The toneclock was discovered by the Dutch composer Peter Schat (1935-2003). He called his system 'a chromatic tonality.'
The toneclock is based on the fact that there are twelve different triads.  All thinkable triads you can reduce to these twelve prime forms. You can represent a triad as a sum. For example, the fourth hour is 1+4 or 4+1. Each figure stands for the interval between tones. 1 means a minor second, 4 means a major third.
Another fact is that you can order these triads in such a way that they can fit four times in a chromatic scale and they use all tones of the chromatic scale once. The first Roman numerial is the hour, the second numerial is the steering hour. (The steering principle will be explained later in this page)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
An exception is the tenth hour. This hour 3+3 is a diminished triad. This hour can only fit in a chromatic field 3 times as a tetrad 3+3+3 (or diminishes seventh).
 
 
 
 

Every hour can be represented in a clock-like graphic, in which the numbers are replaced by the names of the notes, like the first hour:
second hour: third hour:
The triads of an hour are steered by another hour. In the chart above you can see that every first note of the triads are white. These white notes are the steering notes. All these white notes give shape a tetrad. The first hour is steered by the tenth hour (3+3+3), the second hour is steered by the eighth hour (2+4+2), the third hour can be steered by the fifth hour, but also by the seventh hour. In an article of Jenny McLeod you can find more information about the principles of steering. You can found that article here.

Composing with the toneclock continues on the legacy of dodecaphony or twelftone-music.

In twelftone-music  you use a set of the 12 notes of the chromatic scale to form a row. You make a non-repeating arrangement of the 12 tones of the chromatic scale as the unifying basis for a composition. In toneclock-composing the aesthetics of the equality of all the twelve tones is maintained, but offers the composer more flexible material than the rigid 12-tone row of dodecaphony.

When a composer choose a note, he can select another tone of the same triad. When all the notes of that triad are used, the composer can pick out another triad until all the tones of that triad are used. He repeated that procedure again till all the notes of the chromatic scale are used.

When you use the toneclock, you don't have to restrict yourself  to one specific hour. You can use several combinations like 4th hour and 5th hour:

 

Or 7th hour and 8th hour:

  

 
The triad is the basic assumption of the toneclock. This does not mean that tetrads and pentads can not participate in the toneclock,  According to Peter Schat there is tonality when  at least three tones are involved.

Tetrads which can fit 3 times in a chromatic scale are tetrads without a major third. There are seven of them:

1+1+1, or Allen Forte set-name 4-1

 
1+1+5, or 4-6  
 
1+5+1, or 4-9  
 
2+1+2, or 4-10  
 
1+2+3, or 4-13  
 
2+3+2, or 4-23  
 
3+3+3, or 4-28