Excerpts from Harmonic Experience
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.
Editors note: Heres 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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