Text: INTERVAL RATIO Unison 1:1 Pythagorean Komma 81:80 Enharmonic 128:125 Lesser Chromatic Semitone 25:24 Diesis 25:24 Greater Chromatic Semitone 135:128 Minor Diatonic Semitone 17:16 Major Diatonic Semitone 16:15 Limma 16:15 Minor Second 27:25 Smaller Step or Minor Tone 10:9 Greater Step or Major Tone 9:8 Major Second 9:8 Augmented Second 75:64 Minor Third 6:5 Major Third 5:4 Diminished Fourth 32:25 Augmented Third 125:96 Perfect Fourth 4:3 Augmented Fourth 25:18 Tritone 45:32 Diminished Fifth 64:45 Diminished Fifth 36:25 Perfect Fifth 3:2 Augmented Fifth 25:16 Minor Sixth 8:5 Major Sixth 5:3 Augmented Sixth 125:72 Harmonic Seventh 7:4 Dominant or Minor Seventh 16:9 Minor Seventh 9:5 Tonic Seventh 9:5 Major Seventh 15:8 Diminished Octave 48:25 Augmented Seventh 125:64 Octave 2:1 Minor Ninth 32:15 Major Ninth 9:4 Harmonic Minor Tenth 7:31 Minor Tenth 12:5 Major Tenth 5:2 Perfect Eleventh 8:3 Harmonic Eleventh 11:4 Augmented Eleventh 45:16 Perfect Twelfth 3:1 Augmented Twelfth 25:8 Minor Thirteenth 16:5 Harmonic Thirteenth 13:4 Major Thirteenth 10:3 Harmonic Fourteenth 7:2 Dominant Fourteenth 32:9 Tonic Fourteenth 18:5 Major Fourteenth 15:4 Double Octave 4:1 (Editor's Note:) This is not a comprehensive list but only introductory in extent. As these ratios are found out, they will be published from time to time. There is much license in interval definition. Some authorities give the intervals as so many semitones and tones without an accurate definition as to the relative frequency of either. In this publication we will try to stick with the numerically defined ratios thereby diminishing ambiguities. It should also be kept foremost in mind that we are discussing the natural derivation of numbers and NOT sensorial pleasing music. Nature obeys the infinite relations of number and not what Man may find pleasing to his finite senses.)

See Also:

Source: