Editing Interval (music) (section)

== Non-diatonic intervals ==
{{further|Neutral interval|Subminor and supermajor}}

Intervals in non-diatonic scales can be named using analogs of the diatonic interval names, by using a diatonic interval of similar size and distinguishing it by varying the quality, or by adding other modifiers. For example, the just interval 7/6 may be referred to as a ''subminor third'', since it is ~267 cents wide, which is narrower than a minor third (300 cents in 12-TET, ~316 cents for the just interval 6/5), or as the ''[[septimal minor third]]'', since it is a [[7-limit]] interval. These names refer just to the individual interval's size, and the interval number need not correspond to the number of scale degrees of a (heptatonic) scale. This naming is particularly common in [[just intonation]] and [[microtonal]] scales.<ref name="xen-extended">{{cite web|url=https://en.xen.wiki/w/Extended-diatonic_interval_names |title=Extended-diatonic interval names |work=Xenharmonic wiki}}</ref>

The most common of these extended qualities are a [[neutral interval|'''neutral''' interval]], in between a minor and major interval; and [[subminor and supermajor|'''subminor''' and '''supermajor''' intervals]], respectively narrower than a minor or wider than a major interval. The exact size of such intervals depends on the tuning system, but they often vary from the diatonic interval sizes by about a [[quarter tone]] (50 cents, half a chromatic step). For example, the [[neutral second]], the characteristic interval of [[Arabic music]], in 24-TET is 150 cents, exactly halfway between a minor second and major second. Combined, these yield the progression ''diminished, subminor, minor, neutral, major, supermajor, augmented'' for seconds, thirds, sixths, and sevenths. This naming convention can be extended to unisons, fourths, fifths, and octaves with ''sub'' and ''super'', yielding the progression ''diminished, sub, perfect, super, augmented''. This allows one to name all intervals in 24-TET or 31-TET, the latter of which was used by [[Adriaan Fokker]]. Various further extensions are used in [[Xenharmonic music]].<ref name="xen-extended"/>