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) defines melodically incomposite intervals in the following context:

Let us assume that given a systēma, whether pyknon or non-pyknon, no interval less than the remainder of the first concord can be placed next above it, and no interval less than a tone next below it. Let us also assume that each of the notes which are melodically successive in each genus will either form with the fourth note in order from it the concord of a fourth, or will form with the fifth note from it in order the concord of a fifth, or both, and that any note of which none of these things is true is unmelodic relative to those with which it forms no concord. Let us further assume that given that there are four intervals in the fifth, of which two are usually equal (those constituting the pyknon) and two unequal (the remainder of the first concord, and the amount by which the fifth exceeds the fourth), the unequal ones are placed next to the equal ones in the opposite order above and below. Let us assume that notes standing at the same concordant interval from successive notes are in succession with one another. 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]

Aristides Quintilianus (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".^[4]

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.^[5]

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."^[6] 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

^ Aristoxenus, Elementa Harmonica book I, 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): 146–47. ISBN 978-0-521-61697-3.
^ 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.
^ [Aristides Quintilianus, De musica, translation from 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): 410. ISBN 978-0-521-61697-3.
^ 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] Aristoxenus, Elementa Harmonica book I, 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): 146–47. ISBN 978-0-521-61697-3.

[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] [Aristides Quintilianus, De musica, translation from 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): 410. ISBN 978-0-521-61697-3.

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

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

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Sources