Re: iota and centisteps

Hi Margo,

Well it is up and running in FTS, ready for when I do the next upload :-)

I've extended it to non octave scales, e.g. 1300 centisteps to
a 3/1 for Bohlen - Pierce.

One needs to include the octave in the notation for non octave scales -
I do it as 1300 cents=13|3 i.e. 13 equal steps out of 3/1 -
one could write it as 1300 cents=13|3/1 if one wanted.

One would do Wendy Carlos's gamma as 2000 cents=20|3/2

However, that's going to be a bit clumsy if one is working in one of those
all the time. So, I have also done it so that you can choose any of the centisteps
notations, and decide to use it as ones default, or cents notation.

I have a tick box "Set this notation as cents". Defaults of course to 1200 cents per octave,
but you can change the notation, and then tick it for one of the other centisteps
notations instead.

Then, you can enter the values in the ordinary decimal point type fashion as for SCALA
cents, but now it will mean 1700 cents per octave or whatever. Doing it this way
avoids any possibility of confusion about what a value means when you enter it
into the scale definitions.

It is interesting about the a to g in 17-centisteps notation.
The a00 is the fifth of the scale, so it corresponds to a
seven equal division of the "fourth".

Robert

Hi Gene,

FTS users will be able to use your notation too, or any
number of cents per any interval, - it shows it as
[12] * 100 cents per octave
but you can use a floating point number in place of thw
12

[6.12]*100

to give your 612 cents per octave.

I'm interested in the centisteps notation because it
represents 17-tet well, or the other n-tets dep.

Then you can see where ratios are relative to it.
Also you can show a ratio scale and vary the n-tet and
see which ones are close to multiples of 100 cents for that
n-tet, e.g. 200 cents of 900 per octave is close
to 11/9.

It's purely because we are used to numbers to base 10
and to the second power of 10 in percentage notations
that it is quite intuitive seeming. If we were
used to base 12 we'd use that...

612 would seem quite natural to base 12 as it is
430 to base 12
and as 43 to base 12 is the same as 51 to base 10
that means it is a good base for 51-tet.

So far, FTS is limited to 1000 cents per octave in the
alternative bases notation, but it would be pretty
easy to change that; so prob. I will, maybe for this
next upload.

Robert

--- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote:

> I'm interested in the centisteps notation because it
> represents 17-tet well, or the other n-tets dep.

I'm interested in it from the point of view of relative error, comparing one system to another, which is where Paul and I came at it from; and I must say I like my suggested "rc" for relative cents better than "centisteps", which sounds like centipedes and has "steps" in it--what steps? It's a continuous measure.