American Festival of Microtonal Music 1999

May 20 and May 27, 1999 -- both Thursdays -- are concert nights for the
AFMM at St. Paul's Chapel, Columbia University, NYC.

One hightlight (May 20) will be the premiere of "Thirsting For Peace in
a Raging Century" for 2 voices and microlyre by Ed Sanders, leader of the
Fugs. The microlye is an electronic pad instrument invented by Sanders to
play harmonically rich bass in 31-TET. I keep listening to his 20 minute
work over and over again for simple joy. The piece was spurred by the
death of Abbie Hoffman.

Johnny Reinhard
Director
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@idt.net
http://www.echonyc.com/~jhhl/AFMM

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End of TUNING Digest 1540
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On Fri, 2 Oct 1998, William Sethares wrote:

> In any case, one useful formula from trig is:
>
> sin(x) + sin(y) = 2 cos( (x-y)/2 ) sin( (x+y)/2 )
>
> To apply this to the beat cancellation, use this in the form
>
> sin(w t) + sin( (w + dw)t ) = 2 cos( dw t /2) sin( (w+dw/2)t )

I thank that's the right sort of 'flavor' of formula for what I'm trying
to do, but not the exact right one. I think I'm looking for a formula
which somehow involves cos(w*t/d)

A note for the mathematically inclined - trigonometric identities are a
lot easier to verify using the formulas -

sin(x) = i*(e^(-i*x)-e^(i*x))/2

cos(x) = (e^(i*x)+e^(-i*x)/2

Both of which are based on the formula

e^(i*x) = cos(x) + i*sin(x)

-Bram