Pseudo-octave

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Pseudo-octave (2.1:1)

A pseudo-octave, pseudooctave,[1] or paradoxical octave[2] in music is an interval whose frequency ratio is not 2:1 (2.3:1[1] or 1.9:1, for example), that of the octave, but is perceived or treated as equivalent to this ratio, and whose pitches are considered equivalent to each other as with octave equivalency.

Stretched octave

The stretched octave, for example 2.01 : 1 , rather than 2 : 1 (an 8.6 

overtones
, but in tune when played with lower notes whose overtones are themselves naturally stretched by an equivalent amount.

In

simple harmonic oscillator's integer multiple harmonics
.

The effect of strings' small

human hearing
.

The practical consequence of the discrepancy between the sharpened pitches in a bass note's overtone series that treble notes must match, makes it necessary to widen every interval very slightly. Generally, it's more than sufficient to sharpen only whole octaves slightly, rather than separately modifying all intervals that reach individual pitches in the upper octaves (see stretched tuning).

The octaves of Balinese gamelans are never tuned 2:1, but instead are stretched or compressed in a consistent manner throughout the range of each individual gamelan, due to the physical characteristics of their instruments. [citation needed] Another example is the tritave play on clarinets of the Bohlen–Pierce scale (3:1).

Octave stretching is less apparent on large pianos which have longer strings and hence less curvature for a given

upright, or spinet pianos.[citation needed] Another reason is that long strings under high tension can store more acoustic energy than can short strings, making larger instruments louder (hence making a single piano better able to be perceived over the volume of an entire orchestra) and giving them longer sustain than similar, smaller instruments.[citation needed
]

See also

References

  1. ^ a b "Interview with Max Mathews", p.21. Author(s): C. Roads and Max Mathews. Source: Computer Music Journal, Vol. 4, No. 4, (Winter, 1980), pp. 15–22. Published by: The MIT Press.
  2. ^ "The Paradoxes of Octave Identities", p.213. Author(s): Jenő Keuler. Source: Studia Musicologica Academiae Scientiarum Hungaricae, T. 40, Fasc. 1/3, (1999), pp. 211–224. Published by: Akadémiai Kiadó.

External links