So three!

"Whether there's anything here to make my pocket pool more erotic and
satisfying remains to be seen."
In certain places, pocket pool means you are trying to re-adjust your
underwear.
"There might be potential with this fellow's ideas but his
presentation leaves a lot to be desired. If
he presents his ideas more coherently then more people will no doubt
take up his cause if they turn out to have meaning and value."
"I joined your group and looked at your file section which appears to
be filled with lots of data. So much data, in fact, that I was scared
away because it was not immediately evident what it all meant. So I
quit the group. Perhaps you can explain your ideas in more simple
terms so that the more
intellectually challenged musicians like myself can understand what
you intend to convey. I am not hostile but I only devote a limited
time to the tuning group and spend most of my spare time
with my own group. An abstract of your thesis or idea would not go
astray and would better serve your purposes."
Really guys, I wanted to put any debate on the subject on my own blog
against someone that is very willing to challenge it, rather than
just a passive observer. Oh well, I can just cut and paste and
transfer conversations if I get something I can use.
To repeat some of my disclaimers. This is all self taught and a
reinvention of the wheel. Some in this group will find slogging
through it a painful experience. Some will enjoy the reinvention of
the wheel because it suits their purposes for one reason or the other.
What I have come up with that I think is new, at least new in print,
is the "coefficient of consonance."
I use spread sheets to illustrate vibrations. An x indicates one
vibration. To illustrate two identical tones, use two identical rows
of x. When one x occurs at the exact same time as another, the x
will be one on top of the other on the spread sheet. Color the
bottom x red to indicate that it is invisible. That is to say, when
two vibrations occur at the exact same time, you will only be able to
hear one of them.
So there is a proportion or percentage of x that are invisible and
visible. At unison, half the x are invisible. At 2/1 one third of
the x are invisible. At 3/2 one out of every five x are invisible,
and so on and so forth.
When you are making this calculation for more than two tones at the
same time you are going to run into the problem that several x occur
at the same time. For instance, at the point of resolution of a
triad, three x will be lined up vertically. The bottom two will be
colored red and considered invisible. You can't define the bottom
red x as being twice invisible in relation to the black and the red x
above it. So if you want to calculate consonance, and you don't want
to manually count each red and black x, you have to add back in the
invisible red x that has been counted invisible twice.
This is where Bayesian probability comes into play. You may recall
from freshman year that it is taught in conjunction with Venn
diagrams. It uses circles and the capital U to indicate "union," and
an upside-down U to indicate intersection. You might also find the
formulas under the term "set theory." These are the formulas that
are used to create my spread sheets.
This is a superior method for representing consonance. You are
probably accustomed to seeing consonance represented by sine waves
starting and converging on a point of resolution. Any further
analysis than that between the points of resolution is fruitless. It
is a repeating pattern. The same can be said for my method. The
clear implication is that the point of resolution and how quickly you
arrive at it determines consonance. This is completely false for
anything more than an interval.
Take three tones. A B C. There are points of resolution between A &
B, B & C, C & A, and A & B & C. Consonance can be attributed to all
the points of resolution, not just A & B & C.
I do make generalizations about consonance. There are always
exceptions. If you study my results carefully, you will find that it
is remarkably difficult to generalize about consonance at all. The
location of the combined point of resolution, or the point of
resolution of all the tones taken together, happens to be totally
useless in determining and measuring the consonance of a chord. I've
seen supplements to college texts that use purely sine waves and
points of resolution to teach consonance. They sell for good money!
Granted that I have such difficulty making generalizations about
consonance, there can't be a corresponding definition of consonance
that does not conflict with my definition. You simply have to do the
calculations to understand consonance. [That is to say if you are
using math rather than your ear, as has been pointed out to me.]
To the best of my knowledge, no one has ever tried to prove that one
chord is more consonant than another. I ranked about every chord
that I find useful in terms of consonance.
So there!

> To the best of my knowledge, no one has ever tried to prove that one
> chord is more consonant than another.

Well then, you're way out of touch. But I'd still like to look
at your spreadsheet. Did I miss the link?

-Carl

I like you when you're a little mad.

Pocket Pool: Well, duh.

The serious point that I was trying to make is that music is erotics, not economics.

No legs Morgan rolls in on his little cart and looks up at you, pleadingly.

With all the qualifiers, there's much to agree with.

If I had more features with this email system, I'd bold certain things.

Consider these sentences "quoted for agreement":

> If you study my results carefully, you will find that it
> is remarkably difficult to generalize about consonance at all.

> [That is to say if you are
> using math rather than your ear, as has been pointed out to me.]

> I ranked about every chord
> that I find useful in terms of consonance.

This reminds me of a joke that Matt Darriau, a former roommate used to tell.

See if you can get the connection.

He said he'd been hanging with some old jazz musician, who insisted that he practice his scales in "all eight keys".

I find "all eight keys" and the idea that there are useful and non-useful chords hilarious. There are an infinite number of chords. There are an infinite number of chord voicings. There are a supergooglymegaplexalogicallastronomical starry starry number of combinations of chords going from one to another.

The hand in motion, groping the dark confines of the pocket, is wiser than the eye that searches the spreadsheet in vain.

It *is* often the case that chord X is obviously more dissonant than chord Y. Simple comparisons are possible. Subtle shadings are possible. Rankings are pointless.

From the musical point of view, is the sun going down, or is the horizon going up?

On Oct 30, 2008, at 5:06 PM, bjosephmex wrote:

> There are always
> exceptions. If you study my results carefully, you will find that it
> is remarkably difficult to generalize about consonance at all. The
> location of the combined point of resolution, or the point of
> resolution of all the tones taken together, happens to be totally
> useless in determining and measuring the consonance of a chord. I've
> seen supplements to college texts that use purely sine waves and
> points of resolution to teach consonance. They sell for good money!
> Granted that I have such difficulty making generalizations about
> consonance, there can't be a corresponding definition of consonance
> that does not conflict with my definition. You simply have to do the
> calculations to understand consonance. [That is to say if you are
> using math rather than your ear, as has been pointed out to me.]
> To the best of my knowledge, no one has ever tried to prove that one
> chord is more consonant than another. I ranked about every chord
> that I find useful in terms of consonance.
> So there!

I've noted that some people go to great lengths in these matters. It's
not for everyone.

Actually, you will find my approach useful if you have an intention to
not use a single dissonant interval. All my chords are consonant. Not
everyone's cup of tea, but my idea of useful.

I'm extremely committed to the octave, and not so much the 5th, which I
also use. Otherwise, my approach to music is extremely conventional.
I follow the path that consonance leads.

CoefficientOfConsonance@yahoogroups.com
--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > To the best of my knowledge, no one has ever tried to prove that
one
> > chord is more consonant than another.
>
> Well then, you're way out of touch. But I'd still like to look
> at your spreadsheet. Did I miss the link?
>
> -Carl
>

--- In tuning@yahoogroups.com, "bjosephmex" <bjosephmex@...> wrote:
>
> CoefficientOfConsonance@yahoogroups.com

So, uh, that's an e-mail address. I think you meant

/CoefficientOfConsonance

which is available only to members.

So let's go back to the beginning, bjosephmex. Here's one
way to introduce one's self on a mailing list:

"Hi, my name is _______ (<-- your real name goes here).
I'm interested in quantifying consonance. I found this
group by _____________ (how you found us) and thought
maybe people here might be interested in theories of
consonance too. Here's a spreadsheet showing my work:

http://www.xxxxxxxx.com/myspreadsheet.xls

Here's how to read it: The x-axis is ............... etc.

What do people think?

Sincerely,

bjosephmex"

Here's how you introduced yourself:

"Hi, I've developed a theory of consonance that is
completely unique in all the world, while, mysteriously
being a reinvention of the wheel at the same time. I've
gone ahead and created a members-only mailing list devoted
to my theories, for the benefit of the throngs of people
who have demonstrated interest in it. So come over and
check it out -- I'm not interested in contributing here."

See the difference?

-Carl