31 Tone Equal Temperament

Intervals: 15 : Lesser Septimal Tritone

The lesser septimal tritone is a musical interval that corresponds to the difference between the 5th and 7th harmonics (7:5). Unlike 12-ET, 31-ET distinguishes between the lesser septimal tritone and its inversion, the greater septimal tritone (which, as the name suggests, is the wider of the two intervals). The matches of both of these intervals in 31-ET are very close to the perfect intervals, a closer match than fifths and fourths are in 12-ET. This is serendipitous, as these intervals can be tricky to hear and understand.

The lesser septimal tritone sounds very distinct from the undecimal tritone. However, it is harder to distinguish between the lesser and greater septimal tritones. Other than the fact that the septimal tritones are closer in size, one reason for this difficulty is that both septimal tritones have a tonal center outside the interval, and another may be that most people are used to listening to, playing, and singing in 12-ET, where there is only one tritone.

The two septimal tritones are also the two intervals in 31-ET that correspond to a familiar interval from 12-ET, but that have the largest deviation in width from this interval. The lesser septimal tritone is 19.35 cents narrower than the tritone in 12-ET...an easily perceptible difference.

Root of the Septimal Tritone:

People used to 12-ET, in which the tritone is an ambiguous interval, may be surprised that in 31-ET, the septimal tritone implies a root. The implied root of this interval is a major third below the bottom note, or a septimal whole tone above the top note.

Widening this interval by a single step changes it to its inversion, and thus changes the root. (This change corresponds to tritone substitution, which becomes more involved in 31-ET, but also facilitated by this distinction. In contexts where the interval functions as a dissonance or ambiguity, this difference can be negligible, but in contexts where the root is reinforced by the presence of other notes and intervals, the difference can be more noticeable, with one tritone sounding more consonant and the other more dissonant.