Re: Re: Ives's tuning: eighthtones

Joe, I agree the eighthtones are an interesting dimension to Ives. I think
the missing sketch of eighthtones Ives mentions in the Memos can be found on
the first sketch page of Section B of the "Universe Symphony." It's found on
a trumpet line (Lou Harrison agrees) and has the markings printed below with
the note below with deviations in cents:

5 1/4 2 1/8 6 5 1/4 2 1/8 6
>C
Ab -25 Db E -25 B -25 Eb -25 Gb

Joe, I'm not sure it's fruitful to analyze 24-TET and 48-TET with the same
notation rules for extended Pythagorean. It seems to be a contradiction in
terms. They are all part of the smorgasbord that Ives flirts with.

And yes, there is an overtone machine, as well as a just intonation harp in
the "Universe Symphony." There is no doubt about it because he explains it
every which way he can to specify it.

Lou Harrison took exception to the implication by Ives that one needed an
"Acousticon" in order to accurately play Just Intonation. Similarly, it is
ironic to me that Lou never imagined woodwind players as reliable microtonal
performers and so he never wrote for them in this regard.

The actual numbers for Extended Pythagorean with G at 0 cents follow:

Fb=882 Cb=384 Gb=1086 Db=588 Ab=90

Eb=792 Bb-294 F=996 C=498 G=0

D=702 A=204 E=906 B=408 F#=110

C#=612 G#=114 D#=816 A#=318 E#=1020

B#=522 FX=24 CX=726 GX=228 DX=930

AX=432 EX=1134 BX=636

Hope this helps.

Johnny Reinhard
AFMM