brian a m stuckless science forum Guru
Joined: 31 Aug 2005
Posts: 2024

Posted: Sat Jun 24, 2006 3:33 pm Post subject:
Golden Scale of music.



$$ John Baez wrote: > > Dik.Winter@cwi.nl (Dik T. Winter) wrote: >
Quote:  In article <C0B8F249.155F3%rbj@audioimagination.com> robert
bristowjohnson <rbj@audioimagination.com> writes:
this is why we in the "west" ended up with the 12 note/octave
equal tempered scale.
=
In the currently popular "equaltempered" tuning system, each note
on the piano vibrates 2^{1/12} times as fast as the one below it...
at least if we ignore the slight "stretching" of this system that
people use on actual pianos.
There were a number of "welltempered" systems in Bach's day,
none of which was the "equaltempered" system:
http://en.wikipedia.org/wiki/Well_temperament
Nobody really knows which system Bach used. This page:
http://www.kirnberger.fsnet.co.uk/Temps3.htm
argues that it was the Werckmeister III system. They also explain
how this system works.
The advantage of nonequaltempered systems, of course, is
that different keys have different personalities, making for
more interesting music.

$$ GUESS iSS STANDARD GOLDEN Music Scale frequency per iDEAL Second:
$$
$$ Middle C @ 261.8034 cycles/(GUESS iSS STANDARD second); 261.6
$$ C# @ 277.3710 " /( " " " " ) 277.2
$$ D @ 293.8644 (Given as 293.7 Equally Tempered).. 293.6
$$ D# @ 311.3385 311.1
$$ E @ 329.8516 ( .. .. .. ).. 329.6
$$ F @ 349.4656 349.2
$$ F# @ 370.2459 ( .. .. .. ).. 370.0
$$ G @ 392.2619 392.0
$$ G# @ 415.5870 ( .. .. .. ).. 415.3
$$ A @ 440.2991 440.0
$$ A# @ 446.4806 ( ..given as 466.2 " " ).. 466.1
$$ B @ 494.2190 ( .. " " 493.9 " " ).. 493.8
$$ C. @ 523.6068 ( .. .. .. ).. 523.2
$$
$$ Each is multiplied by 1.059463, for a series of twelve intervals.
$$ Upper C is Middle C @ 261.8034 x 12th rt2 x 12th rt2 ..etc etc.,.
$$ All from 100*(GOLDEN Ratio)^2 to 200*(GOLDEN Ratio)^2 cycles/Sec.
$$
$$ 100*(GOLDEN Ratio)^2 1
$$ 100*(GOLDEN Ratio)^2 +  = 1 +  = 1.0594631.
$$ 12 12
$$
$$ One STANDARD Meterlong PENDuLUM beats ONE Second each way @ STP.
$$ One STANDARD Meter beats ONE HALF cycle / Second ..here on EARth.
$$ One STANDARD Meter beats ONE cycle per TWO Second, here on EARth.
$$ One STANDARD Meter beats ONE Second each way, on EARth's surface.
$$ One STANDARD Meter beats ONE Second each way, at EARth radius r3.
$$ Any STANDARD Meter beating ONE Second each way, is NOT ARBiTRARY.
$$ Especially, where the gravitational acceleration is (pi)^2*M/Sec.
$$ You may call that "coincidental" if you will, but not ARBiTRARY.
Re: Gogo NETSCAPE: sci.physics.electromag,alt.sci.nanotech,bit.org.
Re: The physics or mathematics of musical scales.
Re: The geometric Golden Scale of music. End of POST. 
