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