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.
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 |
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.
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 |
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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