13ed5/2

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13ed5/2

14ed5/2 →

Prime factorization	13 (prime)
Step size	122.024 ¢
Octave	10\13ed5/2 (1220.24 ¢) (semiconvergent)
Twelfth	16\13ed5/2 (1952.39 ¢)
Consistency limit	5
Distinct consistency limit	5

13ed5/2 is the equal division of the 5/2 interval into 13 parts of 122.024 cents each. It roughly corresponds to 10edo, and their patent vals match up until the 7-limit.

Theory

Like 10edo, 13ed5/2 tempers out 50/49 in the no-threes 7-limit, supporting 5/2-equivalent jubilic temperament with a generator of ~7/5. In this regard, it could be considered a "no-threes cousin" of 12edo and 13edt, having the basic tuning for the octatonic scale of 5/2-equivalent jubilic (3L 5s⟨5/2⟩). It also tempers out 56/55 in the 11-limit and 65/64 in the 13-limit.

Approximation of harmonics in 13ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+20.2	+50.4	+40.5	+20.2	-51.4	+47.8	+60.7	-21.2	+40.5	-2.5	-31.1
	Relative (%)	+16.6	+41.3	+33.2	+16.6	-42.1	+39.2	+49.8	-17.3	+33.2	-2.0	-25.5
Steps (reduced)		10 (10)	16 (3)	20 (7)	23 (10)	25 (12)	28 (2)	30 (4)	31 (5)	33 (7)	34 (8)	35 (9)

Intervals

#	Cents	Approximate ratios*	Jubilic[8] notation
0	0.000	1/1	C
1	122.024	14/13, 35/32	C#, Db
2	244.048	8/7, 28/25	D
3	366.072	5/4, 16/13, 49/40	D#, Eb
4	488.096	32/25, 64/49	E
5	610.120	7/5, 10/7	F
6	732.144	20/13, 25/16, 49/32	F#, Gb
7	854.168	8/5, 13/8	G
8	976.192	7/4, 25/14	H
9	1098.216	13/7, 64/35	H#, Ab
10	1220.240	2/1, 49/25, 52/25	A
11	1342.264	35/16	A#, Bb
12	1464.288	16/7	B
13	1586.312	5/2	C

* Based on treating 13ed5/2 as a 5/2.5.7.13 subgroup temperament