"Differential Coherence" in 1/1

Hello to all and thanks for the help on my last question on the
strobe tuner...I'll let you know when I finally decide.

I have some questions on the Jacques Dudon article in the latest
edition of 1/1, if anyone else here reads it. I get the jist of the
article but am hung up on a couple of things. Specifically: in the
first collum of page 6, he uses the term "2 (to the nth power)" .
This is written properly as a mathematical power and not in text as I
have it here. Its use seems redundant here. Is it just for octaveing
the frequency into the given set?
Also, I'm having a hard time reading Figure 2. Both the Y axis and
the vertical arcs are labeled as difference tones. ??
Also in general, there seems to be some looseness in terminology, an
inconsistancy of terms, i guess. Do you agree? Maybe it's just a
little past me (as a lot of this is, still)
Hopefully someone can help, I've been getting 1/1 for about 4 issues
now and this is the first technical article that I've really got and
I'm pretty excited abou it and want to understand it all.
Peace,
Chester

P.s. If anyone is intersted, I have the issue of Experimental Musical
instruments with Dudon's article on the photosonic disc instrument as
descibed in this aricle, and would be happy to photocopy it for
anyone interested.

c
c
c
cc
c
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Ok, Maybe I should look before I leap, or something like that...I
didn't realize that you were a part of this group, Jacques, before I
wrote my message. Now I feel a little stupid...well, I suppose that
you are probably the best equipped to handle my questions, so any
help would be greatly appreciated. I also have a question about your
discussion of distortion and maximal opacity in the discs. Please
take my comment on "inconsistancy of terms" with the understanding
that I am very much a novice, at best, in understanding all the terms
and conventions in JI, and I'm probably just not following things.
Peace,
Chester
P.s. I just got "Gravikords, Whirlies and Pyrophones" recently, and
just love your track on the Aquavina. Some of the most engaging yet
peaceful music I know.
--- In tuning@yahoogroups.com, "coitmusic" <cwinowiecki@h...> wrote:
> Hello to all and thanks for the help on my last question on the
> strobe tuner...I'll let you know when I finally decide.
>
> I have some questions on the Jacques Dudon article in the latest
> edition of 1/1, if anyone else here reads it. I get the jist of the
> article but am hung up on a couple of things. Specifically: in the
> first collum of page 6, he uses the term "2 (to the nth power)" .
> This is written properly as a mathematical power and not in text as
I
> have it here. Its use seems redundant here. Is it just for
octaveing
> the frequency into the given set?
> Also, I'm having a hard time reading Figure 2. Both the Y axis and
> the vertical arcs are labeled as difference tones. ??
> Also in general, there seems to be some looseness in terminology,
an
> inconsistancy of terms, i guess. Do you agree? Maybe it's just a
> little past me (as a lot of this is, still)
> Hopefully someone can help, I've been getting 1/1 for about 4
issues
> now and this is the first technical article that I've really got
and
> I'm pretty excited abou it and want to understand it all.
> Peace,
> Chester
>
> P.s. If anyone is intersted, I have the issue of Experimental
Musical
> instruments with Dudon's article on the photosonic disc instrument
as
> descibed in this aricle, and would be happy to photocopy it for
> anyone interested.
>
>
>
> c
> c
> c
> cc
> c
> c

On the 18th of april Chester (coitmusic) wrote :

> I have some questions on the Jacques Dudon article in the latest
> edition of 1/1, if anyone else here reads it. I get the jist of the
> article but am hung up on a couple of things. Specifically: in the
> first collum of page 6, he uses the term "2 (to the nth power)" .
> This is written properly as a mathematical power and not in text as I
> have it here. Its use seems redundant here. Is it just for octaveing
> the frequency into the given set?

May be I should copy this principle, for people who didn't read this article
and because it resumes the whole article :

"The principle (of differential coherence) can be explained as follows:
If f1 and f2 belong to a given set and we find that 2^n(f2 � f1) = f is a member of this set,
then the interval f1 : f2 is deemed to be �coherent.�

Yes, it it just for octaveing the frequency properly into the given set.
First-order differential tones are always lower than the generating tones, then usually only their
octaves can
be in unisson with the generating tones.
They would be in between the generating tones only for intervals larger than the octave, for which
first-order difference tones become less relevant.

> Also, I'm having a hard time reading Figure 2. Both the Y axis and
> the vertical arcs are labeled as difference tones. ??

Any point of the curves indicates, by projection on the X axis, the generating interval,
and by projection on the Y axis, the difference tone generated, regardless of its octave
position. Its tonality, if you prefer. You have to imagine that the real single curve would have
need
to pile up vertically 5 octaves. Here, each time the curve reaches the top of the figure, it starts

again at the bottom. In order to fit in a single page.

> P.s. I just got "Gravikords, Whirlies and Pyrophones" recently, and
> just love your track on the Aquavina. Some of the most engaging yet
> peaceful music I know.

Very simple 3-limit music actually. Thank you.

Jacques,
thanks so much for the reply....it was very helpful and I believe I
understand your article better now.
I have a few other questions, if I'm not being bothersome, and
hopefully, these will be helpful to others, otherwise we can take this
off the tunings list:

In your discussion of distortion, you speak of how you believe the
combination tone arises on your photosonic discs when there is a level
of distortion arising when the "maximal opacity" of the disc is
passed. How can there be a state greater than the "maximal opacity"?
Is there a blacker black?

When you descibe "correcting" a set for greatest coherence in all
orders of difference tones, are you proposing alternate tones that do
not replace, but are used occasionally in combination with some tones
and not others? I tried charting the set of your first example and
found (ovbiously, after the fact) that those corrections, made other
difference tones "incoherent."

thanks again for you kind reply,
Peace,
Chester

Friday 18 th coitmusic wrote :

> Jacques,
> thanks so much for the reply....it was very helpful and I believe I
> understand your article better now.
> I have a few other questions, if I'm not being bothersome, and
> hopefully, these will be helpful to others, otherwise we can take this
> off the tunings list:
> In your discussion of distortion, you speak of how you believe the
> combination tone arises on your photosonic discs when there is a level
> of distortion arising when the "maximal opacity" of the disc is
> passed. How can there be a state greater than the "maximal opacity"?
> Is there a blacker black?

There is not, that's why some distorsion arises, just like electric distorsion cuts
off the peaks of a signal passed certain amplitudes.
On a if we superimpose two waveforms having a maximum of 50% grey,
the resulting image will have some zones of 100% (=black) but no special distorsion.
The same thing with two waveforms having some black or even two 60% grey
will induce distorsion, as 200% or 120% will have to be printed only 100%.
This is my explanation of a certainly more complex phenomena, that provides
anyway in photosonic disks very smooth, natural difference tones.

> When you descibe "correcting" a set for greatest coherence in all
> orders of difference tones, are you proposing alternate tones that do
> not replace, but are used occasionally in combination with some tones
> and not others?

Everycase is different, I don't have fixed receipes and most of times
several types of arrangements are possible, depending on what you're looking for.
Sometimes you can find a single tone that is more coherent with all other tones,
sometimes in order to fix the coherence of one interval you need an optional tone,
sometimes this optional tone works better for several intervals and then it becomes
evident that the scale has a "double tone" here to play with.

> I tried charting the set of your first example and
> found (ovbiously, after the fact) that those corrections, made other
> difference tones "incoherent."

If you talk about the diatonic scale, it is not totally true with 81. When it replaces 80,
it is coherent with 54, 72, 90, 96, 108, and even 80 itself ; 91 is less performant but
still -c with 64, 96, 90, ; 63 is a little bit exotic I admit, but still -c with 48, 54, 60, 64,
72,
(and 81...)
This was just an exemple, but the diatonic genus has an enorm potential of -c scales
of about any harmonic limit.

--- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:

> "The principle (of differential coherence) can be explained as
follows:
> If f1 and f2 belong to a given set and we find that 2^n(f2 – f1)
= f is a member of this set,
> then the interval f1 : f2 is deemed to be "coherent."

That's a definition, not a principle. What is its purpose? What in the
world is all of this about?

Gene Ward Smith wrote :

> --- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:
>
> > "The principle (of differential coherence) can be explained as
> follows:
> > If f1 and f2 belong to a given set and we find that 2^n(f2 � f1)
> = f is a member of this set,
> > then the interval f1 : f2 is deemed to be "coherent."
>
> That's a definition, not a principle. What is its purpose? What in the
> world is all of this about?

It's a formal definition for a more general principle that is :
in a given tonal context (a scale, a chord, or even the thought of those),
when the difference tones of the intervals belong to this context,
this is a factor of musical harmony.
The purpose is essentially to open our listening to new qualities of sound
interactions. For example, differentially-coherent scales allow your listening
to focus on difference tones, of which generating tones can be perceived as
partials. An interval becomes a timbre, and a scale a collection of musical
timbres. A plurarity of levels of audition is available.
Also, while we generally think musical notes in a scale as single,
the application of differential coherence often reveals their multiple facets,
which in interaction with the other tones of the context, become melodic.
You can refine about any scale that way, with appropriate instruments.
My article in the last 1/1 journal of the Just Intonation Network explains all this.
But there is no need to talk more about it, you have to experience it - I gave
several examples on this list you can try for a start.

--- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:
> Gene Ward Smith wrote :
>
> > --- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:
> >
> > > "The principle (of differential coherence) can be explained as
> > follows:
> > > If f1 and f2 belong to a given set and we find that 2^n(f2 – f1)
> > = f is a member of this set,
> > > then the interval f1 : f2 is deemed to be "coherent."
> >
> > That's a definition, not a principle. What is its purpose? What in the
> > world is all of this about?
>
> It's a formal definition for a more general principle that is :
> in a given tonal context (a scale, a chord, or even the thought of
those),
> when the difference tones of the intervals belong to this context,
> this is a factor of musical harmony.

If you want to give a formal definition, I'd suggest calling the set
in question S, and saying if f1<f2 are elements of S, and if
for some integer n, 2^n (f2-f1) is an element of S, then the interval
f1:f2 is S-coherent.

Then you could define what a coherent scale is--for instance, is it
a set S of intervals 1<=s<2 such that 1:s is S-coherent?

> My article in the last 1/1 journal of the Just Intonation Network
explains all this.

That is still not available on-line. I think it would be useful to
explain it here, or over on tuning-math.

> But there is no need to talk more about it, you have to experience
it - I gave
> several examples on this list you can try for a start.

I want to understand what you are saying first.