The one that doesn't talk about numbers (was: JI definitions...)

> From: dkeenanuqnetau <d.keenan@uq.net.au>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, January 27, 2002 9:52 PM
> Subject: [tuning] Re: JI definitions and concepts (for Monz's dictionary)
>
>
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > What happened to Dave Keenan's definition of JI? Taken from the
> > dictionary, no less?
>
> Er yeah? The one based on the Oxford English Dictionary definition.
> The one that doesn't talk about numbers at all, but about how it
> _sounds_.

Er ... I just posted it a little while ago.
Here it is again, uncluttered.

> Dave Keenan:
> message 15836 (Thu Nov 23, 2000 11:39pm)
> /tuning/topicId_15836.html#15836?expand=1
>
>
> >> The Shorter Oxford English Dictionary on Historical Principles.
> >> Just
> >> /Mus./ in /just interval/, etc. :
> >> Harmonically pure; sounding perfectly in tune. 1811.

-monz

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In: /tuning/topicId_33254.html#33254
Margo Schulter posted:

I see the range of perspectives as much larger, with the best
solution maybe being simply to make explicit the different
assumptions and levels of meaning
often attached to the "JI" category.

Incidentally, I might speak specifically of RI -- as opposed
to "JI" -- for a system which seems mainly designed to emulate
some kind of irrational temperament.

If a system features some pure versions of simple ratios,
and especially if it has an epimoric kind of structure,
then I'd freely call it either JI or RI. A Pythagorean
or 3-limit RI system I also consider JI,
since it includes pure concords of 3:2 and
4:3, and also epimore steps of 9:8.
___________________________________

In: /tuning/topicId_33284.html#33284
Robert Valentine posted:

Personally, I think the Just Intonation Network definition
www.dnai.com/~jinetwk
is a good definition describing what modern practitioners
mean when they say that they are working in just intonation.

> "JUST INTONATION is any system of tuning in which all of the
> intervals can be represented by ratios of whole numbers,
> with a strongly-implied preference for the smallest numbers
> compatible with a given musical purpose."
___________________________________________

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> > From: dkeenanuqnetau <d.keenan@u...>
> > To: <tuning@y...>
> > Sent: Sunday, January 27, 2002 9:52 PM
> > Subject: [tuning] Re: JI definitions and concepts
> >(for Monz's dictionary)
> >
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > > What happened to Dave Keenan's definition of JI?
> > > Taken from the dictionary, no less?
> >
> > DK: Er yeah? The one based on the Oxford English
> > Dictionary definition.
> > The one that doesn't talk about numbers at all,
> > but about how it _sounds_.

> JM: Here it is again, uncluttered.
>
> > Dave Keenan:
> > message 15836 (Thu Nov 23, 2000 11:39pm)
> > /tuning/topicId_15836.html#15836?expand=1
> >
> > >> The Shorter Oxford English Dictionary
> > >> on Historical Principles.
> > >> Just
> > >> /Mus./ in /just interval/, etc. :
> > >> Harmonically pure; sounding perfectly in tune. 1811.
___________________________________________________________

J Gill:

When we use the phrase "harmonically pure; sounding
perfectly in tune", should one assume that such a phrase
"doesn't talk about numbers at all,
but about how it _sounds_"?

Does such a *disassociation* between statements such as

"pure versions of simple ratios"

"ratios of whole numbers, with a strongly-implied
preference for the smallest numbers compatible
with a given musical purpose"

and "harmonically pure; sounding perfectly in tune"

preclude the discussion from such "talking about numbers",
thus relegated to only discussing "how it _sounds_"?

If so, of what use are all these mathematical constructs
which attempt to conceptually characterize "tunings"?

While such constructs may describe alignments of sources
generating sinusoidal frequencies only ("twinky tones"),
such constructs appear to belie the reality that sensory
impressions relating to the *combinations* of multiple
tones, such as "sounding perfectly in tune", as well as
"harmonically pure" arise (primarily in the former case,
and exclusively in the latter case) out of the perception
of *complex tones* (including the harmonics of a sinusoidal
fundamental frequency in addition to the presence of an
isolated sinusoidal frequency itself), as opposed to
arising out of the perceptions of *sinusoidal tones*.

To say that "all sounds respresent the combination of
sinusoids", as if that makes simple combinations of
a few "twinky tones" a valid description of spectral
timbral realities, represents a vast over-simplification
of timbral realities, and one which is made in the interest
of attempting to support the alleged validity of conceptual
mathematical models which fall short of encompassing those
timbral realities. Why should we so delude ourselves? Why?

Tonal timbre, then, once again rears its (ugly due to it's
mathematical complexity, yet beautiful due to it's effects)
head. In what systematic manner do such "tuning systems"
address this implicit matter of the timbre of the *complex
tones* (as opposed to "twinky-tones") which, with rare
exception, represents the *actual* spectral reality which
exists when musicians sit down to play their instruments?

Curiously, J Gill

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> Er ... I just posted it a little while ago.
> Here it is again, uncluttered.

Sorry I missed that Monz. Thanks for that. But of course lots of folk
helped me elaborate and refine it considerably (and address many
objections) from that minimal OED entry. Unfortunately I don't have
time now to go back thru the thread and reconstruct some kind of
"final" version. If you've included in your dictionary entry the URL
for the start of that thread, that will have to do for now. Thanks.

I'd like to offer a somewhat belated apology to Bill Alves. I think I
was a bit rude to him towards the end of that thread. Sorry Bill.

-- Dave Keenan

Hi J,

> From: unidala <JGill99@imajis.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, January 28, 2002 1:34 PM
> Subject: [tuning] Re: The one that doesn't talk about numbers (was: JI
definitions...)
>
>
> When we use the phrase "harmonically pure; sounding
> perfectly in tune", should one assume that such a phrase
> "doesn't talk about numbers at all,
> but about how it _sounds_"?
>
> Does such a *disassociation* between statements such as
>
> "pure versions of simple ratios"
>
> "ratios of whole numbers, with a strongly-implied
> preference for the smallest numbers compatible
> with a given musical purpose"
>
> and "harmonically pure; sounding perfectly in tune"
>
> preclude the discussion from such "talking about numbers",
> thus relegated to only discussing "how it _sounds_"?
>
> If so, of what use are all these mathematical constructs
> which attempt to conceptually characterize "tunings"?

Ah ... now you're bumping into the same wall I did a few
years ago which led me to formulate my concept of "finity"
http://www.ixpres.com/interval/dict/finity.htm

In fact, this is exactly what's at the root of the whole
heated debate over how to precisely define "just intonation".

Intervals and larger sound-conglomerates whose frequencies
can be compared as low-integer ratios reveal that the
lowest primes (as factors in the ratio terms) clearly have
a distinctive audible affect, which is why they are important
to tuning theory.

However -- and it's a very big however -- the human auditory
system fails to appreciate differences between these low-integer
ratios and other more complex intervallic relationships
(higher-prime terms, irrationals, etc.) which closely
approximate these low-integer ratios. Thus, the acceptability
of temperament.

Many of us here feel that to a large extent the meaning of
"just intonation" *must* be associated primarily with the
*sound* of intervals and tunings and not simply with only
their mathematical underpinning.

Your subsequent thoughts on how timbre falls into this are
interesting, and somewhat related to the work done by
Wendy Carlos and Bill Sethares.

-monz

_________________________________________________________
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--- In tuning@y..., "monz" <joemonz@y...> wrote:

> Many of us here feel that to a large extent the meaning of
> "just intonation" *must* be associated primarily with the
> *sound* of intervals and tunings and not simply with only
> their mathematical underpinning.

I lean in this direction, it being a more meaningful one, and give
highest props to Dave Keenan and others who have argued in this
direction, but I've also cautioned that the numerically-based
definitions have had a lot of historical importance in the literature
of this topic and one cannot expect to communicate with others in
this field without taking that into account.

On that latter note, your decision to include Lindley's article in
your definition was tremendous. I applaud you, Monz!

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, January 29, 2002 12:43 PM
> Subject: [tuning] Re: The one that doesn't talk about numbers (was: JI
definitions...)
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > Many of us here feel that to a large extent the meaning of
> > "just intonation" *must* be associated primarily with the
> > *sound* of intervals and tunings and not simply with only
> > their mathematical underpinning.
>
> I lean in this direction, it being a more meaningful one, and give
> highest props to Dave Keenan and others who have argued in this
> direction, but I've also cautioned that the numerically-based
> definitions have had a lot of historical importance in the literature
> of this topic and one cannot expect to communicate with others in
> this field without taking that into account.
>
> On that latter note, your decision to include Lindley's article in
> your definition was tremendous. I applaud you, Monz!

Thanks, Paul. And _muchas muchas gracias_ to my anonymous
correspondent, who provided me with this big addition electronically.

Also, regardless of all the great data in the body of the Grove's
quotation, the main reason I wanted it here was for the bibliography.

I challenge all those who argued against my emphasis on the
historical definition of "JI = 5-limit" to take a look at the
books listed here, *then* tell me how valid/invalid my argument is.

Of course I believe that a modern definition of JI should
include reference to odd/prime-limits higher than 5, and
mine does. But the historical usage is important to me
and to many others.

-monz

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--- In tuning@y..., "paulerlich" <paul@s...> wrote:

> On that latter note, your decision to include Lindley's article in
> your definition was tremendous. I applaud you, Monz!

I think the whole thing was quite a piece of work--a dictionary entry I can learn from is always welcome.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_33287.html#33397

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > Many of us here feel that to a large extent the meaning of
> > "just intonation" *must* be associated primarily with the
> > *sound* of intervals and tunings and not simply with only
> > their mathematical underpinning.
>
> I lean in this direction, it being a more meaningful one, and give
> highest props to Dave Keenan and others who have argued in this
> direction, but I've also cautioned that the numerically-based
> definitions have had a lot of historical importance in the
literature
> of this topic and one cannot expect to communicate with others in
> this field without taking that into account.
>
> On that latter note, your decision to include Lindley's article in
> your definition was tremendous. I applaud you, Monz!

****Speaking of which, I didn't see any quotations or discussion by
Dave Keenan, who had some *wonderful* definitions and clarifications
on this list, as I recall...

Joseph

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> On that note, could someone *please* find out the maximum
> amount of stuff from this Grove's definition which I *can*
> legally quote?

There is no numerical maximum--that isn't the way the law is written or interpreted. You have the legal right to "fair use", which is defined in the law, but at what point the publisher would choose to challenge something as unfair would be up to them. An easy and highly effective way to stay out of trouble is not by quoting less than 500 words (an amount sometimes tossed out) but simply to remove anything they object to.

Because of the nature of your web page, your "fair use" priviledge should be pretty high, but fair use is a legal defense in case you were taken to court, which you presumably would not want even if you won.

> From: genewardsmith <genewardsmith@juno.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, January 29, 2002 8:57 PM
> Subject: [tuning] Re: The one that doesn't talk about numbers (was: JI
definitions...)
>
>
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > On that latter note, your decision to include Lindley's article in
> > your definition was tremendous. I applaud you, Monz!
>
> I think the whole thing was quite a piece of work--a dictionary
> entry I can learn from is always welcome.

Thanks, Gene. There's an awful lot of stuff crammed into my
Dictionary at this point -- I encourage you to browse around.
You might be surprised at how much you could learn from it.

(I say that, knowing that your background is in math moreso
than music ... and also because I've learned quite a bit
myself just from being the compiler of the Dictionary.)

Here are some interesting tidbits if you're looking for more:

http://www.ixpres.com/interval/dict/gamut.htm

http://www.ixpres.com/interval/dict/mutation.htm

http://www.ixpres.com/interval/dict/halberstadt.htm

http://www.ixpres.com/interval/dict/pyknon.htm

(Also note the link in the last one to my Tutorial on
tetrachord-theory. Folks here have also found my Aristoxenos
paper fascinating, but it's a mess and needs editing.)

-monz

_________________________________________________________
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Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_unknown.html#33435

> >
> > ****Speaking of which, I didn't see any quotations or discussion
by
> > Dave Keenan, who had some *wonderful* definitions and
clarifications
> > on this list, as I recall...
>
>
> Sheesh, gimme a break, Joe! You know how much work I've put
> into the Dictionary over the last month? A LOT! There's only
> so much I can do.
>

Sorry, Monz!

This really wasn't meant as a criticism of your terrific dictionary.
Upon reading it over, I guess much of that discussion is covered in
the Lindley, anyway, and you *did* include the link, after all...

JP

Many thanks to Joe Monzo for compiling his
Tuning Dictionary definition of Just Intonation.

Thanks to Paul Erlich for the interesting links
found in: /tuning/topicId_33433.html#33433
and /tuning/topicId_33433.html#33433
which address such interesting issues as octave perception,
as well as theory and research pertaining to "complex" tones!

Tons of good stuff to read! :)

In /tuning/topicId_33287.html#33309
I posted the following thoughts and questions:

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> > From: dkeenanuqnetau <d.keenan@u...>
> > To: <tuning@y...>
> > Sent: Sunday, January 27, 2002 9:52 PM
> > Subject: [tuning] Re: JI definitions and concepts
> >(for Monz's dictionary)
> >
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > > What happened to Dave Keenan's definition of JI?
> > > Taken from the dictionary, no less?
> >
> > DK: Er yeah? The one based on the Oxford English
> > Dictionary definition.
> > The one that doesn't talk about numbers at all,
> > but about how it _sounds_.

> JM: Here it is again, uncluttered.
>
> > Dave Keenan:
> > message 15836 (Thu Nov 23, 2000 11:39pm)
> > /tuning/topicId_15836.html#15836?expand=1
> >
> > >> The Shorter Oxford English Dictionary
> > >> on Historical Principles.
> > >> Just
> > >> /Mus./ in /just interval/, etc. :
> > >> Harmonically pure; sounding perfectly in tune. 1811.
___________________________________________________________

J Gill:

When we use the phrase "harmonically pure; sounding
perfectly in tune", should one assume that such a phrase
"doesn't talk about numbers at all,
but about how it _sounds_"?

Does such a *disassociation* between statements such as

"pure versions of simple ratios"

"ratios of whole numbers, with a strongly-implied
preference for the smallest numbers compatible
with a given musical purpose"

and "harmonically pure; sounding perfectly in tune"

preclude the discussion from such "talking about numbers",
thus relegated to only discussing "how it _sounds_"?

If so, of what use are all these mathematical constructs
which attempt to conceptually characterize "tunings"?

While such constructs may describe alignments of sources
generating sinusoidal frequencies only ("twinky tones"),
such constructs appear to belie the reality that sensory
impressions relating to the *combinations* of multiple
tones, such as "sounding perfectly in tune", as well as
"harmonically pure" arise (primarily in the former case,
and exclusively in the latter case) out of the perception
of *complex tones* (including the harmonics of a sinusoidal
fundamental frequency in addition to the presence of an
isolated sinusoidal frequency itself), as opposed to
arising out of the perceptions of *sinusoidal tones*.

To say that "all sounds respresent the combination of
sinusoids", as if that makes simple combinations of
a few "twinky tones" a valid description of spectral
timbral realities, represents a vast over-simplification
of timbral realities, and one which is made in the interest
of attempting to support the alleged validity of conceptual
mathematical models which fall short of encompassing those
timbral realities. Why should we so delude ourselves? Why?

Tonal timbre, then, once again rears its (ugly due to it's
mathematical complexity, yet beautiful due to it's effects)
head. In what systematic manner do such "tuning systems"
address this implicit matter of the timbre of the *complex
tones* (as opposed to "twinky-tones") which, with rare
exception, represents the *actual* spectral reality which
exists when musicians sit down to play their instruments?
__________________________________________________________

In:/tuning/topicId_33287.html#33387
Joe Monzo replied:

<< Ah ... now you're bumping into the same wall I did a few
years ago which led me to formulate my concept of "finity"
http://www.ixpres.com/interval/dict/finity.htm
_______________________________________________

JG: Well, I was speaking to the matter of "harmonic
coincidence" (without implying a phenomenon of a
slightly different frequency described by ratios
factorable by higher-valued prime numbers being
interpreted the as a similar "pitch-class" in a
scale).

Questions regarding "Monzo finity":

(1) How would we manage to isolate - the values of
prime numbers which happen to factor the numerators
and denominators of ratios which describe such ratios
"slightly different" in frequency from a low-numbered
intervallic ratio (such as 3/2) - from the possibility
of the limits of our perception in resolving small
variations in pitch resulting in effects similar to
the "bridging" effects proposed?

(2) How would we *objectively* determine that the
"aural mind" puts such a *higher-integer* ratiometric
frequency into a "bin" associated with a *lower-integer*
ratiometric frequency? Perhaps we, instead "bridge"
from *lower* to *higher*? How could we establish a
"one-way" system? Or do you see it as "bi-directional"?
_______________________________________________________

JM: In fact, this is exactly what's at the root of the whole
heated debate over how to precisely define "just intonation".

Intervals and larger sound-conglomerates whose frequencies
can be compared as low-integer ratios reveal that the
lowest primes (as factors in the ratio terms) clearly have
a distinctive audible affect, which is why they are important
to tuning theory.
__________________

JG: But, since there are *more* "lowest primes" per linear
section of integers which encompass the integer values of
those "lower primes" than in the case of higher primes,
how do we *know* that it is the *small numerical value*
primes which have "more" significance that the *large
numerical value* primes?

It seems to me that - in a system considering sinusoidal
sound source "voices" - the distinction of whether the
*lower* valued primes or the *higher* valued primes hold
a more significant place would be a hard thing to establish.

However, in a system considering "complex" (fundamental plus
harmonics) sound source "voices", we can see that the
"smallness" of the values of prime factors *is* in fact
*differentiable* (in the general, not mathematical sense),
due the phenomena related to "harmonic coincidence". Eh?
________________________________________________________

JM: However -- and it's a very big however -- the human auditory
system fails to appreciate differences between these low-integer
ratios and other more complex intervallic relationships
(higher-prime terms, irrationals, etc.) which closely
approximate these low-integer ratios. Thus, the acceptability
of temperament.
________________

JG: Thus, the "the acceptability of temperament" hinges
upon the human auditory system failing to "appreciate the
differences between these low-integer ratios and
other more complex intervallic relationships
(higher-prime terms, irrationals, etc.)"?
_________________________________________

JM: Many of us here feel that to a large extent the meaning of
"just intonation" *must* be associated primarily with the
*sound* of intervals and tunings and not simply with only
their mathematical underpinning.
_________________________________

JG: But, as Erlich pointed out, *that's* a real
"sticky-wicket" [in that musicians A and B could
rightfully argue until hell freezes over about
which tones are "pure" and (perhaps also) whether
two or more simultaneous tones are "perfectly in
tune", and when that musician passes away, no one
can possibly reproduce that musician's perceptions
relative to any new material]. "Job security" perhaps,
but where does that leave us? Speculating about the
possible underlaying mathematical relationships ....
_____________________________________________________

JM: Your subsequent thoughts on how timbre falls into this are
interesting, and somewhat related to the work done by
Wendy Carlos and Bill Sethares.
________________________________

JG: It seems that perhaps the justifications for
using a given tuning system (when the timbre it
is to be played with is "complex") must ultimately
address more issues than the number of frequencies
within those scales which exist in a ratio of 3/2
to each other (or a handful of other "consonances"),
and encompass the interplay between *all* other
possible frequencies (I wouldn't *dare* call them
pitches) which exist within a given scale. Eh?

J Gill :)

In my message #33473, I stated the following.

> JG: But, since there are *more* "lowest primes" per linear
> section of integers which encompass the integer values of
> those "lower primes" than in the case of higher primes,
> how do we *know* that it is the *small numerical value*
> primes which have "more" significance that the *large
> numerical value* primes?

JG: I add to the above statement:

Does the fact that there *are* "more of them" suffice?

A second question is expressed by the addition of the
following statement to the text quoted above:

How, also, do we determine whether it is the relative
"density" (per section of integers) of the "smaller
valued primes" which makes them "special", OR the
"smallness of the integers" (which turn out to be
largely prime integer values in the case of small
valued integers)?

J Gill :)

> From: unidala <JGill99@imajis.com>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, January 30, 2002 4:51 PM
> Subject: [tuning] Re: The one that doesn't talk about numbers (was: JI
definitions...)
>
>
> Many thanks to Joe Monzo for compiling his
> Tuning Dictionary definition of Just Intonation.

Thanks for the kudos, J (and Joe Pehrson too).

> When we use the phrase "harmonically pure; sounding
> perfectly in tune", should one assume that such a phrase
> "doesn't talk about numbers at all,
> but about how it _sounds_"?
>
> Does such a *disassociation* between statements such as
>
> "pure versions of simple ratios"
>
> "ratios of whole numbers, with a strongly-implied
> preference for the smallest numbers compatible
> with a given musical purpose"
>
> and "harmonically pure; sounding perfectly in tune"
>
> preclude the discussion from such "talking about numbers",
> thus relegated to only discussing "how it _sounds_"?
>
> If so, of what use are all these mathematical constructs
> which attempt to conceptually characterize "tunings"?

My own belief is that Paul's harmonic entropy concept is
a step in the direction of figuring all this out.

> Questions regarding "Monzo finity":
>
> (1) How would we manage to isolate - the values of
> prime numbers which happen to factor the numerators
> and denominators of ratios which describe such ratios
> "slightly different" in frequency from a low-numbered
> intervallic ratio (such as 3/2) - from the possibility
> of the limits of our perception in resolving small
> variations in pitch resulting in effects similar to
> the "bridging" effects proposed?

Again, I refer you to the harmonic entropy concept.

> (2) How would we *objectively* determine that the
> "aural mind" puts such a *higher-integer* ratiometric
> frequency into a "bin" associated with a *lower-integer*
> ratiometric frequency? Perhaps we, instead "bridge"
> from *lower* to *higher*? How could we establish a
> "one-way" system? Or do you see it as "bi-directional"?

Oh, I definitely see it as bi-directional in the sense you mean.

In tempered music or other cases where the composer / performer
makes abundant use of "puns", which I think of as being generally
the same as meaning that they are employing xenharmonic bridges,
our perception of harmony seems to bounce back and forth between
all kinds of possible rational interpretations ... one might
model this as "different harmonic perspectives".

All those perspectives are in effect all the time, and the
process is a very fluid and dynamic one.

And something I'm getting more and more interested in all
the time is how irrational and trancendental numbers relate
to my prime-affect ideas.

Of course, ultimately, my belief is that, whatever the mathematics
involved in the actual tuning, our understanding of our *perception*
of what we hear is grounded in perception of the lowest few primes.
So we're employing xenharmonic bridges all the time when we hear
any tuning that's not alread low-integer RI ("rational intonation").

> _______________________________________________________
>
>
> JM: In fact, this is exactly what's at the root of the whole
> heated debate over how to precisely define "just intonation".
>
> Intervals and larger sound-conglomerates whose frequencies
> can be compared as low-integer ratios reveal that the
> lowest primes (as factors in the ratio terms) clearly have
> a distinctive audible affect, which is why they are important
> to tuning theory.
> __________________
>
> JG: But, since there are *more* "lowest primes" per linear
> section of integers which encompass the integer values of
> those "lower primes" than in the case of higher primes,
> how do we *know* that it is the *small numerical value*
> primes which have "more" significance that the *large
> numerical value* primes?

I think I get the gist of what you're saying here, but it's
not too clear. Please elaborate, maybe with some examples.

> It seems to me that - in a system considering sinusoidal
> sound source "voices" - the distinction of whether the
> *lower* valued primes or the *higher* valued primes hold
> a more significant place would be a hard thing to establish.

Well, it's a foundation of my theory that the brain
"understands" the lowest primes far more easily than higher
ones. This would be primarily because our perception of
pitch is multiplicative rather than additive. The lowest
primes, as factors in ratios, form a sort of ultimate
reduced basis for our comprehension of harmonic relationships.

> However, in a system considering "complex" (fundamental plus
> harmonics) sound source "voices", we can see that the
> "smallness" of the values of prime factors *is* in fact
> *differentiable* (in the general, not mathematical sense),
> due the phenomena related to "harmonic coincidence". Eh?

Again, some examples would make your question clearer to me.

> ________________________________________________________
>
> JM: However -- and it's a very big however -- the human auditory
> system fails to appreciate differences between these low-integer
> ratios and other more complex intervallic relationships
> (higher-prime terms, irrationals, etc.) which closely
> approximate these low-integer ratios. Thus, the acceptability
> of temperament.
> ________________
>
> JG: Thus, the "the acceptability of temperament" hinges
> upon the human auditory system failing to "appreciate the
> differences between these low-integer ratios and
> other more complex intervallic relationships
> (higher-prime terms, irrationals, etc.)"?
> _________________________________________

Right, or to put it another way, the "acceptability of
temperament" hinges upon our (conscious or unconscious)
employment of "xenharmonic bridges".

>
> JM: Many of us here feel that to a large extent the meaning of
> "just intonation" *must* be associated primarily with the
> *sound* of intervals and tunings and not simply with only
> their mathematical underpinning.
> _________________________________
>
> JG: But, as Erlich pointed out, *that's* a real
> "sticky-wicket" [in that musicians A and B could
> rightfully argue until hell freezes over about
> which tones are "pure" and (perhaps also) whether
> two or more simultaneous tones are "perfectly in
> tune", and when that musician passes away, no one
> can possibly reproduce that musician's perceptions
> relative to any new material]. "Job security" perhaps,
> but where does that leave us? Speculating about the
> possible underlaying mathematical relationships ....
> _____________________________________________________

Right ... and that's exactly what all of us heavy-duty
tuning theorists find so interesting.

In a sense, I really feel that all the exploration going on
at tuning-math, as well as the tremendous amount of similar
stuff from the past that's sitting in the tuning literature,
is nothing other than attempts to quantize how finity works.

> JM: Your subsequent thoughts on how timbre falls into this are
> interesting, and somewhat related to the work done by
> Wendy Carlos and Bill Sethares.
> ________________________________
>
> JG: It seems that perhaps the justifications for
> using a given tuning system (when the timbre it
> is to be played with is "complex") must ultimately
> address more issues than the number of frequencies
> within those scales which exist in a ratio of 3/2
> to each other (or a handful of other "consonances"),
> and encompass the interplay between *all* other
> possible frequencies (I wouldn't *dare* call them
> pitches) which exist within a given scale. Eh?

I absolutely postively definitely agree with you there!

The way the human auditory system works, is turning out to
be far more complex than anyone used to think. There seem
to be all kinds of non-linearities involved, for example.
(Attending the ISMA conference in Perugia last September
was very enlightening to me in this respect.)

Certainly, the only way to develop a really comprehensive
theory about tuning is to take into account not only the
mathematics of tuning, but lots of other things too, such
as the workings of the human auditory system, the history
of tuning-theory, perhaps other aspects of psychology besides
psychoacoustics, etc. We're still just babies playing with
rattles compared to what lies ahead.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "unidala" <JGill99@i...> wrote:
> In my message #33473, I stated the following.
>
> > JG: But, since there are *more* "lowest primes" per linear
> > section of integers which encompass the integer values of
> > those "lower primes" than in the case of higher primes,
> > how do we *know* that it is the *small numerical value*
> > primes which have "more" significance that the *large
> > numerical value* primes?
>
> JG: I add to the above statement:
>
> Does the fact that there *are* "more of them" suffice?
>
>
> A second question is expressed by the addition of the
> following statement to the text quoted above:
>
> How, also, do we determine whether it is the relative
> "density" (per section of integers) of the "smaller
> valued primes" which makes them "special", OR the
> "smallness of the integers" (which turn out to be
> largely prime integer values in the case of small
> valued integers)?
>
>
> J Gill :)

I attempted to explain my view of these and your previous questions
in a private e-mail to you. I hope you will accept my humble attempts
to shed light on your puzzles, and I expect nothing in return. Maybe
you could come to see me play someday if I ever come to the Northwest.

--- In tuning@y..., "unidala" <JGill99@i...> wrote:
> JM: Many of us here feel that to a large extent the meaning of
> "just intonation" *must* be associated primarily with the
> *sound* of intervals and tunings and not simply with only
> their mathematical underpinning.
> _________________________________
>
> JG: But, as Erlich pointed out, *that's* a real
> "sticky-wicket" [in that musicians A and B could
> rightfully argue until hell freezes over about
> which tones are "pure" and (perhaps also) whether
> two or more simultaneous tones are "perfectly in
> tune",

They could. But the fact is they don't. Or at least only rarely and
only in the more obscure cases. Try the experiment. Several musicians
asked to tune up a just fifth by ear on the same polyphonic instrument
will all get pretty close to the same result, provided they know
what a just fifth is and are capable of tuning anything by ear, and
provided the instrument has a close to harmonic timbre.

> and when that musician passes away, no one
> can possibly reproduce that musician's perceptions
> relative to any new material]. "Job security" perhaps,
> but where does that leave us? Speculating about the
> possible underlaying mathematical relationships ....

Any visual artists out there should correct me if I'm wrong but isn't
it the case that such artists agree well enough about what constitutes
a "pure" colour of a particular hue and what are tints and shades of
that hue, without the benefit of mathematics or the ability to tune
their palette by ratios. I think this is highly analogous.

I'm quite certain that a purely perceptual definition of justness is
possible. Of course it will always have fuzzy edges, but many useful
definitions are of that kind? Such a definition must be at least
partly _injunctive_. That means it consists partly of instructions or
recipes or injunctions of the form "Do <this> and you will hear
<this>".

Regards,
-- Dave Keenan

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "unidala" <JGill99@i...> wrote:
> > JM: Many of us here feel that to a large extent the meaning of
> > "just intonation" *must* be associated primarily with the
> > *sound* of intervals and tunings and not simply with only
> > their mathematical underpinning.
> > _________________________________
> >
> > JG: But, as Erlich pointed out, *that's* a real
> > "sticky-wicket" [in that musicians A and B could
> > rightfully argue until hell freezes over about
> > which tones are "pure" and (perhaps also) whether
> > two or more simultaneous tones are "perfectly in
> > tune",
>
> They could. But the fact is they don't. Or at least only rarely and
> only in the more obscure cases. Try the experiment. Several musicians
> asked to tune up a just fifth by ear on the same polyphonic instrument
> will all get pretty close to the same result, provided they know
> what a just fifth is and are capable of tuning anything by ear, and
> provided the instrument has a close to harmonic timbre.

JG: Provided that they are (1) musicians, (2) "know" what
a "fifth" is, (3) are capable of tuning by ear, and (4) are making sounds with a (close to) harmonic timbre (where additional "cues" exist relative to a strictly "sinusoidal" case.

But what of the many *other* ratios which are commonly
referred to as "JI" ratios. What of 16/15, 9/8, 10/9, 6/5,
5/4, 4/3, 8/5, 5/3, 9/5, 16/9, 15/8? Would you say the
same about those ratios? What about their strictly sinusoidal
cases (as opposed to harmonic "cues" being present in the
tones)? What about the (entirely) "harmonic" case (where
*all* harmonics of each tone were present)?
>
> > and when that musician passes away, no one
> > can possibly reproduce that musician's perceptions
> > relative to any new material]. "Job security" perhaps,
> > but where does that leave us? Speculating about the
> > possible underlaying mathematical relationships ....
>
> Any visual artists out there should correct me if I'm wrong but isn't
> it the case that such artists agree well enough about what constitutes
> a "pure" colour of a particular hue and what are tints and shades of
> that hue, without the benefit of mathematics or the ability to tune
> their palette by ratios. I think this is highly analogous.

JG: When I choose colors in PaintShop Pro, I use what I like,
as well as what translates in ways that I like to a printed page.
I do not think about "purity" (though there may be those
who do). It seems highly subjective to me ...

But I am more interested in what *you* consider as "pure"
*sound*. I recall (please correct me if I am wrong, guys)
reading an older thread on ATL between you and Monz, where
Monz indicated that he considered the "major triad" as being
"more consonant" (than a minor triad), while you appeared
to indicate that you considered the *minor triad* to be
"more consonant" (than a major triad). I tend to agree
with you. But where does that leave us? Is Monz "wrong"?

If I could show mathematical reasons relating to the
physics of resonators which tended to favor certain
characteristics of a "minor triad" over a "major triad",
would that make Monz any more (or less) "wrong" or "right"?

I do not think so. As a consequence, can we ascribe a sense
of "objectivity" to our "tonal druthers" even with the evident
agreement between you and I, and physical evidence which
relates to the spectra of resonators? None of these things
could (or should) make Monz's opinion "wrong" in this matter.

Therefore (even with interesting numbers), the nature of the
(subject-ive) subject of perception seems to preclude us from
declaring a democratic (statistical) or physical evidentiary
(speculative conceptual) objective "knowledge claim" in the
matter. Would it be different (or simpler) if we were painters?

About "perfectly in tune". Would the agreement enabled by the
perception of beats between harmonics of the fundamentals be
as unanimous if there were no overtones to "cue" upon (as in
the strictly sinusoidal case)? Ears disagree nevertheless.
Only those with "good ears" can appreciate the subtle beauty
which is surely missed with those of "tin ears" (who proceed
unawares of what they are "missing"). Therefore, the sense of
"objectivity" (relating to "perfect tuning") can only extend
to those who report sensory acuity exceeding any "democratic"
population "averages". The "definition" can only be "known"
by those who *already* "understand". When I am gone, will you
"know" what I "would have meant" by "perfectly in tune" when
you "hear it (for) yourself"?

> I'm quite certain that a purely perceptual definition of justness is
> possible. Of course it will always have fuzzy edges, but many useful
> definitions are of that kind? Such a definition must be at least
> partly _injunctive_. That means it consists partly of instructions or
> recipes or injunctions of the form "Do <this> and you will hear
> <this>".

JG: I agree that Nature is indifferent to simplicity,
and that the "knowledge" we speak of is an "indwelled
knowledge" accessible only via direct (aural) experience.

It does seem, though, that all "recipes or injunctions"
must leave room for "personal taste", and in doing so,
one has no certainty as to the "definition" (of an
experience) as it exists in the mind of "another".

How would one then ensure that such a "definition"
would "mean what one had intended it to mean (to others)"?

Regards, J Gill :)

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_33287.html#33487

>
> Any visual artists out there should correct me if I'm wrong but
isn't it the case that such artists agree well enough about what
constitutes a "pure" colour of a particular hue and what are tints
and shades of that hue, without the benefit of mathematics or the
ability to tune their palette by ratios. I think this is highly
analogous.

****I believe this stuff is *incredibly* standardized, particularly
in areas of "graphic design." I believe that's what the "Pantone"
standard is all about, or something like that...

JP

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

/tuning/topicId_33287.html#33495

> JG: I agree that Nature is indifferent to simplicity,
> and that the "knowledge" we speak of is an "indwelled
> knowledge" accessible only via direct (aural) experience.
>
> It does seem, though, that all "recipes or injunctions"
> must leave room for "personal taste", and in doing so,
> one has no certainty as to the "definition" (of an
> experience) as it exists in the mind of "another".
>
> How would one then ensure that such a "definition"
> would "mean what one had intended it to mean (to others)"?
>
>
> Regards, J Gill :)

****Actually, what we're "seeing" here... or rather, what we're
*hearing* here :) is actually *philosophy* as much as tuning.

This is one of the most pervasive and discussed topics in classical
philosophy, as I'm sure you know.

Going back to Plato, all these "cats" found it important to debate
whether there was *any* commonality in perception whatsoever from one
person to the next.

Also, whether there were truly *tangible* objects, or whether, as in
the case of Plato, everything consisted only of "forms" in the head.

Tuning certainly *does* intersect perception and philosophy... and it
seems authors (Mathieu??) are addressing this more presently...

JP

--- In tuning@y..., "unidala" <JGill99@i...> wrote:
> JG: Provided that they are (1) musicians, (2) "know" what
> a "fifth" is, (3) are capable of tuning by ear, and (4) are making
sounds with a (close to) harmonic timbre (where additional "cues"
exist relative to a strictly "sinusoidal" case.
>

Even in the sinusoidal case, nonlinearities in the ear/brain will
generate harmonics, unless the sound is very quiet.

> But what of the many *other* ratios which are commonly
> referred to as "JI" ratios. What of 16/15, 9/8, 10/9, 6/5,
> 5/4, 4/3, 8/5, 5/3, 9/5, 16/9, 15/8? Would you say the
> same about those ratios? What about their strictly sinusoidal
> cases (as opposed to harmonic "cues" being present in the
> tones)? What about the (entirely) "harmonic" case (where
> *all* harmonics of each tone were present)?

The perceptual definition of just _must_ consider the context. What is
just in one context may not be so in another. If we are asking whether
a particular scale is just, I suggest we accept an interval as just if
it can be tuned by listening for slow beats in any context that can be
provided by the rest of the scale. Then if the scale's
just-interval-graph is connected, (where vertices are the pitches and
edges are the just intervals), I'd call the scale just.

I value this discussion, but you could save me a lot of time, and
others some boredom, if you would go back and read thru the thread
starting from the URL in Monz's JI dictionary entry. I've covered a
lot of this stuff before.

> JG: When I choose colors in PaintShop Pro, I use what I like,
> as well as what translates in ways that I like to a printed page.
> I do not think about "purity" (though there may be those
> who do). It seems highly subjective to me ...

It may be simply that no one has ever pointed out to you what pure
colours are. As in "Look at this colour chart. Here are some examples
of pure colours. Now these other ones are colours of the same hue but
different degrees of purity (or saturation). This one is really close
to pure. So now do you get what we mean by "pure"? Do you think this
one is pure?" And so on.

We can do the same thing to teach people what we mean by "just"
for harmony. Maybe twanging a few guitar strings simuktaneously and
varing the pitch of one string while saying stuff like "Hear how
there's a sort of beating effect that slows down and then speeds up
again. When it's so slow that you can only tell its there by listening
for longer than any sustained harmonies you intend to use in actual
music, then that's called "just"." The definition is refined by
listening to more things which are near the boundary and having people
tell you whether they are generally considerd to be just in or just
out of Just. Popular borderline cases are the Hammond Organ,
Barbershop singing and La Monte Young's dream house. I understand most
people would exclude the Hammond and include the other two.

A context-sensitive perceptually-based definition seems to work for
this, although it may make sense to say that the Hammond is just for
those timbres (stop settings) where there are partials whose
relationship to the fundamental is the same as the intervals of the
scale (essentially 12-tET). This is the inharmonic Sethares type of
"justness" that is still unclear (to me) how it should be classified.
It has nothing to do with the fact that the Hammond uses rational
frequency ratios. But to me, the Hammond tuning, when using a nearly
simusoidal timbre, is not just, despite being entirely based on
strict ratios of whole-numbers less than 100.

> But I am more interested in what *you* consider as "pure"
> *sound*.

Now wait a minute. I'm concerned that you think there is some value
judgment (good/bad) involved in the use of the word "pure" here. There
isn't. In both colour and harmony (note: not merely sound) the word
"pure" has a technical meaning that has very little to do with the
word's common usage. Same for "just". In this context "pure" is simply
a synonym for "just".

> I recall (please correct me if I am wrong, guys)
> reading an older thread on ATL between you and Monz, where
> Monz indicated that he considered the "major triad" as being
> "more consonant" (than a minor triad), while you appeared
> to indicate that you considered the *minor triad* to be
> "more consonant" (than a major triad). I tend to agree
> with you. But where does that leave us? Is Monz "wrong"?

I doubt very much I would ever have said that. Certainly not for a
4:5:6 major versus a 1/(6:5:4) (i.e. 10:12:15) minor. But hey I don't
want to get into defining consonance.

...
> Therefore (even with interesting numbers), the nature of the
> (subject-ive) subject of perception seems to preclude us from
> declaring a democratic (statistical) or physical evidentiary
> (speculative conceptual) objective "knowledge claim" in the
> matter. Would it be different (or simpler) if we were painters?

Yes it would be different (simpler) if we were painters. Mathematical
modelling of colour perception is essentially complete and we have
internationally accepted standards based on it. We can now give
precise mathematical specifications of what we mean by particular
colours. Obviously we had to rely on the consensus (or statistical
combination of opinions) of experts to give names to particular
regions of mathematically-modelled colour space.

We are far from that in modelling perception of harmony. The time
dimension seems to make it difficult for one thing. The problem is
that people are trying to give a mathematical definition of "just",
way too early in the piece and failing to recognise the
contradictions they create.

Where do people get this idea that merely because something is
subjective one has to accept that anyone's version of the concept is
as good as anyone elses. This is nonsense. Actually I think it derives
from some of the popular fallacies of post-modernism that ride
roughshod over (or ignore) what has been discovered in hermeneutics.
If you want to know more about the problems of post-modernism, read
any recent book by Ken Wilber. Actually, wait for his first _novel_
due out in April and have some laughs too.

> About "perfectly in tune". Would the agreement enabled by the
> perception of beats between harmonics of the fundamentals be
> as unanimous if there were no overtones to "cue" upon (as in
> the strictly sinusoidal case)?

No.

> Ears disagree nevertheless.
> Only those with "good ears" can appreciate the subtle beauty
> which is surely missed with those of "tin ears" (who proceed
> unawares of what they are "missing").

Yes. The thing is that "good ears" are defined by the fact that they
are by far the largest group that all tend to agree with each other.
The "tin ears" not only don't agree with the "good ears" but they
don't agree with each other either.

This is certainly not a foolproof way of defining things or deciding
whether there is "really something there" in general, as our
"democratic" systems of government should make clear. Although a major
problem here is that is that there can probably never be any experts
in "making everybody happy at the same time" and most people are so
far from knowing anything at all about that (or even caring about it),
that it isn't funny.

> Therefore, the sense of
> "objectivity" (relating to "perfect tuning") can only extend
> to those who report sensory acuity exceeding any "democratic"
> population "averages".

Not those who merely report, but those who form the largest-by-far
community of people who agree with each other (if not on the fine
details at least on the bulk of cases).

> The "definition" can only be "known"
> by those who *already* "understand". When I am gone, will you
> "know" what I "would have meant" by "perfectly in tune" when
> you "hear it (for) yourself"?

Not precisely no. But it doesn't matter, because it doesn't depend on
only you.

> JG: I agree that Nature is indifferent to simplicity,
> and that the "knowledge" we speak of is an "indwelled
> knowledge" accessible only via direct (aural) experience.
>
> It does seem, though, that all "recipes or injunctions"
> must leave room for "personal taste", and in doing so,
> one has no certainty as to the "definition" (of an
> experience) as it exists in the mind of "another".

Not total certainty, no. But a good enough degree of certainty
nonetheless. Enough to let us "just get on with it".

> How would one then ensure that such a "definition"
> would "mean what one had intended it to mean (to others)"?

The more time we spend listening to harmonies together and dialoguing
with another the more certain we will be.

But even if all we had was an ancient book describing justness and
there had been no continuity of shared experience. Provided the author
was not genetically radically different (think of colour-blindness) it
could still be communicated injunctively. We'd soon find that "there's
really something there".

-- Dave Keenan

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> If you want to know more about the problems of post-modernism, read
> any recent book by Ken Wilber. Actually, wait for his first _novel_
> due out in April and have some laughs too.

This is really funny. I'm currently reading (by very random
circumstances) Ken Wilber's big fat book.

> > Ears disagree nevertheless.
> > Only those with "good ears" can appreciate the subtle beauty
> > which is surely missed with those of "tin ears" (who proceed
> > unawares of what they are "missing").
>
> Yes. The thing is that "good ears" are defined by the fact that
they
> are by far the largest group that all tend to agree with each
other.
> The "tin ears" not only don't agree with the "good ears" but they
> don't agree with each other either.

The Mathews-Roberts experiment seemed to show two main classes of
untrained listeners. The "pure" group who liked just chords, and
the "rich" group who likes 15 cent errors from just. Neither group
liked or even was indifferent to 30 cent errors -- those were simply
bad. With a sample of 30-40 untrained subjects, there was not one
clear case of a "tin ear". I saw an estimate that tone deafness
occured in 2% of the population, which seems about right.
>
> > Therefore, the sense of
> > "objectivity" (relating to "perfect tuning") can only extend
> > to those who report sensory acuity exceeding any "democratic"
> > population "averages".
>
> Not those who merely report, but those who form the largest-by-far
> community of people who agree with each other (if not on the fine
> details at least on the bulk of cases).

And subjects of psychoacoustical experiments.

In-Reply-To: <a3cted+6hpk@eGroups.com>
dkeenanuqnetau wrote:

> Now wait a minute. I'm concerned that you think there is some value
> judgment (good/bad) involved in the use of the word "pure" here. There
> isn't. In both colour and harmony (note: not merely sound) the word
> "pure" has a technical meaning that has very little to do with the
> word's common usage. Same for "just". In this context "pure" is simply
> a synonym for "just".

So "just intonation" is defined as containing pure intervals, and "pure"
is a synonym for "just". Can anybody see the logical flaw here?

Graham

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > If you want to know more about the problems of post-modernism,
read
> > any recent book by Ken Wilber. Actually, wait for his first
_novel_
> > due out in April and have some laughs too.
>
> This is really funny. I'm currently reading (by very random
> circumstances) Ken Wilber's big fat book.

Which one? Brief history of Everything? I've mentioned him several
times before on this list, including when he wrote a foreword for a
book on music and spirituality.

> > Yes. The thing is that "good ears" are defined by the fact that
> they
> > are by far the largest group that all tend to agree with each
> other.
> > The "tin ears" not only don't agree with the "good ears" but they
> > don't agree with each other either.
>
> The Mathews-Roberts experiment seemed to show two main classes of
> untrained listeners. The "pure" group who liked just chords, and
> the "rich" group who likes 15 cent errors from just. Neither group
> liked or even was indifferent to 30 cent errors -- those were simply
> bad. With a sample of 30-40 untrained subjects, there was not one
> clear case of a "tin ear". I saw an estimate that tone deafness
> occured in 2% of the population, which seems about right.

Yes, but note that this isn't quite the right experiment. They don't
have to "like" the JI intervals they just have to recoignise that
there's something there and be able to find them again if allowed to
twiddle the knobs.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> >
> > > If you want to know more about the problems of
post-modernism,
> read
> > > any recent book by Ken Wilber. Actually, wait for his first
> _novel_
> > > due out in April and have some laughs too.
> >
> > This is really funny. I'm currently reading (by very random
> > circumstances) Ken Wilber's big fat book.
>
> Which one? Brief history of Everything?

no . . . sex, ecology, spirituality. i got through a little bit and then
started avoiding it . . . bought and read stephen hawking's
universe instead and now started miles beyond . . . don't know if
i'll even get back to the wilber . . .
>
> > > Yes. The thing is that "good ears" are defined by the fact
that
> > they
> > > are by far the largest group that all tend to agree with each
> > other.
> > > The "tin ears" not only don't agree with the "good ears" but
they
> > > don't agree with each other either.
> >
> > The Mathews-Roberts experiment seemed to show two main
classes of
> > untrained listeners. The "pure" group who liked just chords,
and
> > the "rich" group who likes 15 cent errors from just. Neither
group
> > liked or even was indifferent to 30 cent errors -- those were
simply
> > bad. With a sample of 30-40 untrained subjects, there was
not one
> > clear case of a "tin ear". I saw an estimate that tone deafness
> > occured in 2% of the population, which seems about right.
>
> Yes, but note that this isn't quite the right experiment. They
don't
> have to "like" the JI intervals they just have to recoignise that
> there's something there and be able to find them again if
allowed to
> twiddle the knobs.

well i thought the experiment was a good one to bring up given
the questions about trained musicians vs. untrained musicians
that have been brought up.

--- In tuning@y..., graham@m... wrote:
> So "just intonation" is defined as containing pure intervals, and
"pure"
> is a synonym for "just". Can anybody see the logical flaw here?

Gimme a break. There's no logical flaw. It's just that it is obviously
not a "definition" of just intonation to merely say just = pure.
Nevertheless dictionaries are full of such things, even going in
circles. And it may in fact be helpful to someone who already has the
right concept of just intonation but knows it only under the term
"pure". It's the last part of the OED def that is more useful if you
don't already have the concept. "sounding perfectly in tune". And I
never claimed that _that_ was sufficient either. You should be well
aware that I have elaborated on this.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> no . . . sex, ecology, spirituality. i got through a little bit and
then
> started avoiding it . . . bought and read stephen hawking's
> universe instead and now started miles beyond . . . don't know if
> i'll even get back to the wilber . . .

This is a case where he's essentially written two versions of the same
book. The heavy-duty academic version where he hopes to answer all the
objections of his academic critics before they even ask them (Sex,
Ecology, Spirituality) and the more accessible, readable
philospher-in-the-street version (Brief History of Everything). I
recommend you try the latter. Or back up a little and read his most
accessible (and thin) but slightly out of date with his current views,
'No Boundary'.

> well i thought the experiment was a good one to bring up given
> the questions about trained musicians vs. untrained musicians
> that have been brought up.

Oh yes. It was quite relevant. Thanks. I just didn't want anyone to
draw the wrong conclusion.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > no . . . sex, ecology, spirituality. i got through a little bit
and
> then
> > started avoiding it . . . bought and read stephen hawking's
> > universe instead and now started miles beyond . . . don't know if
> > i'll even get back to the wilber . . .
>
> This is a case where he's essentially written two versions of the
same
> book. The heavy-duty academic version where he hopes to answer all
the
> objections of his academic critics before they even ask them (Sex,
> Ecology, Spirituality) and the more accessible, readable
> philospher-in-the-street version (Brief History of Everything).

ok -- now this is really wild.

i'm just glancing at the back cover of miles beyond and there is this
blurb:

"An extraordinary book--brilliant in its conception and delivery--
about one of the greatest musical geniuses of our times. Highly
recommended.
--KEN WILBER, author of _A Brief History of Everything_."

this is the most startling coincidence of my year so far.

ok -- any further off-topic postings on this subject, or on the
subject of practicing, should go to metatuning@yahoogroups.com . . .