Re: Lucy tuning

Hans Aberg wrote:
> Margo Schulter wrote:
>> However, much Renaissance music does _not_
>> assume a circulating system -- and some people who wanted it
>> went further, and used 31-note keyboards which would circulate
>> in 1/4-comma or thereabouts.
> 
> This link says Huygens discovered the close relation****p between 
> meantone and E31:
>   http://www.xs4all.nl/~huygensf/english/huygens.html

It says he demonstrated it.  Not that he discovered it, in 
the sense that nobody knew it before.  And the page itself 
mentions precedents.

> But ETs is just a convenient way to produce tunings. The main point is 
> that the music is diatonic: any choice of minor and major seconds will 
> produce an intonation.

For suitable definitions of "diatonic".  Some of us prefer 
to say "meantone" in a general sense.  The defining feature 
is that four perfect fifths add up to a major third, give or 
take some octaves.  There were plenty of just intonation 
scales called "diatonic" throughout history.

> Only some modern music use the enharmonic equivalence of E12 in an 
> essential way. But for music produced in E12, as in a MIDI file, the 
> problem is to extract the underlying diatonic structure before retuning.

There's more to it than that.  Chromatic chords still have 
to be tuned and sometimes a chord may work best with a 
tuning outside meantone theory.

> If this can be done, there seems to be no practical music difference 
> between the Lucy tuning and E88. The difference between the fifths of 
> the tunings is too small be heard even harmonically.

Yes, probably.


                       Graham