Xenharmonic Wiki

39edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
→Regular temperament properties: +pluto, +mirkat, and a minor correction
Relegate armodue notation to a new notation section
Line 16: Line 16:


== Intervals ==
== Intervals ==
{| class="wikitable"
|-
| '''Armodue nomenclature 5;2 relation'''
|-
|
* '''‡''' = Semisharp (1/5-tone up)
* '''b''' = Flat (3/5-tone down)
* '''#''' = Sharp (3/5-tone up)
* '''v''' = Semiflat (1/5-tone down)
|}
{| class="wikitable center-all right-2 left-3 right-9 right-10"
{| class="wikitable center-all right-2 left-3 right-9 right-10"
|-
|-
! Degree
! Steps
! Cents
! Cents
! Approximate Ratios<br>in 39d [[Val]]
! Approximate Ratios<br>in 39d [[Val]]
! Armodue<br>Notation
! 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]]<br>(Ratio, Cents, Error)
Line 40: Line 27:
| 0.0000
| 0.0000
| [[1/1]]
| [[1/1]]
| 1
| P1
| P1
| perfect unison
| perfect unison
Line 51: Line 37:
| 30.7692
| 30.7692
| [[81/80]], [[36/35]], [[50/49]], [[55/54]], [[56/55]]
| [[81/80]], [[36/35]], [[50/49]], [[55/54]], [[56/55]]
| 1‡ (9#)
| ^1,<br>vm2
| ^1,
vm2
| up unison, <br>downminor 2nd
| up unison, <br>downminor 2nd
| ^D, <br>vEb
| ^D, <br>vEb
Line 63: Line 47:
| 61.5385
| 61.5385
| [[28/27]], [[49/48]], [[33/32]]
| [[28/27]], [[49/48]], [[33/32]]
| 2b
| m2
| m2
| minor 2nd
| minor 2nd
Line 74: Line 57:
| 92.3077
| 92.3077
| [[16/15]], [[25/24]], [[21/20]]
| [[16/15]], [[25/24]], [[21/20]]
| 1#
| ^m2
| ^m2
| upminor 2nd
| upminor 2nd
Line 85: Line 67:
| 123.0769
| 123.0769
| [[15/14]]
| [[15/14]]
| 2v
| ^^m2
| ^^m2
| dupminor 2nd
| dupminor 2nd
Line 96: Line 77:
| 153.8462
| 153.8462
| [[12/11]], [[11/10]]
| [[12/11]], [[11/10]]
| 2
| vvM2
| vvM2
| dudmajor 2nd
| dudmajor 2nd
Line 107: Line 87:
| 184.6154
| 184.6154
| [[10/9]]
| [[10/9]]
| 2‡
| vM2
| vM2
| downmajor 2nd
| downmajor 2nd
Line 115: Line 94:
| +2.2117
| +2.2117
|-
|-
| 7'''·'''
| 7
| 215.3846
| 215.3846
| [[9/8]], [[8/7]]
| [[9/8]], [[8/7]]
| 3b
| M2
| M2
| major 2nd
| major 2nd
Line 129: Line 107:
| 246.1538
| 246.1538
| [[81/70]]
| [[81/70]]
| 2#
| ^M2, <br>vm3
| ^M2, <br>vm3
| upmajor 2nd, <br>downminor 3rd
| upmajor 2nd, <br>downminor 3rd
Line 140: Line 117:
| 276.9231
| 276.9231
| [[7/6]]
| [[7/6]]
| 3v
| m3
| m3
| minor 3rd
| minor 3rd
Line 151: Line 127:
| 307.6923
| 307.6923
| [[6/5]]
| [[6/5]]
| 3
| ^m3
| ^m3
| upminor 3rd
| upminor 3rd
Line 162: Line 137:
| 338.4615
| 338.4615
| [[11/9]]
| [[11/9]]
| 3‡
| ^^m3
| ^^m3
| dupminor 3rd
| dupminor 3rd
Line 170: Line 144:
| +2.3320
| +2.3320
|-
|-
| 12'''·'''
| 12
| 369.2308
| 369.2308
| [[27/22]]
| [[27/22]]
| 4b
| vvM3
| vvM3
| dudmajor 3rd
| dudmajor 3rd
Line 184: Line 157:
| 400.0000
| 400.0000
| [[5/4]]
| [[5/4]]
| 3#
| vM3
| vM3
| downmajor 3rd
| downmajor 3rd
Line 195: Line 167:
| 430.7692
| 430.7692
| [[9/7]], [[14/11]]
| [[9/7]], [[14/11]]
| 4v (5b)
| M3
| M3
| major 3rd
| major 3rd
Line 206: Line 177:
| 461.5385
| 461.5385
| [[35/27]]
| [[35/27]]
| 4
| v4
| v4
| down 4th
| down 4th
Line 217: Line 187:
| 492.3077
| 492.3077
| [[4/3]]
| [[4/3]]
| 4‡ (5v)
| P4
| P4
| perfect 4th
| perfect 4th
Line 225: Line 194:
| +1.0386
| +1.0386
|-
|-
| 17'''·'''
| 17
| 523.0769
| 523.0769
| [[27/20]]
| [[27/20]]
| 5
| ^4
| ^4
| up 4th
| up 4th
Line 239: Line 207:
| 553.8462
| 553.8462
| [[11/8]]
| [[11/8]]
| 5‡ (4#)
| ^^4
| ^^4
| dup 4th
| dup 4th
Line 250: Line 217:
| 584.6154
| 584.6154
| [[7/5]]
| [[7/5]]
| 6b
| vvA4, <br>^d5
| vvA4, <br>^d5
| dudaug 4th, <br>updim 5th
| dudaug 4th, <br>updim 5th
Line 261: Line 227:
| 615.3846
| 615.3846
| [[10/7]]
| [[10/7]]
| 5#
| vA4, <br>^^d5
| vA4, <br>^^d5
| downaug 4th, <br>dupdim 5th
| downaug 4th, <br>dupdim 5th
Line 272: Line 237:
| 646.1538
| 646.1538
| [[16/11]]
| [[16/11]]
| 6v
| vv5
| vv5
| dud 5th
| dud 5th
Line 280: Line 244:
| -2.5283
| -2.5283
|-
|-
| 22'''·'''
| 22
| 676.9231
| 676.9231
| [[40/27]]
| [[40/27]]
| 6
| v5
| v5
| down 5th
| down 5th
Line 294: Line 257:
| 707.6923
| 707.6923
| [[3/2]]
| [[3/2]]
| 6‡
| P5
| P5
| perfect 5th
| perfect 5th
Line 305: Line 267:
| 738.4615
| 738.4615
| [[54/35]]
| [[54/35]]
| 7b
| ^5
| ^5
| up 5th
| up 5th
Line 316: Line 277:
| 769.2308
| 769.2308
| [[14/9]], [[11/7]]
| [[14/9]], [[11/7]]
| 6#
| m6
| m6
| minor 6th
| minor 6th
Line 327: Line 287:
| 800.0000
| 800.0000
| [[8/5]]
| [[8/5]]
| 7v
| ^m6
| ^m6
| upminor 6th
| upminor 6th
Line 335: Line 294:
| -0.9096
| -0.9096
|-
|-
| 27'''·'''
| 27
| 830.7692
| 830.7692
| [[44/27]]
| [[44/27]]
| 7
| ^^m6
| ^^m6
| dupminor 6th
| dupminor 6th
Line 349: Line 307:
| 861.5385
| 861.5385
| [[18/11]]
| [[18/11]]
| 7‡
| vvM6
| vvM6
| dudmajor 6th
| dudmajor 6th
Line 360: Line 317:
| 892.3077
| 892.3077
| [[5/3]]
| [[5/3]]
| 8b
| vM6
| vM6
| downmajor 6th
| downmajor 6th
Line 371: Line 327:
| 923.0769
| 923.0769
| [[12/7]]
| [[12/7]]
| 7#
| M6
| M6
| major 6th
| major 6th
Line 382: Line 337:
| 953.8462
| 953.8462
| [[140/81]]
| [[140/81]]
| 8v
| ^M6, <br>vm7
| ^M6, <br>vm7
| upmajor 6th, <br>downminor 7th
| upmajor 6th, <br>downminor 7th
Line 390: Line 344:
| +1.5873
| +1.5873
|-
|-
| 32'''·'''
| 32
| 984.6154
| 984.6154
| [[16/9]], [[7/4]]
| [[16/9]], [[7/4]]
| 8
| m7
| m7
| minor 7th
| minor 7th
Line 404: Line 357:
| 1015.3846
| 1015.3846
| [[9/5]]
| [[9/5]]
| 8‡
| ^m7
| ^m7
| upminor 7th
| upminor 7th
Line 415: Line 367:
| 1046.1538
| 1046.1538
| [[11/6]], [[20/11]]
| [[11/6]], [[20/11]]
| 9b
| ^^m7
| ^^m7
| dupminor 7th
| dupminor 7th
Line 426: Line 377:
| 1076.9231
| 1076.9231
| [[28/15]]
| [[28/15]]
| 8#
| vvM7
| vvM7
| dudmajor 7th
| dudmajor 7th
Line 437: Line 387:
| 1107.6923
| 1107.6923
| [[15/8]], [[48/25]], [[40/21]]
| [[15/8]], [[48/25]], [[40/21]]
| 9v (1b)
| vM7
| vM7
| downmajor 7th
| downmajor 7th
Line 448: Line 397:
| 1138.4615
| 1138.4615
| [[27/14]], [[96/49]], [[64/33]]
| [[27/14]], [[96/49]], [[64/33]]
| 9
| M7
| M7
| major 7th
| major 7th
Line 459: Line 407:
| 1169.2308
| 1169.2308
| [[160/81]], [[35/18]], [[49/25]], [[55/28]], [[108/55]]
| [[160/81]], [[35/18]], [[49/25]], [[55/28]], [[108/55]]
| 9‡ (1v)
| ^M7,<br>v8
| ^M7,
v8
| upmajor 7th,<br>down 8ve
| upmajor 7th,<br>down 8ve
| ^C#, <br>vD
| ^C#, <br>vD
Line 468: Line 414:
| -0.1271
| -0.1271
|-
|-
| 39'''··'''
| 39
| 1200.0000
| 1200.0000
| [[2/1]]
| [[2/1]]
| 1
| P8
| P8
| perfect 8ve
| perfect 8ve
Line 481: Line 426:


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 ==
=== Armodue notation ===
; Armodue nomenclature 5;2 relation
* '''‡''' = Semisharp (1/5-tone up)
* '''b''' = Flat (3/5-tone down)
* '''#''' = Sharp (3/5-tone up)
* '''v''' = Semiflat (1/5-tone down)
{| class="wikitable center-all right-3 left-5"
|-
! colspan="2" | #
! Cents
! Armodue<br>Notation
! Associated Ratios
|-
| 0
|
| 0.0
| 1
| [[1/1]]
|-
| 1
|
| 30.8
| 1‡ (9#)
|
|-
| 2
|
| 61.5
| 2b
|
|-
| 3
|
| 92.3
| 1#
|
|-
| 4
|
| 123.1
| 2v
|
|-
| 5
|
| 153.8
| 2
| 11/10~12/11
|-
| 6
|
| 184.6
| 2‡
|
|-
| 7
| ·
| 215.4
| 3b
| 8/7
|-
| 8
|
| 246.2
| 2#
|
|-
| 9
|
| 276.9
| 3v
|
|-
| 10
|
| 307.7
| 3
| 6/5~7/6
|-
| 11
|
| 338.5
| 3‡
|
|-
| 12
| ·
| 369.2
| 4b
| 5/4
|-
| 13
|
| 400.0
| 3#
|
|-
| 14
|
| 430.8
| 4v (5b)
|
|-
| 15
|
| 461.5
| 4
|
|-
| 16
|
| 492.3
| 4‡ (5v)
|
|-
| 17
| ·
| 523.1
| 5
| 4/3~11/8
|-
| 18
|
| 553.8
| 5‡ (4#)
|
|-
| 19
|
| 584.6
| 6b
| 10/7
|-
| 20
|
| 615.4
| 5#
| 7/5
|-
| 21
|
| 646.2
| 6v
|
|-
| 22
| ·
| 676.9
| 6
| 3/2~16/11
|-
| 23
|
| 707.7
| 6‡
|
|-
| 24
|
| 738.5
| 7b
|
|-
| 25
|
| 769.2
| 6#
|
|-
| 26
|
| 800.0
| 7v
|
|-
| 27
| ·
| 830.8
| 7
| 8/5
|-
| 28
|
| 861.5
| 7‡
|
|-
| 29
|
| 892.3
| 8b
| 5/3~12/7
|-
| 30
|
| 923.1
| 7#
|
|-
| 31
|
| 953.8
| 8v
|
|-
| 32
| ·
| 984.6
| 8
| 7/4
|-
| 33
|
| 1015.4
| 8‡
|
|-
| 34
|
| 1046.2
| 9b
| 11/6~20/11
|-
| 35
|
| 1076.9
| 8#
|
|-
| 36
|
| 1107.7
| 9v (1b)
|
|-
| 37
|
| 1138.5
| 9
|
|-
| 38
|
| 1169.2
| 9‡ (1v)
|
|-
| 39
| ··
| 1200.0
| 1
| 2/1
|}


== Regular temperament properties ==
== Regular temperament properties ==
Retrieved from "https://en.xen.wiki/w/39edo"