LucyTuning

A tuning invented by John 'Longitude' Harrison in the 1700s and rediscovered and promoted currently by Charles Lucy.

LucyTuning is a type of meantone composed of two different step sizes (designated L and s) such that 5L + 2s = one octave, as in many familiar diatonic scales.


The Large interval (L) is the "whole-tone" (IInd), with the ratio
2^{(1 / 2p)} = ~1.116633 or "the two pi root of two"
That is 1200 / 2p cents = ~190.9858 cents.


The small interval (s) is half the difference between 5 Large intervals and one octave, i.e. (8ve - 5L) / 2 , and is the "flat second" (bIInd), with the ratio
(2 / 2^{(5 / 2p)})^(1/2) = ~1.073344. That is s = ~122.5354 cents.


LucyTuning has a "5th" or generator at the "low end" of the meantone spectrum, with an interval size between that of 1/3-comma meantone and Zarlino's 2/7-comma meantone (see the right side of the graph at the bottom of the meantone entry).

This generator or "5th" is composed of three Large (3L) plus one small note (s), i.e. (3L+s) = (~190.986*3) + (~122.535) = ~695.493 cents or ratio of

2^{(3 / 2p)} * (2 / 2^{(5 / 2p)})^(1/2) = 2^{(2p + 1) / 4p} or 2^{(1/2 + 1/4p)} = ~1.494412.

This generator is audibly indistinguishable from that of 3/10-comma quasi-meantone:

  22/10         * 3-2/10 * 53/10       3/10-comma quasi-meantone "5th"
- 2(2p+1)/4p                           Lucytuning "5th"
---------------------------------
  2(-12p-10)/40p * 3-2/10 * 53/10   =  ~0.010148131 cent = ~1/99 cent


The LucyTuning "major third" has the ratio 2^(1/p) = ~1.246868989 = ~381.9718634 cents.


See the LucyTuning homepage for more information.


[from Joe Monzo, JustMusic: A New Harmony]

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Updated: 2001.12.9, 2001.7.2

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

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