source file: m1414.txt
Date: Wed, 13 May 1998 06:53:57 -0500 (CDT)

Subject: Re: Marketing hype

From: mr88cet@texas.net (Gary Morrison)

>Yes, LucyTuning is a meantone tuning; yet neither 1/3 comma, nor 1/4 comma.
>
>The thing which is significant (instead of references to integer
>frequency ratios), is that LucyTuning at http://www.ilhawaii.net/~lucy is
>developed from a new
>paradigm for harmonic mapping, enabling users to transpose and modulate
>forever plus emulate any other tuning system.

   Best I can tell, here's the "reality" behind what Mr. Lucy has said here:

   Yes, LucyTuning is neither third-comma nor quarter-comma, since its
fifth size in fact somewhere between the two.

   Mr. Lucy has claimed earlier, as he aluded here, that because
LucyTuning's fifth size is built from pi, it ensures that the circle of
fifths never closes.  There is semitruth and falsehood behind that
assertion:

The semitruth:  LucyTuning definitely can stack up more fifths above a tonic
   before approximately closing the circle than either quarter-comma or third-
   comma meantone.  Third-comma meantone comes "close enough" at 19 fifths,
   and quarter-comma at 31 fifths.  LucyTuning doesn't get there until about
   88 fifths.  But this is only a semitruth, because taken in absolutes, the
   circle of fifths never closes in ANY typical meantone tuning.
Falsehood #1:  Lucy claims that his property is because LucyTuning's fifth
   size is based upon pi, pi being irrational.  Pi has nothing to do with this.
   The frequency multiplier for quarter- and third-comma meantone's fifths are
   no more or no less irrational than for LucyTuning's fifth.  They are all
   defined as 3/2 divided by a root of 81:64, and roots of 81:64 (or at least
   the roots used in meantone calculations) are irrational.
Falsehood #2:  LucyTuning in no way invalidates the meaningfulness of integer
   ratios.  Lucy would be extremely hard-pressed to find anybody in the field
   of unusual tunings that will agree with him that the only reason why 3:2
   is significant to our ears is that it's an approximation to one LucyTuned
   fifth, rather than the reverse.  Speaking of ratios, the ratio of people
   who believe the standard JI-based model to those who believe Lucy's model
   is probably on the order of 100:1.
Falsehood #3:  This "new paradigm for mapping harmony" (how many fifths above
   or below a tonic you are) is clumsy at best for emulating other tunings.
   Without a doubt, there certainly are cases where it makes sense to think of
   pitches in terms of how many fifths apart they are, but there are vastly
   more cases where it doesn't.  For example:  Suppose we're looking for a
   LucyTuned approximation of a 9:7 within 2 cents.  Those two pitches would
   have to be 325 LucyTuned fifths apart.  Certainly it's flagrantly obvious
   that to say that two pitches are a 9:7 ratio apart is vastly more intuitively
   meaningful than saying that they are 325 fifths apart!