@Ale-H-H asked .......

"What is the maximun frequency resolution for sine waves? 64 bytes?, the guy that made nanotonality said that picotonality would need 256 BITS, but that is only 32 bytes... you said that pd extended was 32 bit... is there a way to have 64 byte resolution sine waves?!"

The author explains the principle here....... http://home.hku.nl/~pieter.suurmond/CC/NANODEF
Not understanding absolutely the concepts, one thing caught my eye.....
...... that complex and interesting rhythms would arise, and that the listener might have to wait a long time for the pattern to develop.

So........ nano.pd in (obviously) 32-bit extended
The sine waves should beat every 317,079,919.8376459 years, and seem to be on their way when I watch the terminal window, but I get bored easily and thought maybe someone else might verify this for me. I probably should have chosen 440Hz as 1K is pretty horrible.
David.

@whale-av What I´m interested in is the resolution, it says on the page that one octave can be divided into "biljons" (billions)? of nano intervals, I work with sound continuums, and the best resolution now is 100 divisions per half tone, I would be interested in using millions or billions of nanointervals per half tone, to live up to the "continuum", in the sound drawings that i make you can appreciate these beats or natural rhythms that appear, I also love them, and I would be interested in additive synthesis of 1000+ sine waves, and I thought 64 would do the job!

@Ale-H.H. The test patch above seems to prove that 32-bit Pd is capable of generating a sine wave to a frequency precision of 15 decimal places. Sorry, I don't know what part of an octave that represents but it is a very very small part...... you can probably work it out quicker than me!!
It looks more like a billionth of a billionth of an octave.
David.

@Ale-H.H. the problem with the natural beats would be the length of their cycle and pattern, if its too long for our lifetime maybe it would be useful as a concept, As slow as possible by john cage has a duration of 639 years, and obviously it would take different interpreters for it, Satie as far as I know started this with Vexations, a very long piece as well, but maybe for compositions sake you could manage the beats any way you wanted and manipulate them for a "faster" development.

@whale-av hahaha ,but what would a grander resolution mean for the beats? how would these change? if for example we use 256 bit sine waves?

@whale-av OH and this concept (nanotonality and picotonality) is by Pieter Suurmond, very interesting.

I would say that if youre working with sound continuum's the best possible resolution is required, what is the resolution of the osc messages?

http://home.hku.nl/~pieter.suurmond/CC/nano13.html
13 studies in nanotonality

maybe there is a way to calculate the chaos in the beats, and keep that rhythm, or the rhythms you like most, and listen to as much as possible, it would all be for the development of music,

Nanotonality is a bit like saying "if we increment a counter from zero to one, and increase it by epsilon each time, then we will have to increment it 1/epsilon times, and that's a really big number, woo." I suggest that if you really care about generating a signal that will beat every 1 trillion years, then go get yourself a bignum library and write your own dsp code instead of fussing over 32 vs. 64 bits. There are psychoacoustic limits on the ability of humans to perform pitch discrimination, and these limits have been well studied. Here's a typical study: http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1003336