Re: [tuning] Digest Number 730

>Message: 1
> Date: Sun, 6 Aug 2000 12:46:24 +0200
> From: "Manuel Marino" <vanethian@tin.it>
>Subject: R: Microtonal
>This is not a problem for instruments such as the violin, trombone or the
>voice... but how can you create an orchestral soundscape with ONLY
>synthesizers?.. this is what i've done in my music... ;)
>
>
>
>Vanethian,
>
>http://www.mp3.com/Vanethian

Ok, but which piece on your MP3 page? I don't have the time to listen to all of them right now. I just want to listen to the one in which you are using microtonality.

Thanks,
Paolo

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Dave, Re Catler's letter-
Inventors frequently misunderstand patents, their rights and the
obligations of others regarding their patents. Some of what this guy said
is bogus (Catler is required to rat off bent fret offenders? Hah!) but if
he is backed by a big company it can be a problem. The surest way to
derail him is to find all prior art (instances of bent frets through
history) and send it to him. If he tries to enforce his patent, it can be
declared invalid and he has lost several thousand dollars, while if he
backs off there may be suckers waiting to pay him.

John Starrett "We have nothing to fear but
the scary stuff." http://www-math.cudenver.edu/~jstarret/microtone.html

Joseph,

I'm not sure where to begin or how far to go with an elucidation, but let
me make a couple responses: you said,

>However, no practical scale IN EXISTENCE has ever used these kinds of
>mathematical constructs. Ironically, though, 2^Phi is actually very
>close to a perfect fifth, so scales constructed from fundamental
>acoustical intervals are, somewhat coincidentally, very close to the
>conceptual scales generated through abstract mathematics. (Or at least
>arithmetic).

This depends on what you mean by "these mathematical constructs." If you
mean: scales generated by the 2^phi generator, then you're right. But the
mathematical constructs I'm concerned with include a 7-tone scale in a
system of 12 interval categories, 2212221, or
whole-whole-half-whole-whole-whole-half if you prefer, which you can find
in the majority of western music and many non-western musics as well.
Also, a 12-tone scale in a 12 category system (1111111111111): serialist
music; a 5-t scale in a 12-c system (32332): important in Western folk and
popular music; a 5-t in a 7-c system (21221): found in many Eastern musics.
2^phi is not particularly close to 3/2 (its about 39 c sharp). You must
be thinking of the Kornerup golden fifth which is about 6 c flat of the
3/2. The low numbered Kornerup MOS's look a lot like the MOS's of the pure
5th. In my system of interval categories they're equivalent.

>Then there is a curious "scale tree" over in Anaphoria that looks like
>the beautiful bark of a large cut oak, with aging lines filled in with
>numbers. I'm guessing this all has to do with various scale
>generators... but am a little foggy yet here...

Each node on the tree is a family of scales (MOS's). The fractions (which
represent generators) are logarithmic parts of an 8ve, which means, if the
fraction is 4/7, then the interval is 4 steps of 7-tET. For each fraction,
reiterate the interval until you get a scale consisting of only 2 step
sizes, and repeat the process until the numerators of each step are 1's and
2's. So, with 4/7:
4, 3; 2, 2, 3; 2, 1, 2, 1, 1; you can represent it this way also:

0 1 2 3 4 5 6
0 4
0 2 4
0 2 3 4 6

These scales are ET'd approximations to scales on some infinite branch,
such as the MOS's of the pure 5th, or Kornerup's 5th.

jason

Joseph Pehrson wrote,

>>Then there is a curious "scale tree" over in Anaphoria that looks like
>>the beautiful bark of a large cut oak, with aging lines filled in with
>>numbers. I'm guessing this all has to do with various scale
>>generators... but am a little foggy yet here...

Jason Yust wrote,

> Each node on the tree is a family of scales (MOS's). The fractions
(which
>represent generators) are logarithmic parts of an 8ve, which means, if the
>fraction is 4/7, then the interval is 4 steps of 7-tET. For each fraction,
>reiterate the interval until you get a scale consisting of only 2 step
>sizes, and repeat the process until the numerators of each step are 1's and
>2's. So, with 4/7:
>4, 3; 2, 2, 3; 2, 1, 2, 1, 1; you can represent it this way also:

>0 1 2 3 4 5 6
>0 4
>0 2 4
>0 2 3 4 6

> These scales are ET'd approximations to scales on some infinite
branch,
>such as the MOS's of the pure 5th, or Kornerup's 5th.

And each fraction is derived by locating its two "parents" (the fractions
immediately to the left and immediately to the right of, but in upper levels
than, the "child") by taking the "freshman sum": add the numerators of the
parents to form the numerator of the child, and add the denominators of the
parents to form the denominator of the child. The size of the child will
therefore be between the sizes of the parents (this is exactly what we saw
when constructing mediants in the harmonic entropy stuff).

Maybe he should just have a look at Mark Lindley's book on lutes, viols, and
temperaments, which makes a pretty good case for uneven gut fretting in the
meantone era.

----- Original Message -----
From: John Starrett <JSTARRET@MATH.CUDENVER.EDU>
To: <tuning@egroups.com>
Sent: Monday, August 07, 2000 5:33 PM
Subject: Re: [tuning] Digest Number 730

> Dave, Re Catler's letter-
> Inventors frequently misunderstand patents, their rights and the
> obligations of others regarding their patents. Some of what this guy said
> is bogus (Catler is required to rat off bent fret offenders? Hah!) but if
> he is backed by a big company it can be a problem. The surest way to
> derail him is to find all prior art (instances of bent frets through
> history) and send it to him. If he tries to enforce his patent, it can be
> declared invalid and he has lost several thousand dollars, while if he
> backs off there may be suckers waiting to pay him.
>
> John Starrett "We have nothing to fear but
> the scary stuff." http://www-math.cudenver.edu/~jstarret/microtone.html
>
>
>
>
>
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Daniel Wolf wrote,

>Maybe he should just have a look at Mark Lindley's book on lutes, viols,
and
>temperaments, which makes a pretty good case for uneven gut fretting in the
>meantone era.

Uneven fretting, yes; but _bent_ frets? That's the issue here.