Where do the pitches come from? With our own breath and voices we can bring forth the musical pitches from the spheres of our local universe. We can pass our breath through a sea shell conch and create beautiful, melodious tones. Changing our breath intensities can bring forth different pitches. These pitches are often the naturally occurring overtones, a consistent phenomena of aural pitches we can create many different ways. Is the pattern created in the overtone series part of the mystery of the organization of our universe? Are the overtones related in measure to the refraction of white light through a prism creating the colors of the rainbow? For a long time these overtones were the principle pitches in which we tuned our instruments to make our music. Then during the 16 century, the sciences began to emerge and "figure out" a different understanding of the natural world and things began to change in a hurry.
Well, what happened? With the increasing ability to measure and consistently recreate pitch, our music and instruments gradually become more elaborate in their construction. With the advent of the church organ, which initially backed up the choir, tuning the pipes to the "pure" or "just intonation" of the overtone series not only created beautiful pitches and certain true harmonies but horrendously bad wolf tones as well. To fix these wolf tones, to even out the pitches over the entire range of the instrument and allow any chord to be played consistently in tune, musicians gradually adapted to the equal tempered system, which divided the octave into 12 equal parts then tempered this exactness of division back towards the natural overtone series. So, a combination of both? So it seems.
So, what does this create? Well, a system of music whereby the intervals between pitches are not as "pure" as they could be which allows for any of our musical components to be created from any pitch. Really? Yep. Upon any of the 12 pitches created by the "equal" division of the octave we can create any scale or chord. Major or minor, church modes, tone rows, triads, polytonal structures all can be projected from each of the 12 pitches. And thus, we can pair any of these resources as well as modulate between these 12 elements in our compositions, either written out or while improvising. Wow, that's a lot to gain, any losses? Well, we lose the sound of the "pure" or just intonation as based upon the naturally occurring overtone series, thus perhaps remove ourselves a step or two from the balance of the spheres perhaps?
With this in mind, if we were to blow air through the entire length of the tenor saxophone, our resulting fundamental pitch could be said to be Bb. If we decreased the length of the column of air exactly one half the length of the horn, what would happen to the pitch? And does dividing the column of air by half mean anything? It does. We create a new pitch an octave above the fundamental. Example 1.
| melodic motion up one octave | melodic motion down two octaves |
We would name this pitch also Bb, but one octave higher? Yep. Divide this length in half again, our resulting pitch is again Bb, but now two octaves higher than our fundamental Bb. Example 2, comparing octaves.
| melodic motion up two octaves | melodic motion down two octaves |
Wind, string and even some percussion instruments use this simple principle to get different octaves. What about the pitches in between? Well, what if we were to divide our column of air into not two equal parts, as with the octave, but three, four or five equal parts? Each of these different divisions produces what are said to be different partials or overtones in relation to the fundamental pitch and are represented as ratios. These ratios represent how fast a pitch is vibrating in relation to it's fundamental pitch. Thus, the perfect octave ratio is 2 to 1, where the higher pitch 2 is vibrating twice as fast as the the fundamental pitch, 1. Theorist call this phenomena the overtone series, which is an integral part of how we understand the nature and evolution of pitches, from which we can create and tune our instruments.
The following graphics divide a musical string or column of air into various parts to create different the partials. Example 3,
| 1st partial, the fundamental, created by the entire length of a musical string. |
| 2nd partial, divides in half, creates a pitch one octave above the fundamental. |
| 3rd partial, 3 parts, creates a harmonic pitch a perfect fifth above the fundamental. |
| 4th partial, 4 parts, creates a harmonic pitch 2 octaves above the fundamental. |
| 5th partial, 5 parts, creates a harmonic pitch a major third above the fundamental. |
So where are we going with this? This natural breakdown of a string / column of air to produce the pitches was how instruments were tuned and thus the pitches for the creation of their music. Well, what some very hip people did a number of centuries ago in Europe was to redefine this mathematics of overtones by combining these basic ratios of vibration with splitting the octave into 12 equal parts, then to re-temper or retune the ratios. What was created from the reorganization of the older system of modal music is known as the equal tempered system of tonal organization.
What basically happens in this musical system is that the octave is divided in twelve ( 12 ) "equal tempered" parts which become the pitches. Each of these twelve ( 12 ) pitches gets a letter name. When placed in either consecutive ascending or descending order, this group of pitches becomes the chromatic scale. This chromatic group of pitches could be said to be the granddaddy of all the different scales created within the equal tempered system. This equal temperament system of tuning and organization of musical resources is what we use today to create all the harmony and most of the melodies of American music. Example 4.
| a one octave chromatic scale from C down to C |
So, we divide the octave in 12 equal parts then temper these pitches. The theory of equal tempering our tonal resources perhaps best comes to life in an old fashioned wooden piano, ( which when first built in its day created quite a stir ). The piano of today is basically a large harp of different size strings whose pitch range is 7 full octaves. Instrument builders discovered that due to the physical nature of the materials used to create the piano and the natural imperfections of the overtones, that they had to compromise the tuning of the octaves and partials of the instrument. That to get the thing to play in tune, the had to temper the partials as the moved throughout the registration of the instrument. So in one sense, is the piano keyboard laid out in perfect illustration of the 12 pitches of the chromatic scale, the basis of equal temperament? Yes it is. In another sense, do we compromise our ability to tune the pitches perfectly in the division of the octave into 12 equal parts? Yes we do. Here we illustrate the chromatic nature of the piano keys and name the 12 equal tempered pitches of one octave. Example 6.
So, we simply divide the octave into twelve equal parts then shorten or lengthen ( temper ) the octaves and partials just a wee bit depending, so that when we span the many octaves of the piano, our ear perceives the resulting sounds as being "in tune" in the world of "equal temperament." And the result of this tempered tuning process is the ability to create harmony or chords that consistently sound in tune from all of the pitches in all of the octaves? Yep. Which prior to the development of equal temper was a risky venture at best for the players? Yep.
How does this relate to the creation of the various styles of American music? Well, with the initial merging of the various cultures in early America, the newer more precisely tuned European equal temper merged with the older, indefinite tuning of the indigenous native American cultures and the players from Africa and the Caribbean, creating a new music then that we today know as the blues. Blues music, in overly simplistic theory, is a combination of European "in tune" equal tempered chords with a mostly pentatonic melody line of potentially indefinite pitch, i.e., the blue notes. The blues color is the basis of the purely American styles of music. First blues, then the spirituals, then ragtime, then jazz and later rock and roll, from which numerous American styles have and continue to emerge. All of these styles blend the two approaches of tuning to create the American sounds.
So from blowing air through a tube we create a vibrating column of air, which creates a pitch, which is further divided to create partials or other pitches. We temper these pitches and create instruments which play a series of pitches, from low notes to high notes, all of which are relatively "in tune" with one another throughout the comfortable range of our ears. With these pitches we create our melodies. We can combine these pitches together to create our chords by simulating the naturally occurring overtone series in our voicings. Are the pitches we create related to the cosmos and the organization of the spheres? Well, they have to come from somewhere right?
This "tempering" process we then apply to lots of other instruments. What's your instrument? Perhaps research it's history and evolution at your local library to it's present day incarnate. Can you play notes between the equal tempered pitches on your instrument? How do you do it? Why would you want to? Perhaps talk with a piano tuner or find a "how to" tune a piano book to reveal more of the physical and historical mysteries of our modern day way of tuning.
How about rhythms?
| the rhythms / spheres |
Other topics in this section?
| history of chords | a brief discussion of how our present day harmonic resources have evolved. |
| history of scales | examining the historical development of our present day melodic resources. |
| John Coltrane | the "father" of modern American music. |
| major / minor tonality | basic ideas concerning these two essential creative environments. |
| music from the spheres | ideas on the universal and cosmic basis of our music. |
| pitches / spheres | where do our pitches come from? |
| rhythms / spheres | where do our rhythms come from? |
| the evolution of tonality in American music | a brief historical discussion of the dissolution of tonality within American music of the last 4 centuries. |
| theory of equal temperament | discusses the basic organizational principles of the system of music used to create American music. |
| acknowledgements | thanks to friends and teachers and info about the author and the writing of this text. |
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