ScaleCoding confusion (fwd)

---------- Forwarded message ----------
Date: Wed, 21 May 1997 23:31:14 -1000 (HST)
From: Charles Lucy
To: Bill Alves
Subject: ScaleCoding confusion

Bill;

I appreciated your interesting and thoughtful posting about your
coding of modes and scales, yet I see the possibility of confusion
arising between our two different systems.

In about 1989, John Gibbon, Jonathan Glasier, and I, worked together
to design a scalecoding system, and publicized it fairly widely
amongst musicians and music academics. The paper follows. I feel
confident that you will agree that the system covers all and
every contingency for analysing synthesising and coding modes and
scales from a chain of fifths perspective.

The unfortunate similarity of our systems, is that your notation
uses the same numerical pattern that we used.
(3 sets of digits separated by '/')

i.e. xx/yyy/z

In our case the "x" is the number of steps in the chain
"m" is the position(s) of the missing steps
"T" is the "tonic" or "lowest note".

In your case "x" is the number of pitches in the tuning system
"y" is the number of pitches in the subset
"z" is the number of commonly used auxiliary tones

As we have both used the forward slash to separate the groups of
digits, the unwary reader could be confused.
May I suggest that one of us use a different separator to avoid this,
or that we always attach our respective names to the coding to
clarify the possible ambiguity.

The difficulty that I have is that there are already in excess of
10,000 copies of the LucyTuning scalecoding document in circulation from
printed pamphlets, internet fileservers, and downloads over the
last seven or so years. It is also used and explained in the
"LucyTuned Lullabies (from around the world)" booklet.

BTW Bill; If you would be good enough to send me a snail address,
I'll ship you a copy of the Lulls cassette plus booklet.


File on scalecoding follows:

SCALEMAKING - Analysis, Synthesis, and Coding

by Charles E. H. Lucy
copyright 1990 & 1994
This is an extract from "Pitch, Pi, and Other
Musical Paradoxes,
(A Practical Guide To Natural Microtonality)" -
ISBN 0-9512879-0-7

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 scale of D minor
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 the scale of D minor by one Large
interval from D to C, we create a scale of C minor
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 scales,
D minor and C minor, which both use the same mode. This mode of
L-s-L-L-L-s-L is known as the minor, 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.


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 m1 m2 m3 and m4.
Therefore there are four notes missing in the sequence.
Therefore the extent is (x). 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. 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:

(F) 1 (first note in chain) (Lydian) I,II,III,#IV,V,VI, and VII;
(C) 2 (2nd in chain) (Major or Ionian) I,II,III,IV,V,VI,and VII;
(G) 3 (Mixolydian) I,II,III,IV,V,VI,and bVII;
(D) 4 (Dorian) I,II,bIII,IV,V,VI,and bVII;
(A) 5 (Aeolian) I,II,bIII,IV,V,bVI,and bVII;
(E) 6 (Phrygian) I,bII,bIII,IV,V,bVI,and bVII;
(B) 7 (Locrian) I,bII,bIII,IV,bV,bVI, and bVII.

7. The key of the scale and scale is determined by the tonal
center, which may defined as C,D,E,F,G,A, or B with the
appropriate sharps or flats. The scale may then be listed
in ascending frequency order by note name.

8. A scale or mode may therefore be defined as:
Number of steps in chain (x)/position(s) of missing notes
(counted from fourths towards fifths)/Position of tonic
(counted from fourths towards fifths).
Eg. The scale and mode described as 5/25/3 could give the
notes F-G-D-E from the chain F-C-G-D-A-E.
Using the third note of the chain (G) as the starting note
giving a scale of G-D-E-F or the mode of I-V-VI-bVII.



Charles Lucy
lucy@hour.com
http://www.wonderlandinorbit.com/projects/lullaby
http://www.ilhawaii.net/~lucy
http://ourworld.compuserve.com/homepages/lullaby

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