31 Tone Equal Temperament

List of Intervals in 31 Equal Temperament:

# of Steps:Interval Name
2Chromatic Semitone
3Diatonic Semitone
4Neutral Second
5Whole Tone
6Septimal Whole Tone
7Septimal Minor Third
8Minor Third
9Neutral Third
10Major Third
11Septimal Major Third / Undecimal
12Semi-Diminished Fourth
13Perfect Fourth
14Lesser Undecimal Tritone
15Lesser Septimal Tritone
16Greater Septimal Tritone
17Greater Undecimal Tritone
18Perfect Fifth

About the Naming Scheme

There is no universally agreed upon naming scheme for the musical intervals in 31-ET. Some of the musical intervals in 31-ET are familiar from the standard 12-ET tuning common in most western music. However, 31-ET also contains other intervals. In some cases, such as the semitones, or the tritones and their inversions, 31-ET distinguishes between different intervals that are lumped together as the same interval in 12-ET. In other cases, such as with neutral seconds, 31-ET includes intervals that are not commonly used in western music.

This site uses the same names for intervals when the intervals coincide with 12-ET. For other intervals, when there is a good match to a particular natural interval, like with the septimal whole tone and minor thirds, we have used a single name to refer to the new interval. In other cases, we use multiple names, depending on context.

The term septimal means that the interval is associated with the seventh harmonic. Similarly, the term undecimal means that the interval is associated with the 11th harmonic.

The interval consisting of 12 steps is one that does not correspond well with relationships between the small harmonics. To the ear, it usually sounds like an out-of-tune interval, either a sharp major third or a flat perfect fourth.