theory vs. reality

It is beginning to dawn on me just how theoretical most all of music
really is. Any time we have a scale, where notes are mathematically
altered from their real place in the harmonic series or the spiral of
5ths, to fit in the compass of an octave, this is NOT the true sound of
said notes...no, they are REALLY up there somewhere, beyond the range of
our hearing...thus, these scales are not real, they are mathematical
alterations of reality...perhaps we could say that we are sort of
"tempering" the harmonic series/spiral of 5ths. I find it fascinating
that this is the accepted way of doing things...actually, we have no
choice if we want any sort of scalar language at all. I also find it
fascinating that we were given these tools of music (harmonic series,
etc) but actually cannot hear very much of it at all...it's all based on
theories. If we really heard the pitches where they existed, music would
be a much different phenomenon..perhaps there are beings who can hear
way up in the series. Thus, it seems to me that a so called "just
intonated" scale is no more "real," in a fundamental sense, than an
"equal tempered" scale...both are only approximations of
reality...neither one is the "true" sound of the actual pitch.
I have also been messing around with my fretless guitar, and have
come up with a neat tuning of the 6 strings (from the bottom up):
1/1,5/4,3/2,7/4,35/32,.21/16. I have written a piece which involves
using the harmonics of the strings as melodic units...it will be on a
forthcoming CD. Of course, when I say 35/32, it is NOT the actual pitch
of the note...it is an approximation, and as such, it bugs me to call it
what it is not...I don't know what the answer is.
Another related point...just how high up have theorists gone with
the harmonic series? The 1000's...the 1,000,000's? I imagine the
interval between the 1,000,000th and the 1,000,001 harmonic is pretty
teensy...could we "bring it down" mathematically and use it in a scale?
It obviously is a real interval, if a bit teensy. What would music be
like if we had access to these sorts of intervallic units? Maybe we just
need more ear hairs...Hstick

In a message dated 01/24/1999 2:29:29 PM Eastern Standard Time,
stick@uswest.net writes:

> From: Neil Haverstick <stick@uswest.net>
> I also find it
> fascinating that we were given these tools of music (harmonic series,

> etc) but actually cannot hear very much of it at all...it's all based
on
> theories.

Except that harmonics on a string are very real. It's no problem finding
them,
even guitarists that are clueless about just intonation love 'em.

For example: Steve Howe's intro to Roundabout, Jaco's harmonics.
Not that these guys are clueless, I'm really thinking about basement
bands. :)

> If we really heard the pitches where they existed, music would
> be a much different phenomenon..perhaps there are beings who can hear

> way up in the series. Thus, it seems to me that a so called "just
> intonated" scale is no more "real," in a fundamental sense, than an
> "equal tempered" scale...both are only approximations of
> reality...neither one is the "true" sound of the actual pitch.

Maybe a scale like this:

1/1 9/8 5/4 11/8 3/2 13/8 7/4 2/1 would certainly be
real - it's all harmonics.

I remember a couple of years back I moved into my current
apt on the 8th floor of a 12 flr. building. If it's windy outside,
it's even worse around the building. I was in the parking lot
and the wind was howling through all the balcony railings like
a few hundred flutes playing the wildest music I've ever heard.
All harmonics series, I'm sure. Very beautiful & real too.

> I have also been messing around with my fretless guitar, and have

> come up with a neat tuning of the 6 strings (from the bottom up):
> 1/1,5/4,3/2,7/4,35/32,.21/16. I have written a piece which involves
> using the harmonics of the strings as melodic units...it will be on a

> forthcoming CD. Of course, when I say 35/32, it is NOT the actual
pitch
> of the note...it is an approximation, and as such, it bugs me to call
it
> what it is not...I don't know what the answer is.

Playing the 5th harmonic of the 7/4 string would give you 35/32.
Finding the note that way WOULD give you exactly that note.

And while we're at it, 21/16 is 3/2 above 7/4.

> Another related point...just how high up have theorists gone with

> the harmonic series? The 1000's...the 1,000,000's? I imagine the
> interval between the 1,000,000th and the 1,000,001 harmonic is pretty

> teensy...could we "bring it down" mathematically and use it in a
scale?
> It obviously is a real interval, if a bit teensy. What would music be

> like if we had access to these sorts of intervallic units? Maybe we
just
> need more ear hairs...Hstick

La Monte Young, Glen Branca, Horatiu Radulescu all have
made music that uses just the harmonic series (otonalities).
La Monte's sine tone installations climb up the series, I think
the highest prime he's used is the 283rd harmonic.

--
* D a v i d B e a r d s l e y
* xouoxno@virtulink.com
*
* J u x t a p o s i t i o n E z i n e
* M E L A v i r t u a l d r e a m house monitor
*
* http://www.virtulink.com/immp/lookhere.htm

> Any time we have a scale, where notes are mathematically
> altered from their real place in the harmonic series or the spiral of
> 5ths, to fit in the compass of an octave, this is NOT the true sound of
> said notes...

Perhaps that's what Ivor Darreg would have characterized as a perfectly
valid harmony-centric suggestion, but perhaps not as meaningful from a
melodic perspective. From a strictly melodic perspective, there's a
definite appeal to having all step sizes tempered to be the same. There is
appeal in them not being equal too, granted, but one might argue that that
calls attention to the intervals themselves, and can distract attention
from the musical statement of the melody itself.

> Any time we have a scale, where notes are mathematically
> altered from their real place in the harmonic series or the spiral of
> 5ths, to fit in the compass of an octave, this is NOT the true sound of
> said notes...

With due respect to Ivor Darreg and Gary Morrison, I think that Mr.
Haverstick is having a bit of reverie about the problem of distinguishing
between the real and what may be called the 'really real', the world of
platonic ideals.

While my own orientation is more constructivist, a Platonic orientation
towards musical intervals is attractive for many reasons. This view would
hold that our own world of musical intervals is but a reflection of a world
of ideal intervals. The ear and the cognitive apparatus are then
intermediate to these two worlds and our tolerance for approximations, i.e.
temperaments, is a central, not a peripheral, cognitive function.

But I think that Haverstick is missing the point of the Platonic
orientation, which is not to discount the sensual, physical world for its
approximateness, or 'alteration', but rather to enhance our understanding
of this. An ascending c to d with the frequency ratio of 9:8, for example,
does indeed relate to two steps up a chain of fifths with octave reduction
or to the interval between the 8th and 9th partials in a harmonic series as
well as to an infinite number of alternative descriptions, but these
'truths' are entirely compatible with one another and by no means detract
from the 'true sound of said' physical notes.