Re: Keeping it "on list"

> [Joe Pehrson, TD 693.5]
>
> There's been a lot going on around here that I feel I have
> been missing (pobra cita). There has obviously been a big
> discussion between Joe Monzo and Paul Erlich, only the tip
> of the wave we've been seeing, and there have been some
> educational messages to Beckah regarding tuning...
>
> OK, some of it might be "over my head" some of it "under."
> However, I'm a great "scroller" and I would enjoy having all
> of this stuff posted. Is there some reason why people refrain
> from posting the stuff to the list?? I can understand CCing
> to the individuals concerned, but it's leaving others "out
> of the loop."
>
> Or am I out of line, and this is a "loopy" suggestion???

Hi Joe.

Yes, I suppose maybe you're only seeing 'the tip of the wave'
in some of the private discussions Paul Erlich and I have,
but honestly, I do try to post most of this stuff to the List
or ask Paul to post his response to it, because we've gotten
into some *really* heavy give-and-take in our private emails
in the past that a lot of Listers wanted to see.
(you might want to look up our 'Hendrix Chord' discussion,
now stored at Drew Skyfyre's website.)

The recent stuff of ours that you're seeing stems not from
a 'big discussion' we've had recently, but from a webpage
I made near the end of last year that you may have missed:
http://www.ixpres.com/interval/monzo/woolhouse/essay.htm
a summary of W. S. B. Woolhouse's very-hard-to-find
little book on tuning. I'm sure that if you were to read
the webpage you'd understand more about that recent posting.

It so happens that Paul and Woolhouse both calculated exactly
the same tuning as one 'optimal' meantone: 7/26-comma meantone.
I say 'one' because the optimum deviation from JI changes
depending on the criteria used in the calculation. See the
summary table Paul made which I've included in my 'meantone'
definition:
http://www.ixpres.com/interval/dict/meantone.htm

IMO, my biggest strength in tuning theory is my historical
knowledge; I stumble along with the math the best I can,
and in fact have learned a lot of math 'by osmosis' since
getting interested in tuning.

But I'm pretty sure Paul would agree with me and say that
*his* greatest strength as a tuning theorist is his mathematical
ability. So I always ask him for help when my math reaches
a dead-end or, as in the case of Woolhouse, when a mathematical
illustration given by someone has some steps excluded that
I need to have filled in so that I understand what's happening.

At the end of our post-Woolhouse exchange, I asked Paul to
show me how to factor the meantone formula, and I added it
to the end of that webpage. Recently, I got interested in
exploring this again, figured out the several formulae that
Paul quoted in his post by following his original example,
then asked him to derive the general formula for me, as I
couldn't figure it out.

Paul has doubts about the usefulness of prime-factoring
meantones, because the exponents are not integers and
therefore the Fundamental Rule of Arithmetic does not apply.

But it's useful for me because it allows me to plug the
(non-integer) exponents of 2, 3, and 5 into my lattice formula
and illustrate meantones on my lattices, along with JI pitches
for reference. Since my lattice formula can already optionally
include '2' as a factor, I am now able to lattice JI, meantones,
and ETs all on the same graph, which I think is a good thing. :)

My ultimate objective is to be able to plot *any* and all types
of tunings on the same lattice, so that any tuning may be seen
as a subset of the total infinite set of pitches in a way which
makes clear the rational underpinnings of the harmonic
relationships. Paul and I both have our doubts about how
successfully my particular lattice formula does this, but
so far, for me, it works best.

-monz

Joseph L. Monzo San Diego monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
| 'I had broken thru the lattice barrier...' |
| -Erv Wilson |
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