Wiki sports - state of play as of 29/1/04 15:00 hrs GMT

This is the current entry at wiki

<start>
LucyTuning is a form of meantone temperament, in which the fifth is of
size 600+300/π (= approximately 695.5)cents. Its main advocate is
Charles Lucy, who discovered it in the eighteenth century writings of
John 'Longitude' 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.

Dessent follows:

Many musicians believe that extreme precision is significant in musical
tuning, as different beat frequencies are heard, which are
characteristic of each different tuning.

"I appreciate that I could appear to be beating angels on pinheads to
death. Yet......... There is a valid reason for my demands about
precision.

I am thinking beyond only the cent values, and preparing for the day
when the precision of our tuning technology improves,

The production, analysis and discussion of beat frequencies will then
become both practical and significant." (quote from Charles Lucy Jan.
2004.)

End of dissent.

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.

While Smith himself interpreted this somehow to mean that Harrison's
major thirds were a comma flat, it does seem to say that the proportion
of third to octave is 1:π, which only seems to make sense if it is
interpreted so that this proportion is logarithmic, or in other words,
that Harrison's third is the 1200/π third of Lucy tuning.
<end>

As it now seem to be "open season", perhaps others would like to make
their own edits ;-)
If so go to

http://en.wikipedia.org/wiki/Lucy_tuning

Have Fun!

Charles Lucy - lucy@harmonics.com (LucyScaleDevelopments)
------------ Promoting global harmony through LucyTuning -------
for information on LucyTuning go to: http://www.harmonics.com/lucy/
for LucyTuned Lullabies go to http://www.lucytune.com
http://www.lucytune.co.uk or http://www.lullabies.co.uk