Re: Is music theory REALLY so mathematical?


"LJS" <ljschenck@xxxxxxxxx> wrote in message
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On Jul 6, 11:43 pm, "Jon Slaughter" <Jon_Slaugh...@xxxxxxxxxxx> wrote:
"Ludwig77" <gregjg...@xxxxxxxxx> wrote in message

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I often hear people describing music theory as being mathematical,
however I see this as a misassociation.

The presence of numbers in music theory, doesn't make it any more
mathematical than a telephone number.

I know that Pythagorus applied a lot of mathematics in studying
overtones and harmonics and that the physics of string vibrations and
frequencies is VERY mathematical, but am I correct to say that music
theory in and of itself is NOT mathematical?

Sure it uses numbers as labels for chords and notes, but it also uses
letters to label them, YET we don't misassociate it with language
studies.

Furthermore, music theory does NOT even use a single mathematical
operator (multiplication, division, addition or subtraction).

Comments and thoughts?

Greg's Music Theory:
www.gregjonesmusic.com/intro.htm

Music theory is a descriptive language and not really a mathematical or
scientific theory. Its equivilent to english grammar as it is a
methodology
of describing something. But like just about everything else one can
apply
mathematics to it. Mathematics is more about logic, analysis, and
understand
rather than numbers. It just so happens that mathematics applies very
easy
to numbers and one can make a lot of progress when using numbers. This is
why so many things are first converted to numbers when one wants to try
to
undrestand it "mathematically". Its not necessary that just cause it has
numbers that its math but numbers are the most natural setting to use
math.
(and you can call them by some other name or use different symbols as
whats
important is the abstract relationship)

But when people say things like "Music theory is to mathematical" what
they
are really saying is that music theory is useless or to complicated to be
of
use. Most people do not like math or understand it and hence they are
making
an obvious equivilence that really isn't true.

First, Music theory, like I said, isn't so much a theory as it is a
descriptive language. Its used so two people can easily communicate
things
about music. This type of thinking happens in all subject matter who's
ultimate goal is to understand(usually because it requires people to work
together to accomplish something greater than any one person could do by
themselfs).

When people say they don't care about music theory they are simply saying
they don't care about communicating musical ideas in distinct and
precise(relatively) terms. Its really a cop out when people do this as
essentially they are saying thay are to lazy to learn it and don't think
its
useful(which it might not be for them).

Another way to think of music theory is ideas that someone has thought of
are codified in some language for communication. i.e., the terms and
concepts, in an abstract sense, are something that people come up with
naturally as they become better at understanding music. e.g., a chord is
something just about anyone will figure out and so giving it a name helps
people communicate about that concept.

In any case, math(and here I do not mean meta math such as analysis and
logic) can be applied to music with varying degrees of success but most
people take it way to far. For example, there are 12 musical notes in
western music and because of this one would naturally make the
relationship
between the musical alphabet and Z_12 which is a group. A group is like a
abstract version of the natural numbers. Now Z_12 has been extensively
analyzed and has many properties and one might then try to see how these
equivilent properties play out "musically". It may or may not make any
musical sense though but I suppose that is what the people doing this are
trying to determine. Sometimes it does help and farther make sense of
music
but many times it doesn't.

My main point is that anything becomes mathematical when one truely wants
to
understand it on an intellectual level. That is what math is about.
Great
musicians are either somehow channeling the music they create or they are
great mathematicians(although they might not even be able to add well).
Chances are its a combination of both. Any time thinking involved it is
"mathematics"(although maybe its better called logic). The more you think
about something usually the more insight you get into it and understand
it
better.

Now things can be complex for only two reasons. Either you do not
understand
the popularized descriptive language or you do not understand the
intellectual concepts involved. Almost all of music theory has very
simple
concepts(chords, scales, modes, etc...) but the terminology is somewhat
complex(secondary dominants, chromatic mediant relationship, neapolitian,
etc...). In reality these are are not complex but just tend to be
overwhelming to most people because they don't have the time or interest
to
understand them. This is also true of mathematics. Almost everyone
understand mathematics up to the graduate level in some intuitive sense.
The
issues tend to be the formality involved and the huge amount of
terminology
and precise conceptual meanings one needs to be successful.

For example, integration and differentiation are very simple concepts
that
I'm sure everyone has some innate understanding of but most people don't
get
it when put in a mathematical context. Even advanced mathematics tends
to
be very simple concepts but applied in complex ways or just happen to
have a
lot of "overhead" that one has to spend years learning to get the total
picture.

In any case I gess its up for you to make your own mind up about it being
mathematical or not but hopefully I've provided something that will help
;)

Jon

Music theory is not descriptive. There are descriptive elements in an
analysis, but this is not the analysis. There is no analysis involved
in describing what is going on. Music theory is the taking of these
elements and putting them together in a meaningful way that shows how
or why things occur. This is the problem at a lot of levels of music
theory. There is a jazz magazine that is very interesting. I can't
remember the name at the moment. It comes out quarterly. (My copies
were all destroyed) In the articles there are some insights and some
good comments about the musician and the music. I was anxious to get
to the longer more detailed analysis of the pieces that is usually in
another section. As I started to read it it went on to the effect. "In
measure one there is a Dmin chord that goes to a G7-9 and then
proceeds to a Cmin on the upbeat of the last beat." and on and on like
this for pages. This is NOT analysis. In this case, it wasn't even
good preparation for analysis.



The majority of music theory that most people talk about(the 90% of
"musicians") is a descriptive theory. Learning how to name chords,
intervals, progressions, what the function, etc is descriptive and is the
sole purpose of communication(at this stage). Also analysis is not seperate
from description but in this cause the purpose is to learn to describe
things rather than analyze in any real sense.

Sure not all music is descriptice but the majority of music theory that
anyone encounters is about description. Analysis usually involves some
higher purpose than solely to communicate which is what most musicians learn
from music theory. Again, the two are not entirely distinct but the majority
of it is descriptive. Things like schenkerian analysis are of course more
heavy in the anlysis but obviously have to have a descriptive basis(as
everything does).

The difference between the word analysis when used in a mathematical
sense(which is what the OP was asking) is that math's analysis is about
deductive logic and follows very precise analytical thinking. This doesn't
happen in music because music isn't based in logic and its "theory"(or the
part of analysis that it has) is based on common practice. That kinda
analysis doesn't cut it in math(although all intellectual pursuits are
subject to common practice when it involves very large number of people and
time frames).

For "proof" all you need to do is take a random selection of "music theory
books" and look through the chapters and compare how much analysis is really
involved to how much is about description.

Also, When most people talk about music theory they are talking about the
descriptive part... doesn't really matter if its correct or not cause thats
what they do.

I'll give you a recent example. I went to a guitar workshop and the last day
some guy came up to me(another "student") and asked me a few questions and
said he didn't understand what one of the "instructors" was talking about.
He was like "I don't know what dominant means or what the V chord means" and
I don't know what a mode is, etc.

Knowing those terms is not analysis and the reason he didn't know them is
because he didn't learn the terminology. But supposedly the guy is a good
finger picker(another guy said this about him) and he does innately
understand the stuff. Just like you innately understand integration and
differentiation. You most likely do not understand the terminology such as
a neighborhood, refinement, an extrema, etc. You might have ideas about
these terms though because many of them are related to what we use
commonly(and its no coincidence). Of course terms like Darboux integeral
just have to be memorized because there is nothing about the term that is
commonly used outside of science.

The point I'm trying to make is that the majority of what people(in my
experience) call music theory is the descriptive part(sure there is some
analysis involved but its focus is on learning to describe). They believe
it is very mathematical and usually do not learn it well. My original point
is that part of "music theory" is not mathematical in an analysis
sense(although math also is very descriptive as just about any
intellectually advanced subject will be). It might be the case there are
"fringe" things in music theory that are more about analysis I think most
people(maybe 99%) do not encounter it.


If you name the chords, you have description. If you then put them
into Functional Notation, then you have the lowest form of analysis.
You then take the Functional analysis and relate the key areas in a
meaningful way and show that the composer has used them here and here
to create a certain feeling to go along with the text, or that he
develops this in various ways that relates to a certain pattern and
this pattern creates tension or something that goes along with the
form, or that this was done because of the instruments available at
the time or anything that is not apparent by just looking at the score
or that needs further explination other than a pure description, THEN
you are getting into the theory of music. When you take maybe a dozen
examples of a composer's works and show how he is exploring a certain
idea and how it grows relative to his earlier works and talk about the
results of his efforts or how this is different from his peers that do
it this way, then you are getting into the music theory.


Yes, but since analysis and description always overlap its more descriptive
if its less analysis. If you write out the functional notation of some
progression there is very little analysis involved(in general) and you are
just describing the progression. Now determing the function of the chord in
the progression might involve extremely "analytic" techniques its not
exactly the same as mathematical analysis. The reason is in the this case
your ultimate goal is description but in math the ultimate goal is analysis.

Ok, I'll put it this way,

Mathematical analysis uses descriptive language for the purposes of analysis
and understand.

Musical analysis uses analysis for the purpose of describing.


(Although the converse happens in both too, I'm talking about the main
aspect)

I think though I might be getting into some blurry things here. I think they
are very similar in the analysis aspects but it seems the "music theory"
doesn't seem as focused on it as mathematics is. (I'm talking about in
general too)

You can say that this too is a higher level of description, but there
is a difference. Description is not music theory. An analysis may have
descriptive elements, but music theory is relating these events into
something that has reason and purpose. Description is only the 'grunt'
work. (that's why professors have their assistants and students do
this for them lol)


Well, I have to disagree with the grunt work stuff. Description is
fundamental to all forms of higher intellectual matters. Say you want to
paint something. Do you need description? No. But to do math, it is
essential. There are people that can do certain things in there head without
any descriptive language(well, supposedly). But there is no person alive
that, say, can compute an integeral without using descriptive languages...
its in the fabric of math. You can't know what an integeral is without
someone having describe it to you. (of course we all do know those things
innately just like we all understand colors in paintings... but math is much
more involved and is exact unlike painting or music. You can't be half
right in math.

I think the issue here is that there is no fine line between description and
analysis and almost always there are different levels of each working
together. I'm trying to give some answer though that can be used ;) I do
think that majority of "music theory" that most people understand to be
music theory is really descriptive in nature(again, in general).

This is true for all sciences too but, say, with math, its about 50%-50% at
the start. Ok, there is the issue that we all spend many years learning math
by immitation in grade school and there is very little analysis going on
there. So it might actually be very similar to music theory in this respect
except the time scales for learning it are vastly different(most people
learn "music theory" in a semester or year while most people "learn" math
for several years).

To give a final example of what I mean, When you talking about a chord, for
example, such as a G7#5+9 and say something like that to most "musicians",
if they are not jazzers then many will not understand it. They think its
some advanced thing that is beyond them and to mathematical. My point here
is that such things involve no math or analysis(in the general sense).

Of course my idea of "musicians" could be wrong and biasing my point.

Jon


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