Moonlight madness

If you like 15-ET, and if you also like Beethoven, check out these new
MP3's:

http://artists.mp3s.com/artist_song/2884/2884029.html
http://artists.mp3s.com/artist_song/2886/2886928.html
http://artists.mp3s.com/artist_song/2886/2886928.html

Yes, this is Beethoven's Moonlight Sonata, retuned to 15 notes per octave.
The story behind this is that I was playing with a variation of the 11-note
kleismic scale (a.k.a. "David Keenan's chain-of-minor-thirds scale"), and I
used it to retune the third movement, initially just to get a feel for what
the kleismic scale sounded like. It was a conveniently available file I did
a couple of years ago that I had lying around, and it happened to have a
texture similar to what I wanted to use. I soon realized that if I tempered
out the 128/125, it would actually be a fairly good tuning for this piece.
Since 15-ET is a kleismic (15625/15552) temperament that is also an
augmented (128/125) temperament, it was a natural choice, and the third
movement ended up sounding really nice with very few manual changes.

So then I tried the first and second movements. They required more manual
adjustments, and I was never completely satisfied with the way the second
movement came out, but the first movement has some really beautiful parts.
In fact, I realized that without even trying, Beethoven wrote music that
sounds better in 15-ET than anything I'll ever write. It even works well in
other porcupine temperaments (250/243) like 22-ET and 37-ET, if you extend
the scale to more than 15 notes. The syntonic comma is hardly a problem at
all in the first and third movements, so it's possible there might be other
tunings that would work. Part of the reason the porcupine temperament works
so well, though, is the 64/63 comma (which is shared by 12-ET). The seventh
of the dominant seventh chord actually sounds like a harmonic seventh. The
128/125 was sort of a red herring (since the 22 and 37-ET versions work
just fine without it), but at least it led me to 15-ET!

The third movement is done with a hammered dulcimer patch, which is what I
was planning to use for the kleismic piece I was thinking about writing.
Since the first movement is slower, I tried a number of different patches
with long sustains and settled on a nice vibraphone. The second movement
seemed to be a little less objectionable with steel drums, but those commas
really stick out in 15-ET.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

--- In tuning@y..., Herman Miller <hmiller@I...> wrote:

> Yes, this is Beethoven's Moonlight Sonata, retuned to 15 notes per octave.

Thanks for the addition to your mp3.com page! I especially liked the first movement.

The syntonic comma is hardly a problem at
> all in the first and third movements, so it's possible there might be other
> tunings that would work.

In the 5-limit, if you can lift it to both porcupine and meantone you can lift it to 5-limit JI, since all you need to add is the 25/24 neutral thirds temperament, which is pretty much automatic.

In the 7-limit, if you can lift to both septimal meantone and porcupine, you automatically get a complete lifting to 7-limit JI.

Part of the reason the porcupine temperament works
> so well, though, is the 64/63 comma (which is shared by 12-ET). The seventh
> of the dominant seventh chord actually sounds like a harmonic seventh.

In septimal meantone, you'd need to decide if this was a 7/4 or a 16/9, and by so doing, you get your lifting to JI.

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:

> In the 7-limit, if you can lift to both septimal meantone and porcupine, you automatically get a complete lifting to 7-limit JI.

Since it is probably not obvious why this is or how to do it, let me give it as an example.

One way to describe linear temperaments is by an octave+period matrix.
We have a 4x2 matrix for meantone, and a 4x2 matrix for porcupine. Putting them together gives us a 4x4 matrix:

[1 0 1 0]
[1 1 2 -3]
[0 4 3 -5]
[-3 10 2 6]

This matrix is unimodular, meaning it can be inverted to another integral matrix:

[54 -74 36 -7]
[31 -43 21 -4]
[-53 74 -36 7]
[-7 10 -5 1]

The rows of this matrix can be interpreted as defining four rational
numbers:

q1 = 2^54 3^(-74) 5^36 7^(-7)
q2 = 2^31 3^(-43) 5^21 7^(-4)
q3 = 2^(-53) 3^74 5^(-36) 7^7
q4 = 2^(-7) 3^10 5^(-5) 7^1

If a,b,c,d are such that a is the number of octaves and b is the number of periods (in this case, meantone fifths) for meantone, and c is the number of octaves and d is the number of periods (of about 162 cents) for porcupine, then the JI note in question is

q1^a q2^b q3^c q4^d

--- In tuning@y..., Herman Miller <hmiller@I...> wrote:

/tuning/topicId_41009.html#41009

> If you like 15-ET, and if you also like Beethoven, check out these
new
> MP3's:
>
> http://artists.mp3s.com/artist_song/2884/2884029.html
> http://artists.mp3s.com/artist_song/2886/2886928.html
> http://artists.mp3s.com/artist_song/2886/2886928.html
>

***This is strange and quite beautiful. I particularly like the
timbres, which seem considerably more sophisticated than some of the
Herman Miller timbres I remember previously. I wonder what equipment
is being used (maybe a MakeMicroMusic question).

I also didn't realize that Herman is based in Ann Arbor, my
old "haunt..."

Nice!

Joseph Pehrson