Pseudo-octave

[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).

The so-named "piano-tuners' octave" used to compensate for the non-harmonic partials is well approximated by the Railsback curve (which see).

The effect of strings' small inelastic response is that rather than the simple harmonics expected for its overtone series, which would all be integer multiples of the fundamental frequency, the timbre of the note that the string actually produces has slightly inharmonic overtones.

Partials measured in the sounds produced by real musical instruments almost always have a slightly higher pitch than the corresponding idealized harmonic, with the discrepancy being less important for high-pitched instruments (above 5000 Hz) whose high-level overtones fall above the range of human hearing.

[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.