error in Harrison

Yesterday I wrote about an error in the
tuning guide Lou Harrison provided on the score
of his _Incidental Music for Corneille's "Cinna"_
[Xenharmonikon 5].

I thought for the sake of any newbies on the List
or anyone else who's interested I'd build a lattice
illustrating the tuning guide and error. I'll use
the regular triangular lattices with 3 on the
horizontal axis, 5 on the diagonal, and 7 "on top".

The tuning guide is notated in notes and ratios,
which really makes the error glaring.

Harrison starts first with "octave" A's (a 2/1)
then tunes from the lower A a 3/2 up to E and
5/4 up to C# - your basic JI major triad:

C#
/ \
/ \
/ \
A ----- E

Then from E down a 5/4 to C and up a 3/2 from
C to G, and a 2/1 below (to the low G), and
up a 3/2 from G to D:

C#
/ \
/ \
/ \
A ----- E
\ / \
\ / \
\ / \
C ----- G ----- D

Then down a 5/4 from the high G to Eb,
and down a 3/2 from Eb to Ab. Then up a
5/4 from low G to B:

C#
/ \
/ \
/ \
A ----- E------ B
\ / \ / \
\ / \ / \
\ / \ / \
C ------G ----- D
/ \ /
/ \ /
/ \ /
Ab----- Eb

This is where the fun starts. Harrison now
asks to have Bb tuned a 7/6 up from low G.
Then F is a 3/2 above that. ( ) signifies the
note which would complete a 7-limit tetrad; it's
not called for here.

C#
/ \
/ \
/ \
/ \
/ \
A --------- E --------- B
\ /|\ /|\
\ / | \ / | \
\ / | \ / | \
\ / Bb --------- F \
\ / \'-.\ /.-'/ \
C ------\-- G --/------ D
/ \ \ /| /
/ \ \ | /
/ \ / \|/
/ \ / ( )
/ \ /
Ab --------- Eb

And that's it for the tuning guide. F# is
not included, but more surprisingly, the
last interval, from F up to A, is described
as a 5/4. This is incorrect! A 5/4 below A
would give F 16:9, and a 5/4 above F 7:4
would be the septimal (flat) A of 35:32.
Harrison apparently deliberately ignored the
septimal comma of 64/63 between the two different
F's.

Immediately after the tuning guide, the score says
"which result in the following:" and notates in
a scale from low G = 1/1 all the ratios given in
my lattice except F 16:9, and including in the scale
F# 15:8, which was never mentioned in the tuning guide.

This gives a complete system, with the error, of:

C# 25:18
/ \
/ \
/ \
/ \
/ \
A 10:9-------E 5:3-------B 5:4-----(F# 15:8)
/ \ /|\ /|\ /
/ \ / | \ / | \ /
/ \ / | \ / | \ /
/ \ /Bb 7:6-------F 7:4 \ /
/ \ / \'-.\ /.-'/ \ /
[F 16:9]-----C 4:3-----\-G 1:1-/-----D 3:2
\ / \ \ /| /
\ / \ \ | /
\ / \ / \|/
\ / \ / x
\ / \ /
Ab 16:15----Eb 8:5

Here's the middle of the lattice, showing the error:

. . . <snip>

/ \ / | \ / | \ /
/ \ /Bb 7:6-------F 7:4 \ /
/,===========================' \ /
[F 16:9]-----C 4:3-----\-G 1:1-/-----D 3:2
\ / \ \ /| /
. . . <snip>

(this is similar to the way I depict the
"xenharmonic bridges" on my lattices)

I would be interested to get a response from
someone who is familiar with this piece. Has
it ever been performed? How has this error been
handled?

- Monzo
http://www.ixpres.com/interval/monzo/homepage.html

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Joseph L Monzo wrote:

> From: Joseph L Monzo <monz@juno.com>
>
> Yesterday I wrote about an error in the
> tuning guide Lou Harrison provided on the score
> of his _Incidental Music for Corneille's "Cinna"_
> [Xenharmonikon 5].

I for one have committed similar errors to print which I expect will be
caught somewhere in the future. It would be good to break the code on this
one though!
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

>From: Joseph L Monzo <monz@juno.com>
>
>Yesterday I wrote about an error in the
>tuning guide Lou Harrison provided on the score
>of his _Incidental Music for Corneille's "Cinna"_
>[Xenharmonikon 5].

>I would be interested to get a response from
>someone who is familiar with this piece. Has
>it ever been performed? How has this error been
>handled?

On the CD that accompanies Leta Miller and Fred Lieberman's _Lou Harrison:
Composing a Life_ (Oxford 1998), there is a wonderful recording of Lou not
only performing this piece but demonstrating the tuning note by note. The G
to F interval is clearly a 7/4. The F to A interval in his chart should be
80/63. I think it's fair to say that Lou does not consider the 64/63
insignificant -- it's just one of those slips that most of us make
occassionally.

Bill

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