more warped canons

I'm enjoying the "revised" timbre of the Bohlen-Pierce "warped"
Pachelbel. Thanks, also, Paul Erlich for illustrating why this works
better...

And the Blackjack variations are quite interesting as well.

Could somebody please run down how that was done again... I'm a
little confused by the sets that Herman indicates next to the
blackjack tunings...

And what exactly are the tunings "otonal" "utonal" "beating"
and "microstep" ?? and what do the sets of numbers mean again??

Any help toward getting me to understand the basis of this would be
greatly appreciated...

Thanks!

_________ ______ ____
Joseph Pehrson

On Fri, 15 Jun 2001 17:59:12 -0000, jpehrson@rcn.com wrote:

>I'm enjoying the "revised" timbre of the Bohlen-Pierce "warped"
>Pachelbel. Thanks, also, Paul Erlich for illustrating why this works
>better...
>
>And the Blackjack variations are quite interesting as well.
>
>Could somebody please run down how that was done again... I'm a
>little confused by the sets that Herman indicates next to the
>blackjack tunings...
>
>And what exactly are the tunings "otonal" "utonal" "beating"
>and "microstep" ?? and what do the sets of numbers mean again??

I intend to put more information about the various tunings on the page
eventually. The numbers next to the blackjack tunings are decimal notation
(see http://x31eq.com/decimal_lattice.htm).

Each Blackjack tuning uses a different equivalent for the major triad:

otonal 4:5:7
utonal 1/(7:5:4)
beating 1/1 : 11/9 : 32/21
microstep 7:8:10

(actually, the 72-TET approximations of these intervals.)

For instance, the otonal version works out like this:

decimal degrees of 72-TET original

5^ 3^ 1^ 37 23 9 B F# C#
2 0 8^ 6^ 14 0 58 44 G D A E

(that's the basic scale; there's also an extra note, 28 of 72, or "4" in
decimal notation, corresponding to the C natural of the original.)

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