Lucy tuning
Lucy tuning is a form of meantone temperament, in which the fifth is of size 600+300/π centss. Its main advocate is Charles Lucy, who discovered it in old writings of John Harrison. The Lucy tuned perfect fifth is 0.0384 cents sharper than the fifth of 88 tone equal temperament, and a mere 0.01015 cents flatter than 3/10-comma meantone, and therefore is audibly indistinguishable from either.A major tone is two fifths up and an octave down, so in Lucy tuning it will be 2(600+300/π)-1200 = 600/π cents. The major third therefore is two tones, or 1200/π cents, which is an octave divided logarithmically by π or the π-th root of two. This works out as 381.972 cents, 4.342 cents flatter than a just major third. A diatonic semitone is the interval between a major third and a fourth, which in Lucy tuning will be (600-300/π)-1200/π = 600-1500/π cents, or 122.535 cents. Any interval can equally well be expressed in terms of octaves and fifths or whole tones and diatonic semitones. If we call the whole tone L and the diatonic semitone s, the familiar diatonic scale is LLsLLLs, and a Lucy-tuned diatonic scale will be one with the above specific values for L and s.
In Robert Smith's Harmonics of 1749 we find the following description of Harrison's system of tuning:
- He told me he took a thin ruler equal in length to the smallest string of his base viol. and divided it as a monochord, by taking the interval of the major IIId, to that of the VIIIth, as the diameter of a circle, to its circumference. Then by the divisions on the ruler applied to that string, he adjusted the frets upon the neck of the viol. and found the harmony of the consonances so extremely fine that after a very small and gradual lengthening of the other strings at the nut, by reason of their greater stiffness he acquiesced in that manner the placing of the frets.
See also: Musical tuning, meantone temperament, diatonic scale
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