Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited


octave

octave-equivalence


    based on the unique property of intervals that can be most easily interpreted as the 2:1 ratio, commonly called the "octave", that although it is a different pitch from the origin 1:1, it seems to have the same aesthetic affect or properties as 1:1.

    Traditional music theory assumes octave-equivalence, thus the letter-names of the notes repeat in the different "octaves".

    Many tuning systems follow this approach, but not all.

    Examples of tunings which do not exhibit octave equivalence are:

  • the Indonesian pelog and slendro scales, which seem to be based on the ratios of the "inharmonic" timbres of the gamelan instruments

  • the "non-octave non-equal" scales used by Brian McLaren, Gary Morrison's 88CET scale, Wendy Carlos's alpha, beta, and gamma scales, and others.
  • Modern acoustical research yields evidence that most individuals' perception of what is consonant is more complex than the long-held belief by many music-theorists and scientists that consonance is directly related to the size of the integer terms in the ratios and/or the size of the prime- or odd-number factors.

    [McLaren's website will have much information on and quotations from this research - one citation refers to an interval of 12.15 Semitones as that most commonly perceived as a consonant "octave".]

    Johnny Reinhard wrote an interesting paper on a study he did of a song by two Sapmi (also known as Lapp) singers of northern Scandinavia. There were very minute but deliberate interval dissonances between them, and tiny changes in these intervals in each of the 9 repeating verses. One of the most prominent was a frequently-used mistuned harmonic "octave" which ranged from about 11.90 to 12.04 Semitones.

    [from Joe Monzo, JustMusic: A New Harmony]


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