2/1

Interval information

Ratio	2/1
Factorization	2
Monzo	[1⟩
Size in cents	1200¢
Names	octave, ditave, duple, diapason
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]
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English Wikipedia has an article on:

Octave

The octave (abbreviation: 8ve, symbol: oct, frequency 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.

It is the first prime harmonic, with the next being 3/1.

Octave equivalence

Main article: Interval of equivalence

The octave is usually called the interval of equivalence, because tones separated by this interval are perceived as having the same pitch class despite their different absolute pitches. This equivalence is so strong that in most musical notation systems, notes separated by octaves share the same name. For the same reason, most scales repeat at the octave.

Octave stretch

Main article: Stretched and compressed tuning

Some musical systems exhibit stretched (or compressed) octaves where the octave is tuned slightly different from a pure 2:1 ratio. This occurs in piano tuning (to compensate for inharmonicity in piano strings) and in some traditional music systems, such as the Indonesian Pelog and Slendro scales.

Alternative names

Ditave is an alternative name for the interval 2/1, which was proposed to neutralize the terminology against the predominance of heptatonic scales. The name is a contraction of the numeral prefix δι- (di-, Greek for "two") and octave, in analogy to "tritave" (3/1).

Duple is a proposed term which relates itself to the ancient Greek concept of multiples. It also fixes the problem of using part of the word octave.

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".

See also

• Prime interval
• Gallery of Just Intervals
• EDO
• Octave reduction
• Octave complement
• Octave (interval region)