The Unconservatory  

Excerpts from Harmonic Experience

by W.A.Mathieu

Copyright 1997 by W.A. Mathieu. All Rights Reserved.

Definitions to highlighted words can be found in theses short glossary excerpts.

(Excerpts from the glossary)

comma: any very small interval between two tones near in pitch but disparate in harmonic generation.

equal temperament: a system of tuning wherein the octave is divided into intervals of exactly equal size; twelve-tone equal temperament is the standard system of the Western world.

harmony: refers primarily, in this book, to events that can be quantified by ratio, as opposed to events that can be measured by interval.

interval: a quantifier of the melodic distance between two tones, usually without specification as to their harmonic interaction, as distinct from ratio (q.v.).

just intonation: in some texts, the five-limit system of tuning; in this book, any system of tuning using low primes.

lattice: a graphlike configuration where each axis is devoted to tones generated by a specific prime number; a two-dimensional lattice (i.e., on a page) is confined to a tuning system using two primes. A lattice of tones combines the graph principle with staff notation by skewing the direction of both axes. A lattice of twelve notes refers to the twelve most simply derived ratios; an extended lattice includes indefinitely more notes; a chord lattice abandons the staff notation and shows the major and minor triads by chord symbols only; in a key lattice, the symbols stand for keys.

major: large; most narrowly, an adjective modifying a number, as in major sixth.

meend: in Indian music, the sliding from resonance to resonance; the shaping of tones.

melody: refers in this book to the up-and-down aspect of music, that which is quantifiable by intervallic measurement; as distinct from harmony (q.v.).

modality: the quality of music within a mode. Most simply, the term refers to music that establishes clear choices of tones that relate to an unchanging music.

pentamerous: harmony generated by the prime number five, that is, harmony characterized by the presence of 5:4 major thirds and their compounds and reciprocals.

perfect: the quality assigned to 1:1 primes, 3:2 fifths, 4:3 fourths, and all octave expansions of these intervals.

Pythagorean: generally, having to do with the thought (or supposed thought) of Pythagoras. In this book, Pythagorean refers to a three-limit system, that is, a system confined to 2:1 octaves and 3:2 fifths, and their compounds and reciprocals.

resonance: the conventional definition is the reinforcement of tones by synchronous or near-related vibration; as used in this book, the term refers to sensible (that is, singable) combinations of tones related by low-prime ratios.

sargam: in Indian music, the names of the degrees of the scale, specifically, sa, re, ga, ma, pa, dha, and ni, abbreviated s, r, g, m, p, d, and n.

tonal harmony: generally refers to modulating harmony with identifiable tonics. A more narrow definition refers to the dominant-seventh-driven harmony of the common practice period.

Editor’s note: Here’s hoping that the above passages raised more questions than they answered. Harmonic Experience is available at your local bookstore. Order your copy today!

Harmonic Experience Copyright 1997 by W.A. Mathieu. All Rights Reserved.

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Updated: January 25, 2001 (KB)

Copyright 2001 The Unconservatory, All Rights Reserved.