46edo: Difference between revisions

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[[toc|flat]]
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=<span style="color: #300094; font-family: 'Times New Roman',Times,serif; font-size: 113%;">46 tone equal temperament</span>= 
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]].

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.

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.

46edo can be treated as two [[xenharmonic/23edo|23edo]]'s separated by an interval of 26.087 cents.

=46edo srutis= 
[[xenharmonic/Magic22 as srutis#shrutar22assrutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[xenharmonic/Indian|Indian]] music.

=Intervals= 
||~ degrees of 46edo ||~ solfege ||~ cents value ||~ approximate ratios
in the [[xenharmonic/17-limit|17-limit]] ||||||~ [[Ups and Downs Notation|ups and downs notation]] ||
||= 0 ||= do || 0.00 || 1/1 ||= perfect unison ||= P1 ||= D ||
||= 1 ||= di || 26.087 ||   ||= up unison ||= ^1 ||= D^ ||
||= 2 ||= ro || 52.174 ||   ||= downminor 2nd ||= vm2 ||= Ebv ||
||= 3 ||= rih || 78.261 ||   ||= minor 2nd ||= m2 ||= Eb ||
||= 4 ||= ra || 104.348 || 16/15, 17/16, 18/17 ||= upminor 2nd ||= ^m2 ||= Eb^ ||
||= 5 ||= ru (as in supraminor) || 130.435 || 13/12, 14/13, 15/14 ||= downmid 2nd ||= v~2 ||= Eb^^ ||
||= 6 ||= ruh (as in submajor) || 156.522 || 12/11, 11/10 ||= upmid 2nd ||= ^~2 ||= Evv ||
||= 7 ||= reh || 182.609 || 10/9 ||= downmajor 2nd ||= vM2 ||= Ev ||
||= 8 ||= re || 208.696 || 9/8, 17/15 ||= major 2nd ||= M2 ||= E ||
||= 9 ||= ri || 234.783 || 8/7, 15/13* ||= upmajor 2nd ||= ^M2 ||= E^ ||
||= 10 ||= ma || 260.87 || 7/6, 15/13* ||= downminor 3rd ||= vm3 ||= Fv ||
||= 11 ||= meh || 286.957 || 13/11, 20/17 ||= minor 3rd ||= m3 ||= F ||
||= 12 ||= me || 313.043 || 6/5 ||= upminor 3rd ||= ^m3 ||= F^ ||
||= 13 ||= mu || 339.13 || 11/9, 17/14 ||= downmid 3rd ||= v~3 ||= F^^ ||
||= 14 ||= muh || 365.217 || 16/13 ||= upmid 3rd ||= ^~3 ||= F#vv ||
||= 15 ||= mi || 391.304 || 5/4 ||= downmajor 3rd ||= vM3 ||= F#v ||
||= 16 ||= maa || 417.391 || 14/11 ||= major 3rd ||= M3 ||= F# ||
||= 17 ||= mo || 443.478 || 9/7, 13/10, 22/17 ||= upmajor 3rd ||= ^M3 ||= F#^ ||
||= 18 ||= fe || 469.565 || 17/13 ||= down 4th ||= v4 ||= Gv ||
||= 19 ||= fa || 495.652 || 4/3 ||= perfect 4th ||= P4 ||= G ||
||= 20 ||= fih || 521.739 ||   ||= up 4th ||= ^4 ||= G^ ||
||= 21 ||= fu || 547.826 || 11/8, 15/11 ||= double-up 4th ||= ^^4 ||= G^^ ||
||= 22 ||= fi || 573.913 || 7/5, 18/13 ||= double-down aug 4th,
dim 5th ||= vvA4, d5 ||= G#vv, Ab ||
||= 23 ||= seh || 600 || 17/12, 24/17 ||= downaug 4th, updim 5th ||= vA4, ^d5 ||= G#v, Ab^ ||
||= 24 ||= se || 626.087 || 10/7, 13/9 ||= aug 4th, double-up dim 5th ||= A4, ^^d5 ||= G#, Ab^^ ||
||= 25 ||= su || 652.174 || 16/11, 22/15 ||= double-down 5th ||= vv5 ||= Avv ||
||= 26 ||= sih || 678.261 ||   ||= down 5th ||= v5 ||= Av ||
||= 27 ||= sol || 704.348 || 3/2 ||= perfect 5th ||= P5 ||= A ||
||= 28 ||= si || 730.435 || 26/17 ||= up 5th ||= ^5 ||= A^ ||
||= 29 ||= lo || 756.522 || 14/9, 20/13, 17/11 ||= downminor 6th ||= vm6 ||= Bbv ||
||= 30 ||= leh || 782.609 || 11/7 ||= minor 6th ||= m6 ||= Bb ||
||= 31 ||= le || 808.696 || 8/5 ||= upminor 6th ||= ^m6 ||= Bb^ ||
||= 32 ||= lu || 834.783 || 13/8 ||= downmid 6th ||= v~6 ||= Bb^^ ||
||= 33 ||= luh || 860.87 || 18/11, 28/17 ||= upmid 6th ||= ^~6 ||= Bvv ||
||= 34 ||= la || 886.957 || 5/3 ||= downmajor 6th ||= vM6 ||= Bv ||
||= 35 ||= laa || 913.043 || 22/13, 17/10 ||= major 6th ||= M6 ||= B ||
||= 36 ||= li || 939.13 || 12/7, 26/15* ||= upmajor 6th ||= ^M6 ||= B^ ||
||= 37 ||= ta || 965.217 || 7/4, 26/15* ||= downminor 7th ||= vm7 ||= Cv ||
||= 38 ||= teh || 991.304 || 16/9, 30/17 ||= minor 7th ||= m7 ||= C ||
||= 39 ||= te || 1017.391 || 9/5 ||= upminor 7th ||= ^m7 ||= C^ ||
||= 40 ||= tu || 1043.478 || 11/6, 20/11 ||= downmid 7th ||= v~7 ||= C^^ ||
||= 41 ||= tuh || 1069.565 || 24/13, 13/7, 28/15 ||= upmid 7th ||= ^~7 ||= C#vv ||
||= 42 ||= ti || 1095.652 || 15/8, 32/17, 17/9 ||= downmajor 7th ||= vM7 ||= C#v ||
||= 43 ||= taa || 1121.739 ||   ||= major 7th ||= M7 ||= C# ||
||= 44 ||= to || 1147.826 ||   ||= upmajor 7th ||= ^M7 ||= C#^ ||
||= 45 ||= da || 1173.913 ||   ||= down 8ve ||= v8 ||= Dv ||
||= 46 ||= do || 1200 || 2/1 ||= perfect 8ve ||= P8 ||= D ||
*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]].

Combining ups and downs notation with [[Kite's color notation|color notation]], qualities can be associated with colors (higher prime content):
||~ quality ||~ color(s) ||~ monzo ||~ examples ||
||= downminor ||= blue ||= {a, b, 0, c}, c = 1 ||= 7/6, 7/4 ||
||= minor ||= fourthward white ||= {a, b}, b < -1 ||= 16/9, 32/27 ||
||= upminor ||= green ||= {a, b, c}, c = -1 ||= 6/5, 9/5 ||
||= downmid ||= jade ||= {a, b, 0, 0, c}, c = 1 ||= 11/9, 11/6 ||
||= " ||= emerald ||= {a, b, 0, 0, 0, c}, c = 1 ||= 13/8, 13/12 ||
||= upmid ||= amber ||= {a, b, 0, 0, c}, c = -1 ||= 12/11, 16/11 ||
||= " ||= ochre ||= {a, b, 0, 0, 0, c}, c = -1 ||= 16/13, 18/13 ||
||= downmajor ||= yellow ||= {a, b, c}, c = 1 ||= 5/4, 5/3 ||
||= major ||= fifthward white ||= {a, b}, b > 1 ||= 9/8, 27/16 ||
||= upmajor ||= red ||= {a, b, 0, c}, c = -1 ||= 9/7, 12/7 ||
All 46edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:
||~ color of the 3rd ||~ JI chord ||~ notes as edosteps ||~ notes of C chord ||~ written name ||~ spoken name ||
||= blue ||= 6:7:9 ||= 0-10-27 ||= C Ebv G ||= C.vm ||= C downminor ||
||= green ||= 10:12:15 ||= 0-12-27 ||= C Eb^ G ||= C.^m ||= C upminor ||
||= jade ||= 18:22:27 ||= 0-13-27 ||= C Eb^^ G ||= C.v~ ||= C downmid ||
||= yellow ||= 4:5:6 ||= 0-15-27 ||= C Ev G ||= C.v ||= C downmajor or C dot down ||
||= red ||= 14:18:27 ||= 0-17-27 ||= C E^ G ||= C.^ ||= C upmajor or C dot up ||
For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]].

=Linear temperaments= 
||~ Periods
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 || [[Amigo]] || [[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 || [[Ketchup]] ||   ||   ||
|| 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 || [[Semivalentine]] || 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 || [[Bison]] || 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 || [[Bamity]] || 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 || [[Vines]] || 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 ||   ||   ||   ||

=Approximation to Mode 8 of the Harmonic Series= 

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.

8\46edo (208.70¢) stands in for frequency ratio [[xenharmonic/9_8|9:8]] (203.91¢).
7\46edo (182.61¢) stands in for [[xenharmonic/10_9|10:9]] (182.40¢).
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= 
* [[xenharmonic/plum|plum]]
* [[xenharmonic/sensi5|sensi5]]
* [[xenharmonic/sensi8|sensi8]]
* [[xenharmonic/sensi11|sensi11]]
* [[xenharmonic/sensi19|sensi19]]

=Music= 
by [[xenharmonic/Aaron Krister Johnson|Aaron Krister Johnson:]]
[[http://aaronkristerjohnson.bandcamp.com/track/satiesque|Satiesque]]

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]]
[[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.

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]]
[[http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Bach_BWV_1029_E46-Alto-Sax-+-Harpsichord.mp3|Bach BWV 1029 in 46 equal]] Claudi Meneghin version
[[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Bach_Contrapunctus_4-Jeux14-E46.mp3|Bach Contrapunctus 4]] Claudi Meneghin version
[[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/a_seed_planted-starling-46-EDO.mp3|A Seed Planted - (Yet another version: 46 EDO)]] by [[https://soundcloud.com/jdfreivald/a-seed-planted-yet-another|Jake Freivald]]

Original HTML content:

<html><head><title>46edo</title></head><body><!-- ws:start:WikiTextTocRule:14:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><a href="#x46 tone equal temperament">46 tone equal temperament</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#x46edo srutis">46edo srutis</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Approximation to Mode 8 of the Harmonic Series">Approximation to Mode 8 of the Harmonic Series</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: -->
<!-- ws:end:WikiTextTocRule:22 --><hr />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x46 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #300094; font-family: 'Times New Roman',Times,serif; font-size: 113%;">46 tone equal temperament</span></h1>
 The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/octave">octave</a> into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">cent</a>s, an interval close in size to <a class="wiki_link" href="http://xenharmonic.wikispaces.com/66_65">66/65</a>, the interval from <a class="wiki_link" href="http://xenharmonic.wikispaces.com/13_11">13/11</a> to <a class="wiki_link" href="http://xenharmonic.wikispaces.com/6_5">6/5</a>.<br />
<br />
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. <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Rank%20two%20temperaments">Rank two temperaments</a> it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The <a class="wiki_link" href="http://xenharmonic.wikispaces.com/11-limit">11-limit</a> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Target%20tunings">minimax</a> tuning for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Starling%20family">valentine temperament</a>, (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 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/13-limit">13-limit</a>, though others award that distinction to <a class="wiki_link" href="http://xenharmonic.wikispaces.com/41edo">41edo</a>. In fact, while 41 is a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a> but not a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta gap edo</a>, 46 is zeta gap but not zeta integral.<br />
<br />
The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/just%20fifth">just fifth</a> 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.<br />
<br />
46edo can be treated as two <a class="wiki_link" href="http://xenharmonic.wikispaces.com/23edo">23edo</a>'s separated by an interval of 26.087 cents.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x46edo srutis"></a><!-- ws:end:WikiTextHeadingRule:2 -->46edo srutis</h1>
 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Magic22%20as%20srutis#shrutar22assrutis">Shrutar22 as srutis</a> describes a possible use of 46edo for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Indian">Indian</a> music.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h1>
 

<table class="wiki_table">
    <tr>
        <th>degrees of 46edo<br />
</th>
        <th>solfege<br />
</th>
        <th>cents value<br />
</th>
        <th>approximate ratios<br />
in the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17-limit">17-limit</a><br />
</th>
        <th colspan="3"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs notation</a><br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">0<br />
</td>
        <td style="text-align: center;">do<br />
</td>
        <td>0.00<br />
</td>
        <td>1/1<br />
</td>
        <td style="text-align: center;">perfect unison<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;">D<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1<br />
</td>
        <td style="text-align: center;">di<br />
</td>
        <td>26.087<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">up unison<br />
</td>
        <td style="text-align: center;">^1<br />
</td>
        <td style="text-align: center;">D^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2<br />
</td>
        <td style="text-align: center;">ro<br />
</td>
        <td>52.174<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">downminor 2nd<br />
</td>
        <td style="text-align: center;">vm2<br />
</td>
        <td style="text-align: center;">Ebv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3<br />
</td>
        <td style="text-align: center;">rih<br />
</td>
        <td>78.261<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">minor 2nd<br />
</td>
        <td style="text-align: center;">m2<br />
</td>
        <td style="text-align: center;">Eb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4<br />
</td>
        <td style="text-align: center;">ra<br />
</td>
        <td>104.348<br />
</td>
        <td>16/15, 17/16, 18/17<br />
</td>
        <td style="text-align: center;">upminor 2nd<br />
</td>
        <td style="text-align: center;">^m2<br />
</td>
        <td style="text-align: center;">Eb^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5<br />
</td>
        <td style="text-align: center;">ru (as in supraminor)<br />
</td>
        <td>130.435<br />
</td>
        <td>13/12, 14/13, 15/14<br />
</td>
        <td style="text-align: center;">downmid 2nd<br />
</td>
        <td style="text-align: center;">v~2<br />
</td>
        <td style="text-align: center;">Eb^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6<br />
</td>
        <td style="text-align: center;">ruh (as in submajor)<br />
</td>
        <td>156.522<br />
</td>
        <td>12/11, 11/10<br />
</td>
        <td style="text-align: center;">upmid 2nd<br />
</td>
        <td style="text-align: center;">^~2<br />
</td>
        <td style="text-align: center;">Evv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7<br />
</td>
        <td style="text-align: center;">reh<br />
</td>
        <td>182.609<br />
</td>
        <td>10/9<br />
</td>
        <td style="text-align: center;">downmajor 2nd<br />
</td>
        <td style="text-align: center;">vM2<br />
</td>
        <td style="text-align: center;">Ev<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">8<br />
</td>
        <td style="text-align: center;">re<br />
</td>
        <td>208.696<br />
</td>
        <td>9/8, 17/15<br />
</td>
        <td style="text-align: center;">major 2nd<br />
</td>
        <td style="text-align: center;">M2<br />
</td>
        <td style="text-align: center;">E<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9<br />
</td>
        <td style="text-align: center;">ri<br />
</td>
        <td>234.783<br />
</td>
        <td>8/7, 15/13*<br />
</td>
        <td style="text-align: center;">upmajor 2nd<br />
</td>
        <td style="text-align: center;">^M2<br />
</td>
        <td style="text-align: center;">E^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">10<br />
</td>
        <td style="text-align: center;">ma<br />
</td>
        <td>260.87<br />
</td>
        <td>7/6, 15/13*<br />
</td>
        <td style="text-align: center;">downminor 3rd<br />
</td>
        <td style="text-align: center;">vm3<br />
</td>
        <td style="text-align: center;">Fv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">11<br />
</td>
        <td style="text-align: center;">meh<br />
</td>
        <td>286.957<br />
</td>
        <td>13/11, 20/17<br />
</td>
        <td style="text-align: center;">minor 3rd<br />
</td>
        <td style="text-align: center;">m3<br />
</td>
        <td style="text-align: center;">F<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">12<br />
</td>
        <td style="text-align: center;">me<br />
</td>
        <td>313.043<br />
</td>
        <td>6/5<br />
</td>
        <td style="text-align: center;">upminor 3rd<br />
</td>
        <td style="text-align: center;">^m3<br />
</td>
        <td style="text-align: center;">F^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">13<br />
</td>
        <td style="text-align: center;">mu<br />
</td>
        <td>339.13<br />
</td>
        <td>11/9, 17/14<br />
</td>
        <td style="text-align: center;">downmid 3rd<br />
</td>
        <td style="text-align: center;">v~3<br />
</td>
        <td style="text-align: center;">F^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">14<br />
</td>
        <td style="text-align: center;">muh<br />
</td>
        <td>365.217<br />
</td>
        <td>16/13<br />
</td>
        <td style="text-align: center;">upmid 3rd<br />
</td>
        <td style="text-align: center;">^~3<br />
</td>
        <td style="text-align: center;">F#vv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">15<br />
</td>
        <td style="text-align: center;">mi<br />
</td>
        <td>391.304<br />
</td>
        <td>5/4<br />
</td>
        <td style="text-align: center;">downmajor 3rd<br />
</td>
        <td style="text-align: center;">vM3<br />
</td>
        <td style="text-align: center;">F#v<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16<br />
</td>
        <td style="text-align: center;">maa<br />
</td>
        <td>417.391<br />
</td>
        <td>14/11<br />
</td>
        <td style="text-align: center;">major 3rd<br />
</td>
        <td style="text-align: center;">M3<br />
</td>
        <td style="text-align: center;">F#<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">17<br />
</td>
        <td style="text-align: center;">mo<br />
</td>
        <td>443.478<br />
</td>
        <td>9/7, 13/10, 22/17<br />
</td>
        <td style="text-align: center;">upmajor 3rd<br />
</td>
        <td style="text-align: center;">^M3<br />
</td>
        <td style="text-align: center;">F#^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">18<br />
</td>
        <td style="text-align: center;">fe<br />
</td>
        <td>469.565<br />
</td>
        <td>17/13<br />
</td>
        <td style="text-align: center;">down 4th<br />
</td>
        <td style="text-align: center;">v4<br />
</td>
        <td style="text-align: center;">Gv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19<br />
</td>
        <td style="text-align: center;">fa<br />
</td>
        <td>495.652<br />
</td>
        <td>4/3<br />
</td>
        <td style="text-align: center;">perfect 4th<br />
</td>
        <td style="text-align: center;">P4<br />
</td>
        <td style="text-align: center;">G<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">20<br />
</td>
        <td style="text-align: center;">fih<br />
</td>
        <td>521.739<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">up 4th<br />
</td>
        <td style="text-align: center;">^4<br />
</td>
        <td style="text-align: center;">G^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">21<br />
</td>
        <td style="text-align: center;">fu<br />
</td>
        <td>547.826<br />
</td>
        <td>11/8, 15/11<br />
</td>
        <td style="text-align: center;">double-up 4th<br />
</td>
        <td style="text-align: center;">^^4<br />
</td>
        <td style="text-align: center;">G^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">22<br />
</td>
        <td style="text-align: center;">fi<br />
</td>
        <td>573.913<br />
</td>
        <td>7/5, 18/13<br />
</td>
        <td style="text-align: center;">double-down aug 4th,<br />
dim 5th<br />
</td>
        <td style="text-align: center;">vvA4, d5<br />
</td>
        <td style="text-align: center;">G#vv, Ab<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">23<br />
</td>
        <td style="text-align: center;">seh<br />
</td>
        <td>600<br />
</td>
        <td>17/12, 24/17<br />
</td>
        <td style="text-align: center;">downaug 4th, updim 5th<br />
</td>
        <td style="text-align: center;">vA4, ^d5<br />
</td>
        <td style="text-align: center;">G#v, Ab^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">24<br />
</td>
        <td style="text-align: center;">se<br />
</td>
        <td>626.087<br />
</td>
        <td>10/7, 13/9<br />
</td>
        <td style="text-align: center;">aug 4th, double-up dim 5th<br />
</td>
        <td style="text-align: center;">A4, ^^d5<br />
</td>
        <td style="text-align: center;">G#, Ab^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">25<br />
</td>
        <td style="text-align: center;">su<br />
</td>
        <td>652.174<br />
</td>
        <td>16/11, 22/15<br />
</td>
        <td style="text-align: center;">double-down 5th<br />
</td>
        <td style="text-align: center;">vv5<br />
</td>
        <td style="text-align: center;">Avv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">26<br />
</td>
        <td style="text-align: center;">sih<br />
</td>
        <td>678.261<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">down 5th<br />
</td>
        <td style="text-align: center;">v5<br />
</td>
        <td style="text-align: center;">Av<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">27<br />
</td>
        <td style="text-align: center;">sol<br />
</td>
        <td>704.348<br />
</td>
        <td>3/2<br />
</td>
        <td style="text-align: center;">perfect 5th<br />
</td>
        <td style="text-align: center;">P5<br />
</td>
        <td style="text-align: center;">A<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">28<br />
</td>
        <td style="text-align: center;">si<br />
</td>
        <td>730.435<br />
</td>
        <td>26/17<br />
</td>
        <td style="text-align: center;">up 5th<br />
</td>
        <td style="text-align: center;">^5<br />
</td>
        <td style="text-align: center;">A^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">29<br />
</td>
        <td style="text-align: center;">lo<br />
</td>
        <td>756.522<br />
</td>
        <td>14/9, 20/13, 17/11<br />
</td>
        <td style="text-align: center;">downminor 6th<br />
</td>
        <td style="text-align: center;">vm6<br />
</td>
        <td style="text-align: center;">Bbv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">30<br />
</td>
        <td style="text-align: center;">leh<br />
</td>
        <td>782.609<br />
</td>
        <td>11/7<br />
</td>
        <td style="text-align: center;">minor 6th<br />
</td>
        <td style="text-align: center;">m6<br />
</td>
        <td style="text-align: center;">Bb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">31<br />
</td>
        <td style="text-align: center;">le<br />
</td>
        <td>808.696<br />
</td>
        <td>8/5<br />
</td>
        <td style="text-align: center;">upminor 6th<br />
</td>
        <td style="text-align: center;">^m6<br />
</td>
        <td style="text-align: center;">Bb^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">32<br />
</td>
        <td style="text-align: center;">lu<br />
</td>
        <td>834.783<br />
</td>
        <td>13/8<br />
</td>
        <td style="text-align: center;">downmid 6th<br />
</td>
        <td style="text-align: center;">v~6<br />
</td>
        <td style="text-align: center;">Bb^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">33<br />
</td>
        <td style="text-align: center;">luh<br />
</td>
        <td>860.87<br />
</td>
        <td>18/11, 28/17<br />
</td>
        <td style="text-align: center;">upmid 6th<br />
</td>
        <td style="text-align: center;">^~6<br />
</td>
        <td style="text-align: center;">Bvv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">34<br />
</td>
        <td style="text-align: center;">la<br />
</td>
        <td>886.957<br />
</td>
        <td>5/3<br />
</td>
        <td style="text-align: center;">downmajor 6th<br />
</td>
        <td style="text-align: center;">vM6<br />
</td>
        <td style="text-align: center;">Bv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">35<br />
</td>
        <td style="text-align: center;">laa<br />
</td>
        <td>913.043<br />
</td>
        <td>22/13, 17/10<br />
</td>
        <td style="text-align: center;">major 6th<br />
</td>
        <td style="text-align: center;">M6<br />
</td>
        <td style="text-align: center;">B<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">36<br />
</td>
        <td style="text-align: center;">li<br />
</td>
        <td>939.13<br />
</td>
        <td>12/7, 26/15*<br />
</td>
        <td style="text-align: center;">upmajor 6th<br />
</td>
        <td style="text-align: center;">^M6<br />
</td>
        <td style="text-align: center;">B^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">37<br />
</td>
        <td style="text-align: center;">ta<br />
</td>
        <td>965.217<br />
</td>
        <td>7/4, 26/15*<br />
</td>
        <td style="text-align: center;">downminor 7th<br />
</td>
        <td style="text-align: center;">vm7<br />
</td>
        <td style="text-align: center;">Cv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">38<br />
</td>
        <td style="text-align: center;">teh<br />
</td>
        <td>991.304<br />
</td>
        <td>16/9, 30/17<br />
</td>
        <td style="text-align: center;">minor 7th<br />
</td>
        <td style="text-align: center;">m7<br />
</td>
        <td style="text-align: center;">C<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">39<br />
</td>
        <td style="text-align: center;">te<br />
</td>
        <td>1017.391<br />
</td>
        <td>9/5<br />
</td>
        <td style="text-align: center;">upminor 7th<br />
</td>
        <td style="text-align: center;">^m7<br />
</td>
        <td style="text-align: center;">C^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">40<br />
</td>
        <td style="text-align: center;">tu<br />
</td>
        <td>1043.478<br />
</td>
        <td>11/6, 20/11<br />
</td>
        <td style="text-align: center;">downmid 7th<br />
</td>
        <td style="text-align: center;">v~7<br />
</td>
        <td style="text-align: center;">C^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">41<br />
</td>
        <td style="text-align: center;">tuh<br />
</td>
        <td>1069.565<br />
</td>
        <td>24/13, 13/7, 28/15<br />
</td>
        <td style="text-align: center;">upmid 7th<br />
</td>
        <td style="text-align: center;">^~7<br />
</td>
        <td style="text-align: center;">C#vv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">42<br />
</td>
        <td style="text-align: center;">ti<br />
</td>
        <td>1095.652<br />
</td>
        <td>15/8, 32/17, 17/9<br />
</td>
        <td style="text-align: center;">downmajor 7th<br />
</td>
        <td style="text-align: center;">vM7<br />
</td>
        <td style="text-align: center;">C#v<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">43<br />
</td>
        <td style="text-align: center;">taa<br />
</td>
        <td>1121.739<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">major 7th<br />
</td>
        <td style="text-align: center;">M7<br />
</td>
        <td style="text-align: center;">C#<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">44<br />
</td>
        <td style="text-align: center;">to<br />
</td>
        <td>1147.826<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">upmajor 7th<br />
</td>
        <td style="text-align: center;">^M7<br />
</td>
        <td style="text-align: center;">C#^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">45<br />
</td>
        <td style="text-align: center;">da<br />
</td>
        <td>1173.913<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">down 8ve<br />
</td>
        <td style="text-align: center;">v8<br />
</td>
        <td style="text-align: center;">Dv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">46<br />
</td>
        <td style="text-align: center;">do<br />
</td>
        <td>1200<br />
</td>
        <td>2/1<br />
</td>
        <td style="text-align: center;">perfect 8ve<br />
</td>
        <td style="text-align: center;">P8<br />
</td>
        <td style="text-align: center;">D<br />
</td>
    </tr>
</table>

*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 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/consistent">consistent</a> in the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/15-limit">15-limit</a>.<br />
<br />
Combining ups and downs notation with <a class="wiki_link" href="/Kite%27s%20color%20notation">color notation</a>, qualities can be associated with colors (higher prime content):<br />


<table class="wiki_table">
    <tr>
        <th>quality<br />
</th>
        <th>color(s)<br />
</th>
        <th>monzo<br />
</th>
        <th>examples<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">downminor<br />
</td>
        <td style="text-align: center;">blue<br />
</td>
        <td style="text-align: center;">{a, b, 0, c}, c = 1<br />
</td>
        <td style="text-align: center;">7/6, 7/4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">minor<br />
</td>
        <td style="text-align: center;">fourthward white<br />
</td>
        <td style="text-align: center;">{a, b}, b &lt; -1<br />
</td>
        <td style="text-align: center;">16/9, 32/27<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">upminor<br />
</td>
        <td style="text-align: center;">green<br />
</td>
        <td style="text-align: center;">{a, b, c}, c = -1<br />
</td>
        <td style="text-align: center;">6/5, 9/5<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">downmid<br />
</td>
        <td style="text-align: center;">jade<br />
</td>
        <td style="text-align: center;">{a, b, 0, 0, c}, c = 1<br />
</td>
        <td style="text-align: center;">11/9, 11/6<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">&quot;<br />
</td>
        <td style="text-align: center;">emerald<br />
</td>
        <td style="text-align: center;">{a, b, 0, 0, 0, c}, c = 1<br />
</td>
        <td style="text-align: center;">13/8, 13/12<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">upmid<br />
</td>
        <td style="text-align: center;">amber<br />
</td>
        <td style="text-align: center;">{a, b, 0, 0, c}, c = -1<br />
</td>
        <td style="text-align: center;">12/11, 16/11<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">&quot;<br />
</td>
        <td style="text-align: center;">ochre<br />
</td>
        <td style="text-align: center;">{a, b, 0, 0, 0, c}, c = -1<br />
</td>
        <td style="text-align: center;">16/13, 18/13<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">downmajor<br />
</td>
        <td style="text-align: center;">yellow<br />
</td>
        <td style="text-align: center;">{a, b, c}, c = 1<br />
</td>
        <td style="text-align: center;">5/4, 5/3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">major<br />
</td>
        <td style="text-align: center;">fifthward white<br />
</td>
        <td style="text-align: center;">{a, b}, b &gt; 1<br />
</td>
        <td style="text-align: center;">9/8, 27/16<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">upmajor<br />
</td>
        <td style="text-align: center;">red<br />
</td>
        <td style="text-align: center;">{a, b, 0, c}, c = -1<br />
</td>
        <td style="text-align: center;">9/7, 12/7<br />
</td>
    </tr>
</table>

All 46edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:<br />


<table class="wiki_table">
    <tr>
        <th>color of the 3rd<br />
</th>
        <th>JI chord<br />
</th>
        <th>notes as edosteps<br />
</th>
        <th>notes of C chord<br />
</th>
        <th>written name<br />
</th>
        <th>spoken name<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">blue<br />
</td>
        <td style="text-align: center;">6:7:9<br />
</td>
        <td style="text-align: center;">0-10-27<br />
</td>
        <td style="text-align: center;">C Ebv G<br />
</td>
        <td style="text-align: center;">C.vm<br />
</td>
        <td style="text-align: center;">C downminor<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">green<br />
</td>
        <td style="text-align: center;">10:12:15<br />
</td>
        <td style="text-align: center;">0-12-27<br />
</td>
        <td style="text-align: center;">C Eb^ G<br />
</td>
        <td style="text-align: center;">C.^m<br />
</td>
        <td style="text-align: center;">C upminor<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">jade<br />
</td>
        <td style="text-align: center;">18:22:27<br />
</td>
        <td style="text-align: center;">0-13-27<br />
</td>
        <td style="text-align: center;">C Eb^^ G<br />
</td>
        <td style="text-align: center;">C.v~<br />
</td>
        <td style="text-align: center;">C downmid<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">yellow<br />
</td>
        <td style="text-align: center;">4:5:6<br />
</td>
        <td style="text-align: center;">0-15-27<br />
</td>
        <td style="text-align: center;">C Ev G<br />
</td>
        <td style="text-align: center;">C.v<br />
</td>
        <td style="text-align: center;">C downmajor or C dot down<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">red<br />
</td>
        <td style="text-align: center;">14:18:27<br />
</td>
        <td style="text-align: center;">0-17-27<br />
</td>
        <td style="text-align: center;">C E^ G<br />
</td>
        <td style="text-align: center;">C.^<br />
</td>
        <td style="text-align: center;">C upmajor or C dot up<br />
</td>
    </tr>
</table>

For a more complete list, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 -->Linear temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <th>Periods<br />
per octave<br />
</th>
        <th>Generator<br />
</th>
        <th>Cents<br />
</th>
        <th>Temperaments<br />
</th>
        <th>MOS/DE Scales available<br />
</th>
        <th>L:s<br />
</th>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>1\46<br />
</td>
        <td>26.087<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>3\46<br />
</td>
        <td>78.261<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Valentine">Valentine</a><br />
</td>
        <td>1L 14s (15-tone)<br />
15L 1s (16-tone)<br />
16L 15s (31-tone)<br />
</td>
        <td>4:3 ~ <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Maximal%20evenness">quasi-equal</a><br />
3:1<br />
2:1 ~ QE<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>5\46<br />
</td>
        <td>130.435<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Twothirdtonic">Twothirdtonic</a><br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%208s">1L 8s</a> (9-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/9L%201s">9L 1s</a> (10-tone)<br />
9L 10s (19-tone)<br />
9L 19s (28-tone)<br />
9L 28s (37-tone)<br />
</td>
        <td>6:5 ~ QE<br />
5:1<br />
4:1<br />
3:1<br />
2:1 ~ QE<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>7\46<br />
</td>
        <td>182.609<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Minortone">Minortone</a><br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%205s">1L 5s</a> (6-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%201s">6L 1s</a> (7-tone)<br />
7L 6s (13-tone)<br />
13L 7s (20-tone)<br />
13L 20s (33-tone)<br />
</td>
        <td>11:7<br />
7:4<br />
4:3 ~ QE<br />
3:1<br />
2:1 ~ QE<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>9\46<br />
</td>
        <td>234.783<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Rodan">Rodan</a><br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%204s">1L 4s</a> (5-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%205s">1L 5s</a> (6-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%206s">5L 6s</a> (11-tone)<br />
5L 11s (16-tone)<br />
5L 16s (21-tone)<br />
5L 21s (26-tone)<br />
5L 26s (31-tone)<br />
5L 31s (36-tone)<br />
5L 36s (41-tone)<br />
</td>
        <td>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<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>11\46<br />
</td>
        <td>286.957<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%201s">4L 1s</a> (5-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%205s">4L 5s</a> (9-tone)<br />
4L 9s (13-tone)<br />
4L 13s (17-tone)<br />
4L 17s (21-tone)<br />
21L 4s (25-tone)<br />
</td>
        <td>11:2<br />
9:2<br />
7:2<br />
5:2<br />
3:2 ~ QE, Golden<br />
2:1 ~ QE<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>13\46<br />
</td>
        <td>339.13<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Amity">Amity</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/hitchcock">hitchcock</a><br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%203s">4L 3s</a> (7-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/7L%204s">7L 4s</a> (11-tone)<br />
7L 11s (18-tone)<br />
7L 18s (25-tone)<br />
7L 25s (32-tone)<br />
7L 32s (39-tone)<br />
</td>
        <td>7:6 ~ QE<br />
6:1<br />
5:1<br />
4:1<br />
3:1<br />
2:1 ~ QE<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>15\46<br />
</td>
        <td>391.304<br />
</td>
        <td><a class="wiki_link" href="/Amigo">Amigo</a><br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%202s">1L 2s</a> (3-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%201s">3L 1s</a> (4-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%204s">3L 4s</a> (7-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%207s">3L 7s</a> (10-tone)<br />
3L 10s (13-tone)<br />
3L 13s (16-tone)<br />
3L 16s (19-tone)<br />
3L 19s (21-tone)<br />
3L 21s (24-tone)<br />
3L 24s (27-tone)<br />
3L 27s (30-tone)<br />
3L 30s (33-tone)<br />
3L 33s (36-tone)<br />
3L 36s (39-tone)<br />
3L 39s (42-tone)<br />
</td>
        <td>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<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>17\46<br />
</td>
        <td>443.478<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Sensi">Sensi</a><br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%202s">3L 2s</a> (5-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%205s">3L 5s</a> (8-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/8L%203s">8L 3s</a> (11-tone)<br />
8L 11s (19-tone)<br />
19L 8s (27-tone)<br />
</td>
        <td>12:5<br />
7:5<br />
5:2<br />
3:2 ~ QE, Golden<br />
2:1<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>19\46<br />
</td>
        <td>495.652<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Leapday">Leapday</a><br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%203s">2L 3s</a> (5-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%202s">5L 2s</a> (7-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%207s">5L 7s</a> (12-tone)<br />
12L 5s (17-tone)<br />
17L 12s (29-tone)<br />
</td>
        <td>11:8<br />
8:3<br />
5:3 ~ Golden<br />
3:2 ~ QE, Golden<br />
2:1 ~ QE<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>21\46<br />
</td>
        <td>547.826<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Heinz">Heinz</a><br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%203s">2L 3s</a> (5-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%205s">2L 5s</a> (7-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%207s">2L 7s</a> (9-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%209s">2L 9s</a> (11-tone)<br />
11L 2s (13-tone)<br />
11L 13s (24-tone)<br />
11L 24s (35-tone)<br />
</td>
        <td>17:4<br />
13:4<br />
9:4<br />
5:4 ~ QE<br />
4:1<br />
3:1<br />
2:1 ~ QE<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>1\46<br />
</td>
        <td>26.087<br />
</td>
        <td><a class="wiki_link" href="/Ketchup">Ketchup</a><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>2\46<br />
</td>
        <td>52.174<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Shrutar">Shrutar</a><br />
</td>
        <td>2L 2s (4-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%206s">2L 6s</a> (8-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%208s">2L 8s</a> (10-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2010s">2L 10s</a> (12-tone)<br />
2L 12s (14-tone)<br />
2L 14s (16-tone)<br />
2L 16s (18-tone)<br />
2L 18s (20-tone)<br />
2L 20s (22-tone)<br />
22L 2s (24-tone)<br />
</td>
        <td>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<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>3\46<br />
</td>
        <td>78.261<br />
</td>
        <td><a class="wiki_link" href="/Semivalentine">Semivalentine</a><br />
</td>
        <td>2L 2s (4-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%206s">2L 6s</a> (8-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%208s">2L 8s</a> (10-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2010s">2L 10s</a> (12-tone)<br />
2L 12s (14-tone)<br />
14L 2s (16-tone)<br />
16L 14s (30-tone)<br />
</td>
        <td>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<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>4\46<br />
</td>
        <td>104.348<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Srutal">Srutal</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/diaschismic">diaschismic</a><br />
</td>
        <td>2L 2s (4-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%206s">2L 6s</a> (8-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%208s">2L 8s</a> (10-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/10L%202s">10L 2s</a> (12-tone)<br />
12L 10s (22-tone)<br />
12L 22s (34-tone)<br />
</td>
        <td>19:4<br />
15:4<br />
11:4<br />
7:4<br />
4:3 ~ QE<br />
3:1<br />
2:1 ~ QE<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>5\46<br />
</td>
        <td>130.435<br />
</td>
        <td><br />
</td>
        <td>2L 2s (4-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%206s">2L 6s</a> (8-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/8L%202s">8L 2s</a> (10-tone)<br />
8L 10s (18-tone)<br />
18L 10s (28-tone)<br />
</td>
        <td>18:5<br />
13:5<br />
8:5 ~ Golden<br />
5:3 ~ Golden<br />
3:2 ~ QE, Golden<br />
2:1 ~ QE<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>6\46<br />
</td>
        <td>156.522<br />
</td>
        <td><a class="wiki_link" href="/Bison">Bison</a><br />
</td>
        <td>2L 2s (4-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%202s">6L 2s</a> (8-tone)<br />
8L 6s (14-tone)<br />
8L 14s (22-tone)<br />
8L 22s (30-tone)<br />
8L 30s (38-tone<br />
</td>
        <td>17:6<br />
11:6<br />
6:5 ~ QE<br />
5:1<br />
4:1<br />
3:1<br />
2:1 ~ QE<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>7\46<br />
</td>
        <td>182.609<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Unidec">Unidec</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/hendec">hendec</a><br />
</td>
        <td>2L 2s (4-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%202s">6L 2s</a> (8-tone)<br />
6L 8s (14-tone)<br />
6L 14s (20-tone)<br />
20L 6s (26-tone)<br />
</td>
        <td>16:7<br />
9:7<br />
7:2<br />
5:2<br />
3:2 ~ QE, Golden<br />
2:1 ~ QE<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>8\46<br />
</td>
        <td>208.696<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Abigail">Abigail</a><br />
</td>
        <td>2L 2s (4-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%202s">4L 2s</a> (6-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%202s">6L 2s</a> (8-tone)<br />
6L 8s (14-tone)<br />
6L 14s (20-tone)<br />
6L 20s (26-tone)<br />
6L 26s (32-tone)<br />
6L 32s (38-tone)<br />
6L 38s (44-tone)<br />
</td>
        <td>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<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>9\46<br />
</td>
        <td>234.783<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Echidnic">Echidnic</a><br />
</td>
        <td>2L 2s (4-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%202s">4L 2s</a> (6-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%204s">6L 4s</a> (10-tone)<br />
10L 6s (16-tone)<br />
10L 16s (26-tone)<br />
10L 26s (36-tone)<br />
</td>
        <td>14:9<br />
9:5<br />
5:4 ~ QE<br />
4:1<br />
3:1<br />
2:1 ~ QE<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>10\46<br />
</td>
        <td>260.87<br />
</td>
        <td><a class="wiki_link" href="/Bamity">Bamity</a><br />
</td>
        <td>2L 2s (4-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%202s">4L 2s</a> (6-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%206s">4L 6s</a> (10-tone)<br />
4L 10s (14-tone)<br />
14L 4s (18-tone)<br />
14L 18s (32-tone)<br />
</td>
        <td>13:10<br />
10:3<br />
7:3<br />
4:3 ~ QE<br />
3:1<br />
2:1 ~ QE<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>11\46<br />
</td>
        <td>286.957<br />
</td>
        <td><a class="wiki_link" href="/Vines">Vines</a><br />
</td>
        <td>2L 2s (4-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%202s">4L 2s</a> (6-tone)<br />
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%206s">4L 6s</a> (10-tone)<br />
4L 10s (14-tone)<br />
4L 14s (18-tone)<br />
4L 18s (22-tone)<br />
4L 22s (26-tone)<br />
4L 26s (30-tone)<br />
4L 30s (34-tone)<br />
4L 34s (38-tone)<br />
4L 38s (42-tone)<br />
</td>
        <td>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<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>1\46<br />
</td>
        <td>26.087<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Approximation to Mode 8 of the Harmonic Series"></a><!-- ws:end:WikiTextHeadingRule:8 -->Approximation to Mode 8 of the Harmonic Series</h1>
 <br />
46edo represents <a class="wiki_link" href="http://xenharmonic.wikispaces.com/overtone">overtone</a>s 8 through 16 (written as <a class="wiki_link" href="http://xenharmonic.wikispaces.com/JI">JI</a> 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.<br />
<br />
8\46edo (208.70¢) stands in for frequency ratio <a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_8">9:8</a> (203.91¢).<br />
7\46edo (182.61¢) stands in for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/10_9">10:9</a> (182.40¢).<br />
6\46edo (156.52¢) stands in for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/11_10">11:10</a> (165.00¢) and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/12_11">12:11</a> (150.64¢).<br />
5\46edo (130.43¢) stands in for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/13_12">13:12</a> (138.57¢), <a class="wiki_link" href="http://xenharmonic.wikispaces.com/14_13">14:13</a> (128.30¢) and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/15_14">15:14</a> (119.44¢).<br />
4\46edo (104.35¢) stands in for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/16_15">16:15</a> (111.73¢).<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:10 -->Scales</h1>
 <ul><li><a class="wiki_link" href="http://xenharmonic.wikispaces.com/plum">plum</a></li><li><a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi5">sensi5</a></li><li><a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi8">sensi8</a></li><li><a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi11">sensi11</a></li><li><a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi19">sensi19</a></li></ul><br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:12 -->Music</h1>
 by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Aaron%20Krister%20Johnson">Aaron Krister Johnson:</a><br />
<a class="wiki_link_ext" href="http://aaronkristerjohnson.bandcamp.com/track/satiesque" rel="nofollow">Satiesque</a><br />
<br />
by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Gene%20Ward%20Smith">Gene Ward Smith:</a><br />
<a class="wiki_link_ext" href="http://www.archive.org/details/Chromosounds" rel="nofollow">Chromosounds</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3" rel="nofollow">play</a><br />
<a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow">Music For Your Ears</a> <a class="wiki_link_ext" href="http://www.archive.org/download/MusicForYourEars/musicfor.mp3" rel="nofollow">play</a> The central portion is in <a class="wiki_link" href="http://xenharmonic.wikispaces.com/27edo">27edo</a>, the rest in 46edo.<br />
<br />
by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Andrew%20Heathwaite">Andrew Heathwaite</a>: <a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/rats" rel="nofollow" target="_blank">Rats</a>, <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">play</a> <a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/tumbledown-stew" rel="nofollow" target="_blank">Tumbledown Stew</a> <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">play</a>, <a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-1" rel="nofollow" target="_blank">Hypnocloudsmack 1</a> <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">play</a>, <a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-2" rel="nofollow" target="_blank">Hypnocloudsmack 2</a> <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">play</a>, <a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-3" rel="nofollow" target="_blank">Hypnocloudsmack 3</a> <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">play</a><br />
<a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Bach_BWV_1029_E46-Alto-Sax-+-Harpsichord.mp3" rel="nofollow">Bach BWV 1029 in 46 equal</a> Claudi Meneghin version<br />
<a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Bach_Contrapunctus_4-Jeux14-E46.mp3" rel="nofollow">Bach Contrapunctus 4</a> Claudi Meneghin version<br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/a_seed_planted-starling-46-EDO.mp3" rel="nofollow">A Seed Planted - (Yet another version: 46 EDO)</a> by <a class="wiki_link_ext" href="https://soundcloud.com/jdfreivald/a-seed-planted-yet-another" rel="nofollow">Jake Freivald</a></body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 17:18:36 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 17:33:05 UTC</tt>.<br>
-: The original revision id was <tt>621459301</tt>.<br>
+: The original revision id was <tt>621459705</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 75: / Line 75: @@
 Combining ups and downs notation with [[Kite's color notation|color notation]], qualities can be associated with colors (higher prime content):
-||~ quality ||~ color ||~ monzo ||
+||~ quality ||~ color(s) ||~ monzo ||~ examples ||
-||= downminor ||= blue ||= {a, b, 0, c}, c = 1 ||
+||= downminor ||= blue ||= {a, b, 0, c}, c = 1 ||= 7/6, 7/4 ||
-||= minor ||= fourthward white ||= {a, b}, b &lt; -1 ||
+||= minor ||= fourthward white ||= {a, b}, b &lt; -1 ||= 16/9, 32/27 ||
-||= upminor ||= green ||= {a, b, c}, c = -1 ||
+||= upminor ||= green ||= {a, b, c}, c = -1 ||= 6/5, 9/5 ||
-||= downmid ||= jade, emerald ||= {a, b, 0, 0, c} or {a, b, 0, 0, 0, c}, c = 1 ||
+||= downmid ||= jade ||= {a, b, 0, 0, c}, c = 1 ||= 11/9, 11/6 ||
-||= upmid ||= amber, ochre ||= {a, b, 0, 0, c} or {a, b, 0, 0, 0, c}, c = -1 ||
+||= " ||= emerald ||= {a, b, 0, 0, 0, c}, c = 1 ||= 13/8, 13/12 ||
-||= downmajor ||= yellow ||= {a, b, c}, c = 1 ||
+||= upmid ||= amber ||= {a, b, 0, 0, c}, c = -1 ||= 12/11, 16/11 ||
-||= major ||= fifthward white ||= {a, b}, b &gt; 1 ||
+||= " ||= ochre ||= {a, b, 0, 0, 0, c}, c = -1 ||= 16/13, 18/13 ||
-||= upmajor ||= red ||= {a, b, 0, c}, c = -1 ||
+||= downmajor ||= yellow ||= {a, b, c}, c = 1 ||= 5/4, 5/3 ||
+||= major ||= fifthward white ||= {a, b}, b &gt; 1 ||= 9/8, 27/16 ||
+||= upmajor ||= red ||= {a, b, 0, c}, c = -1 ||= 9/7, 12/7 ||
 All 46edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:
 ||~ color of the 3rd ||~ JI chord ||~ notes as edosteps ||~ notes of C chord ||~ written name ||~ spoken name ||
@@ Line 1,192: / Line 1,194: @@
          &lt;th&gt;quality&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;color&lt;br /&gt;
+         &lt;th&gt;color(s)&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;monzo&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;examples&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 1,203: / Line 1,207: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;{a, b, 0, c}, c = 1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7/6, 7/4&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,211: / Line 1,217: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;{a, b}, b &amp;lt; -1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;16/9, 32/27&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,219: / Line 1,227: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;{a, b, c}, c = -1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;6/5, 9/5&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,224: / Line 1,234: @@
          &lt;td style="text-align: center;"&gt;downmid&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;jade, emerald&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;jade&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;{a, b, 0, 0, c} or {a, b, 0, 0, 0, c}, c = 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;{a, b, 0, 0, c}, c = 1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;11/9, 11/6&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;&amp;quot;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;emerald&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;{a, b, 0, 0, 0, c}, c = 1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;13/8, 13/12&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,232: / Line 1,254: @@
          &lt;td style="text-align: center;"&gt;upmid&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;amber, ochre&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;amber&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;{a, b, 0, 0, c} or {a, b, 0, 0, 0, c}, c = -1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;{a, b, 0, 0, c}, c = -1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;12/11, 16/11&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;&amp;quot;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;ochre&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;{a, b, 0, 0, 0, c}, c = -1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;16/13, 18/13&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,243: / Line 1,277: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;{a, b, c}, c = 1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5/4, 5/3&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,251: / Line 1,287: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;{a, b}, b &amp;gt; 1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;9/8, 27/16&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,259: / Line 1,297: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;{a, b, 0, c}, c = -1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;9/7, 12/7&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

46edo: Difference between revisions

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