Second Order GCD's: An Alternative to Fourier Analysis

Hi everyone,

I've uploaded a file which after many years and failed attempts, I finally finished yesterday. It shows a new type of wave analysis, one that (I believe) realistically models musical harmony. It helps to explain how and why we categorise certain intervals together (5:6 and 27:32 are both 'minor third' for eg), how far we can detune them before they become other intervals, why octave equivalence exists, and why we can deduce a tonic when one is not present (as a sine wave fundamental).

Anyway, I'd love to hear your feedback,

Thanks

Rick

Rick,

I've read your paper very good!

What happens with other chords?

Thanks,

Chris

On Thu, Feb 11, 2010 at 9:44 PM, rick <rick_ballan@....au> wrote:

>
>
> Hi everyone,
>
> I've uploaded a file which after many years and failed attempts, I finally
> finished yesterday. It shows a new type of wave analysis, one that (I
> believe) realistically models musical harmony. It helps to explain how and
> why we categorise certain intervals together (5:6 and 27:32 are both 'minor
> third' for eg), how far we can detune them before they become other
> intervals, why octave equivalence exists, and why we can deduce a tonic when
> one is not present (as a sine wave fundamental).
>
> Anyway, I'd love to hear your feedback,
>
> Thanks
>
> Rick
>
>
>

Thanks Chris,

Glad you liked it. Well I used the minor triad as 16:19:24 as an example with the intention of doing more but surprisingly all the possible combo's were such a good match that I thought it unnecessary to say any more. You could use the ~ GCD formula to try say the major triad as 64:81:96 and any other chord you think of. I'd be interested to know the results myself.

-Rick

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Rick,
>
> I've read your paper very good!
>
> What happens with other chords?
>
> Thanks,
>
> Chris
>
> On Thu, Feb 11, 2010 at 9:44 PM, rick <rick_ballan@...> wrote:
>
> >
> >
> > Hi everyone,
> >
> > I've uploaded a file which after many years and failed attempts, I finally
> > finished yesterday. It shows a new type of wave analysis, one that (I
> > believe) realistically models musical harmony. It helps to explain how and
> > why we categorise certain intervals together (5:6 and 27:32 are both 'minor
> > third' for eg), how far we can detune them before they become other
> > intervals, why octave equivalence exists, and why we can deduce a tonic when
> > one is not present (as a sine wave fundamental).
> >
> > Anyway, I'd love to hear your feedback,
> >
> > Thanks
> >
> > Rick
> >
> >
> >
>