(note: regarding use of terms "note" and "tone".
They are synonyms, but with a very slight distinction
i.e tone is aural
note is written on paper
or played on a keyboard.
The two are used nearly
interchangeably in common usage.)

Before I continue on
into the very important subject of
"voice leading",
I think I had best stop
for just a moment
and discuss the subject of
tonal centers.

In music we play in
what are known as

A "key" consists of
a tonal center,
and, typically,
a musical scale
and chords,
at a bare minimum.

When we speak of playing
in the "key of C",
for example

(all of the white keys on the piano board,
with scales beginning and ending
on the white key named "C"),

what we are actually saying
is that we will begin
and end
the song on the tone "C",
(or a close relative of it),
and that we will be using
a scale based upon
the tone "C",
that is to say,
beginning and ending
on the note "C".

So, we will have the note C
the C scale
and the C chord
and derivations from it,
such as
C major
C minor
C diminished
C augmented,
not to mention
thirteenth chords.

All of these chords
being built around
the fundamental building block
known as
"the triad".

(as an aside,
I must confess to having been
very "mystified" by this concept
of "the triad"
as the basic building block,
after having first encountered it
as a young teenager.

Having been raised
with a very strong
and old
family belief
"the Holy Trinity",
and having already been something
of a numerologist,
i.e. searching for some kind
of fundamental order
amongst all of those numbers,
I was immediately
and permantently

So, in summation,

let's take a quick overview.

I am going to use the note "A",
instead of the note "C",
for this one.

While "C" is easier to understand,
thanks to the fact that
this scale consists soley of
all of the white keys
on the piano keyboard,
"A" will be easier to understand
in terms of numbers,
which we are about to look at.

If you have ever been
to a live orchestra concert
you will know
that before the orchestra begins
everyone must tune to one another.

(Oh, oh, don't get me going on this one.

Yes, tuning.

It is a
bigger subject
than you can
or would
ever expect.

Such that it will have to suffice here
to say that the reference note
which everyone will be tuning to
is what is known as

There they are,
so many frequencies,
or beats,
or cycles,
or peaks and troughs,
per second.

That's right.

You are already far,
and deep, and wide
into the notorious netherworld
of quantum mechanics.

Once you have entered
this world of sound waves quantified,
and studied
and meditated upon,
life as you once knew it
has just ended,
without you even being aware
that such is the case,
no less.

As we like to say around here,
you have just entered
"the rabbit hole",
as in Alice through the looking glass.

So, what have we just wrought,
anyway, with this counting
cycles or beats per second?

As it turns out,
if a string vibrates
at 440 cycles per second
it will emit what we refer to as
a sound,
to be exact.

In this case, a "musical" sound.

Now, the search is on
for things which can be made to vibrate
at 440 cycles per second,
with controllability.

How about a column of air?

Or how about a piece of string,
or wire?

Would you believe
that I have just covered
nearly every instrument
in the orchestra
in those two sentences?

String instruments
= string or wire

= air columns of varying length

= air columns of varying length

That only leaves tympani
and percussion.

Where one is now "banging on air"
in a far less precise method.

Now, if I take a column of air
that produces a pulse of vibrations,
and set it to vibrating 440 per second,
I have just created the "reference A"
which the orchestra was, above, tuning to.

If I take a length of string,
such that it will vibrate 440 times per second,
guess what?

Same "reference A" note.

See what the orchestra is actually tuning to?

440 pulses or vibrations per second.

Well, let's have a little bit of fun
while we're at it here.

What if I take two pieces of metal
of exactly the same length
and width
and material
and set them to vibrating
against one another
at 440 vibrations per second.

Did I just invent the tuning fork?

Yes, the very one
used to tune the violin "to pitch".

But, now things are about to get
a whole lot stranger.

Saw that one coming,
didn't you?

Say I take two of these pairs
of vibrating pieces of metal
and place them within inches
of one another.

I will set the one vibrating
by banging on it.

I will do nothing to the second one.


just happened?

The second fork is now vibrating
without having even been touched.

The two forks are vibrating together
as one,
so long as either of the two is vibrating.

This phenomenon is known as

The one fork is said to be
at the
"resonant frequency"
of the second tuning fork.

New and very important term
for your vocabulary.

I trust you will NEVER! forget this term,
so long as you live and breathe,
and will always REMEMBER
that it was I who told you so.

So what?
I can year you saying to yourself.


Maybe I had better
redirect you for a moment.

I will give you a homework assignment
that will clean up this entire mess
in one single instant.

Go sit down
and turn on one of my songs
that has lots of bass and droning.

Sit in front of very large speakers.

Turn up the volume
until the walls are shaking
and the windows are rattling.

close your eyes and feel.

Yes, the entire room is shaking hard
at various different inter-related
frequencies of sound.

The sound has made the room shake.

But, what's this?

The room isn't the only thing shaking,
is it now?


YOU are shaking also.

That's right,
I have made YOU shake.

As a matter of physics.

Resonance, anyone?

Do you suppose
there are parts of you
which "resonate"
just like the tuning forks?

It is as if I have reached down
deep inside of you
and grabbed onto your innermost parts
and set them to vibrating
like a cat when it purrs.

to me,
is what is so marvelous
about music.

It REALLY CAN move you,
in a way
which nothing else is able.

now we have,
(if inadvertently)
established "A440"
as our reference pitch or tone.

And we have learned
that you really do FEEL music.

Back to the tonal centers.

What if I take a column of air,
so many feet long,
and set it to vibrating
at 440 beats per second
(think organ pipe).

I now cut the column in half
(220 beats per second),
and then half again
(110 beats per second),
and set these columns to vibrating.

You now have the first makings
of a "scale".

Here we have just created
"three octaves" of tones.

Now all of you math wiz kids out there

(we know who you are,
and YES,
we ARE watching you ---)

may have noticed
that I got eight (8) of something
by cutting a vibrating column of air in half.

As a matter of fact,
I got three sets of these eights (8s)
from cutting the column of air in half twice.

Something seems amiss here.

Well, it is.

And you can thank the keyboard
and western system of musical scales
for that one.

As it turns out,
we in the west have chosen to divide
the spacing between tones
so that there are twelve divisions
between each halving.

That is what the seven white keys
and five black keys
on the keyboard are.

They are the division of the "octave"
into twelve equal parts.

When playing only the white keys,
the doubling or halving
of the length of the column of air,
as represented by the keys,
notice the following:

c,d,e,f,g,a,b --- c.

Yes, there it is.

The octave.

Eight steps
from C to C one octave above
(or below, in the other direction).

I should note,
as an aside,
not everyone in the world does
or ever has
broken the octave
into twelve equal portions.

Many break it further
into 24 parts.

And most will not use equal parts
[which is the system
known as
"equal temperament tuning",
which was only recently popularized
by J.S. Bach
(1685-1750, if my memory
serves me well)
in his series of compositions
in all 24 major and minor keys
known as
"The Well Tempered Clavier"].

That is to say,
there is some element of arbitrariness, here.

But not through randomness.

They are sort of universal conventions
arrived at through trial and error
during hundreds of years
of considering such a matter.

Let's go back to that
piano/organ keyboard
for just a moment.

Oh, and don't forget
to turn down the stereo,

I don't want the walls
to come crashing in,
just yet.

five black keys,
and seven white keys.

Each of those is able to produce
a nearly infinite number
of what are known as "scales",
with each beginning and ending
upon one of those twelve notes.

Do you see it yet?

Tonal centers?


Twelve of them,
to be exact.

Starting with the note
which has been named "C"
(to the left of the three black keys)

we will have

c,d,e,f,g,a,b,c = all of the white keys

we will also have to have
names for the black keys.

When ascending
(going to the right on the keyboard)
they will be called "sharps".

When descending
(going to the left on the keyboard)
they will be called "flats".

So the black key
to the immediate left of a white key
will take the name of the white key
 and add the word "flat".

Black key immediately to the right,

Starting with the note "C",
to the right = C sharp,
to the left is C flat.

Of course this smashes us
into the concept of
"enharmonic equivalents"

(since here
it is B
which is to the left of C
= B is C flat),
because, in the real world
the sharp and the flat
are NOT the same note.

It is only because of the
"equal temperament tuning" 
that it works out this way
on the modern keyboard.

This can cause confusion,
but really should not,
to the typical musician.

It is only we music theorists
who will go nuts over this one.

And, indeed, we do.

It is not until you are trying
to write out,
for example,
a C flat scale,
that you will begin to see
just how much trouble
you really are in.

But that need not concern
most of you
at this time.

You should just be aware,
so that you know
why most serious composers
are completely,
if not entirely,
out of their minds,
nearly all of the time.

in a good way,

but of course.

I must take a break,
because just describing this stuff
has made me lose
a good deal of my mind,
such that I must go get
my morning cup of coffee

w/love to all

this bright and sunny
beautiful Ventura morning,


at 10:04 a.m.
Ventura, California, USA