Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited


    The relative consonance/dissonance of an interval.

    Rather than use the above phrase (as Partch did), I have adopted the single term sonance, because I agree with the assertion - made by both Schoenberg and Partch, among others - that rather than describing two diametrically-opposed sensations, consonance and dissonance refer instead to the opposite poles of a single continuum of sensation. (An early and influential expression of this idea was presented by Helmholtz - see below.)

    My own theory of sonance actually holds that there are two separate continua of sensation, one determined by the values of the prime-factors of the ratios interpreted by the listener as being that of the two tones in the interval, and the other determined by the values of the exponents of those factors. Dissonance increases (and consonance simultaneously decreases) as both the prime-factors and the values of the exponents of those factors become larger. This idea was expressed earlier by Ben Johnston and others; the earliest reference to it which I have seen is in The true character of modern music, written in 1764 by the mathematician Leonhard Euler. Harmonic lattice diagrams are a graphical representation of this theory of sonance.

    My own theory thus allows that the actual tuning of the interval may be a ratio with far higher primes or exponents, or in fact may not be rational at all (as in the case of temperaments), but that the listener will, at least to some extent, interpret or understand that interval as a rational one with the smallest prime-factors and exponents recognized by his aural and/or music-theoretical experience.

    Recent speculation among tuning theorists (mid-1999) has raised the idea that consonance and dissonance may actually be two separate and not mutually-exclusive dimensions of sonance. I have extrapolated this to the idea that each prime factor may in fact be responsible for a separate dimension of sonance that does not necessarily exclude any of the others.

    It is also important to note that sonance is usually determined not merely as an auditory phenomenon, but rather as a result of musical context, highly dependent on the style of a particular composer or era. Many tuning theorists have recently (1999) come to the consensus that the term cordance (describing the continuum from concordance to discordance) should be used for the former, restricting sonance for the latter.

    see also roughness, harmonic entropy, critical band, cordance.

    [from Joe Monzo, JustMusic: A New Harmony]

    . . . . . . . . . . . . . . .

    I recommend we distinguish between "sensory consonance" (aka roughness, sonance etc.) and "contextual consonance" as Tenney does in his History of Consonance and Dissonance.

    [from John Chalmers, Tuning Forum posting]

    . . . . . . . . . . . . . . .

    Consonance is a continuous, dissonance an intermittent sensation of tone.

    ... We have found that from the most perfect consonance to the most decided dissonance there is a continuous series of degrees, of combinations of sound, which continually increase in roughness, so that there cannot be any sharp line drawn between consonance and dissonance, and the distinction would therefore seem to be merely arbitrary.

    [from Hermann Helmholtz, On the Sensations of Tone, p 226 and 227]

    (Immediately after this quote, Helmholtz devotes three pages to a discussion of Euler's theories of consonance and dissonance.)

(to download a zip file of the entire Dictionary, click here)

  • For many more diagrams and explanations of historical tunings, see my book.
  • If you don't understand my theory or the terms I've used, start here
  • I welcome feedback about this webpage:
    corrections, improvements, good links.
    Let me know if you don't understand something.

    return to the Microtonal Dictionary index
    return to my home page
    return to the Sonic Arts home page