4/3

Interval information

Ratio	4/3
Factorization	22 × 3-1
Monzo	[2 -1⟩
Size in cents	498.045 ¢
Name	just perfect fourth
Color name	w4, wa 4th
FJS name	[math]\displaystyle{ \text{P4} }[/math]
Special properties	square superparticular, reduced, reduced subharmonic
Tenney norm (log2 nd)	3.58496
Weil norm (log2 max(n, d))	4
Wilson norm (sopfr(nd))	7
[sound info]
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Perfect fourth

4/3 is the frequency ratio of the just perfect fourth, which is easily one of the more heavily discussed intervals outside of xenharmony- in fact, some of these usages have gone on to inspire other music theories within xenharmonic contexts, such as certain ideas about tetrachords. As its inversion is the perfect fifth, 3/2, 4/3 is the octave reduced form of the third subharmonic. In the florid organum of Medieval music, 4/3 was reliably considered a consonance, and indeed was frequently emphasized. Once major thirds with a tuning approximating 5/4 began to be treated as consonances, however, the perception of 4/3 was altered to where it was at times considered a dissonance. However, as of late, the perfect fourth is once again being reevaluated as a consonance.

Approximations by EDOs

The following EDOs (up to 200) contain good approximations of the interval 4/3. 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	5\12	1.9550	1.9550	↑	10\24, 15\36
17	7\17	3.9274	5.5637	↓
29	12\29	1.4933	3.6087	↓
41	17\41	0.4840	1.6537	↓	34\82, 51\123, 68\164
53	22\53	0.0682	0.3013	↑	44\106, 66\159
65	27\65	0.4165	2.2563	↑	54\130, 81\195
70	29\70	0.9021	5.2625	↓
77	32\77	0.6563	4.2113	↑
89	37\89	0.8314	6.1663	↑
94	39\94	0.1727	1.3525	↓	78\188
111	46\111	0.7477	6.9162	↓
118	49\118	0.2601	2.5575	↑
135	56\135	0.2672	3.0062	↓
142	59\142	0.5466	6.4675	↑
147	61\147	0.0858	1.0512	↓
171	71\171	0.2006	2.8588	↑
176	73\176	0.3177	4.6600	↓
183	76\183	0.3157	4.8138	↑
200	83\200	0.0450	0.7500	↓

See also

• 3/2 – its octave complement
• 9/8 – its fifth complement
• Fourth complement
• Gallery of just intervals