1271
|-
|-
| 39
| 39
| 1200.0
| 1200.0
| [[2/1]]
| colspan=3 | [[2/1]]
|
|
| P8
| P8
| perfect 8ve
| perfect 8ve
| D
| D
| 2/1
| 1200.00
| None
|}
|}
<nowiki/>* 11-limit in the 39d val, inconsistent intervals in ''italic''
<nowiki/>* 11-limit in the 39d val, inconsistent intervals in ''italic''


Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chords and chord progressions]].
Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chords and chord progressions]].


== Notation ==
== Notation ==
Retrieved from "https://en.xen.wiki/w/39edo"