The same as the Interval Vector, but expressed in a syntax used by Howard Hanson.ĭescribes the specific interval sizes that exist for each generic interval size. A saturation of 0 means the interval is present minimally, a saturation of 1 means it is the maximum possible. Indicates if the scale can be constructed using a generator, and an origin.Ī deep scale is one where the interval vector has 6 different digits, an indicator of maximum hierarchization.ĭefines the scale as the sequence of intervals between one tone and the next.ĭescribes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.įirst described by Michael Buchler (2001), this is a vector showing the prominence of intervals relative to the maximum and minimum possible for the scale's cardinality. This number includes the scale itself, so the number is usually the same as its cardinality unless there are rotational symmetries then there are fewer modes.ĭescribes if this scale is in prime form, using the Starr/Rahn algorithm. Modes are the rotational transformations of this scale. This value is the quantity of imperfections in this scale.

Cohemitonia describes how many such cohemitones exist.Īn imperfection is a tone which does not have a perfect fifth above it in the scale. Hemitonia describes how many such hemitones exist.Ī cohemitone is an instance of two adjacent hemitones.

If a scale is chiral, then it has an enantiomorph.Ī hemitone is two tones separated by a semitone interval. Notably an axis of reflection can occur directly on a tone or half way between two tones.Ī palindromic scale has the same pattern of intervals both ascending and descending.Ī chiral scale can not be transformed into its inverse by rotation. It also implies that the scale has Ridge Tones. If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. If there are any rotational symmetries, these are the intervals of periodicity. Some scales have rotational symmetry, sometimes known as 'limited transposition'. The tones in this scale, expressed as numbers from 0 to 11Ī code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations. Cardinality is the count of how many pitches are in the scale.

Formula harmonic minor scale