equivalence interval, interval of equivalence

"interval of equivalence" = "equivalence interval" = "formal octave" is that interval (much larger than a unison) which, when it occurs between two pitches, we consider them to be, in some sense, (formally if not perceptibly) the same note.

For most scales this is the octave 1:2, and when it is not the octave it is usually some other highly consonant interval such as the "tritave" 1:3. But the essential feature of the interval of equivalence in relation to definitions of scales and types of scales is that when we describe a scale we describe only the pitches that fall within a single interval of equivalence, and we leave it up to the instrument builder to decide the range of the instrument and therefore how many times (including fractions) the interval of equivalence should be repeated.

[from Dave Keenan, Yahoo tuning-math message]

See also:

periodicity,
periodicity interval

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