Cents
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The standard system for comparing intervals of different sizes is with cents. This is a logarithmic scale in which the octave is divided into 1200 equal parts. In equal temperament, each semitone is exactly 100 cents. The value in cents for the interval f1 to f2 is 1200×log2(f2/f1).
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Comparison of different interval naming systems
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| # semitones |
Interval class |
Generic interval |
Common diatonic name |
Comparable just interval |
Comparison of interval width in cents | ||
|---|---|---|---|---|---|---|---|
| equal temperament |
just intonation |
quarter-comma meantone | |||||
| 0 | 0 | 0 | perfect unison | 1:1 | 0 | 0 | 0 |
| 1 | 1 | 1 | minor second | 16:15 | 100 | 112 | 117 |
| 2 | 2 | 1 | major second | 9:8 | 200 | 204 | 193 |
| 3 | 3 | 2 | minor third | 6:5 | 300 | 316 | 310 |
| 4 | 4 | 2 | major third | 5:4 | 400 | 386 | 386 |
| 5 | 5 | 3 | perfect fourth | 4:3 | 500 | 498 | 503 |
| 6 | 6 | 3 4 |
augmented fourth diminished fifth |
45:32 64:45 |
600 | 590 610 |
579 621 |
| 7 | 5 | 4 | perfect fifth | 3:2 | 700 | 702 | 697 wolf fifth 737 |
| 8 | 4 | 5 | minor sixth | 8:5 | 800 | 814 | 814 |
| 9 | 3 | 5 | major sixth | 5:3 | 900 | 884 | 889 |
| 10 | 2 | 6 | minor seventh | 16:9 | 1000 | 996 | 1007 |
| 11 | 1 | 6 | major seventh | 15:8 | 1100 | 1088 | 1083 |
| 12 | 0 | 0 | perfect octave | 2:1 | 1200 | 1200 | 1200 |
It is possible to construct just intervals which are closer to the equal-tempered equivalents, but most of the ones listed above have been used historically in equivalent contexts. In particular the tritone (augmented fourth or diminished fifth), could have other ratios; 17:12 (603 cents) is fairly common. The 7:4 interval (the harmonic seventh) has been a contentious issue throughout the history of music theory; it is 31 cents flatter than an equal-tempered minor seventh. Some assert the 7:4 is one of the blue notes used in jazz.
In the diatonic system, every interval has one or more enharmonic equivalents, such as augmented second for minor third.
