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Encyclopedia of Microtonal Music Theory

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extended reference

[Carl Lumma, Yahoo tuning group message 7954]

A method of notating a melody in which consecutive pitches are given in order, by their distance from a previously-tuned note. The frequency of the first note is arbitrary, and it serves as the reference point for the second note, after which either the first or second note may be the reference, and so on.

Like classical melodic just intonation, extended reference holds that melodic intervals are ideally tuned according to ratios of small whole numbers [i.e., integers]. But extended reference differs from the classical application in two important ways:

1. Rather than mapping notes of the scale to a fixed pitch set and performing modal transpositions on the pitch set, extended reference interprets modal transposition as a change of reference point (tonic) -- maps scale degrees to intervals instead of pitches.

2. Rather than map a single just ratio to each scale degree, extended reference may allow several tunings of a given scalar interval, so long as all occurances of that interval are tuned with the same ratio within a given reference point. [The model borrows from conventional music theory the idea that harmonic progressions function in a sort of "parenthesis-checking" hierarchy, where one must first resolve to the local tonic, then to the next tonic up, and so on up to the master tonic (first note).]

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Boomsliter, Paul C. and Warren Creel. 1961.
"The Long Pattern Hypothesis in Harmony and Hearing",
Journal of Music Theory, vol. 5 no. 2, April 1961, pp. 2-30.

Boomsliter, Paul C. and Warren Creel. 1962a.
Interim Report on the Project on Organization in Auditory Perception
at the State University College. Albany, New York
(with recorded illustrations), February 1962.

Boomsliter, Paul C. and Warren Creel. 1962b.
"Ratio Relationships in Melody",
Journal of the Acoustical Society of America,
vol. 34 no. 9, part 1, September 1962, pp. 1276-1277.

Boomsliter, Paul C. and Warren Creel. 1963.
"Extended Reference: An Unrecognized Dynamic in Melody",
Journal of Music Theory, vol. 2 no. 1, spring 1963, pp. 2-22.

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