reply to Haverstick: Equal temps are "easy"

[Haverstick:]
> Hey Monzo...look, I know you're a sharp fellow, and I enjoy your
> ideas. But, do you really think eq temps are "easier?" Boy, that
> opens up a whole canful of ideas about music and expression...

First off, here's the original statement I made [Monzo, TD 1415]:
> I'll grant that equal temperaments are easy to hear in
> melodic terms, but, aside from the ratios they imply well
> or badly, they don't have much significance from a
> _harmonic_ standpoint.

I posted to TD 1418 a quote from Ben Johnston which describes
how we prefer melodic intervals to be more-or-less equal. My
point was that powers of 2 (which is how we calculate equal-
tempered scales) only have _harmonic_ significance in that
they represent or approximate ratios with higher prime factors.

> ...I mean, I guarantee you that John Starrett's upcoming pieces
> on the forum CD are extraordinarily difficult to play, even though
> they're in 19 eq, and they're great music to boot. On the other
> hand, I've heard a BUNCH of music in pure tunings that didn't
> take much skill or imagination to play...

Agreed. The intonational vehicle one chooses certainly has a
determining influence on the music one creates, but I don't think
it has anything to do with quality -- that's a function of the musician's
talent. Difficulty of playing is determined more by instrument
construction than by anything else -- if your axe is set up to give
you perfect ratios or perfect 12-eq steps, that's basically what
you'll get (excluding variations caused by bending, lipping,
understanding, research, etc.)

>...If you mean that understanding pure tunings is on a higher
> level of some sort, as opposed to the "simpler" eq temps, maybe...

The Johnston article describes four different types of scalar
order, and each one is more complex to understand than the last.
The mechanism for comparing equal intervals is #3, and that for
JI is #4.

> There is surely a depth in the exploration of the harmonic
> series that approaches infinity;...

This is _EXACTLY_ the point I've been making about Schoenberg.
He stuck with 12-eq because JI opened up a world of possibilities
that he felt was just too vast to deal with on a practical level,
resulting in his compromise of accepting the use of all 12 tones
in the 12-eq scale as representing ratios thru a 13-limit.

> ...how intellectual knowledge translates into music and sound is a
whole
> different ballgame, though. I'm not sure if my 34 tone eq temp guitar
is
> any "easier" to play than Rod Poole's 17 tone purely fretted axe. In
> fact, Rod told me that even 22 notes was uncomfortable for him. So,
pure
> or tempered, "easy" is a tricky term to use regarding a choice of
> instruments.

As noted above, "easy" referred to a conceptual aspect of
intonation and not to any "real world" instrumental application.

> People can surely have various reasons why they choose a
> certain tuning system.

In the old days, they might cite the number of planets (ancient
Greeks) or sides on a cube (Zarlino)...

The reasons are as varied as people's personalities are
different, _as long as they are aware that there is a choice_!!!

> As has been pointed out many times, temperaments
> allow a musician to utilize a lot of chord changes,
> while often, pure tunings are more modally oriented...

I'm glad you qualified this with "often". I've heard this so many
times I think I'll puke the next time.

It's true that JI will bring out modal qualities well, as JI pieces
are usually "Monophonic" in Partch's sense. That is, all
pitches in the pieces have a tendency to centralize one
specific reference pitch as an overall "tonic", while ETs
give the same chord/ interval patterns over and over again
on all their degrees, making _exactly transposable_ chord
changes possible.

But as your qualification indicates, this is not always the case.
Much of the theoretical literature on JI is centuries (or even
millennia) old, and does not take into account the intonational
flexibility that we moderns have available to us. It is possible
today to write music in JI that has all of the transposable,
modulatable stuff that ETs have. In fact, it's always been
available to good a cappella singers.

> ... I like and respect any form of profound expression, chordal or
> scalar; I see the study and application of different tuning systems
> one more tool in my musical bag.

This is very similar to the viewpoint I'm coming around to regarding
the ability of Delta Blues musicians to play around with subtle
JI pitch inflections over a 12-eq foundation.

> I try to apply tunings much the same way I do modal ideas in my
> 12 tone playing; as Ivor Darreg often pointed out, each system
> has it's own mood or feel; this is absolutely correct...

Agreed. One single listen to the complete set of Easley Blackwood's
"Microtonal Etudes", one each in an ET from 13-eq to 24-eq,
demonstrates quickly that each ET has a definite mood.

My personal opinion is that this is due at least in part to the
closeness
with which each of these various ETs approximates ratios of various
prime factors -- in keeping with my belief that each prime factor
has its own unique effect/ affect. Various ETs approximate different
prime factors well or badly (12-eq is good for 3, OK for 5, mediocre
for 7, terrible for 11. 24-eq, on the other hand, is great for 11).

> ... So, I will continue to study and apply new concepts of tuning
> in an effort to improve my art...

That's the most important thing.

> But, if I want to expand on Coltrane's "Giant Steps," I'll bet, first
> of all, that it is "harder" than snot to play,...

I've learned it -- it *is* harder than snot to play.

> ... and is much better suited to an equal temp (such as 19,
> where I have adapted it), than it is to a purely tuned instrument
> ...Hstick

"Purely" here certainly means "Just".

I posted this a few weeks ago [Monzo, TD 1403:]
> ... jazz harmony as it developed thru be-bop and beyond
> could not have happened without accepting *a priori* the
> 12-eq scale. Charlie Parker specifically stated that he
> realized how to perform what he had been hearing in his
> head when he found that he could improvise melodies that
> were made up of the higher partials of the tune's chord
> changes...

But the fact that 12-eq (or any ET) is a _closed_ system,
where cycles of intervals return to their origin, was of
fundamental importance in jazz from the 1940s to the 1960s.
"Giant Steps" may not even be possible in a just system, because
it is based on a cyclical interval pattern which keeps returning
to its origin.

(BTW, I'd love to hear your 19-eq version -- it's one of my
favorite tunes).

Joseph L. Monzo
monz@juno.com

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