A pseudo-octave, pseudooctave,[1] or paradoxical octave[2] in music is an interval whose frequency ratio is not exactly 2:1 = octave : tonic expected for perfectly harmonic pitches, but slightly wider or narrower in pitch – for example 1.98:1, 2.01:1, or even as large as 2.3:1 .[1] The pseudo-octave is never-the-less perceived as if it were equivalent to the conventional 2:1 harmonic ratio, and consequently is treated the same: Pitches separated by a pseudo-octave appropriate for a given instrument are considered equivalent to each other just as with normal "pitch classes" (which are typically explained only in terms of the idealized 2:1 octave).
- ^ a b Roads, C.; Mathews, M. (Winter 1980). "Interview with Max Mathews". Computer Music Journal. 4 (4): 15–22, esp. 21.
- ^ Keuler, Jenő (1999). "The paradoxes of octave identities". Studia Musicologica Academiae Scientiarum Hungaricae. 40 (1–3): 211–224, esp. 213.