Diatonic scale are major scales (those with a major third/triad: Ionian, Lydian, and Mixolydian), three are minor (those with a minor third/triad: Dorian, Phrygian, and Aeolian). To these may be added the seventh diatonic scale, with a diminished fifth above the reference note, the Locrian scale. These could be transposed not only to include one flat in the signature (as described by Glarean), but to all twelve notes of the chromatic scale, resulting in a total of eighty-four diatonic scales. The modern musical keyboard originated as a diatonic keyboard with only white keys. The black keys were progressively added for several purposes:
Diatonic scale Pythagorean tuning: Six of the "fifth" intervals (C–G, D–A, E–B, F–C', G–D', A–E') are all = 1.5, but B–F' is the discordant tritone, here ≈ 1.423828125. Extending the series of fifths to eleven fifths would result into the Pythagorean Chromatic scale. It would add pitches for the five "piano black key" notes, for instance A–E–B–F–C–G–D–A–E–B–F–C–G. A and G are commonly thought of as being the same note, but as worked out in this way, G is higher pitch than A by about 1.01364 (, the Pythagorean comma, about 24% of a semitone, = ). Depending on whether one chooses A