Yahoo Tuning Groups Ultimate Backup harmonic_entropy If you could only read one book . . .

--- In harmonic_entropy@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
> _The Science of Musical Sound_ by John R. Pierce, Freeman, 1992 edition.
> Pierce _used_ to subscribe to the Helmoltz/Plomp/Sethares school, but he
> describes how this view *fell apart*, quite literally . . . also, all basic
> psychoacoustics and acoustics is covered . . . for many, all you could ever
> need . . . in a small, 270-page book.

Paul,

I found a (1983, I think) copy of this book, published
by Scientific American Library at the library.

Read Chap 5 (Helmholtz and Harmony) and Chapter 6
(Rameau and Harmony).

Very interesting listening results from the geometrically
"stretched" musical pieces.

Certainly implies that (arithmetic) harmonicity
is implicit in the process of "appreciating"
coincidences of partials, among other aspects
of the musical piece.

Copied around 100 pages of "On the Sensation of Tone",
as well. Pretty amazing how many creative folks have
committed so much *energy* and *time* to these subjects,
and actual implimentations of unique instruments,
throughout periods in history. Quite amazing and
humbling .... :)

J Gill

🔗Paul H. Erlich <PERLICH@...>

nice to hear from you, jeremy. i think kraig was trying to get your
attention recently, i think on metatuning.

did you mean '(approximate) harmonicity' rather than '(arithmetic)
harmonicity' below? if the latter, what do you mean by it? the arithmetic
progression of the frequencies in the harmonic series? that would make
sense, but unfortunately you have to be careful around tuning folks --
'arithmetic', as opposed to 'harmonic', divisions of intervals historically
refer to the arithmetic division of a string, which result in a
*subharmonic*, rather than a *harmonic*, series.

p.s. isn't it remarkable the extent to which this harmonicity requirement is
'malleable'? it doesn't 'break' until the octave is stretched by 10% or so!

-----Original Message-----
From: unidala [mailto:JGill99@...]
Sent: Friday, March 01, 2002 4:09 AM
To: harmonic_entropy@yahoogroups.com
Subject: [harmonic_entropy] Re: If you could only read one book . . .

--- In harmonic_entropy@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
> _The Science of Musical Sound_ by John R. Pierce, Freeman, 1992 edition.
> Pierce _used_ to subscribe to the Helmoltz/Plomp/Sethares school, but he
> describes how this view *fell apart*, quite literally . . . also, all
basic
> psychoacoustics and acoustics is covered . . . for many, all you could
ever
> need . . . in a small, 270-page book.

Paul,

I found a (1983, I think) copy of this book, published
by Scientific American Library at the library.

Read Chap 5 (Helmholtz and Harmony) and Chapter 6
(Rameau and Harmony).

Very interesting listening results from the geometrically
"stretched" musical pieces.

Certainly implies that (arithmetic) harmonicity
is implicit in the process of "appreciating"
coincidences of partials, among other aspects
of the musical piece.

J Gill

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🔗unidala <JGill99@...>

--- In harmonic_entropy@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
> nice to hear from you, jeremy. i think kraig was trying to get your
> attention recently, i think on metatuning.

JG: Found it, thank you.

> did you mean '(approximate) harmonicity' rather than '(arithmetic)
> harmonicity' below? if the latter, what do you mean by it?

JG: I just meant harmonic multiples as integer multiples of a fundamental (hence ocuuring at "arithmetically", as opposed to "geometrically" positions on the number line).

the arithmetic
> progression of the frequencies in the harmonic series?

JG: Yes

that would make
> sense, but unfortunately you have to be careful around tuning folks --
> 'arithmetic', as opposed to 'harmonic', divisions of intervals historically
> refer to the arithmetic division of a string, which result in a
> *subharmonic*, rather than a *harmonic*, series.

JG: Thanks for the tip.

> p.s. isn't it remarkable the extent to which this harmonicity requirement is
> 'malleable'? it doesn't 'break' until the octave is stretched by 10% or so!

JG: If that was in the text I read, I missed it. In fact,
I don't recall the author specifying the percentage of
"geometric stretching" that did occur in those experiments
(perhaps I missed it?).

So you are saying that such "stretching" can approach around
10% *without* much loss of coherence on the part of the
perceptions of the listeners. That *is* amazing, and seems
rather curious (as this amounts to almost a "whole-step"
of such stretching). I would think that things would get
confusing to the listener (in terms of the perception of
harmonic - integer multiple - relationships) with a lot
less stretching that that! What does that say to you about
the nature of our aural perception? Any thoughts?

J Gill

> -----Original Message-----
> From: unidala [mailto:JGill99@i...]
> Sent: Friday, March 01, 2002 4:09 AM
> To: harmonic_entropy@y...
> Subject: [harmonic_entropy] Re: If you could only read one book . . .
>
>
> --- In harmonic_entropy@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
> > _The Science of Musical Sound_ by John R. Pierce, Freeman, 1992 edition.
> > Pierce _used_ to subscribe to the Helmoltz/Plomp/Sethares school, but he
> > describes how this view *fell apart*, quite literally . . . also, all
> basic
> > psychoacoustics and acoustics is covered . . . for many, all you could
> ever
> > need . . . in a small, 270-page book.
>
> Paul,
>
> I found a (1983, I think) copy of this book, published
> by Scientific American Library at the library.
>
> Read Chap 5 (Helmholtz and Harmony) and Chapter 6
> (Rameau and Harmony).
>
> Very interesting listening results from the geometrically
> "stretched" musical pieces.
>
> Certainly implies that (arithmetic) harmonicity
> is implicit in the process of "appreciating"
> coincidences of partials, among other aspects
> of the musical piece.
>
> Copied around 100 pages of "On the Sensation of Tone",
> as well. Pretty amazing how many creative folks have
> committed so much *energy* and *time* to these subjects,
> and actual implimentations of unique instruments,
> throughout periods in history. Quite amazing and
> humbling .... :)
>
>
> J Gill
>
>
>
>
>
> To unsubscribe from this group, send an email to:
> harmonic_entropy-unsubscribe@e...
>
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

🔗Paul H. Erlich <PERLICH@...>

>JG: If that was in the text I read, I missed it. In fact,
>I don't recall the author specifying the percentage of
>"geometric stretching" that did occur in those experiments
>(perhaps I missed it?).

check those two chapters in pierce again.

>So you are saying that such "stretching" can approach around
>10% *without* much loss of coherence on the part of the
>perceptions of the listeners.

right, as long as the partials still 'line up'. they do because what i'm
talking about here is stretching the *tuning* and exactly concomitantly
stretching the *partials*. so the 'coincidences' are exactly the same as
they were before.

>That *is* amazing, and seems
>rather curious (as this amounts to almost a "whole-step"
>of such stretching).

i meant 10% of an octave -- more like a half step. sethares demonstrates
this phenomenon on the cd that comes with his book . . .

>I would think that things would get
>confusing to the listener (in terms of the perception of
harmonic - integer multiple - relationships) with a lot
>less stretching that that! What does that say to you about
>the nature of our aural perception? Any thoughts?

sure -- with small stretches like this, the virtual pitch certainty for each
complex tone is not greatly disturbed -- the choice of a 'best fit harmonic
series' is still relatively unambiguous. each complex tone therefore
maintains its separate identity. meanwhile, the partials are still as
'coincident' as they were before, so there's no dissonance added due to
clashing partials / beating or roughness.

when the stretching gets too large, the brain no longer can determine how to
fit the partials into a harmonic series and determing a virtual pitch. so
the timbre falls apart into unconnected sine waves. one can no longer follow
melodies, or individual voices at all, in a harmonic progression. the many
isolated partials do not group together into a small number of perceived
pitches.

make sense? read that pierce bit carefully again.

nice to be talking to you again,
paul

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