Pumping comma

I have a question concerning the term "pump" as it applies to the "comma
drift."

What is the difference between the "comma pump" which, evidently, Paul
Erlich kindly illustrated for me and the "diesis pump?"

Am I to assume with the "diesis pump" the 1/1 doesn't "pump around" but
another pitch does??

And why is it called "pump?" This can't have any application to organ
tuning terminology, can it?? It seems to imply that rather than just
"drifting," a pitch is "forced."

Please inform... I'm "pumped up" now...

Joseph Pehrson

>What is the difference between the "comma pump" which, evidently, Paul
>Erlich kindly illustrated for me and the "diesis pump?"

The "diesis pump" is an example of a progression requiring enharmonic
equivalence, so, as I just discussed, it doesn't work in meantone or
Vicention's adaptive JI system. Specifically, a "diesis" (without further
qualifications) refers to the difference in JI between three major thirds
and an octave. Starting on Ab, going up a major third to C, another major
third to E, and another major third to G#, we find the diesis Ab:G# =
128:125 = 41 cents. To render this progression without the 41-cent shift, as
would be required for much of Schubert's music for example, one has to use
(on average) the 12-tET major third, either harmonically or as the
horizontal interval in an adaptive JI scheme. I'd be happy to go into more
detail and map this out if you wish.

>And why is it called "pump?"

I think it's because, every time you play the progression in JI with all
common tones observed, the overall pitch shifts by a comma or diesis. So
playing the progression over and over again shifts the pitch more and more,
even though nominally the notes keep returning to the same place. Sort of
like a bicycle pump where you keep pressing the lever, it keeps retuning to
the same place, yet the tire gets more and more full of air . . . ???

In TD 472.19 Joseph Pehrson <josephpehrson@compuserve.com> wrote:
>Subject: Pumping comma
>
>I have a question concerning the term "pump" as it applies to the "comma
>drift."
>
>What is the difference between the "comma pump" which, evidently, Paul
>Erlich kindly illustrated for me and the "diesis pump?"

"comma" and "diesis" are the small intervals by which everything is shifted
after going once around the sequence. The syntonic comma is 80:81 (21.5c).
There are actually two dieses, minor 125:128 (41.1c) and major 625:648
(62.6c).

>Am I to assume with the "diesis pump" the 1/1 doesn't "pump around" but
>another pitch does??

Everything moves, not just the 1/1, and they don't pump "around" but always
in the same direction for a given pump, either up or down.

>And why is it called "pump?" This can't have any application to organ
>tuning terminology, can it??

Nah!

>It seems to imply that rather than just
>"drifting," a pitch is "forced."

Yes indeed (assuming strict JI). It's just that the noun from the verb "to
pump" doesn't really work. i.e. "pumpedness". So we use "drift", despite
its modern association with aimlessness. Perhaps a mixture of metaphors but
it seems to work. In mechanical engineering one still drifts things with a
hammer. But maybe because of its cyclic nature a chord sequence that does
this seems more like a pump than a hammer. Each time around the cycle,
shifts everything by another comma (or diesis or whatever). I suppose we
could call it "shift" rather than "drift".

Diesis pumps don't occur in diatonic scales. Here's two:

,-> III V VIIb I# -. 4 "stacked" minor thirds
| |
`------------------'

,-> II IV# VIIb -. 3 "stacked" major thirds
| |
`----------------'

Diesis pumps are kind of obvious. There's even a discontinuity in the
spelling.

Regards,

-- Dave Keenan
http://dkeenan.com

Dave Keenan wrote,

> ,-> III V VIIb I# -. 4 "stacked" minor thirds
>| |
> `------------------'
>
> ,-> II IV# VIIb -. 3 "stacked" major thirds
>| |
> `----------------'

Actually, the accepted roman numeral terminology would read:

,-> III V bVII #I -. 4 "stacked" minor thirds
| |
`------------------'

,-> II #IV bVII -. 3 "stacked" major thirds
| |
`----------------'

An accidental _after_ the roman numeral has a different meaning -- it means
that the third is altered with respect to its expected diatonic position.