Xenharmonic Wiki

20edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
updated interwiki information
No edit summary
Line 6: Line 6:
}}
}}
20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 [[cent]]s each. It contains smaller [[EDO|edo]]s [[2edo|2]], [[4edo|4]], [[5edo|5]], and [[10edo|10]] and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from [[5edo]]), 11, 13 & 15 (from [[10edo]]), 19 & 27 (from [[4edo]]), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15.
20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 [[cent]]s each. It contains smaller [[EDO|edo]]s [[2edo|2]], [[4edo|4]], [[5edo|5]], and [[10edo|10]] and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from [[5edo]]), 11, 13 & 15 (from [[10edo]]), 19 & 27 (from [[4edo]]), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15.
__FORCETOC__
__FORCETOC__
-----
-----
Line 34: Line 35:
! Degree
! Degree
! Cents
! Cents
! pions
!7mus
! Approximate Ratios
! Approximate Ratios
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and Downs Notation]]
Line 39: Line 42:
|-
|-
| 0
| 0
| style="text-align:right;" | 0
| colspan="3" style="text-align:right;" | 0
| 1/1
| 1/1
| unison
| unison
Line 48: Line 51:
| 1
| 1
| style="text-align:right;" | 60
| style="text-align:right;" | 60
|63.6
|76.8 (4C.D<sub>16</sub>)
| 29/28
| 29/28
| upminor 2nd
| upminor 2nd
Line 56: Line 61:
| 2
| 2
| style="text-align:right;" | 120
| style="text-align:right;" | 120
|127.2
|153.6 (99.A<sub>16</sub>)
| 14/13, 15/14
| 14/13, 15/14
| mid 2nd
| mid 2nd
Line 64: Line 71:
| 3
| 3
| style="text-align:right;" | 180
| style="text-align:right;" | 180
|190.8
|230.4 (EA.6<sub>16</sub>)
| 10/9
| 10/9
| downmajor 2nd
| downmajor 2nd
Line 72: Line 81:
| 4
| 4
| style="text-align:right;" | 240
| style="text-align:right;" | 240
|254.4
|307.2 (133.3<sub>16</sub>)
| 8/7, 15/13
| 8/7, 15/13
| major 2nd, minor 3rd
| major 2nd, minor 3rd
Line 80: Line 91:
| 5
| 5
| style="text-align:right;" | 300
| style="text-align:right;" | 300
|318
|384 (180<sub>16</sub>)
| 13/11, 19/16
| 13/11, 19/16
| upminor 3rd
| upminor 3rd
Line 88: Line 101:
| 6
| 6
| style="text-align:right;" | 360
| style="text-align:right;" | 360
|381.6
|460.8 (1CC.D<sub>16</sub>)
| 16/13, 5/4
| 16/13, 5/4
| mid 3rd
| mid 3rd
Line 96: Line 111:
| 7
| 7
| style="text-align:right;" | 420
| style="text-align:right;" | 420
|445.2
|537.6 (219.A<sub>16</sub>)
| [[14/11]], [[51/40]]
| [[14/11]], [[51/40]]
| downmajor 3rd
| downmajor 3rd
Line 104: Line 121:
| 8
| 8
| style="text-align:right;" | 480
| style="text-align:right;" | 480
|508.8
|614.4 (266.6<sub>16</sub>)
| 25/19, 4/3
| 25/19, 4/3
| major 3rd, perfect fourth
| major 3rd, perfect fourth
Line 112: Line 131:
| 9
| 9
| style="text-align:right;" | 540
| style="text-align:right;" | 540
|572.4
|691.2 (2AA.3<sub>16</sub>)
| 15/11, 11/8
| 15/11, 11/8
| up-fourth
| up-fourth
Line 120: Line 141:
| 10
| 10
| style="text-align:right;" | 600
| style="text-align:right;" | 600
|636
|768 (300<sub>16</sub>)
| 7/5
| 7/5
| double-up fourth, double-down fifth
| double-up fourth, double-down fifth
Line 128: Line 151:
| 11
| 11
| style="text-align:right;" | 660
| style="text-align:right;" | 660
|699.6
|844.8 (34C.D<sub>16</sub>)
| 22/15, 16/11
| 22/15, 16/11
| down-fifth
| down-fifth
Line 136: Line 161:
| 12
| 12
| style="text-align:right;" | 720
| style="text-align:right;" | 720
|763.2
|921.6 (399.A<sub>16</sub>)
| 38/25, 3/2
| 38/25, 3/2
| fifth
| fifth
Line 144: Line 171:
| 13
| 13
| style="text-align:right;" | 780
| style="text-align:right;" | 780
|826.8
|998.4 (3EA.6<sub>16</sub>)
| 11/7, 25/16
| 11/7, 25/16
| upminor 6th
| upminor 6th
Line 152: Line 181:
| 14
| 14
| style="text-align:right;" | 840
| style="text-align:right;" | 840
|890.4
|1095.2 (433.3<sub>16</sub>)
| 13/8, 8/5
| 13/8, 8/5
| mid 6th
| mid 6th
Line 160: Line 191:
| 15
| 15
| style="text-align:right;" | 900
| style="text-align:right;" | 900
|954
|1152 (480<sub>16</sub>)
| 22/13, 32/19
| 22/13, 32/19
| downmajor 6th
| downmajor 6th
Line 168: Line 201:
| 16
| 16
| style="text-align:right;" | 960
| style="text-align:right;" | 960
|1017.6
|1228.8 (4CC.D<sub>16</sub>)
| 7/4, 26/15
| 7/4, 26/15
| major 6th, minor 7th
| major 6th, minor 7th
Line 176: Line 211:
| 17
| 17
| style="text-align:right;" | 1020
| style="text-align:right;" | 1020
|1081.2
|1305.6 (519.A<sub>16</sub>)1208.4
| 9/5
| 9/5
| upminor 7th
| upminor 7th
Line 184: Line 221:
| 18
| 18
| style="text-align:right;" | 1080
| style="text-align:right;" | 1080
|1144.8
|1382.4 (566.6<sub>16</sub>)
| 15/8, 13/7
| 15/8, 13/7
| mid 7th
| mid 7th
Line 192: Line 231:
| 19
| 19
| style="text-align:right;" | 1140
| style="text-align:right;" | 1140
|1208.4
|1459.2 (5AA.3<sub>16</sub>)
| 56/29
| 56/29
| downmajor 7th
| downmajor 7th
Line 200: Line 241:
| 20
| 20
| style="text-align:right;" | 1200
| style="text-align:right;" | 1200
|1272
|1536 (600<sub>16</sub>)
| 2/1
| 2/1
| octave
| octave
Retrieved from "https://en.xen.wiki/w/20edo"