What are cents in music?
José Rodríguez Alvira
Comparisons using cents
We will use the cents to compare intervals according to different temperaments. When we refer to acoustic intervals, we refer to the intervals of the harmonic series. Click on the cents to hear the sounds.
Thirds. Difference in cents with acoustic interval.
| Major third (cents) | Minor third (cents) | |||
|---|---|---|---|---|
| Cents | Difference | Cents | Difference | |
| Acoustic | 386 | 0 | 316 | 0 |
| Pitagorean | 408 | +22 | 294 | -22 |
| Meantone | 386 a 427 | 0 a +41 | 269 a 310 | -47 a -6 |
| Kirnberger III | 386 a 408 | 0 a +22 | 294 a 316 | -22 a 0 |
| Equal | 400 | +14 | 300 | -14 |
Fifths. Difference in cents with acoustic interval.
| Perfect fifth | Wolf fifth | |||
|---|---|---|---|---|
| Cents | Difference | Cents | Difference | |
| Acoustic | 702 | 0 | N/A | N/A |
| Pitagorean | 702 | 0 | 678 | -24 |
| Meantone | 697 | -5 | 738 | +36 |
| Kirnberger III | 697 a 702 | -5 a 0 | N/A | N/A |
| Equal | 700 | -2 | N/A | N/A |
NOTE: The meantone temperament reduces the size of the fifth to have acoustic major thirds. The last fifth that closes the cycle is very large. It is called wolf fifth because it is said to howl like a wolf. In the case of Pythagorean tuning, when using acoustic fifths, the fifth that closes the cycle is very small. These fifths make it impossible to use all the keys in these tunings.
C major scales in different tunings
| Pitagorean | Do (C4) | Re (D4) | Mi (E4) | Fa (F4) | Sol (G4) | La (A4) | Si (B4) |
|---|---|---|---|---|---|---|---|
| Frequency | 260 | 292.5 | 329.1 | 346.7 | 390 | 438.8 | 493.6 |
| Cents | 0 | 204 | 408 | 498 | 702 | 906 | 1110 |
| Just intonation | |||||||
| Frequency | 260 | 292.5 | 325.0 | 346.7 | 390.0 | 433.3 | 487.5 |
| Cents | 0 | 204 | 386 | 498 | 702 | 884 | 1088 |
| Meantone | |||||||
| Frequency | 260 | 290.7 | 325 | 347.7 | 388.8 | 434.7 | 486 |
| Cents | 0 | 193 | 386 | 503 | 697 | 890 | 1083 |
| Kirnberger III | |||||||
| Frequency | 260 | 290.7 | 325 | 346.7 | 388.8 | 434.7 | 487.5 |
| Cents | 0 | 193 | 386 | 498 | 697 | 890 | 1088 |
| Igual | |||||||
| Frequency | 260 | 291.8 | 327.6 | 347.1 | 389.6 | 437.3 | 490.9 |
| Cents | 0 | 200 | 400 | 500 | 700 | 900 | 1100 |
Difference in cents between in relation to equal temperament:
| Do (C4) | Re (D4) | Mi (E4) | Fa (F4) | Sol (G4) | La (A4) | Si (B4) | |
|---|---|---|---|---|---|---|---|
| Pitagorean | 0 | +4 | +8 | -2 | +2 | +6 | +10 |
| Just intonation | 0 | +4 | -14 | -2 | +2 | -16 | -12 |
| Meantone | 0 | -7 | -14 | +3 | -3 | -10 | -17 |
| Kirnberger III | 0 | -8 | -14 | -2 | -3 | -10 | -12 |
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