Concept
Octave
Overview
In music, an octave (Latin: octavus: eighth) or perfect octave (sometimes called the diapason) is an interval between two tones, one having twice the frequency of vibration of the other. For instance, the interval between C4 and C5 (in scientific pitch notation) is an octave.
The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems". The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class.
To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated 8a or 8va (Italian: all'ottava), 8va bassa (Italian: all'ottava bassa, sometimes also 8vb), or simply 8 for the octave in the direction indicated by placing this mark above or below the staff.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
That these are five and no more is proved by reason, as against the man who is all for strings and holes, and wants to explore these points irrationally by the senses; they all have their origin in numerical ratios. The ratio of the fourth is four to three, of the fifth three to two, of the octave two to one, of the octave and fifth three to one, of the double octave four to one. The additional consonance which…
Plutarch, Selected Essays of Plutarch, Vol. II.
Names Octave several times.
These segments, which decrease in length according to the numerical series 1, 2, 3, &c., correspond to tones of increasing pitch--the half string corresponds to the octave, the third part to the fifth of the octave, the fourth to the double octave, and so on. If these high tones are then produced alone, one after another, by making the corresponding part of the string vibrate each time, and if we then return to the…
Wilhelm Max Wundt, An Introduction to Psychology Translated from the Second German Edition
Names Octave several times.
As for the octaves, they keep a double proportion between their two extremes. For example, let the double arithmetical proportion be 6 and 12, this being the interval between the ὑπάτη μέσων and the νήτη διεζευγμένων; 6 therefore and 12 being the two extremes, the former note contains the number 6, and the latter 12. To these are to be added the intermediate numbers, to which the extremes must hold the proportion…
Plutarch, Plutarch's essays and miscellanies, Vol. 1
Names Octave twice; opens on Octave.
Philosophers who discussed Octave
Related ideas
Place in the tradition
Part of Pythagoreanism.