Diatonic major third

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Revision as of 07:52, 27 December 2025 by Vector (talk | contribs) (Created page with "{{Infobox interval|81/64|Name=Diatonic major third}} The '''diatonic major third (M3)''', represented by the frequency ratio '''81/64''', is the larger of the two thirds (2-step intervals) in the MOS form of the diatonic scale. It is generated by stacking 4 fifths octave-reduced. In Pythagorean tuning (and thus purely-tuned just intonation), it is approximately {{Cents from ratio|81/64|ratio=81/64}} cents in size, but as an interval in the abstract diatonic scal...")
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Interval information
Ratio 81/64
Factorization 2-6 × 34
Monzo [-6 4⟩
Size in cents 407.82¢
Name Diatonic major third
Special properties reduced,
reduced harmonic
Harmonic distance (log2 nd) 12.3399
Wilson norm (sopfr(nd)) 24
Open this interval in xen-calc


The diatonic major third (M3), represented by the frequency ratio 81/64, is the larger of the two thirds (2-step intervals) in the MOS form of the diatonic scale. It is generated by stacking 4 fifths octave-reduced. In Pythagorean tuning (and thus purely-tuned just intonation), it is approximately 407.8 cents in size, but as an interval in the abstract diatonic scale it may range from 343 to 480 cents, depending on the tuning.

It can be constructed by stacking two diatonic major seconds, and as such may be called the ditone.

As a harmonic interval, the diatonic major third may be considered either a consonance or a dissonance depending on its tuning. Important tuning targets for the diatonic major third are 5/4 (Meantone temperament), 14/11 (Pentacircle temperament), 9/7 (Archytas temperament) and 13/10 (Oceanfront temperament).

Scale info

The diatonic scale contains three major thirds. In the Ionian mode, major thirds are found on the first, fourth, and fifth degrees of the scale; the other four degrees have minor thirds. This roughly equal distribution leads to diatonic tonality being largely based on the distinction between major and minor thirds and triads.