Xenharmonic Wiki

35edt: Difference between revisions

VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
Created page with "'''Division of the third harmonic into 35 equal parts''' (35edt) is related to 22 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 4..."
Tags: Mobile edit Mobile web edit
 
+subsets and supersets; +see also
 
(13 intermediate revisions by 5 users not shown)
Line 1: Line 1:
'''[[Edt|Division of the third harmonic]] into 35 equal parts''' (35edt) is related to [[22edo|22 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 4.4854 cents compressed and the step size is about 54.3416 cents. It is consistent to the [[11-odd-limit|12-integer-limit]].
{{Infobox ET}}
{{ED intro}}


{| class="wikitable"
== Theory ==
35edt is related to [[22edo]], but with the [[3/1|perfect twelfth]] rather than the [[2/1|octave]] being just. The octave is about 4.4854 cents compressed. Like 22edo, 35edt is [[consistent]] to the [[integer limit|12-integer-limit]].
 
=== Harmonics ===
{{Harmonics in equal|35|3|1|intervals=integer|columns=11}}
{{Harmonics in equal|35|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 35edt (continued)}}
 
=== Subsets and supersets ===
Since 35 factors into primes as {{nowrap| 5 × 7 }}, 35edt has subset edts [[5edt]] and [[7edt]].
 
== Intervals ==
{| class="wikitable center-1 right-2 right-3"
|-
|-
! | degree
! #
! | cents value
! Cents
! | corresponding <br>JI intervals
! Hekts
! | comments
! Approximate ratios*
|-
|-
| | 0
| 0
| | 0.0000
| 0.0
| | '''exact [[1/1]]'''
| 0.0
| |
| 1/1
|-
|-
| | 1
| 1
| | 54.3416
| 54.3
| | [[33/32]], 32/31
| 37.1
| |
| 33/32, 36/35
|-
|-
| | 2
| 2
| | 108.6831
| 108.7
| | 33/31
| 74.3
| |
| 15/14, 16/15, 17/16, 18/17
|-
|-
| | 3
| 3
| | 163.0247
| 163.0
| |
| 111.4
| |
| 10/9, 11/10, 12/11
|-
|-
| | 4
| 4
| | 217.3663
| 217.4
| | [[17/15]]
| 148.6
| |
| 8/7, 9/8
|-
|-
| | 5
| 5
| | 271.7079
| 271.7
| |
| 185.7
| |
| 7/6
|-
|-
| | 6
| 6
| | 326.0494
| 326.0
| |
| 222.9
| |
| 6/5
|-
|-
| | 7
| 7
| | 380.3910
| 380.4
| | 81/65
| 260.0
| | pseudo-[[5/4]]
| 5/4
|-
|-
| | 8
| 8
| | 434.7326
| 434.7
| | [[9/7]]
| 297.1
| |
| 9/7
|-
|-
| | 9
| 9
| | 489.0741
| 489.1
| | 69/52
| 334.3
| |
| 4/3
|-
|-
| | 10
| 10
| | 543.4157
| 543.4
| | [[26/19]]
| 371.4
| |
| 11/8, 15/11, 27/20
|-
|-
| | 11
| 11
| | 597.7573
| 597.8
| | [[24/17]]
| 408.6
| |
| 7/5, 10/7, 17/12, 24/17
|-
|-
| | 12
| 12
| | 652.0989
| 652.1
| | [[35/24]]
| 445.7
| |
| 16/11, 22/15
|-
|-
| | 13
| 13
| | 706.4404
| 706.4
| |
| 482.9
| | pseudo-[[3/2]]
| 3/2
|-
|-
| | 14
| 14
| | 760.7820
| 760.8
| | 45/29
| 520.0
| |
| 11/7, 14/9
|-
|-
| | 15
| 15
| | 815.1236
| 815.1
| | [[8/5]]
| 557.1
| |
| 8/5
|-
|-
| | 16
| 16
| | 869.4651
| 869.5
| | 38/23, 81/49
| 594.3
| |
| 5/3, 18/11, 33/20
|-
|-
| | 17
| 17
| | 923.8067
| 923.8
| | 46/27
| 631.4
| |
| 12/7, 17/10
|-
|-
| | 18
| 18
| | 978.1483
| 978.1
| | 81/46
| 668.6
| |
| 7/4, 30/17
|-
|-
| | 19
| 19
| | 1032.4899
| 1032.5
| | 49/27, 69/38
| 705.7
| |
| 9/5, 11/6, 20/11
|-
|-
| | 20
| 20
| | 1086.8314
| 1086.8
| | [[15/8]]
| 742.9
| |
| 15/8
|-
|-
| | 21
| 21
| | 1141.1730
| 1141.2
| | 29/15
| 780.0
| |
| 21/11, 27/14
|-
|-
| | 22
| 22
| | 1195.5146
| 1195.5
| |
| 817.1
| | pseudo-[[octave]]
| 2/1
|-
|-
| | 23
| 23
| | 1249.8561
| 1249.9
| | [[36/35|72/35]]
| 854.3
| |
| 33/16, 45/22
|-
|-
| | 24
| 24
| | 1304.1977
| 1304.2
| | [[17/16|17/8]]
| 891.4
| |
| 15/7, 17/8, 21/10, 36/17
|-
|-
| | 25
| 25
| | 1358.5393
| 1358.5
| | 57/26
| 928.6
| |
| 11/5, 20/9, 24/11
|-
|-
| | 26
| 26
| | 1412.8809
| 1412.9
| | 52/23
| 965.7
| |
| 9/4
|-
|-
| | 27
| 27
| | 1467.2224
| 1467.2
| | [[7/3]]
| 1002.9
| |
| 7/3
|-
|-
| | 28
| 28
| | 1521.5640
| 1521.6
| | 65/27
| 1040.0
| |
| 12/5
|-
|-
| | 29
| 29
| | 1575.9056
| 1575.9
| |
| 1077.1
| |
| 5/2
|-
|-
| | 30
| 30
| | 1630.2471
| 1630.2
| |
| 1114.3
| |
| 18/7
|-
|-
| | 31
| 31
| | 1684.5887
| 1684.6
| | 45/17
| 1151.4
| |
| 8/3, 21/8
|-
|-
| | 32
| 32
| | 1738.9303
| 1738.9
| |
| 1188.6
| |
| 11/4, 27/10, 30/11
|-
|-
| | 33
| 33
| | 1793.2719
| 1793.3
| | 31/11
| 1225.7
| |
| 14/5, 17/6, 45/16, 48/17
|-
|-
| | 34
| 34
| | 1847.6134
| 1847.6
| | [[16/11|32/11]]
| 1262.9
| |
| 32/11, 35/12
|-
|-
| | 35
| 35
| | 1901.9550
| 1902.0
| | '''exact [[3/1]]'''
| 1300.0
| | [[3/2|just perfect fifth]] plus an octave
| 3/1
|}
|}
<nowiki/>* As a 2.3.5.7.11.17-subgroup temperament


[[Category:Edt]]
== See also ==
[[Category:Edonoi]]
* [[22edo]] – relative edo
* [[57ed6]] – relative ed6
* [[79ed12]] – relative ed12
Retrieved from "https://en.xen.wiki/w/35edt"