Re: cents to any base from 2 to 36

Hi there,

I'm planning an option in FTS to show cents to any base from 2 to 36.

So for example, here is the output for 72-tet in base 12:

0.0 centsc 20.0 centsc 40.0 centsc 60.0 centsc 80.0 centsc a0.0 centsc 100.0 centsc
120.0 centsc 140.0 centsc 160.0 centsc 180.0 centsc 1a0.0 centsc 200.0 centsc
220.0 centsc 240.0 centsc 260.0 centsc 280.0 centsc 2a0.0 centsc 300.0 centsc
.....
900.0 centsc 920.0 centsc 940.0 centsc 960.0 centsc 980.0 centsc 9a0.0 centsc a00.0 centsc
a20.0 centsc a40.0 centsc a60.0 centsc a80.0 centsc aa0.0 centsc b00.0 centsc
b20.0 centsc b40.0 centsc b60.0 centsc b80.0 centsc ba0.0 centsc 1000.0 centsc

Here a stands for 10, and b for 11 as is customary in arbitrary base computing.
Numbers are all to base 12.

Since c stands for 12, seems sensible to call this centsc.

So 1000.0 (base 12) in centsc = 1728 (base 10) centsc per octave

So this is 11-tet in centsb

0.0 centsb 100.0 centsb 200.0 centsb 300.0 centsb 400.0 centsb 500.0 centsb
600.0 centsb 700.0 centsb 800.0 centsb 900.0 centsb a00.0 centsb 1000.0 centsb

This time, 11*11*11 = 1331 cents per octave.

centsa will of course be 10*10*10 = 1000 cents per octave instead of 1200.

Then cents9 = 9*9*9 = 729 cents per octave, and so on.

For example, here is 12-tet in cents8.

0.0 cents8 52.6 cents8 125.3 cents8 200.0 cents8 252.6 cents8 325.3 cents8
400.0 cents8 452.6 cents8 525.3 cents8 600.0 cents8 652.6 cents8 725.3 cents8
1000.0 cents8

Remember in cents8 there are only 8 digits 0 to 7.

So 200 cents8 = (1000 cents8)/4.

For another example:
0.0 centsc 249.8 centsc 497.2 centsc 724.b centsc 972.5 centsc 1000.0 centsc
= 5-tet in centsc.

Robert