Re: iota

Hi Margo,

Thanks for your iota idea which has helped with my programming for FTS!

I had an option in FTS to change the base for cents
notation, so that you could have 1000 cents to an octave
and change the base to, say, 17, then call that
cents
12 = centsa, 13 = centsb,... 17 = centsf

then if you show all the values to base 17 you
will have 17 tones per octave, each of 100
centsf, but since we are working to base 17,
this is 10* 100 centsf, i.e. 1000 centsf

- in base 17 you count
1 2 3 ... 9 a b c d e f 10 11 ... 19 1a 1b 1c 1d 1e 1f 20
.. 90 ... 99 9a 9b 9c 9e 9f 100 etc.

Anyway it worked, but it wasn't that easy to read the results
or comprehend them, mainly because of all the letters that are
needed for showing numbers to appropriate bases for large n-tets.

I somehow missed the idea of just having 1700 ordinary decimal
cents per octave instead.

Now, I can show things like, e.g.

7/6 3/2 2

266.871 701.955 1200.0

13=289.11 13=760.451 13=1300.0
14=311.349 14=818.948 14=1400.0
...
17=378.067 17=994.436 17=1700.0
18=400.306 18=1052.93 18=1800.0
19=422.546 19=1111.43 19=1900.0

where 17= is a shorthand for 17 equal cents
value

so e.g. the 7/6 is 22.546 percent of a 19-tet
tone above the fourth degree of 19-tet
However we see that 18 equal gives a much
better approximation, as 4 steps, or
as 2 steps of 9 equal.

Robert

Hi Margo,

Sorry, should be

10 = centsa, 11 = centsb,... 17 = centsh

1 2 3 ... 9 a b c d e f g 10 11 ... 19 1a 1b 1c 1d 1e 1f 1g 20
.. 90 ... 99 9a 9b 9c 9e 9f 9g 100 etc.

Then for centsa, that would be the one for 10-tet
and use ordinary decimal notation, but with 1000 cents to an
octave.

For 12-tet in that notation one would use centsc, with
1000 (base 12) centsc to an octave, so each semitione is
100 (base 12) centsc, i.e. 144 centsc to a semitone.
It works reasonably well for 12-tet once one gets used
to reading the a and b, but in 31-tet, something like

9ub.hb17 centsv i44.j4nk centsv 1000 centsv

is pretty much unreadable (for me anyway, I expect for
most)

while
31=997.98 31=1813.4 31=3100.0
is quite easy to read once one has got the idea of how
the notation works.

Robert

Hi Margo,

Sorry again:
1 2 3 ... 9 a b c d e f g 10 11 ... 19 1a 1b 1c 1d 1e 1f 1g 20
.. 90 ... a0... b0... ... g0 g1 g2 ...g9 ga gb gc ge gf gg 100 etc.
(how to count to base 17)

Don't want to confuse people!

Robert