III. 2. The Division

of the Intervals

 
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by dr. fazli arslan
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start: 09 january 2007, up-date: 09 january 2007
If we divide any interval into two equal parts, the process to be done is to multiply the numerator and the denominator of the interval by 2 and to find the medium "vasat" number by adding half of the difference between the big number we get and the small number. For example; let's divide 4/3 into two. We get numbers of 4x2=8 and 3x2=6 and these are the big and the small sides. For the medium number we add 1 which is half of 2, the difference of 8 and 6 into the small side. This number is 7. We get the numbers of 6, 7 and 8. In this case a tetrachord is divided into two intervals as 8/7 and 7/6.
 
The intervals can also be divided into parts more than 2. If so, the number intended to be divided into how many numbers is multiplied by the numerator and the denominator.