Jim Coleman's temperaments was Pure.....

[Bernhard Stopper]

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Joe,
The "standard" 12-TET takes 1/12 of the pythagorean comma from the =
fifths.
The pure fifth approach you talked about, puts the pythagorean comma in =
1/7 up to the octave to get pure fifths.

In the pure 12ths approach, i published in 1988, the 12 fifths are split =
up to 12 twelfths and 12 octaves, yielding a circle of 12 twelfths on =
one side and 19 octaves at the other side.

The pure 12ths approach we are talking about here, and for which already =
exists various (free) approaches, puts then a 1/19 of the pythagorean =
comma to the 19 octaves. Complete different thing to the Cordier =
/Coleman thing.
And the existing approaches have some serious problems to be realized, =
even with ETD.

In my new approach every fifth (smaller than pure, not pure)and every =
octave (stretched , not pure) having 1 note together (formig a 3-note =
chord, there are four such combinations) can sound pure, when played =
together and tuned correctly.This is due to my recent discovery, that =
there is a symmetry of the beat ratios to the interval ratios only in =
the P12th tuning.

so the complete temperament will set or calculated by tuning/calculating =
the next note by reffering to two previous notes forming such a 3-note =
combination.
And this method is new, and that is what i filed for patenting. One can =
not patent maths or an idea or a system, but a method you can.

regards,

Bernhard
  ----- Original Message -----=20
  From: Joe Garrett=20
  To: pianotech=20
  Sent: Friday, April 15, 2005 6:59 AM
  Subject: Re: Jim Coleman's temperaments was Pure.....


  Bill Ballard asked: "Joe, just for historical purposes, which of the =
many tuning schemes=20
  Jim has handed out over the years, are you referring to? And of=20
  course, Bernhard has only given us a rough sketch of the aural=20
  version of his temperament"

  Bill,
  There have been several, but the one I was referring to was an article =
in the PTJ a few years back. All based on the perfect 5th, etc. IMO, =
pretty much the same thing. Just presented in a different way. Patenting =
a temperament? Harumph I say! Utter B.S.! Tis better to just publish and =
show the world a different way, that may have some validity, (only to be =
proven with time tested procedures).
  Regards,
  Joe Garrett, R.P.T.
  Captain, Tool Police
  Squares R I
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