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Where do we expect to find symmetry in music. Actually, it seems that the primary place it is located is in the scale and often its tuning. There really aren't that many examples of reversible rhythms except at large levels of the rhythmic structure or melodies except with Bach and such, whose music is definitely for the mathematically inclined and not really the general fare even among Classical or Baroque composers.

Arabic scales known as Maqams and the gamalen's colotomic structure produce very symmetrical scales and rhythms. Two very beautiful musical traditions.

It becomes very obvious that every scale you can play also has a rhythm associated with it when you look at it constructed on a circle with the unison and the octave at the top in the same location. It’s manifestly apparent that some of the Arabic scales have notes which are half-flat or quarter tones for reasons of visual symmetry. It seemed to me unusual that the starting note for many maqams was not the one on the axis of symmetry.

Usually, it places the 1/4 flat on the 6th and/or 7th. That was interesting to me because the seventh degree is the one played microtonally flat or “blue” in Blues, Jazz, Rock and African as well, since that’s where Blues and Jazz comes from primarily. The seventh is often microtonally inflected in the Classical music of India also.


The form of a piece of music is another place where we often find a little symmetry. Beethoven and others were of the opinion that if you are writing a long piece then the beginning goes nowhere fast so you are alerted to the fact it's going to be a longer composition and likewise the ending needed to match the beginning in size somewhat and also relate to the scope of the entire piece.


Jazz tunes play the head, improvise and then return to the head. If the head is short, they play the head twice and the ending twice. This is a kind of symmetry without going to the extent of playing the theme backwards at the end which we don't expect in our tradition.

Symmetry is actually rare in nature except in the faces and bodies of animals. Trees, lakes, rivers, mountains etc. are not symmetrical. Music which does not have the symmetrical elements previously presented has the aesthetic of the nomad not seeing many faces or symmetrical buildings who often lives alone closer to nature and derives his aesthetic from that.

Contemporary composers could write more inter locking rhythms because it creates a smooth rhythmic surface without leaving any holes, just like a beautiful face

Some aestheticians say the reason we are all so concerned with beauty in art and music is because we don't live close enough to nature. We yearn for it and try to create it. I tentatively add that we may be trying to create it in our own image.

Perhaps a reason to use self retrograding rhythmic structures similar to palinromes in literature such as "A man, a plan, a canal. Panama." is not because of a need for symmetry. It's because the retrograde implies a desire to go backwad in time perhaps to a golden age. This is a little regressive however.

Another interpretation is that its a bit revolutionary. Anagrams/permutations imply an even more revolutionary philosophical standpoint.

Then there are philosophical considerations. In the Heterotopia where we actually live, we have to honor the interests and aptitudes of the composer, the performer and the audience. We cannot mirror a utopia in which we do not believe.

One based on elitism, ageism, classism, sexism and all. In my case, I'm a composer whose interests and aptitudes cluster around symbols. As such, when made aware of the fact the very notes themselves have symbollic meaning, these symbols are of interest to me.

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One thing that can be done with additive and subtractive techniques are to create transitions between sections by shortening the last repeat of a section by one beat or whatever because polyrhythmic music has traditionally used rhythm as a structural element rather than harmonic considerations which is another aspect whose stranglehold post-postmoderns are trying to escape. This also helps break up the authority of form which people in the postmodern era have been trying to do but all too often wound up facing 180 degrees and embracing formlessness. 180 degrees of sick is still sick.

180 degrees of burning up is freezing cold. The resulting chaos is something else I do not wish to recreate. Having transitions between sections helps get away from the 3 1/2 minute radio format and 15 second attention span of the verse, verse, chorus, verse, verse, chorus, bridge, chorus of the pop song and the AABA jazz form (when lengthened much becomes quite boring) without succumbing to the formless hour long pieces sometimes found in minimalism.

The historical precedent in the western world for a longer music with transitions, known as the long form, is found in big band arrangements and musical theater although, there, the music isn't rhythmically shortened to make transitions which is more akin to African music.

In Thailand, sometimes the gongs are played in a manner where the parts of the rhythm on beats 2 and 4 would be played the first time through, then the complete rhythm would be played on the next repeat, now including the rhythmic events on beats 1 and 3 also. This is an additive technique. I like this because it is a way to achieve more with less which is similar to minimalism.

Minimalim was mostly just a reaction to modernism. It was primarily based on deconstruction, on negating what went before. Unlike most minimalists, we should know why we're doing additive/subtractive procedures.

I want to avoid elitist music and, more importantly, move toward having several easy parts that don't require very much memorization to learn. I would like music to bring people together in performance not just professional musicians. Good teachers and manuals only introduce 1 new element at a time.

They only add on what is absolutely necessary to what a person already knows one step at a time. Additive procedures are one way to accomplish this educational goal of connecting to a person's prior knowledge. It can be intuitive and user friendly as opposed to counter intuitive and difficult.

I'd like to avoid some of the separation of the audience and performers. I think additive/subtractive procedures help facilitate that.

Another competing force is that the music needs to be likeable. Music does not have to pander to the adolescent 15 second attention span and 3 minute radio format like Britney Spears, yet not stretch the attention so far that it breaks as did early minimalism. Music does not need to sound so different that it alienates the audience.

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Serialism suggested new directions music could go but created slaves to compositional technique again and created a new form more rigid than the old one. Their call to greater chaos and complexity for no other reason than that seems to be the direction we are going is like stepping on the gas while approaching a fatal fall from a cliff. Serialism should only be one technique in an repertoire not an inflexible totality.

Minimalism started out all too formless, limited, repetitive, long and boring. However, it was good for getting more out of the traditional keys and showed that playing in the Major/minor/modal system wasn't dead yet. Minimalism has matured recently often having the flexible form I'm thinking about and not just a bunch of copy cats arriving too late to be respected minimalists.

Like minimalists, contemporary composers could also be working with limited pitch sets such as different forms of the pentatonic and diatonic tetrachords in the range of a perfect fifth. This serves two purposes. This eliminates some of the directionality and linearity of the western traditions and allows a composer to slowly reveal the scale as is done in India's classical music so as not to blow all their cookies too soon in the longer form we could be working in.

The one good thing about ambient music, which isn't much distinguished from minimalism by the lay populace, is bringing back composition for a specific purpose. The church provided this function before but its really a lost cause now. Music for airports fits the bill nicely much better than Muzak.

The minimalists have this down better. Music can be wallpaper until you pay attention to it and then discover its nuances. The way to do that is not through simultaneous keys or atonality which, though somewhat interesting for the musicians, alienates the audience.

The music can be challenging to musicians through simultaneous tempos and rhythms while saving the melody for the audience. The minimalists also broke out of the 31/2 minute radio format along with some rock bands like Yes and Pink Floyd. In fact, we can include the audience without pandering to the junior high school, Britney Spears, lowest common denominator.

Modal jazz artists like Miles Davis and John Coltrane among others had mastered playing over changes and were looking to move toward what they considered to be more spiritual in India's and Africa's music. They utilized a slower harmonic rhythm staying on the same chord for a longer period of time in order to prevent the harmony from controlling the melodic direction and to be given enough time to develop the melody similar to the Indian because India's (and the Middle East's) melodic sensibilities are far superior to the western.

However, the Modal Jazz school (and the New Age movement) are mistaken about Indian music's spiritual purity.

Be that as it may, modal jazz was abandoned because it had been done and it was time to move on because of the contemporary demand for originality and newness which is sometimes a mistake.