Editing Semitone (section)

===Extended just intonations===
In [[7-limit|7&nbsp;limit tuning]] there is the [[septimal diatonic semitone]] of 15:14 ({{Audio|Septimal diatonic semitone on C.mid|play}}) available in between the 5&nbsp;limit [[major seventh]] (15:8) and the [[septimal minor seventh|7&nbsp;limit minor seventh]] / [[harmonic seventh]] (7:4). There is also a smaller [[septimal chromatic semitone]] of 21:20 ({{Audio|Septimal chromatic semitone on C.mid|play}}) between a septimal minor seventh and a fifth (21:8) and an octave and a major third (5:2). Both are more rarely used than their 5&nbsp;limit neighbours, although the former was often implemented by theorist [[Henry Cowell|Cowell]], while [[Harry Partch|Partch]] used the latter as part of [[Harry Partch's 43-tone scale|his 43&nbsp;tone scale]].

Under 11&nbsp;limit tuning, there is a fairly common ''undecimal [[neutral second]]'' (12:11) ({{Audio|Neutral second on C.mid|play}}), but it lies on the boundary between the minor and [[major second]] (150.6&nbsp;cents). In just intonation there are infinitely many possibilities for intervals that fall within the range of the semitone (e.g. the Pythagorean semitones mentioned above), but most of them are impractical.

In 13&nbsp;limit tuning, there is a tridecimal {{sfrac|2|3}} tone (13:12 or 138.57&nbsp;cents) and tridecimal {{sfrac|1|3}} tone (27:26 or 65.34&nbsp;cents).

In 17&nbsp;limit just intonation, the major diatonic semitone is 15:14 or 119.4&nbsp;cents ({{audio|Major diatonic semitone on C.mid|Play}}), and the minor diatonic semitone is 17:16 or 105.0&nbsp;cents,<ref>{{cite book |author-link=Ebenezer Prout |last=Prout |first=E. |year=2004 |title=Harmony |page=325 |publisher=University Press of the Pacific |isbn=1-4102-1920-8}}</ref> and septendecimal limma is 18:17 or 98.95&nbsp;cents.

Though the names ''diatonic'' and ''chromatic'' are often used for these intervals, their musical function is not the same as the meantone semitones. For instance, 15:14 would usually be written as an augmented unison, functioning as the ''chromatic'' counterpart to a ''diatonic'' 16:15. These distinctions are highly dependent on the musical context, and just intonation is not particularly well suited to chromatic use (diatonic semitone function is more prevalent).