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39edo: Difference between revisions

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Relegate armodue notation to a new notation section
→Intervals: precision to 2 decimal places, following the nearby 41edo; sort ratios by complexity
Line 20: Line 20:
! Steps
! Steps
! Cents
! Cents
! Approximate Ratios<br>in 39d [[Val]]
! Approximate Ratios*
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Nearest just interval]]<br>(Ratio, Cents, Error)
! colspan="3" | [[Nearest just interval|Nearest Just Interval]]<br>(Ratio, Cents, Error)
|-
|-
| 0
| 0
| 0.0000
| 0.00
| [[1/1]]
| [[1/1]]
| P1
| P1
Line 31: Line 31:
| D
| D
| 1/1
| 1/1
| 0.0000
| 0.00
| None
| None
|-
|-
| 1
| 1
| 30.7692
| 30.77
| [[81/80]], [[36/35]], [[50/49]], [[55/54]], [[56/55]]
| ''[[36/35]]'', [[50/49]], [[55/54]], [[56/55]], [[81/80]]
| ^1,<br>vm2
| ^1,<br>vm2
| up unison, <br>downminor 2nd
| up unison, <br>downminor 2nd
| ^D, <br>vEb
| ^D, <br>vEb
| 57/56
| 57/56
| 30.6421
| 30.64
| +0.1271
| +0.1271
|-
|-
| 2
| 2
| 61.5385
| 61.54
| [[28/27]], [[49/48]], [[33/32]]
| [[28/27]], [[33/32]], ''[[49/48]]''
| m2
| m2
| minor 2nd
| minor 2nd
| Eb
| Eb
| 29/28
| 29/28
| 60.7513
| 60.75
| +0.7872
| +0.7872
|-
|-
| 3
| 3
| 92.3077
| 92.31
| [[16/15]], [[25/24]], [[21/20]]
| ''[[16/15]]'', [[21/20]], ''[[25/24]]''
| ^m2
| ^m2
| upminor 2nd
| upminor 2nd
| ^Eb
| ^Eb
| 39/37
| 39/37
| 91.1386
| 91.14
| +1.1691
| +1.1691
|-
|-
| 4
| 4
| 123.0769
| 123.08
| [[15/14]]
| [[15/14]]
| ^^m2
| ^^m2
Line 71: Line 71:
| ^^Eb
| ^^Eb
| 44/41
| 44/41
| 122.2555
| 122.26
| +0.8214
| +0.8214
|-
|-
| 5
| 5
| 153.8462
| 153.85
| [[12/11]], [[11/10]]
| [[11/10]], [[12/11]]
| vvM2
| vvM2
| dudmajor 2nd
| dudmajor 2nd
| vvE
| vvE
| 35/32
| 35/32
| 155.1396
| 155.14
| -1.2934
| -1.2934
|-
|-
| 6
| 6
| 184.6154
| 184.62
| [[10/9]]
| [[10/9]]
| vM2
| vM2
Line 91: Line 91:
| vE
| vE
| 10/9
| 10/9
| 182.4037
| 182.40
| +2.2117
| +2.2117
|-
|-
| 7
| 7
| 215.3846
| 215.38
| [[9/8]], [[8/7]]
| [[9/8]], ''[[8/7]]''
| M2
| M2
| major 2nd
| major 2nd
| E
| E
| 17/15
| 17/15
| 216.6867
| 216.69
| -1.3021
| -1.3021
|-
|-
| 8
| 8
| 246.1538
| 246.15
| [[81/70]]
| [[81/70]]
| ^M2, <br>vm3
| ^M2, <br>vm3
Line 111: Line 111:
| ^E, <br>vF
| ^E, <br>vF
| 15/13
| 15/13
| 247.7411
| 247.74
| -1.5873
| -1.5873
|-
|-
| 9
| 9
| 276.9231
| 276.92
| [[7/6]]
| [[7/6]]
| m3
| m3
Line 121: Line 121:
| F
| F
| 27/23
| 27/23
| 277.5907
| 277.59
| -0.6676
| -0.6676
|-
|-
| 10
| 10
| 307.6923
| 307.69
| [[6/5]]
| [[6/5]]
| ^m3
| ^m3
Line 131: Line 131:
| ^F
| ^F
| 43/36
| 43/36
| 307.6077
| 307.61
| +0.0846
| +0.0846
|-
|-
| 11
| 11
| 338.4615
| 338.46
| [[11/9]]
| [[11/9]]
| ^^m3
| ^^m3
Line 141: Line 141:
| ^^F
| ^^F
| 17/14
| 17/14
| 336.1295
| 336.13
| +2.3320
| +2.3320
|-
|-
| 12
| 12
| 369.2308
| 369.23
| [[27/22]]
| [[27/22]]
| vvM3
| vvM3
Line 151: Line 151:
| vvF#
| vvF#
| 26/21
| 26/21
| 369.7468
| 369.75
| -0.5160
| -0.5160
|-
|-
| 13
| 13
| 400.0000
| 400.00
| [[5/4]]
| [[5/4]]
| vM3
| vM3
Line 161: Line 161:
| vF#
| vF#
| 34/27
| 34/27
| 399.0904
| 399.09
| +0.9096
| +0.9096
|-
|-
| 14
| 14
| 430.7692
| 430.77
| [[9/7]], [[14/11]]
| [[9/7]], [[14/11]]
| M3
| M3
Line 171: Line 171:
| F#
| F#
| 41/32
| 41/32
| 429.0624
| 429.06
| +1.7068
| +1.7068
|-
|-
| 15
| 15
| 461.5385
| 461.54
| [[35/27]]
| [[35/27]]
| v4
| v4
Line 181: Line 181:
| vG
| vG
| 30/23
| 30/23
| 459.9944
| 459.99
| +1.5441
| +1.5441
|-
|-
| 16
| 16
| 492.3077
| 492.31
| [[4/3]]
| [[4/3]]
| P4
| P4
Line 191: Line 191:
| G
| G
| 85/64
| 85/64
| 491.2691
| 491.27
| +1.0386
| +1.0386
|-
|-
| 17
| 17
| 523.0769
| 523.08
| [[27/20]]
| [[27/20]]
| ^4
| ^4
Line 201: Line 201:
| ^G
| ^G
| 23/17
| 23/17
| 523.3189
| 523.32
| -0.2420
| -0.2420
|-
|-
| 18
| 18
| 553.8462
| 553.85
| [[11/8]]
| [[11/8]]
| ^^4
| ^^4
Line 211: Line 211:
| ^^G
| ^^G
| 11/8
| 11/8
| 551.3179
| 551.32
| +2.5283
| +2.5283
|-
|-
| 19
| 19
| 584.6154
| 584.62
| [[7/5]]
| [[7/5]]
| vvA4, <br>^d5
| vvA4, <br>^d5
Line 221: Line 221:
| vvG#, <br>^Ab
| vvG#, <br>^Ab
| 7/5
| 7/5
| 582.5122
| 582.51
| +2.1032
| +2.1032
|-
|-
| 20
| 20
| 615.3846
| 615.38
| [[10/7]]
| [[10/7]]
| vA4, <br>^^d5
| vA4, <br>^^d5
Line 231: Line 231:
| vG#, <br>^^Ab
| vG#, <br>^^Ab
| 10/7
| 10/7
| 617.4878
| 617.49
| -2.1032
| -2.1032
|-
|-
| 21
| 21
| 646.1538
| 646.15
| [[16/11]]
| [[16/11]]
| vv5
| vv5
Line 241: Line 241:
| vvA
| vvA
| 16/11
| 16/11
| 648.6821
| 648.68
| -2.5283
| -2.5283
|-
|-
| 22
| 22
| 676.9231
| 676.92
| [[40/27]]
| [[40/27]]
| v5
| v5
Line 251: Line 251:
| vA
| vA
| 34/23
| 34/23
| 676.6811
| 676.68
| +0.2420
| +0.2420
|-
|-
| 23
| 23
| 707.6923
| 707.69
| [[3/2]]
| [[3/2]]
| P5
| P5
Line 261: Line 261:
| A
| A
| 128/85
| 128/85
| 708.7309
| 708.73
| -1.0386
| -1.0386
|-
|-
| 24
| 24
| 738.4615
| 738.46
| [[54/35]]
| [[54/35]]
| ^5
| ^5
Line 271: Line 271:
| A^
| A^
| 23/15
| 23/15
| 740.0056
| 740.01
| -1.5441
| -1.5441
|-
|-
| 25
| 25
| 769.2308
| 769.23
| [[14/9]], [[11/7]]
| [[11/7]], [[14/9]]
| m6
| m6
| minor 6th
| minor 6th
| Bb
| Bb
| 64/41
| 64/41
| 770.9376
| 770.94
| -1.7068
| -1.7068
|-
|-
| 26
| 26
| 800.0000
| 800.00
| [[8/5]]
| [[8/5]]
| ^m6
| ^m6
Line 291: Line 291:
| ^Bb
| ^Bb
| 27/17
| 27/17
| 800.9096
| 800.91
| -0.9096
| -0.9096
|-
|-
| 27
| 27
| 830.7692
| 830.77
| [[44/27]]
| [[44/27]]
| ^^m6
| ^^m6
Line 301: Line 301:
| ^^Bb
| ^^Bb
| 21/13
| 21/13
| 830.2532
| 830.25
| +0.5160
| +0.5160
|-
|-
| 28
| 28
| 861.5385
| 861.54
| [[18/11]]
| [[18/11]]
| vvM6
| vvM6
Line 311: Line 311:
| vvB
| vvB
| 28/17
| 28/17
| 863.8705
| 863.87
| -2.3320
| -2.3320
|-
|-
| 29
| 29
| 892.3077
| 892.31
| [[5/3]]
| [[5/3]]
| vM6
| vM6
Line 321: Line 321:
| vB
| vB
| 72/43
| 72/43
| 892.3923
| 892.39
| -0.0846
| -0.0846
|-
|-
| 30
| 30
| 923.0769
| 923.08
| [[12/7]]
| [[12/7]]
| M6
| M6
Line 331: Line 331:
| B
| B
| 46/27
| 46/27
| 922.4093
| 922.41
| +0.6676
| +0.6676
|-
|-
| 31
| 31
| 953.8462
| 953.85
| [[140/81]]
| [[140/81]]
| ^M6, <br>vm7
| ^M6, <br>vm7
Line 341: Line 341:
| ^B, <br>vC
| ^B, <br>vC
| 26/15
| 26/15
| 952.2589
| 952.26
| +1.5873
| +1.5873
|-
|-
| 32
| 32
| 984.6154
| 984.62
| [[16/9]], [[7/4]]
| ''[[7/4]]'', [[16/9]]
| m7
| m7
| minor 7th
| minor 7th
| C
| C
| 30/17
| 30/17
| 983.3133
| 983.31
| +1.3021
| +1.3021
|-
|-
| 33
| 33
| 1015.3846
| 1015.38
| [[9/5]]
| [[9/5]]
| ^m7
| ^m7
Line 361: Line 361:
| ^C
| ^C
| 9/5
| 9/5
| 1017.5963
| 1017.60
| -2.2117
| -2.2117
|-
|-
| 34
| 34
| 1046.1538
| 1046.15
| [[11/6]], [[20/11]]
| [[11/6]], [[20/11]]
| ^^m7
| ^^m7
Line 371: Line 371:
| ^^C
| ^^C
| 64/35
| 64/35
| 1044.8604
| 1044.86
| +1.2934
| +1.2934
|-
|-
| 35
| 35
| 1076.9231
| 1076.92
| [[28/15]]
| [[28/15]]
| vvM7
| vvM7
Line 381: Line 381:
| vvC#
| vvC#
| 41/22
| 41/22
| 1077.7445
| 1077.74
| -0.8214
| -0.8214
|-
|-
| 36
| 36
| 1107.6923
| 1107.69
| [[15/8]], [[48/25]], [[40/21]]
| ''[[15/8]]'', [[40/21]], ''[[48/25]]''
| vM7
| vM7
| downmajor 7th
| downmajor 7th
| vC#
| vC#
| 74/39
| 74/39
| 1108.8614
| 1108.86
| -1.1691
| -1.1691
|-
|-
| 37
| 37
| 1138.4615
| 1138.46
| [[27/14]], [[96/49]], [[64/33]]
| [[27/14]], ''[[96/49]]'', [[64/33]]
| M7
| M7
| major 7th
| major 7th
| C#
| C#
| 56/29
| 56/29
| 1139.2487
| 1139.25
| -0.7872
| -0.7872
|-
|-
| 38
| 38
| 1169.2308
| 1169.23
| [[160/81]], [[35/18]], [[49/25]], [[55/28]], [[108/55]]
| ''[[35/18]]'', [[49/25]], [[55/28]], [[108/55]], [[160/81]]
| ^M7,<br>v8
| ^M7,<br>v8
| upmajor 7th,<br>down 8ve
| upmajor 7th,<br>down 8ve
| ^C#, <br>vD
| ^C#, <br>vD
| 112/57
| 112/57
| 1169.3579
| 1169.36
| -0.1271
| -0.1271
|-
|-
| 39
| 39
| 1200.0000
| 1200.00
| [[2/1]]
| [[2/1]]
| P8
| P8
Line 421: Line 421:
| D
| D
| 2/1
| 2/1
| 1200.0000
| 1200.00
| None
| None
|}
|}
<nowiki>*</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]].
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