Re: How to find a scale that will easily produce microtonal pop musi

Michael wrote :

> (Gene):
> > "Please keep me happy and don't use 24 as a mohajira tuning!"
>
> So then...what TETs and steps in those TETs would you recommend for > Mohaijira?

Like Gene said, 31 or 55.
Knowing your attirance for Ptolemy's Homalon, I think you would like 31, because it has the most even seconds intervals.
Instead of 3 + 4 + 3 + 4 + 3 + 4 + 3 steps in 24-ET, Mohajira would be 4 + 5 + 4 + 5 + 4 + 5 + 4 steps (or other modes) in 31-ET,
and instead of 4 + 3 + 3 + 4 + 4 + 3 + 3 in 24-ET, Arabic Rast (closer to Ptolemy's Homalon) would be 5 + 4 + 4 + 5 + 5 + 4 + 4 steps in 31-ET.
Or, one classical -c / eq-b fractal version of Mohajira would be :
octave 1200c.,
generator 348.91261178844 c.

Manuel wrote a 7 tones version in dudon_mohajira.scl
- - - - - - -
Jacques

--- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:

> Knowing your attirance for Ptolemy's Homalon, I think you would like
> 31, because it has the most even seconds intervals.
> Instead of 3 + 4 + 3 + 4 + 3 + 4 + 3 steps in 24-ET, Mohajira would
> be 4 + 5 + 4 + 5 + 4 + 5 + 4 steps (or other modes) in 31-ET,
> and instead of 4 + 3 + 3 + 4 + 4 + 3 + 3 in 24-ET, Arabic Rast
> (closer to Ptolemy's Homalon) would be 5 + 4 + 4 + 5 + 5 + 4 + 4
> steps in 31-ET.

Five of these showed up in my survey of proper 7 note scales in 31et. The patterns were:

4554454 (Sikah)
4444555
4554445
4544455
4545454 (Mohajira)

The upshot is that the step sizes are so close that all five circular permutations give a proper scale.

A side note of the Homalon series as a popular scale...
I love the Homalon series and find it a bit annoying that history seems to have so much "ignored Ptolemy" and almost completely focused on expanding Pythagorean-based ideas for harmony (namely mean-tone and then 12TET).

The one huge weakness I find in the Homalon scales is the way they run into the nasty 16/11 and 17/11 "alternative 5th" and other that disrupt the ability for many of the sort of arpeggios so many musicians love to use (IE this seems not to simply pertaining to things like emulating 12TET triads).
Thus most of my "Ptolemy-based scales" have a large amount of effort put into finding patterns that both estimate the Homalon scales fairly well and do so with more usable 5ths. I've found 22/15 and 50/33 work much better than 16/11 and 17/11 and many other fractions in the area nearing 3/2 (Igs suggested both of those options to me, btw)...but other suggestions are of course welcome. :-)

Jacques> Instead of 3 + 4 + 3 + 4 + 3 + 4 + 3 steps in 24-ET, Mohajira would
> be 4 + 5 + 4 + 5 + 4 + 5 + 4 steps (or other modes) in 31-ET,
> and instead of 4 + 3 + 3 + 4 + 4 + 3 + 3 in 24-ET, Arabic Rast
> (closer to Ptolemy's Homalon) would be 5 + 4 + 4 + 5 + 5 + 4 + 4
> steps in 31-ET.

Gene>"Five of these showed up in my survey of proper 7 note scales in 31et. The patterns were:
4554454 (Sikah)
4444555
4554445
4544455
4545454 (Mohajira)"

So here's a question that I strongly believe pertains strongly to the above scales and if/how they may work in making "popular microtonal music":
what do the near-5ths (IE intervals between 7/5 and 8/5) in those scales look like?

-Michael

On 9th of May 2010 Gene wrote :

(Chris) :
> > Hi Gene,
> >
> > Thanks for the answer. I have another question - I assume there must
> > be some advantage presenting a generator as a polynominal.
> >
> > Can you tell me why that is preferred - or what are the > advantages? If
> > I were to guess it has something to do with the data set represented
> > by the solution line and / or area.
>
> First, it gives an exact definition of the generator. Second, it > tells someone who wants to set up a recurrent sequence to do > something similar where to start. Third, it tells us about beat > relationships.

I agree and I am adding a few others :

4. it allows you to find the perfect generator for precise prefered musical chords or harmonies in a temperament ;
5. there is an infinity of them and this will allow for more choices and refinements than ever ;
6. it is based on acoustic, audible facts and not conceptual criterias and approximations ;
7. it will help in return to analyse other sytems such as edos or other linear generators in regard to refined complementary acoustic properties ;
8. the infinity of recurrent sequences it permits at various degrees of convergence or divergence, from different whole numbers and at different places in the series offer for each algorithm many different harmonic versions ;
9. harmonic/rational versions will even have more synchronous and JI polyrythmic beating properties ;
10. harmonic/rational versions will reveal and integrate higher limit JI complementary relationships ;
11. harmonic/rational versions can cumulate locally several sequences and therefore even more acoustic properties ;
12. harmonic/rational versions are more or less unequal and therefore propose differents modes of the same scale (the same way a well-temperament has more subtleties and possibilities of adaptation than a equal-temperament) ;
13. polynomials indicates you immediately the differential coherence properties of a temperament ;
14. this allows you to synthesize waveforms and timbres in ideal adequations with the tunings ;

- - - - - - -
Jacques

Hi Jacques,

All of these attributes suggest the polynominal is being used for more
than just the one solution, that is one number.

Can you (or anyone) describe how the other the other attributes are
derived from the polynominal?

This also makes me wonder, since human hearing works in natural log (I
think) then if some differential equations which have logarithmic
solutions might be even more applicable.

Chris

On Mon, May 10, 2010 at 4:08 AM, Jacques Dudon <fotosonix@...> wrote:
>
>
>
> On 9th of May 2010 Gene wrote :
>
> (Chris) :
>
> > Hi Gene,
> >
> > Thanks for the answer. I have another question - I assume there must
> > be some advantage presenting a generator as a polynominal.
> >
> > Can you tell me why that is preferred - or what are the advantages? If
> > I were to guess it has something to do with the data set represented
> > by the solution line and / or area.
> First, it gives an exact definition of the generator. Second, it tells someone who wants to set up a recurrent sequence to do something similar where to start. Third, it tells us about beat relationships.
>
> I agree and I am adding a few others :
> 4. it allows you to find the perfect generator for precise prefered musical chords or harmonies in a temperament ;
> 5. there is an infinity of them and this will allow for more choices and refinements than ever ;
> 6. it is based on acoustic, audible facts and not conceptual criterias and approximations ;
> 7. it will help in return to analyse other sytems such as edos or other linear generators in regard to refined complementary acoustic properties ;
> 8. the infinity of recurrent sequences it permits at various degrees of convergence or divergence, from different whole numbers and at different places in the series offer for each algorithm many different harmonic versions ;
> 9. harmonic/rational versions will even have more synchronous and JI polyrythmic  beating properties ;
> 10. harmonic/rational versions will reveal and integrate higher limit JI complementary relationships ;
> 11. harmonic/rational versions can cumulate locally several sequences and therefore even more acoustic properties ;
> 12. harmonic/rational versions are more or less unequal and therefore propose differents modes of the same scale (the same way a well-temperament has more subtleties and possibilities of adaptation than a equal-temperament) ;
> 13. polynomials indicates you immediately the differential coherence  properties of a temperament ;
> 14. this allows you to synthesize waveforms and timbres in ideal adequations with the tunings ;
> - - - - - - -
> Jacques

Jacques>"14. this allows you to synthesize waveforms and timbres in ideal adequations with the tunings ;"

How does one go about this directly? Is there a formula through which to translate tuning-creation formulas to timbre-creation formulas?