31 Tone Equal Temperament

Tempering Out

In tuning, the concept of tempering out refers to a tuning removing the distinction between two intervals close in size, or the identification with unison of a narrow interval. When this happen, it is said that the tuning tempers out the interval or the difference between the two intervals. The concept of tempering out intervals is usually used in reference to the intervals of just intonation.

The tempering out of a small interval to unison, and the tempering out the difference between two intervals are equivalent concepts. For example:

Differences Tempered Out in 12-ET but not 31-ET:

This list is not exhaustive but serves just to give some examples:

Although technically true that 12-ET "tempers out" the difference between neutral seconds and neutral thirds, and the other intervals more closely matched by 12-ET, it doesn't necessarily make much sense to say this because these intervals fall almost exactly halfway in between the steps of the 12-ET scale.

Differences that 31-ET Tempers Out:

31-ET tempers out a large number of intervals, but the main relevant ones are those involving harmonics up through the 11th.