KEYWORDS: Symmetric Harmony
ABSTRACT:
In the recording of “Giant Steps” in 1960,John Coltrane introduced a new direction to the Language Of Modern Jazz. He broadened the strictness of the Bebop, and reassessed the tonal ways of making melodies. In view of the findings that each of the tonal idea can be played with different meanings.
[1.1] The connection between classical tonal melodies and early jazz is clear. Jazz music embraced functional harmony as a major way of expressing ideas, and the use of the tonic and dominant was the body and soul of the music. In the early days of jazz, improvisation was based on the melodies. When Bebop arrived at the scene, the mainstream of the players and composers used chromatic harmony and melody as a central way of expressing ideas, and tonality had reached its limitation. Then, Symmetric Harmony arrived.
[1.2] Tonality used to denote the western system of music based on major and minor keys and a series of chords and notes related to a central tonic note which determines the key of a piece. Tonality can divide into two groups according to their kinetic potential: static tones and dynamic tones. Melodic progression, which emanate from the gravitational force between code of tonal system creates tonal tension. (8) The key to create melodies in early jazz music was based on these tonal principles.
[1.3] In order to create more tension and release in the harmony, Bebop music used “color notes”. Altered upper extensions (like the 7th, #9th, b9th, #11th, 13th, b13th) on the dominant chord. (Heterogeneous chords) Figure 2 . In that way the melody line sounded more chromatic than it did in the early days of jazz. The use of secondary dominants, tri-sub-V chord, mixo#11 scale, altered dominant scale, related II-chords, and all other substitution were the main component in the language of Bebop. (3) The symmetric technique that was presented by Coltrane, introduced a new linear way to implement tension and release, it was base on polytonality (more than one tonic at the same time). (6)
[1.4] The main concept is to move between symmetric tonal centers. It causes an illusion of wandering between the present time and the past. The new melody line, functions as a substitute to the original line and the listeners are able to experience the tension that is being formed, between the traditional harmony and the symmetric one. However the harmonic rhythm changes, and playing long phrases might be too much for the listener to process. As a result, the best way to avoid that stress, is to use the ternary form, a three-section form: A B A. The A parts are in the traditional or bebop language (or something else), and the B section to employ the new symmetric approach. The form can be in any size, small or large.
.
[2.1] The symmetric Harmony theory deals with dividing the octave into symmetric tonal centers. An octave can split into the next category: (Chords are spelled according to common jazz terminology)
1) C-F#-C Triton
2) C-E-G#-C Major Third
3) C-Eb-Gb-Bbb(A)-C Minor Third
4) C-D-E-F#-G#-A#-C Whole-tone
5) C-C#-D-D#-E-F-F#-G-G#-A-A#-B-C Semitone
In order to form a tonal center, we need to add the dominant before each chord so that the new succession is expanded.
1) G7-C C#7-F# G7 C
2) G7-C B7-E D#7-G# G7-C (Figure 1.)
3) G7-C Bb7-Eb Db7-Gb E7-A G7-C
4) G7-C A7-D B7-E C#7-F# D#7-G# F7-Bb G7-C
5) G7-C G#7-C# A7-D Bb7-Eb B7-E C7-F C#7-F# D7-G D#7-G# E7-A F7-Bb F#7-B G7-C
Figure 1. (Based on Major Third)

[2.2] The new melody is now a succession of linear chords . According to this method, if a new melody line is played simultaneously with the original, it creates a new polytonal color. Polytonality may be considered partly as an extension of contrapuntal practice - a sharpeninig of the edges of individual lines - and partly as a form of tonal organization. (9) The previous harmony, always begin from the same area that the symmetric melody line starts, but they go in separate ways and meet at the end of the musical phrase. A new harmonic entity is created.
[2.3] In the Coltrane method, there is a change in the succession order wich is called Permutation, ( change the sequence of pitches and chords). The original line is: G7-C B7-E Eb7-Ab G7-C and Coltrane’s cycle alteres it G7-C Eb7-Ab B7-E G7-C (4)
In Figure 2 we can observe the differences between the chromatic language of the Bebop and Coltrane’s cycle. The altered extensions that I use on the dominant are (#9th, b9th, #5th ). (3)

[3.1] When the harmony is simple, sometimes the melodies are complicated, but when we deal with complicated symmetric harmony, it is expected that the triad will come out as a major method of building musical language. Many twentieth century composers have presupposed the theory that symmetry via repetition is important for clarity.(1) And in order to emphasize that principle, Coltrane uses simple repetiton motives in his melodies.

[3.2] In Figure 3 we can notice that the use of the triad with an extra passing note forms 4 swinging notes. And on the dominant there is a repetitive Bebop motive. (This emphasizes the connection between Bebop and the new language). Frequently, the new melodies make use of close intervals that lead the notes one into another smoothly, so the melody line curve is changing up and down.
[3.3] In order to expand the cycle, we can use a chromatic approach. Because of the similarity between the dominant and tri-sub-V chord all dominant can be replaced by the these substitutes. As a result, the new arrangment of the chords that is built on the major third can be: C A7-Ab F7-E Db7-C

[4.1] The quality of a chord (major, minor, dominant, diminished, etc.) can be changed into another quality. This can radically change the atmosphere of a piece or a phrase. For example, we can take the dominant quality and apply it to the whole sequence. The melody line can match the first 4 bars of a “C Blues” because it has a sustained dominant sound.

[4.2] We can experience a symmetry change in the chords quality. For example when the chord is Major and the next diminished.

[4.3] A sequence that is being constructed from minor third, develops into longer musical Phrase because of division the octave into 4 tonal centers. As a result we can leave behind the dominant and concentrate on the tonic. A possibility for the new phrase can be: C-Eb-Gb-A(Bbb)-C

[4.4] In the minor field, it is best to use minor structure. Except on the last dominant. (G7) In a symmetric minor movement each chord has at list on note identical to the next chord. That strengthens the harmony line.

[5.1] By applying the concepts listed, one is able to create new scales or modes that can be play in any situation. (against any chord progression). The scales are longer than an octave, and one must maintain the order of the nots. Yet one can change the direction of the melody line and create an interesting contour.

[6.1] The main feature of Coltrane changes is tonality movement by major thirds. The progression to “Giant Steps” is:
|| Bmaj7 D7 | Gmaj7 Bb7 | Ebmaj7 | Am7 D7 |
| Gmaj7
Bb7 | Ebmaj7 F#7
| Bmaj7 | Fm7
Bb7
|
| Ebmaj7 | Am7 D7 | Gmaj7 | C#m7 F#7 |
| Bmaj7 | Fm7 Bb7 | Ebmaj7 | C#m7 F#7 ||
The first key center here is B, then G, then Eb, and it continues to cycle through these three keys, which are a major third apart.
Coltrane was able to develop this idea in many ways. For example, he used it as a substitute for an ordinary ii-V progression. The progression to “Countdown” is loosely based on that to the Miles Davis composition “Tune-up”. The latter tune begins with the four-measure progression:
| Em7 | A7 | Dmaj7 | Dmaj7 |
this progression is a ii-V-I progression in D major. The first four bars of “Countdown”
are:
| Em7 F7 | Bbmaj7 Db7 | Gbmaj7 A7 | Dmaj7 |
Coltrane starts with the same ii chord, and then modulates to the dominant seventh chord one half step higher. From there, he launches into the cycle of major thirds, going from the key of Bb to Gb and finally backs to D. The next four bars of the tune are identical harmonically, except they are based on an ii-V in the key of C; the next four bars are the same in the key of Bb.
[6.2] An example that is examines the cycle on well-known song “I Got Rhythm” presented in figure 10. The basic chord progress I-VI-II-V has changed accordingly to the coltrane idea.

[7.1] In the matrix that is presented beneath, we can make chords succession in any direction. If we decided to go in the vertical direction we meet the minor third, and if we go in the horizontal we meet the major third. We can go up and down and make any chords sequences.
|
C |
Ab |
E |
C |
|
A |
F |
Db |
A |
|
F# |
D |
Bb |
F# |
|
Eb |
B |
G |
Eb |
|
C |
Ab |
E |
C |
Here Are some possibility :

[8.1] Pattern in music is revealed in horizontal movement, i.e., in the relationships of sounds in succession. (9) Diminished chord are unique by having a symmetric structure. We can link the minor thirds with 3 chromatic notes in a symmetric technique. The result is a new pattern that sounds very modernistic. The idea of pattern carries with it the implication of regularity of design produced by mechanical rather than imaginative means, though the artistic significance of such order might appear to be somewhat limited (9) but as fast it play the best it sound. In figure 12 the diminished chord is presented every two beats. (5)

[9.1] Triad lacks complete definition if its third is omitted, and the resultant interval, a perfect fifth in root position or a perfect fourth in invertion, has bare effect which sound assertive in environment of classical harmony with its interplay of varied intervals. (9) Chords which are intentionally constructed of intervals of fourth or seconds, for express purpose of “breaking free” from functionality associated with it. (8) We can create a new melody sound by using symmetric movement of fourths. In each tonal center, we play a cycle of fourth or fourth + seconds.

[10.1] The diversity of the styles in Jazz is reflected in its many stylistic resources for creating melodies. In the early days of Jazz the melody was the bassis of improvising. When Bebop arrived, complex harmony was the motive of the melody language. Coltrane and his symmetric system, opened the door to new concepts that suggested a theoretical framework with a new philosophy. The adoption of the new method by young players demonstrates a growing awareness to the revolution that Coltrane created. Improvised music usually develops in a wide range of ways. It is expected that the young players, with the intention of dealing with the new Language Of Modern Jazz Music, would create new ideas in the future. In my opinion, the preferable way is to find an integrated technique that combines tradition approach and innovation.
1.
Symmetry as a
Compositional Determinant copyright © Larry J. Solomon, 1973, revised 2000
7. David Baker, The Jazz Style Of …. This is a series that include vol- umes on Miles Davis, John Coltrane, Cannonball Adderly, Sonny Rollins, Fats Navarro, and Clifford Brown. Each volume includes a brief biography and summary of the musical style of the subject. Several transcribed solos and analyses of them make up the bulk of each volume.
8. Yizhak Sadai, Harmony in its systemic and phenomenological aspects
9. Wilfrid dunwell, The Evolution of Twentieth century harmony
Copyright © 2001 All rights reserved.