For your Listening Pleasure - tuning thoughts

[Bernhard Stopper]

Hi Ric,
my thoughts on the pure 12th tuning is  not only a tuning idea, its relates
to a complete new musical system, as described in my publication.

I know that there were several persons that had this tuning idea probably
independant from mine around the world at about the same time. Also some old
concert tuners used the match of M 6ths with double octave + M 3rd, whithout
exactly knowing, that this has nothing to do with the normal 5ths circle
theory. (as result the 12th was pure, what was not recognized by them)
In my publication i described the 12th tuning as a basis of a complete new
musical system that is described by a 12 - 12ths circle that fits with 19
octaves, with consequences that goes much far than "just another tuning"
idea.

The classic circle of 12 5ths and 7 octaves can be represented as (pc =
pythagorean comma)

(3/12)^12 = 2^7 * pc

the dodecachord system this transforms the 12th circle (that fits with 19
octaves) to:

3^(12) = 2^(19) * pc

The "dodecachord" system (was realized on a harpsichord built by Michael
Scheer, shown on the Frankfurt Musikmesse 1990) has a keyboard with a key
pattern that repeats after a 12th instead of an octave.
The dodecachord together with the pure 12th tuning as its base, is a new
music system that shows interesting symmetric musical structures that are
hidden when looking on the scales only over the span of an octave.

The center key pattern is (1 for tone, x for half tone):

1 x 1 1 1 x 1 1 1 x 1

instead of the octave pattern on the "normal" keyboard that has a pattern of

1 x 1 1 1 x 1

the major and minor scales over a 12th are simply inverse symmetric, when
viewed from the 4. step upward and downward from the center:

major scale (4. step upwards):

 > 1 1 x 1 1 1 x 1 1 x 1

minor scale (4. step downwards):

1 x 1  1 x 1 1 1 x 1 1 <

other symmetry pairs are: dorian/mixolydian, phrygian/lydian.

Another major importance in the dodecachord system is the possibility to
represent every keyboard interval as a ratio combination of 3^y, with y as
x/19 and x as any integer, what is a main key for representing musical
structures in 3 dimensional structures that are similar to structure like
crystal zeolithes (1) or on neural networks (and what makes it possible for
us to "recognize" musical structures). The reason, why a pure 12th tuning
sounds that great, since is that it "fits" easier in the brains
landscape....

(1) Spektrum der Wissenschaft, 9/89, p. 94

Ric, still believe i am not crazy? <g>

best regards,

Bernhard

BTW the Mensurx 5.0 is out now, and i have included the MiniMens string
simulator.

----- Original Message ----- 
From: "Richard Brekne" <Richard.Brekne@grieg.uib.no>
To: "Pianotech" <pianotech@ptg.org>
Sent: Thursday, May 27, 2004 11:35 AM
Subject: Re: For your Listening Pleasure - tuning thoughts


> Hi Bernhard.
>
> You are the third person I've run into that lay claims to this tuning.
> Evidently a couple fellows from the states also thought of this idea
> independently of your own publications about 15-20 years back, and
> another a few years later.  Myself I was unaware of anyone having done
> this before and developed my own P-12ths tuning with the help of Tune
> Lab 97 whilst learning a good deal about tuning theory that I had
> skipped over earlier in life.
>
> While I am happy to acknowledge any prior invention on the part of
> yourself and anyone else, the fact that this actually has been thought
> of independently and successfully (very successfully I might add) used
> in different places in different times strikes me as significant with
> regards to its usefulness and viability....  A good thing is often
> pondered by several different minds in different places.
>
> What I really like about it is its easy of implementation from an ETD
> standpoint... and... if you get the knack of it... from an aural
> standpoint as well. Kind of redunditates all these extremely fancy
> methods of contriving a tuning curve.
>
> In any case... I wouldnt call you crazy... in fact I cant see how anyone
> who knows enough about tuning theory to be able to run some basic
> numbers around could avoid seeing the basic sense in the approach.
> Clean as a whistle as it were.
>
> Cheers
> RicB
>
> Bernhard Stopper wrote:
>
> > Ric,
> > thank you very much for your statements about the pure 12th tuning...
> >
> > 15 years after its publication in euro piano 3/88 ("Stopper tuning -
> > Equally temepered scale based on pure dudecimos (12th, pure octave +
> > pure 5th) it seems to become accepted.
> > At the time i did the publication, most technicians called me crazy
> > and there were only a few who understood what my intention was.
> >
> >
> > Isaac,
> >
> > maybe your opinion about the pure 12th may change if you hear this
> > tuning done by someone who is familiar with tuning it. I can not agree
> > that the 5ths are more strange than in normal tuning, since they are
> > less sharp than your preferred normal VT tuning.
> >
> > best regards,
> >
> > Bernhard Stopper
> >
> > for more information about the pure 12th tuning (in german):
> >
> >  http://www.piano-stopper.de/html/stotun.htm
> >
>
>
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