Re: LIMIT OF JUSTNESS OR RATIONALITY? in terms of n-th partials overtones

--- In tuning@yahoogroups.com, "a_sparschuh" <a_sparschuh@y...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> > > > But Richard , what do you mean by small ? if we choose
> > denominator as
> > > > 8,10 , 11 , 15 , the ratio is just?
> > >If you are tuning by eliminating audible low freq beating, then
> > you
> > > are most likely approaching an interval within say the 9 or 11
> > limit,
> > > or whatever your talented ear can hear,
> >
> > Playing with sawtooth waves with headphones, I could tune ratios
as
> > complex as 17:13 by eliminating beats by ear. But this is quite a
bit
> > beyond what I could hear in a practical musical situation.
>
>
> Andreas Werckmeister resolved in his
> "Muiscalische Temperatur" inbetween the first 20 partial
> overtones that on organ tube produces serial
> one after an other, when air pressure is raised slowly.

I'm not sure what this refers to or how it's related to what I wrote
or the issue at hand.

> The same distinction can be found in J.S.Bachs score
> for clarino parts espicially composed for his famous trumpeter
> Gottfried Reiche in Leipzig.

Likewise.

> Bach learned discriminating that at first form his own father
> Ambrosius, later from his brother who were both professional
> <Stadtpfeifers>=<offical trumpeter/hornist of town>
> Remember:
> At baroque time trumpets and horns had generally none valves as
today.
> So the ratios: 16:17:18:19:20 were quite common used in order
> to express sharp and flat accidentials.

If these numbers represent the resonance modes that the horns are
being overblown to, they don't necessarily coincide with the true
harmonic partials of their spectra. And anyway what we are talking
about is matching such partials by ear when two notes are played
simultaneously, not whether the resulting intervals happen to also
occur between different notes played at different times in the score.

> Only few generations later:
> Michael Hadyn, a brother of Josef extended that range
> upwards to the 26. partial for early classical musics,
> but only few trumpeters were able to master such high pitches.
> Bachs and Hadyns scores demand rapid melodic jumpes form 1 to 12
> partials up and down very frequently:
> All that had to be executed only by change of lip tension.
> Later:
> the Orgel theoretican JG Töpfer (1791 – 1870)
> distincts clearly the first 32 partials from each other
> only by his ears.
> I.m.o:
> The limit of discriminating just ratios depends on:
> 1. individual ablility
> 2. and it's training.

Again, all of this, including resolving upper partials (throat
singers do it all the time) seems completely unrelated to the
question of whether one can distinguish a set of just ratios from
other intervals. The space between the 31st and 32nd partials is 55
cents -- a huge interval by microtonal standards. Meanwhile, hearing
justness in ratios of 31 in general means that both 32/31 and 31/30
sound "special", and that for intervals larger than 32/31 and smaller
than 31/30, one would have to hear a region of "non-justness" or at
least some distinct-sounding, higher-number ratios. Since 32/31 and
31/30 are only 1.8 cents apart, we're talking about an ability to
discriminate intervals that differ by less than a cent. Not
impossible, but a far cry from merely hearing the 31st and 32nd
partials clearly!