Re: [tuning] Digest Number 6182--Phi, Lorne Temes, etc.

Just for the record, Lorne Temes was a college student when he wrote his letter on phi scales.

John Chowning, who invented FM synthesis, used the ninth root of Phi in his piece 'Stria.'

The first mention I know of regarding scales built using phi is in this reference: Young, William Lyman. Report to the Swedish Royal Academy of music on the discovery of two classical scales and their natural keyboards. Privately printed, 1961. Young calls the golden ratio the "Sectional Sixth" and mentions the 7 and 10 tone MOSs generated by cycles of 25 degrees of 36-EDO. As this work was published in 1961, it predates David Schoer's "aureotonality," the exact details of which I've been unable to find, but it is described below in a report of a seminar on electronic music composition in October, 1965 under the auspices of the Audio Engineering Society of America and reported by Herbert Deutsch.

"Additional lectures were given by one of the participants_
David Schroer, a mathematician at the University of Illinois.
One dealt with the analysis and synthesis of bell tones, and
the other was in an area he refers to as "aureotonality". This
is the application of the "golden ratio" to two frequencies
and the construction of scales and intervals as created by
the second and third orders of sum and difference frequencies
resulting from their combination. The musical effect, aside
from the scales made available, is an attractive clangorous tone
which can be partially synthesized by frequency modulation."

--John

And the earliest mention I've found is from the middle of the 17th century, by this guy:

http://en.wikipedia.org/wiki/William_Brouncker,_2nd_Viscount_Brouncker

I'm not at my computer so I'll have to find the more precise info later.

And a practical implementation of Phi and its logarithmic inverse (and at least two other intervals found in successive golden sections in the frequency realm) dates from some 2400 hundred years ago, though I'm sure there was no golden section intent, it is probably rather the byproduct of another characteristic of phi, but more on that later (just have a moment checking my mails here).

--- In tuning@yahoogroups.com, "John H. Chalmers" <JHCHALMERS@...> wrote:
>
> Just for the record, Lorne Temes was a college student when he wrote his
> letter on phi scales.
>
> John Chowning, who invented FM synthesis, used the ninth root of Phi in
> his piece 'Stria.'
>
> The first mention I know of regarding scales built using phi is in this
> reference: Young, William Lyman. Report to the Swedish Royal Academy of
> music on the discovery of two classical scales and their natural
> keyboards. Privately printed, 1961. Young calls the golden ratio the
> "Sectional Sixth" and mentions the 7 and 10 tone MOSs generated by
> cycles of 25 degrees of 36-EDO. As this work was published in 1961, it
> predates David Schoer's "aureotonality," the exact details of which I've
> been unable to find, but it is described below in a report of a seminar
> on electronic music composition in October, 1965 under the auspices of
> the Audio Engineering Society of America and reported by Herbert Deutsch.
>
>
> "Additional lectures were given by one of the participants_
> David Schroer, a mathematician at the University of Illinois.
> One dealt with the analysis and synthesis of bell tones, and
> the other was in an area he refers to as "aureotonality". This
> is the application of the "golden ratio" to two frequencies
> and the construction of scales and intervals as created by
> the second and third orders of sum and difference frequencies
> resulting from their combination. The musical effect, aside
> from the scales made available, is an attractive clangorous tone
> which can be partially synthesized by frequency modulation."
>
>
> --John
>

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> And the earliest mention I've found is from the middle of
> the 17th century, by this guy:
>
> http://en.wikipedia.org
> /wiki/William_Brouncker,_2nd_Viscount_Brouncker

For creating scales?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@> wrote:
> >
> > And the earliest mention I've found is from the middle of
> > the 17th century, by this guy:
> >
> > http://en.wikipedia.org
> > /wiki/William_Brouncker,_2nd_Viscount_Brouncker
>
> For creating scales?
>
> -Carl
>

Yes, with practical scale. Back atcha to-nite or tomorrow morning on this. But the ancient one is even better.

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@> wrote:
> > >
> > > And the earliest mention I've found is from the middle of
> > > the 17th century, by this guy:
> > >
> > > http://en.wikipedia.org
> > > /wiki/William_Brouncker,_2nd_Viscount_Brouncker
> >
> > For creating scales?
> >
> > -Carl
> >
>
> Yes, with practical scale. Back atcha to-nite or tomorrow morning on this. But the ancient one is even better.
>

What do you know- it's in the Scala archive ("phi_17") and and a good part of Cambridge is online so I don't even have to go to the library tomorrow, oh the wonders of the amberian abacus!

Brouncker, 1653. (3+(sqrt5))/2:1 in 17 equal semitones, aka, 17 logarithmically equal divisions of Phi+1; and ((sqrt2)+1):1 into 15 equal semitones, aka 15 equal divisions of the silver mean.

(Hm, the online Cambridge gives the correct figures of Phi and the silver mean, but has mistakes in the formulas, with typos of "-" instead of "+", but I don't recall the physical edition in the university library having this error.)

--- In tuning@yahoogroups.com, "John H. Chalmers" <JHCHALMERS@...> wrote:
>
> Just for the record, Lorne Temes was a college student when he wrote his
> letter on phi scales.
>
> John Chowning, who invented FM synthesis, used the ninth root of Phi in
> his piece 'Stria.'
>
> The first mention I know of regarding scales built using phi is in this
> reference: Young, William Lyman. Report to the Swedish Royal Academy of
> music on the discovery of two classical scales and their natural
> keyboards. Privately printed, 1961. Young calls the golden ratio the
> "Sectional Sixth" and mentions the 7 and 10 tone MOSs generated by
> cycles of 25 degrees of 36-EDO. As this work was published in 1961, it
> predates David Schoer's "aureotonality," the exact details of which I've
> been unable to find, but it is described below in a report of a seminar
> on electronic music composition in October, 1965 under the auspices of
> the Audio Engineering Society of America and reported by Herbert Deutsch.
>
>
> "Additional lectures were given by one of the participants_
> David Schroer, a mathematician at the University of Illinois.
> One dealt with the analysis and synthesis of bell tones, and
> the other was in an area he refers to as "aureotonality". This
> is the application of the "golden ratio" to two frequencies
> and the construction of scales and intervals as created by
> the second and third orders of sum and difference frequencies
> resulting from their combination. The musical effect, aside
> from the scales made available, is an attractive clangorous tone
> which can be partially synthesized by frequency modulation."
>
>
> --John
>
Thanks John,

Having recently discovered for myself that 25deg36EDO corresponds very closely to PHI and yet conserves 12EDO as a subset, it is good to know, yet hardly surprising, to also learn that I am late by about 50 years. Incidentally, you wouldn't happen to recall the MOSs around 7 and 10? I've been trying to calculate them, but with interval 25 generating all 35 notes I can't see the trees for the forest.

-Rick