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39edo: Difference between revisions

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Explain exactly why 39d is better. Move other mappings to their subsection
→Intervals: break off the tri-column of color notation for a clean table
Line 26: Line 26:
{| class="wikitable center-all right-2 left-3 left-4 left-5 right-9 right-10"
{| class="wikitable center-all right-2 left-3 left-4 left-5 right-9 right-10"
|-
|-
! rowspan="2" | Steps
! rowspan="2" | #
! rowspan="2" | Cents
! rowspan="2" | Cents
! rowspan="2" | Ratios of the<br>[[2.3.5.11 subgroup]]
! 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]]
|-
|-
! Patent val
! Patent val
Line 38: Line 37:
| 0.0
| 0.0
| colspan=3 | [[1/1]]
| colspan=3 | [[1/1]]
|-
| 1
| 30.8
| [[55/54]], [[81/80]]
| ''[[28/27]]'', [[64/63]]
| ''[[36/35]]'', [[50/49]], ''[[56/55]]''
|-
| 2
| 61.5
| [[33/32]]
| ''[[21/20]]'', [[36/35]]
| [[28/27]], ''[[49/48]]''
|-
| 3
| 92.3
| ''[[16/15]]'', ''[[25/24]]''
| ''[[50/49]]''
| [[21/20]]
|-
| 4
| 123.1
|
|
| [[15/14]]
|-
| 5
| 153.8
| [[11/10]], [[12/11]]
| ''[[15/14]]''
|
|-
| 6
| 184.6
| [[10/9]]
|
|
|-
| 7
| 215.4
| [[9/8]]
|
| ''[[8/7]]''
|-
| 8
| 246.2
|
| [[8/7]], ''[[7/6]]''
| [[81/70]]
|-
| 9
| 276.9
|
| ''[[81/70]]''
| [[7/6]]
|-
| 10
| 307.7
| [[6/5]]
|
|
|-
| 11
| 338.5
| [[11/9]]
|
|
|-
| 12
| 369.2
| [[27/22]]
|
|
|-
| 13
| 400.0
| [[5/4]]
| ''[[14/11]]''
|
|-
| 14
| 430.8
|
| ''[[35/27]]''
| [[9/7]], [[14/11]]
|-
| 15
| 461.5
|
| ''[[9/7]]''
| [[35/27]]
|-
| 16
| 492.3
| [[4/3]]
|
|
|-
| 17
| 523.1
| [[27/20]]
|
|
|-
| 18
| 553.8
| [[11/8]]
| ''[[7/5]]''
|
|-
| 19
| 584.6
|
|
| [[7/5]]
|-
| 20
| 615.4
|
|
| [[10/7]]
|-
| 21
| 646.2
| [[16/11]]
| ''[[10/7]]''
|
|-
| 22
| 676.9
| [[40/27]]
|
|
|-
| 23
| 707.7
| [[3/2]]
|
|
|-
| 24
| 738.5
|
| ''[[14/9]]''
| [[54/35]]
|-
| 25
| 769.2
|
| ''[[54/35]]''
| [[11/7]], [[14/9]]
|-
| 26
| 800.0
| [[8/5]]
| ''[[11/7]]''
|
|-
| 27
| 830.8
| [[44/27]]
|
|
|-
| 28
| 861.5
| [[18/11]]
|
|
|-
| 29
| 892.3
| [[5/3]]
|
|
|-
| 30
| 923.1
|
| ''[[140/81]]''
| [[12/7]]
|-
| 31
| 953.8
|
| [[7/4]], ''[[12/7]]''
| [[140/81]]
|-
| 32
| 984.6
| [[16/9]]
|
| ''[[7/4]]''
|-
| 33
| 1015.4
| [[9/5]]
|
|
|-
| 34
| 1046.2
| [[11/6]], [[20/11]]
| ''[[28/15]]''
|
|-
| 35
| 1076.9
|
|
| [[28/15]]
|-
| 36
| 1107.7
| ''[[15/8]]'', ''[[48/25]]''
| ''[[49/25]]''
| [[40/21]]
|-
| 37
| 1138.5
| [[64/33]]
| [[35/18]], ''[[40/21]]''
| [[27/14]], ''[[96/49]]''
|-
| 38
| 1169.2
| [[108/55]], [[160/81]]
| [[63/32]], ''[[27/14]]''
| ''[[35/18]]'', [[49/25]]
|-
| 39
| 1200.0
| colspan=3 | [[2/1]]
|}
=== Proposed interval names and solfèges ===
{| class="wikitable mw-collapsible mw-collapsed center-1 right-2 center-3 center-5"
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
|-
! #
! Cents
! colspan="3" | [[Ups and downs notation]]
|-
| 0
| 0.0
| P1
| P1
| perfect unison
| perfect unison
Line 44: Line 287:
| 1
| 1
| 30.8
| 30.8
| [[55/54]], [[81/80]]
| ''[[28/27]]'', [[64/63]]
| ''[[36/35]]'', [[50/49]], ''[[56/55]]''
| ^1, <br>vm2
| ^1, <br>vm2
| up unison, <br>downminor 2nd
| up unison, <br>downminor 2nd
Line 53: Line 293:
| 2
| 2
| 61.5
| 61.5
| [[33/32]]
| ''[[21/20]]'', [[36/35]]
| [[28/27]], ''[[49/48]]''
| m2
| m2
| minor 2nd
| minor 2nd
Line 62: Line 299:
| 3
| 3
| 92.3
| 92.3
| ''[[16/15]]'', ''[[25/24]]''
| ''[[50/49]]''
| [[21/20]]
| ^m2
| ^m2
| upminor 2nd
| upminor 2nd
Line 71: Line 305:
| 4
| 4
| 123.1
| 123.1
|
|
| [[15/14]]
| ^^m2
| ^^m2
| dupminor 2nd
| dupminor 2nd
Line 80: Line 311:
| 5
| 5
| 153.8
| 153.8
| [[11/10]], [[12/11]]
| ''[[15/14]]''
|
| vvM2
| vvM2
| dudmajor 2nd
| dudmajor 2nd
Line 89: Line 317:
| 6
| 6
| 184.6
| 184.6
| [[10/9]]
|
|
| vM2
| vM2
| downmajor 2nd
| downmajor 2nd
Line 98: Line 323:
| 7
| 7
| 215.4
| 215.4
| [[9/8]]
|
| ''[[8/7]]''
| M2
| M2
| major 2nd
| major 2nd
Line 107: Line 329:
| 8
| 8
| 246.2
| 246.2
|
| [[8/7]], ''[[7/6]]''
| [[81/70]]
| ^M2, <br>vm3
| ^M2, <br>vm3
| upmajor 2nd, <br>downminor 3rd
| upmajor 2nd, <br>downminor 3rd
Line 116: Line 335:
| 9
| 9
| 276.9
| 276.9
|
| ''[[81/70]]''
| [[7/6]]
| m3
| m3
| minor 3rd
| minor 3rd
Line 125: Line 341:
| 10
| 10
| 307.7
| 307.7
| [[6/5]]
|
|
| ^m3
| ^m3
| upminor 3rd
| upminor 3rd
Line 134: Line 347:
| 11
| 11
| 338.5
| 338.5
| [[11/9]]
|
|
| ^^m3
| ^^m3
| dupminor 3rd
| dupminor 3rd
Line 143: Line 353:
| 12
| 12
| 369.2
| 369.2
| [[27/22]]
|
|
| vvM3
| vvM3
| dudmajor 3rd
| dudmajor 3rd
Line 152: Line 359:
| 13
| 13
| 400.0
| 400.0
| [[5/4]]
| ''[[14/11]]''
|
| vM3
| vM3
| downmajor 3rd
| downmajor 3rd
Line 161: Line 365:
| 14
| 14
| 430.8
| 430.8
|
| ''[[35/27]]''
| [[9/7]], [[14/11]]
| M3
| M3
| major 3rd
| major 3rd
Line 170: Line 371:
| 15
| 15
| 461.5
| 461.5
|
| ''[[9/7]]''
| [[35/27]]
| v4
| v4
| down 4th
| down 4th
Line 179: Line 377:
| 16
| 16
| 492.3
| 492.3
| [[4/3]]
|
|
| P4
| P4
| perfect 4th
| perfect 4th
Line 188: Line 383:
| 17
| 17
| 523.1
| 523.1
| [[27/20]]
|
|
| ^4
| ^4
| up 4th
| up 4th
Line 197: Line 389:
| 18
| 18
| 553.8
| 553.8
| [[11/8]]
| ''[[7/5]]''
|
| ^^4
| ^^4
| dup 4th
| dup 4th
Line 206: Line 395:
| 19
| 19
| 584.6
| 584.6
|
|
| [[7/5]]
| vvA4, <br>^d5
| vvA4, <br>^d5
| dudaug 4th, <br>updim 5th
| dudaug 4th, <br>updim 5th
Line 215: Line 401:
| 20
| 20
| 615.4
| 615.4
|
|
| [[10/7]]
| vA4, <br>^^d5
| vA4, <br>^^d5
| downaug 4th, <br>dupdim 5th
| downaug 4th, <br>dupdim 5th
Line 224: Line 407:
| 21
| 21
| 646.2
| 646.2
| [[16/11]]
| ''[[10/7]]''
|
| vv5
| vv5
| dud 5th
| dud 5th
Line 233: Line 413:
| 22
| 22
| 676.9
| 676.9
| [[40/27]]
|
|
| v5
| v5
| down 5th
| down 5th
Line 242: Line 419:
| 23
| 23
| 707.7
| 707.7
| [[3/2]]
|
|
| P5
| P5
| perfect 5th
| perfect 5th
Line 251: Line 425:
| 24
| 24
| 738.5
| 738.5
|
| ''[[14/9]]''
| [[54/35]]
| ^5
| ^5
| up 5th
| up 5th
Line 260: Line 431:
| 25
| 25
| 769.2
| 769.2
|
| ''[[54/35]]''
| [[11/7]], [[14/9]]
| m6
| m6
| minor 6th
| minor 6th
Line 269: Line 437:
| 26
| 26
| 800.0
| 800.0
| [[8/5]]
| ''[[11/7]]''
|
| ^m6
| ^m6
| upminor 6th
| upminor 6th
Line 278: Line 443:
| 27
| 27
| 830.8
| 830.8
| [[44/27]]
|
|
| ^^m6
| ^^m6
| dupminor 6th
| dupminor 6th
Line 287: Line 449:
| 28
| 28
| 861.5
| 861.5
| [[18/11]]
|
|
| vvM6
| vvM6
| dudmajor 6th
| dudmajor 6th
Line 296: Line 455:
| 29
| 29
| 892.3
| 892.3
| [[5/3]]
|
|
| vM6
| vM6
| downmajor 6th
| downmajor 6th
Line 305: Line 461:
| 30
| 30
| 923.1
| 923.1
|
| ''[[140/81]]''
| [[12/7]]
| M6
| M6
| major 6th
| major 6th
Line 314: Line 467:
| 31
| 31
| 953.8
| 953.8
|
| [[7/4]], ''[[12/7]]''
| [[140/81]]
| ^M6, <br>vm7
| ^M6, <br>vm7
| upmajor 6th, <br>downminor 7th
| upmajor 6th, <br>downminor 7th
Line 323: Line 473:
| 32
| 32
| 984.6
| 984.6
| [[16/9]]
|
| ''[[7/4]]''
| m7
| m7
| minor 7th
| minor 7th
Line 332: Line 479:
| 33
| 33
| 1015.4
| 1015.4
| [[9/5]]
|
|
| ^m7
| ^m7
| upminor 7th
| upminor 7th
Line 341: Line 485:
| 34
| 34
| 1046.2
| 1046.2
| [[11/6]], [[20/11]]
| ''[[28/15]]''
|
| ^^m7
| ^^m7
| dupminor 7th
| dupminor 7th
Line 350: Line 491:
| 35
| 35
| 1076.9
| 1076.9
|
|
| [[28/15]]
| vvM7
| vvM7
| dudmajor 7th
| dudmajor 7th
Line 359: Line 497:
| 36
| 36
| 1107.7
| 1107.7
| ''[[15/8]]'', ''[[48/25]]''
| ''[[49/25]]''
| [[40/21]]
| vM7
| vM7
| downmajor 7th
| downmajor 7th
Line 368: Line 503:
| 37
| 37
| 1138.5
| 1138.5
| [[64/33]]
| [[35/18]], ''[[40/21]]''
| [[27/14]], ''[[96/49]]''
| M7
| M7
| major 7th
| major 7th
Line 377: Line 509:
| 38
| 38
| 1169.2
| 1169.2
| [[108/55]], [[160/81]]
| [[63/32]], ''[[27/14]]''
| ''[[35/18]]'', [[49/25]]
| ^M7, <br>v8
| ^M7, <br>v8
| upmajor 7th, <br>down 8ve
| upmajor 7th, <br>down 8ve
Line 386: Line 515:
| 39
| 39
| 1200.0
| 1200.0
| colspan=3 | [[2/1]]
| P8
| P8
| perfect 8ve
| perfect 8ve
Line 392: Line 520:
|}
|}


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 [[Kite's ups and downs notation #Chords and chord progressions]].


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