AW.: RE: The world according to Rothenberg (re Kraig Grady); my cont...

Several Items:

(1) Paul Erlich:

Have you been able to use your decatonics as meaningful scales in any pieces?

I ask because a piece of mine, _Pequod, for Lou Harrison_ (1986) used
complementary dekanies from the (1,3,5,7,9,11) and (1,3,7,9,11,15)
eikosanies, for example, the dekany

1*3*11, 1*5*11, 1*7*11, 1*9*11, 3*5*11, 3*7*11, 3*9*11, 5*7*11, 5*9*11,
7*9*11 was contrasted
with
1*3*5, 1*3*7, 1*3*9, 1*5*7, 1*5*9, 1*7*9, 3*5*7, 3*5*9, 3*7*9, 5*7*9

I found that each dekany collection was coherent, but not as a scale.
Although each had a regular pattern of scale steps, they were too dense to
function akin to a diatonic or pentatonic scale or not dense and even enough
to function like a chromatic scale. Instead, subsets of each dekany seemed
to form the most important local melodic units and the dekany as a whole
formed the collection or pool of harmonic resources. I am fond of the
ambiguous character of the dekanies, but just can't call them scales.

(2) Carl Lumma

Rothenberg's main source of information about Indonesia was Suryabrata, a
Dutch-Indonesian with an interesting autobiography but not a serious source
of information about tunings. (His book, _The Island of Music_ has some
interesting things among many howlers). Relevant to Rothenberg, the idea
that change in the pitch of a gamelan over time would lead to changes in the
perceived tuning has got to be tempered (as it were) by the fact that
Javanese owners of gamelan retune their instruments when they go out of tune,
if they can afford it, just as piano owners would. Even the most valued old
instruments (i.e. Kyai Kanyu Mesem in the Istana Mankunegara) have been
retuned in recent memory. The situation in Sunda is somewhat different to
that of Central Java, although Rothenberg seems to use the two
interchangeably, but largely because of the existence of a speculative
theoretical tradition in Sunda. This, however, had little or no relevance to
or impact on performance practice. Andrew Weintraub's dissertation covers
this topic well.

I know of one example, in the gamelan Selonding of Tenganan, Bali, where the
tuning of one pitch on one set of instruments shifted enough to require
transposing the repertoire, but this was more-or-less an ordinary shift in
the series of fifths, and the net result is modulation by a fifth.

(3) Joe Monzo:

Your take on MOS's is very good. Wilson's work divides largely into two
parts, with the melodic systems generated by 'linear series' on the one hand,
and the harmonic systems (CPSs, Diamonds etc.) on the other, with the
keyboard mappings and notation designs linking both kinds of systems in
practical designs.

I would only like to add in emphasis that in the MOS's, whether in a
temperament or in just intonation, not only are the linear series of
generating intervals subtended by the same numbers of tones, but the melodic
intervals within the generating intervals are exactly symmetrical over the
entire linear series.

Thus, the pentatonic scale C,D,F,G,A generated by 4/3s in the series
A-D-G-C-F-(A) exhibits the following symmetry:

A 32/27 C 9/8 D
D 32/27 F 9/8 G
G 9/8 A 32/27 C
C 9/8 D 32/27 F
F 9/8 G 9/8 A

In a five-limit just version, with two sizes of generating intervals, the
melodic symmetry is preserved coarsely but not exactly.

(4) For Kraig Grady and Joe Monzo: Wilson's term "subtend" is standard
English usage, while "freshman sum" is standard mathematics. In fact, I
happened to be at the table when (the composer/mathematician) David Feldman
told Wilson that he was taking freshman sums.