Revised thoughts: "One-string chord"

In my post #26519 I made some statements about overtone relationships which a reader named "Jon" emailed an inquiry to me about. In my post #26520 I included Jon's questions, and made some further statements regarding my original thoughts, in response to Jon's queries.

However, having given the points which Jon makes further thought in relation to the veracity of my original statements, I must here state that Jon has, rightly so, pointed out some conceptually flawed statements which I have erroneously made, and did even *reiterate* in my post #26520. I will here attempt to explain my thoughts in an accurate, rather than flawed context...

Below are Jon's valid and accurate dissensions:

<I don't get this: why do you say there is a key for every harmonic on such
an instrument? Having the fundamental be 1 Hz or 100 kHz doesn't change
any of this. Each *low* harmonic of 1 Hz will be represented quite well by
a degree of the 72-tet scale, but already in the 8th octave there will be
more than 72 partials to map onto notes, and you won't have enough.
Similar problem for harmonics of the 72-tet keys: in fact *none* of them,
except for harmonics of keys a whole number of octaves above 1 Hz, will
also be harmonics of 1 Hz. Consider the 1st overtone of the 15th key in
the lowest octave - which harmonic of 1 Hz does this represent? It falls
between 2 and 3 Hz.>

My statements regarding dividing the octave into greater and greater numbers of subdivisions of an *octave* approaching a "limit" where there would exist "an individual key" (keyboard key, not musical key) "for *each and every* possible harmonic", and "where, relative to the 1 Hz 'tonic', ALL of its natural harmonics are represented, and ALL of the harmonics of any of the keys also represent integer multiples of that 1 Hz fundamental" are (as Jon has pointed out), plain and simply, INCORRECT.

My reasoning that divsions of an octave into greater and greater sub-divisions by increasing the number of notes per octave in a scale results in *more* harmonics of the lower valued elements of such as set of tones being represented in higher valued elements of such a scale has some validity, as it appears (to me) that Jon acknowledges in his statement, "Each *low* harmonic of 1 Hz will be represented quite well by
a degree of the 72-tet scale...". However, I concur with his accurate critique of my assertion regarding any "limit" condition where these tendencies as I described them would approach universality.

Similarly, at the smaller end of things, while the 12-tone "Duodene" scale appears to represent a coherent and symmetrical patterned system within which the interactions of harmonic overtones define which "keys" (as keyboard locations, rather than musical key) may sound "con-" or "dis-"
"cordant" when sounded simultaneously, and this represents a system which may be found to be aesthetically satisfying in its characteristics, that a particular JI 12-tone scale does not represent the only, or the lowest numbered scale where such effects (although perhaps not possessing a similar symmetry) do also occur.

So, upon further reflections, spurred, in part, by Jon's valid criticisms, I would say that, while the concept of mathematical "limits" (existing as the number of notes subdividing an octave approaches large or small values) is not an accurate or productive concept to apply in relation to what (I think) remains a relevant (though not absolute) observation concerning the general "tendencies" or "trend" which seems to evolve in the comparison of the stated characteristics of scales having smaller and larger numbers of notes existing in that scale subdividing an octave.

The more that I learn, the more aware I become aware of how little I know about the world... While my style of communication (which evolves in an interest of stating my thoughts clearly) tends toward the verbose, I find that its quantity and intended scope leads to imperfections and inaccuracies at times, and while I strive to get things right the first time, I'm just a curious guy who is trying to communicate my present thoughts (which allways, in retrospect, appear imperfect, incomplete, and sometimes embarassing!)

I thank Jon for taking the time to point out to me the errors in my thinking, and appreciate, and want to learn from, such dialogue with others. While the contents of these archives are not absolute, its serves no purpose for there to exist information that is just plain wrong, so please *do* let me know if and when you think that I have unintentionally crossed that line...

Respectfully, J Gill

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

/tuning/topicId_26533.html#26533

>
> My statements regarding dividing the octave into greater and
greater numbers of subdivisions of an *octave* approaching a "limit"
where there would exist "an individual key" (keyboard key, not
musical key) "for *each and every* possible harmonic", and "where,
relative to the 1 Hz 'tonic',
> ALL of its natural harmonics are represented, and ALL of the
harmonics of any of the keys also represent integer multiples of
that 1 Hz fundamental" are (as Jon has pointed out), plain and
simply, INCORRECT.
>

I mean no disrespect, but I find a little bit of humor in this...
maybe we should try a Salvador Dali "limp watch" type keyboard, where
the physical keys keep getting smaller and smaller until they
eventually melt and drip off the upper end!

_________ ______ ______
Joseph Pehrson

> From: <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, July 30, 2001 5:38 PM
> Subject: [tuning] Re: Revised thoughts: "One-string chord"
>
>
> I mean no disrespect, but I find a little bit of humor in this...
> maybe we should try a Salvador Dali "limp watch" type keyboard, where
> the physical keys keep getting smaller and smaller until they
> eventually melt and drip off the upper end!

Disrespect?! Heck, Joe, that's a *fantastic* idea! (literally!)

Sounds like a great new idea for a JustMusic window!

love / peace / harmony ...

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

_________________________________________________________
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Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: <jpehrson@r...>
> > To: <tuning@y...>
> > Sent: Monday, July 30, 2001 5:38 PM
> > Subject: [tuning] Re: Revised thoughts: "One-string chord"
> >
> >
> > I mean no disrespect, but I find a little bit of humor in this...
> > maybe we should try a Salvador Dali "limp watch" type keyboard,
where
> > the physical keys keep getting smaller and smaller until they
> > eventually melt and drip off the upper end!
>
>
> Disrespect?! Heck, Joe, that's a *fantastic* idea! (literally!)
>
> Sounds like a great new idea for a JustMusic window!

If you folks should need any "pinheads" with intellects small enough
to reach those tiny, tiny keys, my services are available...

Thoroughly (self)embarrased by my faux pas, J Gill