An often used definition of a microtone is one which creates an
interval smaller than a semi-tone. However, for practical
reasons I am going to use the term microtone to mean any tone
not found in the presesnt 12 tone equal temperament scale. (In
this scale every semi-tone has a frequency ratio of the twelfth
root of 2.)Here is an example of the the ordinary 12 tone
chromatic scale but in just-intonation; this means all frequency
ratios of intervals are expressed as ratios of whole numbers;
none of the semi-tones give ratios equal to the twelfth root of
2 and none are in our 12 tone equal- tempered scale! The ratios
given are in relation to the first tone, C. C: C# : D : D# : E :
F : F# : G : G# : A : A# : B : C . 1: 25/24: 9/8:
22/27:5/4:4/3:45/32:3/2: 25/16 :5/3: 16/7 :15/8 : 2. There are
many possibilities to use as ratios in just-intonation. (See
some of the websites listed below for this section.) Notice that
to go from one tone to another in the above scale we multiple
ratios; for instance, to go a majo