Yahoo Tuning Groups Ultimate Backup tuning Re: [tuning] infinite/finite

Neil!
I will have to disagree with you here. In certain contexts Higher Harmonics are not only
perceptible but are preferred by the ear. Navarro probably lies at the lead of those chords
formed out of the superposition of harmonic steps. In example 17-23-29-35-41-47-53-59 (all
separated by 6, take 4 at a time in sequence, {666!} lots of primes) . If you change one of
these, the consonance falls apart. We hear commas all the time. In the case of the 256/243 we
learn the sound directly, the ear does not run up so many 5th and 3rds to process it. La
Monte Young is already up into the 200's, he has a long way to go, but he is examining each
step not to miss a thing on the way. I have tunings that use up into the thousands ( occurring
in Navarro like contexts). In 1975 people told me they couldn't hear the difference with 31
tones, latter it just sounded like out of tune 12. The human ear and mind is capable of
processing such a great degree of perceptible data that is astounding. In the realm of light ,
under the best circumstances the eye can detect a singe photon. Why would we assume that the
human ear be that much worse!
This argument usually goes with the idea how long you hold the interval. There is another
case. It took me a few years (my first exposure) to have 31 soak in to the points when I could
not stand the whole tone. The nature of tuning over a long period of time will reveal itself.

Neil Haverstick wrote:

> One of the things about the higher harmonics is the fact that, after
> a certain point, we cannot hear them (sorry, I don't know just where
> that point is scientifically). They are "brought down mathematically" to
> be within the scope of human hearing. I think of this as tempering the
> harmonic series, in a way...we are not actually hearing the REAL note,
> we are hearing a lower octave representation of that pitch. It would be
> fascinating if human hearing was broader, and we could hear those real
> high pitches...but, we can't. I like to keep that in mind as I listen to
> music that uses these unhearable intervals...Hstick

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

🔗johnlink@con2.com

Paul Erlich wrote:

>That's not a one-to-one mapping of the 3x5 lattice to the harmonic series,
>only of the first quadrant of the 3x5 lattice to the harmonic series. So
>this statement doesn't seem right:
>
>>if
>>you have an infinite set of JI pitches, their membership will correspond
>one
>>to one with the membership of the (likewise infinite) harmonic series, even
>>though the first series is a sieved subset of the second...
>
>especially if you keep track of factors of 2, which were Haverstick's main
>concern.
>
>But you could of course create a 1-to-1 mapping that includes all quadrants.
>The relevance of which is?

My question as well. The existence of a 1-to-1 mapping is simply the result
of the fact that both sets in question are countably infinite.

John Link

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🔗David Beardsley <xouoxno@virtulink.com>

🔗ppagano@bellsouth.net

There is an infinite set of points between 1/1 and 2/1 No?
all harmonics should be included inside them.
take it away ......Daniel
Pat

David Beardsley wrote:

> "Paul H. Erlich" wrote:
> >
> > >Look, Haverstick complained about JI going high up in the harmonic series.
> > >Erlich responded with:
> >
> > >"you don't need to go infinitely high in the harmonic series
> > >to get an infinite JI set of pitches"
> >
> > >which is nonsense.
> >
> > It's not nonsense at all. If all voices and instruments only produced the
> > first 6 harmonics, we'd still have the same, infinite 5-limit JI lattice.
>
> I thought JI IS an infinite set of pitches.
>
> --
> * D a v i d B e a r d s l e y
> * xouoxno@virtulink.com
> *
> * 49/32 R a d i o "all microtonal, all the time"
> * M E L A v i r t u a l d r e a m house monitor
> *
> * http://www.virtulink.com/immp/lookhere.htm
>
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🔗David Beardsley <xouoxno@virtulink.com>

🔗ppagano@bellsouth.net

Sorry David there was like 400 infinite/finite ones i just picked one
i don't think i had my browser to display them in order but by person
sorry if i wacked the threads
Pat

"Paul H. Erlich" wrote:

> Pat, that's exactly the idea Neil Haverstick was originally objecting to,
> since octave transposition is required to bring those harmonics down into an
> audible octave. Now go back and read how I responded to Neil.
>
> -----Original Message-----
> From: ppagano@bellsouth.net [mailto:ppagano@bellsouth.net]
> Sent: Wednesday, April 19, 2000 7:02 PM
> To: tuning@egroups.com
> Subject: Re: [tuning] infinite/finite
>
> There is an infinite set of points between 1/1 and 2/1 No?
> all harmonics should be included inside them.
> take it away ......Daniel
> Pat
>
> David Beardsley wrote:
>
> > "Paul H. Erlich" wrote:
> > >
> > > >Look, Haverstick complained about JI going high up in the harmonic
> series.
> > > >Erlich responded with:
> > >
> > > >"you don't need to go infinitely high in the harmonic series
> > > >to get an infinite JI set of pitches"
> > >
> > > >which is nonsense.
> > >
> > > It's not nonsense at all. If all voices and instruments only produced
> the
> > > first 6 harmonics, we'd still have the same, infinite 5-limit JI
> lattice.
> >
> > I thought JI IS an infinite set of pitches.
> >
> > --
> > * D a v i d B e a r d s l e y
> > * xouoxno@virtulink.com
> > *
> > * 49/32 R a d i o "all microtonal, all the time"
> > * M E L A v i r t u a l d r e a m house monitor
> > *
> > * http://www.virtulink.com/immp/lookhere.htm
> >
> > ------------------------------------------------------------------------
> > Good friends, school spirit, hair-dos you'd like to forget.
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Re: [tuning] infinite/finite

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗johnlink@con2.com

🔗David Beardsley <xouoxno@virtulink.com>

🔗ppagano@bellsouth.net

🔗David Beardsley <xouoxno@virtulink.com>

🔗ppagano@bellsouth.net