Xenharmonic Wiki

21edo: Difference between revisions

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Line 21: Line 21:
! | Degree
! | Degree
! | Cents
! | Cents
!pions
!7mus
! colspan="3" | [[Ups_and_Downs_Notation|Up/down notation]]
! colspan="3" | [[Ups_and_Downs_Notation|Up/down notation]]
! | 5L3s Octotonic Notation
! | 5L3s Octotonic Notation
Line 29: Line 31:
|-
|-
| style="text-align:center;" | 0
| style="text-align:center;" | 0
| style="text-align:center;" | 0
| colspan="3" style="text-align:center;" | 0
| style="text-align:right;" | 1
| style="text-align:right;" | 1
| style="text-align:center;" | unison
| style="text-align:center;" | unison
Line 41: Line 43:
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 57.14
| style="text-align:center;" | 57.14
|60.57
|73.14 (49.24<sub>16</sub>)
| style="text-align:right;" | ^1
| style="text-align:right;" | ^1


Line 58: Line 62:
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:center;" | 114.29
| style="text-align:center;" | 114.29
|121.14
|146.29 (92.49<sub>16</sub>)
| style="text-align:right;" | ^^1
| style="text-align:right;" | ^^1


Line 75: Line 81:
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:center;" | 171.43
| style="text-align:center;" | 171.43
|181.71
|219.43 (DB.6E<sub>16</sub>)
| style="text-align:right;" | 2
| style="text-align:right;" | 2
| style="text-align:center;" | 2nd
| style="text-align:center;" | 2nd
Line 86: Line 94:
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:center;" | 228.57
| style="text-align:center;" | 228.57
|242.29
|292.57 (124.92<sub>16</sub>)
| style="text-align:right;" | ^2
| style="text-align:right;" | ^2


Line 103: Line 113:
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:center;" | 285.71
| style="text-align:center;" | 285.71
|302.86
|365.71 (16D.B7<sub>16</sub>)
| style="text-align:right;" | ^^2
| style="text-align:right;" | ^^2


Line 120: Line 132:
| style="text-align:center;" | 6
| style="text-align:center;" | 6
| style="text-align:center;" | 342.86
| style="text-align:center;" | 342.86
|363.43
|438.86 (1B6.DB<sub>16</sub>)
| style="text-align:right;" | 3
| style="text-align:right;" | 3
| style="text-align:center;" | 3rd
| style="text-align:center;" | 3rd
Line 131: Line 145:
| style="text-align:center;" | 7
| style="text-align:center;" | 7
| style="text-align:center;" | 400
| style="text-align:center;" | 400
|424
|512 (200<sub>16</sub>)
| style="text-align:right;" | ^3
| style="text-align:right;" | ^3


Line 148: Line 164:
| style="text-align:center;" | 8
| style="text-align:center;" | 8
| style="text-align:center;" | 457.14
| style="text-align:center;" | 457.14
|484.57
|585.14 (249.24<sub>16</sub>)
| style="text-align:right;" | ^^3
| style="text-align:right;" | ^^3


Line 165: Line 183:
| style="text-align:center;" | 9
| style="text-align:center;" | 9
| style="text-align:center;" | 514.29
| style="text-align:center;" | 514.29
|545.14
|658.29 (292.49<sub>16</sub>)
| style="text-align:right;" | 4
| style="text-align:right;" | 4
| style="text-align:center;" | 4th
| style="text-align:center;" | 4th
Line 176: Line 196:
| style="text-align:center;" | 10
| style="text-align:center;" | 10
| style="text-align:center;" | 571.43
| style="text-align:center;" | 571.43
|605.71
|731.43 (2DB.6E<sub>16</sub>)
| style="text-align:right;" | ^4
| style="text-align:right;" | ^4


Line 193: Line 215:
| style="text-align:center;" | 11
| style="text-align:center;" | 11
| style="text-align:center;" | 628.57
| style="text-align:center;" | 628.57
|666.29
|804.57 (324.92<sub>16</sub>)
| style="text-align:right;" | ^^4
| style="text-align:right;" | ^^4


Line 210: Line 234:
| style="text-align:center;" | 12
| style="text-align:center;" | 12
| style="text-align:center;" | 685.71
| style="text-align:center;" | 685.71
|726.86
|877.71 (36D.B7<sub>16</sub>)
| style="text-align:right;" | 5
| style="text-align:right;" | 5
| style="text-align:center;" | 5th
| style="text-align:center;" | 5th
Line 221: Line 247:
| style="text-align:center;" | 13
| style="text-align:center;" | 13
| style="text-align:center;" | 742.86
| style="text-align:center;" | 742.86
|787.43
|950.86 (3B6.DB<sub>16</sub>)
| style="text-align:right;" | ^5
| style="text-align:right;" | ^5


Line 238: Line 266:
| style="text-align:center;" | 14
| style="text-align:center;" | 14
| style="text-align:center;" | 800
| style="text-align:center;" | 800
|848
|1024 (400<sub>16</sub>)
| style="text-align:right;" | ^^5
| style="text-align:right;" | ^^5


Line 255: Line 285:
| style="text-align:center;" | 15
| style="text-align:center;" | 15
| style="text-align:center;" | 857.14
| style="text-align:center;" | 857.14
|908.57
|1097.14 (449.24<sub>16</sub>)
| style="text-align:right;" | 6
| style="text-align:right;" | 6
| style="text-align:center;" | 6th
| style="text-align:center;" | 6th
Line 266: Line 298:
| style="text-align:center;" | 16
| style="text-align:center;" | 16
| style="text-align:center;" | 914.29
| style="text-align:center;" | 914.29
|969.14
|1170.29 (492.49<sub>16</sub>)
| style="text-align:right;" | ^6
| style="text-align:right;" | ^6


Line 283: Line 317:
| style="text-align:center;" | 17
| style="text-align:center;" | 17
| style="text-align:center;" | 971.43
| style="text-align:center;" | 971.43
|1029.71
|1243.43 (4DB.6E<sub>16</sub>)
| style="text-align:right;" | ^^6
| style="text-align:right;" | ^^6


Line 300: Line 336:
| style="text-align:center;" | 18
| style="text-align:center;" | 18
| style="text-align:center;" | 1028.57
| style="text-align:center;" | 1028.57
|1090.29
|1316.57 (524.92<sub>16</sub>)
| style="text-align:right;" | 7
| style="text-align:right;" | 7
| style="text-align:center;" | 7th
| style="text-align:center;" | 7th
Line 311: Line 349:
| style="text-align:center;" | 19
| style="text-align:center;" | 19
| style="text-align:center;" | 1085.71
| style="text-align:center;" | 1085.71
|1150.86
|1389.71 (56D.B7<sub>16</sub>)
| style="text-align:right;" | ^7
| style="text-align:right;" | ^7


Line 328: Line 368:
| style="text-align:center;" | 20
| style="text-align:center;" | 20
| style="text-align:center;" | 1142.86
| style="text-align:center;" | 1142.86
|1211.43
|1462.86 (5B6.DB<sub>16</sub>)
| style="text-align:right;" | ^^7
| style="text-align:right;" | ^^7


Line 345: Line 387:
| style="text-align:center;" | 21
| style="text-align:center;" | 21
| style="text-align:center;" | 1200
| style="text-align:center;" | 1200
|1272
|1536 (600<sub>16</sub>)
| style="text-align:right;" | 8
| style="text-align:right;" | 8
| style="text-align:center;" | 8ve
| style="text-align:center;" | 8ve
Line 393: Line 437:
! | Steps
! | Steps
! | Cents
! | Cents
!pions
!7mus
! | Ratio
! | Ratio
! | Example in C
! | Example in C
Line 400: Line 446:
| style="text-align:center;" | 0-5-10
| style="text-align:center;" | 0-5-10
| style="text-align:center;" | 0-286-571
| style="text-align:center;" | 0-286-571
|0-303-606
|0-366-731 (0-16E-2DB<sub>16</sub>)
| style="text-align:center;" | 23:27:32
| style="text-align:center;" | 23:27:32
| | C Ev Gvv
| | C Ev Gvv
Line 407: Line 455:
| style="text-align:center;" | 0-4-11
| style="text-align:center;" | 0-4-11
| style="text-align:center;" | 0-229-629
| style="text-align:center;" | 0-229-629
|0-242-666
|0-293-805 (0-125-325<sub>16</sub>)
| style="text-align:center;" | 7:8:10
| style="text-align:center;" | 7:8:10
| | C Evv Gv
| | C Evv Gv
Line 414: Line 464:
| style="text-align:center;" | 0-6-11
| style="text-align:center;" | 0-6-11
| style="text-align:center;" | 0-343-629
| style="text-align:center;" | 0-343-629
|0-363-666
|0-439-805 (0-1B7-325<sub>16</sub>)
| style="text-align:center;" | 9:11:13
| style="text-align:center;" | 9:11:13
| | C E Gv
| | C E Gv
Line 421: Line 473:
| style="text-align:center;" | 0-5-13
| style="text-align:center;" | 0-5-13
| style="text-align:center;" | 0-286-743
| style="text-align:center;" | 0-286-743
|0-363-787
|0-439-951 (0-1B7-3B7<sub>16</sub>)
| style="text-align:center;" | 11:13:17
| style="text-align:center;" | 11:13:17
| | C Ev G^
| | C Ev G^
Line 428: Line 482:
| style="text-align:center;" | 0-8-13
| style="text-align:center;" | 0-8-13
| style="text-align:center;" | 0-457-743
| style="text-align:center;" | 0-457-743
|0-485-787
|0-585-951 (0-249-3B7<sub>16,)</sub>
| style="text-align:center;" | 13:17:20
| style="text-align:center;" | 13:17:20
| | C Fv G^
| | C Fv G^
Line 435: Line 491:
| style="text-align:center;" | 0-5-15
| style="text-align:center;" | 0-5-15
| style="text-align:center;" | 0-286-857
| style="text-align:center;" | 0-286-857
|0-303-1090
|0-366-1317 (0-16E-525<sub>16</sub>)
| style="text-align:center;" | 11:13:18
| style="text-align:center;" | 11:13:18
| | C Ev A
| | C Ev A
Line 461: Line 519:
! | Step Pattern
! | Step Pattern
! | Cents
! | Cents
!pions
!7mus
! | Example
! | Example
! | Name*
! | Name*
Line 467: Line 527:
| style="text-align:center;" | 3, 3, 3
| style="text-align:center;" | 3, 3, 3
| style="text-align:center;" | (0)-171-343-(514)
| style="text-align:center;" | (0)-171-343-(514)
|(0)-182-363-(545)
|(0)-219-439-(658) ([0]-DB-1B7-[292]<sub>16</sub>)
| | C D E F
| | C D E F
| style="text-align:center;" | Equable diatonic
| style="text-align:center;" | Equable diatonic
Line 473: Line 535:
| style="text-align:center;" | 4, 3, 2
| style="text-align:center;" | 4, 3, 2
| style="text-align:center;" | (0)-229-400-(514)
| style="text-align:center;" | (0)-229-400-(514)
|(0)-242-424-(545)
|(0)-293-512-(658) ([0]-125-200-[292]<sub>16</sub>)
| | C D^ E^ F
| | C D^ E^ F
| style="text-align:center;" | Soft diatonic
| style="text-align:center;" | Soft diatonic
Line 479: Line 543:
| style="text-align:center;" | 4, 4, 1
| style="text-align:center;" | 4, 4, 1
| style="text-align:center;" | (0)-229-457-(514)
| style="text-align:center;" | (0)-229-457-(514)
|(0)-242-485-(545)
|(0)-293-585-(658) ([0]-125-249-[292]<sub>16</sub>)
| | C D^ E^^ F
| | C D^ E^^ F
| style="text-align:center;" | Intense diatonic
| style="text-align:center;" | Intense diatonic
Line 485: Line 551:
| style="text-align:center;" | 5, 3, 1
| style="text-align:center;" | 5, 3, 1
| style="text-align:center;" | (0)-286-457-(514)
| style="text-align:center;" | (0)-286-457-(514)
|(0)-303-485-(545)
|(0)-366-585-(658) ([0]-16E-249-[292]<sub>16</sub>)
| | C D^^ E^^ F
| | C D^^ E^^ F
| style="text-align:center;" | Archytas chromatic
| style="text-align:center;" | Archytas chromatic
Line 491: Line 559:
| style="text-align:center;" | 5, 2, 2
| style="text-align:center;" | 5, 2, 2
| style="text-align:center;" | (0)-286-400-(514)
| style="text-align:center;" | (0)-286-400-(514)
|(0)-303-424-(545)
|(0)-366-512-(658) ([0]-16E-200-[292]<sub>16</sub>)
| | C D^^ E^ F
| | C D^^ E^ F
| style="text-align:center;" | Weak chromatic
| style="text-align:center;" | Weak chromatic
Line 497: Line 567:
| style="text-align:center;" | 6, 2, 1
| style="text-align:center;" | 6, 2, 1
| style="text-align:center;" | (0)-343-457-(514)
| style="text-align:center;" | (0)-343-457-(514)
|(0)-363-485-(545)
|(0)-439-585-(658) ([0]-1B7-249-[292]<sub>16</sub>)
| | C D^<span style="font-size: 90%; vertical-align: super;">3</span> E^^ F
| | C D^<span style="font-size: 90%; vertical-align: super;">3</span> E^^ F
| style="text-align:center;" | Strong enharmonic
| style="text-align:center;" | Strong enharmonic
Line 503: Line 575:
| style="text-align:center;" | 7, 1, 1
| style="text-align:center;" | 7, 1, 1
| style="text-align:center;" | (0)-400-457-(514)
| style="text-align:center;" | (0)-400-457-(514)
|(0)-424-485-(545)
|(0)-512-585-(658) ([0]-200-249-[292]<sub>16</sub>)
| | C D^<span style="font-size: 90%; vertical-align: super;">4</span> E^^ F
| | C D^<span style="font-size: 90%; vertical-align: super;">4</span> E^^ F
| style="text-align:center;" | Pythagorean enharmonic
| style="text-align:center;" | Pythagorean enharmonic
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