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You may think of scalemaking as
some sort of esoteric musical alchemy. This is near the truth,
for as with alchemy the intent may be to transmute something
of little value into gold. This may be in the form of a valuable
piece of music. The process, like chemistry, may be approached
from two opposite directions: starting from an existing scale
and by analysis breaking it down to its constituent parts
to discover how it works, or by synthesis constructing a scale
using some form of recipe.
First a few definitions:
A scale is a series of notes which
are used in a piece of music. These may be identified by their
musical names using the letters A through G. Each of these
letters may also be followed by any number of sharp or flat
symbols. For example the notes D-E-F-G-A-B-C-D make a minor
scale from D.
Any scale may be transposed by
changing the starting note which will change the other note
names and the key signature. If we flatten all the notes of
this minor scale from D by one Large interval from D to C,
we create a minor scale from C [C-D-Eb-F-G-A-Bb-C] and the
key signature now has two flats (Bb and Eb). Our two examples
here have shown us two minor scales, from D and from C minor,
which both use the same mode.
This mode of L-s-L-L-L-s-L is
known as the Dorian or Kafi mode. (The name is dependent upon
whether you are using the English, Greek or Indian names for
the mode).
A mode is a sequence of intervals,
which may be defined by Large and small intervals. The sequence
for the two minor scales used in the examples above are both
L-s-L-L-L-s-L, which we described as the minor mode. This
sequence of intervals added together gives a total of five
Large and two small intervals, which gives us one octave.
We can therefore consider this
pattern as circular. That is it ends on the octave note above
where it started. Using this same circular sequence we could
start it at any point and each of the seven starting points
gives us another mode. In this case we can make all the Greek
modes using this sequence, which are the basis of Western
music and harmony. These seven different notes are contiguous
on the spiral of fourths and fifths, and arranged in pitch
ascending order, give us a megamode. This is the circular
pattern from which the seven Greek modes are derived.
A megamode is a circular sequence
of intervals from which modes are derived. The megamode of
seven contiguous positions on the spiral of fourths and fifths
produce all the Greek modes. We could describe this as an
expanse of six steps which contains seven notes. There is
a comparable megamode of four steps which produces five contiguous
notes and generates five pentatonic scales.
To analyse a collection of
notes.
1. List all the different
notes which are used in the piece regardless of octave.
2. Arrange the note names
in order of fourths (flats) in one direction and fifths (sharps)
in the other, leaving blank spaces where notes are missing.
[Sequence ascending in fifths is: Bbb Fb Cb Gb Db Ab Eb Bb
F C G D A E B F# C# G# D# A# E# B# F## C## etc.] The fifth
may be considered as the dominant, and the fourth as the sub-dominant.
3. Count the total number
of steps between the fourthmost (flat) and fifthmost (sharp)
note. This is the extent of the string, or chain of fourths/fifths
(x).
4. List the missing notes.
Identify them by numbering the flatmost as 1 and the following
as ascending numbers moving through fifths. Each of the missing
notes may be defined as between 2 and x.
5. The megamode may now
be defined by the number of steps and the position of the
missing notes (m1, m2, etc.). Eg. x=12 m1=2; m2=5; m3=9; and
m4=11. Therefore there are four notes missing in the sequence.
The extent is (x)=12. So there are thirteen notes of which
four (m1 to m4) are missing leaving 13-4 = 9 notes. In this
case numbers 1, 3, 4, 6, 7, 8, 9, 10, and 12. 6.
6.The mode is determined
by which of the notes is chosen as the start of a sequence
of ascending frequencies. This starting note may be identified
by stating its position on the chain of fifths. For example,
if the notes were six consecutive steps (Eg. F C G D A E B);
these pitches could be arranged in seven modes of different
ascending pitch orders.
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