Incomposite interval

In the Ancient Greek theory of music, since incomposite (Template:Lang-el) means uncompounded, an incomposite interval (Template:Lang-de) is the Ancient Greek concept of a musical interval (Template:Lang-el) between successive notes in a scale, and which for that reason does not contain smaller intervals. Aristoxenus (fl. 335 BCE) says, "Let us assume that in each genus an interval is melodically incomposite if the voice, in singing a melody, cannot divide it into intervals."^[1] The voice and other instruments have difficulty producing successively smaller intervals, and doing so may contradict established practice.^{[citation needed]}

An incomposite interval is "bounded by successive notes" 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".^[2] Gaudentius (before the 6th century CE) explains incomposite intervals as scale-building elements:

Intervals are incomposite when between the notes comprising the intervals, not even one note can be sung that is melodic with respect to the notes in the genus in which the incomposite interval is taken. Intervals are composite within which a note or notes are sung. These are also spoken of as scales, for a scale is simply an interval compounded of more than one interval. The incomposite and primary intervals in accord with each genus are the common measures of the rest of the intervals or scales in the same genus.^[3]

Thus whether an interval is composite or incomposite is a matter of context, or rather opinion, which may vary with time and musical or technological ability.^{[citation needed]} A semitone may be considered an incomposite interval, as quarter tone intervals may be difficult to sing in tune and is not contained in the diatonic scale, or it may be considered a composite interval, as quarter tones may easily be produced on a synthesizer or appropriately tuned piano and are contained in scales such maqamat.^{[original research?]}

Following the strict definition found in Nicola Vicentino'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 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.^[4]

One 20th-century interpretation is more restrictive than the definitions found in Ancient Greek sources, referring to "a large interval which appears as a melodic step or second in a scale, but which is a skip in other parts of the scale."^[5] For example the augmented second in the harmonic minor scale, on A, occurs as a step between F and G♯, though the equivalent minor third occurs elsewhere, such as a skip between A & C.

Sources

^ Barker, Andrew (1989). Greek Musical Writings, p.147. ISBN 978-0-521-61697-3.^{[full citation needed]}
^ Aristoxenus, Harmonic Introduction III:2, translated in Andrew Barker, Greek Musical Writings: Volume 2, Harmonic and Acoustic Theory, Cambridge Readings in the Literature of Music 2 (Cambridge and New York: Cambridge University Press, 1989): 172. ISBN 978-0-521-61697-3.
^ Gaudentius, “Harmonic Introduction”, in Oliver Strunk (trans. and ed.), Source Readings in Music History, revised by Leo Treitler, 66–85 (New York: W. W. Norton & Company, 1998). ISBN 9780393037524. Citation on p. 69.
^ Henry W. Kaufmann, "Vicentino and the Greek Genera", Journal of the American Musicological Society 16, no. 3 (Autumn 1963): 325–46. Citation on 331.
^ Chalmers, John H. (1993). Divisions of the Tetrachord, p.209. ISBN 978-0-945996-04-0.^{[full citation needed]}

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[1] Barker, Andrew (1989). Greek Musical Writings, p.147. ISBN 978-0-521-61697-3.^{[full citation needed]}

[2] Aristoxenus, Harmonic Introduction III:2, translated in Andrew Barker, Greek Musical Writings: Volume 2, Harmonic and Acoustic Theory, Cambridge Readings in the Literature of Music 2 (Cambridge and New York: Cambridge University Press, 1989): 172. ISBN 978-0-521-61697-3.

[3] Gaudentius, “Harmonic Introduction”, in Oliver Strunk (trans. and ed.), Source Readings in Music History, revised by Leo Treitler, 66–85 (New York: W. W. Norton & Company, 1998). ISBN 9780393037524. Citation on p. 69.

[4] Henry W. Kaufmann, "Vicentino and the Greek Genera", Journal of the American Musicological Society 16, no. 3 (Autumn 1963): 325–46. Citation on 331.

[5] Chalmers, John H. (1993). Divisions of the Tetrachord, p.209. ISBN 978-0-945996-04-0.^{[full citation needed]}

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Sources