Interordinal

Interordinals are interval categories halfway between adjacent interval classes of some MOS (usually diatonic). For example, 250c is an interordinal because it falls between 200c (the 12edo major second) and 300c (the 12edo minor third).

19edo and 24edo are notable edos with interordinals. Notable JI interordinals include 15/13 (a semifourth) and 13/10 (a semisixth).

The following table shows various ways to name interordinals:

Interordinal nomenclature

24edo interval	"semi" names	Greek-derived names	"inter" names	"ultra"/"infra"
250c, 5\24	semifourth	chthonic	second-inter-third	ultramajor second inframinor third
450c, 9\24	semisixth	naiadic	third-inter-fourth	ultramajor third infrafourth
750c, 15\24	semitenth	cocytic	fifth-inter-sixth	ultrafifth inframinor sixth
950c, 19\24	semitwelfth	ouranic	sixth-inter-seventh	ultramajor sixth inframinor seventh