The Twenty-First Century
by
Don Robertson
©
2005 Rising World Entertainment
Part
Four: Scales and Chords
<-previous
->next
Scales relate to melody and
chords to harmony.
A scale is the series of
notes that are defined between two notes an octave apart. The
major scale in western music is C,D,E,F,G,A,B,C.
Two Notes: Intervals
When two notes sound one
after the other in a melody or are played together in a harmony,
the distance between these two notes is called
an interval.
The
following diagram shows the intervals between the pitches in the
overtone series:
Classification
of Intervals |
Minor
2nd |
1
half-step |
Major
2nd |
2
half-steps (1 whole-step) |
Minor
3rd |
3
half-steps |
Major
3rd |
2
whole-steps (4 half-steps) |
Perfect
4th |
5
half-steps |
Tritone |
3
whole-steps |
Perfect
5th |
7
half-steps |
Minor
6th |
A
perfect 5th plus a half-step (4 whole-steps) |
Major
6th |
A
perfect 5th plus a whole-step (9 half-steps) |
Minor
7th |
A
perfect 5th plus a minor third (5 whole-stops) |
Major
7th |
A
perfect 5th plus a major third (11 half-steps) |
Octave |
A
perfect 5th plus a perfect 4th (12 half-steps) |
Three Notes
When
three notes are played together, we have what is called a three-note chord. If the three
notes each skip a scale note, the resultant three-note chord is called a
triad (examples: C,
E, G; C, Eb, G; C#, Eb, Gb; etc.). Three notes that are repeated over and
over in melody is called a three-note arpeggio.
Four Notes
Four notes played
together in harmony, skipping a scale note between, is called a 7th chord because the added note is the 7th of the
scale (1,3,5,7). Four notes
played over and over in melody is called a four-note arpeggio.
Five Notes: the
Pentatonic Scale
Chords can be constructed
with five or more notes. When continual skipping of a scale note
takes place, then the fifth note added to the seventh chord
creates a 9th chord, one more skipped note an 11th
chord, then finally, one
more is called a 13th chord (in actual usage, some of the
notes might be omitted). In melody, 5 notes can become a scale. These scales
are called pentatonic scales.
The
natural pentatonic scale (also called Pythagorean
and Chinese: using C as a base:
C,D,E,G,A) is the most harmonious of all scales, since it uses
the most concordant intervals of any scale. (I will explain
concord and discord shortly). It is the basis of many
folk tunes (like "She'll be coming around the
mountain") in many cultures, and it is the basis of most all
Chinese music (see Yo
Ki).
Seven Notes
The basic music scale
consists of seven notes. Scales with more than 7 notes can be
created and played, and
this is a field with much experimentation. North Indian scales are
based on five and seven, just as are ours. However, extra notes are
often included when the basic seven-note scales (called thats)
are expanded into ragas.
Debussy frequently used whole-tone scales (they have 6 notes) in
his early music: (C,D,E,F#G#,A#), and Stravinsky octatonic
(8-note, or diminished) scales (C,C#,D#,E,F#,G,A,Bb).
It is true that the overtone series
does not exactly create a Western major scale, although it
outlines the triad and the octave. The major
scale on C is created from the overtones of C, and the overtones
of F and G:
Note
Name |
Ratio
To C |
C |
1 |
D |
9/8 |
E |
5/4 |
F |
4/3 |
G |
3/2 |
A |
5/3 |
B |
15/8 |
C |
2 |
Modes are variations of a
particular scale that are made by making the basis of the scale
on a different note of that scale. For example, these are the 5
modes of the natural pentatonic scale:
Scale
|
North Indian Classical Raga
Name
|
C,D,E,G,A
|
Bhupali (among others) |
D,E,G,A,C |
Megh |
E,G,A,C,D |
Malkauns
(aka malkosh) |
G,A,C,D,E |
Durga |
A,C,D,E,G |
Dhani |
These are all very powerful scales used in the ragas of the
same name. Indian music is FULL of many variations of pentatonic
scales:
Scale |
Raga
Name |
C,D,Eb,F,A |
Abogi |
C,Db,Eb,G,Ab |
Bhupal
Todi |
C,D,E,G,A |
Bhupali |
C,Db,E,G,Ab |
Bibhas |
C,D,F,G,B, |
Sarang |
C,Eb,F,Ab,B |
Chandrakauns |
C,Eb,F,Ab,Bb |
Malkauns |
C,Eb,F,G,Bb |
Dhani |
C,D,F,G,A |
Durga |
C,D,Eb,G,A |
Shivarangani |
C,Db,F,G,Ab |
Gunkali |
C,D,E,G,B |
Hansadhvani |
C,E,F#,A,B |
Hindol |
C,D,F,G,Bb |
Megh |
By viewing just these simple pentatonic scales used in India, we
begin to understand the wealth that we can learn from India's
ancient traditions. While Europe developed harmony, India
developed melody.
These are the 7 modes that are derived
from the Western
major scale:
Scale |
Mode |
C,D,E,F,G,A,B |
Major |
D,E,F,G,A,B,C |
Dorian |
E,F,G,A,B,C,D |
Phryigian |
F,G,A,B,C,D,E |
Lydian |
G,A,B,C,D,E,F |
Mixolydian |
A,B,C,D,E,F,G |
Minor |
B,C,D,E,F,G,A |
Locrian |
The Triad
As I
discussed, the triad is a three-note chord that skips a scale
note. Here are the main types of triads:
Triad
Type |
Example |
Major |
C,E,G |
Minor |
C,Eb,G |
Diminished |
C,Eb,Gb |
Augmented |
C,E,G# |
The simple major triad is
the underpinning of ALL harmony. It is the chord that underlies
the overtone series.
The
Major and Minor Triads
A major or minor triad is classified
depending on whether a minor or a major third is used as the middle
note. The major and minor triads are the two primary chords of
all music. When a music composition is based on a key
substantiated by a major triad, or built with a major scale,
then this composition is said to be in a major key. If the scale
and key are minor, then the composition is in a minor key.
Besides major and minor triads there are others, such as the augmented and
diminished triad and other variations such as sus4. These
are all used as passing chords, not as the base of compositions
because they either are unstable because they don't use a
perfect fifth, or they do not contain a third.
Beethoven once wrote a trivial piano
piece called Lustig-Traurig (Happy-Sad). The happy
section was written in a major key, the sad in minor. It is
true that the these two emotional associations have long been assigned to
major and minor, and it is a likely association. The
Chinese, in
the ancient document Yo Ki, stated that if that middle note is
altered (from major), sadness would prevail, and that is what the blues scale
is all about. Blues uses major chords while the singer or player
bends the third down to a minor third,
and that is what creates 'the blues' (amongst other things, of
course).
If you want to write sad music,
like a requiem, use minor. Happy music, upbeat things? They are
always written
in major. During the years I spent in an intensive study of
gospel music, both black and white, I found only two gospel
songs
written in minor keys! You don't shout praises the Lord in
minor!
However, a minor scale is suited for a
passive state of experiencing the divine within. That's why
Indian raga Darbari Kanada (VERY basically,
C,D,Eb,F,G,Ab,Bb,C,Ab,Bb,G,F,G,Eb,F
,D,C) and Kausi Kanada (C,Eb,F,Ab,Bb,C,Ab,Bb,G,F,G,Eb,
F,D,C) are so spiritually powerful if sung by a master, such as
the old master singers in India.
What about the Gregorian
chant melodies that were written in
the dorian mode with its minor triad base? They are very
powerful devotional melodies. The natural sixth in
that scale does offset the minorness a bit. Dorian
mode itself has its own "vibe."
Major is outgoing and masculine, while minor is
inward and feminine. When I used to counsel people who
needed help, I often used music for therapeutic reasons. I remember one lady
who came to me who wanted me to recommend that she listen to
Gregorian chant, but I told her she needed to listen to Haydn
masses instead, outgoing music that had power! This listening helped
draw her out of herself where, through her own misdirection, she
had gotten hung up very deeply. Another lady, who was constantly
outgoing, got my most sacred chant records to listen to, sung by Benedictine
nuns. One night of that turned her life completely around. She
went from a heroine addict to a minister working in the prison
system full time.
My
own definition of major and minor is quite different than any
definition you may have ever seen. You won't find it anywhere else. Please give it some thought: Major
= Joy Minor
= Love Joy
and Love are two different energies!
Joy is active (+), Love is
passive (-), and sadness is just a form
of Love. Just meditate on this little gem that I am passing
on to you.
The Duochord
The
duochord was another one of my discoveries, this one
taking place in 1968. I was struggling with the
creation of my Last Piece, a complex discordant musical composition that
I was writing under the tutelage of my teacher Morton
Feldman. The music in the composition was based on two
intervals, the minor 2nd and the tritone (I was being drawn to the dissonant end of the harmonic
spectrum).
At that time, I felt that composers like Stockhausen and Boulez were ruining their discordant compositions by accepting obvious
concordant intervals, such as major 3rds, into the midst of all the
chaos of the music.
Morty, as I called my teacher, was puzzled by
my insistence in stripping my composition of
consonant intervals, but helped me with the process for nearly a
year. Finally one day he told me that I was being too limited in
my choice of intervals. My order of preference was first the tritone,
the most
important, next the minor second followed by the minor second, and
fourth, the major 7th. After explaining to him in detail what I was trying to do, he
reflected for a bit, then looked up at me and said: "I understand. You are going
beyond Cage and myself, and you should. You belong to the next
generation."
We continued to work away at the puzzle of
this single composition. I wished that I had a
computer. I would use it to map out harmonies and melodies all
belonging to a complete composition, measure distances forward
from a note for the distance that they would be strongly
retained in the listener's memory, then measure all other notes
against this and make harmonic choices based on my order of
interval priority. But computers were not easy to come by in
1968, so I continued to work away, trying to avoid even distant consonant intervallic
associations if I could.
Meanwhile,
while all of this was going on, I had begun studying the great
and ancient art of music from North India with Ustad
Ali Akbar Khan.
One day
I was reading one of Corinne Heline's
books when I noticed a diagram in the
book that demonstrated how the twelve notes of the musical
chromatic scale corresponded with the twelve signs of the
astrological zodiac. At that time I was interested in astrology
and I thought this was a fascinating concept. The way she
explained it, the notes were placed counter-clockwise on the
circle of the zodiac as follows: C, D, E, F, G, A, B, C#, D#,
F#, G#, A#. I don’t know where she learned this, but it was
very interesting. It was the 7-note major scale (the white keys
of the keyboard), followed by the 5-note pentatonic scale (the
black keys of the keyboard): the two most perfect scales in
music.
I was fascinated by this
discovery. Astrology is based on a circle, around which are
drawn the twelve astrological signs. Positive and negative
relationships in astrology are determined by where one sign
stands in relationship to another. I began to wonder that if
this was the case in astrology, wouldn’t it also prove to be the case for
the twelve notes of the musical chromatic scale (the chromatic
scale in music includes all the black and white keys within an
octave).
With this in mind, I
did exactly what I had just a few months before learned to do,
and that was to create an astrological chart with trines
and squares. Trines on the zodiac are triangles, and they
always represent positive elements. If you have lots of trines
in your natal chart, an astrologer might tell you that you had some
good things going on, depending on whatever else was happening in
the chart. Squares, on the other had were negative. After I had
completed this chart, I assigned Corinne
Heline’s note values to it. What I found out astounded
me:
The trines created four triads: two
major and two minor!
This showed me that by assigning the notes to the circle as she
had described, the overlaying of triangles yielded the very
foundational elements of music itself: major and minor triads!
After marveling at this for a
while, I then drew squares. In astrology,
squares represent the negative elements: discord and lack of
harmony. I drew the three possible squares. I looked at what
ensued and was completely shocked! There before my eyes I saw
the very chords that were the foundation of all of the music that I had
been composing for the past year! Each square defined a four-note chord
consisting of two
half tones separated by a tritone:
Three duochords
I named this four-note chord the duochord.
Whether you believe in astrology
or not is unimportant. Here we are dealing with mathematics and
symbolism which is important because they give insights into
the inner workings of nature. I realized that I was looking
at a mathematical representation of the very conflict that I was
beginning to feel emotionally in my life: the music that I was
composing with Morton Feldman on one hand, and the music that I was
leaning from Ustad Ali Akbar Khan on the other. One was based on
triangles, the other on squares. With Morty, I was composing
music that was completely negative!
That realization bothered me a
great deal, and I contemplated it for a while. I loved the music
that I
was writing, and if what I was beginning to understand was true, I would have to abandon it, because I knew in my
heart that I did not want to create something that was negative.
Finally, I decided to speak with
Morty about this. I told him that I had a conflict developing within me. He
listened carefully.
"Do you think that this
music that you and I write is…," I stumbled for a
tasteful word to use, "…unnatural?"
He answered me immediately,
without reflection with an answer that completely surprised me. He said:
"Yes, it
is unnatural, but
if you ever quote me on that, I will deny that I ever said
it."
I realized that this was to be
our last lesson. The two years of weekly visits would be over. I
was sad, but I knew what I should do.
For months I struggled within
because there was still a part of me that had a strong desire to
write duochordal music. But one night I dreamed I was listening to
a very powerful brass ensemble who were playing a composition
that I had written. The piece consisted of a long
series of sustained chords, played as loudly as possible, and
these chords were the most grinding, awful discords that I had
been able to conceive of.
Every time one of these loud chords sounded, it sent a cold shiver
up my back and I felt a wave of darkness flow over me. I awoke
in a state of panic and terrifying fear, sweat dripping from my
body.
I knew at once that I
had to completely forgo my desire to compose and enjoy
duochordal music.
That summer, I moved away from
New York, following Ustad Ali Akbar Khan to Berkeley, California
where he was setting up a school in North Indian music in a
summer-vacated frat house. While in the San Francisco bay area, I recorded my album Dawn
that reflected my struggle between the two shades of music: light and dark. It was my last battlefield. After the album was completed, my wife,
Suzanne, and I left San Francisco for Mexico and Guatemala where I was
transformed by the sunlight of Yucatan and the Mayans, and where
I gradually purged my system of negative music. After I purified myself, I prepared to move onto the
light side of the path.
(For an example of duochordal
music click HERE
)
In 1970, I
published my findings in a long-out-of-print book.
As we saw in the illustration of the duochord, there are two triads that
form the basis of harmony. They
are used in many cultures besides our own because they are a
naturally-occurring phenomena. The major triad (positive
polarity) uses the following 7 intervals:
C - E = major third
E - G = minor third
C - G = perfect fifth
G - C = perfect forth
C - C = unison
C - C = octave
E - C = minor sixth
These are the most harmonious intervals! The minor triad has the same
intervals except there is a major sixth instead of a minor sixth:
C
- Eb = minor third
Eb - G = major third
C - G = perfect fifth
G - C = perfect forth
C - C = unison
C - C = octave
Eb - C = major sixth
The natural pentatonic scale, the most
harmonious of all scales, has the same intervals as the major
triad plus 3 new ones:
C - D major second
D - C minor seventh
C - A major sixth
<-previous
->next
|