Glossary

This page lists various terms conventionally used in xenharmony (or in some cases, general music theory as it applies to xen) that can be briefly described.

Don't put idiosyncratic terms here. When using personal terminology in an article, either explain it there or link to an article about your theory that explains the term.

Cent

A cent (abbreviated to c or ¢) is the conventional measurement unit of the logarithmic distance between frequencies; in other words, the size of the interval between them. A cent is defined as a frequency ratio of 2^(1/1200), or a factor of about 1.0005778, such that the octave (2/1) spans exactly 1200 cents, and therefore that each step of 12edo spans exactly 100.

Equave

An equave or interval of equivalence is an interval that separates notes that are considered equivalent. Most commonly the octave (2/1), but 3/1, 3/2, and other intervals are sometimes used.

Signature

A signature is a list of numbers giving useful but incomplete information about the object it pertains to. Usually refers to one of:

• a step signature, a list of how many of each step size a scale has; e.g. 4L3m2s.
• a delta signature, a list of frequency increases between adjacent notes measured relative to a reference frequency increase, e.g. +1+1+2.

Superparticular

A superparticular or Delta-1 ratio is a ratio between two whole numbers which differ by 1: e.g. 2/1, 3/2, 4/3, 5/4, etc, representing intervals between consecutive members of the harmonic series. These are distinguished from superpartient ratios (all other rational ratios), which can be classified as Delta-2, Delta-3, etc. by the difference between their numerator and denominator. Note that the ratio between consecutive superparticulars is itself superparticular.

Ternary

A ternary scale is a scale with exactly three step sizes (usually denoted L, m, and s).

Variety

Variety (or interval variety) refers to how many interval sizes the set of all k-step intervals (called an interval class) come in. We often refer to maximum variety (MV) or strict variety (SV). For example, MOS scales can be defined as scales that are MV2.