A diatonic scale consists of three sets of major triads. Major triads are collections of three notes with frequencies in the ratio 4:5:6. Within an octave, three major triads can be constructed as follows.

There are three intervals in this scale 9:8 (1.125), 10:9 (1.111), and 16:15 (1.067). The first two are called whole steps and the third a half step (or semitone), even though two half steps are larger than one whole step.

The diatonic scale is of ancient origin, but the particular tuning incorporated into modern just intonation (see below) is due to Ptolemy, and probably dates from the second century A.D. Ptolemy gave it as one of a dozen or so possible tunings for the diatonic scale (calling it the "syntonic diatonic"). It was rediscovered by Gaffurio in the late 15th century, from whom Zarlino learned about it, and it has remained the basic scale used in western music ever since (Jeans 1938, p. 164). In particular, all of the church modes (dorian, phrygian, lydian, myxolydian, and aeolian) are rotations of the so-called major scale are diatonic.

In just intonation, the diatonic scale (as well as other scales) work differently for different starting notes, leading to the concept of the key. For example, music written in just intonation would have to be re-written if the scale were shifted in starting note in order to preserve consonance. The scale used on piano and fretted instruments is actually an approximation to the exact ratios given above because modern western music uses an equal temperament scale, allowing music to be transposed while slightly sacrificing the euphony of chords.

Major Scale, Mode, Scale

References

Barker, A. (Ed.). Greek Musical Writings, Vol. 2: Harmonic and Acoustic Theory. Cambridge, England: Cambridge University Press, 1990.

Zarlino. Istutione Harmoniche. 1558.