On Certainty vs Liberty

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> /tuning/topicId_31804.html#32134
>
> > Joseph, musicians give pitches an octave apart the same
> > name. OK, that isn't a TOTAL equivalence,
> > but what would you call it? How about
> > octave similarity?

JP Responds:

> Hi Paul...
> Well, of course... that's the whole notion of "pitch class"
> in "traditional" set theory, etc., etc.
> However, J. Gill seemed to want to make a bigger case for
> "octave equivalence" than really exists...
> at least it seemed that way to me.

JG: Joe, I would say (of the posts which I have made recently surrounding the existing impressions and assumptions regarding a perceptual "equivalence/similarity" of octave related pitches) that - rather than "making a case" *for* an "octave equivalence", I have attempted to explore every possible exception, uncertainty, and doubt (potentially indicated) surrounding the so often held and applied assumptions that "a sub-octave equates to an octave equates to a raised-octave, etc..."!

The purpose of asking these questions has been to explore the veracity of those assumptions. The reason for such exploration is that - if one is considering *basing* one's own thinking (about "aural perception", and the sometimes alleged mathematic-musical relationships between them) on a *basis* including such assumptions as "octave equivalence/similarity", then one has a legitimate interest in determining whether such assumptions are either "universally accepted", "accepted in certain limited cases only by certain persons", or "universally unaccepted"...

The inherent subjectivity of such "aural perceptions" [even relative to a single person - in various listening contexts, moods, and when armed with various sets of expectations as to the intended/desired resultant perception(s)] is problematic for those (ambitious, and perhaps foolhardy, souls) who endeavor to create mathematical viewpoints which they might posit (to the critical masses of reductionists in "white-coats" wearing "pocket-protectors") have merit (substantiated beyond the level of, "yeah, brother, I know what you mean, I can *feel* that Venus is in Uranus, too..., I can *feel* the the spiritual jetstream of mathematical *truth*" as Harmonic Convergence shield us like a hyper-cube from the glitches and core-dumps of our minds", etc.). :)

Now (while I am an electronic designer), I'm no "technocrat". This son of a philosopher (now you may be saying, "ah, that's where he gets his ultra-verbose tendencies") with only average abilities in math/science (if that) has managed to manipulate numbers (transfer functions and frequency responses) in ways which have pleased his own "aural mind" [and that of a few others, though there are no universal "solutions" to (the illusory) "problem" of "mapping pleasure" (for its eventual "mass-production" by "white-coats", of course, to be marketed by "little technocrats" wearing "pocket protectors", just like the "white-coated gods" they so admire)].

However, my (and perhaps "our") "aural mind(s)" are not amenable to "manipulation" for the purpose of suggesting, affirming, and thus retaining, the "sanctity" of *numbers* (whether it be for purposes of conceptual "tidiness", "convenience", or plain-old "intellectual vanity"). Musical "behaviorism" aside, we would all (I imagine, at least) prefer to think of the functioning of our "aural minds" as a "process" unique, unscripted, and (thus) *non-reducable* to equations by "white-coated gods" who aspire to "know the unknowable", who aspire to "package our dreams" shippable in cartons marked "Sony".

Let us, then, sing a song (in the "key" of our own choice) for those "misguided modernists" who would (so conveniently) slip our creativity, joy, and undefinable raptures into a "neat little box" (whether it be the ultra-sexy Archemedian solids which cause our souls to undulate with an impending "sense of deep meaning", or the more common Freudian shapes such as tubular and toroidal). And now, bretheren, ... Lattice pray ...

JP Continues:
> I think you summed the whole issue up in about five lines
> back aways when you said that
> the concept of "octave equivalence" was somewhat
> limited...

JG: We must admit (must not we?) that - if "octave equivalence" is *limited*, then so are all of our assumptions drawn therefrom, and are all of the conceptual "glass menageries" which we are tempted to so admire (as they stand so neatly on our shelves and bookcases)???

I believe that I could count the number of "theories" (which I, in my naive role as "student of the tuning lists", have seen), and which are *not* premised upon "octave equivalence" (however convenient that may be for the purposes of numerical analysis) on (less than) one hand...

For - if we are to find solace in "throwing our theories at a wall, to see if they stick", how are we to "know" whether it is an (objective, verifiable, repeatable, blah blah) "wall" to which they adhere, or simply, a self-erected edifice to our own "certainties".

Truly, a "spot of brandy", and the ear of a "sympathetic stranger", go along way towards allowing ourselves to convince ourselves that, indeed, we are the last in a long line of "great medieval thinkers"!

In allowing such edifications to live and breath within the confines of our subjective (but wanna-be objective) "knowledge claims", do we not risk becoming a "(petty)-tyrannical-majority" by choosing to overlook the "emporer's decided paucity of attire"?

Your friend and associate, J Gill

--- In tuning@y..., J Gill <JGill99@i...> wrote:

> to overlook the
> "emporer's decided paucity of attire"?

Unidala (wryly) points out that it should be:

"emperor's decided paucity of attire" :)

--- In tuning@y..., J Gill <JGill99@i...> wrote:

/tuning/topicId_32159.html#32159

>
> JP Responds:
>
> > Hi Paul...
> > Well, of course... that's the whole notion of "pitch class"
> > in "traditional" set theory, etc., etc.
> > However, J. Gill seemed to want to make a bigger case for
> > "octave equivalence" than really exists...
> > at least it seemed that way to me.
>
> JG: Joe, I would say (of the posts which I have made recently
surrounding
> the existing impressions and assumptions regarding a perceptual
> "equivalence/similarity" of octave related pitches) that - rather
than
> "making a case" *for* an "octave equivalence", I have attempted to
explore
> every possible exception, uncertainty, and doubt (potentially
indicated)
> surrounding the so often held and applied assumptions that "a sub-
octave
> equates to an octave equates to a raised-octave, etc..."!
>

***** Hello J. J.!

Actually, on the way back from the library where I have been doing my
postings, I realized that I had phrased this wrong.

You are trying to investigate the *assumptions* of octave
equivalence, and it's made a very good read.

I guess what I was infering is that you thought that "octave
equivalence" should really be a much *more pervasive* and influential
phenominon than it is in order for it to work overall in a "general"
case.

It seems to me you are really onto something here. Of course, as
Paul and others have stated, octaves are not really *equivalent* but
only "similar..."

Sure helps to set up scales, though... or otherwise we would need, I
believe, keyboards extending out into infinity! :)

By the way, the classical "White Coat Syndrome" is a true medical
condition. When a doctor goes in the room of a patient and is,
ostensibly, wearing a "white coat" the patient's blood pressure goes
up.

Best to avoid any such situations if possible...

Happy New Year.

Joe Pehrson

--- In tuning@y..., J Gill <JGill99@i...> wrote:

> JP Continues:
> > I think you summed the whole issue up in about five lines
> > back aways when you said that
> > the concept of "octave equivalence" was somewhat
> > limited...
>
> JG: We must admit (must not we?) that - if "octave equivalence"
is
> *limited*, then so are all of our assumptions drawn therefrom,
and are all
> of the conceptual "glass menageries" which we are tempted to
so admire (as
> they stand so neatly on our shelves and bookcases)???

This is not a big deal, Jeremy. You are free to remove the
assumption of octave equivalence (which is always taken to be
_limited_ in the way I indicated anyway) and get rid of it, either by
replacing it with a different equivalence relation or by not having
any equivalence relations at all. No big edifice is going to come
crashing down if you want to do that. But why have you seemingly
given up on pursuing those matters which pertain to your own
attempts to build your own theoretical edifice? It would seem
much more productive if we were to continue with _that_.

> I believe that I could count the number of "theories" (which I, in
my naive
> role as "student of the tuning lists", have seen), and which are
*not*
> premised upon "octave equivalence" (however convenient that
may be for the
> purposes of numerical analysis) on (less than) one hand...

This is simply false, Jeremy. I would say that, for example,
Gene's understanding of pitch relations via multilinear algebra,
etc., is not premised on "octave equivalence" in the slightest.

>
> For - if we are to find solace in "throwing our theories at a wall,
to see
> if they stick", how are we to "know" whether it is an (objective,
> verifiable, repeatable, blah blah) "wall" to which they adhere, or
simply,
> a self-erected edifice to our own "certainties".

You are free to choose your own standards of verification, etc. . . .
so let's get on with it!!