5-limit

The 5-limit (aka pental) consists of all ratios in just intonation whose ratios contain no prime factors greater than 5; for example 5/4, 16/15, and 81/80. The 5-limit is considered the basis of western harmony, with the ratios of the 5-odd-limit being considered consonances. The main consonant chords of the 5-limit are the 4:5:6 major triad and the 10:12:15 minor triad. The smallest EDOs that approximate these triads within 20 cents are 12, 15, 19, 22, etc.

The 5-limit is associated with the 7-form, though this is a weaker match than the 2.3.7 subgroup and the 5-form. (The fundamental 5-limit diatonic temperament, meantone, is not a 7-cluster temperament but rather is tuned optimally near a golden generator, unlike with archy). The main other 5-limit form is the 12-form, as in meantone[12], augmented[12], diminished[12], and diaschismic[12].

Aberrismic theory

Main article: Aberrisma#Quasi-diatonic aberrismic scales

The fundamental pental aberrismic scale is blackdye.