46edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 04:18:08 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 16:30:56 UTC</tt>.

: The original revision id was <tt>~~621435931~~</tt>.

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

=~~Linear temperaments~~=

=Intervals=

||~ ~~Periods~~

||~ degrees of 46edo ||~ solfege ||~ cents value ||~ approximate ratios

~~per octave~~ ||~ ~~Generator~~ ||~ ~~Cents~~ ||~ ~~Temperaments~~ ||~ ~~MOS~~/~~DE Scales available~~ ||~~~ L:s~~ ||

in the [[xenharmonic/17-limit|17-limit]] ||||||~ [[Ups and Downs Notation|ups and downs notation]] ||

|| 1 || ~~1\46~~ || 26.087 || || || ||

||= 0 ||= do || 0.00 || 1/1 ||= perfect unison ||= P1 ||= D ||

|| 1 || ~~3\46~~ || 78.261 || ~~[[xenharmonic~~/~~Valentine~~|~~Valentine]]~~ || ~~1L 14s (15-tone)~~

||= 1 ||= di || 26.087 || ||= up unison ||= ^1 ||= D^ ||

~~15L 1s~~ (~~16-tone~~)

||= 2 ||= ro || 52.174 || ||= downminor 2nd ||= vm2 ||= Ebv ||

~~16L 15s~~ (~~31-tone~~) || ~~4:3~~ ~ ~~[[xenharmonic~~/~~Maximal evenness~~|~~quasi-equal]]~~

||= 3 ||= rih || 78.261 || ||= minor 2nd ||= m2 ||= Eb ||

3:1

||= 4 ||= ra || 104.348 || 16/15, 17/16, 18/17 ||= upminor 2nd ||= ^m2 ||= Eb^ ||

~~2:1~~ ~ QE ||

||= 5 ||= ru (as in supraminor) || 130.435 || 13/12, 14/13, 15/14 ||= downmid 2nd ||= v~2 ||= Eb^^ ||

|| 1 || 5~~\46~~ || ~~130~~.~~435~~ || ~~[[xenharmonic~~/~~Twothirdtonic~~|~~Twothirdtonic]]~~ || ~~[[xenharmonic~~/~~1L 8s~~|~~1L 8s]] (9-tone)~~

||= 6 ||= ruh (as in submajor) || 156.522 || 12/11, 11/10 ||= upmid 2nd ||= ^~2 ||= Evv ||

~~[[xenharmonic~~/~~9L 1s~~|~~9L 1s]] (10-tone)~~

||= 7 ||= reh || 182.609 || 10/9 ||= downmajor 2nd ||= vM2 ||= Ev ||

~~9L 10s (~~19-~~tone)~~

||= 8 ||= re || 208.696 || 9/8, 17/15 ||= major 2nd ||= M2 ||= E ||

~~9L 19s (28~~-~~tone)~~

||= 9 ||= ri || 234.783 || 8/7, 15/13* ||= upmajor 2nd ||= ^M2 ||= E^ ||

~~9L 28s (37~~-~~tone)~~ || ~~6:5 ~ QE~~

||= 10 ||= ma || 260.87 || 7/6, 15/13* ||= downminor 3rd ||= vm3 ||= Fv ||

~~5:1~~

||= 11 ||= meh || 286.957 || 13/11, 20/17 ||= minor 3rd ||= m3 ||= F ||

~~4:1~~

||= 12 ||= me || 313.043 || 6/5 ||= upminor 3rd ||= ^m3 ||= F^ ||

3:1

||= 13 ||= mu || 339.13 || 11/9, 17/14 ||= downmid 3rd ||= v~3 ||= F^^ ||

~~2:1 ~ QE~~ ||

||= 14 ||= muh || 365.217 || 16/13 ||= upmid 3rd ||= ^~3 ||= F#vv ||

|| 1 || 7~~\46~~ || ~~182~~.~~609~~ || ~~[[xenharmonic~~/~~Minortone~~|~~Minortone]]~~ || ~~[[xenharmonic~~/~~1L 5s~~|~~1L 5s]] (~~6~~-tone)~~

||= 15 ||= mi || 391.304 || 5/4 ||= downmajor 3rd ||= vM3 ||= F#v ||

~~[[xenharmonic~~/~~6L 1s~~|~~6L 1s]] (7-tone)~~

||= 16 ||= maa || 417.391 || 14/11 ||= major 3rd ||= M3 ||= F# ||

~~7L 6s (~~13~~-tone)~~

||= 17 ||= mo || 443.478 || 9/7, 13/10, 22/17 ||= upmajor 3rd ||= ^M3 ||= F#^ ||

~~13L 7s (20-tone)~~

||= 18 ||= fe || 469.565 || 17/13 ||= down 4th ||= v4 ||= Gv ||

~~13L 20s (33-tone)~~ || ~~11:~~7

||= 19 ||= fa || 495.652 || 4/3 ||= perfect 4th ||= P4 ||= G ||

7:4

||= 20 ||= fih || 521.739 || ||= up 4th ||= ^4 ||= G^ ||

~~4:3~~ ~ QE

||= 21 ||= fu || 547.826 || 11/8, 15/11 ||= double-up 4th ||= ^^4 ||= G^^ ||

~~3:1~~

||= 22 ||= fi || 573.913 || 7/5, 18/13 ||= double-down aug 4th,

~~2:1~~ ~ QE ||

dim 5th ||= vvA4, d5 ||= G#vv, Ab ||

|| 1 || 9\46 || ~~234.783~~ || [[xenharmonic/~~Rodan~~|~~Rodan~~]] || [[xenharmonic/~~1L 4s~~|~~1L 4s~~]] (5-~~tone)~~

||= 23 ||= seh || 600 || 17/12, 24/17 ||= downaug 4th, updim 5th ||= vA4, ^d5 ||= G#v, Ab^ ||

[[xenharmonic/~~1L 5s~~|~~1L 5s~~]] ~~(6-tone)~~

||= 24 ||= se || 626.087 || 10/7, 13/9 ||= aug 4th, double-up dim 5th ||= A4, ^^d5 ||= G#, Ab^^ ||

[[xenharmonic/~~5L 6s~~|~~5L 6s~~]] (11-tone)

||= 25 ||= su || 652.174 || 16/11, 22/15 ||= double-down 5th ||= vv5 ||= Avv ||

~~5L 11s~~ (16-tone)

||= 26 ||= sih || 678.261 || ||= down 5th ||= v5 ||= Av ||

~~5L 16s (21-tone)~~

||= 27 ||= sol || 704.348 || 3/2 ||= perfect 5th ||= P5 ||= A ||

~~5L 21s (26-tone)~~

||= 28 ||= si || 730.435 || 26/17 ||= up 5th ||= ^5 ||= A^ ||

~~5L 26s~~ (31~~-tone)~~

||= 29 ||= lo || 756.522 || 14/9, 20/13, 17/11 ||= downminor 6th ||= vm6 ||= Bbv ||

~~5L 31s (36-tone)~~

||= 30 ||= leh || 782.609 || 11/7 ||= minor 6th ||= m6 ||= Bb ||

~~5L 36s (41~~-tone) || 10:9 ~QE

||= 31 ||= le || 808.696 || 8/5 ||= upminor 6th ||= ^m6 ||= Bb^ ||

~~9:1~~

||= 32 ||= lu || 834.783 || 13/8 ||= downmid 6th ||= v~6 ||= Bb^^ ||

~~8:1~~

||= 33 ||= luh || 860.87 || 18/11, 28/17 ||= upmid 6th ||= ^~6 ||= Bvv ||

~~7:1~~

||= 34 ||= la || 886.957 || 5/3 ||= downmajor 6th ||= vM6 ||= Bv ||

~~6:1~~

||= 35 ||= laa || 913.043 || 22/13, 17/10 ||= major 6th ||= M6 ||= B ||

~~5:1~~

||= 36 ||= li || 939.13 || 12/7, 26/15* ||= upmajor 6th ||= ^M6 ||= B^ ||

~~4:1~~

||= 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]].

All 46edo chords can be named using ups and downs:

0-10-27 = C Ebv G = C.vm = "C downminor"

0-12-27 = C Eb^ G = C.^m = "C upminor"

0-14-27 = C Evv G = C.^~ = "C upmid"

0-16-27 = C E G = "C major" or "C"

0-17-27 = C E^ G = C.^= "C upmajor" or "C dot up"

etc.

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 || ~~11\46 || 286.957 || || [[xenharmonic/4L 1s|4L 1s]] (~~5~~-tone)~~

|| 1 || 5\46 || 130.435 || [[xenharmonic/Twothirdtonic|Twothirdtonic]] || [[xenharmonic/1L 8s|1L 8s]] (9-tone)

~~[[xenharmonic/4L 5s|4L 5s]] (9-tone)~~

[[xenharmonic/9L 1s|9L 1s]] (10-tone)

~~4L 9s (13-tone)~~

9L 10s (19-tone)

~~4L 13s (17-tone)~~

9L 19s (28-tone)

~~4L 17s (21-tone)~~

9L 28s (37-tone) || 6:5 ~ QE

~~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)

|| 1 || 7\46 || 182.609 || [[xenharmonic/Minortone|Minortone]] || [[xenharmonic/1L 5s|1L 5s]] (6-tone)

[[xenharmonic/3L 1s|3L 1s]] (4-tone)

[[xenharmonic/6L 1s|6L 1s]] (7-tone)

[[xenharmonic/3L 4s|3L 4s]] (7-tone)

7L 6s (13-tone)

[[xenharmonic/~~3L 7s~~|~~3L 7s~~]] (10-tone)

13L 7s (20-tone)

~~3L 10s~~ (13-tone)

13L 20s (33-tone) || 11:7

~~3L 13s~~ (16-tone)

7:4

3L 16s ~~(19-tone)~~

4:3 ~ QE

~~3L 19s~~ (21-tone)

3:1

3L 21s (~~24-tone)~~

2:1 ~ QE ||

~~3L 24s (27-tone)~~

|| 1 || 9\46 || 234.783 || [[xenharmonic/Rodan|Rodan]] || [[xenharmonic/1L 4s|1L 4s]] (5-tone)

~~3L 27s (30~~-tone)

[[xenharmonic/1L 5s|1L 5s]] (6-tone)

~~3L 30s~~ (33-tone)

[[xenharmonic/5L 6s|5L 6s]] (11-tone)

~~3L 33s~~ (36-tone)

5L 11s (16-tone)

3L 36s (~~39-tone)~~

5L 16s (21-tone)

~~3L 39s (42~~-tone) || 16:15 ~ QE

5L 21s (26-tone)

~~15:1~~

5L 26s (31-tone)

~~14:1~~

5L 31s (36-tone)

~~13:1~~

5L 36s (41-tone) || 10:9 ~QE

~~12:1~~

~~11:1~~

~~10:1~~

9:1

8:1

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3:1

2:1 ~ QE ||

|| 1 || 17\46 || ~~443~~.~~478 |~~| ~~[[xenharmonic/Sensi~~|~~Sensi]]~~ || [[xenharmonic/~~3L 2s~~|~~3L 2s~~]] (5-tone)

|| 1 || 11\46 || 286.957 || || [[xenharmonic/4L 1s|4L 1s]] (5-tone)

[[xenharmonic/3L 5s|3L 5s]] (8-tone)

[[xenharmonic/4L 5s|4L 5s]] (9-tone)

~~[[xenharmonic/8L 3s|8L 3s]]~~ (11-tone)

4L 9s (13-tone)

~~8L 11s~~ (19-tone)

4L 13s (17-tone)

~~19L 8s~~ (27-tone) || 12:5

4L 17s (21-tone)

7:5

21L 4s (25-tone) || 11:2

9:2

7:2

5:2

3:2 ~ QE, Golden

2:1 ||

2:1 ~ QE ||

|| 1 || 19\46 || ~~495~~.~~652~~ || [[xenharmonic/~~Leapday~~|~~Leapday~~]] ~~|| [[xenharmonic~~/~~2L 3s|2L 3s]] (5-tone)~~

|| 1 || 13\46 || 339.13 || [[xenharmonic/Amity|Amity]]/[[xenharmonic/hitchcock|hitchcock]] || [[xenharmonic/4L 3s|4L 3s]] (7-tone)

[[xenharmonic/~~5L 2s~~|~~5L 2s~~]] ~~(7-tone)~~

[[xenharmonic/7L 4s|7L 4s]] (11-tone)

~~[[xenharmonic/5L 7s|5L 7s]] (12-tone)~~

7L 11s (18-tone)

~~12L 5s (17-tone)~~

7L 18s (25-tone)

~~17L 12s (29-tone) || 11:8~~

7L 25s (32-tone)

~~8:3~~

7L 32s (39-tone) || 7:6 ~ QE

~~5:3 ~ Golden~~

6:1

~~3:2 ~ QE, Golden~~

5:1

~~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~~]] ~~|| || ||~~

|| 1 || 15\46 || 391.304 || [[Amigo]] || [[xenharmonic/1L 2s|1L 2s]] (3-tone)

~~|| 2 || 2\46 || 52.174~~ || [[xenharmonic/~~Shrutar~~|~~Shrutar~~]] ~~|| 2L 2s~~ (4-tone)

[[xenharmonic/3L 1s|3L 1s]] (4-tone)

[[xenharmonic/~~2L 4s~~|~~2L 4s~~]] (6-tone)

[[xenharmonic/3L 4s|3L 4s]] (7-tone)

[[xenharmonic/~~2L 6s~~|~~2L 6s~~]] (8-tone)

[[xenharmonic/3L 7s|3L 7s]] (10-tone)

[[xenharmonic/~~2L 8s~~|~~2L 8s~~]] (10-tone)

3L 10s (13-tone)

~~[[xenharmonic/2L~~ 10s~~|2L 10s]]~~ (12-tone)

3L 13s (16-tone)

~~2L 12s~~ (14-tone)

3L 16s (19-tone)

~~2L 14s~~ (16-tone)

3L 19s (21-tone)

~~2L 16s~~ (18-tone)

3L 21s (24-tone)

~~2L 18s~~ (20-tone)

3L 24s (27-tone)

~~2L 20s~~ (22-tone)

3L 27s (30-tone)

~~22L 2s~~ (24-tone) || 21:2

3L 30s (33-tone)

19:2

3L 33s (36-tone)

17:2

3L 36s (39-tone)

15:2

3L 39s (42-tone) || 16:15 ~ QE

13:2

15:1

11:2

14:1

9:2

13:1

7:2

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 ||

|| 2 || 3\46 || 78.~~261~~ || [[~~Semivalentine~~]] || 2L 2s (4-tone)

|| 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)

Line 175:

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[[xenharmonic/2L 10s|2L 10s]] (12-tone)

2L 12s (14-tone)

14L 2s (16-tone)

2L 14s (16-tone)

16L 14s (30-tone) || 20:3

2L 16s (18-tone)

17:3

2L 18s (20-tone)

14:3

2L 20s (22-tone)

11:3

22L 2s (24-tone) || 21:2

8:3

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

Line 293:

Line 356:

2:1 ~ QE ||

|| 23 || 1\46 || 26.087 || || || ||

~~=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]].

~~All 46edo chords can be named using ups and downs:~~

=Approximation to Mode 8 of the Harmonic Series=

~~0-10-27~~ = ~~C Ebv G~~ = ~~C.vm = "C downminor"~~

~~0-12-27 = C Eb^ G = C.^m = "C upminor"~~

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.

~~0-14-27 = C Evv G = C.^~ = "C upmid"~~

0-16~~-27 = C E G = "C major" or "C"~~

8\46edo (208.70¢) stands in for frequency ratio [[xenharmonic/9_8|9:8]] (203.91¢).

0~~-17-27 = C E^ G = C~~.~~^= "C upmajor" or "C dot up"~~

7\46edo (182.61¢) stands in for [[xenharmonic/10_9|10:9]] (182.40¢).

~~etc.~~

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¢).

~~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]]~~.

4\46edo (104.35¢) stands in for [[xenharmonic/16_15|16:15]] (111.73¢).

~~=Approximation to Mode~~ 8 ~~of the Harmonic Series=~~

=Scales=

* [[xenharmonic/plum|plum]]

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.~~

* [[xenharmonic/sensi5|sensi5]]

* [[xenharmonic/sensi8|sensi8]]

~~8\46edo~~ (~~208~~.~~70¢~~) stands in for ~~frequency ratio~~ [[xenharmonic/~~9_8~~|9:8]] (~~203~~.~~91¢~~).

* [[xenharmonic/sensi11|sensi11]]

~~7\46edo~~ (~~182~~.~~61¢~~) ~~stands in for~~ [[xenharmonic/~~10_9~~|10:9]] (~~182~~.~~40¢~~).

* [[xenharmonic/sensi19|sensi19]]

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¢).~~

=Music=

~~4\46edo (104.35¢) stands in for~~ [[xenharmonic/~~16_15~~|~~16:15~~]] ~~(111.73¢).~~

by [[xenharmonic/Aaron Krister Johnson|Aaron Krister Johnson:]]

[[http://aaronkristerjohnson.bandcamp.com/track/satiesque|Satiesque]]

=~~Scales~~=

* [[xenharmonic/~~plum~~|~~plum~~]]

by [[xenharmonic/Gene Ward Smith|Gene Ward Smith:]]

* [[~~xenharmonic~~/~~sensi5~~|~~sensi5~~]]

[[http://www.archive.org/details/Chromosounds|Chromosounds]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3|play]]

* [[xenharmonic/~~sensi8~~|~~sensi8~~]]

[[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.

* [[~~xenharmonic~~/~~sensi11~~|~~sensi11~~]]

* [[~~xenharmonic~~/~~sensi19|sensi19]]~~

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

~~=Music=~~

[[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Bach_Contrapunctus_4-Jeux14-E46.mp3|Bach Contrapunctus 4]] Claudi Meneghin version

~~by [[xenharmonic~~/~~Aaron Krister Johnson~~|~~Aaron Krister Johnson:~~]]

[[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]]</pre></div>

[[http://~~aaronkristerjohnson~~.~~bandcamp~~.~~com~~/~~track~~/~~satiesque~~|~~Satiesque~~]]

<h4>Original HTML content:</h4>

<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"><html><head><title>46edo</title></head><body><a href="#x46 tone equal temperament">46 tone equal temperament</a> | <a href="#x46edo srutis">46edo srutis</a> | <a href="#Intervals">Intervals</a> | <a href="#Linear temperaments">Linear temperaments</a> | <a href="#Approximation to Mode 8 of the Harmonic Series">Approximation to Mode 8 of the Harmonic Series</a> | <a href="#Scales">Scales</a> | <a href="#Music">Music</a>

~~by [[xenharmonic/Gene Ward Smith|Gene Ward Smith:]]~~

<hr />

[[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~~.

<h1 id="toc0"><a name="x46 tone equal temperament"></a>46 tone equal temperament</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>.

~~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~~

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.

[[~~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]]~~</pre~~></div>~~

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.

~~<h4>Original HTML content~~:~~</h4>~~

~~<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"><html><head><title>46edo</title></head><body><a href="#x46 tone equal temperament">46 tone equal temperament</a> | <a href="#x46edo srutis">46edo srutis</a> | <a href="#~~Linear temperaments~~">~~Linear temperaments~~</a> | <a href="#~~Intervals~~">~~Intervals~~</a> | <a href="#Approximation to Mode 8 of the Harmonic Series">Approximation to Mode 8 of the Harmonic Series</a> | <a href="#Scales">Scales</a> | <a href="#Music">Music</a>

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.

<hr />

<h1 id="toc1"><a name="x46edo srutis"></a>46edo srutis</h1>

<h1 id="toc0"><a name="x46 tone equal temperament"></a>46 tone equal temperament</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.

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>.

<h1 id="toc2"><a name="Intervals"></a>Intervals</h1>

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.

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.

<tr>

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.

<th>degrees of 46edo

</th>

<h1 id="toc1"><a name="x46edo srutis"></a>46edo srutis</h1>

<th>solfege

<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.

</th>

<th>cents value

<h1 id="toc2"><a name="~~Linear temperaments~~"></a&~~gt;Linear temperaments~~</~~h1>~~

</th>

<th>approximate ratios

in the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17-limit">17-limit</a>

~~<table class="wiki_table"~~>

</th>

<th colspan="3"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs notation</a>

</th>

</tr>

<tr>

<td style="text-align: center;">0

</td>

<td style="text-align: center;">do

</td>

<td>0.00

</td>

<td>1/1

</td>

<td style="text-align: center;">perfect unison

</td>

<td style="text-align: center;">P1

</td>

<td style="text-align: center;">D

</td>

</tr>

<tr>

<td style="text-align: center;">1

</td>

<td style="text-align: center;">di

</td>

<td>26.087

</td>

<td>

</td>

<td style="text-align: center;">up unison

</td>

<td style="text-align: center;">^1

</td>

<td style="text-align: center;">D^

</td>

</tr>

<tr>

<~~th>Periods ~~

<td style="text-align: center;">2

~~per octave ~~

~~</th>~~

~~<th>Generator ~~

~~</th>~~

~~<th>Cents ~~

~~</th>~~

~~<th>Temperaments ~~

~~</th>~~

~~<th>MOS/DE Scales available ~~

~~</th>~~

~~<th>L~~:~~s ~~

~~</th>~~

~~&lt~~;~~/tr>~~

~~<tr>~~

~~<td~~>1

</td>

<td>~~1\46~~

<td style="text-align: center;">ro

</td>

<td>26.~~087~~

<td>52.174

</td>

<td>

</td>

<td>

<td style="text-align: center;">downminor 2nd

</td>

<td style="text-align: center;">vm2

</td>

<td>

<td style="text-align: center;">Ebv

</td>

</tr>

<tr>

<td>1

<td style="text-align: center;">3

</td>

<td>~~3\46~~

<td style="text-align: center;">rih

</td>

<td>78.261

</td>

<td><~~a class="wiki_link" href="http:~~//~~xenharmonic.wikispaces.com/Valentine"~~>~~Valentine~~</a>

<td>

</td>

<td style="text-align: center;">minor 2nd

</td>

<td~~>1L 14s (15~~-~~tone)&lt~~;~~br /~~>

<td style="text-align: center;">m2

~~15L 1s (16-tone) ~~

~~16L 15s (31-tone)~~

</td>

<td~~>4:3 ~ <a class="wiki_link" href~~="~~http://xenharmonic.wikispaces.com/Maximal%20evenness">quasi~~-~~equal</a> ~~

<td style="text-align: center;">Eb

3:~~1&lt~~;~~br /~~>

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>1

<td style="text-align: center;">4

</td>

<td>~~5\46~~

<td style="text-align: center;">ra

</td>

<td>~~130~~.~~435~~

<td>104.348

</td>

<td>~~<a class="wiki_link" href="http:~~//~~xenharmonic.wikispaces.com~~/~~Twothirdtonic">Twothirdtonic</a>~~

<td>16/15, 17/16, 18/17

</td>

<td~~><a class~~="~~wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/1L%208s">1L 8s</a> (9-tone) ~~

<td style="text-align: center;">upminor 2nd

~~&lt~~;~~a class=~~"~~wiki_link" href="http://xenharmonic.wikispaces.com/9L%201s">9L 1s</a~~> ~~(10-tone) ~~

~~9L 10s (19-tone) ~~

~~9L 19s (28-tone) ~~

~~9L 28s (37-tone)~~

</td>

<td>~~6:5 ~ QE~~

<td style="text-align: center;">^m2

~~5:1~~

</td>

~~4:1~~<~~br />~~

<td style="text-align: center;">Eb^

3:~~1&lt~~;~~br /~~>

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>1

<td style="text-align: center;">5

</td>

<td>~~7\46~~

<td style="text-align: center;">ru (as in supraminor)

</td>

<td>~~182~~.~~609~~

<td>130.435

</td>

<td>~~<a class="wiki_link" href="http:~~//~~xenharmonic.wikispaces.com~~/~~Minortone">Minortone</a>~~

<td>13/12, 14/13, 15/14

</td>

<td~~><a class~~="~~wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/1L%205s">1L 5s</a> (6-tone) ~~

<td style="text-align: center;">downmid 2nd

~~&lt~~;~~a class=~~"~~wiki_link" href="http://xenharmonic.wikispaces.com/6L%201s">6L 1s</a~~> ~~(7-tone) ~~

~~7L 6s (13-tone) ~~

~~13L 7s (20-tone) ~~

~~13L 20s (33-tone)~~

</td>

<td>~~11:7~~

<td style="text-align: center;">v~2

~~7:4~~

</td>

~~4:3 ~ QE~~<~~br />~~

<td style="text-align: center;">Eb^^

3:~~1&lt~~;~~br /~~>

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>1

<td style="text-align: center;">6

</td>

<td style="text-align: center;">ruh (as in submajor)

</td>

<td>156.522

</td>

<td>~~9\46~~

<td>12/11, 11/10

</td>

<td>~~234.783~~

<td style="text-align: center;">upmid 2nd

</td>

<td~~><a class="wiki_link" href~~="~~http~~:~~//xenharmonic.wikispaces.com/Rodan~~">~~Rodan</a>~~

<td style="text-align: center;">^~2

</td>

<td~~><a class="wiki_link" href~~="~~http://xenharmonic.wikispaces.com/1L%204s">1L 4s</a> (5~~-~~tone) ~~

<td style="text-align: center;">Evv

~~<a class="wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/1L%205s">1L 5s&lt~~;~~/a> (6-tone) ~~

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%206s~~">~~5L 6s</a> (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)~~

</td>

<td>~~10:9 ~QE~~

</tr>

9:1

<tr>

~~8:1~~

<td style="text-align: center;">7

~~7:1~~

</td>

6:1

<td style="text-align: center;">reh

~~5:1~~

</td>

4:1

<td>182.609

~~3:1~~

</td>

2:~~1 ~ QE~~

<td>10/9

</td>

<td style="text-align: center;">downmajor 2nd

</td>

<td style="text-align: center;">vM2

</td>

<td style="text-align: center;">Ev

</td>

</tr>

<tr>

<td>1

<td style="text-align: center;">8

</td>

<td>~~11\46~~

<td style="text-align: center;">re

</td>

<td>~~286~~.~~957~~

<td>208.696

</td>

<td>

<td>9/8, 17/15

</td>

<td~~><a class~~="~~wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/4L%201s">4L 1s</a> (5-tone) ~~

<td style="text-align: center;">major 2nd

~~&lt~~;~~a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%205s~~">~~4L 5s</a> (9-tone)~~

</td>

~~4L 9s (13-tone)~~

<td style="text-align: center;">M2

~~4L 13s (17-tone)~~<~~br />~~

~~4L 17s (21~~-~~tone)&lt~~;~~br /~~>

~~21L 4s (25-tone)~~

</td>

<td~~>11~~:~~2&lt~~;~~br /~~>

<td style="text-align: center;">E

~~9:2 ~~

~~7:2 ~~

~~5:2 ~~

~~3:2 ~ QE, Golden ~~

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>1

<td style="text-align: center;">9

</td>

<td style="text-align: center;">ri

</td>

<td>~~13\46~~

<td>234.783

</td>

<td>~~339.~~13

<td>8/7, 15/13*

</td>

<td~~><a class="wiki_link" href~~="~~http~~:~~//xenharmonic.wikispaces.com/Amity"&gt~~;~~Amity</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/hitchcock~~">~~hitchcock</a>~~

<td style="text-align: center;">upmajor 2nd

</td>

<td~~><a class~~="~~wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/4L%203s">4L 3s&lt~~;~~/a> (7-tone) ~~

<td style="text-align: center;">^M2

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/7L%204s~~">~~7L 4s</a> (11-tone) ~~

~~7L 11s (18-tone) ~~

~~7L 18s (25-tone) ~~

~~7L 25s (32-tone) ~~

~~7L 32s (39-tone)~~

</td>

<td~~>7~~:~~6 ~ QE&lt~~;~~br /~~>

<td style="text-align: center;">E^

~~6:1 ~~

~~5:1 ~~

~~4:1 ~~

~~3:1 ~~

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>1

<td style="text-align: center;">10

</td>

<td style="text-align: center;">ma

</td>

<td>260.87

</td>

<td>15~~\46~~

<td>7/6, 15/13*

</td>

<td>~~391.304~~

<td style="text-align: center;">downminor 3rd

</td>

<td~~><a class~~="~~wiki_link" href="/Amigo~~">~~Amigo</a>~~

<td style="text-align: center;">vm3

</td>

<td~~><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%202s">1L 2s</a> (3-tone) ~~

<td style="text-align: center;">Fv

~~<a class="wiki_link" href~~="~~http://xenharmonic.wikispaces.com/3L%201s">3L 1s</a> (4~~-~~tone) ~~

~~<a class="wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/3L%204s">3L 4s</a> (7-tone) ~~

~~&lt~~;~~a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%207s~~">~~3L 7s</a> (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) ~~

~~</td>~~

~~<td>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~~

</td>

</tr>

<tr>

<td>1

<td style="text-align: center;">11

</td>

<td style="text-align: center;">meh

</td>

<td>~~17\46~~

<td>286.957

</td>

<td>~~443.478~~

<td>13/11, 20/17

</td>

<td~~><a class="wiki_link" href~~="~~http~~:~~//xenharmonic.wikispaces.com/Sensi~~">~~Sensi</a>~~

<td style="text-align: center;">minor 3rd

</td>

<td~~><a class~~="~~wiki_link" href="http://xenharmonic.wikispaces.com/3L%202s">3L 2s</a> (5~~-~~tone) ~~

<td style="text-align: center;">m3

~~<a class="wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/3L%205s">3L 5s</a> (8-tone) ~~

~~&lt~~;~~a class="wiki_link" href="http://xenharmonic.wikispaces.com/8L%203s~~">~~8L 3s</a> (11-tone) ~~

~~8L 11s (19-tone) ~~

~~19L 8s (27-tone)~~

</td>

<td~~>12:5 ~~

<td style="text-align: center;">F

7:~~5&lt~~;~~br /~~>

~~5:2 ~~

~~3:2 ~ QE, Golden ~~

~~2:1~~

</td>

</tr>

<tr>

<td>1

<td style="text-align: center;">12

</td>

<td>~~19\46~~

<td style="text-align: center;">me

</td>

<td>~~495~~.~~652~~

<td>313.043

</td>

<td><~~a class="wiki_link" href="http:~~//~~xenharmonic.wikispaces.com/Leapday"~~>~~Leapday~~</a>

<td>6/5

</td>

<td style="text-align: center;">upminor 3rd

</td>

<td~~><a class~~="~~wiki_link" href="http://xenharmonic.wikispaces.com/2L%203s">2L 3s</a> (5~~-~~tone) ~~

<td style="text-align: center;">^m3

~~<a class="wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/5L%202s">5L 2s</a> (7-tone) ~~

~~&lt~~;~~a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%207s~~">~~5L 7s</a> (12-tone) ~~

~~12L 5s (17-tone) ~~

~~17L 12s (29-tone)~~

</td>

<td~~>11:8 ~~

<td style="text-align: center;">F^

8:~~3&lt~~;~~br /~~>

~~5:3 ~ Golden ~~

~~3:2 ~ QE, Golden ~~

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>1

<td style="text-align: center;">13

</td>

<td style="text-align: center;">mu

</td>

<td>~~21\46~~

<td>339.13

</td>

<td>~~547.826~~

<td>11/9, 17/14

</td>

<td~~><a class="wiki_link" href~~="~~http~~:~~//xenharmonic.wikispaces.com/Heinz~~">~~Heinz</a>~~

<td style="text-align: center;">downmid 3rd

</td>

<td~~><a class~~="~~wiki_link" href="http://xenharmonic.wikispaces.com/2L%203s">2L 3s</a> (5~~-~~tone) ~~

<td style="text-align: center;">v~3

~~<a class="wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/2L%205s">2L 5s&lt~~;~~/a> (7-tone) ~~

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%207s~~">~~2L 7s</a> (9-tone) ~~

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%209s">2L 9s</a> (11-tone) ~~

~~11L 2s (13-tone) ~~

~~11L 13s (24-tone) ~~

~~11L 24s (35-tone)~~

</td>

<td~~>17:4 ~~

<td style="text-align: center;">F^^

13:~~4&lt~~;~~br /~~>

~~9:4 ~~

~~5:4 ~ QE ~~

~~4:1 ~~

~~3:1 ~~

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>2

<td style="text-align: center;">14

</td>

<td style="text-align: center;">muh

</td>

<td>~~1\46~~

<td>365.217

</td>

<td>~~26.087~~

<td>16/13

</td>

<td~~><a class~~="~~wiki_link" href="/Ketchup~~">~~Ketchup</a>~~

<td style="text-align: center;">upmid 3rd

</td>

<td>

<td style="text-align: center;">^~3

</td>

<td>

<td style="text-align: center;">F#vv

</td>

</tr>

<tr>

<td>2

<td style="text-align: center;">15

</td>

<td style="text-align: center;">mi

</td>

<td>391.304

</td>

<td>~~2\46~~

<td>5/4

</td>

<td>~~52.174~~

<td style="text-align: center;">downmajor 3rd

</td>

<td~~><a class="wiki_link" href~~="~~http~~:~~//xenharmonic.wikispaces.com/Shrutar~~">~~Shrutar</a>~~

<td style="text-align: center;">vM3

</td>

<td~~>2L 2s (4-tone) ~~

<td style="text-align: center;">F#v

~~<a class="wiki_link" href~~="~~http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6~~-~~tone) ~~

~~<a class="wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/2L%206s">2L 6s</a> (8-tone)&lt~~;~~br />~~

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%208s~~">~~2L 8s</a> (10-tone) ~~

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2010s">2L 10s</a> (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)~~

</td>

~~<td>21:2~~

</tr>

~~19:2~~<~~br /~~>

<tr>

~~17:2~~<~~br />~~

<td style="text-align: center;">16

~~15:2 ~~

~~13:2 ~~

~~11:2 ~~

~~9:2 ~~

7:~~2&lt~~;~~br /~~>

~~5:2 ~~

~~3:2 ~ QE, Golden ~~

~~2:1 ~ QE~~

</td>

~~</tr>~~

<td style="text-align: center;">maa

~~<tr>~~

<td>2

</td>

<td>~~3\46~~

<td>417.391

</td>

<td>~~78.261~~

<td>14/11

</td>

<td~~><a class~~="~~wiki_link" href="/Semivalentine~~">~~Semivalentine</a>~~

<td style="text-align: center;">major 3rd

</td>

<td~~>2L 2s (4-tone) ~~

<td style="text-align: center;">M3

~~<a class~~="~~wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6~~-~~tone) ~~

~~<a class="wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/2L%206s">2L 6s</a&gt~~; ~~(8-tone) ~~

~~<a class=~~"~~wiki_link" href="http://xenharmonic.wikispaces.com/2L%208s">2L 8s</a> (10-tone) ~~

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2010s">2L 10s</a> (12-tone)

~~2L 12s (14-tone) ~~

~~14L 2s (16-tone) ~~

~~16L 14s (30-tone)~~

</td>

<td~~>20~~:~~3&lt~~;~~br /~~>

<td style="text-align: center;">F#

~~17:3 ~~

~~14:3 ~~

~~11:3 ~~

~~8:3 ~~

~~5:3 ~ Golden ~~

~~3:2 ~ QE, Golden ~~

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>2

<td style="text-align: center;">17

</td>

<td style="text-align: center;">mo

</td>

<td>~~4\46~~

<td>443.478

</td>

<td>~~104.348~~

<td>9/7, 13/10, 22/17

</td>

<td~~><a class="wiki_link" href~~="~~http~~:~~//xenharmonic.wikispaces.com/Srutal"&gt~~;~~Srutal</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/diaschismic~~">~~diaschismic</a>~~

<td style="text-align: center;">upmajor 3rd

</td>

<td~~>2L 2s (4-tone) ~~

<td style="text-align: center;">^M3

~~<a class~~="~~wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6~~-~~tone) ~~

~~<a class="wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/2L%206s">2L 6s</a> (8-tone)&lt~~;~~br />~~

~~<a class=~~"~~wiki_link" href="http://xenharmonic.wikispaces.com/2L%208s">2L 8s</a~~> ~~(10-tone) ~~

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/10L%202s">10L 2s</a> (12-tone) ~~

~~12L 10s (22-tone) ~~

~~12L 22s (34-tone)~~

</td>

<td~~>19:4 ~~

<td style="text-align: center;">F#^

15:~~4&lt~~;~~br /~~>

~~11:4 ~~

~~7:4 ~~

~~4:3 ~ QE ~~

~~3:1 ~~

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>2

<td style="text-align: center;">18

</td>

<td style="text-align: center;">fe

</td>

<td>~~5\46~~

<td>469.565

</td>

<td>~~130.435~~

<td>17/13

</td>

<td>

<td style="text-align: center;">down 4th

</td>

<td~~>2L 2s (4-tone) ~~

<td style="text-align: center;">v4

~~<a class~~="~~wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6~~-~~tone) ~~

~~<a class="wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/2L%206s">2L 6s</a&gt~~; ~~(8-tone) ~~

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/8L%202s~~">~~8L 2s</a> (10-tone) ~~

~~8L 10s (18-tone) ~~

~~18L 10s (28-tone)~~

</td>

<td~~>18~~:~~5&lt~~;~~br /~~>

<td style="text-align: center;">Gv

~~13:5 ~~

~~8:5 ~ Golden ~~

~~5:3 ~ Golden ~~

~~3:2 ~ QE, Golden ~~

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>2

<td style="text-align: center;">19

</td>

<td>~~6\46~~

<td style="text-align: center;">fa

</td>

<td>~~156~~.~~522~~

<td>495.652

</td>

<td>~~<a class="wiki_link" href="~~/~~Bison">Bison</a>~~

<td>4/3

</td>

<td~~>2L 2s (4-tone) ~~

<td style="text-align: center;">perfect 4th

~~<a class~~="~~wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/2L%204s"&gt~~;~~2L 4s</a> (6-tone) ~~

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%202s~~">~~6L 2s</a> (8-tone) ~~

~~8L 6s (14-tone) ~~

~~8L 14s (22-tone) ~~

~~8L 22s (30-tone) ~~

~~8L 30s (38-tone~~

</td>

<td~~>17~~:~~6&lt~~;~~br />~~

<td style="text-align: center;">P4

11:6

</td>

~~6:5 ~ QE~~

<td style="text-align: center;">G

~~5:1~~

~~4:1~~<~~br />~~

3:~~1&lt~~;~~br /~~>

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>2

<td style="text-align: center;">20

</td>

<td style="text-align: center;">fih

</td>

<td>~~7\46~~

<td>521.739

</td>

<td>~~182.609~~

<td>

</td>

<td~~><a class="wiki_link" href~~="~~http~~:~~//xenharmonic.wikispaces.com/Unidec"&gt~~;~~Unidec</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/hendec~~">~~hendec</a>~~

<td style="text-align: center;">up 4th

</td>

<td~~>2L 2s (4-tone) ~~

<td style="text-align: center;">^4

~~<a class~~="~~wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6-tone) ~~

~~&lt~~;~~a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%202s~~">~~6L 2s</a> (8-tone) ~~

~~6L 8s (14-tone) ~~

~~6L 14s (20-tone) ~~

~~20L 6s (26-tone)~~

</td>

<td~~>16~~:~~7&lt~~;~~br /~~>

<td style="text-align: center;">G^

~~9:7 ~~

~~7:2 ~~

~~5:2 ~~

~~3:2 ~ QE, Golden ~~

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>2

<td style="text-align: center;">21

</td>

<td>~~8\46~~

<td style="text-align: center;">fu

</td>

<td>547.826

</td>

<td>~~208.696~~

<td>11/8, 15/11

</td>

<td~~><a class="wiki_link" href~~="~~http~~:~~//xenharmonic.wikispaces.com/Abigail~~">~~Abigail</a>~~

<td style="text-align: center;">double-up 4th

</td>

<td~~>2L 2s (4-tone) ~~

<td style="text-align: center;">^^4

~~<a class~~="~~wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/4L%202s"&gt~~;~~4L 2s</a> (6-tone) ~~

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%202s~~">~~6L 2s</a> (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)~~

</td>

<td~~>15:8 ~~

<td style="text-align: center;">G^^

~~8:7 ~ QE ~~

~~8:1 ~~

7:~~1&lt~~;~~br /~~>

~~6:1 ~~

~~5:1 ~~

~~4:1 ~~

~~3:1 ~~

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>2

<td style="text-align: center;">22

</td>

<td style="text-align: center;">fi

</td>

<td>~~9\46~~

<td>573.913

</td>

<td>~~234.783~~

<td>7/5, 18/13

</td>

<td~~><a class~~="~~wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/Echidnic~~">~~Echidnic~~</a>

<td style="text-align: center;">double-down aug 4th,

dim 5th

</td>

<td~~>2L 2s (4-tone) ~~

<td style="text-align: center;">vvA4, d5

~~<a class~~="~~wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/4L%202s">4L 2s</a&gt~~; ~~(6-tone) ~~

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%204s~~">~~6L 4s</a> (10-tone) ~~

~~10L 6s (16-tone) ~~

~~10L 16s (26-tone) ~~

~~10L 26s (36-tone)~~

</td>

<td~~>14~~:~~9&lt~~;~~br /~~>

<td style="text-align: center;">G#vv, Ab

~~9:5 ~~

~~5:4 ~ QE ~~

~~4:1 ~~

~~3:1 ~~

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>2

<td style="text-align: center;">23

</td>

<td>~~10\46~~

<td style="text-align: center;">seh

</td>

<td>~~260.87~~

<td>600

</td>

<td>17/12, 24/17

</td>

<td~~><a class~~="~~wiki_link" href="/Bamity~~">~~Bamity</a>~~

<td style="text-align: center;">downaug 4th, updim 5th

</td>

<td~~>2L 2s (4-tone) ~~

<td style="text-align: center;">vA4, ^d5

~~<a class~~="~~wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/4L%202s">4L 2s</a&gt~~; ~~(6-tone) ~~

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%206s~~">~~4L 6s</a> (10-tone) ~~

~~4L 10s (14-tone) ~~

~~14L 4s (18-tone) ~~

~~14L 18s (32-tone)~~

</td>

<td~~>13~~:~~10&lt~~;~~br /~~>

<td style="text-align: center;">G#v, Ab^

~~10:3 ~~

~~7:3 ~~

~~4:3 ~ QE ~~

~~3:1 ~~

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>2

<td style="text-align: center;">24

</td>

<td>~~11\46~~

<td style="text-align: center;">se

</td>

<td>~~286~~.~~957~~

<td>626.087

</td>

<td>~~<a class="wiki_link" href="~~/~~Vines">Vines<~~/~~a>~~

<td>10/7, 13/9

</td>

<td~~>2L 2s (4-tone) ~~

<td style="text-align: center;">aug 4th, double-up dim 5th

~~<a class~~="~~wiki_link" href="http~~:~~//xenharmonic.wikispaces.com/4L%202s"&gt~~;~~4L 2s</a> (6-tone) ~~

</td>

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%206s~~">~~4L 6s</a> (10~~-~~tone)~~

<td style="text-align: center;">A4, ^^d5

~~4L 10s (14-tone)~~

~~4L 14s (18-tone)~~<~~br />~~

~~4L 18s (22~~-~~tone)&lt~~;~~br />~~

~~4L 22s (26-tone) ~~

~~4L 26s (30-tone) ~~

4L 30s (34-tone)

~~4L 34s (38-tone) ~~

~~4L 38s (42-tone)~~

</td>

<td~~>12:11 ~ QE ~~

<td style="text-align: center;">G#, Ab^^

~~11:1 ~~

~~10:1 ~~

9:~~1&lt~~;~~br /~~>

~~8:1 ~~

~~7:1 ~~

~~6:1 ~~

~~5:1 ~~

~~4:1 ~~

~~3:1 ~~

~~2:1 ~ QE~~

</td>

</tr>

<tr>

<td>23

<td style="text-align: center;">25

</td>

<td>~~1\46~~

<td style="text-align: center;">su

</td>

<td>652.174

</td>

<td>~~26.087~~

<td>16/11, 22/15

</td>

<td>

<td style="text-align: center;">double-down 5th

</td>

<td>

<td style="text-align: center;">vv5

</td>

<td>

<td style="text-align: center;">Avv

</td>

</tr>

~~</table>~~

~~<h1 id="toc3"><a name="Intervals"></a>Intervals</h1>~~

~~<table class="wiki_table">~~

<tr>

<th>~~degrees of 46edo~~

<td style="text-align: center;">26

</th>

</td>

<th>~~solfege~~

<td style="text-align: center;">sih

</th>

</td>

<th>~~cents value~~

<td>678.261

</th>

</td>

<th>~~approximate ratios~~

<td>

~~in the~~ <~~a class="wiki_link" href="http://xenharmonic.wikispaces.com~~/~~17-limit"~~>~~17-limit~~</a>

</td>

</th>

<td style="text-align: center;">down 5th

<~~th colspan~~="3"><~~a class="wiki_link" href="~~/~~Ups%20and%20Downs%20Notation"~~>~~ups and downs notation~~</a>

</td>

</th>

<td style="text-align: center;">v5

</td>

<td style="text-align: center;">Av

</td>

</tr>

<tr>

<td style="text-align: center;">0

<td style="text-align: center;">27

</td>

<td style="text-align: center;">do

<td style="text-align: center;">sol

</td>

<td>0.00

<td>704.348

</td>

<td>1/1

<td>3/2

</td>

<td style="text-align: center;">perfect ~~unison~~

<td style="text-align: center;">perfect 5th

</td>

<td style="text-align: center;">P1

<td style="text-align: center;">P5

</td>

<td style="text-align: center;">D

<td style="text-align: center;">A

</td>

</tr>

<tr>

<td style="text-align: center;">1

<td style="text-align: center;">28

</td>

<td style="text-align: center;">di

<td style="text-align: center;">si

</td>

<td>26.~~087~~

<td>730.435

</td>

<td>

<td>26/17

</td>

<td style="text-align: center;">up ~~unison~~

<td style="text-align: center;">up 5th

</td>

<td style="text-align: center;">^1

<td style="text-align: center;">^5

</td>

<td style="text-align: center;">D^

<td style="text-align: center;">A^

</td>

</tr>

<tr>

<td style="text-align: center;">2

<td style="text-align: center;">29

</td>

<td style="text-align: center;">ro

<td style="text-align: center;">lo

</td>

<td>52.~~174~~

<td>756.522

</td>

<td>

<td>14/9, 20/13, 17/11

</td>

<td style="text-align: center;">downminor ~~2nd~~

<td style="text-align: center;">downminor 6th

</td>

<td style="text-align: center;">~~vm2~~

<td style="text-align: center;">vm6

</td>

<td style="text-align: center;">~~Ebv~~

<td style="text-align: center;">Bbv

</td>

</tr>

<tr>

<td style="text-align: center;">3

<td style="text-align: center;">30

</td>

<td style="text-align: center;">~~rih~~

<td style="text-align: center;">leh

</td>

<td>78.~~261~~

<td>782.609

</td>

<td>

<td>11/7

</td>

<td style="text-align: center;">minor ~~2nd~~

<td style="text-align: center;">minor 6th

</td>

<td style="text-align: center;">m2

<td style="text-align: center;">m6

</td>

<td style="text-align: center;">Eb

<td style="text-align: center;">Bb

</td>

</tr>

<tr>

<td style="text-align: center;">4

<td style="text-align: center;">31

</td>

<td style="text-align: center;">ra

<td style="text-align: center;">le

</td>

<td>~~104~~.~~348~~

<td>808.696

</td>

<td>16/~~15, 17/16, 18/17~~

<td>8/5

</td>

<td style="text-align: center;">upminor ~~2nd~~

<td style="text-align: center;">upminor 6th

</td>

<td style="text-align: center;">^m2

<td style="text-align: center;">^m6

</td>

<td style="text-align: center;">Eb^

<td style="text-align: center;">Bb^

</td>

</tr>

<tr>

<td style="text-align: center;">5

<td style="text-align: center;">32

</td>

<td style="text-align: center;">~~ru (as in supraminor)~~

<td style="text-align: center;">lu

</td>

<td>~~130~~.~~435~~

<td>834.783

</td>

<td>13/~~12, 14/13, 15/14~~

<td>13/8

</td>

<td style="text-align: center;">downmid ~~2nd~~

<td style="text-align: center;">downmid 6th

</td>

<td style="text-align: center;">v~2

<td style="text-align: center;">v~6

</td>

<td style="text-align: center;">Eb^^

<td style="text-align: center;">Bb^^

</td>

</tr>

<tr>

<td style="text-align: center;">6

<td style="text-align: center;">33

</td>

<td style="text-align: center;">~~ruh (as in submajor)~~

<td style="text-align: center;">luh

</td>

<td>~~156~~.~~522~~

<td>860.87

</td>

<td>12/11, 11/10

<td>18/11, 28/17

</td>

<td style="text-align: center;">upmid ~~2nd~~

<td style="text-align: center;">upmid 6th

</td>

<td style="text-align: center;">^~2

<td style="text-align: center;">^~6

</td>

<td style="text-align: center;">~~Evv~~

<td style="text-align: center;">Bvv

</td>

</tr>

<tr>

<td style="text-align: center;">7

<td style="text-align: center;">34

</td>

<td style="text-align: center;">~~reh~~

<td style="text-align: center;">la

</td>

<td>~~182~~.~~609~~

<td>886.957

</td>

<td>10/9

<td>5/3

</td>

<td style="text-align: center;">downmajor ~~2nd~~

<td style="text-align: center;">downmajor 6th

</td>

<td style="text-align: center;">~~vM2~~

<td style="text-align: center;">vM6

</td>

<td style="text-align: center;">Ev

<td style="text-align: center;">Bv

</td>

</tr>

<tr>

<td style="text-align: center;">8

<td style="text-align: center;">35

</td>

<td style="text-align: center;">re

<td style="text-align: center;">laa

</td>

<td>~~208~~.~~696~~

<td>913.043

</td>

<td>9/8, 17/15

<td>22/13, 17/10

</td>

<td style="text-align: center;">major ~~2nd~~

<td style="text-align: center;">major 6th

</td>

<td style="text-align: center;">M2

<td style="text-align: center;">M6

</td>

<td style="text-align: center;">E

<td style="text-align: center;">B

</td>

</tr>

<tr>

<td style="text-align: center;">9

<td style="text-align: center;">36

</td>

<td style="text-align: center;">ri

<td style="text-align: center;">li

</td>

<td>~~234~~.~~783~~

<td>939.13

</td>

<td>8/7, 15~~/13~~*

<td>12/7, 26/15*

</td>

<td style="text-align: center;">upmajor ~~2nd~~

<td style="text-align: center;">upmajor 6th

</td>

<td style="text-align: center;">^M2

<td style="text-align: center;">^M6

</td>

<td style="text-align: center;">E^

<td style="text-align: center;">B^

</td>

</tr>

<tr>

<td style="text-align: center;">10

<td style="text-align: center;">37

</td>

<td style="text-align: center;">ma

<td style="text-align: center;">ta

</td>

<td>~~260~~.87

<td>965.217

</td>

<td>7/6, 15~~/13~~*

<td>7/4, 26/15*

</td>

<td style="text-align: center;">downminor ~~3rd~~

<td style="text-align: center;">downminor 7th

</td>

<td style="text-align: center;">~~vm3~~

<td style="text-align: center;">vm7

</td>

<td style="text-align: center;">Fv

<td style="text-align: center;">Cv

</td>

</tr>

<tr>

<td style="text-align: center;">11

<td style="text-align: center;">38

</td>

<td style="text-align: center;">~~meh~~

<td style="text-align: center;">teh

</td>

<td>~~286~~.~~957~~

<td>991.304

</td>

<td>13/11, 20/17

<td>16/9, 30/17

</td>

<td style="text-align: center;">minor ~~3rd~~

<td style="text-align: center;">minor 7th

</td>

<td style="text-align: center;">m3

<td style="text-align: center;">m7

</td>

<td style="text-align: center;">F

<td style="text-align: center;">C

</td>

</tr>

<tr>

<td style="text-align: center;">12

<td style="text-align: center;">39

</td>

<td style="text-align: center;">me

<td style="text-align: center;">te

</td>

<td>~~313~~.~~043~~

<td>1017.391

</td>

<td>6/5

<td>9/5

</td>

<td style="text-align: center;">upminor ~~3rd~~

<td style="text-align: center;">upminor 7th

</td>

<td style="text-align: center;">^m3

<td style="text-align: center;">^m7

</td>

<td style="text-align: center;">F^

<td style="text-align: center;">C^

</td>

</tr>

<tr>

<td style="text-align: center;">13

<td style="text-align: center;">40

</td>

<td style="text-align: center;">mu

<td style="text-align: center;">tu

</td>

<td>~~339~~.13

<td>1043.478

</td>

<td>11/9, 17/14

<td>11/6, 20/11

</td>

<td style="text-align: center;">downmid ~~3rd~~

<td style="text-align: center;">downmid 7th

</td>

<td style="text-align: center;">v~3

<td style="text-align: center;">v~7

</td>

<td style="text-align: center;">F^^

<td style="text-align: center;">C^^

</td>

</tr>

<tr>

<td style="text-align: center;">14

<td style="text-align: center;">41

</td>

<td style="text-align: center;">~~muh~~

<td style="text-align: center;">tuh

</td>

<td>~~365~~.~~217~~

<td>1069.565

</td>

<td>16/13

<td>24/13, 13/7, 28/15

</td>

<td style="text-align: center;">upmid ~~3rd~~

<td style="text-align: center;">upmid 7th

</td>

<td style="text-align: center;">^~3

<td style="text-align: center;">^~7

</td>

<td style="text-align: center;">F#vv

<td style="text-align: center;">C#vv

</td>

</tr>

<tr>

<td style="text-align: center;">15

<td style="text-align: center;">42

</td>

<td style="text-align: center;">mi

<td style="text-align: center;">ti

</td>

<td>~~391~~.~~304~~

<td>1095.652

</td>

<td>5/4

<td>15/8, 32/17, 17/9

</td>

<td style="text-align: center;">downmajor ~~3rd~~

<td style="text-align: center;">downmajor 7th

</td>

<td style="text-align: center;">~~vM3~~

<td style="text-align: center;">vM7

</td>

<td style="text-align: center;">F#v

<td style="text-align: center;">C#v

</td>

</tr>

<tr>

<td style="text-align: center;">16

<td style="text-align: center;">43

</td>

<td style="text-align: center;">~~maa~~

<td style="text-align: center;">taa

</td>

<td>~~417~~.~~391~~

<td>1121.739

</td>

<td>~~14/11~~

<td>

</td>

<td style="text-align: center;">major ~~3rd~~

<td style="text-align: center;">major 7th

</td>

<td style="text-align: center;">M3

<td style="text-align: center;">M7

</td>

<td style="text-align: center;">F#

<td style="text-align: center;">C#

</td>

</tr>

<tr>

<td style="text-align: center;">17

<td style="text-align: center;">44

</td>

<td style="text-align: center;">mo

<td style="text-align: center;">to

</td>

<td>~~443~~.~~478~~

<td>1147.826

</td>

<td>~~9/7, 13/10, 22/17~~

<td>

</td>

<td style="text-align: center;">upmajor ~~3rd~~

<td style="text-align: center;">upmajor 7th

</td>

<td style="text-align: center;">^M3

<td style="text-align: center;">^M7

</td>

<td style="text-align: center;">F#^

<td style="text-align: center;">C#^

</td>

</tr>

<tr>

<td style="text-align: center;">18

<td style="text-align: center;">45

</td>

<td style="text-align: center;">fe

<td style="text-align: center;">da

</td>

<td>~~469~~.~~565~~

<td>1173.913

</td>

<td>~~17/13~~

<td>

</td>

<td style="text-align: center;">down ~~4th~~

<td style="text-align: center;">down 8ve

</td>

<td style="text-align: center;">v4

<td style="text-align: center;">v8

</td>

<td style="text-align: center;">Gv

<td style="text-align: center;">Dv

</td>

</tr>

<tr>

<td style="text-align: center;">19

<td style="text-align: center;">46

</td>

<td style="text-align: center;">fa

<td style="text-align: center;">do

</td>

<td>~~495.652~~

<td>1200

</td>

<td>4/3

<td>2/1

</td>

<td style="text-align: center;">perfect ~~4th~~

<td style="text-align: center;">perfect 8ve

</td>

<td style="text-align: center;">P4

<td style="text-align: center;">P8

</td>

<td style="text-align: center;">~~G ~~

<td style="text-align: center;">D

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td style="text-align: center;">20 ~~

~~</td>~~

~~<td style="text-align: center;">fih ~~

~~</td>~~

~~<td>521.739 ~~

~~</td>~~

~~<td> ~~

~~</td>~~

~~<td style="text-align: center;">up 4th ~~

~~</td>~~

~~<td style="text-align: center;">^4 ~~

~~</td>~~

~~<td style="text-align: center;">G^~~

</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>.

All 46edo chords can be named using ups and downs:

0-10-27 = C Ebv G = C.vm = &quot;C downminor&quot;

0-12-27 = C Eb^ G = C.^m = &quot;C upminor&quot;

0-14-27 = C Evv G = C.^~ = &quot;C upmid&quot;

0-16-27 = C E G = &quot;C major&quot; or &quot;C&quot;

0-17-27 = C E^ G = C.^= &quot;C upmajor&quot; or &quot;C dot up&quot;

etc.

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>.

<h1 id="toc3"><a name="Linear temperaments"></a>Linear temperaments</h1>

<tr>

<~~td style="text-align: center~~;">21

<th>Periods

</td>

per octave

<~~td style="text-align~~: ~~center~~;">fu

</th>

</td>

<th>Generator

<td>~~547.826~~

</th>

<th>Cents

</th>

<th>Temperaments

</th>

<th>MOS/DE Scales available

</th>

<th>L:s

</th>

</tr>

<tr>

<td>1

</td>

<td>1\46

</td>

<td>~~11/8, 15/11~~

<td>26.087

</td>

<td ~~style="text-align: center;"~~>~~double-up 4th~~

<td>

</td>

<td ~~style="text-align: center;"~~>~~^^4~~

<td>

</td>

<td ~~style="text-align: center;"~~>~~G^^~~

<td>

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>22

<td>1

</td>

<td ~~style="text-align: center;"~~>fi

<td>3\46

</td>

<td>~~573~~.~~913~~

<td>78.261

</td>

<td>7/~~5, 18~~/13

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Valentine">Valentine</a>

</td>

<td ~~style="text~~-~~align: center~~;">~~double~~-~~down aug 4th,~~

<td>1L 14s (15-tone)

~~dim 5th~~

15L 1s (16-tone)

16L 15s (31-tone)

</td>

<td ~~style~~="~~text-align~~: ~~center;~~">~~vvA4, d5~~

<td>4:3 ~ <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Maximal%20evenness">quasi-equal</a>

</td>

3:1

<~~td style="text-align: center;"~~>~~G#vv, Ab~~

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>23

<td>1

</td>

<td ~~style="text-align: center;"~~>~~seh~~

<td>5\46

</td>

<td>~~600~~

<td>130.435

</td>

<td>17/~~12, 24~~/17

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Twothirdtonic">Twothirdtonic</a>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~downaug 4th, updim 5th~~

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%208s">1L 8s</a> (9-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/9L%201s">9L 1s</a> (10-tone)

9L 10s (19-tone)

9L 19s (28-tone)

9L 28s (37-tone)

</td>

<td ~~style="text-align~~: ~~center~~;">~~vA4, ^d5~~

<td>6:5 ~ QE

</td>

5:1

<~~td style="text-align: center;"~~>~~G#v, Ab^~~

4:1

3:1

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>24

<td>1

</td>

<td ~~style="text-align: center;"~~>se

<td>7\46

</td>

<td>~~626~~.~~087~~

<td>182.609

</td>

<td>10/~~7, 13~~/9

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Minortone">Minortone</a>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~aug 4th, double~~-~~up dim 5th~~

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%205s">1L 5s</a> (6-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%201s">6L 1s</a> (7-tone)

7L 6s (13-tone)

13L 7s (20-tone)

13L 20s (33-tone)

</td>

<td ~~style="text-align~~: ~~center~~;">~~A4, ^^d5~~

<td>11:7

7:4

4:3 ~ QE

3:1

2:1 ~ QE

</td>

~~<td style="text-align: center;">G#, Ab^^ ~~

</tr>

~~</td>~~

</tr>

<tr>

<td ~~style="text-align: center;"~~>25

<td>1

</td>

<td ~~style="text-align: center;"~~>su

<td>9\46

</td>

<td>~~652~~.~~174~~

<td>234.783

</td>

<td>16/~~11, 22~~/15

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Rodan">Rodan</a>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~double~~-~~down 5th~~

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%204s">1L 4s</a> (5-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%205s">1L 5s</a> (6-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%206s">5L 6s</a> (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)

</td>

<td ~~style="text-align~~: ~~center~~;">~~vv5~~

<td>10:9 ~QE

</td>

9:1

<~~td style="text-align~~: ~~center~~;">~~Avv~~

8:1

7:1

6:1

5:1

4:1

3:1

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>26

<td>1

</td>

<td ~~style="text-align: center;"~~>~~sih~~

<td>11\46

</td>

<td>~~678~~.~~261~~

<td>286.957

</td>

<td>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~down 5th~~

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%201s">4L 1s</a> (5-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%205s">4L 5s</a> (9-tone)

4L 9s (13-tone)

4L 13s (17-tone)

4L 17s (21-tone)

21L 4s (25-tone)

</td>

<td ~~style="text-align~~: ~~center~~;">v5

<td>11:2

</td>

9:2

<~~td style="text-align~~: ~~center~~;">Av

7:2

5:2

3:2 ~ QE, Golden

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>27

<td>1

</td>

<td ~~style="text-align: center;"~~>~~sol~~

<td>13\46

</td>

<td>~~704~~.~~348~~

<td>339.13

</td>

<td>3/2

<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>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~perfect 5th~~

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%203s">4L 3s</a> (7-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/7L%204s">7L 4s</a> (11-tone)

7L 11s (18-tone)

7L 18s (25-tone)

7L 25s (32-tone)

7L 32s (39-tone)

</td>

<td ~~style="text-align~~: ~~center~~;">P5

<td>7:6 ~ QE

</td>

6:1

<~~td style="text-align~~: ~~center~~;">A

5:1

4:1

3:1

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>28

<td>1

</td>

<td ~~style="text-align: center;"~~>si

<td>15\46

</td>

<td>~~730~~.~~435~~

<td>391.304

</td>

<td>26/17

<td><a class="wiki_link" href="/Amigo">Amigo</a>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~up 5th~~

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%202s">1L 2s</a> (3-tone)

</td>

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%201s">3L 1s</a> (4-tone)

<~~td style~~="~~text~~-~~align: center~~;">^5

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%204s">3L 4s</a> (7-tone)

</td>

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%207s">3L 7s</a> (10-tone)

<td ~~style="text-align~~: ~~center~~;">A^

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)

</td>

<td>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

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>29

<td>1

</td>

<td ~~style="text-align: center;"~~>lo

<td>17\46

</td>

<td>~~756~~.~~522~~

<td>443.478

</td>

<td>14/~~9, 20~~/~~13, 17~~/11

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Sensi">Sensi</a>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~downminor 6th~~

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%202s">3L 2s</a> (5-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%205s">3L 5s</a> (8-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/8L%203s">8L 3s</a> (11-tone)

8L 11s (19-tone)

19L 8s (27-tone)

</td>

<td ~~style="text-align~~: ~~center~~;">~~vm6~~

<td>12:5

</td>

7:5

<~~td style="text-align: center;"~~>~~Bbv~~

5:2

3:2 ~ QE, Golden

2:1

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>30

<td>1

</td>

<td ~~style="text-align: center;"~~>~~leh~~

<td>19\46

</td>

<td>~~782~~.~~609~~

<td>495.652

</td>

<td>11/7

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Leapday">Leapday</a>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~minor 6th~~

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%203s">2L 3s</a> (5-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%202s">5L 2s</a> (7-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%207s">5L 7s</a> (12-tone)

12L 5s (17-tone)

17L 12s (29-tone)

</td>

<td ~~style="text-align~~: ~~center~~;">m6

<td>11:8

</td>

8:3

<~~td style="text-align: center;"~~>Bb

5:3 ~ Golden

3:2 ~ QE, Golden

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>31

<td>1

</td>

<td ~~style="text-align: center;"~~>le

<td>21\46

</td>

<td>~~808~~.~~696~~

<td>547.826

</td>

<td>8/5

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Heinz">Heinz</a>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~upminor 6th~~

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%203s">2L 3s</a> (5-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%205s">2L 5s</a> (7-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%207s">2L 7s</a> (9-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%209s">2L 9s</a> (11-tone)

11L 2s (13-tone)

11L 13s (24-tone)

11L 24s (35-tone)

</td>

<td ~~style="text-align~~: ~~center~~;">~~^m6~~

<td>17:4

</td>

13:4

<~~td style="text-align~~: ~~center~~;">~~Bb^~~

9:4

5:4 ~ QE

4:1

3:1

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>32

<td>2

</td>

<td ~~style="text-align: center;"~~>lu

<td>1\46

</td>

<td>~~834~~.~~783~~

<td>26.087

</td>

<td>13/8

<td><a class="wiki_link" href="/Ketchup">Ketchup</a>

</td>

<td ~~style="text-align: center;"~~>~~downmid 6th~~

<td>

</td>

<td ~~style="text-align: center;">v~6 ~~

<td>

~~</td>~~

~~<td style="text-align: center;"~~>~~Bb^^~~

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>33

<td>2

</td>

<td ~~style="text-align: center;"~~>~~luh~~

<td>2\46

</td>

<td>~~860~~.87

<td>52.174

</td>

<td>18/~~11, 28~~/17

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Shrutar">Shrutar</a>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~upmid 6th~~

<td>2L 2s (4-tone)

</td>

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6-tone)

<~~td style~~="~~text~~-~~align: center~~;">~~^~6~~

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%206s">2L 6s</a> (8-tone)

</td>

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%208s">2L 8s</a> (10-tone)

<td ~~style="text-align~~: ~~center~~;">~~Bvv~~

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2010s">2L 10s</a> (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)

</td>

<td>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

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>34

<td>2

</td>

<td ~~style="text-align: center;"~~>la

<td>3\46

</td>

<td>~~886~~.~~957~~

<td>78.261

</td>

<td>5/3

<td><a class="wiki_link" href="/Semivalentine">Semivalentine</a>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~downmajor 6th~~

<td>2L 2s (4-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%206s">2L 6s</a> (8-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%208s">2L 8s</a> (10-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2010s">2L 10s</a> (12-tone)

2L 12s (14-tone)

14L 2s (16-tone)

16L 14s (30-tone)

</td>

<td ~~style="text-align~~: ~~center~~;">~~vM6~~

<td>20:3

</td>

17:3

<~~td style="text-align~~: ~~center~~;">Bv

14:3

11:3

8:3

5:3 ~ Golden

3:2 ~ QE, Golden

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>35

<td>2

</td>

<td ~~style="text-align: center;"~~>~~laa~~

<td>4\46

</td>

<td>~~913~~.~~043~~

<td>104.348

</td>

<td>22/~~13, 17~~/10

<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>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~major 6th~~

<td>2L 2s (4-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%206s">2L 6s</a> (8-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%208s">2L 8s</a> (10-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/10L%202s">10L 2s</a> (12-tone)

12L 10s (22-tone)

12L 22s (34-tone)

</td>

<td ~~style="text-align~~: ~~center~~;">M6

<td>19:4

</td>

15:4

<~~td style="text-align~~: ~~center~~;">B

11:4

7:4

4:3 ~ QE

3:1

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>36

<td>2

</td>

<td ~~style="text-align: center;"~~>li

<td>5\46

</td>

<td>~~939~~.13

<td>130.435

</td>

<td>12/7, 26/15*

<td>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~upmajor 6th~~

<td>2L 2s (4-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%206s">2L 6s</a> (8-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/8L%202s">8L 2s</a> (10-tone)

8L 10s (18-tone)

18L 10s (28-tone)

</td>

<td ~~style="text-align~~: ~~center~~;">~~^M6~~

<td>18:5

</td>

13:5

<~~td style="text-align~~: ~~center~~;">B^

8:5 ~ Golden

5:3 ~ Golden

3:2 ~ QE, Golden

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>37

<td>2

</td>

<td ~~style="text-align: center;"~~>ta

<td>6\46

</td>

<td>~~965~~.~~217~~

<td>156.522

</td>

<td>7/~~4, 26~~/15*

<td><a class="wiki_link" href="/Bison">Bison</a>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center;~~">~~downminor 7th~~

<td>2L 2s (4-tone)

</td>

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6-tone)

<~~td style="text~~-~~align: center~~;">~~vm7~~

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%202s">6L 2s</a> (8-tone)

8L 6s (14-tone)

8L 14s (22-tone)

8L 22s (30-tone)

8L 30s (38-tone

</td>

<td ~~style="text-align~~: ~~center~~;">Cv

<td>17:6

11:6

6:5 ~ QE

5:1

4:1

3:1

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>38

<td>2

</td>

<td ~~style="text-align: center;"~~>~~teh~~

<td>7\46

</td>

<td>~~991~~.~~304~~

<td>182.609

</td>

<td>16/~~9, 30~~/17

<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>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~minor 7th~~

<td>2L 2s (4-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%204s">2L 4s</a> (6-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%202s">6L 2s</a> (8-tone)

6L 8s (14-tone)

6L 14s (20-tone)

20L 6s (26-tone)

</td>

<td ~~style="text-align~~: ~~center~~;">m7

<td>16:7

</td>

9:7

<~~td style="text-align~~: ~~center~~;">C

7:2

5:2

3:2 ~ QE, Golden

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>39

<td>2

</td>

<td ~~style="text-align: center;"~~>te

<td>8\46

</td>

<td>~~1017~~.~~391~~

<td>208.696

</td>

<td>9/5

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Abigail">Abigail</a>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~upminor 7th~~

<td>2L 2s (4-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%202s">4L 2s</a> (6-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%202s">6L 2s</a> (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)

</td>

<td ~~style="text-align~~: ~~center~~;">~~^m7~~

<td>15:8

</td>

8:7 ~ QE

<~~td style="text-align~~: ~~center~~;">C^

8:1

7:1

6:1

5:1

4:1

3:1

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>40

<td>2

</td>

<td ~~style="text-align: center;"~~>tu

<td>9\46

</td>

<td>~~1043~~.~~478~~

<td>234.783

</td>

<td>11/~~6, 20~~/11

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Echidnic">Echidnic</a>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~downmid 7th~~

<td>2L 2s (4-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%202s">4L 2s</a> (6-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%204s">6L 4s</a> (10-tone)

10L 6s (16-tone)

10L 16s (26-tone)

10L 26s (36-tone)

</td>

<td ~~style="text-align~~: ~~center~~;">~~v~7~~

<td>14:9

</td>

9:5

<~~td style="text-align~~: ~~center~~;">~~C^^~~

5:4 ~ QE

4:1

3:1

2:1 ~ QE

</td>

</tr>

<tr>

<td ~~style="text-align: center;"~~>41

<td>2

</td>

<td ~~style="text-align: center;"~~>~~tuh~~

<td>10\46

</td>

<td>~~1069~~.~~565~~

<td>260.87

</td>

<td>24/~~13, 13~~/~~7, 28/15~~

<td><a class="wiki_link" href="/Bamity">Bamity</a>

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~upmid 7th~~

<td>2L 2s (4-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%202s">4L 2s</a> (6-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%206s">4L 6s</a> (10-tone)

4L 10s (14-tone)

14L 4s (18-tone)

14L 18s (32-tone)

</td>

<td ~~style="text-align~~: ~~center~~;">^~7

<td>13:10

10:3

7:3

4:3 ~ QE

3:1

2:1 ~ QE

</td>

<td ~~style~~="~~text~~-~~align~~: ~~center~~;">~~C#vv~~

</tr>

<tr>

<td>2

</td>

<td>11\46

</td>

<td>286.957

</td>

<td><a class="wiki_link" href="/Vines">Vines</a>

</td>

<td>2L 2s (4-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%202s">4L 2s</a> (6-tone)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%206s">4L 6s</a> (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)

</td>

<td>12:11 ~ QE

11:1

10:1

9:1

8:1

7:1

6:1

5:1

4:1

3:1

2:1 ~ QE

</td>

</tr>

<tr>

<td>23

</td>

<td>1\46

</td>

~~</tr>~~

<td>26.087

~~<tr>~~

~~<td style="text-align: center;">42 ~~

~~</td>~~

~~<td style="text-align: center;">ti ~~

~~</td>~~

~~<td>1095.652 ~~

~~</td>~~

~~<td>15/8, 32/17, 17/9 ~~

~~</td>~~

~~<td style="text-align: center;">downmajor 7th ~~

~~</td>~~

~~<td style="text-align: center;">vM7 ~~

~~</td>~~

~~<td style="text-align: center;">C#v ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td style="text-align: center;">43 ~~

~~</td>~~

~~<td style="text-align: center;">taa ~~

~~</td>~~

<td>~~1121~~.~~739~~

</td>

<td>

~~</td>~~

~~<td style="text-align: center;">major 7th ~~

~~</td>~~

~~<td style="text-align: center;">M7 ~~

~~</td>~~

~~<td style="text-align: center;">C# ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td style="text-align: center;">44 ~~

~~</td>~~

~~<td style="text-align: center;">to ~~

~~</td>~~

~~<td>1147.826 ~~

</td>

<td>

~~</td>~~

~~<td style="text-align: center;">upmajor 7th ~~

~~</td>~~

~~<td style="text-align: center;">^M7 ~~

~~</td>~~

~~<td style="text-align: center;">C#^ ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td style="text-align: center;">45 ~~

~~</td>~~

~~<td style="text-align: center;">da ~~

~~</td>~~

~~<td>1173.913 ~~

</td>

<td>

~~</td>~~

~~<td style="text-align: center;">down 8ve ~~

~~</td>~~

~~<td style="text-align: center;">v8 ~~

~~</td>~~

~~<td style="text-align: center;">Dv ~~

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td style="text-align: center;">46 ~~

~~</td>~~

~~<td style="text-align: center;">do ~~

~~</td>~~

~~<td>1200 ~~

~~</td>~~

~~<td>2/1 ~~

~~</td>~~

~~<td style="text-align: center;">perfect 8ve ~~

~~</td>~~

~~<td style="text-align: center;">P8 ~~

~~</td>~~

~~<td style="text-align: center;">D ~~

</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>.

~~ ~~

~~All 46edo chords can be named using ups and downs: ~~

~~0-10-27 = C Ebv G = C.vm = &quot;C downminor&quot; ~~

~~0-12-27 = C Eb^ G = C.^m = &quot;C upminor&quot; ~~

~~0-14-27 = C Evv G = C.^~ = &quot;C upmid&quot; ~~

~~0-16-27 = C E G = &quot;C major&quot; or &quot;C&quot; ~~

~~0-17-27 = C E^ G = C.^= &quot;C upmajor&quot; or &quot;C dot up&quot; ~~

~~etc. ~~

~~ ~~

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>.

<h1 id="toc4"><a name="Approximation to Mode 8 of the Harmonic Series"></a>Approximation to Mode 8 of the Harmonic Series</h1>

@@ 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 04:18:08 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 16:30:56 UTC</tt>.<br>
-: The original revision id was <tt>621435931</tt>.<br>
+: The original revision id was <tt>621457975</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 21: / Line 21: @@
 [[xenharmonic/Magic22 as srutis#shrutar22assrutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[xenharmonic/Indian|Indian]] music.
-=Linear temperaments=
+=Intervals=
-||~ Periods
+||~ degrees of 46edo ||~ solfege ||~ cents value ||~ approximate ratios
-per octave ||~ Generator ||~ Cents ||~ Temperaments ||~ MOS/DE Scales available ||~ L:s ||
+in the [[xenharmonic/17-limit|17-limit]] ||||||~ [[Ups and Downs Notation|ups and downs notation]] ||
-|| 1 || 1\46 || 26.087 ||   ||   ||   ||
+||= 0 ||= do || 0.00 || 1/1 ||= perfect unison ||= P1 ||= D ||
-|| 1 || 3\46 || 78.261 || [[xenharmonic/Valentine|Valentine]] || 1L 14s (15-tone)
+||= 1 ||= di || 26.087 ||   ||= up unison ||= ^1 ||= D^ ||
-L 1s (16-tone)
+||= 2 ||= ro || 52.174 ||   ||= downminor 2nd ||= vm2 ||= Ebv ||
-L 15s (31-tone) || 4:3 ~ [[xenharmonic/Maximal evenness|quasi-equal]]
+||= 3 ||= rih || 78.261 ||   ||= minor 2nd ||= m2 ||= Eb ||
-:1
+||= 4 ||= ra || 104.348 || 16/15, 17/16, 18/17 ||= upminor 2nd ||= ^m2 ||= Eb^ ||
-:1 ~ QE ||
+||= 5 ||= ru (as in supraminor) || 130.435 || 13/12, 14/13, 15/14 ||= downmid 2nd ||= v~2 ||= Eb^^ ||
-|| 1 || 5\46 || 130.435 || [[xenharmonic/Twothirdtonic|Twothirdtonic]] || [[xenharmonic/1L 8s|1L 8s]] (9-tone)
+||= 6 ||= ruh (as in submajor) || 156.522 || 12/11, 11/10 ||= upmid 2nd ||= ^~2 ||= Evv ||
-[[xenharmonic/9L 1s|9L 1s]] (10-tone)
+||= 7 ||= reh || 182.609 || 10/9 ||= downmajor 2nd ||= vM2 ||= Ev ||
-L 10s (19-tone)
+||= 8 ||= re || 208.696 || 9/8, 17/15 ||= major 2nd ||= M2 ||= E ||
-L 19s (28-tone)
+||= 9 ||= ri || 234.783 || 8/7, 15/13* ||= upmajor 2nd ||= ^M2 ||= E^ ||
-L 28s (37-tone) || 6:5 ~ QE
+||= 10 ||= ma || 260.87 || 7/6, 15/13* ||= downminor 3rd ||= vm3 ||= Fv ||
-:1
+||= 11 ||= meh || 286.957 || 13/11, 20/17 ||= minor 3rd ||= m3 ||= F ||
-:1
+||= 12 ||= me || 313.043 || 6/5 ||= upminor 3rd ||= ^m3 ||= F^ ||
-:1
+||= 13 ||= mu || 339.13 || 11/9, 17/14 ||= downmid 3rd ||= v~3 ||= F^^ ||
-:1 ~ QE ||
+||= 14 ||= muh || 365.217 || 16/13 ||= upmid 3rd ||= ^~3 ||= F#vv ||
-|| 1 || 7\46 || 182.609 || [[xenharmonic/Minortone|Minortone]] || [[xenharmonic/1L 5s|1L 5s]] (6-tone)
+||= 15 ||= mi || 391.304 || 5/4 ||= downmajor 3rd ||= vM3 ||= F#v ||
-[[xenharmonic/6L 1s|6L 1s]] (7-tone)
+||= 16 ||= maa || 417.391 || 14/11 ||= major 3rd ||= M3 ||= F# ||
-L 6s (13-tone)
+||= 17 ||= mo || 443.478 || 9/7, 13/10, 22/17 ||= upmajor 3rd ||= ^M3 ||= F#^ ||
-L 7s (20-tone)
+||= 18 ||= fe || 469.565 || 17/13 ||= down 4th ||= v4 ||= Gv ||
-L 20s (33-tone) || 11:7
+||= 19 ||= fa || 495.652 || 4/3 ||= perfect 4th ||= P4 ||= G ||
-:4
+||= 20 ||= fih || 521.739 ||   ||= up 4th ||= ^4 ||= G^ ||
-:3 ~ QE
+||= 21 ||= fu || 547.826 || 11/8, 15/11 ||= double-up 4th ||= ^^4 ||= G^^ ||
-:1
+||= 22 ||= fi || 573.913 || 7/5, 18/13 ||= double-down aug 4th,
-:1 ~ QE ||
+dim 5th ||= vvA4, d5 ||= G#vv, Ab ||
-|| 1 || 9\46 || 234.783 || [[xenharmonic/Rodan|Rodan]] || [[xenharmonic/1L 4s|1L 4s]] (5-tone)
+||= 23 ||= seh || 600 || 17/12, 24/17 ||= downaug 4th, updim 5th ||= vA4, ^d5 ||= G#v, Ab^ ||
-[[xenharmonic/1L 5s|1L 5s]] (6-tone)
+||= 24 ||= se || 626.087 || 10/7, 13/9 ||= aug 4th, double-up dim 5th ||= A4, ^^d5 ||= G#, Ab^^ ||
-[[xenharmonic/5L 6s|5L 6s]] (11-tone)
+||= 25 ||= su || 652.174 || 16/11, 22/15 ||= double-down 5th ||= vv5 ||= Avv ||
-L 11s (16-tone)
+||= 26 ||= sih || 678.261 ||   ||= down 5th ||= v5 ||= Av ||
-L 16s (21-tone)
+||= 27 ||= sol || 704.348 || 3/2 ||= perfect 5th ||= P5 ||= A ||
-L 21s (26-tone)
+||= 28 ||= si || 730.435 || 26/17 ||= up 5th ||= ^5 ||= A^ ||
-L 26s (31-tone)
+||= 29 ||= lo || 756.522 || 14/9, 20/13, 17/11 ||= downminor 6th ||= vm6 ||= Bbv ||
-L 31s (36-tone)
+||= 30 ||= leh || 782.609 || 11/7 ||= minor 6th ||= m6 ||= Bb ||
-L 36s (41-tone) || 10:9 ~QE
+||= 31 ||= le || 808.696 || 8/5 ||= upminor 6th ||= ^m6 ||= Bb^ ||
-:1
+||= 32 ||= lu || 834.783 || 13/8 ||= downmid 6th ||= v~6 ||= Bb^^ ||
-:1
+||= 33 ||= luh || 860.87 || 18/11, 28/17 ||= upmid 6th ||= ^~6 ||= Bvv ||
-:1
+||= 34 ||= la || 886.957 || 5/3 ||= downmajor 6th ||= vM6 ||= Bv ||
-:1
+||= 35 ||= laa || 913.043 || 22/13, 17/10 ||= major 6th ||= M6 ||= B ||
-:1
+||= 36 ||= li || 939.13 || 12/7, 26/15* ||= upmajor 6th ||= ^M6 ||= B^ ||
-:1
+||= 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]].
+All 46edo chords can be named using ups and downs:
+-10-27 = C Ebv G = C.vm = "C downminor"
+-12-27 = C Eb^ G = C.^m = "C upminor"
+-14-27 = C Evv G = C.^~ = "C upmid"
+-16-27 = C E G = "C major" or "C"
+-17-27 = C E^ G = C.^= "C upmajor" or "C dot up"
+etc.
+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)
+L 1s (16-tone)
+L 15s (31-tone) || 4:3 ~ [[xenharmonic/Maximal evenness|quasi-equal]]
 :1
 :1 ~ QE ||
-|| 1 || 11\46 || 286.957 ||   || [[xenharmonic/4L 1s|4L 1s]] (5-tone)
+|| 1 || 5\46 || 130.435 || [[xenharmonic/Twothirdtonic|Twothirdtonic]] || [[xenharmonic/1L 8s|1L 8s]] (9-tone)
-[[xenharmonic/4L 5s|4L 5s]] (9-tone)
+[[xenharmonic/9L 1s|9L 1s]] (10-tone)
-L 9s (13-tone)
+L 10s (19-tone)
-L 13s (17-tone)
+L 19s (28-tone)
-L 17s (21-tone)
+L 28s (37-tone) || 6:5 ~ QE
-L 4s (25-tone) || 11:2
-:2
-:2
-:2
-:2 ~ QE, Golden
-: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)
-L 11s (18-tone)
-L 18s (25-tone)
-L 25s (32-tone)
-L 32s (39-tone) || 7:6 ~ QE
-:1
 :1
 :1
 :1
 :1 ~ QE ||
-|| 1 || 15\46 || 391.304 || [[Amigo]] || [[xenharmonic/1L 2s|1L 2s]] (3-tone)
+|| 1 || 7\46 || 182.609 || [[xenharmonic/Minortone|Minortone]] || [[xenharmonic/1L 5s|1L 5s]] (6-tone)
-[[xenharmonic/3L 1s|3L 1s]] (4-tone)
+[[xenharmonic/6L 1s|6L 1s]] (7-tone)
-[[xenharmonic/3L 4s|3L 4s]] (7-tone)
+L 6s (13-tone)
-[[xenharmonic/3L 7s|3L 7s]] (10-tone)
+L 7s (20-tone)
-L 10s (13-tone)
+L 20s (33-tone) || 11:7
-L 13s (16-tone)
+:4
-L 16s (19-tone)
+:3 ~ QE
-L 19s (21-tone)
+:1
-L 21s (24-tone)
+:1 ~ QE ||
-L 24s (27-tone)
+|| 1 || 9\46 || 234.783 || [[xenharmonic/Rodan|Rodan]] || [[xenharmonic/1L 4s|1L 4s]] (5-tone)
-L 27s (30-tone)
+[[xenharmonic/1L 5s|1L 5s]] (6-tone)
-L 30s (33-tone)
+[[xenharmonic/5L 6s|5L 6s]] (11-tone)
-L 33s (36-tone)
+L 11s (16-tone)
-L 36s (39-tone)
+L 16s (21-tone)
-L 39s (42-tone) || 16:15 ~ QE
+L 21s (26-tone)
-:1
+L 26s (31-tone)
-:1
+L 31s (36-tone)
-:1
+L 36s (41-tone) || 10:9 ~QE
-:1
-:1
-:1
 :1
 :1
@@ Line 116: / Line 128: @@
 :1
 :1 ~ QE ||
-|| 1 || 17\46 || 443.478 || [[xenharmonic/Sensi|Sensi]] || [[xenharmonic/3L 2s|3L 2s]] (5-tone)
+|| 1 || 11\46 || 286.957 ||   || [[xenharmonic/4L 1s|4L 1s]] (5-tone)
-[[xenharmonic/3L 5s|3L 5s]] (8-tone)
+[[xenharmonic/4L 5s|4L 5s]] (9-tone)
-[[xenharmonic/8L 3s|8L 3s]] (11-tone)
+L 9s (13-tone)
-L 11s (19-tone)
+L 13s (17-tone)
-L 8s (27-tone) || 12:5
+L 17s (21-tone)
-:5
+L 4s (25-tone) || 11:2
+:2
+:2
 :2
 :2 ~ QE, Golden
-:1 ||
+:1 ~ QE ||
-|| 1 || 19\46 || 495.652 || [[xenharmonic/Leapday|Leapday]] || [[xenharmonic/2L 3s|2L 3s]] (5-tone)
+|| 1 || 13\46 || 339.13 || [[xenharmonic/Amity|Amity]]/[[xenharmonic/hitchcock|hitchcock]] || [[xenharmonic/4L 3s|4L 3s]] (7-tone)
-[[xenharmonic/5L 2s|5L 2s]] (7-tone)
+[[xenharmonic/7L 4s|7L 4s]] (11-tone)
-[[xenharmonic/5L 7s|5L 7s]] (12-tone)
+L 11s (18-tone)
-L 5s (17-tone)
+L 18s (25-tone)
-L 12s (29-tone) || 11:8
+L 25s (32-tone)
-:3
+L 32s (39-tone) || 7:6 ~ QE
-:3 ~ Golden
+:1
-:2 ~ QE, Golden
+:1
-: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)
-L 2s (13-tone)
-L 13s (24-tone)
-L 24s (35-tone) || 17:4
-:4
-:4
-:4 ~ QE
 :1
 :1
 :1 ~ QE ||
-|| 2 || 1\46 || 26.087 || [[Ketchup]] ||   ||   ||
+|| 1 || 15\46 || 391.304 || [[Amigo]] || [[xenharmonic/1L 2s|1L 2s]] (3-tone)
-|| 2 || 2\46 || 52.174 || [[xenharmonic/Shrutar|Shrutar]] || 2L 2s (4-tone)
+[[xenharmonic/3L 1s|3L 1s]] (4-tone)
-[[xenharmonic/2L 4s|2L 4s]] (6-tone)
+[[xenharmonic/3L 4s|3L 4s]] (7-tone)
-[[xenharmonic/2L 6s|2L 6s]] (8-tone)
+[[xenharmonic/3L 7s|3L 7s]] (10-tone)
-[[xenharmonic/2L 8s|2L 8s]] (10-tone)
+L 10s (13-tone)
-[[xenharmonic/2L 10s|2L 10s]] (12-tone)
+L 13s (16-tone)
-L 12s (14-tone)
+L 16s (19-tone)
-L 14s (16-tone)
+L 19s (21-tone)
-L 16s (18-tone)
+L 21s (24-tone)
-L 18s (20-tone)
+L 24s (27-tone)
-L 20s (22-tone)
+L 27s (30-tone)
-L 2s (24-tone) || 21:2
+L 30s (33-tone)
-:2
+L 33s (36-tone)
-:2
+L 36s (39-tone)
-:2
+L 39s (42-tone) || 16:15 ~ QE
-:2
+:1
-:2
+:1
-:2
+:1
-:2
+:1
+:1
+:1
+:1
+:1
+:1
+:1
+:1
+:1
+:1
+: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)
+L 11s (19-tone)
+L 8s (27-tone) || 12:5
+:5
 :2
+:2 ~ QE, Golden
+: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)
+L 5s (17-tone)
+L 12s (29-tone) || 11:8
+:3
+:3 ~ Golden
 :2 ~ QE, Golden
 :1 ~ QE ||
-|| 2 || 3\46 || 78.261 || [[Semivalentine]] || 2L 2s (4-tone)
+|| 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)
+L 2s (13-tone)
+L 13s (24-tone)
+L 24s (35-tone) || 17:4
+:4
+:4
+:4 ~ QE
+:1
+:1
+: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)
@@ Line 175: / Line 217: @@
 [[xenharmonic/2L 10s|2L 10s]] (12-tone)
 L 12s (14-tone)
-L 2s (16-tone)
+L 14s (16-tone)
-L 14s (30-tone) || 20:3
+L 16s (18-tone)
-:3
+L 18s (20-tone)
-:3
+L 20s (22-tone)
-:3
+L 2s (24-tone) || 21:2
-:3
+:2
+:2
+:2
+:2
+:2
+:2
+:2
+:2
+:2 ~ QE, Golden
+: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)
+L 12s (14-tone)
+L 2s (16-tone)
+L 14s (30-tone) || 20:3
+:3
+:3
+:3
+:3
 :3 ~ Golden
 :2 ~ QE, Golden
@@ Line 293: / Line 356: @@
 :1 ~ QE ||
 || 23 || 1\46 || 26.087 ||   ||   ||   ||
-=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]].
-All 46edo chords can be named using ups and downs:
+=Approximation to Mode 8 of the Harmonic Series=
--10-27 = C Ebv G = C.vm = "C downminor"
--12-27 = C Eb^ G = C.^m = "C upminor"
+edo 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.
--14-27 = C Evv G = C.^~ = "C upmid"
--16-27 = C E G = "C major" or "C"
+\46edo (208.70¢) stands in for frequency ratio [[xenharmonic/9_8|9:8]] (203.91¢).
--17-27 = C E^ G = C.^= "C upmajor" or "C dot up"
+\46edo (182.61¢) stands in for [[xenharmonic/10_9|10:9]] (182.40¢).
-etc.
+\46edo (156.52¢) stands in for [[xenharmonic/11_10|11:10]] (165.00¢) and [[xenharmonic/12_11|12:11]] (150.64¢).
+\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¢).
-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]].
+\46edo (104.35¢) stands in for [[xenharmonic/16_15|16:15]] (111.73¢).
-=Approximation to Mode 8 of the Harmonic Series=
+=Scales=
+* [[xenharmonic/plum|plum]]
-edo 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.
+* [[xenharmonic/sensi5|sensi5]]
+* [[xenharmonic/sensi8|sensi8]]
-\46edo (208.70¢) stands in for frequency ratio [[xenharmonic/9_8|9:8]] (203.91¢).
+* [[xenharmonic/sensi11|sensi11]]
-\46edo (182.61¢) stands in for [[xenharmonic/10_9|10:9]] (182.40¢).
+* [[xenharmonic/sensi19|sensi19]]
-\46edo (156.52¢) stands in for [[xenharmonic/11_10|11:10]] (165.00¢) and [[xenharmonic/12_11|12:11]] (150.64¢).
-\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¢).
+=Music=
-\46edo (104.35¢) stands in for [[xenharmonic/16_15|16:15]] (111.73¢).
+by [[xenharmonic/Aaron Krister Johnson|Aaron Krister Johnson:]]
+[[http://aaronkristerjohnson.bandcamp.com/track/satiesque|Satiesque]]
-=Scales=
-* [[xenharmonic/plum|plum]]
+by [[xenharmonic/Gene Ward Smith|Gene Ward Smith:]]
-* [[xenharmonic/sensi5|sensi5]]
+[[http://www.archive.org/details/Chromosounds|Chromosounds]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3|play]]
-* [[xenharmonic/sensi8|sensi8]]
+[[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.
-* [[xenharmonic/sensi11|sensi11]]
-* [[xenharmonic/sensi19|sensi19]]
+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
-=Music=
+[[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Bach_Contrapunctus_4-Jeux14-E46.mp3|Bach Contrapunctus 4]] Claudi Meneghin version
-by [[xenharmonic/Aaron Krister Johnson|Aaron Krister Johnson:]]
+[[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]]</pre></div>
-[[http://aaronkristerjohnson.bandcamp.com/track/satiesque|Satiesque]]
+<h4>Original HTML content:</h4>
+<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="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Linear temperaments"&gt;Linear temperaments&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;
-by [[xenharmonic/Gene Ward Smith|Gene Ward Smith:]]
+&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;hr /&gt;
-[[http://www.archive.org/details/Chromosounds|Chromosounds]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3|play]]
+&lt;br /&gt;
-[[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.
+&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;
-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]]
+&lt;br /&gt;
-[[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
+et 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;
-[[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Bach_Contrapunctus_4-Jeux14-E46.mp3|Bach Contrapunctus 4]] Claudi Meneghin version
+&lt;br /&gt;
-[[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]]</pre></div>
+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;
-<h4>Original HTML content:</h4>
+&lt;br /&gt;
-<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;
+edo 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;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;hr /&gt;
+&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;!-- 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;
+  &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;
-  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;
-&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals&lt;/h1&gt;
-et 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;table class="wiki_table"&gt;
-&lt;br /&gt;
+    &lt;tr&gt;
-edo 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;th&gt;degrees of 46edo&lt;br /&gt;
-&lt;br /&gt;
+&lt;/th&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;th&gt;solfege&lt;br /&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;/th&gt;
-&lt;br /&gt;
+        &lt;th&gt;cents value&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;/th&gt;
+        &lt;th&gt;approximate ratios&lt;br /&gt;
+in the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/17-limit"&gt;17-limit&lt;/a&gt;&lt;br /&gt;
-&lt;table class="wiki_table"&gt;
+&lt;/th&gt;
+        &lt;th colspan="3"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;ups and downs notation&lt;/a&gt;&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;do&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;td style="text-align: center;"&gt;perfect unison&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;di&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 style="text-align: center;"&gt;up unison&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D^&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;th&gt;Periods&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
-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 style="text-align: center;"&gt;ro&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;26.087&lt;br /&gt;
+         &lt;td&gt;52.174&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;downminor 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;vm2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Ebv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3\46&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;rih&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;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1L 14s (15-tone)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;m2&lt;br /&gt;
-L 1s (16-tone)&lt;br /&gt;
-L 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;
+         &lt;td style="text-align: center;"&gt;Eb&lt;br /&gt;
-:1&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5\46&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;ra&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;130.435&lt;br /&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/Twothirdtonic"&gt;Twothirdtonic&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;16/15, 17/16, 18/17&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;td style="text-align: center;"&gt;upminor 2nd&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;
-L 10s (19-tone)&lt;br /&gt;
-L 19s (28-tone)&lt;br /&gt;
-L 28s (37-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;6:5 ~ QE&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^m2&lt;br /&gt;
-:1&lt;br /&gt;
+&lt;/td&gt;
-:1&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;Eb^&lt;br /&gt;
-:1&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7\46&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;ru (as in supraminor)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;182.609&lt;br /&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/Minortone"&gt;Minortone&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;13/12, 14/13, 15/14&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;td style="text-align: center;"&gt;downmid 2nd&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;
-L 6s (13-tone)&lt;br /&gt;
-L 7s (20-tone)&lt;br /&gt;
-L 20s (33-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11:7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v~2&lt;br /&gt;
-:4&lt;br /&gt;
+&lt;/td&gt;
-:3 ~ QE&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;Eb^^&lt;br /&gt;
-:1&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;ruh (as in submajor)&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;156.522&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9\46&lt;br /&gt;
+         &lt;td&gt;12/11, 11/10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;234.783&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;upmid 2nd&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 style="text-align: center;"&gt;^~2&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;td style="text-align: center;"&gt;Evv&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;
-L 11s (16-tone)&lt;br /&gt;
-L 16s (21-tone)&lt;br /&gt;
-L 21s (26-tone)&lt;br /&gt;
-L 26s (31-tone)&lt;br /&gt;
-L 31s (36-tone)&lt;br /&gt;
-L 36s (41-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;10:9 ~QE&lt;br /&gt;
+    &lt;/tr&gt;
-:1&lt;br /&gt;
+    &lt;tr&gt;
-:1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
-:1&lt;br /&gt;
+&lt;/td&gt;
-:1&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;reh&lt;br /&gt;
-:1&lt;br /&gt;
+&lt;/td&gt;
-:1&lt;br /&gt;
+        &lt;td&gt;182.609&lt;br /&gt;
-:1&lt;br /&gt;
+&lt;/td&gt;
-:1 ~ QE&lt;br /&gt;
+        &lt;td&gt;10/9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmajor 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;vM2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Ev&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11\46&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;re&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;286.957&lt;br /&gt;
+         &lt;td&gt;208.696&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;9/8, 17/15&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;td style="text-align: center;"&gt;major 2nd&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;
+&lt;/td&gt;
-L 9s (13-tone)&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;M2&lt;br /&gt;
-L 13s (17-tone)&lt;br /&gt;
-L 17s (21-tone)&lt;br /&gt;
-L 4s (25-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11:2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
-:2&lt;br /&gt;
-:2&lt;br /&gt;
-:2&lt;br /&gt;
-:2 ~ QE, Golden&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;ri&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;13\46&lt;br /&gt;
+         &lt;td&gt;234.783&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;339.13&lt;br /&gt;
+         &lt;td&gt;8/7, 15/13*&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 style="text-align: center;"&gt;upmajor 2nd&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;td style="text-align: center;"&gt;^M2&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;
-L 11s (18-tone)&lt;br /&gt;
-L 18s (25-tone)&lt;br /&gt;
-L 25s (32-tone)&lt;br /&gt;
-L 32s (39-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7:6 ~ QE&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;E^&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;ma&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;260.87&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;15\46&lt;br /&gt;
+         &lt;td&gt;7/6, 15/13*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;391.304&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;downminor 3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/Amigo"&gt;Amigo&lt;/a&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vm3&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;td style="text-align: center;"&gt;Fv&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;
-L 10s (13-tone)&lt;br /&gt;
-L 13s (16-tone)&lt;br /&gt;
-L 16s (19-tone)&lt;br /&gt;
-L 19s (21-tone)&lt;br /&gt;
-L 21s (24-tone)&lt;br /&gt;
-L 24s (27-tone)&lt;br /&gt;
-L 27s (30-tone)&lt;br /&gt;
-L 30s (33-tone)&lt;br /&gt;
-L 33s (36-tone)&lt;br /&gt;
-L 36s (39-tone)&lt;br /&gt;
-L 39s (42-tone)&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;16:15 ~ QE&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;meh&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;17\46&lt;br /&gt;
+         &lt;td&gt;286.957&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;443.478&lt;br /&gt;
+         &lt;td&gt;13/11, 20/17&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 style="text-align: center;"&gt;minor 3rd&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;td style="text-align: center;"&gt;m3&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;
-L 11s (19-tone)&lt;br /&gt;
-L 8s (27-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;12:5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
-:5&lt;br /&gt;
-:2&lt;br /&gt;
-:2 ~ QE, Golden&lt;br /&gt;
-:1&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;19\46&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;me&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;495.652&lt;br /&gt;
+         &lt;td&gt;313.043&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;6/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upminor 3rd&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;td style="text-align: center;"&gt;^m3&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;
-L 5s (17-tone)&lt;br /&gt;
-L 12s (29-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11:8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F^&lt;br /&gt;
-:3&lt;br /&gt;
-:3 ~ Golden&lt;br /&gt;
-:2 ~ QE, Golden&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;mu&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;21\46&lt;br /&gt;
+         &lt;td&gt;339.13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;547.826&lt;br /&gt;
+         &lt;td&gt;11/9, 17/14&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 style="text-align: center;"&gt;downmid 3rd&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;td style="text-align: center;"&gt;v~3&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;
-L 2s (13-tone)&lt;br /&gt;
-L 13s (24-tone)&lt;br /&gt;
-L 24s (35-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;17:4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F^^&lt;br /&gt;
-:4&lt;br /&gt;
-:4&lt;br /&gt;
-:4 ~ QE&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;muh&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1\46&lt;br /&gt;
+         &lt;td&gt;365.217&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;26.087&lt;br /&gt;
+         &lt;td&gt;16/13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/Ketchup"&gt;Ketchup&lt;/a&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;upmid 3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^~3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F#vv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;mi&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;391.304&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2\46&lt;br /&gt;
+         &lt;td&gt;5/4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;52.174&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;downmajor 3rd&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 style="text-align: center;"&gt;vM3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F#v&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;
-L 12s (14-tone)&lt;br /&gt;
-L 14s (16-tone)&lt;br /&gt;
-L 16s (18-tone)&lt;br /&gt;
-L 18s (20-tone)&lt;br /&gt;
-L 20s (22-tone)&lt;br /&gt;
-L 2s (24-tone)&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td&gt;21:2&lt;br /&gt;
+    &lt;/tr&gt;
-:2&lt;br /&gt;
+    &lt;tr&gt;
-:2&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
-:2&lt;br /&gt;
-:2&lt;br /&gt;
-:2&lt;br /&gt;
-:2&lt;br /&gt;
-:2&lt;br /&gt;
-:2&lt;br /&gt;
-:2 ~ QE, Golden&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
-    &lt;/tr&gt;
+         &lt;td style="text-align: center;"&gt;maa&lt;br /&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;417.391&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;78.261&lt;br /&gt;
+         &lt;td&gt;14/11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/Semivalentine"&gt;Semivalentine&lt;/a&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;major 3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M3&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;
-L 12s (14-tone)&lt;br /&gt;
-L 2s (16-tone)&lt;br /&gt;
-L 14s (30-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;20:3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F#&lt;br /&gt;
-:3&lt;br /&gt;
-:3&lt;br /&gt;
-:3&lt;br /&gt;
-:3&lt;br /&gt;
-:3 ~ Golden&lt;br /&gt;
-:2 ~ QE, Golden&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;mo&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;4\46&lt;br /&gt;
+         &lt;td&gt;443.478&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;104.348&lt;br /&gt;
+         &lt;td&gt;9/7, 13/10, 22/17&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 style="text-align: center;"&gt;upmajor 3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^M3&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;
-L 10s (22-tone)&lt;br /&gt;
-L 22s (34-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;19:4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F#^&lt;br /&gt;
-:4&lt;br /&gt;
-:4&lt;br /&gt;
-:4&lt;br /&gt;
-:3 ~ QE&lt;br /&gt;
-:1&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;fe&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5\46&lt;br /&gt;
+         &lt;td&gt;469.565&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;130.435&lt;br /&gt;
+         &lt;td&gt;17/13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;down 4th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v4&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;
-L 10s (18-tone)&lt;br /&gt;
-L 10s (28-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;18:5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Gv&lt;br /&gt;
-:5&lt;br /&gt;
-:5 ~ Golden&lt;br /&gt;
-:3 ~ Golden&lt;br /&gt;
-:2 ~ QE, Golden&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;6\46&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;fa&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;156.522&lt;br /&gt;
+         &lt;td&gt;495.652&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/Bison"&gt;Bison&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;4/3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;perfect 4th&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;
-L 6s (14-tone)&lt;br /&gt;
-L 14s (22-tone)&lt;br /&gt;
-L 22s (30-tone)&lt;br /&gt;
-L 30s (38-tone&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;17:6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P4&lt;br /&gt;
-:6&lt;br /&gt;
+&lt;/td&gt;
-:5 ~ QE&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;fih&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7\46&lt;br /&gt;
+         &lt;td&gt;521.739&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;182.609&lt;br /&gt;
+         &lt;td&gt;&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 style="text-align: center;"&gt;up 4th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^4&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;
-L 8s (14-tone)&lt;br /&gt;
-L 14s (20-tone)&lt;br /&gt;
-L 6s (26-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16:7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G^&lt;br /&gt;
-:7&lt;br /&gt;
-:2&lt;br /&gt;
-:2&lt;br /&gt;
-:2 ~ QE, Golden&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;8\46&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;fu&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;547.826&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;208.696&lt;br /&gt;
+         &lt;td&gt;11/8, 15/11&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 style="text-align: center;"&gt;double-up 4th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^^4&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;
-L 8s (14-tone)&lt;br /&gt;
-L 14s (20-tone)&lt;br /&gt;
-L 20s (26-tone)&lt;br /&gt;
-L 26s (32-tone)&lt;br /&gt;
-L 32s (38-tone)&lt;br /&gt;
-L 38s (44-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;15:8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G^^&lt;br /&gt;
-:7 ~ QE&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;22&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;fi&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9\46&lt;br /&gt;
+         &lt;td&gt;573.913&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;234.783&lt;br /&gt;
+         &lt;td&gt;7/5, 18/13&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 style="text-align: center;"&gt;double-down aug 4th,&lt;br /&gt;
+dim 5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vvA4, d5&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;
-L 6s (16-tone)&lt;br /&gt;
-L 16s (26-tone)&lt;br /&gt;
-L 26s (36-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;14:9&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G#vv, Ab&lt;br /&gt;
-:5&lt;br /&gt;
-:4 ~ QE&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;10\46&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;seh&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;260.87&lt;br /&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;td&gt;&lt;a class="wiki_link" href="/Bamity"&gt;Bamity&lt;/a&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;downaug 4th, updim 5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vA4, ^d5&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;
-L 10s (14-tone)&lt;br /&gt;
-L 4s (18-tone)&lt;br /&gt;
-L 18s (32-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;13:10&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G#v, Ab^&lt;br /&gt;
-:3&lt;br /&gt;
-:3&lt;br /&gt;
-:3 ~ QE&lt;br /&gt;
-:1&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11\46&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;se&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;286.957&lt;br /&gt;
+         &lt;td&gt;626.087&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/Vines"&gt;Vines&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;10/7, 13/9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;aug 4th, double-up dim 5th&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;/td&gt;
-&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%206s"&gt;4L 6s&lt;/a&gt; (10-tone)&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;A4, ^^d5&lt;br /&gt;
-L 10s (14-tone)&lt;br /&gt;
-L 14s (18-tone)&lt;br /&gt;
-L 18s (22-tone)&lt;br /&gt;
-L 22s (26-tone)&lt;br /&gt;
-L 26s (30-tone)&lt;br /&gt;
-L 30s (34-tone)&lt;br /&gt;
-L 34s (38-tone)&lt;br /&gt;
-L 38s (42-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;12:11 ~ QE&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G#, Ab^^&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1&lt;br /&gt;
-:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;23&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1\46&lt;br /&gt;
+        &lt;td style="text-align: center;"&gt;su&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;652.174&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;26.087&lt;br /&gt;
+         &lt;td&gt;16/11, 22/15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-down 5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vv5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Avv&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;
-&lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;th&gt;degrees of 46edo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;26&lt;br /&gt;
-&lt;/th&gt;
+&lt;/td&gt;
-         &lt;th&gt;solfege&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;sih&lt;br /&gt;
-&lt;/th&gt;
+&lt;/td&gt;
-         &lt;th&gt;cents value&lt;br /&gt;
+         &lt;td&gt;678.261&lt;br /&gt;
-&lt;/th&gt;
+&lt;/td&gt;
-         &lt;th&gt;approximate ratios&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
-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;/th&gt;
+        &lt;td style="text-align: center;"&gt;down 5th&lt;br /&gt;
-         &lt;th colspan="3"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;ups and downs notation&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
-&lt;/th&gt;
+         &lt;td style="text-align: center;"&gt;v5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Av&lt;br /&gt;
+&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;27&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;do&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;sol&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0.00&lt;br /&gt;
+         &lt;td&gt;704.348&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1/1&lt;br /&gt;
+         &lt;td&gt;3/2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;perfect unison&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;perfect 5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;28&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;di&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;si&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;26.087&lt;br /&gt;
+         &lt;td&gt;730.435&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;26/17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;up unison&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up 5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;D^&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;29&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;ro&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;lo&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;52.174&lt;br /&gt;
+         &lt;td&gt;756.522&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;14/9, 20/13, 17/11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;downminor 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;downminor 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;vm2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vm6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Ebv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Bbv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;30&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;rih&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;leh&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;78.261&lt;br /&gt;
+         &lt;td&gt;782.609&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;11/7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;minor 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;minor 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;m2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;m6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Eb&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Bb&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;31&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;ra&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;le&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;104.348&lt;br /&gt;
+         &lt;td&gt;808.696&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16/15, 17/16, 18/17&lt;br /&gt;
+         &lt;td&gt;8/5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;upminor 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;upminor 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^m2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^m6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Eb^&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Bb^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;32&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;ru (as in supraminor)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;lu&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;130.435&lt;br /&gt;
+         &lt;td&gt;834.783&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;13/12, 14/13, 15/14&lt;br /&gt;
+         &lt;td&gt;13/8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;downmid 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;downmid 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;v~2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v~6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Eb^^&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Bb^^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;33&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;ruh (as in submajor)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;luh&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;156.522&lt;br /&gt;
+         &lt;td&gt;860.87&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;12/11, 11/10&lt;br /&gt;
+         &lt;td&gt;18/11, 28/17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;upmid 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;upmid 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^~2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^~6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Evv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Bvv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;34&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;reh&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;la&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;182.609&lt;br /&gt;
+         &lt;td&gt;886.957&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;10/9&lt;br /&gt;
+         &lt;td&gt;5/3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;downmajor 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;downmajor 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;vM2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vM6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Ev&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Bv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;35&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;re&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;laa&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;208.696&lt;br /&gt;
+         &lt;td&gt;913.043&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9/8, 17/15&lt;br /&gt;
+         &lt;td&gt;22/13, 17/10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;major 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;major 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;M2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;36&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;ri&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;li&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;234.783&lt;br /&gt;
+         &lt;td&gt;939.13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;8/7, 15/13*&lt;br /&gt;
+         &lt;td&gt;12/7, 26/15*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;upmajor 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;upmajor 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^M2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^M6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;E^&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;B^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;ma&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;ta&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;260.87&lt;br /&gt;
+         &lt;td&gt;965.217&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7/6, 15/13*&lt;br /&gt;
+         &lt;td&gt;7/4, 26/15*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;downminor 3rd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;downminor 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;vm3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vm7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Fv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Cv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;38&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;meh&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;teh&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;286.957&lt;br /&gt;
+         &lt;td&gt;991.304&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;13/11, 20/17&lt;br /&gt;
+         &lt;td&gt;16/9, 30/17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;minor 3rd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;minor 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;m3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;m7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;39&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;me&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;te&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;313.043&lt;br /&gt;
+         &lt;td&gt;1017.391&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;6/5&lt;br /&gt;
+         &lt;td&gt;9/5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;upminor 3rd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;upminor 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^m3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^m7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F^&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;40&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;mu&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;tu&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;339.13&lt;br /&gt;
+         &lt;td&gt;1043.478&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11/9, 17/14&lt;br /&gt;
+         &lt;td&gt;11/6, 20/11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;downmid 3rd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;downmid 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;v~3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v~7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F^^&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C^^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;41&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;muh&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;tuh&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;365.217&lt;br /&gt;
+         &lt;td&gt;1069.565&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16/13&lt;br /&gt;
+         &lt;td&gt;24/13, 13/7, 28/15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;upmid 3rd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;upmid 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^~3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^~7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F#vv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C#vv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;42&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;mi&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;ti&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;391.304&lt;br /&gt;
+         &lt;td&gt;1095.652&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5/4&lt;br /&gt;
+         &lt;td&gt;15/8, 32/17, 17/9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;downmajor 3rd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;downmajor 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;vM3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;vM7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F#v&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C#v&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;43&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;maa&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;taa&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;417.391&lt;br /&gt;
+         &lt;td&gt;1121.739&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;14/11&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;major 3rd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;major 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;M3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F#&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C#&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;44&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;mo&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;to&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;443.478&lt;br /&gt;
+         &lt;td&gt;1147.826&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9/7, 13/10, 22/17&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;upmajor 3rd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;upmajor 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^M3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^M7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F#^&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C#^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;45&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;fe&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;da&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;469.565&lt;br /&gt;
+         &lt;td&gt;1173.913&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;17/13&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;down 4th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;down 8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;v4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Gv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Dv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;fa&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;do&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;495.652&lt;br /&gt;
+         &lt;td&gt;1200&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;4/3&lt;br /&gt;
+         &lt;td&gt;2/1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;perfect 4th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;perfect 8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;P4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;fih&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;td style="text-align: center;"&gt;up 4th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;^4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;G^&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;
+&lt;br /&gt;
+All 46edo chords can be named using ups and downs:&lt;br /&gt;
+-10-27 = C Ebv G = C.vm = &amp;quot;C downminor&amp;quot;&lt;br /&gt;
+-12-27 = C Eb^ G = C.^m = &amp;quot;C upminor&amp;quot;&lt;br /&gt;
+-14-27 = C Evv G = C.^~ = &amp;quot;C upmid&amp;quot;&lt;br /&gt;
+-16-27 = C E G = &amp;quot;C major&amp;quot; or &amp;quot;C&amp;quot;&lt;br /&gt;
+-17-27 = C E^ G = C.^= &amp;quot;C upmajor&amp;quot; or &amp;quot;C dot up&amp;quot;&lt;br /&gt;
+etc.&lt;br /&gt;
+&lt;br /&gt;
+For a more complete list, see &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs"&gt;Ups and Downs Notation - Chord names in other EDOs&lt;/a&gt;.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Linear temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Linear temperaments&lt;/h1&gt;
+&lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
+         &lt;th&gt;Periods&lt;br /&gt;
-&lt;/td&gt;
+per octave&lt;br /&gt;
-         &lt;td style="text-align: center;"&gt;fu&lt;br /&gt;
+&lt;/th&gt;
-&lt;/td&gt;
+        &lt;th&gt;Generator&lt;br /&gt;
-         &lt;td&gt;547.826&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;11/8, 15/11&lt;br /&gt;
+         &lt;td&gt;26.087&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;double-up 4th&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^^4&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;G^^&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;22&lt;br /&gt;
+         &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;fi&lt;br /&gt;
+         &lt;td&gt;3\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;573.913&lt;br /&gt;
+         &lt;td&gt;78.261&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7/5, 18/13&lt;br /&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 style="text-align: center;"&gt;double-down aug 4th,&lt;br /&gt;
+         &lt;td&gt;1L 14s (15-tone)&lt;br /&gt;
-dim 5th&lt;br /&gt;
+L 1s (16-tone)&lt;br /&gt;
+L 15s (31-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;vvA4, d5&lt;br /&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;
-&lt;/td&gt;
+:1&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;G#vv, Ab&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
+         &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;seh&lt;br /&gt;
+         &lt;td&gt;5\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;600&lt;br /&gt;
+         &lt;td&gt;130.435&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;17/12, 24/17&lt;br /&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 style="text-align: center;"&gt;downaug 4th, updim 5th&lt;br /&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;
+L 10s (19-tone)&lt;br /&gt;
+L 19s (28-tone)&lt;br /&gt;
+L 28s (37-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;vA4, ^d5&lt;br /&gt;
+         &lt;td&gt;6:5 ~ QE&lt;br /&gt;
-&lt;/td&gt;
+:1&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;G#v, Ab^&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
+         &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;se&lt;br /&gt;
+         &lt;td&gt;7\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;626.087&lt;br /&gt;
+         &lt;td&gt;182.609&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;10/7, 13/9&lt;br /&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 style="text-align: center;"&gt;aug 4th, double-up dim 5th&lt;br /&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;
+L 6s (13-tone)&lt;br /&gt;
+L 7s (20-tone)&lt;br /&gt;
+L 20s (33-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;A4, ^^d5&lt;br /&gt;
+         &lt;td&gt;11:7&lt;br /&gt;
+:4&lt;br /&gt;
+:3 ~ QE&lt;br /&gt;
+:1&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;G#, Ab^^&lt;br /&gt;
+     &lt;/tr&gt;
-&lt;/td&gt;
-     &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
+         &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;su&lt;br /&gt;
+         &lt;td&gt;9\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;652.174&lt;br /&gt;
+         &lt;td&gt;234.783&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16/11, 22/15&lt;br /&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 style="text-align: center;"&gt;double-down 5th&lt;br /&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;
+L 11s (16-tone)&lt;br /&gt;
+L 16s (21-tone)&lt;br /&gt;
+L 21s (26-tone)&lt;br /&gt;
+L 26s (31-tone)&lt;br /&gt;
+L 31s (36-tone)&lt;br /&gt;
+L 36s (41-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;vv5&lt;br /&gt;
+         &lt;td&gt;10:9 ~QE&lt;br /&gt;
-&lt;/td&gt;
+:1&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;Avv&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;26&lt;br /&gt;
+         &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;sih&lt;br /&gt;
+         &lt;td&gt;11\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;678.261&lt;br /&gt;
+         &lt;td&gt;286.957&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;down 5th&lt;br /&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;
+L 9s (13-tone)&lt;br /&gt;
+L 13s (17-tone)&lt;br /&gt;
+L 17s (21-tone)&lt;br /&gt;
+L 4s (25-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;v5&lt;br /&gt;
+         &lt;td&gt;11:2&lt;br /&gt;
-&lt;/td&gt;
+:2&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;Av&lt;br /&gt;
+:2&lt;br /&gt;
+:2&lt;br /&gt;
+:2 ~ QE, Golden&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;27&lt;br /&gt;
+         &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;sol&lt;br /&gt;
+         &lt;td&gt;13\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;704.348&lt;br /&gt;
+         &lt;td&gt;339.13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3/2&lt;br /&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 style="text-align: center;"&gt;perfect 5th&lt;br /&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;
+L 11s (18-tone)&lt;br /&gt;
+L 18s (25-tone)&lt;br /&gt;
+L 25s (32-tone)&lt;br /&gt;
+L 32s (39-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;P5&lt;br /&gt;
+         &lt;td&gt;7:6 ~ QE&lt;br /&gt;
-&lt;/td&gt;
+:1&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;28&lt;br /&gt;
+         &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;si&lt;br /&gt;
+         &lt;td&gt;15\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;730.435&lt;br /&gt;
+         &lt;td&gt;391.304&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;26/17&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Amigo"&gt;Amigo&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;up 5th&lt;br /&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;/td&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;td style="text-align: center;"&gt;^5&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;/td&gt;
+&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%207s"&gt;3L 7s&lt;/a&gt; (10-tone)&lt;br /&gt;
-         &lt;td style="text-align: center;"&gt;A^&lt;br /&gt;
+L 10s (13-tone)&lt;br /&gt;
+L 13s (16-tone)&lt;br /&gt;
+L 16s (19-tone)&lt;br /&gt;
+L 19s (21-tone)&lt;br /&gt;
+L 21s (24-tone)&lt;br /&gt;
+L 24s (27-tone)&lt;br /&gt;
+L 27s (30-tone)&lt;br /&gt;
+L 30s (33-tone)&lt;br /&gt;
+L 33s (36-tone)&lt;br /&gt;
+L 36s (39-tone)&lt;br /&gt;
+L 39s (42-tone)&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;16:15 ~ QE&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;29&lt;br /&gt;
+         &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;lo&lt;br /&gt;
+         &lt;td&gt;17\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;756.522&lt;br /&gt;
+         &lt;td&gt;443.478&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;14/9, 20/13, 17/11&lt;br /&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 style="text-align: center;"&gt;downminor 6th&lt;br /&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;
+L 11s (19-tone)&lt;br /&gt;
+L 8s (27-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;vm6&lt;br /&gt;
+         &lt;td&gt;12:5&lt;br /&gt;
-&lt;/td&gt;
+:5&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;Bbv&lt;br /&gt;
+:2&lt;br /&gt;
+:2 ~ QE, Golden&lt;br /&gt;
+:1&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;30&lt;br /&gt;
+         &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;leh&lt;br /&gt;
+         &lt;td&gt;19\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;782.609&lt;br /&gt;
+         &lt;td&gt;495.652&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11/7&lt;br /&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 style="text-align: center;"&gt;minor 6th&lt;br /&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;
+L 5s (17-tone)&lt;br /&gt;
+L 12s (29-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;m6&lt;br /&gt;
+         &lt;td&gt;11:8&lt;br /&gt;
-&lt;/td&gt;
+:3&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;Bb&lt;br /&gt;
+:3 ~ Golden&lt;br /&gt;
+:2 ~ QE, Golden&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;31&lt;br /&gt;
+         &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;le&lt;br /&gt;
+         &lt;td&gt;21\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;808.696&lt;br /&gt;
+         &lt;td&gt;547.826&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;8/5&lt;br /&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 style="text-align: center;"&gt;upminor 6th&lt;br /&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;
+L 2s (13-tone)&lt;br /&gt;
+L 13s (24-tone)&lt;br /&gt;
+L 24s (35-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^m6&lt;br /&gt;
+         &lt;td&gt;17:4&lt;br /&gt;
-&lt;/td&gt;
+:4&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;Bb^&lt;br /&gt;
+:4&lt;br /&gt;
+:4 ~ QE&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;32&lt;br /&gt;
+         &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;lu&lt;br /&gt;
+         &lt;td&gt;1\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;834.783&lt;br /&gt;
+         &lt;td&gt;26.087&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;13/8&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Ketchup"&gt;Ketchup&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;downmid 6th&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;v~6&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;Bb^^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;33&lt;br /&gt;
+         &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;luh&lt;br /&gt;
+         &lt;td&gt;2\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;860.87&lt;br /&gt;
+         &lt;td&gt;52.174&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;18/11, 28/17&lt;br /&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 style="text-align: center;"&gt;upmid 6th&lt;br /&gt;
+         &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
-&lt;/td&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;td style="text-align: center;"&gt;^~6&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;/td&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;td style="text-align: center;"&gt;Bvv&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;
+L 12s (14-tone)&lt;br /&gt;
+L 14s (16-tone)&lt;br /&gt;
+L 16s (18-tone)&lt;br /&gt;
+L 18s (20-tone)&lt;br /&gt;
+L 20s (22-tone)&lt;br /&gt;
+L 2s (24-tone)&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td&gt;21:2&lt;br /&gt;
+:2&lt;br /&gt;
+:2&lt;br /&gt;
+:2&lt;br /&gt;
+:2&lt;br /&gt;
+:2&lt;br /&gt;
+:2&lt;br /&gt;
+:2&lt;br /&gt;
+:2&lt;br /&gt;
+:2 ~ QE, Golden&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;34&lt;br /&gt;
+         &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;la&lt;br /&gt;
+         &lt;td&gt;3\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;886.957&lt;br /&gt;
+         &lt;td&gt;78.261&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5/3&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Semivalentine"&gt;Semivalentine&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;downmajor 6th&lt;br /&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;
+L 12s (14-tone)&lt;br /&gt;
+L 2s (16-tone)&lt;br /&gt;
+L 14s (30-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;vM6&lt;br /&gt;
+         &lt;td&gt;20:3&lt;br /&gt;
-&lt;/td&gt;
+:3&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;Bv&lt;br /&gt;
+:3&lt;br /&gt;
+:3&lt;br /&gt;
+:3&lt;br /&gt;
+:3 ~ Golden&lt;br /&gt;
+:2 ~ QE, Golden&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;35&lt;br /&gt;
+         &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;laa&lt;br /&gt;
+         &lt;td&gt;4\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;913.043&lt;br /&gt;
+         &lt;td&gt;104.348&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;22/13, 17/10&lt;br /&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 style="text-align: center;"&gt;major 6th&lt;br /&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;
+L 10s (22-tone)&lt;br /&gt;
+L 22s (34-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;M6&lt;br /&gt;
+         &lt;td&gt;19:4&lt;br /&gt;
-&lt;/td&gt;
+:4&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
+:4&lt;br /&gt;
+:4&lt;br /&gt;
+:3 ~ QE&lt;br /&gt;
+:1&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;36&lt;br /&gt;
+         &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;li&lt;br /&gt;
+         &lt;td&gt;5\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;939.13&lt;br /&gt;
+         &lt;td&gt;130.435&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;12/7, 26/15*&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;upmajor 6th&lt;br /&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;
+L 10s (18-tone)&lt;br /&gt;
+L 10s (28-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^M6&lt;br /&gt;
+         &lt;td&gt;18:5&lt;br /&gt;
-&lt;/td&gt;
+:5&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;B^&lt;br /&gt;
+:5 ~ Golden&lt;br /&gt;
+:3 ~ Golden&lt;br /&gt;
+:2 ~ QE, Golden&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
+         &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;ta&lt;br /&gt;
+         &lt;td&gt;6\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;965.217&lt;br /&gt;
+         &lt;td&gt;156.522&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7/4, 26/15*&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Bison"&gt;Bison&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;downminor 7th&lt;br /&gt;
+         &lt;td&gt;2L 2s (4-tone)&lt;br /&gt;
-&lt;/td&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;td style="text-align: center;"&gt;vm7&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;
+L 6s (14-tone)&lt;br /&gt;
+L 14s (22-tone)&lt;br /&gt;
+L 22s (30-tone)&lt;br /&gt;
+L 30s (38-tone&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Cv&lt;br /&gt;
+         &lt;td&gt;17:6&lt;br /&gt;
+:6&lt;br /&gt;
+:5 ~ QE&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;38&lt;br /&gt;
+         &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;teh&lt;br /&gt;
+         &lt;td&gt;7\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;991.304&lt;br /&gt;
+         &lt;td&gt;182.609&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16/9, 30/17&lt;br /&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 style="text-align: center;"&gt;minor 7th&lt;br /&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;
+L 8s (14-tone)&lt;br /&gt;
+L 14s (20-tone)&lt;br /&gt;
+L 6s (26-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;m7&lt;br /&gt;
+         &lt;td&gt;16:7&lt;br /&gt;
-&lt;/td&gt;
+:7&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
+:2&lt;br /&gt;
+:2&lt;br /&gt;
+:2 ~ QE, Golden&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;39&lt;br /&gt;
+         &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;te&lt;br /&gt;
+         &lt;td&gt;8\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1017.391&lt;br /&gt;
+         &lt;td&gt;208.696&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9/5&lt;br /&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 style="text-align: center;"&gt;upminor 7th&lt;br /&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;
+L 8s (14-tone)&lt;br /&gt;
+L 14s (20-tone)&lt;br /&gt;
+L 20s (26-tone)&lt;br /&gt;
+L 26s (32-tone)&lt;br /&gt;
+L 32s (38-tone)&lt;br /&gt;
+L 38s (44-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^m7&lt;br /&gt;
+         &lt;td&gt;15:8&lt;br /&gt;
-&lt;/td&gt;
+:7 ~ QE&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;C^&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;40&lt;br /&gt;
+         &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;tu&lt;br /&gt;
+         &lt;td&gt;9\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1043.478&lt;br /&gt;
+         &lt;td&gt;234.783&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11/6, 20/11&lt;br /&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 style="text-align: center;"&gt;downmid 7th&lt;br /&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;
+L 6s (16-tone)&lt;br /&gt;
+L 16s (26-tone)&lt;br /&gt;
+L 26s (36-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;v~7&lt;br /&gt;
+         &lt;td&gt;14:9&lt;br /&gt;
-&lt;/td&gt;
+:5&lt;br /&gt;
-        &lt;td style="text-align: center;"&gt;C^^&lt;br /&gt;
+:4 ~ QE&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;41&lt;br /&gt;
+         &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;tuh&lt;br /&gt;
+         &lt;td&gt;10\46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1069.565&lt;br /&gt;
+         &lt;td&gt;260.87&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;24/13, 13/7, 28/15&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="/Bamity"&gt;Bamity&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;upmid 7th&lt;br /&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;
+L 10s (14-tone)&lt;br /&gt;
+L 4s (18-tone)&lt;br /&gt;
+L 18s (32-tone)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^~7&lt;br /&gt;
+         &lt;td&gt;13:10&lt;br /&gt;
+:3&lt;br /&gt;
+:3&lt;br /&gt;
+:3 ~ QE&lt;br /&gt;
+:1&lt;br /&gt;
+:1 ~ QE&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;C#vv&lt;br /&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;a class="wiki_link" href="/Vines"&gt;Vines&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/4L%206s"&gt;4L 6s&lt;/a&gt; (10-tone)&lt;br /&gt;
+L 10s (14-tone)&lt;br /&gt;
+L 14s (18-tone)&lt;br /&gt;
+L 18s (22-tone)&lt;br /&gt;
+L 22s (26-tone)&lt;br /&gt;
+L 26s (30-tone)&lt;br /&gt;
+L 30s (34-tone)&lt;br /&gt;
+L 34s (38-tone)&lt;br /&gt;
+L 38s (42-tone)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12:11 ~ QE&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+:1&lt;br /&gt;
+: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;/tr&gt;
+         &lt;td&gt;26.087&lt;br /&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;42&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;ti&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;td style="text-align: center;"&gt;downmajor 7th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;vM7&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;C#v&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;43&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;taa&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;td style="text-align: center;"&gt;major 7th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;M7&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;C#&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;44&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;to&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;td style="text-align: center;"&gt;upmajor 7th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;^M7&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;C#^&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;45&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;da&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;td style="text-align: center;"&gt;down 8ve&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;v8&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;Dv&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: center;"&gt;46&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;do&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1200&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;2/1&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;perfect 8ve&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;D&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;
-&lt;br /&gt;
-All 46edo chords can be named using ups and downs:&lt;br /&gt;
--10-27 = C Ebv G = C.vm = &amp;quot;C downminor&amp;quot;&lt;br /&gt;
--12-27 = C Eb^ G = C.^m = &amp;quot;C upminor&amp;quot;&lt;br /&gt;
--14-27 = C Evv G = C.^~ = &amp;quot;C upmid&amp;quot;&lt;br /&gt;
--16-27 = C E G = &amp;quot;C major&amp;quot; or &amp;quot;C&amp;quot;&lt;br /&gt;
--17-27 = C E^ G = C.^= &amp;quot;C upmajor&amp;quot; or &amp;quot;C dot up&amp;quot;&lt;br /&gt;
-etc.&lt;br /&gt;
-&lt;br /&gt;
-For a more complete list, see &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs"&gt;Ups and Downs Notation - Chord names in other EDOs&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 &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;