OnlyPure Recordings

[Ric Brekne]

Hi Bernard

Most of this was discussed back and forth on this list  by Dr. Coleman and myself  3 and a half years back. I would like to point out that when imposing P 12ths onto a equal temperament perspective, the inside and outside 5ths you relate to octaves very naturally fall into place as a result of the stretch the P 12th  creates.  I've  looked a bit closer at this since your last  posts and find there is really little or no room at all for fudging. 4ths, 5ths, and octaves still have relationships that can only be strained so far before they become just plain unexceptable. The P 12th interval evenly divided as I have described results in the same kind of results your tuning displays. The same kinds of comments were tossed around back then, most notibly comments regarding the  5th-6th octave area.  Its all in the archives.

As far as the bass is concerned. I do not recommend extending the P 12ths concept down there. My own feeling is that this results in a far to tight stretch for the bass. This was also something Dr Coleman commented on when we discussed all this.  

Pure octaves, pure 12ths, or anything else to begin with is a dubious concept to begin with. There is nothing really pure about any of these, There is only at best the kind of pureness that Virgil Smith has talked about these past 35 or so years, and it is in that sense of the word Pureness in tuning intervals has any meaning aside from specifiying coincident partials as pure.  This more general sense of purness lies at the heart of my own P 12th approach, and I fail to see at all how your approach does anything other then explain the result in different terms.  In anycase... the basic sound picture created is the same, except in the bass where I feel P 12ths just dont work. But to be sure... to each his/her own.

Also, your comments regarding the convergence of coincidents in the bass is very old news indeed.  Rick Baldersins book "On Pitch" describes this probably better then any other text I've run into.  In fact his whole approach to explaining coincident behaviour in both ETD and aural perspectives should be required reading IMHO, for anyone really interested in understanding the anatomy of tunings.

Cleaness of tuning is a most natural of tendancies amoung highly accomplished tuners.  Such tuners have been naturally fudging theoretical correct ET in this basic direction for years and years.  The only thing new is an awareness of what exactly that fudging has been about. A quantification if you will.

I dont really want to get into an argument about  patents, who discovered what, or any of the rest of it.  So I will simply  repeat what I've said for these past 4 + years on the matter.  The P 12th perspective provides a very natural and pleasing stretch to any  pianos inharmonicity characteristics.  It is the most natural of results from imposing the pure 3:1 coincident on an otherwise equal temperament template. The clarity this provides is grounded upon the re-enforcment of some  fundemenally important coincidents in 5ths, octaves, 12ths and double octaves that occurs when these are so closely alligned to same frequencies. They flat out support and build up one another when played together.  Nothing mystical about this at all.  And nothing suprising about the fact that tuners have been leaning in this direction for a very long time.

Cheers
RicB

Ric,
thank you for your merits. But ;) 

The 3 note frequency modulation of a chord consisting of an octave and
inner upper fifth and octave and inner lower fifth for temperament
setup and tuning up the treble and down the bass is the main base of
the OnlyPure method. Whithout using this 3 note chord frequency
modulations, you cant get these chords to the same clean level by using
2 note intervals sequentially.  This is as impossible as tuning a 2
note interval pure by tuning the 2 notes sequentially and not together
with the judgment of the frequency modulation of the 2 notes. Be sure
there is a difference to usual temperament setting. Maybe one cannot
here it clear enough on a 16 bit digital recording.

By the way, if you have a concert grand, with lengths progression
nearly doubling per octave in some regions (for example on a Steinway
D)  choosing no matter what partial pair conicident (as the 6:3  octave
in your ETD solution) will lead you always to a pure octave, since the
resulting inharmonicity slope makes all octave partial pairs coincident
in this case.

If tuning P12 equal temperament, one must let fall the pure octaves
completely down, since the stretch is needed to phase out with the
fifths in the  3 note chords. So forget to try to get any of the octave
partial pairs coicident.  Tuning really pure twelfths ET is the choice
to adding the pythagorean comma to the octaves side.

best regards,

Bernhard