RE: [tuning] infinite/finite

Neil -- just intonation does not have to be thought of as being a
represenation of the harmonic series. It can simply be thought of as a
tuning system built up from the most acoustically blending intervals, which
turn out to be simple ratios such as 3/2, 5/3, etc. Also, the infinite
lattice Polychroni was referring to could simply be an infinite chain of
3/2s and 4/3s, or a 2-dimensional grid of 3/2s and 5/4s, or a 7-limit
lattice, etc.; you don't need to go infinitely high in the harmonic series
to get an infinite JI set of pitches. -- Paul

> Paul Erlich wrote:
>
> >
> >But you could of course create a 1-to-1 mapping that includes all
quadrants.
> >The relevance of which is?
>

I was considering my "1" to be the southwestern-most pitch encountered, so
quadrants are irrelevant.

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.

You betcha!

-----Original Message-----
From: David Beardsley [mailto:xouoxno@virtulink.com]
Sent: Wednesday, April 19, 2000 6:19 PM
To: tuning@egroups.com
Subject: Re: [tuning] infinite/finite

"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.
Classmates.com has them all. And with 4.4 million alumni already
registered, there's a good chance you'll find your friends here:
http://click.egroups.com/1/2886/1/_/239029/_/956186458/
------------------------------------------------------------------------

You do not need web access to participate. You may subscribe through
email. Send an empty email to one of these addresses:
tuning-subscribe@egroups.com - join the tuning group.
tuning-unsubscribe@egroups.com - unsubscribe from the tuning group.
tuning-nomail@egroups.com - put your email message delivery on hold for
the tuning group.
tuning-digest@egroups.com - change your subscription to daily digest mode.
tuning-normal@egroups.com - change your subscription to individual emails.

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.
> Classmates.com has them all. And with 4.4 million alumni already
> registered, there's a good chance you'll find your friends here:
> http://click.egroups.com/1/2886/1/_/239029/_/956186458/
> ------------------------------------------------------------------------
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@egroups.com - join the tuning group.
> tuning-unsubscribe@egroups.com - unsubscribe from the tuning group.
> tuning-nomail@egroups.com - put your email message delivery on hold for
the tuning group.
> tuning-digest@egroups.com - change your subscription to daily digest
mode.
> tuning-normal@egroups.com - change your subscription to individual
emails.

------------------------------------------------------------------------
Good friends, school spirit, hair-dos you'd like to forget.
Classmates.com has them all. And with 4.4 million alumni already
registered, there's a good chance you'll find your friends here:
http://click.egroups.com/1/2885/1/_/239029/_/956188921/
------------------------------------------------------------------------

You do not need web access to participate. You may subscribe through
email. Send an empty email to one of these addresses:
tuning-subscribe@egroups.com - join the tuning group.
tuning-unsubscribe@egroups.com - unsubscribe from the tuning group.
tuning-nomail@egroups.com - put your email message delivery on hold for
the tuning group.
tuning-digest@egroups.com - change your subscription to daily digest mode.
tuning-normal@egroups.com - change your subscription to individual emails.