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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