The Tone Clock, by Theo Hoogstins

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In the past jazz has always been an artform in which musicians were invariably looking for new musical ideas. The evolution of composing and improvising has been the most important ingredient in which jazz could develope into the most diverse musicform. Think for instance of player/composers like Charlie Parker, Charles Mingus, John Coltrane, Miles Davis and Ornette Coleman. As the end of the century comes closer musicians start reaching back more and more to the music of the past, and jazz turns into a kind of museum music in which the art of reproduction becomes more important then the art of creation. Very few musicians of our time are still looking for new ideas and angles to help jazz enter a new century of possibilities. Classical music has been developing over the last few ages, for instance through Arnold Schoenberg in the beginning of this century. When he introduced the twelve tone system, a whole host of possibilities was added to music. What Schoenberg did not provide was a satisfying solution for harmony in this new tone system. Untill then harmony had been based on the "Traité de l'harmony" by Jean Philippe Rameau from 1722, based on the diatonic scale. This system is based on three chords taken from this scale: tonic, dominant and subdominant, and their relation to each other. This simple and very basic hierarchy of tones, has been the basis on which classical music could develope. But when Schoenberg introduced the twelve tone system, based on the chromatic scale, the diatonic harmony system was not relevant anymore. Composers throughout the whole century have been looking for a solution to this problem, and it was Peter Schat who came up with an inventory of possible triads in the chromatic scale, which he concieved to connect to the time points or time markers of the clock, thus giving a possibility of reference and comunication to ideas of tonality in the chromatic scale.

The Tone Clock
Before being able to explain the tone clock we have to set a few rules:

When you make an inventory then, you will come to the following result:

1-1-10, 1-2-9, 1-3-8, 1-4-7, 1-5-6.......1-6-5 ?

The last one is allready mentioned in a different order, so we have to continue with the next new combination, wich is:

2-2-8, 2-3-7, 2-4-6, 2-5-5, 3-3-6, 3-4-5, 4-4-4.

Exactly twelve triads appear and they are placed on the twelve hours of a clock in the above mentioned order. The triads are placed in a module which is also based on a clock, only now the hours are replaced by the twelve notes:

If we draw the triad C-E-G in the module the following triangle appears:

and in the following module we see that this combination of intervals fits three times in the module: two major triads and two minor triads. This figure we find on the eleventh hour of the tone clock. All the other combinations mentioned above, fit in the module four times except the diminished triad, wich is displayed as a tetrad, fitting three times in the module. Combining all the modules with their four complementary triads on the face of a clock results in the tone clock as displayed on the first page of this article. The triads of every hour are steered through the twelve-tone- field by one or more hours as is shown in the following example.

Due to the fact that every hour contains only its own intervals, the complementary triads and tetrads sound very consistant in combination with each other. Every hour repesents its own colour, and the complete instrument of the tone clock provides a palet of twelve different harmonic colours.

Melodies and twelve tone sequenses are very well supported by these harmonies, and allthough there is no recognizible tone center, a very transparent opennes can be derived from this way of composing. An example of this is the composition "La Riviere Souterraine", which is an impression on an underground river in France.

It starts of with a lonely trumpet, reflecting the silence, and grows in volume and orchestration to an explosion of sound, of which the echo's repeatedly come back. The echo's slowly die and the silence returns in the cave. Analysing this composition with the tone clock, we see in bar 26 a bass figure in E-minor and the horns play the three complementary chords from the eleventh hour:

Then a series of eight complementary triads from the eightth hour follows. In bar 21 till 26 the melody is a twelve tone sequence, harmonised with tetrads of the seventh hour. Three of these tetrads are also complemetary and placed in the module look like this:

To see by which hour these tetrads are steered, we first have to put the chords all in the same position.

We now see that these tetrads are steered by the twelfth hour, the open notes demonstrate the movement of the chords. All of the four triads of the twelfth hour are represented in this steering. If we look at the first note of every one of these triads and put them in a sequence we get the steering on the "second level", which is the steering of the steering groups. These notes are: C-B-D-F. We saw earlier that the twelfth hour was only steered by the first hour. It can however be steered by other hours, but this allways results in the same four triads. If we change the last note in this sequence into the closest one, we get C-B-D-Dflat, wich is the BACH motive transposed with a whole tone. In "La Riviere Souterraine" I have chosen for free improvisation, with this restriction that the musicians get the instruction to use the composed material as basis for the improvisation, wich leads to very surprising results, especially in the pianosolo by Jan Jongbloed on the CD "Ear Opener". It is also possible to improvise on harmonic structures, derived from the tone clock. To obtain a jazzy sound, I like to use tetrads instead of triads, so it is necessairy to translate the tone clock into jazzharmonies. To obtain this I developed a system comparible to Ornette Coleman's Harmolodics. The basic idea behind this is that three complementary tetrads also create a complete twelve tone structure. I found a lot of combinations, wich can be derived from different hours. A few examples:
Derived from the eleventh hour:

Derived from the twelfth hour:

Derived from the sixth hour:

The twelfthhour variation can be heard in the alto solo and the bass-solo in "2soon2die"; the eleventh hour variation in the bass-solo on "Onweer", and the C-melody sax solo in the same composition is based on the sixth hour variation. Both tunes can be found on the CD "Ear Opener" by the Theo Hoogstins Octet.

Oda a Walt Whitman
To show how I derive tetrads from the tone clock triads and how steering on more levels can be achieved, I will show how I created the harmonic structure of "Ode to Walt Whitman", based on a poem by Garcia Lorca.

I took triads from the fourth hour steered by the eighth hour, and distributed the notes from the third chord over the other three:

These chords I used in the first group of six chords. For the second group I made another distribution and then changed the steering:

This gave the following result:

The tetrads ate steered by the eighth hour. On the second level the groups of three tetrads are steered through the twelve tone field by the third hour. I continued this steering for two more groups (1-3-1-3-1) resulting in six groups of three tetrads.

Now I have two triads of the third hour on the second level. Then we steer these groups again through the twelve tone field by the ninth hour, thus adding the six remaining complementary triads of the third hour to the second level steering:

The steering on the third level is a symmetrical tetrad of the seventh hour, so the next step is to steer this tetrad on the fourth level through the twelve tone field by the twelfth hour.

This results in a harmonic structure of a 108 chords. Now the composer must go to work to convert this theoretically built structure into music, because it is always the composer, and never the method, who makes the music. Elswhere on this page you can see a part of the result. I hope it has become clear that the tone clock is merely a harmony system in the chromatic scale, and not a composition method, allthough steering on more levels is a more methodical procedure. The posibilities of it for composing and analysing are unlimited and more and more composers find it a useful tool.

"The Tone Clock" by Peter Schat.
Contemporary Music Studies: Volume 7
Harwood academic publishers USA.

CD: "Ear Opener" by the Theo Hoogstins Octet
Disckus Records DC-06.

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