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→Modern renditions: Add Akira Yamaoka's Lakeview Hotel Music Box (2001) microtonal cover in 46edo by Bryan Deister
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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| en = 46edo
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<h4>Original Wikitext content:</h4>
{{Infobox ET}}
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
{{ED intro}}
----


=&lt;span style="color: #300094; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;46 tone equal temperament&lt;/span&gt;=  
== Theory ==
The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the [[xenharmonic/octave|octave]] into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 [[xenharmonic/cent|cent]]s, an interval close in size to [[xenharmonic/66_65|66/65]], the interval from [[xenharmonic/13_11|13/11]] to [[xenharmonic/6_5|6/5]].
In the opinion of some, 46edo is the first equal division to deal adequately with the [[13-limit]], though others award that distinction to [[41edo]] or [[53edo]]. 46edo's fifth is slightly sharp of just, which some people (e.g. [[Margo Schulter]]) prefer, sometimes strongly, over both the [[3/2|just fifth]] and fifths of temperaments with flat fifths, such as meantone. Many say that sharp fifths give a characteristic bright sound to 5-limit triads, and consider the sound of meantone triads to be more mellow in comparison. 46edo is not a [[zeta peak edo]], but it is a [[zeta gap edo]]. It is distinctly [[consistent]] in the [[9-odd-limit]], and it is consistent to the [[13-odd-limit]] or the no-15 no-19 [[23-odd-limit]].


46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. [[xenharmonic/Rank two temperaments|Rank two temperaments]] it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The [[xenharmonic/11-limit|11-limit]] [[xenharmonic/Target tunings|minimax]] tuning for [[xenharmonic/Starling family|valentine temperament]], (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the [[xenharmonic/13-limit|13-limit]], though others award that distinction to [[xenharmonic/41edo|41edo]]. In fact, while 41 is a [[xenharmonic/The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] but not a [[xenharmonic/The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta gap edo]], 46 is zeta gap but not zeta integral.
46edo is also notable for being the smallest edo to approximate odd harmonics 1–13 with less than 25% [[relative interval error|relative error]].


The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the [[xenharmonic/just fifth|just fifth]] and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.
[[Magic22 as srutis #Shrutar.5B22.5D_as_srutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian]] music.


46edo can be treated as two [[xenharmonic/23edo|23edo]]'s separated by an interval of 26.087 cents.
=== Prime harmonics ===
{{Harmonics in equal|46|columns=11}}
{{Harmonics in equal|46|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 46edo (continued)}}


=46edo srutis=  
=== As a tuning of other temperaments ===
[[xenharmonic/Magic22 as srutis#shrutar22assrutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[xenharmonic/Indian|Indian]] music.
46edo is a superb tuning for [[sensi]] and [[leapday]]. It also [[support]]s but tunes less optimally [[valentine]], [[shrutar]], [[rodan]], and [[unidec]]. The [[11-odd-limit]] [[minimax tuning]] for valentine, (11/7)<sup>1/10</sup>, is only 0.01 cents flat of 3\46, but [[77edo]] has a lower average error overall.  


=Linear temperaments=  
=== Subsets and supersets ===
||~ Periods
46edo can be treated as two circles of [[23edo]] separated by an interval of 26.087 cents. Supersets [[414edo]] and [[460edo]] are also notable for their high consistency.
per octave ||~ Generator ||~ Cents ||~ Temperaments ||~ MOS/DE Scales available ||~ L:s ||
|| 1 || 1\46 || 26.087 ||  ||  ||  ||
|| 1 || 3\46 || 78.261 || [[xenharmonic/Valentine|Valentine]] || 1L 14s (15-tone)
15L 1s (16-tone)
16L 15s (31-tone) || 4:3 ~ [[xenharmonic/Maximal evenness|quasi-equal]]
3:1
2:1 ~ QE ||
|| 1 || 5\46 || 130.435 || [[xenharmonic/Twothirdtonic|Twothirdtonic]] || [[xenharmonic/1L 8s|1L 8s]] (9-tone)
[[xenharmonic/9L 1s|9L 1s]] (10-tone)
9L 10s (19-tone)
9L 19s (28-tone)
9L 28s (37-tone) || 6:5 ~ QE
5:1
4:1
3:1
2:1 ~ QE ||
|| 1 || 7\46 || 182.609 || [[xenharmonic/Minortone|Minortone]] || [[xenharmonic/1L 5s|1L 5s]] (6-tone)
[[xenharmonic/6L 1s|6L 1s]] (7-tone)
7L 6s (13-tone)
13L 7s (20-tone)
13L 20s (33-tone) || 11:7
7:4
4:3 ~ QE
3:1
2:1 ~ QE ||
|| 1 || 9\46 || 234.783 || [[xenharmonic/Rodan|Rodan]] || [[xenharmonic/1L 4s|1L 4s]] (5-tone)
[[xenharmonic/1L 5s|1L 5s]] (6-tone)
[[xenharmonic/5L 6s|5L 6s]] (11-tone)
5L 11s (16-tone)
5L 16s (21-tone)
5L 21s (26-tone)
5L 26s (31-tone)
5L 31s (36-tone)
5L 36s (41-tone) || 10:9 ~QE
9:1
8:1
7:1
6:1
5:1
4:1
3:1
2:1 ~ QE ||
|| 1 || 11\46 || 286.957 ||  || [[xenharmonic/4L 1s|4L 1s]] (5-tone)
[[xenharmonic/4L 5s|4L 5s]] (9-tone)
4L 9s (13-tone)
4L 13s (17-tone)
4L 17s (21-tone)
21L 4s (25-tone) || 11:2
9:2
7:2
5:2
3:2 ~ QE, Golden
2:1 ~ QE ||
|| 1 || 13\46 || 339.13 || [[xenharmonic/Amity|Amity]]/[[xenharmonic/hitchcock|hitchcock]] || [[xenharmonic/4L 3s|4L 3s]] (7-tone)
[[xenharmonic/7L 4s|7L 4s]] (11-tone)
7L 11s (18-tone)
7L 18s (25-tone)
7L 25s (32-tone)
7L 32s (39-tone) || 7:6 ~ QE
6:1
5:1
4:1
3:1
2:1 ~ QE ||
|| 1 || 15\46 || 391.304 ||  || [[xenharmonic/1L 2s|1L 2s]] (3-tone)
[[xenharmonic/3L 1s|3L 1s]] (4-tone)
[[xenharmonic/3L 4s|3L 4s]] (7-tone)
[[xenharmonic/3L 7s|3L 7s]] (10-tone)
3L 10s (13-tone)
3L 13s (16-tone)
3L 16s (19-tone)
3L 19s (21-tone)
3L 21s (24-tone)
3L 24s (27-tone)
3L 27s (30-tone)
3L 30s (33-tone)
3L 33s (36-tone)
3L 36s (39-tone)
3L 39s (42-tone) || 16:15 ~ QE
15:1
14:1
13:1
12:1
11:1
10:1
9:1
8:1
7:1
6:1
5:1
4:1
3:1
2:1 ~ QE ||
|| 1 || 17\46 || 443.478 || [[xenharmonic/Sensi|Sensi]] || [[xenharmonic/3L 2s|3L 2s]] (5-tone)
[[xenharmonic/3L 5s|3L 5s]] (8-tone)
[[xenharmonic/8L 3s|8L 3s]] (11-tone)
8L 11s (19-tone)
19L 8s (27-tone) || 12:5
7:5
5:2
3:2 ~ QE, Golden
2:1 ||
|| 1 || 19\46 || 495.652 || [[xenharmonic/Leapday|Leapday]] || [[xenharmonic/2L 3s|2L 3s]] (5-tone)
[[xenharmonic/5L 2s|5L 2s]] (7-tone)
[[xenharmonic/5L 7s|5L 7s]] (12-tone)
12L 5s (17-tone)
17L 12s (29-tone) || 11:8
8:3
5:3 ~ Golden
3:2 ~ QE, Golden
2:1 ~ QE ||
|| 1 || 21\46 || 547.826 || [[xenharmonic/Heinz|Heinz]] || [[xenharmonic/2L 3s|2L 3s]] (5-tone)
[[xenharmonic/2L 5s|2L 5s]] (7-tone)
[[xenharmonic/2L 7s|2L 7s]] (9-tone)
[[xenharmonic/2L 9s|2L 9s]] (11-tone)
11L 2s (13-tone)
11L 13s (24-tone)
11L 24s (35-tone) || 17:4
13:4
9:4
5:4 ~ QE
4:1
3:1
2:1 ~ QE ||
|| 2 || 1\46 || 26.087 ||  ||  ||  ||
|| 2 || 2\46 || 52.174 || [[xenharmonic/Shrutar|Shrutar]] || 2L 2s (4-tone)
[[xenharmonic/2L 4s|2L 4s]] (6-tone)
[[xenharmonic/2L 6s|2L 6s]] (8-tone)
[[xenharmonic/2L 8s|2L 8s]] (10-tone)
[[xenharmonic/2L 10s|2L 10s]] (12-tone)
2L 12s (14-tone)
2L 14s (16-tone)
2L 16s (18-tone)
2L 18s (20-tone)
2L 20s (22-tone)
22L 2s (24-tone) || 21:2
19:2
17:2
15:2
13:2
11:2
9:2
7:2
5:2
3:2 ~ QE, Golden
2:1 ~ QE ||
|| 2 || 3\46 || 78.261 ||  || 2L 2s (4-tone)
[[xenharmonic/2L 4s|2L 4s]] (6-tone)
[[xenharmonic/2L 6s|2L 6s]] (8-tone)
[[xenharmonic/2L 8s|2L 8s]] (10-tone)
[[xenharmonic/2L 10s|2L 10s]] (12-tone)
2L 12s (14-tone)
14L 2s (16-tone)
16L 14s (30-tone) || 20:3
17:3
14:3
11:3
8:3
5:3 ~ Golden
3:2 ~ QE, Golden
2:1 ~ QE ||
|| 2 || 4\46 || 104.348 || [[xenharmonic/Srutal|Srutal]]/[[xenharmonic/diaschismic|diaschismic]] || 2L 2s (4-tone)
[[xenharmonic/2L 4s|2L 4s]] (6-tone)
[[xenharmonic/2L 6s|2L 6s]] (8-tone)
[[xenharmonic/2L 8s|2L 8s]] (10-tone)
[[xenharmonic/10L 2s|10L 2s]] (12-tone)
12L 10s (22-tone)
12L 22s (34-tone) || 19:4
15:4
11:4
7:4
4:3 ~ QE
3:1
2:1 ~ QE ||
|| 2 || 5\46 || 130.435 ||  || 2L 2s (4-tone)
[[xenharmonic/2L 4s|2L 4s]] (6-tone)
[[xenharmonic/2L 6s|2L 6s]] (8-tone)
[[xenharmonic/8L 2s|8L 2s]] (10-tone)
8L 10s (18-tone)
18L 10s (28-tone) || 18:5
13:5
8:5 ~ Golden
5:3 ~ Golden
3:2 ~ QE, Golden
2:1 ~ QE ||
|| 2 || 6\46 || 156.522 ||  || 2L 2s (4-tone)
[[xenharmonic/2L 4s|2L 4s]] (6-tone)
[[xenharmonic/6L 2s|6L 2s]] (8-tone)
8L 6s (14-tone)
8L 14s (22-tone)
8L 22s (30-tone)
8L 30s (38-tone || 17:6
11:6
6:5 ~ QE
5:1
4:1
3:1
2:1 ~ QE ||
|| 2 || 7\46 || 182.609 || [[xenharmonic/Unidec|Unidec]]/[[xenharmonic/hendec|hendec]] || 2L 2s (4-tone)
[[xenharmonic/2L 4s|2L 4s]] (6-tone)
[[xenharmonic/6L 2s|6L 2s]] (8-tone)
6L 8s (14-tone)
6L 14s (20-tone)
20L 6s (26-tone) || 16:7
9:7
7:2
5:2
3:2 ~ QE, Golden
2:1 ~ QE ||
|| 2 || 8\46 || 208.696 || [[xenharmonic/Abigail|Abigail]] || 2L 2s (4-tone)
[[xenharmonic/4L 2s|4L 2s]] (6-tone)
[[xenharmonic/6L 2s|6L 2s]] (8-tone)
6L 8s (14-tone)
6L 14s (20-tone)
6L 20s (26-tone)
6L 26s (32-tone)
6L 32s (38-tone)
6L 38s (44-tone) || 15:8
8:7 ~ QE
8:1
7:1
6:1
5:1
4:1
3:1
2:1 ~ QE ||
|| 2 || 9\46 || 234.783 || [[xenharmonic/Echidnic|Echidnic]] || 2L 2s (4-tone)
[[xenharmonic/4L 2s|4L 2s]] (6-tone)
[[xenharmonic/6L 4s|6L 4s]] (10-tone)
10L 6s (16-tone)
10L 16s (26-tone)
10L 26s (36-tone) || 14:9
9:5
5:4 ~ QE
4:1
3:1
2:1 ~ QE ||
|| 2 || 10\46 || 260.87 ||  || 2L 2s (4-tone)
[[xenharmonic/4L 2s|4L 2s]] (6-tone)
[[xenharmonic/4L 6s|4L 6s]] (10-tone)
4L 10s (14-tone)
14L 4s (18-tone)
14L 18s (32-tone) || 13:10
10:3
7:3
4:3 ~ QE
3:1
2:1 ~ QE ||
|| 2 || 11\46 || 286.957 ||  || 2L 2s (4-tone)
[[xenharmonic/4L 2s|4L 2s]] (6-tone)
[[xenharmonic/4L 6s|4L 6s]] (10-tone)
4L 10s (14-tone)
4L 14s (18-tone)
4L 18s (22-tone)
4L 22s (26-tone)
4L 26s (30-tone)
4L 30s (34-tone)
4L 34s (38-tone)
4L 38s (42-tone) || 12:11 ~ QE
11:1
10:1
9:1
8:1
7:1
6:1
5:1
4:1
3:1
2:1 ~ QE ||
|| 23 || 1\46 || 26.087 ||  ||  ||  ||
=Intervals=  
|| degrees of 46edo || cents value || approximate ratios in the [[xenharmonic/17-limit|17-limit]] ||
|| 0 || 0.00 || 1/1 ||
|| 1 || 26.087 ||  ||
|| 2 || 52.174 ||  ||
|| 3 || 78.261 ||  ||
|| 4 || 104.348 || 16/15, 17/16, 18/17 ||
|| 5 || 130.435 || 13/12, 14/13, 15/14 ||
|| 6 || 156.522 || 12/11, 11/10 ||
|| 7 || 182.609 || 10/9 ||
|| 8 || 208.696 || 9/8, 17/15 ||
|| 9 || 234.783 || 8/7, 15/13* ||
|| 10 || 260.87 || 7/6, 15/13* ||
|| 11 || 286.957 || 13/11, 20/17 ||
|| 12 || 313.043 || 6/5 ||
|| 13 || 339.13 || 11/9, 17/14 ||
|| 14 || 365.217 || 16/13 ||
|| 15 || 391.304 || 5/4 ||
|| 16 || 417.391 || 14/11 ||
|| 17 || 443.478 || 9/7, 13/10, 22/17 ||
|| 18 || 469.565 || 17/13 ||
|| 19 || 495.652 || 4/3 ||
|| 20 || 521.739 ||  ||
|| 21 || 547.826 || 11/8, 15/11 ||
|| 22 || 573.913 || 7/5, 18/13 ||
|| 23 || 600 || 17/12, 24/17 ||
|| 24 || 626.087 || 10/7, 13/9 ||
|| 25 || 652.174 || 16/11, 22/15 ||
|| 26 || 678.261 ||  ||
|| 27 || 704.348 || 3/2 ||
|| 28 || 730.435 || 26/17 ||
|| 29 || 756.522 || 14/9, 20/13, 17/11 ||
|| 30 || 782.609 || 11/7 ||
|| 31 || 808.696 || 8/5 ||
|| 32 || 834.783 || 13/8 ||
|| 33 || 860.87 || 18/11, 28/17 ||
|| 34 || 886.957 || 5/3 ||
|| 35 || 913.043 || 22/13, 17/10 ||
|| 36 || 939.13 || 12/7, 26/15* ||
|| 37 || 965.217 || 7/4, 26/15* ||
|| 38 || 991.304 || 16/9, 30/17 ||
|| 39 || 1017.391 || 9/5 ||
|| 40 || 1043.478 || 11/6, 20/11 ||
|| 41 || 1069.565 || 24/13, 13/7, 28/15 ||
|| 42 || 1095.652 || 15/8, 32/17, 17/9 ||
|| 43 || 1121.739 ||  ||
|| 44 || 1147.826 ||  ||
|| 45 || 1173.913 ||  ||
*15/13 (and its inversion 26/15) appears twice on the list. 9\46edo is closest to 15/13 by a hair; 10\46edo represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13. This discrepancy occurs because 46edo is not [[xenharmonic/consistent|consistent]] in the [[xenharmonic/15-limit|15-limit]].


=Approximation to Mode 8 of the Harmonic Series=  
== Intervals ==
{| class="wikitable center-all right-2 left-3 left-4 left-7"
|-
! #
! Cents
! Approximate ratios<ref name="interval ratios" group="note">{{safesubst:Subgroup note|limit=2.3.5.7.11.13.17.23-subgroup}} However, ratios of 15 are not included here, as except for 15/8 and 16/15 themselves 46edo has intervals involving the 15th harmonic poorly approximated in general. This is because, while the 3rd and 5th harmonics are sharp and their deviations from just intonation add up, 7, 11, and 13 are all tuned flat, making the difference even larger. This prevents it from being [[consistent]] in the [[15-odd-limit]], as there is a discrepancy approximating [[15/13]] and [[26/15]]&mdash;9\46 is closer to 15/13 by a hair, but 10\46 represents the difference between 46edo's 15/8 and 13/8 and is more likely to appear in chords actually functioning as 15/13.</ref>
! [[Kite's ups and downs notation|Ups and downs notation]]
|-
| 0
| 0.0
| [[1/1]]
| {{UDnote|step=0}}
|-
| 1
| 26.1
| [[49/48]], [[64/63]], [[81/80]]
| {{UDnote|step=1}}
|-
| 2
| 52.2
| [[28/27]], [[33/32]], [[36/35]]
| {{UDnote|step=2}}
|-
| 3
| 78.3
| [[21/20]], [[22/21]], [[24/23]], [[23/22]], [[25/24]]
| {{UDnote|step=3}}
|-
| 4
| 104.3
| [[16/15]], [[17/16]], [[18/17]]
| {{UDnote|step=4}}
|-
| 5
| 130.4
| [[13/12]], [[14/13]], [[15/14]]
| {{UDnote|step=5}}
|-
| 6
| 156.5
| [[11/10]], [[12/11]], [[23/21]]
| {{UDnote|step=6}}
|-
| 7
| 182.6
| [[10/9]]
| {{UDnote|step=7}}
|-
| 8
| 208.7
| [[9/8]]
| {{UDnote|step=8}}
|-
| 9
| 234.8
| [[8/7]], [[23/20]]
| {{UDnote|step=9}}
|-
| 10
| 260.9
| [[7/6]]
| {{UDnote|step=10}}
|-
| 11
| 287.0
| [[13/11]], [[20/17]]
| {{UDnote|step=11}}
|-
| 12
| 313.0
| [[6/5]]
| {{UDnote|step=12}}
|-
| 13
| 339.1
| [[11/9]], [[17/14]], [[28/23]]
| {{UDnote|step=13}}
|-
| 14
| 365.2
| [[16/13]], [[21/17]], [[26/21]]
| {{UDnote|step=14}}
|-
| 15
| 391.3
| [[5/4]]
| {{UDnote|step=15}}
|-
| 16
| 417.4
| [[14/11]], [[23/18]]
| {{UDnote|step=16}}
|-
| 17
| 443.5
| [[9/7]], [[13/10]], [[22/17]]
| {{UDnote|step=17}}
|-
| 18
| 469.6
| [[17/13]], [[21/16]]
| {{UDnote|step=18}}
|-
| 19
| 495.7
| [[4/3]]
| {{UDnote|step=19}}
|-
| 20
| 521.7
| [[23/17]], [[27/20]]
| {{UDnote|step=20}}
|-
| 21
| 547.8
| [[11/8]]
| {{UDnote|step=21}}
|-
| 22
| 573.9
| [[7/5]], [[18/13]], [[32/23]]
| {{UDnote|step=22}}
|-
| 23
| 600.0
| [[17/12]], [[24/17]]
| {{UDnote|step=23}}
|-
| 24
| 626.1
| [[10/7]], [[13/9]], [[23/16]]
| {{UDnote|step=24}}
|-
| 25
| 652.2
| [[16/11]]
| {{UDnote|step=25}}
|-
| 26
| 678.3
| [[34/23]], [[40/27]]
| {{UDnote|step=26}}
|-
| 27
| 704.3
| [[3/2]]
| {{UDnote|step=27}}
|-
| 28
| 730.4
| [[26/17]], [[32/21]]
| {{UDnote|step=28}}
|-
| 29
| 756.5
| [[14/9]], [[17/11]], [[20/13]]
| {{UDnote|step=29}}
|-
| 30
| 782.6
| [[11/7]]
| {{UDnote|step=30}}
|-
| 31
| 808.7
| [[8/5]]
| {{UDnote|step=31}}
|-
| 32
| 834.8
| [[13/8]], [[21/13]], [[34/21]]
| {{UDnote|step=32}}
|-
| 33
| 860.9
| [[18/11]], [[23/14]], [[28/17]]
| {{UDnote|step=33}}
|-
| 34
| 887.0
| [[5/3]]
| {{UDnote|step=34}}
|-
| 35
| 913.0
| [[17/10]], [[22/13]]
| {{UDnote|step=35}}
|-
| 36
| 939.1
| [[12/7]]
| {{UDnote|step=36}}
|-
| 37
| 965.2
| [[7/4]], [[40/23]]
| {{UDnote|step=37}}
|-
| 38
| 991.3
| [[16/9]], [[23/13]]
| {{UDnote|step=38}}
|-
| 39
| 1017.4
| [[9/5]]
| {{UDnote|step=39}}
|-
| 40
| 1043.5
| [[11/6]], [[20/11]], [[42/23]]
| {{UDnote|step=40}}
|-
| 41
| 1069.6
| [[13/7]], [[24/13]], [[28/15]]
| {{UDnote|step=41}}
|-
| 42
| 1095.7
| [[15/8]], [[17/9]], [[32/17]]
| {{UDnote|step=42}}
|-
| 43
| 1121.7
| [[21/11]], [[23/12]], [[40/21]], [[44/23]], [[48/25]]
| {{UDnote|step=43}}
|-
| 44
| 1147.8
| [[27/14]], [[35/18]], [[64/33]]
| {{UDnote|step=44}}
|-
| 45
| 1173.9
| [[63/32]], [[96/49]], [[160/81]]
| {{UDnote|step=45}}
|-
| 46
| 1200.0
| [[2/1]]
| {{UDnote|step=46}}
|}
<references group="note" />


46edo represents [[xenharmonic/overtone|overtone]]s 8 through 16 (written as [[xenharmonic/JI|JI]] ratios 8:9:10:11:12:13:14:15:16) with degrees 0, 8, 15, 21, 27, 32, 37, 42, 46. In steps-in-between, that's 8, 7, 6, 6, 5, 5, 5, 4.
=== Proposed interval names and solfèges ===
{| class="wikitable center-all right-2 left-2 left-3 left-6 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
|-
! #
! Cents
! colspan="3" | [[Kite's ups and downs notation|Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>5</sup>A1 and ^^d2)
! colspan="3" | [[SKULO interval names|SKULO notation]] (K or S = 1, U = 2)
! colspan="2" | [[Solfège]]s
|-
| 0
| 0.0
| perfect unison
| P1
| D
| Perfect unison
| P1
| D
| da
| do
|-
| 1
| 26.1
| up unison
| ^1
| ^D
| comma-wide unison, <br>super unison
| K1, S1
| KD, SD
| du
| di
|-
| 2
| 52.2
| downminor 2nd
| vm2
| vEb
| subminor 2nd, uber unison
| sm2, U1
| sEb, UD
| fro
| ro
|-
| 3
| 78.3
| minor 2nd
| m2
| Eb
| minor 2nd, <br>classic augmented unison
| m2, kkA1
| Eb, kkD#
| fra
| rih
|-
| 4
| 104.3
| upminor 2nd
| ^m2
| ^Eb
| classic minor 2nd, <br>comma-narrow aug unison
| Km2, kA1
| KEb, kD#
| fru
| ra
|-
| 5
| 130.4
| dupminor 2nd
| ^^m2
| ^^Eb
| lesser neutral second, augmented unison
| n2, A1
| UEb, D#
| fri
| ru<ref name="intervals2" group="note">/u/ as in s'''u'''praminor</ref>
|-
| 6
| 156.5
| dudmajor 2nd
| vvM2
| vvE
| greater neutral second, <br>super aug unison
| N2, sA1
| uE, sD#
| ri
| ruh<ref name="intervals3" group="note">/ʌ/ as in s'''u'''bmajor</ref>
|-
| 7
| 182.6
| downmajor 2nd
| vM2
| vE
| classic/comma-narrow major 2nd
| kM2
| kE
| ro
| reh
|-
| 8
| 208.7
| major 2nd
| M2
| E
| major 2nd
| M2
| E
| ra
| re
|-
| 9
| 234.8
| upmajor 2nd
| ^M2
| ^E
| supermajor 2nd
| SM2
| SE
| ru
| ri
|-
| 10
| 260.9
| downminor 3rd
| vm3
| vF
| subminor 3rd
| sm3
| sF
| no
| ma
|-
| 11
| 287.0
| minor 3rd
| m3
| F
| minor 3rd
| m3
| F
| na
| meh
|-
| 12
| 313.0
| upminor 3rd
| ^m3
| ^F
| classic minor 3rd
| Km3
| KF
| nu
| me
|-
| 13
| 339.1
| dupminor 3rd
| ^^m3
| ^^F
| lesser neutral 3rd
| n3
| UF
| ni
| mu<ref name="intervals2" group="note" />
|-
| 14
| 365.2
| dudmajor 3rd
| vvM3
| vvF#
| greater neutral 3rd
| N3
| uF#
| mi
| muh<ref name="intervals3" group="note" />
|-
| 15
| 391.3
| downmajor 3rd
| vM3
| vF#
| classic major 3rd
| kM3
| kF#
| mo
| mi
|-
| 16
| 417.4
| major 3rd
| M3
| F#
| major 3rd
| M3
| F#
| ma
| maa
|-
| 17
| 443.5
| upmajor 3rd
| ^M3
| ^F#
| supermajor 3rd
| SM3
| SF#
| mu
| mo
|-
| 18
| 469.6
| down 4th
| v4
| vG
| sub 4th
| s4
| sG
| fo
| fe
|-
| 19
| 495.7
| perfect 4th
| P4
| G
| perfect 4th
| P4
| G
| fa
| fa
|-
| 20
| 521.7
| up 4th
| ^4
| ^G
| comma-wide 4th
| K4
| KG
| fu
| fih
|-
| 21
| 547.8
| dup 4th
| ^^4
| ^^G
| uber 4th, sub diminished 5th
| U4, sd5
| UG, sAb
| fi/sho
| fu
|-
| 22
| 573.9
| dudaug 4th, <br>dim 5th
| vvA4, d5
| vvG#, Ab
| classic augmented 4th, diminished 5th
| kkA4, d5
| kkG#, Ab
| pi/sha
| fi
|-
| 23
| 600.0
| downaug 4th, updim 5th
| vA4, ^d5
| vG#, ^Ab
| comma-narrow aug 4th, <br>comma-wide dim 5th
| kA4, Kd5
| kG#, KAb
| po/shu
| seh
|-
| 24
| 626.1
| aug 4th, dupdim 5th
| A4, ^^d5
| G#, ^^Ab
| augmented 4th, <br>classic diminished 5th
| A4, KKd5
| G#, KKAb
| pa/shi
| se
|-
| 25
| 652.2
| dud 5th
| vv5
| vvA
| super augmented 4th, <br>unter 5th
| SA4, u5
| SG#, uA
| pu/si
| su
|-
| 26
| 678.3
| down 5th
| v5
| vA
| comma-narrow 5th
| k5
| kA
| so
| sih
|-
| 27
| 704.3
| perfect 5th
| P5
| A
| perfect 5th
| P5
| A
| sa
| sol
|-
| 28
| 730.4
| up 5th
| ^5
| ^A
| super 5th
| S5
| SA
| su
| si
|-
| 29
| 756.5
| downminor 6th
| vm6
| vBb
| subminor 6th
| sm6
| sBb
| flo
| lo
|-
| 30
| 782.6
| minor 6th
| m6
| Bb
| minor 6th
| m6
| Bb
| fla
| leh
|-
| 31
| 808.7
| upminor 6th
| ^m6
| ^Bb
| classic minor 6th
| Km6
| KBb
| flu
| le
|-
| 32
| 834.8
| dupminor 6th
| ^^m6
| ^^Bb
| lesser neutral 6th
| n6
| UBb
| fli
| lu<ref name="intervals2" group="note" />
|-
| 33
| 860.9
| dudmajor 6th
| vvM6
| vvB
| greater neutral 6th
| N6
| uB
| li
| luh<ref name="intervals3" group="note" />
|-
| 34
| 887.0
| downmajor 6th
| vM6
| vB
| classic major 6th
| kM6
| kB
| lo
| la
|-
| 35
| 913.0
| major 6th
| M6
| B
| major 6th
| M6
| B
| la
| laa
|-
| 36
| 939.1
| upmajor 6th
| ^M6
| ^B
| supermajor 6th
| SM6
| SB
| lu
| li
|-
| 37
| 965.2
| downminor 7th
| vm7
| vC
| subminor 7th
| sm7
| sC
| tho
| ta
|-
| 38
| 991.3
| minor 7th
| m7
| C
| minor 7th
| m7
| C
| tha
| teh
|-
| 39
| 1017.4
| upminor 7th
| ^m7
| ^C
| classic/comma-wide minor 7th
| Km7
| KC
| thu
| te
|-
| 40
| 1043.5
| dupminor 7th
| ^^m7
| ^^C
| lesser neutral 7th, sub diminished 8ve
| n7, sd8
| UC, sDb
| thi
| tu<ref name="intervals2" group="note" />
|-
| 41
| 1069.6
| dudmajor 7th
| vvM7
| vvC#
| greater neutral 7th,
diminished 8ve
| N7, d8
| uC#, Db
| ti
| tuh<ref name="intervals3" group="note" />
|-
| 42
| 1095.7
| downmajor 7th
| vM7
| vC#
| classic major 7th,
comma-wide dim 8ve
| kM7, Kd8
| kC#, KDb
| to
| ti
|-
| 43
| 1121.7
| major 7th
| M7
| C#
| major 7th, <br>classic diminished 8ve
| M7, KKd8
| C#, KKDb
| ta
| taa
|-
| 44
| 1147.8
| upmajor 7th
| ^M7
| ^C#
| supermajor 7th, unter 8ve
| SM7, u8
| SC#, uD
| tu
| to
|-
| 45
| 1173.9
| down 8ve
| v8
| vD
| comma-narrow 8ve, sub 8ve
| k8/s8
| kD, sD
| do
| da
|-
| 46
| 1200.0
| perfect 8ve
| P8
| D
| perfect 8ve
| P8
| D
| da
| do
|}


8\46edo (208.70¢) stands in for frequency ratio [[xenharmonic/9_8|9:8]] (203.91¢).
=== Interval quality and chord names in color notation ===
7\46edo (182.61¢) stands in for [[xenharmonic/10_9|10:9]] (182.40¢).
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:
6\46edo (156.52¢) stands in for [[xenharmonic/11_10|11:10]] (165.00¢) and [[xenharmonic/12_11|12:11]] (150.64¢).
5\46edo (130.43¢) stands in for [[xenharmonic/13_12|13:12]] (138.57¢), [[xenharmonic/14_13|14:13]] (128.30¢) and [[xenharmonic/15_14|15:14]] (119.44¢).
4\46edo (104.35¢) stands in for [[xenharmonic/16_15|16:15]] (111.73¢).


=Scales=
{| class="wikitable center-all"
* [[xenharmonic/plum|plum]]
|-
* [[xenharmonic/sensi5|sensi5]]
! Quality
* [[xenharmonic/sensi8|sensi8]]
! Color
* [[xenharmonic/sensi11|sensi11]]
! Monzo format
* [[xenharmonic/sensi19|sensi19]]
! Examples
|-
| downminor
| zo
| {{Monzo| ''a'' ''b'' 0 1 }}
| 7/6, 7/4
|-
| minor
| fourthward wa
| {{Monzo| ''a'' ''b'' }}, ''b'' < −1
| 32/27, 16/9
|-
| upminor
| gu
| {{Monzo| ''a'' ''b'' −1 }}
| 6/5, 9/5
|-
| dupminor
| ilo
| {{Monzo| ''a'' ''b'' 0 0 1 }}
| 11/9, 11/6
|-
| dudmajor
| lu
| {{Monzo| ''a'' ''b'' 0 0 −1 }}
| 12/11, 18/11
|-
| downmajor
| yo
| {{Monzo| ''a'' ''b'' 1 }}
| 5/4, 5/3
|-
| major
| fifthward wa
| {{Monzo| ''a'' ''b'' }}, ''b'' > 1
| 9/8, 27/16
|-
| upmajor
| ru
| {{Monzo| ''a'' ''b'' 0 −1 }}
| 9/7, 12/7
|}
All 46edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. Ups or downs immediately after the chord root affect the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Here are the zo, gu, ilo, lu, yo and ru triads:


=Music=
{| class="wikitable center-all"
by [[xenharmonic/Gene Ward Smith|Gene Ward Smith:]]
|-
[[http://www.archive.org/details/Chromosounds|Chromosounds]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3|play]]
! Color of the 3rd
[[http://www.archive.org/details/MusicForYourEars|Music For Your Ears]] [[http://www.archive.org/download/MusicForYourEars/musicfor.mp3|play]] The central portion is in [[xenharmonic/27edo|27edo]], the rest in 46edo.
! JI chord
! Notes as edosteps
! Notes of C chord
! Written name
! Spoken name
|-
| zo
| 6:7:9
| 0–10–27
| C vEb G
| Cvm
| C downminor
|-
| gu
| 10:12:15
| 0–12–27
| C ^Eb G
| C^m
| C upminor
|-
| ilo
| 18:22:27
| 0–13–27
| C ^^Eb G
| C^^m
| C dupminor
|-
| lu
| 22:27:33
| 0–14–27
| C vvE G
| Cvv
| C dudmajor or C dud
|-
| yo
| 4:5:6
| 0–15–27
| C vE G
| Cv
| C downmajor or C down
|-
| ru
| 14:18:21
| 0–17–27
| C ^E G
| C^
| C upmajor or C up
|}
For a more complete list, see [[Ups and downs notation #Chords and chord progressions]].


by [[xenharmonic/Andrew Heathwaite|Andrew Heathwaite]]: [[@http://andrewheathwaite.bandcamp.com/track/rats|Rats]], [[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2001%20Rats.mp3|play]] [[@http://andrewheathwaite.bandcamp.com/track/tumbledown-stew|Tumbledown Stew]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2012%20Tumbledown%20Stew.mp3|play]], [[@http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-1|Hypnocloudsmack 1]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2004%20Hypnocloudsmack%201.mp3|play]], [[@http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-2|Hypnocloudsmack 2]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2009%20Hypnocloudsmack%202.mp3|play]], [[@http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-3|Hypnocloudsmack 3]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2013%20Hypnocloudsmack%203.mp3|play]]</pre></div>
== Notation ==
<h4>Original HTML content:</h4>
=== Stein–Zimmermann–Gould notation ===
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;46edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:14:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;a href="#x46 tone equal temperament"&gt;46 tone equal temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#x46edo srutis"&gt;46edo srutis&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#Linear temperaments"&gt;Linear temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt; | &lt;a href="#Approximation to Mode 8 of the Harmonic Series"&gt;Approximation to Mode 8 of the Harmonic Series&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Scales"&gt;Scales&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt; | &lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;
[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;hr /&gt;
{{Sharpness-sharp5-szg}}
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x46 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #300094; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;46 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/octave"&gt;octave&lt;/a&gt; into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent"&gt;cent&lt;/a&gt;s, an interval close in size to &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/66_65"&gt;66/65&lt;/a&gt;, the interval from &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/13_11"&gt;13/11&lt;/a&gt; to &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/6_5"&gt;6/5&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Rank%20two%20temperaments"&gt;Rank two temperaments&lt;/a&gt; it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/11-limit"&gt;11-limit&lt;/a&gt; &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Target%20tunings"&gt;minimax&lt;/a&gt; tuning for &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Starling%20family"&gt;valentine temperament&lt;/a&gt;, (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/13-limit"&gt;13-limit&lt;/a&gt;, though others award that distinction to &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/41edo"&gt;41edo&lt;/a&gt;. In fact, while 41 is a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta integral edo&lt;/a&gt; but not a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta gap edo&lt;/a&gt;, 46 is zeta gap but not zeta integral.&lt;br /&gt;
&lt;br /&gt;
The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/just%20fifth"&gt;just fifth&lt;/a&gt; and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.&lt;br /&gt;
&lt;br /&gt;
46edo can be treated as two &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/23edo"&gt;23edo&lt;/a&gt;'s separated by an interval of 26.087 cents.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="x46edo srutis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;46edo srutis&lt;/h1&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Magic22%20as%20srutis#shrutar22assrutis"&gt;Shrutar22 as srutis&lt;/a&gt; describes a possible use of 46edo for &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Indian"&gt;Indian&lt;/a&gt; music.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Linear temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Linear temperaments&lt;/h1&gt;


&lt;table class="wiki_table"&gt;
=== Kite's ups and downs notation ===
    &lt;tr&gt;
46edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp, etc., and likewise down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
        &lt;th&gt;Periods&lt;br /&gt;
{{Ups and downs sharpness}}
per octave&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Generator&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Temperaments&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;MOS/DE Scales available&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;L:s&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26.087&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;78.261&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Valentine"&gt;Valentine&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1L 14s (15-tone)&lt;br /&gt;
15L 1s (16-tone)&lt;br /&gt;
16L 15s (31-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4:3 ~ &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Maximal%20evenness"&gt;quasi-equal&lt;/a&gt;&lt;br /&gt;
3:1&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;130.435&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Twothirdtonic"&gt;Twothirdtonic&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%208s"&gt;1L 8s&lt;/a&gt; (9-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/9L%201s"&gt;9L 1s&lt;/a&gt; (10-tone)&lt;br /&gt;
9L 10s (19-tone)&lt;br /&gt;
9L 19s (28-tone)&lt;br /&gt;
9L 28s (37-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6:5 ~ QE&lt;br /&gt;
5:1&lt;br /&gt;
4:1&lt;br /&gt;
3:1&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;182.609&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Minortone"&gt;Minortone&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%205s"&gt;1L 5s&lt;/a&gt; (6-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%201s"&gt;6L 1s&lt;/a&gt; (7-tone)&lt;br /&gt;
7L 6s (13-tone)&lt;br /&gt;
13L 7s (20-tone)&lt;br /&gt;
13L 20s (33-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11:7&lt;br /&gt;
7:4&lt;br /&gt;
4:3 ~ QE&lt;br /&gt;
3:1&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;234.783&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Rodan"&gt;Rodan&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%204s"&gt;1L 4s&lt;/a&gt; (5-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%205s"&gt;1L 5s&lt;/a&gt; (6-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%206s"&gt;5L 6s&lt;/a&gt; (11-tone)&lt;br /&gt;
5L 11s (16-tone)&lt;br /&gt;
5L 16s (21-tone)&lt;br /&gt;
5L 21s (26-tone)&lt;br /&gt;
5L 26s (31-tone)&lt;br /&gt;
5L 31s (36-tone)&lt;br /&gt;
5L 36s (41-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10:9 ~QE&lt;br /&gt;
9:1&lt;br /&gt;
8:1&lt;br /&gt;
7:1&lt;br /&gt;
6:1&lt;br /&gt;
5:1&lt;br /&gt;
4:1&lt;br /&gt;
3:1&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;286.957&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%201s"&gt;4L 1s&lt;/a&gt; (5-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%205s"&gt;4L 5s&lt;/a&gt; (9-tone)&lt;br /&gt;
4L 9s (13-tone)&lt;br /&gt;
4L 13s (17-tone)&lt;br /&gt;
4L 17s (21-tone)&lt;br /&gt;
21L 4s (25-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11:2&lt;br /&gt;
9:2&lt;br /&gt;
7:2&lt;br /&gt;
5:2&lt;br /&gt;
3:2 ~ QE, Golden&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;339.13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Amity"&gt;Amity&lt;/a&gt;/&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/hitchcock"&gt;hitchcock&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%203s"&gt;4L 3s&lt;/a&gt; (7-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/7L%204s"&gt;7L 4s&lt;/a&gt; (11-tone)&lt;br /&gt;
7L 11s (18-tone)&lt;br /&gt;
7L 18s (25-tone)&lt;br /&gt;
7L 25s (32-tone)&lt;br /&gt;
7L 32s (39-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7:6 ~ QE&lt;br /&gt;
6:1&lt;br /&gt;
5:1&lt;br /&gt;
4:1&lt;br /&gt;
3:1&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;391.304&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%202s"&gt;1L 2s&lt;/a&gt; (3-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%201s"&gt;3L 1s&lt;/a&gt; (4-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%204s"&gt;3L 4s&lt;/a&gt; (7-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%207s"&gt;3L 7s&lt;/a&gt; (10-tone)&lt;br /&gt;
3L 10s (13-tone)&lt;br /&gt;
3L 13s (16-tone)&lt;br /&gt;
3L 16s (19-tone)&lt;br /&gt;
3L 19s (21-tone)&lt;br /&gt;
3L 21s (24-tone)&lt;br /&gt;
3L 24s (27-tone)&lt;br /&gt;
3L 27s (30-tone)&lt;br /&gt;
3L 30s (33-tone)&lt;br /&gt;
3L 33s (36-tone)&lt;br /&gt;
3L 36s (39-tone)&lt;br /&gt;
3L 39s (42-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16:15 ~ QE&lt;br /&gt;
15:1&lt;br /&gt;
14:1&lt;br /&gt;
13:1&lt;br /&gt;
12:1&lt;br /&gt;
11:1&lt;br /&gt;
10:1&lt;br /&gt;
9:1&lt;br /&gt;
8:1&lt;br /&gt;
7:1&lt;br /&gt;
6:1&lt;br /&gt;
5:1&lt;br /&gt;
4:1&lt;br /&gt;
3:1&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;443.478&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Sensi"&gt;Sensi&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%202s"&gt;3L 2s&lt;/a&gt; (5-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%205s"&gt;3L 5s&lt;/a&gt; (8-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/8L%203s"&gt;8L 3s&lt;/a&gt; (11-tone)&lt;br /&gt;
8L 11s (19-tone)&lt;br /&gt;
19L 8s (27-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12:5&lt;br /&gt;
7:5&lt;br /&gt;
5:2&lt;br /&gt;
3:2 ~ QE, Golden&lt;br /&gt;
2:1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;495.652&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Leapday"&gt;Leapday&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%203s"&gt;2L 3s&lt;/a&gt; (5-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%202s"&gt;5L 2s&lt;/a&gt; (7-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%207s"&gt;5L 7s&lt;/a&gt; (12-tone)&lt;br /&gt;
12L 5s (17-tone)&lt;br /&gt;
17L 12s (29-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11:8&lt;br /&gt;
8:3&lt;br /&gt;
5:3 ~ Golden&lt;br /&gt;
3:2 ~ QE, Golden&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;547.826&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Heinz"&gt;Heinz&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%203s"&gt;2L 3s&lt;/a&gt; (5-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%205s"&gt;2L 5s&lt;/a&gt; (7-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%207s"&gt;2L 7s&lt;/a&gt; (9-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%209s"&gt;2L 9s&lt;/a&gt; (11-tone)&lt;br /&gt;
11L 2s (13-tone)&lt;br /&gt;
11L 13s (24-tone)&lt;br /&gt;
11L 24s (35-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17:4&lt;br /&gt;
13:4&lt;br /&gt;
9:4&lt;br /&gt;
5:4 ~ QE&lt;br /&gt;
4:1&lt;br /&gt;
3:1&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26.087&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;52.174&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Shrutar"&gt;Shrutar&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s"&gt;2L 4s&lt;/a&gt; (6-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%206s"&gt;2L 6s&lt;/a&gt; (8-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%208s"&gt;2L 8s&lt;/a&gt; (10-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2010s"&gt;2L 10s&lt;/a&gt; (12-tone)&lt;br /&gt;
2L 12s (14-tone)&lt;br /&gt;
2L 14s (16-tone)&lt;br /&gt;
2L 16s (18-tone)&lt;br /&gt;
2L 18s (20-tone)&lt;br /&gt;
2L 20s (22-tone)&lt;br /&gt;
22L 2s (24-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21:2&lt;br /&gt;
19:2&lt;br /&gt;
17:2&lt;br /&gt;
15:2&lt;br /&gt;
13:2&lt;br /&gt;
11:2&lt;br /&gt;
9:2&lt;br /&gt;
7:2&lt;br /&gt;
5:2&lt;br /&gt;
3:2 ~ QE, Golden&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;78.261&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s"&gt;2L 4s&lt;/a&gt; (6-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%206s"&gt;2L 6s&lt;/a&gt; (8-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%208s"&gt;2L 8s&lt;/a&gt; (10-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2010s"&gt;2L 10s&lt;/a&gt; (12-tone)&lt;br /&gt;
2L 12s (14-tone)&lt;br /&gt;
14L 2s (16-tone)&lt;br /&gt;
16L 14s (30-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20:3&lt;br /&gt;
17:3&lt;br /&gt;
14:3&lt;br /&gt;
11:3&lt;br /&gt;
8:3&lt;br /&gt;
5:3 ~ Golden&lt;br /&gt;
3:2 ~ QE, Golden&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;104.348&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Srutal"&gt;Srutal&lt;/a&gt;/&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/diaschismic"&gt;diaschismic&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s"&gt;2L 4s&lt;/a&gt; (6-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%206s"&gt;2L 6s&lt;/a&gt; (8-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%208s"&gt;2L 8s&lt;/a&gt; (10-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/10L%202s"&gt;10L 2s&lt;/a&gt; (12-tone)&lt;br /&gt;
12L 10s (22-tone)&lt;br /&gt;
12L 22s (34-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19:4&lt;br /&gt;
15:4&lt;br /&gt;
11:4&lt;br /&gt;
7:4&lt;br /&gt;
4:3 ~ QE&lt;br /&gt;
3:1&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;130.435&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s"&gt;2L 4s&lt;/a&gt; (6-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%206s"&gt;2L 6s&lt;/a&gt; (8-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/8L%202s"&gt;8L 2s&lt;/a&gt; (10-tone)&lt;br /&gt;
8L 10s (18-tone)&lt;br /&gt;
18L 10s (28-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18:5&lt;br /&gt;
13:5&lt;br /&gt;
8:5 ~ Golden&lt;br /&gt;
5:3 ~ Golden&lt;br /&gt;
3:2 ~ QE, Golden&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;156.522&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s"&gt;2L 4s&lt;/a&gt; (6-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%202s"&gt;6L 2s&lt;/a&gt; (8-tone)&lt;br /&gt;
8L 6s (14-tone)&lt;br /&gt;
8L 14s (22-tone)&lt;br /&gt;
8L 22s (30-tone)&lt;br /&gt;
8L 30s (38-tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17:6&lt;br /&gt;
11:6&lt;br /&gt;
6:5 ~ QE&lt;br /&gt;
5:1&lt;br /&gt;
4:1&lt;br /&gt;
3:1&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;182.609&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Unidec"&gt;Unidec&lt;/a&gt;/&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/hendec"&gt;hendec&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s"&gt;2L 4s&lt;/a&gt; (6-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%202s"&gt;6L 2s&lt;/a&gt; (8-tone)&lt;br /&gt;
6L 8s (14-tone)&lt;br /&gt;
6L 14s (20-tone)&lt;br /&gt;
20L 6s (26-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16:7&lt;br /&gt;
9:7&lt;br /&gt;
7:2&lt;br /&gt;
5:2&lt;br /&gt;
3:2 ~ QE, Golden&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;208.696&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Abigail"&gt;Abigail&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%202s"&gt;4L 2s&lt;/a&gt; (6-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%202s"&gt;6L 2s&lt;/a&gt; (8-tone)&lt;br /&gt;
6L 8s (14-tone)&lt;br /&gt;
6L 14s (20-tone)&lt;br /&gt;
6L 20s (26-tone)&lt;br /&gt;
6L 26s (32-tone)&lt;br /&gt;
6L 32s (38-tone)&lt;br /&gt;
6L 38s (44-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15:8&lt;br /&gt;
8:7 ~ QE&lt;br /&gt;
8:1&lt;br /&gt;
7:1&lt;br /&gt;
6:1&lt;br /&gt;
5:1&lt;br /&gt;
4:1&lt;br /&gt;
3:1&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;234.783&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Echidnic"&gt;Echidnic&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%202s"&gt;4L 2s&lt;/a&gt; (6-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%204s"&gt;6L 4s&lt;/a&gt; (10-tone)&lt;br /&gt;
10L 6s (16-tone)&lt;br /&gt;
10L 16s (26-tone)&lt;br /&gt;
10L 26s (36-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14:9&lt;br /&gt;
9:5&lt;br /&gt;
5:4 ~ QE&lt;br /&gt;
4:1&lt;br /&gt;
3:1&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;260.87&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%202s"&gt;4L 2s&lt;/a&gt; (6-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%206s"&gt;4L 6s&lt;/a&gt; (10-tone)&lt;br /&gt;
4L 10s (14-tone)&lt;br /&gt;
14L 4s (18-tone)&lt;br /&gt;
14L 18s (32-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13:10&lt;br /&gt;
10:3&lt;br /&gt;
7:3&lt;br /&gt;
4:3 ~ QE&lt;br /&gt;
3:1&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;286.957&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%202s"&gt;4L 2s&lt;/a&gt; (6-tone)&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%206s"&gt;4L 6s&lt;/a&gt; (10-tone)&lt;br /&gt;
4L 10s (14-tone)&lt;br /&gt;
4L 14s (18-tone)&lt;br /&gt;
4L 18s (22-tone)&lt;br /&gt;
4L 22s (26-tone)&lt;br /&gt;
4L 26s (30-tone)&lt;br /&gt;
4L 30s (34-tone)&lt;br /&gt;
4L 34s (38-tone)&lt;br /&gt;
4L 38s (42-tone)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12:11 ~ QE&lt;br /&gt;
11:1&lt;br /&gt;
10:1&lt;br /&gt;
9:1&lt;br /&gt;
8:1&lt;br /&gt;
7:1&lt;br /&gt;
6:1&lt;br /&gt;
5:1&lt;br /&gt;
4:1&lt;br /&gt;
3:1&lt;br /&gt;
2:1 ~ QE&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26.087&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Intervals&lt;/h1&gt;
=== Sagittal notation ===
This notation uses the same sagittal sequence as [[39edo #Sagittal notation|39edo]].


&lt;table class="wiki_table"&gt;
==== Evo flavor ====
    &lt;tr&gt;
{{Sagittal chart|Evo}}
        &lt;td&gt;degrees of 46edo&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;cents value&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;approximate ratios in the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/17-limit"&gt;17-limit&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.00&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26.087&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;52.174&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;78.261&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;104.348&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/15, 17/16, 18/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;130.435&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/12, 14/13, 15/14&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;156.522&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/11, 11/10&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;182.609&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;208.696&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8, 17/15&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;234.783&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/7, 15/13*&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;260.87&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6, 15/13*&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;286.957&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/11, 20/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;313.043&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;339.13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/9, 17/14&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;365.217&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;391.304&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;417.391&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;443.478&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7, 13/10, 22/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;469.565&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;495.652&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;521.739&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;547.826&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8, 15/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;573.913&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5, 18/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/12, 24/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;626.087&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/7, 13/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;652.174&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/11, 22/15&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;678.261&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;704.348&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;730.435&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;756.522&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9, 20/13, 17/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;782.609&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;808.696&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;834.783&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/8&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;860.87&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/11, 28/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;886.957&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;913.043&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/13, 17/10&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;939.13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7, 26/15*&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;965.217&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4, 26/15*&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;991.304&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9, 30/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1017.391&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1043.478&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/6, 20/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1069.565&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;24/13, 13/7, 28/15&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1095.652&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/8, 32/17, 17/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1121.739&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1147.826&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1173.913&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


*15/13 (and its inversion 26/15) appears twice on the list. 9\46edo is closest to 15/13 by a hair; 10\46edo represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13. This discrepancy occurs because 46edo is not &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/consistent"&gt;consistent&lt;/a&gt; in the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/15-limit"&gt;15-limit&lt;/a&gt;.&lt;br /&gt;
==== Revo flavor ====
&lt;br /&gt;
{{Sagittal chart}}
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Approximation to Mode 8 of the Harmonic Series"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Approximation to Mode 8 of the Harmonic Series&lt;/h1&gt;
 
&lt;br /&gt;
== Approximation to JI ==
46edo represents &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/overtone"&gt;overtone&lt;/a&gt;s 8 through 16 (written as &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/JI"&gt;JI&lt;/a&gt; ratios 8:9:10:11:12:13:14:15:16) with degrees 0, 8, 15, 21, 27, 32, 37, 42, 46. In steps-in-between, that's 8, 7, 6, 6, 5, 5, 5, 4.&lt;br /&gt;
[[File:46ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 15-limit intervals approximated in 46edo]]
&lt;br /&gt;
 
8\46edo (208.70¢) stands in for frequency ratio &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_8"&gt;9:8&lt;/a&gt; (203.91¢).&lt;br /&gt;
=== 17-odd-limit interval mappings ===
7\46edo (182.61¢) stands in for &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/10_9"&gt;10:9&lt;/a&gt; (182.40¢).&lt;br /&gt;
{{Q-odd-limit intervals|46|17}}
6\46edo (156.52¢) stands in for &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/11_10"&gt;11:10&lt;/a&gt; (165.00¢) and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/12_11"&gt;12:11&lt;/a&gt; (150.64¢).&lt;br /&gt;
 
5\46edo (130.43¢) stands in for &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/13_12"&gt;13:12&lt;/a&gt; (138.57¢), &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/14_13"&gt;14:13&lt;/a&gt; (128.30¢) and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/15_14"&gt;15:14&lt;/a&gt; (119.44¢).&lt;br /&gt;
=== Consistent circles ===
4\46edo (104.35¢) stands in for &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/16_15"&gt;16:15&lt;/a&gt; (111.73¢).&lt;br /&gt;
46edo is home to a number of [[consistent circle]]s, both ones closing after generating all 46 notes and ones closing after generating 23edo.
&lt;br /&gt;
{| class="wikitable center-1 center-2 center-3"
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Scales&lt;/h1&gt;
|+ style="font-size: 105%;" | 46-note circles by gen. with related temperaments organized by period
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/plum"&gt;plum&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi5"&gt;sensi5&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi8"&gt;sensi8&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi11"&gt;sensi11&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi19"&gt;sensi19&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
|-
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Music&lt;/h1&gt;
! [[Interval]] !! [[Closing error|Closing<br />Error]] !! [[Circle #Definitions|Consistency]] !! 1\1 !! 1\2
by &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Gene%20Ward%20Smith"&gt;Gene Ward Smith:&lt;/a&gt;&lt;br /&gt;
|-
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Chromosounds" rel="nofollow"&gt;Chromosounds&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
| [[68/65]] || 25.9% || Normal || [[Valentine]] || [[Semivalentine]]
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow"&gt;Music For Your Ears&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.archive.org/download/MusicForYourEars/musicfor.mp3" rel="nofollow"&gt;play&lt;/a&gt; The central portion is in &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/27edo"&gt;27edo&lt;/a&gt;, the rest in 46edo.&lt;br /&gt;
|-
&lt;br /&gt;
| [[10/9]] || 36.1% || Normal || [[Mitonic]] || [[Unidec]], [[hendec]]
by &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;: &lt;a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/rats" rel="nofollow" target="_blank"&gt;Rats&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2001%20Rats.mp3" rel="nofollow"&gt;play&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/tumbledown-stew" rel="nofollow" target="_blank"&gt;Tumbledown Stew&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2012%20Tumbledown%20Stew.mp3" rel="nofollow"&gt;play&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-1" rel="nofollow" target="_blank"&gt;Hypnocloudsmack 1&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2004%20Hypnocloudsmack%201.mp3" rel="nofollow"&gt;play&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-2" rel="nofollow" target="_blank"&gt;Hypnocloudsmack 2&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2009%20Hypnocloudsmack%202.mp3" rel="nofollow"&gt;play&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-3" rel="nofollow" target="_blank"&gt;Hypnocloudsmack 3&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2013%20Hypnocloudsmack%203.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
|-
| [[31/24]] || 70.2% || Weak || [[Sensible]], [[sensi]] add-31 || [[Bison]] add-31, [[bisensi]] add-31
|}
 
{| class="wikitable center-all left-4"
|+ style="font-size: 105%;" | 23-note circles by gen. with related half-octave temperaments
|-
! [[Interval]] !! [[Closing error|Closing<br />Error]] !! [[Circle #Definitions|Consistency]] !! Temperaments
|-
| [[17/16]] || 53.5% || Weak || [[Diaschismic]]
|-
| [[23/21]] || 85.7% || Weak || [[Bison]]
|-
| [[44/39]] || 12.3% || Super-strong || [[Abigail]]
|-
| [[21/17]] || 53.6% || Weak || ?
|-
| [[14/11]] || 10.2% || Super-strong || ?
|-
| [[21/16]] || 107% || Sub-weak || ?
|}
 
For the 23rd-octave temperament that 46edo supports which combines all above 23-note circles, see [[icositritonic]].
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 73 -46 }}
| {{mapping| 46 73 }}
| −0.755
| 0.75
| 2.89
|-
| 2.3.5
| 2048/2025, 78732/78125
| {{mapping| 46 73 107 }}
| −1.219
| 0.90
| 3.45
|-
| 2.3.5.7
| 126/125, 245/243, 1029/1024
| {{mapping| 46 73 107 129 }}
| −0.595
| 1.34
| 5.12
|-
| 2.3.5.7.11
| 121/120, 126/125, 176/175, 245/243
| {{mapping| 46 73 107 129 159 }}
| −0.274
| 1.36
| 5.20
|-
| 2.3.5.7.11.13
| 91/90, 121/120, 169/168, 176/175, 245/243
| {{mapping| 46 73 107 129 159 170 }}
| +0.030
| 1.41
| 5.42
|-
| 2.3.5.7.11.13.17
| 91/90, 121/120, 154/153, 169/168, 176/175, 245/243
| {{mapping| 46 73 107 129 159 170 188 }}
| +0.047
| 1.31
| 5.02
|-
| 2.3.5.7.11.13.17.23
| 91/90, 121/120, 154/153, 169/168, 176/175, 208/207, 231/230
| {{mapping| 46 73 107 129 159 170 188 208 }}
| +0.101
| 1.23
| 4.72
|}
* 46et is lower in relative error than any previous equal temperaments in the 17-, 19-, 23-limit, and others. The next equal temperaments doing better in the aforementioned subgroups are 72, 72, 94, respectively. 46et is even more prominent in the no-19 23-limit, and the next equal temperament doing better in this subgroup is 140.
 
=== Commas ===
This is a partial list of the [[commas]] that 46et [[tempering out|tempers out]] with its [[patent val]], {{val| 24 38 56 67 83 89 }}.  
 
{| class="commatable wikitable center-1 center-2 right-4 center-5"
|-
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name(s)
|-
| 5
| <abbr title="50331648/48828125">(16 digits)</abbr>
| {{monzo| 24 1 -11 }}
| 52.50
| Salegu
| [[Magus comma]]
|-
| 5
| <abbr title="1990656/1953125">(14 digits)</abbr>
| {{monzo| 13 5 -9 }}
| 32.95
| Satritrigu
| [[Valentine comma]]
|-
| 5
| [[2048/2025]]
| {{monzo| 11 -4 -2 }}
| 19.55
| Sagugu
| Diaschisma
|-
| 5
| [[78732/78125]]
| {{monzo| 2 9 -7 }}
| 13.40
| Sepgu
| Sensipent comma
|-
| 5
| <abbr title="1600000/1594323">(14 digits)</abbr>
| {{monzo| 9 -13 5 }}
| 6.15
| Saquinyo
| [[Amity comma]]
|-
| 7
| [[686/675]]
| {{monzo| 1 -3 -2 3 }}
| 27.99
| Trizo-agugu
| Senga
|-
| 7
| [[245/243]]
| {{monzo| 0 -5 1 2 }}
| 14.19
| Zozoyo
| Sensamagic comma
|-
| 7
| [[126/125]]
| {{monzo| 1 2 -3 1 }}
| 13.80
| Zotrigu
| Starling comma
|-
| 7
| [[1029/1024]]
| {{monzo| -10 1 0 3 }}
| 8.43
| Latrizo
| Gamelisma
|-
| 7
| [[5120/5103]]
| {{monzo| 10 -6 1 -1 }}
| 5.76
| Saruyo
| Hemifamity comma, aberschisma
|-
| 7
| <abbr title="2147483648/2144153025">(20 digits)</abbr>
| {{monzo| 31 -6 -2 -6 }}
| 2.69
| Sasa-tribiru-agugu
| [[Pessoalisma]]
|-
| 7
| [[4375/4374]]
| {{monzo| -1 -7 4 1 }}
| 0.40
| Zoquadyo
| Ragisma
|-
| 11
| [[121/120]]
| {{monzo|-3 -1 -1 0 2 }}
| 14.37
| Lologu
| Biyatisma
|-
| 11
| [[176/175]]
| {{monzo| 4 0 -2 -1 1 }}
| 9.86
| Lorugugu
| Valinorsma
|-
| 11
| [[896/891]]
| {{monzo| 7 -4 0 1 -1 }}
| 9.69
| Saluzo
| Pentacircle comma
|-
| 11
| [[385/384]]
| {{monzo|-7 -1 1 1 1 }}
| 4.50
| Lozoyo
| Keenanisma
|-
| 11
| [[441/440]]
| {{monzo| -3 2 -1 2 -1 }}
| 3.93
| Luzozogu
| Werckisma
|-
| 13
| [[91/90]]
| {{monzo| -1 -2 -1 1 0 1 }}
| 19.13
| Thozogu
| Superleap comma, biome comma
|-
| 13
| [[169/168]]
| {{monzo| -3 -1 0 -1 0 2 }}
| 10.27
| Thothoru
| Buzurgisma, dhanvantarisma
|-
| 13
| [[196/195]]
| {{monzo| 2 -1 -1 2 0 -1 }}
| 8.86
| Thuzozogu
| Mynucuma
|-
| 13
| [[507/500]]
| {{monzo| -2 1 -3 0 0 2 }}
| 24.07
| Thothotrigu
|
|-
| 13
| [[351/350]]
| {{Monzo| -1 3 -2 -1 0 1 }}
| 4.94
| Thorugugu
| Ratwolfsma
|-
| 13
| [[352/351]]
| {{monzo| 5 -3 0 0 1 -1 }}
| 4.93
| Thulo
| Minor minthma
|-
| 17
| [[256/255]]
| {{monzo| 8 -1 -1 0 0 0 -1 }}
| 6.78
| Sugu
| Charisma, septendecimal kleisma
|-
| 17
| [[289/288]]
| {{monzo| -5 -2 0 0 0 0 2 }}
| 6.00
| Soso
| Semitonisma
|}
<references group="note" />
 
=== Rank-2 temperaments ===
{| class="wikitable center-1 center-2 center-3 center-4"
|-
! Periods<br>per 8ve
! Generator
! Cents
! Temperaments
! MOS scales
! L:s
|-
| rowspan="11" | 1
| 1\46
| 26.087
| [[Sfourth]]
|
|
|-
| 3\46
| 78.261
| [[Valentine]]
| 1L&nbsp;14s (15-tone)<br>15L&nbsp;1s (16-tone)<br>16L&nbsp;15s (31-tone)
| 4:3 ~ [[Maximal evenness|quasi-equal]]<br>3:1<br>2:1 ~ QE
|-
| 5\46
| 130.435
| [[Twothirdtonic]]
| [[1L&nbsp;8s]] (9-tone)<br>[[9L&nbsp;1s]] (10-tone)<br>9L&nbsp;10s (19-tone)<br>9L&nbsp;19s (28-tone)<br>9L&nbsp;28s (37-tone)
| 6:5 ~ QE<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
|-
| 7\46
| 182.609
| [[Minortone]] / [[mitonic]]
| [[1L&nbsp;5s]] (6-tone)<br>[[6L&nbsp;1s]] (7-tone)<br>7L&nbsp;6s (13-tone)<br>13L&nbsp;7s (20-tone)<br>13L&nbsp;20s (33-tone)
| 11:7<br>7:4<br>4:3 ~ QE<br>3:1<br>2:1 ~ QE
|-
| 9\46
| 234.783
| [[Rodan]]
| [[1L&nbsp;4s]] (5-tone)<br>[[1L&nbsp;5s]] (6-tone)<br>[[5L&nbsp;6s]] (11-tone)<br>5L&nbsp;11s (16-tone)<br>5L&nbsp;16s (21-tone)<br>5L&nbsp;21s (26-tone)<br>5L&nbsp;26s (31-tone)<br>5L&nbsp;31s (36-tone)<br>5L&nbsp;36s (41-tone)
| 10:9 ~QE<br>9:1<br>8:1<br>7:1<br>6:1<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
|-
| 11\46
| 286.957
| [[Amity_family#Gamity|Gamity]]
| [[4L&nbsp;1s]] (5-tone)<br>[[4L&nbsp;5s]] (9-tone)<br>4L&nbsp;9s (13-tone)<br>4L&nbsp;13s (17-tone)<br>4L&nbsp;17s (21-tone)<br>21L&nbsp;4s (25-tone)
| 11:2<br>9:2<br>7:2<br>5:2<br>3:2 ~ QE, Golden<br>2:1 ~ QE
|-
| 13\46
| 339.130
| [[Amity]] / [[Amity_family#Hitchcock|Hitchcock]]
| [[4L&nbsp;3s]] (7-tone)<br>[[7L&nbsp;4s]] (11-tone)<br>7L&nbsp;11s (18-tone)<br>7L&nbsp;18s (25-tone)<br>7L&nbsp;25s (32-tone)<br>7L&nbsp;32s (39-tone)
| 7:6 ~ QE<br>6:1<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
|-
| 15\46
| 391.304
| [[Magus]] / [[amigo]]
| [[1L&nbsp;2s]] (3-tone)<br>[[3L&nbsp;1s]] (4-tone)<br>[[3L&nbsp;4s]] (7-tone)<br>[[3L&nbsp;7s]] (10-tone)<br>3L&nbsp;10s (13-tone)<br>3L&nbsp;13s (16-tone)<br>3L&nbsp;16s (19-tone)<br>3L&nbsp;19s (21-tone)<br>3L&nbsp;21s (24-tone)<br>3L&nbsp;24s (27-tone)<br>3L&nbsp;27s (30-tone)<br>3L&nbsp;30s (33-tone)<br>3L&nbsp;33s (36-tone)<br>3L&nbsp;36s (39-tone)<br>3L&nbsp;39s (42-tone)
| 16:15 ~ QE<br>15:1<br>14:1<br>13:1<br>12:1<br>11:1<br>10:1<br>9:1<br>8:1<br>7:1<br>6:1<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
|-
| 17\46
| 443.478
| [[Sensi]]
| [[3L&nbsp;2s]] (5-tone)<br>[[3L&nbsp;5s]] (8-tone)<br>[[8L&nbsp;3s]] (11-tone)<br>8L&nbsp;11s (19-tone)<br>19L&nbsp;8s (27-tone)
| 12:5<br>7:5<br>5:2<br>3:2 ~ QE, Golden<br>2:1
|-
| 19\46
| 495.652
| [[Leapday]]
| [[2L&nbsp;3s]] (5-tone)<br>[[5L&nbsp;2s]] (7-tone)<br>[[5L&nbsp;7s]] (12-tone)<br>12L&nbsp;5s (17-tone)<br>17L&nbsp;12s (29-tone)
| 11:8<br>8:3<br>5:3 ~ Golden<br>3:2 ~ QE, Golden<br>2:1 ~ QE
|-
| 21\46
| 547.826
| [[Heinz]]
| [[2L&nbsp;3s]] (5-tone)<br>[[2L&nbsp;5s]] (7-tone)<br>[[2L&nbsp;7s]] (9-tone)<br>[[2L&nbsp;9s]] (11-tone)<br>11L&nbsp;2s (13-tone)<br>11L&nbsp;13s (24-tone)<br>11L&nbsp;24s (35-tone)
| 17:4<br>13:4<br>9:4<br>5:4 ~ QE<br>4:1<br>3:1<br>2:1 ~ QE
|-
| rowspan="11" | 2
| 1\46
| 26.087
| [[Ketchup]]
|
|
|-
| 2\46
| 52.174
| [[Shrutar]]
| 2L&nbsp;2s (4-tone)<br>[[2L&nbsp;4s]] (6-tone)<br>[[2L&nbsp;6s]] (8-tone)<br>[[2L&nbsp;8s]] (10-tone)<br>[[2L&nbsp;10s]] (12-tone)<br>2L&nbsp;12s (14-tone)<br>2L&nbsp;14s (16-tone)<br>2L&nbsp;16s (18-tone)<br>2L&nbsp;18s (20-tone)<br>2L&nbsp;20s (22-tone)<br>22L&nbsp;2s (24-tone)
| 21:2<br>19:2<br>17:2<br>15:2<br>13:2<br>11:2<br>9:2<br>7:2<br>5:2<br>3:2 ~ QE, Golden<br>2:1 ~ QE
|-
| 3\46
| 78.261
| [[Semivalentine]]
| 2L&nbsp;2s (4-tone)<br>[[2L&nbsp;4s]] (6-tone)<br>[[2L&nbsp;6s]] (8-tone)<br>[[2L&nbsp;8s]] (10-tone)<br>[[2L&nbsp;10s]] (12-tone)<br>2L&nbsp;12s (14-tone)<br>14L&nbsp;2s (16-tone)<br>16L&nbsp;14s (30-tone)
| 20:3<br>17:3<br>14:3<br>11:3<br>8:3<br>5:3 ~ Golden<br>3:2 ~ QE, Golden<br>2:1 ~ QE
|-
| 4\46
| 104.348
| [[Srutal]] / [[diaschismic]]
| 2L&nbsp;2s (4-tone)<br>[[2L&nbsp;4s]] (6-tone)<br>[[2L&nbsp;6s]] (8-tone)<br>[[2L&nbsp;8s]] (10-tone)<br>[[10L&nbsp;2s]] (12-tone)<br>12L&nbsp;10s (22-tone)<br>12L&nbsp;22s (34-tone)
| 19:4<br>15:4<br>11:4<br>7:4<br>4:3 ~ QE<br>3:1<br>2:1 ~ QE
|-
| 5\46
| 130.435
|
| 2L&nbsp;2s (4-tone)<br>[[2L&nbsp;4s]] (6-tone)<br>[[2L&nbsp;6s]] (8-tone)<br>[[8L&nbsp;2s]] (10-tone)<br>8L&nbsp;10s (18-tone)<br>18L&nbsp;10s (28-tone)
| 18:5<br>13:5<br>8:5 ~ Golden<br>5:3 ~ Golden<br>3:2 ~ QE, Golden<br>2:1 ~ QE
|-
| 6\46
| 156.522
| [[Bison]]
| 2L&nbsp;2s (4-tone)<br>[[2L&nbsp;4s]] (6-tone)<br>[[6L&nbsp;2s]] (8-tone)<br>8L&nbsp;6s (14-tone)<br>8L&nbsp;14s (22-tone)<br>8L&nbsp;22s (30-tone)<br>8L&nbsp;30s (38-tone
| 17:6<br>11:6<br>6:5 ~ QE<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
|-
| 7\46
| 182.609
| [[Unidec]] / [[hendec]]
| 2L&nbsp;2s (4-tone)<br>[[2L&nbsp;4s]] (6-tone)<br>[[6L&nbsp;2s]] (8-tone)<br>6L&nbsp;8s (14-tone)<br>6L&nbsp;14s (20-tone)<br>20L&nbsp;6s (26-tone)
| 16:7<br>9:7<br>7:2<br>5:2<br>3:2 ~ QE, Golden<br>2:1 ~ QE
|-
| 8\46
| 208.696
| [[Abigail]]
| 2L&nbsp;2s (4-tone)<br>[[4L&nbsp;2s]] (6-tone)<br>[[6L&nbsp;2s]] (8-tone)<br>6L&nbsp;8s (14-tone)<br>6L&nbsp;14s (20-tone)<br>6L&nbsp;20s (26-tone)<br>6L&nbsp;26s (32-tone)<br>6L&nbsp;32s (38-tone)<br>6L&nbsp;38s (44-tone)
| 15:8<br>8:7 ~ QE<br>8:1<br>7:1<br>6:1<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
|-
| 9\46
| 234.783
| [[Echidnic]]
| 2L&nbsp;2s (4-tone)<br>[[4L&nbsp;2s]] (6-tone)<br>[[6L&nbsp;4s]] (10-tone)<br>10L&nbsp;6s (16-tone)<br>10L&nbsp;16s (26-tone)<br>10L&nbsp;26s (36-tone)
| 14:9<br>9:5<br>5:4 ~ QE<br>4:1<br>3:1<br>2:1 ~ QE
|-
| 10\46
| 260.87
| [[Bamity]]
| 2L&nbsp;2s (4-tone)<br>[[4L&nbsp;2s]] (6-tone)<br>[[4L&nbsp;6s]] (10-tone)<br>4L&nbsp;10s (14-tone)<br>14L&nbsp;4s (18-tone)<br>14L&nbsp;18s (32-tone)
| 13:10<br>10:3<br>7:3<br>4:3 ~ QE<br>3:1<br>2:1 ~ QE
|-
| 11\46
| 286.957
| [[Vines]]
| 2L&nbsp;2s (4-tone)<br>[[4L&nbsp;2s]] (6-tone)<br>[[4L&nbsp;6s]] (10-tone)<br>4L&nbsp;10s (14-tone)<br>4L&nbsp;14s (18-tone)<br>4L&nbsp;18s (22-tone)<br>4L&nbsp;22s (26-tone)<br>4L&nbsp;26s (30-tone)<br>4L&nbsp;30s (34-tone)<br>4L&nbsp;34s (38-tone)<br>4L&nbsp;38s (42-tone)
| 12:11 ~ QE<br>11:1<br>10:1<br>9:1<br>8:1<br>7:1<br>6:1<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
|-
| 23
| 1\46
| 26.087
| [[Icositritonic]]
|
|
|}
 
== Scales ==
{{Main| List of MOS scales in 46edo }}
 
* [[Plum]]
* [[Compdye]]
* [[Smi2s]]
 
; Sensi
* [[Sensi5]]
* [[Sensi8]]
* [[Sensi11]]
* [[Sensi19]]
 
; Elfleapday
* [[Elfleapday7]]
* [[Elfleapday8d]]
* [[Elfleapday9]]
* [[Elfleapday10]]
* [[Elfleapday12]]
* [[Elfleapday12f]]
 
; Elfsensus
* [[Elfsensus7]]
* [[Elfsensus8d]]
* [[Elfsensus9]]
* [[Elfsensus10]]
* [[Elfsensus12]]
* [[Elfsensus12f]]
 
=== Harmonic scales ===
46edo represents [[harmonic series|overtones]] 8 through 16 (written as [[JI]] ratios 8:9:10:11:12:13:14:15:16) with degrees 0, 8, 15, 21, 27, 32, 37, 42, 46. This corresponds to scale steps of 8, 7, 6, 6, 5, 5, 5, 4.
* 8\46 (208.696{{c}}) stands in for frequency ratio [[9/8]] (203.910{{c}}).
* 7\46 (182.609{{c}}) stands in for [[10/9]] (182.404{{c}}).
* 6\46 (156.522{{c}}) stands in for [[11/10]] (165.004{{c}}) and [[12/11]] (150.637{{c}}).
* 5\46 (130.435{{c}}) stands in for [[13/12]] (138.573{{c}}), [[14/13]] (128.298{{c}}) and [[15/14]] (119.443{{c}}).
* 4\46 (104.348{{c}}) stands in for [[16/15]] (111.731{{c}}).
 
{| class="wikitable center-all"
|-
! Harmonic
! Note (starting from C)
|-
! 1
| style="font-size: 16px;" | C
|-
! 3
| style="font-size: 16px;" | G
|-
! 5
| style="font-size: 16px;" | E{{naturaldown|40}}
|-
! 7
| style="font-size: 16px;" | G&#x1D12A;, B{{flatdown|40}}
|-
! 9
| style="font-size: 16px;" | D
|-
! 11
| style="font-size: 16px;" | E&#x266F;, F{{naturalup2|40}}
|-
! 13
| style="font-size: 16px;" | G&#x266F;, A{{flatup2|40}}
|-
! 15
| style="font-size: 16px;" | B{{naturaldown|40}}
|}
 
== Instruments ==
=== Lumatone ===
* [[Lumatone mapping for 46edo]]
 
=== Skip fretting ===
'''[[Skip fretting system 46 2 11]]''' is a [[skip fretting]] system for playing 46-edo on a 23-edo stringed instrument.
 
 
'''Skip fretting system 46 7 11''' is another skip fretting system for 46edo. The examples on this page are for 7-string [[guitar]].
 
; Harmonics
1/1: string 2 open
 
2/1: string 3 fret 5
 
3/2: not easily accessible
 
5/4: string 5 fret 4
 
== Music ==
=== Modern renditions ===
; {{W|Johann Sebastian Bach}}
* [http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Bach_BWV_1029_E46-Alto-Sax-+-Harpsichord.mp3 Sonata No. 3 in G minor, BWV 1029]{{dead link}} (late 1730s – early 1740s) – arranged and rendered by Claudi Meneghin
* [https://www.youtube.com/watch?v=wMEdFl2puL0 "Ricercar a 6" from ''The Musical Offering'', BWV 1079] (1747) – with syntonic-comma adjustment, rendered by Claudi Meneghin (2025)
* [http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Bach_Contrapunctus_4-Jeux14-E46.mp3 "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080]{{dead link}} (1742–1749) – arranged and rendered by Claudi Meneghin
* "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – arranged and rendered by Claudi Meneghin
** [https://www.youtube.com/watch?v=4yetEubmIk0 organ rendering] (2024) · [https://www.youtube.com/watch?v=fwGBD-oGNxI harpsichord rendering] (2025)
 
; {{W|Nicolaus Bruhns}}
* [https://www.youtube.com/watch?v=_YiCc81ktBI ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)
 
; {{W|Frederick Chopin}}
* [https://www.youtube.com/shorts/nCKtRb7fD2w ''Prelude op. 28 no. 7 in A major''] (1836) – rendered by Claudi Meneghin (2025)
* ''"Waterfall" Étude from 12 Études, op. 10'' (1829–1832) – with syntonic comma adjustment, rendered with fortepiano tone by Claudi Meneghin (2025)
** [https://www.youtube.com/shorts/AkKCmAtAQCg ''fortepiano rendering'']
** [https://www.youtube.com/shorts/QCN0H2Gnmk4 ''sine wave rendering'']
 
; {{W|Scott Joplin}}
* ''Maple Leaf Rag'' (1899) – arranged for harpsichord and rendered by Claudi Meneghin
** with syntonic comma adjustment ([https://www.youtube.com/watch?v=GXIoWsvFMzI 2024], [https://www.youtube.com/watch?v=55iWVqnaox8&lc=Ugz472kn24J1Bw_vHtV4AaABAg 2025])
** without syntonic comma adjustment (super-Pythagorean) ([https://www.youtube.com/shorts/2OOXUO2H9qA 2026])
 
; Claude Larson ({{W|Klaus Netzle|German Wikipedia|s=de}})
* [https://www.youtube.com/shorts/fxEWnqvZtjY "Memory Image" from ''Soundscapes Vol.2''] (1986) – covered by [[Bryan Deister]] (2025)
 
; {{W|Akira Yamaoka}}
* [https://www.youtube.com/shorts/WyY-7Im0zkw ''Lakeview Hotel Music Box''] via ''{{W|Silent Hill 2}}'' (2001) – microtonal cover in 46edo by [[Bryan Deister]] (2026)
 
=== 21st century ===
; [[Bryan Deister]]
* [https://www.youtube.com/watch?v=SCpbbov1fSQ ''music box 46edo''] (2025)
* [https://www.youtube.com/shorts/K-Gu_YkjYS4 ''46edo improv''] (2025)
* [https://www.youtube.com/shorts/IWYJPyWE_Ao ''46edo waltz''] (2025)
 
; [[Jake Freivald]] ([https://soundcloud.com/jdfreivald site])
* [https://soundcloud.com/jdfreivald/a-seed-planted-yet-another ''A Seed Planted''] [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/a_seed_planted-starling-46-EDO.mp3 play]{{dead link}}
 
; [[groundfault]]
* "Glimmer Extrication", from ''Souvenirs of the Affliction'' (2025) – [https://groundfco.bandcamp.com/track/glimmer-extrication-46edo-2 Bandcamp] | [https://www.youtube.com/watch?v=rrjuGmmodn0&t=969 YouTube (16:09–21:11)]
 
; [[Andrew Heathwaite]]
* [https://andrewheathwaite.bandcamp.com/track/rats ''Rats''] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2001%20Rats.mp3 play]{{dead link}} (2012)
* [https://andrewheathwaite.bandcamp.com/track/tumbledown-stew ''Tumbledown Stew''] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2012%20Tumbledown%20Stew.mp3 play]{{dead link}} (2012)
* [https://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-1 ''Hypnocloudsmack 1''] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2004%20Hypnocloudsmack%201.mp3 play]{{dead link}} (2012)
* [https://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-2 ''Hypnocloudsmack 2''] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2009%20Hypnocloudsmack%202.mp3 play]{{dead link}} (2012)
* [https://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-3 ''Hypnocloudsmack 3''] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2013%20Hypnocloudsmack%203.mp3 play]{{dead link}} (2012)
 
; [[Aaron Krister Johnson]]
* [https://aaronkristerjohnson.bandcamp.com/track/satiesque ''Satiesque''] (2014)
 
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=-6ORgyqom5M ''Les Regrets''] (2019) – chaconne & fugue a 5, for recorder, cornett, viola da braccio, bassoon, gamba, and continuo.
* [https://www.youtube.com/watch?v=1r55c2nppe8 ''El Rossinyol''] (2020) – for organ
* [https://www.youtube.com/watch?v=JwjoT6ceU20 ''Arietta with 5 Variations''] (2020) – for organ
* [https://www.youtube.com/watch?v=rmgWC_jruSg ''Sensi Fugue''] (2024) – fugue for two organs, in sensi, 46edo tuning
* [https://www.youtube.com/shorts/iZQElKqq6Hw "Closing Jingle"], from [https://www.youtube.com/playlist?list=PLC6ZSKWKnVz14UQd32K1sXc2zvstkPN6V ''Mikrokosmos''] (2026)
 
; [[Herman Miller]]
* [https://soundcloud.com/morphosyntax-1/light-at-the-end ''Light at the End''] (2020)
 
; [[Joseph Monzo]]
* [https://www.youtube.com/watch?v=gL90m2ri5kw ''I Love the Blackness (unfinished)''] (2008)
 
; [[Ray Perlner]]
* [https://www.youtube.com/watch?v=QDFLKyTXZgs ''Fugue in 46EDO Bohlen-Pierce-Stearns 9 (Sensi Extension) LssLsLsLs "Lambda"'']
 
; [[Gene Ward Smith]]
* [https://www.archive.org/details/Chromosounds ''Chromosounds''] [http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3 play]
* [https://www.archive.org/details/MusicForYourEars ''Music For Your Ears''] [https://www.archive.org/download/MusicForYourEars/musicfor.mp3 play] – The central portion is in [[27edo]]; the rest is in 46edo.
 
; [[Tristan Bay]]
* [https://www.youtube.com/watch?v=s61YY80E_IA ''Catalyst''] (2025)
 
; [[vivi mouse]]
* ''valentine's day'', from ''2025'' (2025) – [https://soundcloud.com/vivi-mouse-emoji/valentines-day SoundCloud] | [https://vivimouse.bandcamp.com/track/valentines-day Bandcamp] – in valentine, 46edo tuning
 
[[Category:Chromosounds]]
[[Category:Leapday]]
[[Category:Sensi]]
[[Category:Shrutar]]
[[Category:Valentine]]
[[Category:Quartismic]]
[[Category:Listen]]
[[Category:Diaschismic]]
Retrieved from "https://en.xen.wiki/w/46edo"