To Paul Erlich

Shohe Tanaka's dissertation _Studien im Gebiete der reinen Stimmung_ is i=
n
volume 6 (1890) of the Vierteljarhsschrift fu''r Musikwissenschaft. My
translation of the full text is in revision; a rough translation of a sma=
ll
part of the text was made for Larry Hansen some years ago and was publish=
ed
(a surprise to me) in an issue of Xenharmonikon (for what it is, the
translation is okay but the layout is lousy). =


Tanaka's graphing techniques develop those of Hauptmann and von Oettingen=
;
only Wilson's development of graphing techniques for additional dimension=
s
and Tenney's observations about the logarithmic distances illustrated by
graphs represent major music-theoretical advance s on work of the
nineteenth century, although it may be added that none of these technique=
s,
from a mathematical standpoint, are anything other than obvious.

I stand by my comments on Balzano's work. He gave a presentation in Santa=

Cruz in 1982 and said specifically that 20 was chosen because he was
working with group characteristics and 20 was a reasonably small number
with the same number of factors as 12. Indeed, it could be said that he w=
as
looking for an alternative tuning with which he might confirm some
hypotheses regarding 12. However, once he started work with 20, he became=

quite pleased with the tuning (Balzano has perfect pitch memory and rapid=
ly
had command over the set of 20).

My disparaging comments about Richter Herf and his _Ekmelische Musik_ are=
a
private aesthetic opinion. Austria's history is full of minor cultural
figures with minor followings. I'd rate him and his group as both smaller=

and considerably less important than Hauer and his group. Ezra Sims is a
rough contemporary, a clearer thinker and a far better composer, so let's=

let Ezra take the 72-tone chair. (If we want to argue on the basis of
priority, then Bosanquet gets all multiples of 12, followed by Carrillo).=


As to Partch's tuning on the harmonium: The voicing of a harmonium reed c=
an
retune individual partials; his tuning was close but not exact by any
means. (I am working at present with aluminum rods fixed at one end. An
ideal rod should yield three first partials in the ratios of 1 : 6.27 :
17.55; I have yet to meet such a rod, but have found that with a little
filing in the right places I can tune the partials close to 1 : 8 : 16 =


SMTPOriginator: tuning@eartha.mills.edu
From: "Paul H. Erlich"
Subject: RE: next step in tunings
PostedDate: 25-11-97 10:17:46
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