72 Equal Temperament - Interval Size

Interval Size

Below are the sizes of some intervals (common and esoteric) in this tuning. For reference, differences of less than 5 cents are melodically imperceptible to most people:

play diatonic scale in 72-et

contrast with just diatonic scale

contrast with diatonic scale in 12-et

Although 12-ET can be viewed as a subset of 72-ET, the closest matches to most commonly used intervals under 72-ET are distinct from the closest matches under 12-ET. For example, the major third of 12-ET, which is sharp, exists as the 24-step interval within 72-ET, but the 23-step interval is a much closer match to the 5:4 ratio of the just major third.

All intervals involving harmonics up through the 11th are matched very closely in this system; no intervals formed as the difference of any two of these intervals are tempered out by this tuning system. Thus 72-ET can be seen as offering an almost perfect approximation to 7-, 9-, and 11-limit music. When it comes to the higher harmonics, a number of intervals are still matched quite well, but some are tempered out. For instance, the comma 169:168 is tempered out, but other intervals involving the 13-th harmonic are distinguished.

Unlike tunings such as 31-ET and 41-ET, 72-ET contains many intervals which do not closely match any small-number (<16) harmonics in the harmonic series.