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Encyclopedia of Microtonal Music Theory

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chroma (χρωμα)

[Joe Monzo]

A Greek word which means literally "color". It is generally used in music to indicate the perceived sensation of pitch disregarding the note's octave registration -- i.e., the tuning has an equivalence-interval, which by definition is ignored in determining the chroma.

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[John Chalmers, Divisions of the Tetrachord]

chroma, chromatikon

(Greek: "color", "colored", "chromatic")

The genus with a minor third and two semitones.

Neo-Chromatic is used to describe the permutation(s) of the intervals which place the minor third in the middle of the tetrachord. Such tetrachords are found in

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[Gene Ward Smith, Yahoo tuning message 55265 (Aug 6, 2004 1:50 pm)]

Before August 2004, Gene Ward Smith was using "chroma" with his own definition:

A "chroma" for an n-note chain scale of a temperament is an interval which when wedged with (the complement of) a linear temperament wedgie gives (complement again) a val v such that v[1]=+-n, which is an n-equal val supported by the temperament. So it's only a chroma relative to a specific size of chain (MOS, without the DE assumption,) and more precisely only relative to a particular val.

Another way to say it is that the chroma is mapped to the difference between the start and end of the chain by the temperament. 25/24 would be a chroma for 7 notes of meantone, but so would 78125000/78121827. Chromas which shift concordances, particularly the generator (presuming it is concordant), to some other concordance, are particularly interesting from the point of view of circulation.

For example, 40/39 is a chroma for the 13-limit meantone from the standard vals for 31 and 50. The val you get wedging it with the wedgie is <12 19 28 34 41 45|, which is one version but hardly the only one for 12-et in the 13-limit. A nice thing about it is that (3/2)*(40/39) = 20/13, a 13-limit concordance; another nice thing is that 36/35 is a chroma with the exact same val, and (5/4)*(36/35)=9/7.

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