Re: Ives's pythagorean tuning

> [Johnny Reinhard, TD 306.16]
>
> It seems that Charles Ives envisioned an extended Pythagorean
> tuning for his music. Ives wanted sharps higher than flats.
> He states in his Memos on the Concord Sonata that B# is an
> 1/8th tone higher than C. That smells like Pythagorean to me.

I got a whiff of that. Just thought I'd flesh out Johnny's
comment with some numbers:

If 'C' is our reference tone at 0 cents, then the Pythagorean
'B#' which is 12 'perfect 5ths' (3:2 ratio) above it, when
'octave'-reduced, measures ~23.46 cents.

If 'tone' was defined by Ives as the 9:8 ratio, then a logarithmic
1/8 of that is ~25.49 cents.

If Ives's 'tone' was defined as the regular 12-tET ratio of
2^(2/12):1, a logarithmic 1/8-tone is exactly 25 cents.

To me, those odors are similar enough to buy your proposition.

However...

I've scanned thru my entire copy of Ives's _Essays Before A
Sonata, The Majority, and Other Writings_ (W. W. Norton, 1970)
and don't see the statement to which you refer.

In fact, only some statements in the 'Epilog' of _Essays Before
A Sonata_ and Ives's essay _Some 'Quarter-tone Impressions_
are specifically musical; the rest of the book is basically
philosophical.

Where is the reference to the B# 1/8-tone higher than C?
(can Dan Stearns help out here?)

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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To read about Ives's predilections in tuning you must turn to the Memos,
specifically to the chapter on the Concord Sonata.

Johnny Reinhard
AFMM

[Joe Monzo:]
> (can Dan Stearns help out here?)

No, I don't know - but I'd bet (I don't have a copy of it so I can't
check) that it would be in the "Memos."

One thing that I do seem to remember him writing about, was that he
felt he could not only imply, but also feel a tangible difference (on
a plain old unembellished 12e piano) in (what people called) his
unorthodox or obstinate note spellings... which I guess I would
quickly and personally epitomize (or mis-epitomize) as something like
this: that in the end these spellings could (hopefully) enable a
performer to approach these "misspelled" notes 'differently,' thereby
altering the actual feel (and mostly by way of a philosophic
projection of intent which would physically alter a non-intonational
dynamic) of a 1200� B# or C (or a Gb major third in the key of D, and
so forth).

Dan

Dan, I believe that Ives imagined a tuning that the piano could only
approximate. He says so in this same chapter of the Memos. Finally, it
makes sense to me that his use of quartertones and eighthtones were
integrated into the 12TET of the piano and the spiral of fifths ideal that
made him so ornery with those trying to alter his accidentals.

Johnny Reinhard
AFMM

[Johnny Reinhard:]
> Dan, I believe that Ives imagined a tuning that the piano could only
approximate.

Yes, I would agree... I just seem to remember that there was more to
some of these spelling curios than the inert possibilities of
unrealized intonation.

Dan