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The Twenty-First Century
by Don Robertson

© 2005 Rising World Entertainment

Part Four: Scales and Chords

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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:


North Indian Classical Raga Name


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

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