Why are we writing?

Thanks, Aline Surman, for your moderate observation
that ET is useful when migrating tonally in a piece.

I'd tune differently for playing Bach and Rameau, and maybe
even keep a roomful of harpsichords, which is easy to do
nowadays, with computers. Though, heaven knows, a real
harpsichord DOES feel extremely different.

May I speak to my own problems? I want to know where we're going.

I have spent a long time in school, and am becoming full of
degrees and erudition, but still I don't know where we're going.

My teachers seem to feel that I should just "be myself," but
in practice my self incorporates more problems than simplifications.

It is only a recent phenomenon that any working musician would
dream of leaving "da folks" out of his work, even granted that
in 1750 "da folks" were aristocrats. Aristocrats, now as then,
are notoriously lazy and ignorant. They have lots in common with
everybody else.

So, where are we going? Why are we working to write music?


Will

wgrant@cats.ucsc.edu

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>Would the 'natural' scale then be in the ratios
> 1, 9/8, 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 2
> for the scale CDEFGA(B-flat)Bc ? Do I get this right?

The way list members been using "natural" has not been as a specific
definition as much as a descriptive adjective. By those standards, that
tuning would certainly qualify as natural.




>What would this scale be called, and how would it sound ?

I have called that tuning an octave-repeating harmonic-series-fragment
tuning. Partch would further characterize it as "utonality". Wendy Carlos
called something a lot like that "perfect tuning".




>What would the scale be called
> 1, 9/8, 5/4, 4/3, 3/2, ......., where the fourth is tuned as a
>perfect fifth below ?

I don't know of any specific name for such a tuning.





>Would this be the JI scale?

Yes, all of these would be examples of Just Intonation.

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>>What would this scale be called, and how would it sound ?
> I have called that tuning an octave-repeating harmonic-series-fragment
>tuning. Partch would further characterize it as "utonality". Wendy Carlos
>called something a lot like that "perfect tuning".

Whoops! Sorry, that's Otonality, not Utonality.

How would that sound? Well, it's kinda difficult to describe in words.
It's fair to say certain things about it:
1. It has as many different sizes of steps as it has steps, so it doesn't
have that feeling of whole- and half-steps.
2, It's probably fair to say that, to 12TET trained ears with little experience
in unusual tunings, it sounds very strange, especially harmonically.

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Pieter Smit wrote:

>Would the 'natural' scale then be in the ratios
> 1, 9/8, 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 2
> for the scale CDEFGA(B-flat)Bc ? Do I get this right? What would
>this scale be called, and how would it sound ?

Pieter, I missed your question but saw some other replies. When you
use the word "natural" I have some very definite opionions about this.
If you go to my WWW pages (URL below) you can get the long version which
I think you might enjoy given the questions you are thinking about.

While there is some validity to what you have done in your post, it is
not the complete story. In practice if you just take frequencies 1, 2,
3, 4, 5, etc and work out the notes by transposing back to one octave
then you have assumed that the ratio of 2 (the octave transpose) is more
important than all other ratios. That is actually true, but the ratios
3, 5, 7 etc are successively less important. Therefore the ratios of 11
and 13 are rather seldom really found in music and your 11/8 is more
likely to be 21/16 but is generally really 4/3.

>What would the scale be called
> 1, 9/8, 5/4, 4/3, 3/2, ......., where the fourth is tuned as a
>perfect fifth below ? Would this be the JI scale?

Yes. The JI scale is 1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2. The next two
most common notes that can be added to the JI scale are 7/6 and 7/4 for
Eb* and Bb* if the above scale is C. I like to express this by
eliminating the denominator as: 24 27 (28) 30 32 36 40 (42) 45 48.

[* What is the correct notation for this? Is it Mi-flat and Ti-flat?]

In nature the ratios of 2, 3, 5, 7, 11, 13, ... tend to occur with a
commonness of about 100, 42, 17, 10, 5, 4, ... so that when we have
numbers with just one ratio of 5 present we can expect 2 or 3 ratios of
3 and about 6 ratios of 2 and a ratio of 7 would then have about a 60%
chance of being present.

-- Ray Tomes -- rtomes@kcbbs.gen.nz -- Harmonics Theory --
http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm

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