Xenharmonic Wiki

80edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Jkarimak (talk | contribs)
191 edits
→Intervals of 80edo: Removed 7mus column
m Cleanup
Line 1: Line 1:
The ''80 equal temperament'', often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 [[cent|cent]]s. 80et is the first equal temperament that represents the [[19-limit|19-limit]] [[Tonality_diamond|tonality diamond]] [[consistent|consistent]]ly (it barely manages to do so).
The '''80 equal temperament''', often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 [[cent|cent]]s. 80et is the first equal temperament that represents the [[19-limit]] [[tonality diamond]] [[consistent|consistently]] (it barely manages to do so).


80 et [[tempering_out|tempers out]] 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.
80et [[Tempering_out|tempers out]] 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.


80 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:
80 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:
Line 25: Line 25:
In each case, the numbers joined by an ampersand represent 19-limit [[Patent_val|patent vals]] (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.
In each case, the numbers joined by an ampersand represent 19-limit [[Patent_val|patent vals]] (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.


=Intervals of 80edo=
== Intervals ==


{| class="wikitable"
{| class="wikitable center-all right-2 left-3"
|-
|-
! | degrees
! Degree
! | cents
! Cents
! | ratios*
! Approximate Ratios*
|-
|-
| 0
| 0
|0
| 0
| | 1/1
| 1/1
|-
|-
| | 1
| 1
| | 15
| 15
| | 64/63
| 64/63
|-
|-
| | 2
| 2
| | 30
| 30
| | 81/80
| 81/80
|-
|-
| | 3
| 3
| | 45
| 45
| | 34/33, 36/35
| 34/33, 36/35
|-
|-
| | 4
| 4
| | 60
| 60
| | 26/25, 28/27, 33/32, 35/34
| 26/25, 28/27, 33/32, 35/34
|-
|-
| | 5
| 5
| | 75
| 75
| | 22/21, 25/24, 27/26
| 22/21, 25/24, 27/26
|-
|-
| | 6
| 6
| | 90
| 90
| | 19/18, 20/19, 21/20
| 19/18, 20/19, 21/20
|-
|-
| | 7
| 7
| | 105
| 105
| | 16/15, 17/16, 18/17
| 16/15, 17/16, 18/17
|-
|-
| | 8
| 8
| | 120
| 120
| | 14/13, 15/14
| 14/13, 15/14
|-
|-
| | 9
| 9
| | 135
| 135
| | 13/12
| 13/12
|-
|-
| | 10
| 10
| | 150
| 150
| | 12/11
| 12/11
|-
|-
| | 11
| 11
| | 165
| 165
| | 11/10
| 11/10
|-
|-
| | 12
| 12
| | 180
| 180
| | 10/9, 21/19
| 10/9, 21/19
|-
|-
| | 13
| 13
| | 195
| 195
| | 19/17
| 19/17
|-
|-
| | 14
| 14
| | 210
| 210
| | 9/8, 17/15
| 9/8, 17/15
|-
|-
| | 15
| 15
| | 225
| 225
| | 8/7
| 8/7
|-
|-
| | 16
| 16
| | 240
| 240
| |  
|  
|-
|-
| | 17
| 17
| | 255
| 255
| | 15/13, 22/19
| 15/13, 22/19
|-
|-
| | 18
| 18
| | 270
| 270
| | 7/6
| 7/6
|-
|-
| | 19
| 19
| | 285
| 285
| | 13/11, 20/17
| 13/11, 20/17
|-
|-
| | 20
| 20
| | 300
| 300
| | 19/16, 25/21
| 19/16, 25/21
|-
|-
| | 21
| 21
| | 315
| 315
| | 6/5
| 6/5
|-
|-
| | 22
| 22
| | 330
| 330
| | 17/14
| 17/14
|-
|-
| | 23
| 23
| | 345
| 345
| | 11/9
| 11/9
|-
|-
| | 24
| 24
| | 360
| 360
| | 16/13, 21/17
| 16/13, 21/17
|-
|-
| | 25
| 25
| | 375
| 375
| |  
|  
|-
|-
| | 26
| 26
| | 390
| 390
| | 5/4
| 5/4
|-
|-
| | 27
| 27
| | 405
| 405
| | 19/15, 24/19
| 19/15, 24/19
|-
|-
| | 28
| 28
| | 420
| 420
| | 14/11
| 14/11
|-
|-
| | 29
| 29
| | 435
| 435
| | 9/7
| 9/7
|-
|-
| | 30
| 30
| | 450
| 450
| | 13/10, 22/17
| 13/10, 22/17
|-
|-
| | 31
| 31
| | 465
| 465
| | 17/13
| 17/13
|-
|-
| | 32
| 32
| | 480
| 480
| | 21/16, 25/19
| 21/16, 25/19
|-
|-
| | 33
| 33
| | 495
| 495
| | 4/3
| 4/3
|-
|-
| | 34
| 34
| | 510
| 510
| |  
|  
|-
|-
| | 35
| 35
| | 525
| 525
| | 19/14
| 19/14
|-
|-
| | 36
| 36
| | 540
| 540
| | 26/19
| 26/19
|-
|-
| | 37
| 37
| | 555
| 555
| | 11/8
| 11/8
|-
|-
| | 38
| 38
| | 570
| 570
| | 18/13
| 18/13
|-
|-
| | 39
| 39
| | 585
| 585
| | 7/5
| 7/5
|-
|-
| | 40
| 40
| | 600
| 600
| | 17/12, 24/17
| 17/12, 24/17
|}
|}
*based on treating 80edo as a [[19-limit|19-limit]] temperament; other approaches are possible.
<nowiki>*</nowiki> based on treating 80edo as a [[19-limit]] temperament; other approaches are possible.
 
[[Category:19-limit]]
[[Category:19-limit]]
[[Category:21-limit]]
[[Category:21-limit]]
[[Category:edo]]
[[Category:edo]]
Retrieved from "https://en.xen.wiki/w/80edo"