Re: Non octave over / under scale

Hi Dan,

> There's still a bug in the boat somewhere... try checking a 2-tone
> series with a 2/1 period and say 50 decimal places of x... now check
> the max error result... it should be zero!

Ok fixed, - it was rounding errors, which you always get in high
precision decimal point type calculations on a computer -
the value shown was e.g. 2.2737367544323206e-13
which means 2.2737367544323206*10^-13
but the e-13 was hidden because I made the text field too small
to show it. Anyway I've rounded it to max of 12 decimal places, so
should show 0 now.

http://www.tunesmithy.co.uk/uo_non_oct.htm

> Also the cents values in the scale examples are sometimes rounded and
> sometimes not, could you have them as no decimal places all the time?
> I think that's much cleaner there.

What's happening here is that it shows a maximum of one decimal place,
rather than always showing one place. So if the decimal value is 0 it
leaves it out.

I've changed this to show a fixed number of decimal places - that
also helps when comparing the two sets of cents figures
as they line up nicely. Also set the default to show no decimal
places so you'll see whole numbers of cents.

Robert

HI there,

For anyone who is following this, I've now done the
scale tree for the case of the original ou scales
and the ones repeating at integer repeats.
I can't yet see the pattern for the general
rational case.

http://tunesmithy.co.uk/uo_non_oct.htm

Try entering any integer for the scale repeat.

Then click to make both the scale tree and the
lookup - by the lookup I mean Dan's et scale tree
which you use to look up ratios in the
ratio scale tree.

It's easiest to click Both, then you see what you
are looking for in brackets after it:

E.g. for r = 3 and x = 3.5 you make:

0/10 (1/1) 14/14 (3/1) [1]
14/24 (4/2) [2]
14/34 (5/3) 28/38 (7/3) [3]
14/44 (6/4) 28/58 (9/5) 42/62 (11/5) 42/52 (10/4) [4]

This means that for example you'll find the 7/3
as the 28th entry in the 38 note over/ under scale

To test that, put 28 as the scale degree, and 38 as
the number of notes and click make uo scale,
and look in the Value field and you will find that
it is indeed 7/3.

I've posted to the tuning-maths list with the
experimental data.

Also haven't proved anything yet, leaving that
for later.

Robert