3/2

Interval information

Ratio	3/2
Factorization	2-1 × 3
Monzo	[-1 1⟩
Size in cents	701.955¢
Name	just perfect fifth
Color name	w5, wa 5th
FJS name	[math]\displaystyle{ \text{P5} }[/math]
Special properties	superparticular, reduced, reduced harmonic
Tenney height (log2 nd)	2.58496
Weil height (log2 max(n, d))	3.16993
Wilson height (sopfr(nd))	5
[sound info]
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Main article: Just perfect fifth

3/2 is the frequency ratio of the just perfect fifth. What tunes it well, is one of variants of 12edo or 17edo (such as 24edo, 34edo and 36edo). Other edos tune it well too (5, 7, 29, 41, 53, 200). But not all edos are like this. 35edo is great for 2, 5, 7, 9, 11 and 17 but fails on 3.

Approximations by EDOs

Following EDOs (up to 200) contain good approximations of the interval 3/2. Errors are given by magnitude, the arrows in the table show if the EDO representation is sharp (↑) or flat (↓).

EDO	deg\edo	Absolute error (¢)	Relative error (r¢)	↕	Equally acceptable multiples
12	7\12	1.9550	1.9550	↓	14\24, 21\36
17	10\17	3.9274	5.5637	↑
29	17\29	1.4933	3.6087	↑
41	24\41	0.4840	1.6537	↑	48\82, 72\123, 96\164
53	31\53	0.0682	0.3013	↓	62\106, 93\159
65	38\65	0.4165	2.2563	↓	76\130, 114\195
70	41\70	0.9021	5.2625	↑
77	45\77	0.6563	4.2113	↓
89	52\89	0.8314	6.1663	↓
94	55\94	0.1727	1.3525	↑	110\188
111	65\111	0.7477	6.9162	↑
118	69\118	0.2601	2.5575	↓
135	79\135	0.2672	3.0062	↑
142	83\142	0.5466	6.4675	↓
147	86\147	0.0858	1.0512	↑
171	100\171	0.2006	2.8588	↓
176	103\176	0.3177	4.6600	↑
183	107\183	0.3157	4.8138	↓
200	117\200	0.0450	0.7500	↑

See also

• Gallery of Just Intervals
• 4/3 – its octave complement

Todo: merge articles 3/2 and just perfect fifth