Equal temperament 路 Just intonation C major scale
frequency ratios relative to C (root)
Equal temperament (12-TET)
Just intonation (pure ratios)
Note Equal temperament
ratio (decimal)		 Just intonation
ratio (fraction 路 decimal)
C 1.00000 1/1 = 1.0000
D 1.12246 9/8 = 1.1250
E 1.25992 5/4 = 1.2500
F 1.33484 4/3 = 1.3333
G 1.49831 3/2 = 1.5000
A 1.68179 5/3 = 1.6667
B 1.88775 15/8 = 1.8750
C 2.00000 2/1 = 2.0000
pure harmonic third = 5 : 4 (1.25)
just E is lower than equal E by about 14 cents
馃幍 Equal temperament
  • 12 equal semitones
  • ratio = 2^(n/12)
  • all keys usable
  • slight beating in thirds
馃幖 Just intonation
  • whole-number ratios
  • based on harmonic series
  • pure, beatless chords
  • key鈥慸ependent
C = 1/1 路 D = 9/8 路 E = 5/4 路 F = 4/3 路 G = 3/2 路 A = 5/3 路 B = 15/8 路 C = 2/1