49edo

← 48edo

49edo

50edo →

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

The 49 equal divisions of the octave (49edo), or the 49(-tone) equal temperament (49tet, 49et) when viewed from a regular temperament perspective, divides the octave into 49 equal parts of about 24.5 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-limit, 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 (*)	Notation
0	0.000	1/1	D
1	24.490	50/49	^D
2	48.980	81/80, 28/27, 36/35, 49/48	Eb/^^D
3	73.469	25/24, 22/21, 33/32	^Eb/^^^D
4	97.959	16/15, 21/20	^^Eb/Fb/vvvD#
5	122.449	15/14	^^^Eb/vvD#
6	146.939	12/11	vvvE/vD#
7	171.429	10/9, 11/10	vvE/D#
8	195.918	28/25	vE
9	220.408	9/8, 8/7	E
10	244.898	125/108, 144/125	^E/vF
11	269.388	7/6	F
12	293.878	33/28	^F
13	318.367	6/5	^^F/Gb
14	342.857	11/9	^^^F/^Gb
15	367.347	27/22	vvvF#/^^Gb
16	391.837	5/4	vvF#/E#
17	416.327	14/11	vF#
18	440.816	9/7	F#
19	465.306	125/96, 162/125	^F#
20	489.796	4/3, 21/16	G
21	514.286	75/56	^G/vAb
22	538.776	27/20, 15/11	Ab/^^G
23	563.265	11/8	^Ab/^^^G
24	587.755	7/5	^^Ab/vvvG#
25	612.245	10/7	vvG#/^^^Ab
26	636.735	16/11	vG#/vvvA
27	661.244	40/27, 22/15	G#/vvA
28	685.714	112/75	vA/^G#
29	710.204	3/2, 32/21	A
30	734.694	125/81, 192/125	^A/vBb
31	759.184	14/9	Bb/^^A
32	783.673	11/7	^Bb/vCb/^^^A
33	808.163	8/5	Cb/^^Bb/vvvA#
34	832.653	44/27	^^^Bb/^Cb/vvA#
35	857.143	18/11	vvvB/^^Cb/vA#
36	881.633	5/3	vvB/^^^Cb/A#
37	906.122	56/33	vB/vvvC
38	930.612	12/7	B/vvC
39	955.102	125/72, 216/125	^B/vC
40	979.592	16/9, 7/4	C/^^B
41	1004.082	25/14	^C/^^^B
42	1028.571	9/5, 20/11	^^C/vvvB#/Db
43	1053.061	11/6	^^^C/vvB#/^Db
44	1077.551	28/15	vvvC#/vB#/^^Db
45	1102.041	15/8, 40/21	vvC#/B#/^^^Db
46	1126.531	48/25, 21/11, 64/33	vC#/vvvD
47	1151.020	160/81, 27/14, 35/18, 96/49	C#/vvD
48	1175.510	49/25	vD
49	1200.000	2/1	D

(*) Based on 49edo's 11-limit patent val ⟨49 78 114 138 170] mapping

Just approximation

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

Rank-2 temperaments by generators

Periods per octave	Generator	Temperaments
1	1\49	Sengagen
1	4\49	Passion
1	6\49	Bohpier
1	11\49	Infraorwell
1	13\49	Hanson/Catalan
1	16\49	Magus
1	18\49	Clyde
1	19\49	Semisept
1	20\49	Archy/Superpyth
7	20\49	Sevond/seville