Lately I was thinking about how to generate subtones and overtones using modular synths. I came up with using clock dividers and multipliers. 

Assuming our clock divider and clock multiplier has outputs × or ÷ from 1 to 8 we can write the the frequency ratios in the following way.

	1	2	3	4	5	6	7	8
1/1	1	2	3	4	5	6	7	8
1/2	1/2	1	3/2	2	5/2	3	7/2	4
1/3	1/3	2/3	1	4/3	5/3	2	7/3	8/3
1/4	1/4	1/2	3/4	1	5/4	3/2	7/4	2
1/5	1/5	2/5	3/5	4/5	1	6/5	7/5	8/5
1/6	1/6	1/3	1/2	2/3	5/6	1	7/6	4/3
1/7	1/7	2/7	3/7	4/7	5/7	6/7	1	8/7
1/8	1/8	1/4	3/8	1/2	5/8	3/4	7/8	1

Their note represenation is the following.

Going right in a row we can see the overtones built on the leftmost note. Going down in a cloumn we obtain the subtones of a certain note. Walking on the diagonal the operations cancel out resulting in the original frequency.

Of the above only some are unique. These are the unique notes that can be obtained using a single clock divider and a multiplier.

As it turns out this system is quite similar to that of the tone diamond of Harry Partch.