| Prime factorization
|
72
|
| Step size
|
24.4898 ¢
|
| Fifth
|
29\49 (710.204 ¢)
|
| Semitones (A1:m2)
|
7:2 (171.4 ¢ : 48.98 ¢)
|
| Dual sharp fifth
|
29\49 (710.204 ¢)
|
| Dual flat fifth
|
28\49 (685.714 ¢) (→ 4\7)
|
| Dual major 2nd
|
8\49 (195.918 ¢)
|
| Consistency limit
|
7
|
| Distinct consistency limit
|
7
|
49-EDO, or 49 equal temperament divides the octave into 49 equal parts of 24.490 cents each.
Theory
49edo is very much on the sharp side of things, with sharp tunings of harmonics 3 (it is the first square equal division with a "real" 3 of step coprime to its cardinality), 5, 7, and 11. It is the optimal patent val for superpyth temperament in the 7 and 11 limits, archytas (7-limit) and ares (11-limit) planar temperaments and almost identical to the e-based analog of Lucy tuning. It tempers out 64/63, 245/243 and 3125/3087 in the 7-limit, and 100/99 and 1375/1372 in the 11-limit.
Intervals
| #
|
Cents
|
Approximate Ratios
|
| 0
|
0.000
|
1/1
|
| 1
|
24.490
|
50/49
|
| 2
|
48.980
|
81/80, 28/27, 36/35, 49/48
|
| 3
|
73.469
|
25/24, 22/21, 33/32
|
| 4
|
97.959
|
16/15, 21/20
|
| 5
|
122.449
|
15/14
|
| 6
|
146.939
|
12/11
|
| 7
|
171.429
|
10/9, 11/10
|
| 8
|
195.918
|
|
| 9
|
220.408
|
9/8, 8/7
|
| 10
|
244.898
|
|
| 11
|
269.388
|
7/6
|
| 12
|
293.878
|
|
| 13
|
318.367
|
6/5
|
| 14
|
342.857
|
11/9
|
| 15
|
367.347
|
27/22
|
| 16
|
391.837
|
5/4
|
| 17
|
416.327
|
14/11
|
| 18
|
440.816
|
9/7
|
| 19
|
465.306
|
|
| 20
|
489.796
|
4/3, 21/16
|
| 21
|
514.286
|
|
| 22
|
538.776
|
27/20, 15/11
|
| 23
|
563.265
|
11/8
|
| 24
|
587.755
|
7/5
|
| 25
|
612.245
|
10/7
|
| 26
|
636.735
|
16/11
|
| 27
|
661.244
|
40/27, 22/15
|
| 28
|
685.714
|
|
| 29
|
710.204
|
3/2, 32/21
|
| 30
|
734.694
|
|
| 31
|
759.184
|
14/9
|
| 32
|
783.673
|
11/7
|
| 33
|
808.163
|
8/5
|
| 34
|
832.653
|
44/27
|
| 35
|
857.143
|
18/11
|
| 36
|
881.633
|
5/3
|
| 37
|
906.122
|
|
| 38
|
930.612
|
12/7
|
| 39
|
955.102
|
|
| 40
|
979.592
|
16/9, 7/4
|
| 41
|
1004.082
|
|
| 42
|
1028.571
|
9/5, 20/11
|
| 43
|
1053.061
|
11/6
|
| 44
|
1077.551
|
28/15
|
| 45
|
1102.041
|
15/8, 40/21
|
| 46
|
1126.531
|
48/25, 21/11, 64/33
|
| 47
|
1151.020
|
160/81, 27/14, 35/18, 96/49
|
| 48
|
1175.510
|
49/25
|
| 49
|
1200.000
|
2/1
|
Just approximation
Selected just intervals
|
|
prime 2
|
prime 3
|
prime 5
|
prime 7
|
prime 11
|
prime 13
|
| Error
|
absolute (¢)
|
0.0
|
+8.2
|
+5.5
|
+10.8
|
+11.9
|
-7.9
|
| relative (%)
|
0.0
|
+33.7
|
+22.6
|
+44.0
|
+48.8
|
-32.2
|
Temperament measures
The following table shows TE temperament measures (RMS normalized by the rank) of 49et.
|
|
3-limit
|
5-limit
|
7-limit
|
11-limit
|
| Octave stretch (¢)
|
-2.60
|
-2.53
|
-2.85
|
-2.97
|
| Error
|
absolute (¢)
|
2.60
|
2.12
|
1.92
|
1.74
|
| relative (%)
|
10.62
|
8.69
|
7.87
|
7.11
|
Rank-2 temperaments