Re: 17WT paper

Hello, everyone, and I would like to join George in saying how
impressed with your piece in 17-WT, Hudson.

While George has nicely summed up some of the technical points, I
would like to emphasize above all the beauty, space, and melodic
integration of the piece. The opening has the kind of cosmic scale one
might associate with a Baroque organ prelude or toccata, and also sets
the tone for the kind of mainly quartal or quintal harmony that George
describes based on 6:7:8:9. The development of the melody unifies the
episodes and also is very delightful in itself.

It is on one level a very meditative piece, or at least so I found in
my own response; at the same time, there is lots of excitement, as
with the episode about 40 seconds into the piece with the more complex
sonorities. I very much like the timbres.

While I'm not sure if this was intended specifically to be a
"neomedieval" piece, there are some features that would make it a very
nice one. The figure where accompanying voices form a fifth and the
melody descends from a major second or ninth (i.e. 8:9:12 or 4:6:9)
to a unison or octave is typical of 13th-14th century European music,
and it is a delight to meet this familiar friend in a new environment
provided both by George's 17-WT and your creative use of it -- an
environment where it seems very much at home!

A quick point which I hope might be helpful for people interested in
trying some the kinds of sonorities used in the piece and discussed by
George in a variety of tuning systems where more or less reasonable
fascimiles might be found.

One possible JI model for two of those sonorities, each with four
notes, could use this five-note set:

1/1 7/6 4/3 3/2 56/33
0 267 498 702 916
7:6 8:7 9:8 112:99
267 231 204 214

The ratio of the five notes together is 66:77:88:99:112. The lower
four together form a 6:7:8:9 sonority. The upper four form a sonority
with the lowest three voices as 7:8:9 and the highest voice at 16:11
to the lowest, or 77:88:99:112.

As George says, more generally, the second sonority is like 7:8:9 with
a fourth voice considerably higher than it would be in 7:8:9:10, by a
comma or so. In 17-WT, it's often between 13:9 (637 cents) and 16:11
(648 cents) -- in contrast to 10:7 (617 cents).

Anyway, this has given me an idea for a piece -- as your
improvisation, Hudson, could do for lots of people.

Peace and love,

Margo

Margo Schulter escreveu:
> Hello, everyone, and I would like to join George in saying how
> impressed with your piece in 17-WT, Hudson.
> > While George has nicely summed up some of the technical points, I
> would like to emphasize above all the beauty, space, and melodic
> integration of the piece. The opening has the kind of cosmic scale one
> might associate with a Baroque organ prelude or toccata, and also sets
> the tone for the kind of mainly quartal or quintal harmony that George
> describes based on 6:7:8:9. The development of the melody unifies the
> episodes and also is very delightful in itself.
> > It is on one level a very meditative piece, or at least so I found in
> my own response; at the same time, there is lots of excitement, as
> with the episode about 40 seconds into the piece with the more complex
> sonorities. I very much like the timbres.

Hi Margo,

Thanks for your kind words about my piece. As George has said, those episodes of `excitement' use also the harmonics 11 and 13, and also a `detuned' 15 (more like 29):

Fundamental D
A C D E F# Ab A A# (Db)
6 7 8 9 /|10 11 12 13 (29)

Fundamental C
Bb C D E Gb G G# Bb (A#)
7 8 9 /|10 11 12 13 14 (29)

> > While I'm not sure if this was intended specifically to be a
> "neomedieval" piece, there are some features that would make it a very
> nice one. The figure where accompanying voices form a fifth and the
> melody descends from a major second or ninth (i.e. 8:9:12 or 4:6:9)
> to a unison or octave is typical of 13th-14th century European music,
> and it is a delight to meet this familiar friend in a new environment
> provided both by George's 17-WT and your creative use of it -- an
> environment where it seems very much at home!

I find that the more consonant sonorities in 17-WT are the quartal/quintal ones (including major seconds/ninths and minor sevenths). Those sonorities can easily lead to a reference to medieval music. Such a reference was intended only in the introductory section of the improvisation.

> > A quick point which I hope might be helpful for people interested in
> trying some the kinds of sonorities used in the piece and discussed by
> George in a variety of tuning systems where more or less reasonable
> fascimiles might be found.
> > One possible JI model for two of those sonorities, each with four
> notes, could use this five-note set:
> > 1/1 7/6 4/3 3/2 56/33
> 0 267 498 702 916
> 7:6 8:7 9:8 112:99
> 267 231 204 214
> > The ratio of the five notes together is 66:77:88:99:112. The lower
> four together form a 6:7:8:9 sonority. The upper four form a sonority
> with the lowest three voices as 7:8:9 and the highest voice at 16:11
> to the lowest, or 77:88:99:112.
> > As George says, more generally, the second sonority is like 7:8:9 with
> a fourth voice considerably higher than it would be in 7:8:9:10, by a
> comma or so. In 17-WT, it's often between 13:9 (637 cents) and 16:11
> (648 cents) -- in contrast to 10:7 (617 cents).
> > Anyway, this has given me an idea for a piece -- as your
> improvisation, Hudson, could do for lots of people.

Nice to know. :-)

> > Peace and love,
> > Margo

Cheers,
Hudson

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