An incomposite interval (; ) is a concept in the Ancient Greek theory of

music Music is generally defined as the The arts, art of arranging sound to create some combination of Musical form, form, harmony, melody, rhythm or otherwise Musical expression, expressive content. Exact definition of music, definitions of mu ...

concerning

melodic A melody (from Greek μελῳδία, ''melōidía'', "singing, chanting"), also tune, voice or line, is a linear succession of musical tones that the listener perceives as a single entity. In its most literal sense, a melody is a combina ...

musical intervals () between neighbouring notes in a

tetrachord In music theory, a tetrachord ( el, τετράχορδoν; lat, tetrachordum) is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency pr ...

scale Scale or scales may refer to: Mathematics * Scale (descriptive set theory), an object defined on a set of points * Scale (ratio), the ratio of a linear dimension of a model to the corresponding dimension of the original * Scale factor, a number ...

which, for that reason, do not encompass smaller intervals. ( means "uncompounded".)

Aristoxenus Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have bee ...

(

fl. ''Floruit'' (; abbreviated fl. or occasionally flor.; from Latin for "they flourished") denotes a date or period during which a person was known to have been alive or active. In English, the unabbreviated word may also be used as a noun indicatin ...

335 BCE) defines melodically incomposite intervals in the following context: In another place, Aristoxenus clarifies that It is thus not an issue of the voice being physically incapable of singing a note within an incomposite interval. For example, in the

enharmonic genus In the musical system of ancient Greece, genus (Greek: γένος 'genos'' pl. γένη 'genē'' Latin: ''genus'', pl. ''genera'' "type, kind") is a term used to describe certain classes of intonations of the two movable notes within a tetracho ...

the distance from the neighbouring scale degrees ''lichanos'' () to ''mesē'' () is a

ditone In music, a ditone (, from , "of two tones") is the interval of a major third. The size of a ditone varies according to the sizes of the two tones of which it is compounded. The largest is the Pythagorean ditone, with a ratio of 81:64, also cal ...

—a gap equivalent to the

major-third In classical music, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third () is a third spanning four semitones. Forte, Allen (1979). ''Tonal Harmony in Concept and ...

interval between F and A in the modern scale. In such a case the function of the note λιχανός is such that "the 'nature of μελῳδία' somehow requires that it should leap forward at least as far as μέση, without touching down anywhere in between. Any smaller distance is melodically impossible or unintelligible, ἐκμελής". The nature of the

chromatic genus In the musical system of ancient Greece, genus (Greek: γένος 'genos'' pl. γένη 'genē'' Latin: ''genus'', pl. ''genera'' "type, kind") is a term used to describe certain classes of intonations of the two movable notes within a tetracho ...

, too, is an attribute of the ''kinēsis phonēs'' (, "potentiality of the sounds"), so that certain

melody type Melody type or type-melody is a set of melodic formulas, figures, and patterns. Term and typical meanings "Melody type" is a fundamental notion for understanding a nature of Western and non-Western musical modes, according to Harold Powers' ...

s are "brought into being". In other words, "being composite" and "being incomposite" are attributes of the dynamic character of melodic motion. "None of these consists in the voice's coming to rest at points separated by distances of specific and determinate sizes". An incomposite interval is "bounded by successive

note Note, notes, or NOTE may refer to: Music and entertainment * Musical note, a pitched sound (or a symbol for a sound) in music * Notes (album), ''Notes'' (album), a 1987 album by Paul Bley and Paul Motian * ''Notes'', a common (yet unofficial) sho ...

s" in a scale: "If the bounding notes are successive, no note has been left out; if none has been left out, none will intervene; if none intervenes, none will divide the interval; and what does not admit of division will not be composite". Gaudentius (before the 6th century CE) explains incomposite intervals as scale-building elements:

Aristides Quintilianus Aristides Quintilianus (Greek: Ἀριστείδης Κοϊντιλιανός) was the Greek author of an ancient musical treatise, ''Perì musikês'' (Περὶ Μουσικῆς, i.e. ''On Music''; Latin: ''De Musica'') According to Theodore Kar ...

(writing probably in the 3rd century AD) enumerates the incomposite intervals: "the smallest, so far as their use in melody is concerned, is the enharmonic diesis, followed—to speak rather roughly—by the semitone, which is twice the diesis, the tone, which is twice the semitone, and finally the ditone, which is twice the tone". These various sizes of incomposite interval depend on the genus of the tetrachord, as explained by

Nicomachus Nicomachus of Gerasa ( grc-gre, Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician and music theorist, best known for his works '' Introduction to Arithmetic'' and '' Manual of Harmonics'' in Greek. He was born ...

in the first century AD: Thus, whether an interval is composite or incomposite is a matter of context (that is, the genus in effect at that point in the melody). A

semitone A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent no ...

is an incomposite interval in the

diatonic Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a p ...

or chromatic genera, but not because

quarter tone A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, ...

intervals may be difficult to sing in tune. It is a composite interval in the enharmonic genus, where the semitone occurs only as the outer interval of the ''pyknon'', made of two quarter tones. Following the strict definition found in

Nicola Vicentino Nicola Vicentino (1511 – 1575 or 1576) was an Italian music theorist and composer of the Renaissance. He was one of the most progressive musicians of the age, inventing, among other things, a microtonal keyboard. Life Little is known of hi ...

's ''L'antica musica ridotta alla moderna prattica'' (1555), all intervals larger than the major third (or ditone) are necessarily composite. However, for the purpose of his discussion of the "modern practice" of the 16th century, he extended the definition to include larger intervals within the octave. Accordingly, a

perfect fourth A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to th ...

is "composite" if it is filled in stepwise in a composition (C-D-E-F), but is "incomposite" when it occurs as a melodic leap or harmonic interval, without any intermediary tones. One 20th-century interpretation is more restrictive than the definitions found in Ancient Greek sources, referring to "a large interval which appears as a

step or second in a

, but which is a

skip Skip or Skips may refer to: Acronyms * SKIP (Skeletal muscle and kidney enriched inositol phosphatase), a human gene * Simple Key-Management for Internet Protocol * SKIP of New York (Sick Kids need Involved People), a non-profit agency aiding ...

in other parts of the scale."John H. Chalmers, ''Divisions of the Tetrachord'' (Lebanon, New Hampshire: Frog Peak Music, 1993): 209. . For example the

augmented second In classical music from Western culture, an augmented second is an interval that, in equal temperament, is sonically equivalent to a minor third, spanning three semitones, and is created by widening a major second by a chromatic semitone.Benw ...

in the

harmonic minor scale In music theory, the minor scale is three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending) – rather than just two as with the major scale, which als ...

, on A, occurs as a step between F and G, though the equivalent

minor third In music theory, a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval number). The minor third is one of two com ...

occurs elsewhere, such as a skip between A & C.

References

{{Intervals Intervals (music)

See also

References