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Date: Mon, 9 Jul 2001 10:08:18 -0700 (PDT)
From: Winslow Yerxa
Subject: Ed's newbie questions

>Why are there only 12 keys - if you have 7 notes A
>thru G AND the sharps or flats (whichever way you
>want to cut the pie) the total comes up 14 - not 12 -
>where are the other two (where are Cb and Fb if
>looking just at flats)?

The pattern of sharps and flats is not consistent.
Looking at a piano keyboard illustrates this very
graphically. instead of a steady alternation of white
and black keys, there are gaps where there are no
black keys, leaving alternating clusters of 2 black
keys, then 3 in each octave.

The first cluster (2 black keys) goes C-D-E in the
white keys and C#/Db - and D#/Eb in the black keys.
But there is no E#/Fb black key. Technically, E
natural is Fb (in the rare cases when it comes up) and
E# is F natural (again, fairly rare).

The second cluster, involving 3 black keys, gives us:

white keys F-G-A-B,

and black keys F#/Gb-G#/Ab-A#/Bb

But between B and C there is no black key. Again, B#
is C and Cb is B - both fairly rare.

Why the gaps? European music did not spring fully
formed from the mind of a mathematician. It evolved
organically over several centuries, partly from other
systems thousands of years old. We have inherited the
results, which seem to have a basis in acoustics (a
related but separate discussion). But even though
there are these odd assymetries, a logically
consistent set of relationships has grown up around
them, and it's easy to understand and learn.

>Scales - Major for now - is there any rhyme or reason
>to them - some have sharps or flats some don't - why?

Now, let's say that the smallest distance between two
notes is a semitone (like E to F or C to Db), and that
two semitones make a whole tone, or just tone.

S = semitone
T = whole tone

here is the pattern of a major scale:

T T S T T T S

you can see that the whole tones also cluster in twos
and threes, separated by a semitone - the ones that
occur between E/F and B/C. The white keys on the piano
give us a C major scale.

These white keys also bear the seven note names we
use:

C D E F G A B

(c) T (d) T (e) S (f) T (g) T (a) T (b) S (c)

The sharps and flats don't have their own names. For
instance, the black key between C and D can be named
as a "lowered" D: Db (D-flat) or as a "raised" C:
C-sharp (C#).

Now, let's say we want to play in the key of G. If we
start on G and look at the pattern of tones and
semitones it creates:

T T S T T S T

(g) T (a) T (b) S (c) T (d) T (e) S (f) T (g)

We can see that it doesn't quite fit - the end of the
pattern should go "T S" and instead goes "S T".

If we raise F to F#, then we get the proper pattern:

(g) T (a) T (b) S (c) T (d) T (e) T (f#) S (g)

Notice that G is a 5th above C. So, if we were to take
the G major scale:

G A B C D E F# G

and start it on D, we'd get the same pattern we had
when we started a C scale on G. And to get a D major
scale, we'd have alter the scale the same way: raise
the 7th by a semitone:

>From

(d) T (e) T (f#) S (g) T (a) T (b) S (c) T (d)

to

(d) T (e) T (f#) S (g) T (a) T (b) T (c#) T (d)

So, for a D major scale, we have two sharps, F#
(inherited from the G major scale) and C#.

Now, notice two things about patterns developing.

As we go up a fifth in key, we are adding one sharp
for each new key. The added sharps themselves are
going up a fifth and collecting one after the other:

G major (up a 5th from C) has F#

D (up a 5th from G) has F# and C# (up a 5th from F#)

So the sharp keys - the keys that use sharps to create
a major scale - progress up by a fifth, and so do the
accumulation of sharps they use.

In common parlance, musicians will speak of "one
sharp", two sharps" and so on, meaning a key signature
containing that number of sharps, and everyone knows
that this refers to G major, D major and so on.

Sharp keys: G, D, A, E, B, F#

Exercise: Figure out how may sharps each of these keys
has, and what they are (C# + F# + ???)

By the time we get to F#, we have six sharps. If we go
to C#, we have seven sharps - all seven note of the
scale are raised. But if we use flats instead and call
it Db, we only need 5 flats. So F# is as far as sharp
keys usually go. While F# is six sharps, Gb is also
six flats. So the flip-over point happens halfway
around the cycle of 5ths from C, which has no sharps
or flats.

While sharp keys always have to raise the 7th degree
as the go up a fifth, flat keys have to *lower the 4th
degree as they go *down a fifth.

If we go down a 5th from C, we're at F. Apply the
pattern of the white keys, starting on F and we get:

T T *T S T T S or

(f) T (g) T (a) *T (b) S (c) T (d) T (e) S (f)

The 4th degree - B, needs to come down a semitone to
Bb to give us an F major scale.

(f) T (g) T (a) S (Bb) T (c) T (d) T (e) S (f)

let's say we take the resulting scale, go down a 5th
to Bb, look at the pattern of tones and semitones.
We'd find the same as we did with F relative to the C
scale. So to convert F major to Bb major, once again
we need to lower the 4th degree - E - to Eb. And so
on.

As the key goes down a 5th, so does the new flat added
to the key signature:

F - uses Bb

Bb - uses Bb and Eb

Flat keys include:

F Bb Eb Ab Db and Gb

Exercise: Find how many flats each of these keys has,
and what they are (Bb + Eb + ???)

>I understand the operating principle behind the
>circle of fifths - that is positions relative to the
>key of the music - but so what - how does the rubber
>hit the road (so to speak)? In other words if you
>have tab for the red river valley - is the same tab
>valid for all 12 positions - if not what is the point
>to positions especially if you end up "huntin an
>peckin" for the "right sounding" notes.
Tab tells you which hole to play and what to do when
you're there - blow, draw bend etc. So it will be
different for each position.

Let's say you want to play three notes - Do-Re-Mi, the
first three notes in the scale, like 1-2-3. In first
position, this will be 1B 1D 2B (B=blow, D=draw), no
matter what key the harp is in. But let's say it's a
C-harp - you've just played the tune in C, and the
notes are C-D-E.

In second position, the key has gone up a 5th - you're
now in G. Do-Re-Mi in G involves different notes - the
first three notes of the G major scale: G-A-B. These
notes will be found easiest as: 6B 6D 7D.

In third position, D on a C harp, the notes are
D-E-F#. Now, F# is not in the C major scale, so right
away we know we'll need a bend for the F#.

We can play 1D 2B 2Db (b = flat, one semitone of bend)

or

8D 8B 9Bb

or

4D 5B 5B# (# = 1 semitone of overblow)

And so on.

The reason we talk about positions is that they are a
shorthand for the relationship between the key of the
music and the key of the harmonica.

G on a C harp, Eb on an Ab harp, F# on a B harp are
all second position - a fifth up from the key of the
harp. To play the same tune in second position on any
of these harps, you'd use the exact same action
pattern of holes, breaths and bends, therefore they
would tab out the same. Third position for the same
tune would tab out differently from second position,
but would be the same for third position on all keys
of harmonica.

Most experienced harmonica players can listen to
another player and know what position is being played,
without knowing the key of the music or the key of the
harp. They can hear the realtionship between music and
harp keys due to the action patterns, tone colors, and
articulations that give away each position to the
experienced ear.

>If somebody says to you What are you playin? an you
>answer I'm playin 3rd position relative to the key of
>the song - an he (or she) says So?? How do you
>answer - if at all - maybe the question isn't even
>relative!!

You mean relavent? Depends on who's asking. This stuff
means nothing to guitarists or singers, or anyone but
other harmonica players.

Hope this helps.

Winslow

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