Tone Duration Model of Ton de Leeuw

Ton de Leeuws works after 1980 are based on the tone duration model. A tone duration model is a hidden melody with often the same note values. This hidden melody is repeated several times during a composition.

On a tone duration model you can apply different types of selection methods, to manifest into sound the tones you trigger with that selection method.

To demonstrate the principles of tone duration model, we have created a tone duration model of 24 notes. This model is considerable shorter than the models Mr. De Leeuw have used in his works. His models take up more than hundred notes.

In our model we alternate a broken minor seventh chord on d with a broken e minor triad.

The first selection method we are going to use is a melodic canon. The melody we use is kyrie nr XIb.

This melody starts with an e. When the e occurs in the model, we hold this note until the f occurs in the tone duration model. This f is the second note of the melody and will be sustained until e occurs, the third note of the melody. We repeat this procedure until all the notes of the melody have sounded. You can follow the T.D.M. in the stave above.

When you click with your mouse at the example, you will hear a midi-file of the cello part.

The consequence of this method is that the melody gets a capricious rhythm.

Now we make a string quartet with this melody. The melody starts successively at e (cello), b (viola), e (2nd violin) and b (1st violin). You can follow the tone duration model in the stave above. The result is a 'polyphonic unison'.

To view and hear the result, click here.

 

Now we try another selection method. We apply a rhythmic canon. The values are:

We get a constant rhythm, but now the melodies are capricious. The Tone Duration Model dictates the melody and because the rhythmical formula starts constant at different places in the T.D.M. , the melodies differ constantly.

We continue our string quartet and apply this selection method. The parts start after 2 1/2 beats after one another. In this example all the tones of the Tone Duration Model are revealed. But nevertheless every time the T.D.M. is passed, it sound completely different than the foregoing cycle.

To view and hear the result, click here.

 

Another selection method is that you  hold a specific note when it occurs in the Tone Duration Model until that note occurs again in the T.D.M.    From that moment you play all the notes of the Tone Duration Model until the specific note occurs again in the T.D.M. From that moment you hold the note again (so you redo procedure again).

This technique worked out in a trio for windintruments you find here.

Some other possibilities to vary is to change the mode of the model by lowering or lifting some notes of our model.

For example by lifting the F to F sharp.

By lifting F and C with a minor second:

Plus the G:

Or you can lower the B to B flat.

Or B and E:

Or you can lower B and E and lift F and C.

You can also color the sound by putting a fifth above the selected notes.

In every cycle the trombones play the rhythm of the trumpets backwards.
The following example represent the rhythms of the first cycle.

Mr. De Leeuw made cadences to make clear the beginnings and endings of the cycles. He called this cadences kolotomie. In this passages he thicken the tones of the tone duration model with other intervals like thirds, seventh etc.

 

The methods we describe are just a few; there are a lot of possibilities thinkable. You can also apply some different selection methods simultaneously. Maybe you can figure out some new methods. Let us know about it!

Are you interested in some models Ton de Leeuw used in his music? Here are two examples of his models.

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