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 talk about acoustic intervals, we are talking about the intervals of the harmonic series. Click on the cents to listen to the sounds.
Thirds. Difference in cents with acoustic interval.
| Major third (cents) | Minor third (cents) | |||
|---|---|---|---|---|
| Cents | Difference | Cents | Difference | |
| Acoustic | 386 | 316 | ||
| Pitagorean | 408 | +22 | 294 | -22 |
| Meantone | 386 to 427 | 0 to +41 | 269 to 310 | -47 a -6 |
| Kirnberger III | 386 to 408 | 0 to +22 | 294 to 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 | N/A | N/A | |
| Pitagorean | 702 | 0 | 678 | -24 |
| Meantone | 697 | -5 | 738 | +36 |
| Kirnberger III | 697 to 702 | -5 to 0 | N/A | N/A |
| Equal | 700 | -2 | N/A | N/A |
NOTE: The Meantone temperament reduces the size of the fifth in order to have acoustic major thirds. The last fifth, which completes the cycle, is very large. It is called the wolf's fifth because it is said to howl like a wolf. In the case of Pythagorean tuning, when acoustic fifths are used, 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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