Octave (interval region)

Interval information

Ratio	2/1
Factorization	2
Monzo	[1⟩
Size in cents	1200¢
Name	octave
Color name	w8, wa 8ve
FJS name	[math]\displaystyle{ \text{P8} }[/math]
Special properties	superparticular, harmonic, prime harmonic, highly composite harmonic
Tenney norm (log2 nd)	1
Weil norm (log2 max(n, d))	2
Wilson norm (sopfr(nd))	2
[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 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.

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.

Strangely enough, 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.

Links

• Anatomy of an Octave by Kyle Gann

See also

• Prime interval
• Gallery of Just Intervals
• Toctave
• EDO
• Ditave - an alternative more neutral name
• Octave reduction
• Octave complement