Paul's brilliant analysis of Graham's Blackjack"pump" progression [was: (unknown)]

> From: Paul Erlich <paul@...>
> To: <MakeMicroMusic@yahoogroups.com>
> Sent: Thursday, August 09, 2001 4:24 PM
> Subject: [MMM] (unknown)
>
>
> --- In MakeMicroMusic@y..., "John Starrett" <jstarret@c...> wrote:
>
> > How strange! Now when I listen to it it seems to repeat every seven
> > chords.
>
> You are correct. I was hoping more people would listen before this
> was revealed. Oh well.
>
> The reason, I believe, that both you and Joseph Pehrson heard this
> progression as non-repeating, is 12-tET conditioning. If you
> approximated these chords in 12-tET, and observed all the common
> tones, the progression would end up drifting a semitone every seven
> chords. So in a sense, your ear doesn't immediately recognize the
> chord progression, since it's trying to interpret it within a 12-tET
> grid. Although the pitch level is the same after every seven chords,
> your ear is a bit confused because the intervals have carried you to
> a place that "should" be different.
>
> If the chords were exact 7-limit JI tetrads, the chord progression
> would drift by the ratio of 2401:2400 every seven chords. This is
> less than 1 cent, but is represented by 100 cents in 12-tET.
>
> > Sounds close to 31tet, sort of.
>
> Now your familiarity with 31-tET may be kicking in -- 2401:2400 does
> vanish in 31-tET (as it does in 72-tET, the tuning this was actually
> in), so this chord progression would "work" in 31-tET. Also, 31-tET
> has the best approximations of 7-limit tetrads of any ET with fewer
> than 68 notes per octave -- but 72-tET is twice as good.

Paul, your analysis of Graham's progression is brilliant. Thanks.
I've noticed exactly this phenomenon you describe, along with John
and Joe P., and kind of shrugged it off because I really didn't
understand what was happening. Now you've enabled me to understand
*why* I heard it.

Thanks also for the acknowledgement of my contributions to this
sound-file, which you've repeated many times to various people.

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

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