The qualification of cohemitonia versus ancohemitonia combines with the cardinality of semitones, giving terms like: dicohemitonic, triancohemitonic, and so forth.
In general, the number of semitones is more important to the perception of dissonance than the adjacency (or lack thereof) of any pair of them.
A special monotonic relationship exists between semitones and tritones as scales are built by projection, q.v.
The harmonic relationship of all these categories comes from the perception that semitones and tritones are the severest of dissonances, and that avoiding them is often desirable.
[10] In both later cases, however, there is a distinct preference for ancohemitonia, as the lack of adjacency of any two semitones goes a long way towards softening the increasing dissonance.
In general, ancohemitonic combinations are fewer for a given chord or scale size, but used much more frequently so that their names are well known.
Column "2C", row "7", another local minimum, refers to the Neapolitan major scale, which is cohemitonic and somewhat less common but still popular enough to bear a name.
(January 2020)">verification needed] Column "2A", row "4", another minimum, represents a few frankly dissonant, yet strangely resonant harmonic combinations: mM9 with no 5, 11♭9, dom13♭9, and M7♯11.
In addition, this is the maximal number of notes taken consecutively from the circle of fifths for which is it still possible to avoid a semitone.
In addition, this is the maximal number of notes taken consecutively from the circle of fifths for which is it still possible to avoid a tritone.
This allows a leading tone from below resolving upwards, as well as a descending flat-supertonic upper neighbor, both converging on the tonic.
It is very common that a cohemitonic (or even hemitonic) scale (e.g.: Hungarian minor { C D E♭ F♯ G A♭ B }) be displaced preferentially to a mode where the halfstep span is split (e.cont.
[23] Cohemitonic scales with multiple halfstep spans present the additional possibility of modulating between tonics each furnished with both upper and lower neighbors.
The following lists the key signatures for all possible untransposed modes of the aforementioned heptatonic scales using the note C as the tonic.