[tuning] Found the 7th harmonic in common practice music :)

Finally, it happened :)

I started putting Drei Equale No2 'Poco Adagio' in tonal-ji 2 days ago.
(yes that's no2 , not no1 'Andante' which I did earlyer)

It seemed like such a simple little piece, yet it gave me trouble in one
part.
I've now found a 7-limit interval in it! :)

Here is the part:

D(4/3) - A(2/1) - D(8/3) - F#(10/3)
C#(5/4) - A(2/1) - E(3/1) - G(18/5)
D(4/3) - A(2/1) - D(8/3) - F#(10/3)
G#(15/8) - B(9/4) - D(8/3) - F(16/5)
G#(15/8) - B(9/4) - D(8/3) - E(3/1)
G#(15/8) - B(9/4) - D(8/3) - E(3/1)
G(9/5) - Bb(21/10) - C#(5/2) - E(3/1)
C#(5/4) - A(2/1) - E(3/1) - G(18/5)
D(4/3) - A(2/1) - D(8/3) - F#(10/3)
D(4/3) - A(2/1) - D(8/3) - F#(10/3)

All the above is in the harmonic root of A(1/1).

See the 7th in the second diminished chord of 9/5 - 21/10 - 5/2 - 3/1

Beethoven could have easily stayed in 6-limit, by simply playing G(9/5) -
A(1/1) - C#(5/2) - E(3/1). Or even G(9/5) - B(9/4) - C#(5/4) - E(3/1).
The 6-limit A and even B versions sound more natural and "in the mode", but
I love the spice the 7th harmonic Bb gives here :)

This piece of music solves the main 2 remaining questions I still had open
on the implications of my theory (I thought and hoped it was like this
allready but now I have actual music to back it up).

1: What happends when you play 2 diminished chords after eachother, a
semitone or whole tone appart.
My theory does not allow a diminished chord to go into another diminished
chord in 6-limit, as there is only one diminished chord possible in the
6-limit harmonic model of 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1,
which is 9/8 4/3 8/5 15/8. And all chords must go to another chord in the
same harmonic model with the same root (so only chords that can exist in 2
harmonic model roots at once can change the harmonic model root)
I was wondering wether if you did play 2 diminished chords one after another
if this ment going to 7-limit or 8-limit (8-limit I would have haaated for
several reasons).
The above piece of music makes clear we go to 7-limit and stay in the same
harmonic root :) A lovely solution I'm very happy with. (the 7-limit
diminished chord CAN change root btw, so after the 7-limit diminished we can
have a 6-limit diminished again with a different root)

2: What happends when the music makes it really really clear we're playing a
1/1 5/4 3/2 9/5 seventh chord, and yet then we raise the 1/1 by a semitone.
This is something that can't be done in 6-limit.
(The 1/1 5/4 3/2 16/9 seventh chord (root 4/3) can do this in 6-limit to
become 16/15 5/4 3/2 16/9 (root 4/3), better seen from the 4/3 root as 8/5
15/8 9/4 8/3, the normal 6-limit diminished chord.)
I allready noticed that even in 12tet when you raise the 1/1 in a clear 1/1
5/4 3/2 9/5 seventh chord, that it sounds different, has a different "feel"
than when raising a normal dominant V7 into a 6-limit diminished.
Now it is clear to me, it rasing the 1/1 in 1/1 5/4 3/2 9/5 indeed becomes
21/20 5/4 3/2 9/5 :)
The 7-limit diminished chord. Again by far the nicest solution, following
perfectly the logic of my system, and it sounds great.

Anyhow, I was so happy to find my first 7th harmonic in common practice
music I had to share :)
Hope someone finds it interesting.

I'll finish up the Drei Equale No2 soon and render it with a real trombone
quartet using Melodyne.
I think I'll have it ready within a week.

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
> G(9/5) - Bb(21/10) - C#(5/2) - E(3/1)
> See the 7th in the second diminished chord 9/5 - 21/10 - 5/2 - 3/1
> ...
> Beethoven could have easily stayed in 6-limit, by simply playing
> G(9/5) - A(1/1) - C#(5/2) - E(3/1).
> Or even G(9/5) - B(9/4) - C#(5/4) - E(3/1)....
> I love the spice the 7th harmonic Bb gives here :)

Hi Marcel,
me too,
because yours fine analysis supports Mark Lindley's hypothesis
that Beethoven had really something different in mind than 12-ET:

/tuning/topicId_85623.html#85782

at least for his Piano-Variations: Opus #34.

Preview sketch of the Preface:

http://www.google.de/url?sa=t&source=web&ct=res&cd=2&ved=0CAsQFjAB&url=http%3A%2\
F%2Fwww.sim.spk-berlin.de%2Fuploads%2F04-publikationen%2Fsimpk_kub02_inhalt.pdf&\
rct=j&q=mark-lindley+beethoven+stimmung&ei=nhJWS8_wLIa5_Qb45NWdCg&usg=AFQjCNF-kQ\
dxuygXYO59diPemiU_sbKoOQ

Complete score as PDF
http://imslp.org/wiki/6_Variations_on_an_Original_Theme,_Op.34_%28Beethoven,_Ludwig_van%29

bye
A.S.

bye
A.S.

Just for fun I did a little experiment with the drei equale no1.
I interpreted the chords and their position to the root alternatively (in a
crazy and wrong way), to give 7-limit music.
I'm NOT saying this is what it was ment to be (as it clearly isn't) or
anything like that.
And I just did it quickly, and the second half and especially the ending
aren't logical at all even in the crazy interpretation way I should've done
them differently but not putting the time in now.
But anyhow, again just for fun, here it is:

http://sites.google.com/site/develdenet/mp3/Drei_Equale_No1_%287-limit_test_19-04-2010%29.mid

I think people here will enjoy it :)
Strong 7-limit chords.

Marcel

Finished the Drei Equale No2 :)

It's a much more interesting and microtonal piece than I first thought.
For instance many 27/25 steps, and one 7-limit interval.

Here's the retuned MIDI:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No2_%28Tonal-JI_20-04-2010%29.mid

Here the transcription:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No2_%28Tonal-JI_20-04-2010%29.png

Here the 12tet MIDI for comparison:
http://sites.google.com/site/develdenet/mp3/Drei_Equale_No2_%2812tet%29.mid

The Scala sequence file are also at http://www.develde.net/mp3

I'll go make the Melodyne retuned real trombone quartet rendering now.
Should have it finished soon and will do another post then.

Btw, I removed the stupid out of tune 7-limit Drei Equale No1 experiment, I
didn't think it was funny or interesting anymore.

Marcel

> Here the transcription:
>
> http://sites.google.com/site/develdenet/mp3/Drei_Equale_No2_%28Tonal-JI_20-04-2010%29.png

Had an error in the transcription (3/1 instead of 8/3 in chords 27-29), went
even so far along with it as to label them wolfs lol.
Corrected it and re-uploaded.
Error is only in the transcription, not in the retuned MIDI or seq file.

Thought I'd post this, just in case anybody is listening and learning (to in
tune music, true microtonality based on a revolutionary theory), instead of
talking nonsense about 12tet vs blabla.. (150+ messages about nonsense yet
this one none, this list is crazy.. think I'm leaving soon)

Marcel