Interval quality: Difference between revisions

Given a scale, a ''relative interval quality'' is a specific interval size that occurs in a given  [[interval class]] of the scale. An interval class is the set of all intervals in the scale that span a given number of [[step]]s. For example, all intervals that span two steps of a scale are ''thirds'' or ''2-steps''. (The latter is often used to avoid confusion with absolute interval quality and to make interval arithmetic in unfamiliar scales easier.) Scales with a higher density of notes typically have smaller 2-steps; as a result, in a scale with more or fewer notes per octave than the diatonic scale, 2-steps may fall outside of the usual range for diatonic thirds (i.e. between 240{{cent}} and 480{{cent}}).

In an [[equal tuning|equal scale]], each interval class contains exactly one interval; in other words, every interval is perfect. Both 5\[[8edo|8]] and 5\[[13edo|13]] are perfect 5-steps (or perfect sixths) within their respective [[edo]] taken as a scale, even though they have significantly different sizes.

In [[moment of symmetry]] (MOS) scales, each interval class contains two intervals except for the unison class, which only contains the unison, and the period class, which only contains the period. The two interval classes that correspond to the [[Modal UDP notation#Generalizing to arbitrary MOS scales: bright and dark generators (chroma-positive and chroma-negative)|bright and dark generators]] contain only perfect intervals except for one ''imperfect'' interval, which is either ''augmented'' or ''diminished'' depending on its size relative to the perfect generator. The other interval classes contain major and minor intervals.

Another way to generalize interval qualities from traditional theory is to define [[interval region]]s corresponding to the 12 tones of the chromatic scale. That way, similar intervals, such as [[13/11]] (~289{{cent}}), 3\12 (300{{cent}}), [[6/5]] (~316{{cent}}), and 3\[[11edo|11]] (~327{{cent}}), can all be considered different flavours of minor thirds. These regions can further be subdivided into finer categories; for instance, smaller minor thirds could be qualified as "narrow minor thirds", "subminor thirds", etc.

 

Interval regions can also be defined using a different framework than the diatonic scale. However, the diatonic scale is often preferred because it offers a familiar point of reference for many musicians.

[[Category:Terms]]