Octave
Ratio | 2/1 |
Factorization | 2 |
Monzo | [1⟩ |
Size in cents | 1200¢ |
Names | octave, ditave, diapason |
Color name | w8, wa 8ve |
FJS name | [math]\text{P8}[/math] |
Special properties | superparticular, harmonic |
Tenney height (log_{2} nd) | 1 |
Weil height (log_{2} max(n, d)) | 2 |
Wilson height (sopfr (nd)) | 2 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~3.27036 bits |
[sound info] | |
open this interval in xen-calc |
The octave (interval ratio 2/1) is one of the most basic intervals found in musical systems throughout the entire world. It has a frequency ratio of 2/1 and a size of 1200 cents. It is used as the standard of (logarithmic) measurement for all intervals, regardless if they are justly tuned or not.
Octave equivalence
The octave is usually called the interval of equivalence, because tones separated by an octave are perceived to have the same or similar pitch class to the average human listener. The reason for this phenomenon is probably due to the strong region of attraction of low harmonic entropy, or the strong amplitude of the second harmonic in most harmonic instruments.
The Pelog and Slendro scales of the Javanese contain near-octaves even though Gamelan instruments exhibit inharmonic spectra. It is most likely reminiscent of an older musical system, or derived using the human voice instead of inharmonic instruments.
The Wikipedia article includes a short discussion on its ongoing nature–nurture debate and its psychoacoustic bases. For example, it is shown that many animals including monkeys and rats experience octave equivalence to a certain extent^{[1]}. Meanwhile, an article in Current Biology including an 8-minute video shows that octave equivalence might be a cultural phenomenon^{[2]}.
A generalisation where we let a different interval define equivalence is equave, such as the tritave.
Alternate names
Ditave is an alternative name for the interval 2/1, which was proposed to neutralize the terminology against the predominance of 7-tone scales. The name is derived from the numeral prefix δι- (di-, Greek for "two") in analogy to "tritave" (3/1). A brief but complementary description about it is here.
Diapason is another term also sometimes applied to 2/1. It is also of Greek origin, but not related to the number two; instead it is formed from διά (dia) + πασων (pason), meaning something like "through all the notes".