The following is the Introduction from The Just Intonation Primer
by David B. Doty, © 1993, 1994, 2002
The Just Intonation Primer, Chapter 1 by David B. Doty is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License. You may download, copy, and distribute this document, provided that you do not remove the publisher and author credits or the copyright notice, or make any other alterations.
Introduction
What is Just Intonation? (the long version)
What is Just Intonation? Although, like most composers working with this unfamiliar tuning system, I am frequently asked this troublesome question, I have yet to devise an answer that is suitable for casual conversation. Technically, Just Intonation is any system of tuning in which all of the intervals can be represented by whole-number frequency ratios, with a strongly implied preference for the simplest ratios compatible with a given musical purpose. Unfortunately this definition, although concise and accurate, is more likely to result in a glazed expression indicative of confusion than in the gleam of understanding. It is, in short, a definition that is perfectly clear to the comparative few who have the background to understand it, and who could, therefore, formulate it for themselves, and perfectly opaque to everyone else, including, unfortunately, most trained musicians. (It is my experience that most musicians are as ignorant of the details of twelve-tone equal temperament, the predominant tuning system in Western cultures for the past 200 years, as they are of Just Intonation. If you doubt this, ask the next dozen musicians you meet to explain why there are twelve semitones in a chromatic scale and how to go about accurately tuning those twelve equal semitones.) A detailed answer that incorporates all the necessary background on the physics of sound, the physiology and psychology of human hearing, the history of music, and the mathematics of tuning systems, far exceeds the limits of casual conversation. It could, in fact, fill a book.
A formal definition of Just Intonation may be difficult for the novice to grasp, but the aesthetic experience of just intervals is unmistakable. Although it is difficult to describe the special qualities of just intervals to those who have never heard them, words such as clarity, purity, smoothness, and stability come readily to mind. The supposedly consonant intervals and chords of equal temperament, which deviate from simple ratios to varying degrees, sound rough, restless, or muddy in comparison.
The simple-ratio intervals upon which Just Intonation is based are "special relationships" that the human auditory system is able to detect and distinguish from one another, and from a host of more complex stimuli. They are what the human auditory system recognizes as consonance, if it ever has the opportunity to hear them in a musical context. Although the importance of these whole-number ratios is recognized both by musical tradition and by modern acoustic and psychoacoustic research, for the last 200 years Western music has been burdened with a tuning system in which all of the supposed consonances, with the exception of the octave, deviate significantly from their optimal, integer-ratio forms. Indeed, some consonant intervals are so compromised in twelve-tone equal temperament that they are hardly represented at all.
Just Intonation provides a greater variety and superior quality of consonances and concords than equal temperament, but its resources are by no means limited to unrelieved consonance. Just Intonation also has the potential to provide more varied and powerful dissonances than the current system. This is the case in part because the simple, consonant intervals can be compounded in a great many ways to yield more complex dissonant intervals, and in part because the consonant intervals being truly consonant, the dissonances are rendered that much sharper in contrast. Further, because dissonances in Just Intonation are the products of concatenations of simpler intervals, consonance and dissonance coexist in a rational framework and their mutual relations are readily comprehensible.
The virtues of Just Intonation and the shortcomings of equal temperament are not limited to the affective properties of their respective intervals and chords. An equally serious problem with twelve-tone equal temperament is that it supplies composers with an artificially simplified, one-dimensional model of musical relationships. By substituting twelve equally spaced, fixed tones for a potentially unlimited number of tones, interconnected by a web of subtle and complex musical relationships, equal temperament not only impoverished the sonic palette of Western music, but also deprived composers and theorists of the means for thinking clearly about tonal relationships, causing them to confuse close relationships with remote ones and consonances with dissonances. Not only does Just Intonation provide a vast array of superior new musical resources, but, when properly understood, provides the tools necessary for organizing and manipulating these greatly expanded resources.
Just Intonation is not a particular scale, nor is it tied to any particular musical style. It is, rather, a set of principles which can be applied to a limited number of musically significant intervals to generate an enormous variety of scales and chords, or to organize music without reference to any fixed scale. The principles of Just Intonation are applicable to any style of tonal or modal music (or even, if you wish, to atonal styles). Just Intonation is not primarily a tool for improving the consonance of existing musics, although it can, in some cases, be used this way. Just Intonation can give rise to new styles and forms of music which, although truly innovative, are, unlike those created by the proponents of the various "avant-garde-isms" of this century, comprehensible to the ear of the listener as well as to the intellects of the composer and analyst. Ultimately, Just Intonation is a method for understanding and navigating through the boundless reaches of the pitch continuum—a method that transcends the musical practices of any particular culture.
Just Intonation has depth and breadth. Its fundamental principles are relatively simple but its ramifications are vast. At present, the musical realm that comprises Just Intonation remains largely unexplored. A few pioneering composers and theorists have sketched some of its most striking features, but the map still contains many blank spaces where the adventurous composer may search for new musical treasures.