Musical Intervals

Harmony is concerned with chords, and every chord is a combination of intervals sounded simultaneously. Any systematic study of harmony must therefore begin with an examination of intervals. The following interval data was found in many obscure and not so obscure sources. We found others but only included those having numeric values. You will note, some information conflicts with others. The intervals that form the basis of music, and their measurements relative to one another are (generally held) as follows:

Unison                       1 : 1
Pythagorean comma       531441 : 52428
Schisma (Coutts)         32805 : 32768
Schisma(?)               10240 : 10125
Comma (Minor)            10240 : 10125
Diaschisma               10240 : 10125
Komma                       81 : 80
Comma of Pythagoras         81 : 80
Comma (Major)               81 : 80
Comma (syntonic)            81 : 80
Enharmonic Diesis          128 : 125
Enharmonic                 128 : 125
Chromatic Diesis            25 : 24
Semitone Minimus            25 : 24
Minor Semitone              25 : 24
Semitone or Diesis          25 : 24
Lesser Chromatic Semitone   25 : 24
Leimma (Plato, Theon)      256 : 243
Pythagorean Semitone       256 : 243
Greater Chromatic Semitone 135 : 128
Semitone Medius            135 : 128
Chromatic Semitone         135 : 128
Semitone Maximus            27 : 25
Major Semitone              16 : 15
Limma                       16 : 15
Diatonic Semitone           16 : 15
Apotome Pythagorica       2187 : 2048
Minor Second                27 : 25
Minor Tone                  10 : 9
Smaller Step or Minor Tone  10 : 9
Greater Step or Minor Tone   9 : 8
Major Second                 9 : 8
Sesquioctave                 9 : 8
Major Tone                   9 : 8
Augmented Second            75 : 64
Minor Third                  6 : 5
Sesquiquintan                6 : 5
Major Third                  5 : 4
Sesquiquartan                5 : 4
Diminished Fourth           32 : 25
Augmented Third            125 : 96
Perfect Fourth               4 : 3
Sesquitertan                 4 : 3
Augmented Fourth            25 : 18
Tritone                     45 : 32
Diminished Fifth            64 : 45
Diminished Fifth            36 : 25
Perfect Fifth                3 : 2
Trihemitone                  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 : 3
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