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Line 46: Line 46:
| -8
| -8
|-
|-
! colspan="2" | [[nearest edomapping]]
! colspan="2" | [[Nearest edomapping]]
| 46
| 46
| 27
| 27
Line 569: Line 569:
For a more complete list, see [[Ups and Downs Notation #Chords and Chord Progressions]].
For a more complete list, see [[Ups and Downs Notation #Chords and Chord Progressions]].


== Just approximation ==
== JI approximation ==
=== Selected just intervals ===
=== 15-odd-limit interval mappings ===
The following table shows how [[15-odd-limit intervals]] are represented in 46edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.
The following table shows how [[15-odd-limit intervals]] are represented in 46edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.
{| class="wikitable center-all"
{| class="wikitable center-all"
Line 651: Line 651:
|}
|}


=== Temperament measures ===
== Regular temperament properties ==
The following table shows [[TE temperament measures]] (RMS normalized by the rank) of 46et.
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-all"
! rowspan="2" | Subgroup
! colspan="2" |
! rowspan="2" | [[Comma list]]
! 3-limit
! rowspan="2" | [[Mapping]]
! 5-limit
! rowspan="2" | Optimal<br>8ve stretch (¢)
! 7-limit
! colspan="2" | Tuning error
! 11-limit
|-
! 13-limit
! [[TE error|Absolute]] (¢)
! 17-limit
! [[TE simple badness|Relative]] (%)
! 23-limit no-19
|-
|-
! colspan="2" |Octave stretch (¢)
| 2.3
| {{monzo| 73 -46 }}
| [{{val| 46 73 }}]
| -0.755
| -0.755
| 0.75
| 2.89
|-
| 2.3.5
| 2048/2025, 78732/78125
| [{{val| 46 73 107 }}]
| -1.219
| -1.219
| 0.90
| 3.45
|-
| 2.3.5.7
| 126/125, 245/243, 1029/1024
| [{{val| 46 73 107 129 }}]
| -0.595
| -0.595
| 1.34
| 5.12
|-
| 2.3.5.7.11
| 121/120, 126/125, 176/175, 245/243
| [{{val| 46 73 107 129 159 }}]
| -0.274
| -0.274
| 1.36
| 5.20
|-
| 2.3.5.7.11.13
| 91/90, 121/120, 169/168, 176/175, 245/243
| [{{val| 46 73 107 129 159 170 }}]
| +0.030
| +0.030
| 1.41
| 5.42
|-
| 2.3.5.7.11.13.17
| 91/90, 121/120, 154/153, 169/168, 176/175, 245/243
| [{{val| 41 65 95 115 142 152 174 188 }}]
| +0.047
| +0.047
| 1.31
| 5.02
|-
| 2.3.5.7.11.13.17.23
| 91/90, 121/120, 154/153, 169/168, 176/175, 208/207, 231/230
| [{{val| 41 65 95 115 142 152 174 188 208 }}]
| +0.101
| +0.101
|-
! rowspan="2" |Error
! [[TE error|absolute]] (¢)
| 0.75
| 0.90
| 1.34
| 1.36
| 1.41
| 1.31
| 1.23
| 1.23
|-
! [[TE simple badness|relative]] (%)
| 2.89
| 3.45
| 5.12
| 5.20
| 5.42
| 5.02
| 4.72
| 4.72
|}
|}


* 46et has a lower relative error than any previous ETs in the 17-, 19-, 23-limit, and others. The next ET that does better in the aforementioned subgroups is 72, 72, 94, respectively.  
46et is lower in relative error than any previous equal temperaments in the 17-, 19-, 23-limit, and others. The next ETs better in the aforementioned subgroups are 72, 72, 94, respectively. 46et is even more prominent in the no-19 23-limit, and the next ET that does better in this subgroup is 140.  
* 46et is prominent in the no-19 23-limit. The next ET that does better in this subgroup is 140.  


== Linear temperaments ==
=== Rank-2 temperaments ===


{| class="wikitable"
{| class="wikitable center-1 center-2 center-3"
|-
|-
! Periods <br>per octave
! Periods <br>per octave
Line 703: Line 722:
! Cents
! Cents
! Temperaments
! Temperaments
! MOS/DE Scales available
! MOS Scales
! L:s
! L:s
|-
|-
Line 709: Line 728:
| 1\46
| 1\46
| 26.087
| 26.087
|  
| [[Sfourth]]
|  
|  
|  
|  
Line 717: Line 736:
| 78.261
| 78.261
| [[Valentine]]
| [[Valentine]]
| 1L 14s (15-tone)
| 1L 14s (15-tone)<br>15L 1s (16-tone)<br>16L 15s (31-tone)
 
| 4:3 ~ [[Maximal evenness|quasi-equal]]<br>3:1<br>2:1 ~ QE
15L 1s (16-tone)
 
16L 15s (31-tone)
| 4:3 ~ [[Maximal_evenness|quasi-equal]]
 
3:1
 
2:1 ~ QE
|-
|-
| 1
| 1
Line 732: Line 743:
| 130.435
| 130.435
| [[Twothirdtonic]]
| [[Twothirdtonic]]
| [[1L_8s|1L 8s]] (9-tone)
| [[1L 8s]] (9-tone)<br>[[9L 1s]] (10-tone)<br>9L 10s (19-tone)<br>9L 19s (28-tone)<br>9L 28s (37-tone)
 
| 6:5 ~ QE<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE
[[9L_1s|9L 1s]] (10-tone)
 
9L 10s (19-tone)
 
9L 19s (28-tone)
 
9L 28s (37-tone)
| 6:5 ~ QE
 
5:1
 
4:1
 
3:1
 
2:1 ~ QE
|-
|-
| 1
| 1
| 7\46
| 7\46
| 182.609
| 182.609
| [[Minortone]]
| [[Minortone]] / [[mitonic]]
| [[1L 5s]] (6-tone)
| [[1L 5s]] (6-tone)<br>[[6L 1s]] (7-tone)<br>7L 6s (13-tone)<br>13L 7s (20-tone)<br>13L 20s (33-tone)
 
| 11:7<br>7:4<br>4:3 ~ QE<br>3:1<br>2:1 ~ QE
[[6L 1s]] (7-tone)
 
7L 6s (13-tone)
 
13L 7s (20-tone)
 
13L 20s (33-tone)
| 11:7
 
7:4
 
4:3 ~ QE
 
3:1
 
2:1 ~ QE
|-
|-
| 1
| 1
Line 778: Line 757:
| 234.783
| 234.783
| [[Rodan]]
| [[Rodan]]
| [[1L 4s]] (5-tone)
| [[1L 4s]] (5-tone)<br>[[1L 5s]] (6-tone)<br>[[5L 6s]] (11-tone)<br>5L 11s (16-tone)<br>5L 16s (21-tone)<br>5L 21s (26-tone)<br>5L 26s (31-tone)<br>5L 31s (36-tone)<br>5L 36s (41-tone)
 
| 10:9 ~QE<br>9:1<br>8:1<br>7:1<br>6:1<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE, Pathological
[[1L 5s]] (6-tone)
 
[[5L 6s]] (11-tone)
 
5L 11s (16-tone)
 
5L 16s (21-tone)
 
5L 21s (26-tone)
 
5L 26s (31-tone)
 
5L 31s (36-tone)
 
5L 36s (41-tone)
| 10:9 ~QE
 
9:1
 
8:1
 
7:1
 
6:1
 
5:1
 
4:1
 
3:1
 
2:1 ~ QE, Pathological
|-
|-
| 1
| 1
Line 817: Line 764:
| 286.957
| 286.957
|  
|  
| [[4L 1s]] (5-tone)
| [[4L 1s]] (5-tone)<br>[[4L 5s]] (9-tone)<br>4L 9s (13-tone)<br>4L 13s (17-tone)<br>4L 17s (21-tone)<br>21L 4s (25-tone)
 
| 11:2<br>9:2<br>7:2<br>5:2<br>3:2 ~ QE, Golden<br>2:1 ~ QE
[[4L 5s]] (9-tone)
 
4L 9s (13-tone)
 
4L 13s (17-tone)
 
4L 17s (21-tone)
 
21L 4s (25-tone)
| 11:2
 
9:2
 
7:2
 
5:2
 
3:2 ~ QE, Golden
 
2:1 ~ QE
|-
|-
| 1
| 1
| 13\46
| 13\46
| 339.130
| 339.130
| [[Amity]]/[[hitchcock]]
| [[Amity]] / [[hitchcock]]
| [[4L 3s]] (7-tone)
| [[4L 3s]] (7-tone)<br>[[7L 4s]] (11-tone)<br>7L 11s (18-tone)<br>7L 18s (25-tone)<br>7L 25s (32-tone)<br>7L 32s (39-tone)
 
| 7:6 ~ QE<br>6:1<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE! Pathological
[[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! Pathological
|-
|-
| 1
| 1
| 15\46
| 15\46
| 391.304
| 391.304
| [[Amigo]]
| [[Magus]] / [[amigo]]
| [[1L 2s]] (3-tone)
| [[1L 2s]] (3-tone)<br>[[3L 1s]] (4-tone)<br>[[3L 4s]] (7-tone)<br>[[3L 7s]] (10-tone)<br>3L 10s (13-tone)<br>3L 13s (16-tone)<br>3L 16s (19-tone)<br>3L 19s (21-tone)<br>3L 21s (24-tone)<br>3L 24s (27-tone)<br>3L 27s (30-tone)<br>3L 30s (33-tone)<br>3L 33s (36-tone)<br>3L 36s (39-tone)<br>3L 39s (42-tone)
 
| 16:15 ~ QE<br>15:1<br>14:1<br>13:1<br>12:1<br>11:1<br>10:1<br>9:1<br>8:1<br>7:1<br>6:1<br>5:1<br>4:1<br>3:1 ~ Pathological<br>2:1 ~ QE, Pathological
[[3L 1s]] (4-tone)
 
[[3L 4s]] (7-tone)
 
[[3L 7s]] (10-tone)
 
3L 10s (13-tone)
 
3L 13s (16-tone)
 
3L 16s (19-tone)
 
3L 19s (21-tone)
 
3L 21s (24-tone)
 
3L 24s (27-tone)
 
3L 27s (30-tone)
 
3L 30s (33-tone)
 
3L 33s (36-tone)
 
3L 36s (39-tone)
 
3L 39s (42-tone)
| 16:15 ~ QE
 
15:1
 
14:1
 
13:1
 
12:1
 
11:1
 
10:1
 
9:1
 
8:1
 
7:1
 
6:1
 
5:1
 
4:1
 
3:1 ~ Pathological
 
2:1 ~ QE, Pathological
|-
|-
| 1
| 1
Line 934: Line 785:
| 443.478
| 443.478
| [[Sensi]]
| [[Sensi]]
| [[3L 2s]] (5-tone)
| [[3L 2s]] (5-tone)<br>[[3L 5s]] (8-tone)<br>[[8L 3s]] (11-tone)<br>8L 11s (19-tone)<br>19L 8s (27-tone)
 
| 12:5<br>7:5<br>5:2<br>3:2 ~ QE, Golden<br>2:1
[[3L 5s]] (8-tone)
 
[[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
| 1
Line 957: Line 792:
| 495.652
| 495.652
| [[Leapday]]
| [[Leapday]]
| [[2L 3s]] (5-tone)
| [[2L 3s]] (5-tone)<br>[[5L 2s]] (7-tone)<br>[[5L 7s]] (12-tone)<br>12L 5s (17-tone)<br>17L 12s (29-tone)
 
| 11:8<br>8:3<br>5:3 ~ Golden<br>3:2 ~ QE, Golden<br>2:1 ~ QE
[[5L 2s]] (7-tone)
 
[[5L 7s]] (12-tone)
 
12L 5s (17-tone)
 
17L 12s (29-tone)
| 11:8
 
8:3
 
5:3 ~ Golden
 
3:2 ~ QE, Golden
 
2:1 ~ QE
|-
|-
| 1
| 1
Line 980: Line 799:
| 547.826
| 547.826
| [[Heinz]]
| [[Heinz]]
| [[2L 3s]] (5-tone)
| [[2L 3s]] (5-tone)<br>[[2L 5s]] (7-tone)<br>[[2L 7s]] (9-tone)<br>[[2L 9s]] (11-tone)<br>11L 2s (13-tone)<br>11L 13s (24-tone)<br>11L 24s (35-tone)
 
| 17:4<br>13:4<br>9:4<br>5:4 ~ QE<br>4:1<br>3:1<br>2:1 ~ QE
[[2L 5s]] (7-tone)
 
[[2L 7s]] (9-tone)
 
[[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
| 2
Line 1,018: Line 813:
| 52.174
| 52.174
| [[Shrutar]]
| [[Shrutar]]
| 2L 2s (4-tone)
| 2L 2s (4-tone)<br>[[2L 4s]] (6-tone)<br>[[2L 6s]] (8-tone)<br>[[2L 8s]] (10-tone)<br>[[2L 10s]] (12-tone)<br>2L 12s (14-tone)<br>2L 14s (16-tone)<br>2L 16s (18-tone)<br>2L 18s (20-tone)<br>2L 20s (22-tone)<br>22L 2s (24-tone)
 
| 21:2<br>19:2<br>17:2<br>15:2<br>13:2<br>11:2<br>9:2<br>7:2<br>5:2<br>3:2 ~ QE, Golden<br>2:1 ~ QE
[[2L 4s]] (6-tone)
 
[[2L 6s]] (8-tone)
 
[[2L 8s]] (10-tone)
 
[[2L 10s]] (12-tone)
 
2L 12s (14-tone)
 
2L 14s (16-tone)
 
2L 16s (18-tone)
 
2L 18s (20-tone)
 
2L 20s (22-tone)
 
22L 2s (24-tone)
| 21:2
 
19:2
 
17:2
 
15:2
 
13:2
 
11:2
 
9:2
 
7:2
 
5:2
 
3:2 ~ QE, Golden
 
2:1 ~ QE
|-
|-
| 2
| 2
Line 1,065: Line 820:
| 78.261
| 78.261
| [[Semivalentine]]
| [[Semivalentine]]
| 2L 2s (4-tone)
| 2L 2s (4-tone)<br>[[2L 4s]] (6-tone)<br>[[2L 6s]] (8-tone)<br>[[2L 8s]] (10-tone)<br>[[2L 10s]] (12-tone)<br>2L 12s (14-tone)<br>14L 2s (16-tone)<br>16L 14s (30-tone)
 
| 20:3<br>17:3<br>14:3<br>11:3<br>8:3<br>5:3 ~ Golden<br>3:2 ~ QE, Golden<br>2:1 ~ QE
[[2L 4s]] (6-tone)
 
[[2L 6s]] (8-tone)
 
[[2L 8s]] (10-tone)
 
[[2L 10s]] (12-tone)
 
2L 12s (14-tone)
 
14L 2s (16-tone)
 
16L 14s (30-tone)
| 20:3
 
17:3
 
14:3
 
11:3
 
8:3
 
5:3 ~ Golden
 
3:2 ~ QE, Golden
 
2:1 ~ QE
|-
|-
| 2
| 2
| 4\46
| 4\46
| 104.348
| 104.348
| [[Srutal]]/[[diaschismic]]
| [[Srutal]] / [[diaschismic]]
| 2L 2s (4-tone)
| 2L 2s (4-tone)<br>[[2L 4s]] (6-tone)<br>[[2L 6s]] (8-tone)<br>[[2L 8s]] (10-tone)<br>[[10L 2s]] (12-tone)<br>12L 10s (22-tone)<br>12L 22s (34-tone)
 
| 19:4<br>15:4<br>11:4<br>7:4<br>4:3 ~ QE<br>3:1<br>2:1 ~ QE
[[2L 4s]] (6-tone)
 
[[2L 6s]] (8-tone)
 
[[2L 8s]] (10-tone)
 
[[10L 2s]] (12-tone)
 
12L 10s (22-tone)
 
12L 22s (34-tone)
| 19:4
 
15:4
 
11:4
 
7:4
 
4:3 ~ QE
 
3:1
 
2:1 ~ QE
|-
|-
| 2
| 2
Line 1,131: Line 834:
| 130.435
| 130.435
|  
|  
| 2L 2s (4-tone)
| 2L 2s (4-tone)<br>[[2L 4s]] (6-tone)<br>[[2L 6s]] (8-tone)<br>[[8L 2s]] (10-tone)<br>8L 10s (18-tone)<br>18L 10s (28-tone)
 
| 18:5<br>13:5<br>8:5 ~ Golden<br>5:3 ~ Golden<br>3:2 ~ QE, Golden<br>2:1 ~ QE
[[2L 4s]] (6-tone)
 
[[2L 6s]] (8-tone)
 
[[8L 2s]] (10-tone)
 
8L 10s (18-tone)
 
18L 10s (28-tone)
| 18:5
 
13:5
 
8:5 ~ Golden
 
5:3 ~ Golden
 
3:2 ~ QE, Golden
 
2:1 ~ QE
|-
|-
| 2
| 2
Line 1,158: Line 841:
| 156.522
| 156.522
| [[Bison]]
| [[Bison]]
| 2L 2s (4-tone)
| 2L 2s (4-tone)<br>[[2L 4s]] (6-tone)<br>[[6L 2s]] (8-tone)<br>8L 6s (14-tone)<br>8L 14s (22-tone)<br>8L 22s (30-tone)<br>8L 30s (38-tone
 
| 17:6<br>11:6<br>6:5 ~ QE<br>5:1<br>4:1<br>3:1<br>2:1 ~ QE, Pathological
[[2L 4s]] (6-tone)
 
[[6L 2s]] (8-tone)
 
8L 6s (14-tone)
 
8L 14s (22-tone)
 
8L 22s (30-tone)
 
8L 30s (38-tone
| 17:6
 
11:6
 
6:5 ~ QE
 
5:1
 
4:1
 
3:1
 
2:1 ~ QE, Pathological
|-
|-
| 2
| 2
| 7\46
| 7\46
| 182.609
| 182.609
| [[Unidec]]/[[Hendec|hendec]]
| [[Unidec]] / [[hendec]]
| 2L 2s (4-tone)
| 2L 2s (4-tone)<br>[[2L 4s]] (6-tone)<br>[[6L 2s]] (8-tone)<br>6L 8s (14-tone)<br>6L 14s (20-tone)<br>20L 6s (26-tone)
 
| 16:7<br>9:7<br>7:2<br>5:2<br>3:2 ~ QE, Golden<br>2:1 ~ QE
[[2L 4s]] (6-tone)
 
[[6L 2s]] (8-tone)
 
6L 8s (14-tone)
 
6L 14s (20-tone)
 
20L 6s (26-tone)
| 16:7
 
9:7
 
7:2
 
5:2
 
3:2 ~ QE, Golden
 
2:1 ~ QE
|-
|-
| 2
| 2
Line 1,216: Line 855:
| 208.696
| 208.696
| [[Abigail]]
| [[Abigail]]
| 2L 2s (4-tone)
| 2L 2s (4-tone)<br>[[4L 2s]] (6-tone)<br>[[6L 2s]] (8-tone)<br>6L 8s (14-tone)<br>6L 14s (20-tone)<br>6L 20s (26-tone)<br>6L 26s (32-tone)<br>6L 32s (38-tone)<br>6L 38s (44-tone)
 
| 15:8<br>8:7 ~ QE<br>8:1<br>7:1<br>6:1<br>5:1<br>4:1<br>3:1 ~ Pathological<br>2:1 ~ QE, Pathological
[[4L 2s]] (6-tone)
 
[[6L 2s]] (8-tone)
 
6L 8s (14-tone)
 
6L 14s (20-tone)
 
6L 20s (26-tone)
 
6L 26s (32-tone)
 
6L 32s (38-tone)
 
6L 38s (44-tone)
| 15:8
 
8:7 ~ QE
 
8:1
 
7:1
 
6:1
 
5:1
 
4:1
 
3:1 ~ Pathological
 
2:1 ~ QE, Pathological
|-
|-
| 2
| 2
Line 1,255: Line 862:
| 234.783
| 234.783
| [[Echidnic]]
| [[Echidnic]]
| 2L 2s (4-tone)
| 2L 2s (4-tone)<br>[[4L 2s]] (6-tone)<br>[[6L 4s]] (10-tone)<br>10L 6s (16-tone)<br>10L 16s (26-tone)<br>10L 26s (36-tone)
 
| 14:9<br>9:5<br>5:4 ~ QE<br>4:1<br>3:1<br>2:1 ~ QE
[[4L 2s]] (6-tone)
 
[[6L 4s]] (10-tone)
 
10L 6s (16-tone)
 
10L 16s (26-tone)
 
10L 26s (36-tone)
| 14:9
 
9:5
 
5:4 ~ QE
 
4:1
 
3:1
 
2:1 ~ QE
|-
|-
| 2
| 2
Line 1,282: Line 869:
| 260.87
| 260.87
| [[Bamity]]
| [[Bamity]]
| 2L 2s (4-tone)
| 2L 2s (4-tone)<br>[[4L 2s]] (6-tone)<br>[[4L 6s]] (10-tone)<br>4L 10s (14-tone)<br>14L 4s (18-tone)<br>14L 18s (32-tone)
 
| 13:10<br>10:3<br>7:3<br>4:3 ~ QE<br>3:1<br>2:1 ~ QE
[[4L 2s]] (6-tone)
 
[[4L 6s]] (10-tone)
 
4L 10s (14-tone)
 
14L 4s (18-tone)
 
14L 18s (32-tone)
| 13:10
 
10:3
 
7:3
 
4:3 ~ QE
 
3:1
 
2:1 ~ QE
|-
|-
| 2
| 2
Line 1,309: Line 876:
| 286.957
| 286.957
| [[Vines]]
| [[Vines]]
| 2L 2s (4-tone)
| 2L 2s (4-tone)<br>[[4L 2s]] (6-tone)<br>[[4L 6s]] (10-tone)<br>4L 10s (14-tone)<br>4L 14s (18-tone)<br>4L 18s (22-tone)<br>4L 22s (26-tone)<br>4L 26s (30-tone)<br>4L 30s (34-tone)<br>4L 34s (38-tone)<br>4L 38s (42-tone)
 
| 12:11 ~ QE<br>11:1<br>10:1<br>9:1<br>8:1<br>7:1<br>6:1<br>5:1<br>4:1<br>3:1 ~ Pathological<br>2:1 ~ QE, Pathological
[[4L 2s]] (6-tone)
 
[[4L 6s]] (10-tone)
 
4L 10s (14-tone)
 
4L 14s (18-tone)
 
4L 18s (22-tone)
 
4L 22s (26-tone)
 
4L 26s (30-tone)
 
4L 30s (34-tone)
 
4L 34s (38-tone)
 
4L 38s (42-tone)
| 12:11 ~ QE
 
11:1
 
10:1
 
9:1
 
8:1
 
7:1
 
6:1
 
5:1
 
4:1
 
3:1 ~ Pathological
 
2:1 ~ QE, Pathological
|-
|-
| 23
| 23
| 1\46
| 1\46
| 26.087
| 26.087
|  
| [[Icositritonic]]
|  
|  
|  
|  
Line 1,361: Line 888:


== Scales ==
== Scales ==
*[[plum]]
* [[Plum]]
*[[sensi5]]
* [[Sensi5]]
*[[sensi8]]
* [[Sensi8]]
*[[sensi11]]
* [[Sensi11]]
*[[sensi19]]
* [[Sensi19]]
 
=== Approximation to Mode 8 of the Harmonic Series ===


46edo represents [[Overtone series|overtones]] 8 through 16 (written as [[JI]] ratios 8:9:10:11:12:13:14:15:16) with degrees 0, 8, 15, 21, 27, 32, 37, 42, 46. In steps-in-between, that's 8, 7, 6, 6, 5, 5, 5, 4.
=== Harmonic scales ===
46edo represents [[harmonic series|overtones]] 8 through 16 (written as [[JI]] ratios 8:9:10:11:12:13:14:15:16) with degrees 0, 8, 15, 21, 27, 32, 37, 42, 46. In steps-in-between, that's 8, 7, 6, 6, 5, 5, 5, 4.


* 8\46edo (208.696¢) stands in for frequency ratio [[9/8|9:8]] (203.910¢).
* 8\46edo (208.696¢) stands in for frequency ratio [[9/8]] (203.910¢).
* 7\46edo (182.609¢) stands in for [[10/9|10:9]] (182.404¢).
* 7\46edo (182.609¢) stands in for [[10/9]] (182.404¢).
* 6\46edo (156.522¢) stands in for [[11/10|11:10]] (165.004¢) and [[12/11|12:11]] (150.637¢).
* 6\46edo (156.522¢) stands in for [[11/10]] (165.004¢) and [[12/11]] (150.637¢).
* 5\46edo (130.435¢) stands in for [[13/12|13:12]] (138.573¢), [[14/13|14:13]] (128.298¢) and [[15/14|15:14]] (119.443¢).
* 5\46edo (130.435¢) stands in for [[13/12]] (138.573¢), [[14/13]] (128.298¢) and [[15/14]] (119.443¢).
* 4\46edo (104.348¢) stands in for [[16/15|16:15]] (111.731¢).
* 4\46edo (104.348¢) stands in for [[16/15]] (111.731¢).


== Music ==
== Music ==
* [http://aaronkristerjohnson.bandcamp.com/track/satiesque Satiesque] by [[Aaron Krister Johnson]].
* [http://aaronkristerjohnson.bandcamp.com/track/satiesque Satiesque] by [[Aaron Krister Johnson]].
* [http://www.archive.org/details/Chromosounds Chromosounds] [http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3 play] by [[Gene Ward Smith]].
* [http://www.archive.org/details/Chromosounds Chromosounds] [http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3 play] by [[Gene Ward Smith]].
Retrieved from "https://en.xen.wiki/w/46edo"