Xenharmonic Wiki

95ed5: Difference between revisions

← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,543 edits
m {{todo|expand}} & collapsible
ArrowHead294 (talk | contribs)
14,512 edits
mNo edit summary
 
(6 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
'''[[Ed5|Division of the 5th harmonic]] into 95 equal parts''' (95ed5) is related to [[41edo|41 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 2.5143 cents stretched and the step size is about 29.3296 cents. This tuning has a generally sharp tendency for harmonics up to 12. Unlike 41edo, it is only consistent up to the [[11-odd-limit|12-integer-limit]], with discrepancy for the 13th harmonic.
{{ED intro}}
 
== Theory ==
95ed5 is related to [[41edo]], but with the 5th harmonic rather than the [[2/1|octave]] being just. The octave is about 2.51 cents stretched. This tuning has a generally sharp tendency for [[harmonic]]s up to 12. Unlike 41edo, it is only [[consistent]] up to the [[integer limit|12-integer-limit]], with discrepancy for the [[13/1|13th harmonic]].
 
=== Harmonics ===
{{Harmonics in equal|95|5|1|intervals=integer}}
{{Harmonics in equal|95|5|1|intervals=integer|columns=12|start=12|collapsed=1|title=Approximation of harmonics in 95ed5 (continued)}}
 
=== Subsets and supersets ===
Since 95 factors into primes as {{nowrap| 5 × 19 }}, 95ed5 contains [[5ed5]] and [[19ed5]] as subset ed5's.


== Intervals ==
== Intervals ==
{| class="wikitable mw-collapsible"
{| class="wikitable center-1 right-2"
|-
|-
! | degree
! #
! | cents value
! Cents
! | corresponding <br>JI intervals
! Approximate ratios
! | comments
|-
|-
| | 0
| 0
| | 0.0000
| 0.0
| | '''exact [[1/1]]'''
| [[1/1]]
| |
|-
|-
| | 1
| 1
| | 29.3296
| 29.3
| |
| [[49/48]], [[50/49]], [[64/63]], [[81/80]]
| |
|-
|-
| | 2
| 2
| | 58.6592
| 58.7
| | 931/900
| [[25/24]], [[28/27]], [[33/32]], [[36/35]]
| |
|-
|-
| | 3
| 3
| | 87.9889
| 88.0
| | 81/77, [[20/19]]
| [[19/18]], [[20/19]], [[21/20]], [[22/21]]
| |
|-
|-
| | 4
| 4
| | 117.3185
| 117.3
| | 1280/1197
| [[14/13]], [[15/14]], [[16/15]]
| |
|-
|-
| | 5
| 5
| | 146.6481
| 146.6
| | 209/192, [[49/45]]
| [[12/11]], [[13/12]]
| |
|-
|-
| | 6
| 6
| | 175.9777
| 176.0
| | 448/405
| [[10/9]], [[11/10]], [[21/19]]
| |
|-
|-
| | 7
| 7
| | 205.3073
| 205.3
| |
| [[9/8]]
| |
|-
|-
| | 8
| 8
| | 234.6369
| 234.6
| | [[63/55]], [[55/48]]
| [[8/7]], [[15/13]]
| |
|-
|-
| | 9
| 9
| | 263.9666
| 264.0
| | 220/189
| [[7/6]], [[22/19]]
| |
|-
|-
| | 10
| 10
| | 293.2962
| 293.3
| |
| [[13/11]], [[19/16]], [[32/27]]
| |
|-
|-
| | 11
| 11
| | 322.6258
| 322.6
| | 135/112
| [[6/5]]
| |
|-
|-
| | 12
| 12
| | 351.9554
| 352.0
| | [[60/49]], 256/209
| [[11/9]], [[16/13]]
| |
|-
|-
| | 13
| 13
| | 381.2850
| 381.3
| | 399/320
| [[5/4]], [[26/21]]
| | pseudo-[[5/4]]
|-
|-
| | 14
| 14
| | 410.6147
| 410.6
| | [[19/15]]
| [[19/15]]
| |
|-
|-
| | 15
| 15
| | 439.9443
| 439.9
| | 1200/931
| [[9/7]], [[32/25]]
| |
|-
|-
| | 16
| 16
| | 469.2739
| 469.3
| | [[21/16]]
| [[21/16]], [[13/10]]
| |
|-
|-
| | 17
| 17
| | 498.6035
| 498.6
| | [[4/3]]
| [[4/3]]
| |
|-
|-
| | 18
| 18
| | 527.9331
| 527.9
| |
| [[15/11]], [[19/14]], [[27/20]]
| |
|-
|-
| | 19
| 19
| | 557.2627
| 557.3
| | 243/176
| [[11/8]], [[18/13]], [[26/19]]
| |
|-
|-
| | 20
| 20
| | 586.5924
| 586.6
| | 108/77, 275/196, 80/57
| [[7/5]], [[45/32]]
| |
|-
|-
| | 21
| 21
| | 615.9220
| 615.9
| |
| [[10/7]], [[64/45]]
| |
|-
|-
| | 22
| 22
| | 645.2516
| 645.3
| | 209/144, 196/135
| [[13/9]], [[16/11]], [[19/13]]
| |
|-
|-
| | 23
| 23
| | 674.5812
| 674.6
| | 2025/1372
| [[22/15]], [[28/19]], [[40/27]]
| |
|-
|-
| | 24
| 24
| | 703.9108
| 703.9
| | 1539/1024
| [[3/2]]
| | pseudo-[[3/2]]
|-
|-
| | 25
| 25
| | 733.2405
| 733.2
| | 171/112, 84/55, 55/36
| [[20/13]], [[32/21]]
| |
|-
|-
| | 26
| 26
| | 762.5701
| 762.6
| |
| [[14/9]], [[25/16]]
| |
|-
|-
| | 27
| 27
| | 791.8997
| 791.9
| |
| [[11/7]], [[19/12]], [[30/19]]
| |
|-
|-
| | 28
| 28
| | 821.2293
| 821.2
| | 45/28
| [[8/5]], [[21/13]]
| |
|-
|-
| | 29
| 29
| | 850.5589
| 850.6
| | 1024/627
| [[13/8]], [[18/11]]
| |
|-
|-
| | 30
| 30
| | 879.8885
| 879.9
| | 133/80
| [[5/3]]
| | pseudo-[[5/3]]
|-
|-
| | 31
| 31
| | 909.2182
| 909.2
| | 1232/729, 3645/2156, 225/133
| [[22/13]], [[27/16]], [[32/19]]
| |
|-
|-
| | 32
| 32
| | 938.5478
| 938.5
| |
| [[12/7]], [[19/11]]
| |
|-
|-
| | 33
| 33
| | 967.8774
| 967.9
| | [[7/4]]
| [[7/4]], [[26/15]]
| |
|-
|-
| | 34
| 34
| | 997.2070
| 997.2
| | [[16/9]]
| [[16/9]]
| |
|-
|-
| | 35
| 35
| | 1026.5366
| 1026.5
| |
| [[9/5]]
| |
|-
|-
| | 36
| 36
| | 1055.8662
| 1055.9
| | 81/44
| [[11/6]]
| |
|-
|-
| | 37
| 37
| | 1085.1959
| 1085.2
| | 144/77, 275/147, 320/171
| [[13/7]], [[15/8]]
| |
|-
|-
| | 38
| 38
| | 1114.5255
| 1114.5
| |
| [[19/10]], [[21/11]]
| |
|-
|-
| | 39
| 39
| | 1143.8551
| 1143.9
| | 209/108, 405/209
| [[27/14]], [[35/18]]
| |
|-
|-
| | 40
| 40
| | 1173.1847
| 1173.2
| | 675/343
| [[49/25]], [[55/28]], [[63/32]]
| |
|-
|-
| | 41
| 41
| | 1202.5143
| 1202.5
| | 513/256, 441/220
| [[2/1]]
| | pseudo-[[octave]]
|-
|-
| | 42
| 42
| | 1231.8440
| 1231.8
| | 57/28, [[56/55|112/55]], [[55/54|55/27]]
| [[45/22]], [[49/24]], [[55/27]], [[81/40]]
| |
|-
|-
| | 43
| 43
| | 1261.1736
| 1261.2
| |
| [[25/12]], [[33/16]]
| |
|-
|-
| | 44
| 44
| | 1290.5032
| 1290.5
| |
| [[19/9]], [[21/10]]
| |
|-
|-
| | 45
| 45
| | 1319.8328
| 1319.8
| | [[15/14|15/7]]
| [[15/7]]
| |
|-
|-
| | 46
| 46
| | 1349.1624
| 1349.2
| |
| [[13/6]]
| |
|-
|-
| | 47
| 47
| | 1378.4920
| 1378.5
| | 133/60, 539/243
| [[11/5]]
| |
|-
|-
| | 48
| 48
| | 1407.8217
| 1407.8
| | 1215/539, 300/133
| [[9/4]]
| |
|-
|-
| | 49
| 49
| | 1437.1513
| 1437.2
| |
| [[16/7]]
| |
|-
|-
| | 50
| 50
| | 1466.4809
| 1466.5
| | [[7/3]]
| [[7/3]]
| |
|-
|-
| | 51
| 51
| | 1495.8105
| 1495.8
| |
| [[19/8]]
| |
|-
|-
| | 52
| 52
| | 1525.1401
| 1525.1
| |
| [[12/5]]
| |
|-
|-
| | 53
| 53
| | 1554.4698
| 1554.5
| | [[27/22|27/11]], 275/112, 140/57
| [[22/9]], [[27/11]]
| |
|-
|-
| | 54
| 54
| | 1583.7994
| 1583.8
| | 1100/441, 1280/513
| [[5/2]]
| | pseudo-[[5/2]]
|-
|-
| | 55
| 55
| | 1613.1290
| 1613.1
| | 343/135
| [[28/11]], [[33/13]]
| |
|-
|-
| | 56
| 56
| | 1642.4586
| 1642.5
| | 209/81, 540/209
| [[18/7]]
| |
|-
|-
| | 57
| 57
| | 1671.7882
| 1671.8
| |
| [[21/8]]
| |
|-
|-
| | 58
| 58
| | 1701.1178
| 1701.1
| | 171/64, 147/55, 385/144
| [[8/3]]
| |
|-
|-
| | 59
| 59
| | 1730.4475
| 1730.4
| | 220/81
| [[19/7]]
| |
|-
|-
| | 60
| 60
| | 1759.7771
| 1759.8
| |
| [[11/4]]
| |
|-
|-
| | 61
| 61
| | 1789.1067
| 1789.1
| | [[45/32|45/16]]
| [[14/5]]
| |
|-
|-
| | 62
| 62
| | 1818.4363
| 1818.4
| | [[10/7|20/7]]
| [[20/7]]
| |
|-
|-
| | 63
| 63
| | 1847.7659
| 1847.8
| |
| [[26/9]]
| |
|-
|-
| | 64
| 64
| | 1877.0956
| 1877.1
| | 133/45, 2156/729, 3645/1232
| [[44/15]]
| |
|-
|-
| | 65
| 65
| | 1906.4252
| 1906.4
| | 400/133
| [[3/1]]
| | pseudo-[[3/1]]
|-
|-
| | 66
| 66
| | 1935.7548
| 1935.8
| | 3135/1024
| [[40/13]]
| |
|-
|-
| | 67
| 67
| | 1965.0844
| 1965.1
| | [[14/9|28/9]]
| [[25/8]], [[28/9]]
| |
|-
|-
| | 68
| 68
| | 1994.4140
| 1994.4
| |
| [[19/6]], [[22/7]]
| |
|-
|-
| | 69
| 69
| | 2023.7436
| 2023.7
| |
| [[16/5]]
| |
|-
|-
| | 70
| 70
| | 2053.0733
| 2053.1
| | [[18/11|36/11]], 275/84, 560/171
| [[13/4]]
| |
|-
|-
| | 71
| 71
| | 2082.4029
| 2082.4
| | 5120/1539
| [[10/3]]
| | pseudo-[[10/3]]
|-
|-
| | 72
| 72
| | 2111.7325
| 2111.7
| | 1372/405
| [[27/8]]
| |
|-
|-
| | 73
| 73
| | 2141.0621
| 2141.1
| | 675/196, 720/209
| [[24/7]]
| |
|-
|-
| | 74
| 74
| | 2170.3917
| 2170.4
| |
| [[7/2]]
| |
|-
|-
| | 75
| 75
| | 2199.7214
| 2199.7
| | 57/16, 196/55, 385/108
| [[25/7]]
| |
|-
|-
| | 76
| 76
| | 2229.0510
| 2229.1
| | 880/243
| [[18/5]]
| |
|-
|-
| | 77
| 77
| | 2258.3806
| 2258.4
| |
| [[11/3]]
| |
|-
|-
| | 78
| 78
| | 2287.7102
| 2287.7
| | [[15/4]]
| [[15/4]]
| |
|-
|-
| | 79
| 79
| | 2317.0398
| 2317.0
| | [[40/21|80/21]]
| [[19/5]]
| |
|-
|-
| | 80
| 80
| | 2346.3694
| 2346.4
| | 931/240
| [[27/7]], [[35/9]]
| |
|-
|-
| | 81
| 81
| | 2375.6991
| 2375.7
| | 75/19
| [[55/14]], [[63/16]]
| |
|-
|-
| | 82
| 82
| | 2405.0287
| 2405.0
| | 1600/399
| [[4/1]]
| | pseudo-[[4/1]]
|-
|-
| | 83
| 83
| | 2434.3583
| 2434.4
| | 1045/256, [[49/48|49/12]]
| [[49/12]], [[81/20]]
| |
|-
|-
| | 84
| 84
| | 2463.6879
| 2463.7
| | [[28/27|112/27]]
| [[25/6]], [[33/8]]
| |
|-
|-
| | 85
| 85
| | 2493.0175
| 2493.0
| |
| [[21/5]]
| |
|-
|-
| | 86
| 86
| | 2522.3472
| 2522.3
| | 189/44
| [[30/7]]
| |
|-
|-
| | 87
| 87
| | 2551.6768
| 2551.7
| | [[12/11|48/11]], 275/63
| [[13/3]]
| |
|-
|-
| | 88
| 88
| | 2581.0064
| 2581.0
| |
| [[22/5]]
| |
|-
|-
| | 89
| 89
| | 2610.3360
| 2610.3
| | 2025/448
| [[9/2]]
| |
|-
|-
| | 90
| 90
| | 2639.6656
| 2639.7
| | 225/49, 960/209
| [[16/7]]
| |
|-
|-
| | 91
| 91
| | 2668.9952
| 2669.0
| | 1197/256
| [[14/3]]
| |
|-
|-
| | 92
| 92
| | 2698.3249
| 2698.3
| | 19/4, 385/81
| [[19/4]]
| |
|-
|-
| | 93
| 93
| | 2727.6545
| 2727.7
| | 4500/931
| [[24/5]]
| |
|-
|-
| | 94
| 94
| | 2756.9841
| 2757.0
| |
| [[39/8]]
| |
|-
|-
| | 95
| 95
| | 2786.3137
| 2786.3
| | '''exact [[5/1]]'''
| [[5/1]]
| | just major third plus two octaves
|}
|}


== Harmonics ==
== As a generator ==
{{Harmonics in equal
95ed5 can also be thought of as a [[generator]] of the 2.3.5.7.11.19-subgroup temperament which tempers out 1540/1539, 3025/3024, 6875/6859, and 184877/184320, which is a [[cluster temperament]] with 41 clusters of notes in an octave. While the small chroma interval between adjacent notes in each cluster represents 385/384 ~ 441/440 ~ 1479016/1476225 ~ 194579/194400 ~ 204800/204687 ~ 176000/175959 tempered together, the step interval is very versatile, representing 16807/16500 ~ 19551/19200 ~ 18000/17689 ~ 72900/71687 ~ 273375/268912 ~ 295245/290521 ~ 12100/11907 ~ 64/63 all tempered together. This temperament is supported by [[41edo]], [[491edo]] (491e val), and [[532edo]] (532d val) among others.
| steps = 95
| num = 5
| denom = 1
}}
{{Harmonics in equal
| steps = 95
| num = 5
| denom = 1
| start = 12
| collapsed = 1
}}


==95ed5 as a generator==
== See also ==
95ed5 can also be thought of as a [[generator]] of the 2.3.5.7.11.19 subgroup temperament which tempers out 1540/1539, 3025/3024, 6875/6859, and 184877/184320, which is a [[cluster temperament]] with 41 clusters of notes in an octave. While the small chroma interval between adjacent notes in each cluster represents 385/384 ~ 441/440 ~ 1479016/1476225 ~ 194579/194400 ~ 204800/204687 ~ 176000/175959 tempered together, the step interval is very versatile, representing 16807/16500 ~ 19551/19200 ~ 18000/17689 ~ 72900/71687 ~ 273375/268912 ~ 295245/290521 ~ 12100/11907 ~ 64/63 all tempered together. This temperament is supported by [[41edo]], [[491edo]] (491e val), and [[532edo]] (532d val) among others.
* [[24edf]] – relative edf
* [[41edo]] – relative edo
* [[65edt]] – relative edt
* [[106ed6]] – relative ed6
* [[147ed12]] – relative ed12
* [[361ed448]] – close to the zeta-optimized tuning for 41edo


[[Category:Ed5]]
[[Category:41edo]]
[[Category:Edonoi]]
{{todo|expand}}
Retrieved from "https://en.xen.wiki/w/95ed5"