Hi!

Hi everyone. My name's Rick Ballan. Bill Sethares suggested I contact you. As a jazz guitarist I don't get much chance to play in alternate tunings and so do most of my stuff on my humble calculator. Still, I've written a thesis on wave theory (for theoretical physics dept) and have a question. Though I've been working with the 12 tones, reading through some of your discussions I'm sure the question applies to any other tunings as well.

I've been looking for ratios which approximate equal tempered intervals. My "system" is not very rigorous but it does seem to give me some results. For eg given the minor 3rd , 2 to the power of 1/4 = 1.1892..., I take 2 to the power of N + 1/4, N = 0, 1, 2, 3,..., either round it off to nearest odd number or, if the whole numbered part is already odd, ignore the numbers after the decimal point, and then divide by 2 to the power of N to get the nearest octave. Many values of N will simply give octaves so then I just move on. 2 to the power of 4.25 (i.e. N = 4) gives 19.027...rounds to 19 and 19/16 = 1.1875. The next relevant value is N = 9 giving 609/512 = 1.189453125.

Now my question is: are our tempered intervals truly irrational, which would make them aperiodic and non-tonal by definition, or is it really the case that they approximate these or other ratios in the rarefied upper realms of the harmonic series? In other words, perhaps there is a limit to what we can do in the physical world and we can only create (and/or hear) to a few decimal places?

Thanks folks and please excuse my ignorance cause I'm new to this field.

Get the name you always wanted with the new y7mail email address.
www.yahoo7.com.au/mail

Equal-tempered intervals are theoretically irrational.

Beyond that, every strange variation of temperament has been tried at
some time.

Problem is, who cares what the mathematical rationality is if people
can't experience a difference? As Bill explains so wonderfully,
timbre has a major factor in that. And the limits of human perception
and psychology do as well.

Some of these questions have not been scientifically answered yet, but
it is my opinion that by trying to rationalize 12ET, you are just
trying to find patterns and conclusions where there aren't any. 12ET
is essentially related to Pythagorean and meantone temperaments and so
essentially works with thirds and fifths. But, instruments are so
rarely tuned to perfect temperament that all sorts of other issues are
there.

I'll put it this way: if you aren't carefully intonating your guitar
as "perfect" as possible, and then playing extremely long sustained
chords with absolutely no vibrato or bending, then you aren't
harmonically focusing on some exact rational harmony. Jazz guitar is
based more on vaguely going toward certain more or less consonant
sounds, but really based more on voice-leading than on specific harmonies.

-Aaron Wolf

--- In tuning@yahoogroups.com, rick ballan <rick_ballan@...> wrote:
>
> Hi everyone. My name's Rick Ballan. Bill Sethares suggested I
contact you. As a jazz guitarist I don't get much chance to play in
alternate tunings and so do most of my stuff on my humble calculator.
Still, I've written a thesis on wave theory (for theoretical physics
dept) and have a question. Though I've been working with the 12 tones,
reading through some of your discussions I'm sure the question applies
to any other tunings as well.
>
> I've been looking for ratios which approximate equal tempered
intervals. My "system" is not very rigorous but it does seem to give
me some results. For eg given the minor 3rd , 2 to the power of 1/4 =
1.1892..., I take 2 to the power of N + 1/4, N = 0, 1, 2, 3,...,
either round it off to nearest odd number or, if the whole numbered
part is already odd, ignore the numbers after the decimal point, and
then divide by 2 to the power of N to get the nearest octave. Many
values of N will simply give octaves so then I just move on. 2 to the
power of 4.25 (i.e. N = 4) gives 19.027...rounds to 19 and 19/16 =
1.1875. The next relevant value is N = 9 giving 609/512 = 1.189453125.
>
> Now my question is: are our tempered intervals truly irrational,
which would make them aperiodic and non-tonal by definition, or is it
really the case that they approximate these or other ratios in the
rarefied upper realms of the harmonic series? In other words, perhaps
there is a limit to what we can do in the physical world and we can
only create (and/or hear) to a few decimal places?
>
> Thanks folks and please excuse my ignorance cause I'm new to this field.
>
>
>
> Get the name you always wanted with the new y7mail email address.
> www.yahoo7.com.au/mail
>

Hi Rick,

> Now my question is: are our tempered intervals truly irrational,
> which would make them aperiodic and non-tonal by definition, or
> is it really the case that they approximate these or other ratios
> in the rarefied upper realms of the harmonic series? In other
> words, perhaps there is a limit to what we can do in the physical
> world and we can only create (and/or hear) to a few decimal places?

The intervals exist abstractly with infinite precision but
of course can never be tuned or performed with infinite
precision. It's equivalent to whether you believe in
real numbers. Is that your question?

-Carl

Thanks Carl. Yes I suppose that's one way of stating the question. More precisely this gap between the abstract real numbers and those which are actually tuned or performed is not only one between the ideal and reality, but more importantly between periodicity and aperiodicity. As you no doubt know, given a ratio between two frequencies a/b where a and b are whole, then the resultant wave will be periodic, the frequency being the highest common factor between the two. Extending this to all possible combinations, then the class of these represents both the number of "instruments" which could play this frequency (note) and also the basis of harmonic intervals/chords i.e. tonality. But if the waves bear an irrational relation, then a and b do not exist and no periodic wave is produced (e.g. Pythagoras' proof that no ratio a/b corresponds to the sq root of 2, which is the flat-fifth interval).

Now the reason I ask is not in my capacity as a jazz guitarist but because I've written a theoretical physics paper on general wave theory that applies to electro-magnetics and quantum waves as well, and which is currently being reviewed at Sydney uni. If all waves are in reality periodic, then they are also harmonic. In fact my paper shows many mathematical proof to this effect. It does this by showing that it always leads into self-contradiction otherwise. It also debunks much of the experimental evidence used as "proof" that light and matter waves are irrational. So you see that to answer this question precisely will have repercussions throughout all of physics. Bill Sethares suggested that I get you guys onto the problem because you are the ones to do it and the more experimental proof the better.

Thanks again Carl

Rick

----- Original Message ----
From: Carl Lumma <carl@lumma.org>
To: tuning@yahoogroups.com
Sent: Tuesday, 27 May, 2008 2:33:31 AM
Subject: [tuning] Re: Hi!

Hi Rick,

> Now my question is: are our tempered intervals truly irrational,
> which would make them aperiodic and non-tonal by definition, or
> is it really the case that they approximate these or other ratios
> in the rarefied upper realms of the harmonic series? In other
> words, perhaps there is a limit to what we can do in the physical
> world and we can only create (and/or hear) to a few decimal places?

The intervals exist abstractly with infinite precision but
of course can never be tuned or performed with infinite
precision. It's equivalent to whether you believe in
real numbers. Is that your question?

-Carl

Get the name you always wanted with the new y7mail email address.
www.yahoo7.com.au/mail

I'm really glad to see that Rick is looking at this from a scientific POV.
Maybe he'll be able to pin down more precisely what is happening and come up with a model which works for all wave patterns,

I suspect that we are eventually going to find that the "old" paradigms were very rough and ready approximations, and a new way of looking at them will resolve many of the obvious paradoxes.

I'd work on it myself, but I'm too long in the tooth nowadays to spend six years getting a PhD in Physics;-)

and the next generation little Lucy is still only doing equiv of 12th grade, and more interested in art, graphics, languages, and computers.

On 27 May 2008, at 08:36, rick ballan wrote:

>
> Thanks Carl. Yes I suppose that's one way of stating the question. > More precisely this gap between the abstract real numbers and those > which are actually tuned or performed is not only one between the > ideal and reality, but more importantly between periodicity and > aperiodicity. As you no doubt know, given a ratio between two > frequencies a/b where a and b are whole, then the resultant wave > will be periodic, the frequency being the highest common factor > between the two. Extending this to all possible combinations, then > the class of these represents both the number of "instruments" which > could play this frequency (note) and also the basis of harmonic > intervals/chords i.e. tonality. But if the waves bear an irrational > relation, then a and b do not exist and no periodic wave is produced > (e.g. Pythagoras' proof that no ratio a/b corresponds to the sq root > of 2, which is the flat-fifth interval).
>
> Now the reason I ask is not in my capacity as a jazz guitarist but > because I've written a theoretical physics paper on general wave > theory that applies to electro-magnetics and quantum waves as well, > and which is currently being reviewed at Sydney uni. If all waves > are in reality periodic, then they are also harmonic. In fact my > paper shows many mathematical proof to this effect. It does this by > showing that it always leads into self-contradiction otherwise. It > also debunks much of the experimental evidence used as "proof" that > light and matter waves are irrational. So you see that to answer > this question precisely will have repercussions throughout all of > physics. Bill Sethares suggested that I get you guys onto the > problem because you are the ones to do it and the more experimental > proof the better.
>
> Thanks again Carl
>
> Rick
>
> ----- Original Message ----
> From: Carl Lumma <carl@...>
> To: tuning@yahoogroups.com
> Sent: Tuesday, 27 May, 2008 2:33:31 AM
> Subject: [tuning] Re: Hi!
>
> Hi Rick,
>
> > Now my question is: are our tempered intervals truly irrational,
> > which would make them aperiodic and non-tonal by definition, or
> > is it really the case that they approximate these or other ratios
> > in the rarefied upper realms of the harmonic series? In other
> > words, perhaps there is a limit to what we can do in the physical
> > world and we can only create (and/or hear) to a few decimal places?
>
> The intervals exist abstractly with infinite precision but
> of course can never be tuned or performed with infinite
> precision. It's equivalent to whether you believe in
> real numbers. Is that your question?
>
> -Carl
>
>
>
> Get the name you always wanted with the new y7mail email address.
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

I never thought I'd see this in a tuning forum, but that is a very,
very, very deep and interesting question that I think everyone has
considered in some form or another.

Although I usually consider the counter-question -- if two frequencies
are in a 2/1 ratio, and they can't be physically tuned to that
precision, are they actually periodic at all?

Or if two lines on a blackboard are supposed to be an inch apart, but
they aren't really an inch apart, how many inches apart are they? Will
the ratio of actual distance to one inch be rational or irrational?

So the question is, is ANYTHING in nature perfectly periodic/rational?
You say yes, but to an extremely fine degree, if I understand
correctly.

I am interested in seeing your proof of this.

-Mike

On Tue, May 27, 2008 at 3:36 AM, rick ballan <rick_ballan@...> wrote:
> Thanks Carl. Yes I suppose that's one way of stating the question. More
> precisely this gap between the abstract real numbers and those which are
> actually tuned or performed is not only one between the ideal and reality,
> but more importantly between periodicity and aperiodicity. As you no doubt
> know, given a ratio between two frequencies a/b where a and b are whole,
> then the resultant wave will be periodic, the frequency being the highest
> common factor between the two. Extending this to all possible combinations,
> then the class of these represents both the number of "instruments" which
> could play this frequency (note) and also the basis of harmonic
> intervals/chords i.e. tonality. But if the waves bear an irrational
> relation, then a and b do not exist and no periodic wave is produced (e.g.
> Pythagoras' proof that no ratio a/b corresponds to the sq root of 2, which
> is the flat-fifth interval).
>
> Now the reason I ask is not in my capacity as a jazz guitarist but because
> I've written a theoretical physics paper on general wave theory that applies
> to electro-magnetics and quantum waves as well, and which is currently being
> reviewed at Sydney uni. If all waves are in reality periodic, then they are
> also harmonic. In fact my paper shows many mathematical proof to this
> effect. It does this by showing that it always leads into self-contradiction
> otherwise. It also debunks much of the experimental evidence used as "proof"
> that light and matter waves are irrational. So you see that to answer this
> question precisely will have repercussions throughout all of physics. Bill
> Sethares suggested that I get you guys onto the problem because you are the
> ones to do it and the more experimental proof the better.
>
> Thanks again Carl
>
> Rick
>
> ----- Original Message ----
> From: Carl Lumma <carl@...>
> To: tuning@yahoogroups.com
> Sent: Tuesday, 27 May, 2008 2:33:31 AM
> Subject: [tuning] Re: Hi!
>
> Hi Rick,
>
>> Now my question is: are our tempered intervals truly irrational,
>> which would make them aperiodic and non-tonal by definition, or
>> is it really the case that they approximate these or other ratios
>> in the rarefied upper realms of the harmonic series? In other
>> words, perhaps there is a limit to what we can do in the physical
>> world and we can only create (and/or hear) to a few decimal places?
>
> The intervals exist abstractly with infinite precision but
> of course can never be tuned or performed with infinite
> precision. It's equivalent to whether you believe in
> real numbers. Is that your question?
>
> -Carl
>
>
> ________________________________
> Get the name you always wanted with the new y7mail email address.
>

having heard JI in a various degrees of accuracy, the closer and more you get to perfect, there is a logarithmic sweep toward various phenomenon. It seems in the real non electrically guided sound world, there does not seem to be any real attraction toward periodic. We know that pendulum clocks will move toward synchronization, so maybe we need to hold the tones longer.

How can such things be measured though.
what if the wave is a million years
to pick a short one

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
> I never thought I'd see this in a tuning forum, but that is a very,
> very, very deep and interesting question that I think everyone has
> considered in some form or another.
>
> Although I usually consider the counter-question -- if two frequencies
> are in a 2/1 ratio, and they can't be physically tuned to that
> precision, are they actually periodic at all?
>
> Or if two lines on a blackboard are supposed to be an inch apart, but
> they aren't really an inch apart, how many inches apart are they? Will
> the ratio of actual distance to one inch be rational or irrational?
>
> So the question is, is ANYTHING in nature perfectly periodic/rational?
> You say yes, but to an extremely fine degree, if I understand
> correctly.
>
> I am interested in seeing your proof of this.
>
> -Mike
>
> On Tue, May 27, 2008 at 3:36 AM, rick ballan <rick_ballan@... > <mailto:rick_ballan%40yahoo.com.au>> wrote:
> > Thanks Carl. Yes I suppose that's one way of stating the question. More
> > precisely this gap between the abstract real numbers and those which are
> > actually tuned or performed is not only one between the ideal and > reality,
> > but more importantly between periodicity and aperiodicity. As you no > doubt
> > know, given a ratio between two frequencies a/b where a and b are whole,
> > then the resultant wave will be periodic, the frequency being the > highest
> > common factor between the two. Extending this to all possible > combinations,
> > then the class of these represents both the number of "instruments" > which
> > could play this frequency (note) and also the basis of harmonic
> > intervals/chords i.e. tonality. But if the waves bear an irrational
> > relation, then a and b do not exist and no periodic wave is produced > (e.g.
> > Pythagoras' proof that no ratio a/b corresponds to the sq root of 2, > which
> > is the flat-fifth interval).
> >
> > Now the reason I ask is not in my capacity as a jazz guitarist but > because
> > I've written a theoretical physics paper on general wave theory that > applies
> > to electro-magnetics and quantum waves as well, and which is > currently being
> > reviewed at Sydney uni. If all waves are in reality periodic, then > they are
> > also harmonic. In fact my paper shows many mathematical proof to this
> > effect. It does this by showing that it always leads into > self-contradiction
> > otherwise. It also debunks much of the experimental evidence used as > "proof"
> > that light and matter waves are irrational. So you see that to > answer this
> > question precisely will have repercussions throughout all of > physics. Bill
> > Sethares suggested that I get you guys onto the problem because you > are the
> > ones to do it and the more experimental proof the better.
> >
> > Thanks again Carl
> >
> > Rick
> >
> > ----- Original Message ----
> > From: Carl Lumma <carl@... <mailto:carl%40lumma.org>>
> > To: tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>
> > Sent: Tuesday, 27 May, 2008 2:33:31 AM
> > Subject: [tuning] Re: Hi!
> >
> > Hi Rick,
> >
> >> Now my question is: are our tempered intervals truly irrational,
> >> which would make them aperiodic and non-tonal by definition, or
> >> is it really the case that they approximate these or other ratios
> >> in the rarefied upper realms of the harmonic series? In other
> >> words, perhaps there is a limit to what we can do in the physical
> >> world and we can only create (and/or hear) to a few decimal places?
> >
> > The intervals exist abstractly with infinite precision but
> > of course can never be tuned or performed with infinite
> > precision. It's equivalent to whether you believe in
> > real numbers. Is that your question?
> >
> > -Carl
> >
> >
> > ________________________________
> > Get the name you always wanted with the new y7mail email address.
> >
>
>

Pendulums???

I realise that this could be seen as a case of "have hammer - only see nails" :

http://www.lucytune.com/academic/freq_to_wave.html

http://hyperphysics.phy-astr.gsu.edu/Hbase/pend.html

http://scienceworld.wolfram.com/physics/Pendulum.html

On 27 May 2008, at 22:28, Kraig Grady wrote:

> having heard JI in a various degrees of accuracy, the closer and more
> you get to perfect, there is a logarithmic sweep toward various
> phenomenon. It seems in the real non electrically guided sound world,
> there does not seem to be any real attraction toward periodic. We know
> that pendulum clocks will move toward synchronization, so maybe we > need
> to hold the tones longer.
>
> How can such things be measured though.
> what if the wave is a million years
> to pick a short one
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://> anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Mike Battaglia wrote:
> >
> > I never thought I'd see this in a tuning forum, but that is a very,
> > very, very deep and interesting question that I think everyone has
> > considered in some form or another.
> >
> > Although I usually consider the counter-question -- if two > frequencies
> > are in a 2/1 ratio, and they can't be physically tuned to that
> > precision, are they actually periodic at all?
> >
> > Or if two lines on a blackboard are supposed to be an inch apart, > but
> > they aren't really an inch apart, how many inches apart are they? > Will
> > the ratio of actual distance to one inch be rational or irrational?
> >
> > So the question is, is ANYTHING in nature perfectly periodic/> rational?
> > You say yes, but to an extremely fine degree, if I understand
> > correctly.
> >
> > I am interested in seeing your proof of this.
> >
> > -Mike
> >
> > On Tue, May 27, 2008 at 3:36 AM, rick ballan <rick_ballan@...
> > <mailto:rick_ballan%40yahoo.com.au>> wrote:
> > > Thanks Carl. Yes I suppose that's one way of stating the > question. More
> > > precisely this gap between the abstract real numbers and those > which are
> > > actually tuned or performed is not only one between the ideal and
> > reality,
> > > but more importantly between periodicity and aperiodicity. As > you no
> > doubt
> > > know, given a ratio between two frequencies a/b where a and b > are whole,
> > > then the resultant wave will be periodic, the frequency being the
> > highest
> > > common factor between the two. Extending this to all possible
> > combinations,
> > > then the class of these represents both the number of > "instruments"
> > which
> > > could play this frequency (note) and also the basis of harmonic
> > > intervals/chords i.e. tonality. But if the waves bear an > irrational
> > > relation, then a and b do not exist and no periodic wave is > produced
> > (e.g.
> > > Pythagoras' proof that no ratio a/b corresponds to the sq root > of 2,
> > which
> > > is the flat-fifth interval).
> > >
> > > Now the reason I ask is not in my capacity as a jazz guitarist but
> > because
> > > I've written a theoretical physics paper on general wave theory > that
> > applies
> > > to electro-magnetics and quantum waves as well, and which is
> > currently being
> > > reviewed at Sydney uni. If all waves are in reality periodic, then
> > they are
> > > also harmonic. In fact my paper shows many mathematical proof to > this
> > > effect. It does this by showing that it always leads into
> > self-contradiction
> > > otherwise. It also debunks much of the experimental evidence > used as
> > "proof"
> > > that light and matter waves are irrational. So you see that to
> > answer this
> > > question precisely will have repercussions throughout all of
> > physics. Bill
> > > Sethares suggested that I get you guys onto the problem because > you
> > are the
> > > ones to do it and the more experimental proof the better.
> > >
> > > Thanks again Carl
> > >
> > > Rick
> > >
> > > ----- Original Message ----
> > > From: Carl Lumma <carl@... <mailto:carl%40lumma.org>>
> > > To: tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>
> > > Sent: Tuesday, 27 May, 2008 2:33:31 AM
> > > Subject: [tuning] Re: Hi!
> > >
> > > Hi Rick,
> > >
> > >> Now my question is: are our tempered intervals truly irrational,
> > >> which would make them aperiodic and non-tonal by definition, or
> > >> is it really the case that they approximate these or other ratios
> > >> in the rarefied upper realms of the harmonic series? In other
> > >> words, perhaps there is a limit to what we can do in the physical
> > >> world and we can only create (and/or hear) to a few decimal > places?
> > >
> > > The intervals exist abstractly with infinite precision but
> > > of course can never be tuned or performed with infinite
> > > precision. It's equivalent to whether you believe in
> > > real numbers. Is that your question?
> > >
> > > -Carl
> > >
> > >
> > > ________________________________
> > > Get the name you always wanted with the new y7mail email address.
> > >
> >
> >
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Huygens!

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Charles Lucy wrote:
>
> Pendulums???
>
>
> I realise that this could be seen as a case of "have hammer - only see > nails" :
>
> http://www.lucytune.com/academic/freq_to_wave.html > <http://www.lucytune.com/academic/freq_to_wave.html>
>
> http://hyperphysics.phy-astr.gsu.edu/Hbase/pend.html > <http://hyperphysics.phy-astr.gsu.edu/Hbase/pend.html>
>
> http://scienceworld.wolfram.com/physics/Pendulum.html > <http://scienceworld.wolfram.com/physics/Pendulum.html>
>
>
> On 27 May 2008, at 22:28, Kraig Grady wrote:
>
>> having heard JI in a various degrees of accuracy, the closer and more >> you get to perfect, there is a logarithmic sweep toward various >> phenomenon. It seems in the real non electrically guided sound world, >> there does not seem to be any real attraction toward periodic. We know >> that pendulum clocks will move toward synchronization, so maybe we need >> to hold the tones longer.
>>
>> How can such things be measured though.
>> what if the wave is a million years
>> to pick a short one
>>
>> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
>> _'''''''_ ^North/Western ! Hemisphe re: >> North American Embassy of Anaphoria Island <http://anaphoria.com/ >> <http://anaphoria.com/>>
>>
>> _'''''''_ ^South/Eastern Hemisphere:
>> Austronesian Outpost of Anaphoria >> <http://anaphoriasouth.blogspot.com/ >> <http://anaphoriasouth.blogspot.com/>>
>>
>> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>>
>> Mike Battaglia wrote:
>> >
>> > I never thought I'd see this in a tuning forum, but that is a very,
>> > very, very deep and interesting question that I think everyone has
>> > considered in some form or another.
>> >
>> > Although I usually consider the counter-question -- if two frequencies
>> > are in a 2/1 ratio, and they can't be physically tuned to that
>> > precision, are they actually periodic at all?
>> >
>> > Or if two lines on a blackboard are supposed to be an inch apart, but
>> > they aren't really an inch apart, how many inches apart are they? Will
>> > the ratio of actual distance to one inch be rational or irrational?
>> >
>> > So the question is, is ANYTHING in nature perfectly periodic/rational?
>> > You say yes, but to an extremely fine degree, if I understand
>> > correctly.
>> >
>> > I am interested in seeing your proof of this.
>> >
>> > -Mike
>> >
>> > On Tue, May 27, 2008 at 3:36 AM, rick ballan >> <rick_ballan@... <mailto:rick_ballan%40yahoo.com.au> >> > <mailto:rick_ballan%40yahoo.com.au>> wrote:
>> > > Thanks Carl. Yes I suppose that's one way of stating the question. >> More
>> > > precisely this gap between the abstract real numbers and those >> which are
>> > > actually tuned or performed is not only one between the ideal and >> > reality,
>> > > but more importantly between periodicity and aperiodicity. As you no >> > doub! t
>> > > know, given a ratio between two frequencies a/b where a and b are >> whole,
>> > > then the resultant wave will be periodic, the frequency being the >> > highest
>> > > common factor between the two. Extending this to all possible >> > combinations,
>> > > then the class of these represents both the number of "instruments" >> > which
>> > > could play this frequency (note) and also the basis of harmonic
>> > > intervals/chords i.e. tonality. But if the waves bear an irrational
>> > > relation, then a and b do not exist and no periodic wave is produced >> > (e.g.
>> > > Pythagoras' proof that no ratio a/b corresponds to the sq root of 2, >> > which
>> > > is the flat-fifth interval).
>> > >
>> > > Now the reason I ask is not in my capacity as a jazz guitarist but >> > because
>> > > I've written a theoretical physics paper on general wave theory that >> > applies
>> > > to electro-magnetics and quantum waves as well, and which is >> > currently being
>> > > reviewed at Sydney uni. If all waves are in reality periodic, then >> > they are
>> > > also harmonic. In fact my paper shows many mathematical proof to this
>> > > effect. It does this by showing that it always leads into >> > self-contradiction
>> > > otherwise. It also debunks much of the experimental evidence used as >> > "proof"
>> > > that light and matter waves are irrational. So you see that to >> > answer this
>> > > question precisely will have repercussions throughou! t all of >> > physics. Bill
>> > > Sethares suggested that I get you guys onto the problem because you >> > are the
>> > > ones to do it and the more experimental proof the better.
>> > >
>> > > Thanks again Carl
>> > >
>> > > Rick
>> > >
>> > > ----- Original Message ----
>> > > From: Carl Lumma <carl@... >> <mailto:carl%40lumma.org> <mailto:carl%40lumma.org>>
>> > > To: tuning@yahoogroups.com >> <mailto:tuning%40yahoogroups.com> <mailto:tuning%40yahoogroups.com>
>> > > Sent: Tuesday, 27 May, 2008 2:33:31 AM
>> > > Subject: [tuning] Re: Hi!
>> > >
>> > > Hi Rick,
>> > >
>> > >> Now my question is: are our tempered intervals truly irrational,
>> > >> which would make them aperiodic and non-tonal by definition, or
>> > >> is it really the case that they approximate these or other ratios
>> > >> in the rarefied upper realms of the harmonic series? In other
>> > >> words, perhaps there is a limit to what we can do in the physical
>> > >> world and we can only create (and/or hear) to a few decimal places?
>> > >
>> > > The intervals exist abstractly with infinite precision but
>> > > of course can never be tuned or performed with infinite
>> > > precision. It's equivalent to whether you believe in
>> > > real numbers. Is that your question?
>> > >
>> > > -Carl
>> > >
>> > >
>> > > ________________________________
>> > > Get the name you always wanted with the new y7mail email address.
>> > >
>> >
>> > >>
>
> Charles Lucy
> lucy@... <mailto:lucy@...>
>
> - Promoting global harmony through LucyTuning -
>
> for information on LucyTuning go to:
> http://www.lucytune.com <http://www.lucytune.com>
>
> For LucyTuned Lullabies go to:
> http://www.lullabies.co.uk <http://www.lullabies.co.uk>
>
>
>
>

put pendulum clocks on a wall and see what happens
how do these formulas relate to this?

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Kraig Grady wrote:
>
> Huygens!
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Charles Lucy wrote:
> >
> > Pendulums???
> >
> >
> > I realise that this could be seen as a case of "have hammer - only see
> > nails" :
> >
> > http://www.lucytune.com/academic/freq_to_wave.html > <http://www.lucytune.com/academic/freq_to_wave.html>
> > <http://www.lucytune.com/academic/freq_to_wave.html > <http://www.lucytune.com/academic/freq_to_wave.html>>
> >
> > http://hyperphysics.phy-astr.gsu.edu/Hbase/pend.html > <http://hyperphysics.phy-astr.gsu.edu/Hbase/pend.html>
> > <http://hyperphysics.phy-astr.gsu.edu/Hbase/pend.html > <http://hyperphysics.phy-astr.gsu.edu/Hbase/pend.html>>
> >
> > http://scienceworld.wolfram.com/physics/Pendulum.html > <http://scienceworld.wolfram.com/physics/Pendulum.html>
> > <http://scienceworld.wolfram.com/physics/Pendulum.html > <http://scienceworld.wolfram.com/physics/Pendulum.html>>
> >
> >
> > On 27 May 2008, at 22:28, Kraig Grady wrote:
> >
> >> having heard JI in a various degrees of accuracy, the closer and more
> >> you get to perfect, there is a logarithmic sweep toward various
> >> phenomenon. It seems in the real non electrically guided sound world,
> >> there does not seem to be any real attraction toward periodic. We know
> >> that pendulum clocks will move toward synchronization, so maybe we > need
> >> to hold the tones longer.
> >>
> >> How can such things be measured though.
> >> what if the wave is a million years
> >> to pick a short one
> >>
> >> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> >> _'''''''_ ^North/Western ! Hemisphe re:
> >> North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>
> >> <http://anaphoria.com/ <http://anaphoria.com/>>>
> >>
> >> _'''''''_ ^South/Eastern Hemisphere:
> >> Austronesian Outpost of Anaphoria
> >> <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>
> >> <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>>
> >>
> >> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >>
> >> Mike Battaglia wrote:
> >> >
> >> > I never thought I'd see this in a tuning forum, but that is a very,
> >> > very, very deep and interesting question that I think everyone has
> >> > considered in some form or another.
> >> >
> >> > Although I usually consider the counter-question -- if two > frequencies
> >> > are in a 2/1 ratio, and they can't be physically tuned to that
> >> > precision, are they actually periodic at all?
> >> >
> >> > Or if two lines on a blackboard are supposed to be an inch apart, but
> >> > they aren't really an inch apart, how many inches apart are they? > Will
> >> > the ratio of actual distance to one inch be rational or irrational?
> >> >
> >> > So the question is, is ANYTHING in nature perfectly > periodic/rational?
> >> > You say yes, but to an extremely fine degree, if I understand
> >> > correctly.
> >> >
> >> > I am interested in seeing your proof of this.
> >> >
> >> > -Mike
> >> >
> >> > On Tue, May 27, 2008 at 3:36 AM, rick ballan
> >> <rick_ballan@... <mailto:rick_ballan%40yahoo.com.au> > <mailto:rick_ballan%40yahoo.com.au>
> >> > <mailto:rick_ballan%40yahoo.com.au>> wrote:
> >> > > Thanks Carl. Yes I suppose that's one way of stating the question.
> >> More
> >> > > precisely this gap between the abstract real numbers and those
> >> which are
> >> > > actually tuned or performed is not only one between the ideal and
> >> > reality,
> >> > > but more importantly between periodicity and aperiodicity. As > you no
> >> > doub! t
> >> > > know, given a ratio between two frequencies a/b where a and b are
> >> whole,
> >> > > then the resultant wave will be periodic, the frequency being the
> >> > highest
> >> > > common factor between the two. Extending this to all possible
> >> > combinations,
> >> > > then the class of these represents both the number of > "instruments"
> >> > which
> >> > > could play this frequency (note) and also the basis of harmonic
> >> > > intervals/chords i.e. tonality. But if the waves bear an irrational
> >> > > relation, then a and b do not exist and no periodic wave is > produced
> >> > (e.g.
> >> > > Pythagoras' proof that no ratio a/b corresponds to the sq root > of 2,
> >> > which
> >> > > is the flat-fifth interval).
> >> > >
> >> > > Now the reason I ask is not in my capacity as a jazz guitarist but
> >> > because
> >> > > I've written a theoretical physics paper on general wave theory > that
> >> > applies
> >> > > to electro-magnetics and quantum waves as well, and which is
> >> > currently being
> >> > > reviewed at Sydney uni. If all waves are in reality periodic, then
> >> > they are
> >> > > also harmonic. In fact my paper shows many mathematical proof > to this
> >> > > effect. It does this by showing that it always leads into
> >> > self-contradiction
> >> > > otherwise. It also debunks much of the experimental evidence > used as
> >> > "proof"
> >> > > that light and matter waves are irrational. So you see that to
> >> > answer this
> >> > > question precisely will have repercussions throughou! t all of
> >> > physics. Bill
> >> > > Sethares suggested that I get you guys onto the problem because > you
> >> > are the
> >> > > ones to do it and the more experimental proof the better.
> >> > >
> >> > > Thanks again Carl
> >> > >
> >> > > Rick
> >> > >
> >> > > ----- Original Message ----
> >> > > From: Carl Lumma <carl@... <mailto:carl%40lumma.org>
> >> <mailto:carl%40lumma.org> <mailto:carl%40lumma.org>>
> >> > > To: tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>
> >> <mailto:tuning%40yahoogroups.com> <mailto:tuning%40yahoogroups.com>
> >> > > Sent: Tuesday, 27 May, 2008 2:33:31 AM
> >> > > Subject: [tuning] Re: Hi!
> >> > >
> >> > > Hi Rick,
> >> > >
> >> > >> Now my question is: are our tempered intervals truly irrational,
> >> > >> which would make them aperiodic and non-tonal by definition, or
> >> > >> is it really the case that they approximate these or other ratios
> >> > >> in the rarefied upper realms of the harmonic series? In other
> >> > >> words, perhaps there is a limit to what we can do in the physical
> >> > >> world and we can only create (and/or hear) to a few decimal > places?
> >> > >
> >> > > The intervals exist abstractly with infinite precision but
> >> > > of course can never be tuned or performed with infinite
> >> > > precision. It's equivalent to whether you believe in
> >> > > real numbers. Is that your question?
> >> > >
> >> > > -Carl
> >> > >
> >> > >
> >> > > ________________________________
> >> > > Get the name you always wanted with the new y7mail email address.
> >> > >
> >> >
> >> >
> >>
> >
> > Charles Lucy
> > lucy@... <mailto:lucy%40lucytune.com> > <mailto:lucy@... <mailto:lucy%40lucytune.com>>
> >
> > - Promoting global harmony through LucyTuning -
> >
> > for information on LucyTuning go to:
> > http://www.lucytune.com <http://www.lucytune.com> > <http://www.lucytune.com <http://www.lucytune.com>>
> >
> > For LucyTuned Lullabies go to:
> > http://www.lullabies.co.uk <http://www.lullabies.co.uk> > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>
> >
> >
> >
> >
>
>

Sorry but I don't know what JI is.

How can such things be measured though.
what if the wave is a million years
to pick a short one

This is related to a standard philosophical question called Hume's problem of induction. It basically states that we are not justified in assuming that the laws of physics will be the same tomorrow as they are today. But what if our sense of regularity in time itself comes from periodic light, sound and matter waves, all of which can be proved by experiment? And while one wave might decay, there is still an infinite number to deal with at any one moment e.g. the colour of light is periodic, the energy of matter, and the sine waves of any sound analysis.

----- Original Message ----
From: Kraig Grady <kraiggrady@...>
To: tuning@yahoogroups.com
Sent: Wednesday, 28 May, 2008 7:28:54 AM
Subject: Re: [tuning] Re: Hi!

having heard JI in a various degrees of accuracy, the closer and more
you get to perfect, there is a logarithmic sweep toward various
phenomenon. It seems in the real non electrically guided sound world,
there does not seem to be any real attraction toward periodic. We know
that pendulum clocks will move toward synchronization, so maybe we need
to hold the tones longer.

How can such things be measured though.
what if the wave is a million years
to pick a short one

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere:
North American Embassy of Anaphoria Island <http://anaphoria. com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>

',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,

Mike Battaglia wrote:
>
> I never thought I'd see this in a tuning forum, but that is a very,
> very, very deep and interesting question that I think everyone has
> considered in some form or another.
>
> Although I usually consider the counter-question -- if two frequencies
> are in a 2/1 ratio, and they can't be physically tuned to that
> precision, are they actually periodic at all?
>
> Or if two lines on a blackboard are supposed to be an inch apart, but
> they aren't really an inch apart, how many inches apart are they? Will
> the ratio of actual distance to one inch be rational or irrational?
>
> So the question is, is ANYTHING in nature perfectly periodic/rational?
> You say yes, but to an extremely fine degree, if I understand
> correctly.
>
> I am interested in seeing your proof of this.
>
> -Mike
>
> On Tue, May 27, 2008 at 3:36 AM, rick ballan <rick_ballan@ yahoo.com. au
> <mailto:rick_ ballan%40yahoo. com.au>> wrote:
> > Thanks Carl. Yes I suppose that's one way of stating the question. More
> > precisely this gap between the abstract real numbers and those which are
> > actually tuned or performed is not only one between the ideal and
> reality,
> > but more importantly between periodicity and aperiodicity. As you no
> doubt
> > know, given a ratio between two frequencies a/b where a and b are whole,
> > then the resultant wave will be periodic, the frequency being the
> highest
> > common factor between the two. Extending this to all possible
> combinations,
> > then the class of these represents both the number of "instruments"
> which
> > could play this frequency (note) and also the basis of harmonic
> > intervals/chords i.e. tonality. But if the waves bear an irrational
> > relation, then a and b do not exist and no periodic wave is produced
> (e.g.
> > Pythagoras' proof that no ratio a/b corresponds to the sq root of 2,
> which
> > is the flat-fifth interval).
> >
> > Now the reason I ask is not in my capacity as a jazz guitarist but
> because
> > I've written a theoretical physics paper on general wave theory that
> applies
> > to electro-magnetics and quantum waves as well, and which is
> currently being
> > reviewed at Sydney uni. If all waves are in reality periodic, then
> they are
> > also harmonic. In fact my paper shows many mathematical proof to this
> > effect. It does this by showing that it always leads into
> self-contradiction
> > otherwise. It also debunks much of the experimental evidence used as
> "proof"
> > that light and matter waves are irrational. So you see that to
> answer this
> > question precisely will have repercussions throughout all of
> physics. Bill
> > Sethares suggested that I get you guys onto the problem because you
> are the
> > ones to do it and the more experimental proof the better.
> >
> > Thanks again Carl
> >
> > Rick
> >
> > ----- Original Message ----
> > From: Carl Lumma <carl@... <mailto:carl% 40lumma.org> >
> > To: tuning@yahoogroups. com <mailto:tuning% 40yahoogroups. com>
> > Sent: Tuesday, 27 May, 2008 2:33:31 AM
> > Subject: [tuning] Re: Hi!
> >
> > Hi Rick,
> >
> >> Now my question is: are our tempered intervals truly irrational,
> >> which would make them aperiodic and non-tonal by definition, or
> >> is it really the case that they approximate these or other ratios
> >> in the rarefied upper realms of the harmonic series? In other
> >> words, perhaps there is a limit to what we can do in the physical
> >> world and we can only create (and/or hear) to a few decimal places?
> >
> > The intervals exist abstractly with infinite precision but
> > of course can never be tuned or performed with infinite
> > precision. It's equivalent to whether you believe in
> > real numbers. Is that your question?
> >
> > -Carl
> >
> >
> > ____________ _________ _________ __
> > Get the name you always wanted with the new y7mail email address.
> >
>
>

Get the name you always wanted with the new y7mail email address.
www.yahoo7.com.au/mail

I'm still curious as to the answer to my question -- how is it that
you know that ALL waves are periodic, rather than all waves are NOT
periodic?

Just curious.

-Mike

On Wed, May 28, 2008 at 12:17 AM, rick ballan <rick_ballan@...> wrote:
> Sorry but I don't know what JI is.
>
> How can such things be measured though.
> what if the wave is a million years
> to pick a short one
>
> This is related to a standard philosophical question called Hume's problem
> of induction. It basically states that we are not justified in assuming that
> the laws of physics will be the same tomorrow as they are today. But what if
> our sense of regularity in time itself comes from periodic light, sound and
> matter waves, all of which can be proved by experiment? And while one wave
> might decay, there is still an infinite number to deal with at any one
> moment e.g. the colour of light is periodic, the energy of matter, and the
> sine waves of any sound analysis.
>
> ----- Original Message ----
> From: Kraig Grady <kraiggrady@...>
> To: tuning@yahoogroups.com
> Sent: Wednesday, 28 May, 2008 7:28:54 AM
> Subject: Re: [tuning] Re: Hi!
>
> having heard JI in a various degrees of accuracy, the closer and more
> you get to perfect, there is a logarithmic sweep toward various
> phenomenon. It seems in the real non electrically guided sound world,
> there does not seem to be any real attraction toward periodic. We know
> that pendulum clocks will move toward synchronization, so maybe we need
> to hold the tones longer.
>
> How can such things be measured though.
> what if the wave is a million years
> to pick a short one
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria. com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>
>
> ',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,
>
> Mike Battaglia wrote:
>>
>> I never thought I'd see this in a tuning forum, but that is a very,
>> very, very deep and interesting question that I think everyone has
>> considered in some form or another.
>>
>> Although I usually consider the counter-question -- if two frequencies
>> are in a 2/1 ratio, and they can't be physically tuned to that
>> precision, are they actually periodic at all?
>>
>> Or if two lines on a blackboard are supposed to be an inch apart, but
>> they aren't really an inch apart, how many inches apart are they? Will
>> the ratio of actual distance to one inch be rational or irrational?
>>
>> So the question is, is ANYTHING in nature perfectly periodic/rational?
>> You say yes, but to an extremely fine degree, if I understand
>> correctly.
>>
>> I am interested in seeing your proof of this.
>>
>> -Mike
>>
>> On Tue, May 27, 2008 at 3:36 AM, rick ballan <rick_ballan@ yahoo.com. au
>> <mailto:rick_ ballan%40yahoo. com.au>> wrote:
>> > Thanks Carl. Yes I suppose that's one way of stating the question. More
>> > precisely this gap between the abstract real numbers and those which are
>> > actually tuned or performed is not only one between the ideal and
>> reality,
>> > but more importantly between periodicity and aperiodicity. As you no
>> doubt
>> > know, given a ratio between two frequencies a/b where a and b are whole,
>> > then the resultant wave will be periodic, the frequency being the
>> highest
>> > common factor between the two. Extending this to all possible
>> combinations,
>> > then the class of these represents both the number of "instruments"
>> which
>> > could play this frequency (note) and also the basis of harmonic
>> > intervals/chords i.e. tonality. But if the waves bear an irrational
>> > relation, then a and b do not exist and no periodic wave is produced
>> (e.g.
>> > Pythagoras' proof that no ratio a/b corresponds to the sq root of 2,
>> which
>> > is the flat-fifth interval).
>> >
>> > Now the reason I ask is not in my capacity as a jazz guitarist but
>> because
>> > I've written a theoretical physics paper on general wave theory that
>> applies
>> > to electro-magnetics and quantum waves as well, and which is
>> currently being
>> > reviewed at Sydney uni. If all waves are in reality periodic, then
>> they are
>> > also harmonic. In fact my paper shows many mathematical proof to this
>> > effect. It does this by showing that it always leads into
>> self-contradiction
>> > otherwise. It also debunks much of the experimental evidence used as
>> "proof"
>> > that light and matter waves are irrational. So you see that to
>> answer this
>> > question precisely will have repercussions throughout all of
>> physics. Bill
>> > Sethares suggested that I get you guys onto the problem because you
>> are the
>> > ones to do it and the more experimental proof the better.
>> >
>> > Thanks again Carl
>> >
>> > Rick
>> >
>> > ----- Original Message ----
>> > From: Carl Lumma <carl@... <mailto:carl% 40lumma.org> >
>> > To: tuning@yahoogroups. com <mailto:tuning% 40yahoogroups. com>
>> > Sent: Tuesday, 27 May, 2008 2:33:31 AM
>> > Subject: [tuning] Re: Hi!
>> >
>> > Hi Rick,
>> >
>> >> Now my question is: are our tempered intervals truly irrational,
>> >> which would make them aperiodic and non-tonal by definition, or
>> >> is it really the case that they approximate these or other ratios
>> >> in the rarefied upper realms of the harmonic series? In other
>> >> words, perhaps there is a limit to what we can do in the physical
>> >> world and we can only create (and/or hear) to a few decimal places?
>> >
>> > The intervals exist abstractly with infinite precision but
>> > of course can never be tuned or performed with infinite
>> > precision. It's equivalent to whether you believe in
>> > real numbers. Is that your question?
>> >
>> > -Carl
>> >
>> >
>> > ____________ _________ _________ __
>> > Get the name you always wanted with the new y7mail email address.
>> >
>>
>>
>
> ________________________________
> Get the name you always wanted with the new y7mail email address.
>
>

Sorry, forgot your actual question. In fact I never said that ALL waves are periodic but only that they must have the potential to be. What I have proved is that superposition and harmony is a universal law of nature, perhaps the most fundamental. Thus, a perfect fifth will transform to a perfect fifth, a flat-fifth (irrational) to a flat-fifth, but not a perfect fifth to a flat-fifth. Logical and obvious I know, but that is not what is currently being maintained in relativity and quantum mechanics.

----- Original Message ----
From: Mike Battaglia <battaglia01@...>
To: tuning@yahoogroups.com
Sent: Wednesday, 28 May, 2008 2:27:26 PM
Subject: Re: [tuning] Re: Hi!

I'm still curious as to the answer to my question -- how is it that
you know that ALL waves are periodic, rather than all waves are NOT
periodic?

Just curious.

-Mike

On Wed, May 28, 2008 at 12:17 AM, rick ballan <rick_ballan@ yahoo.com. au> wrote:
> Sorry but I don't know what JI is.
>
> How can such things be measured though.
> what if the wave is a million years
> to pick a short one
>
> This is related to a standard philosophical question called Hume's problem
> of induction. It basically states that we are not justified in assuming that
> the laws of physics will be the same tomorrow as they are today. But what if
> our sense of regularity in time itself comes from periodic light, sound and
> matter waves, all of which can be proved by experiment? And while one wave
> might decay, there is still an infinite number to deal with at any one
> moment e.g. the colour of light is periodic, the energy of matter, and the
> sine waves of any sound analysis.
>
> ----- Original Message ----
> From: Kraig Grady <kraiggrady@anaphori a.com>
> To: tuning@yahoogroups. com
> Sent: Wednesday, 28 May, 2008 7:28:54 AM
> Subject: Re: [tuning] Re: Hi!
>
> having heard JI in a various degrees of accuracy, the closer and more
> you get to perfect, there is a logarithmic sweep toward various
> phenomenon. It seems in the real non electrically guided sound world,
> there does not seem to be any real attraction toward periodic. We know
> that pendulum clocks will move toward synchronization, so maybe we need
> to hold the tones longer.
>
> How can such things be measured though.
> what if the wave is a million years
> to pick a short one
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria. com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>
>
> ',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,
>
> Mike Battaglia wrote:
>>
>> I never thought I'd see this in a tuning forum, but that is a very,
>> very, very deep and interesting question that I think everyone has
>> considered in some form or another.
>>
>> Although I usually consider the counter-question -- if two frequencies
>> are in a 2/1 ratio, and they can't be physically tuned to that
>> precision, are they actually periodic at all?
>>
>> Or if two lines on a blackboard are supposed to be an inch apart, but
>> they aren't really an inch apart, how many inches apart are they? Will
>> the ratio of actual distance to one inch be rational or irrational?
>>
>> So the question is, is ANYTHING in nature perfectly periodic/rational?
>> You say yes, but to an extremely fine degree, if I understand
>> correctly.
>>
>> I am interested in seeing your proof of this.
>>
>> -Mike
>>
>> On Tue, May 27, 2008 at 3:36 AM, rick ballan <rick_ballan@ yahoo.com. au
>> <mailto:rick_ ballan%40yahoo. com.au>> wrote:
>> > Thanks Carl. Yes I suppose that's one way of stating the question. More
>> > precisely this gap between the abstract real numbers and those which are
>> > actually tuned or performed is not only one between the ideal and
>> reality,
>> > but more importantly between periodicity and aperiodicity. As you no
>> doubt
>> > know, given a ratio between two frequencies a/b where a and b are whole,
>> > then the resultant wave will be periodic, the frequency being the
>> highest
>> > common factor between the two. Extending this to all possible
>> combinations,
>> > then the class of these represents both the number of "instruments"
>> which
>> > could play this frequency (note) and also the basis of harmonic
>> > intervals/chords i.e. tonality. But if the waves bear an irrational
>> > relation, then a and b do not exist and no periodic wave is produced
>> (e.g.
>> > Pythagoras' proof that no ratio a/b corresponds to the sq root of 2,
>> which
>> > is the flat-fifth interval).
>> >
>> > Now the reason I ask is not in my capacity as a jazz guitarist but
>> because
>> > I've written a theoretical physics paper on general wave theory that
>> applies
>> > to electro-magnetics and quantum waves as well, and which is
>> currently being
>> > reviewed at Sydney uni. If all waves are in reality periodic, then
>> they are
>> > also harmonic. In fact my paper shows many mathematical proof to this
>> > effect. It does this by showing that it always leads into
>> self-contradiction
>> > otherwise. It also debunks much of the experimental evidence used as
>> "proof"
>> > that light and matter waves are irrational. So you see that to
>> answer this
>> > question precisely will have repercussions throughout all of
>> physics. Bill
>> > Sethares suggested that I get you guys onto the problem because you
>> are the
>> > ones to do it and the more experimental proof the better.
>> >
>> > Thanks again Carl
>> >
>> > Rick
>> >
>> > ----- Original Message ----
>> > From: Carl Lumma <carl@... <mailto:carl% 40lumma.org> >
>> > To: tuning@yahoogroups. com <mailto:tuning% 40yahoogroups. com>
>> > Sent: Tuesday, 27 May, 2008 2:33:31 AM
>> > Subject: [tuning] Re: Hi!
>> >
>> > Hi Rick,
>> >
>> >> Now my question is: are our tempered intervals truly irrational,
>> >> which would make them aperiodic and non-tonal by definition, or
>> >> is it really the case that they approximate these or other ratios
>> >> in the rarefied upper realms of the harmonic series? In other
>> >> words, perhaps there is a limit to what we can do in the physical
>> >> world and we can only create (and/or hear) to a few decimal places?
>> >
>> > The intervals exist abstractly with infinite precision but
>> > of course can never be tuned or performed with infinite
>> > precision. It's equivalent to whether you believe in
>> > real numbers. Is that your question?
>> >
>> > -Carl
>> >
>> >
>> > ____________ _________ _________ __
>> > Get the name you always wanted with the new y7mail email address.
>> >
>>
>>
>
> ____________ _________ _________ __
> Get the name you always wanted with the new y7mail email address.
>
>

Get the name you always wanted with the new y7mail email address.
www.yahoo7.com.au/mail

Hi Mike. I sent you my paper and an email but it doesn't seem to want to get through. I'm getting so many emails I'm confusing myself and can't find where to stop them.

----- Original Message ----
From: Mike Battaglia <battaglia01@...>
To: tuning@yahoogroups.com
Sent: Wednesday, 28 May, 2008 6:20:16 AM
Subject: Re: [tuning] Re: Hi!

I never thought I'd see this in a tuning forum, but that is a very,
very, very deep and interesting question that I think everyone has
considered in some form or another.

Although I usually consider the counter-question -- if two frequencies
are in a 2/1 ratio, and they can't be physically tuned to that
precision, are they actually periodic at all?

Or if two lines on a blackboard are supposed to be an inch apart, but
they aren't really an inch apart, how many inches apart are they? Will
the ratio of actual distance to one inch be rational or irrational?

So the question is, is ANYTHING in nature perfectly periodic/rational?
You say yes, but to an extremely fine degree, if I understand
correctly.

I am interested in seeing your proof of this.

-Mike

On Tue, May 27, 2008 at 3:36 AM, rick ballan <rick_ballan@ yahoo.com. au> wrote:
> Thanks Carl. Yes I suppose that's one way of stating the question. More
> precisely this gap between the abstract real numbers and those which are
> actually tuned or performed is not only one between the ideal and reality,
> but more importantly between periodicity and aperiodicity. As you no doubt
> know, given a ratio between two frequencies a/b where a and b are whole,
> then the resultant wave will be periodic, the frequency being the highest
> common factor between the two. Extending this to all possible combinations,
> then the class of these represents both the number of "instruments" which
> could play this frequency (note) and also the basis of harmonic
> intervals/chords i.e. tonality. But if the waves bear an irrational
> relation, then a and b do not exist and no periodic wave is produced (e.g.
> Pythagoras' proof that no ratio a/b corresponds to the sq root of 2, which
> is the flat-fifth interval).
>
> Now the reason I ask is not in my capacity as a jazz guitarist but because
> I've written a theoretical physics paper on general wave theory that applies
> to electro-magnetics and quantum waves as well, and which is currently being
> reviewed at Sydney uni. If all waves are in reality periodic, then they are
> also harmonic. In fact my paper shows many mathematical proof to this
> effect. It does this by showing that it always leads into self-contradiction
> otherwise. It also debunks much of the experimental evidence used as "proof"
> that light and matter waves are irrational. So you see that to answer this
> question precisely will have repercussions throughout all of physics. Bill
> Sethares suggested that I get you guys onto the problem because you are the
> ones to do it and the more experimental proof the better.
>
> Thanks again Carl
>
> Rick
>
> ----- Original Message ----
> From: Carl Lumma <carl@...>
> To: tuning@yahoogroups. com
> Sent: Tuesday, 27 May, 2008 2:33:31 AM
> Subject: [tuning] Re: Hi!
>
> Hi Rick,
>
>> Now my question is: are our tempered intervals truly irrational,
>> which would make them aperiodic and non-tonal by definition, or
>> is it really the case that they approximate these or other ratios
>> in the rarefied upper realms of the harmonic series? In other
>> words, perhaps there is a limit to what we can do in the physical
>> world and we can only create (and/or hear) to a few decimal places?
>
> The intervals exist abstractly with infinite precision but
> of course can never be tuned or performed with infinite
> precision. It's equivalent to whether you believe in
> real numbers. Is that your question?
>
> -Carl
>
>
> ____________ _________ _________ __
> Get the name you always wanted with the new y7mail email address.
>

Get the name you always wanted with the new y7mail email address.
www.yahoo7.com.au/mail

What is this 'transformation' you are talking about?

The properties of periodic functions, Fourier series, etc. have been
known mathematically for decades or centuries now, and form a basic
part of the theory of optics, quantum mechanics, field theory and so
on, so I think it is unlikely you have found anything new. It is also
worrying if you rely on ill-defined terminology like a wave 'having
the potential to be periodic'. What could this mean?
~~~T~~~

--- In tuning@yahoogroups.com, rick ballan <rick_ballan@...> wrote:
>
> Sorry, forgot your actual question. In fact I never said that ALL
waves are periodic but only that they must have the potential to be.
What I have proved is that superposition and harmony is a universal
law of nature, perhaps the most fundamental. Thus, a perfect fifth
will transform to a perfect fifth, a flat-fifth (irrational) to a
flat-fifth, but not a perfect fifth to a flat-fifth. Logical and
obvious I know, but that is not what is currently being maintained in
relativity and quantum mechanics.
>
>
> ----- Original Message ----
> From: Mike Battaglia <battaglia01@...>
> To: tuning@yahoogroups.com
> Sent: Wednesday, 28 May, 2008 2:27:26 PM
> Subject: Re: [tuning] Re: Hi!
>
>
> I'm still curious as to the answer to my question -- how is it that
> you know that ALL waves are periodic, rather than all waves are NOT
> periodic?
>
> Just curious.
>
> -Mike
>

Hi Kraig,

Did you hear the good news? A close friend of mine (John Wardle) has
been working closely with the NSW state gov't to repeal all these laws
(called POPE laws) which have been blocking musical performance in
public places. These have to do with liquor licensing, safety, and
noise pollution, and they effectively destroyed whole musical careers
since 96'. For instance, before it cost $65000 for a small restaurant
to have a jazz guitarist and serve alcohol, while having a DJ and TV
screen was a tax incentive. Now it has been reduced to $500 per year
and having a DJ or TV screen costs hefty performing rights fees. Also
these "noise" laws were being used by fierce lobbyist property
developers to close venues and buy them up for development at a cheap
price. We argued that music is by definition not noise so the law
doesn't apply (if it is noise, then this is an educational issue).

Anyway, I've been invited to play for the state premier at lunchtime
today as a symbolic thank you. Bit nerve racking as I was only invited
last night at 1am and I haven't touched the guitar for weeks.

----- Original Message ----
From: Kraig Grady <kraiggrady@...>
To: tuning@yahoogroups.com
Sent: Wednesday, 28 May, 2008 7:28:54 AM
Subject: Re: [tuning] Re: Hi!

having heard JI in a various degrees of accuracy, the closer and more
you get to perfect, there is a logarithmic sweep toward various
phenomenon. It seems in the real non electrically guided sound world,
there does not seem to be any real attraction toward periodic. We know
that pendulum clocks will move toward synchronization, so maybe we need
to hold the tones longer.

How can such things be measured though.
what if the wave is a million years
to pick a short one

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere:
North American Embassy of Anaphoria Island <http://anaphoria. com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>

',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,

Mike Battaglia wrote:
>
> I never thought I'd see this in a tuning forum, but that is a very,
> very, very deep and interesting question that I think everyone has
> considered in some form or another.
>
> Although I usually consider the counter-question -- if two frequencies
> are in a 2/1 ratio, and they can't be physically tuned to that
> precision, are they actually periodic at all?
>
> Or if two lines on a blackboard are supposed to be an inch apart, but
> they aren't really an inch apart, how many inches apart are they? Will
> the ratio of actual distance to one inch be rational or irrational?
>
> So the question is, is ANYTHING in nature perfectly periodic/rational?
> You say yes, but to an extremely fine degree, if I understand
> correctly.
>
> I am interested in seeing your proof of this.
>
> -Mike
>
> On Tue, May 27, 2008 at 3:36 AM, rick ballan <rick_ballan@ yahoo.com. au
> <mailto:rick_ ballan%40yahoo. com.au>> wrote:
> > Thanks Carl. Yes I suppose that's one way of stating the question. More
> > precisely this gap between the abstract real numbers and those which are
> > actually tuned or performed is not only one between the ideal and
> reality,
> > but more importantly between periodicity and aperiodicity. As you no
> doubt
> > know, given a ratio between two frequencies a/b where a and b are whole,
> > then the resultant wave will be periodic, the frequency being the
> highest
> > common factor between the two. Extending this to all possible
> combinations,
> > then the class of these represents both the number of "instruments"
> which
> > could play this frequency (note) and also the basis of harmonic
> > intervals/chords i.e. tonality. But if the waves bear an irrational
> > relation, then a and b do not exist and no periodic wave is produced
> (e.g.
> > Pythagoras' proof that no ratio a/b corresponds to the sq root of 2,
> which
> > is the flat-fifth interval).
> >
> > Now the reason I ask is not in my capacity as a jazz guitarist but
> because
> > I've written a theoretical physics paper on general wave theory that
> applies
> > to electro-magnetics and quantum waves as well, and which is
> currently being
> > reviewed at Sydney uni. If all waves are in reality periodic, then
> they are
> > also harmonic. In fact my paper shows many mathematical proof to this
> > effect. It does this by showing that it always leads into
> self-contradiction
> > otherwise. It also debunks much of the experimental evidence used as
> "proof"
> > that light and matter waves are irrational. So you see that to
> answer this
> > question precisely will have repercussions throughout all of
> physics. Bill
> > Sethares suggested that I get you guys onto the problem because you
> are the
> > ones to do it and the more experimental proof the better.
> >
> > Thanks again Carl
> >
> > Rick
> >
> > ----- Original Message ----
> > From: Carl Lumma <carl@... <mailto:carl% 40lumma.org> >
> > To: tuning@yahoogroups. com <mailto:tuning% 40yahoogroups. com>
> > Sent: Tuesday, 27 May, 2008 2:33:31 AM
> > Subject: [tuning] Re: Hi!
> >
> > Hi Rick,
> >
> >> Now my question is: are our tempered intervals truly irrational,
> >> which would make them aperiodic and non-tonal by definition, or
> >> is it really the case that they approximate these or other ratios
> >> in the rarefied upper realms of the harmonic series? In other
> >> words, perhaps there is a limit to what we can do in the physical
> >> world and we can only create (and/or hear) to a few decimal places?
> >
> > The intervals exist abstractly with infinite precision but
> > of course can never be tuned or performed with infinite
> > precision. It's equivalent to whether you believe in
> > real numbers. Is that your question?
> >
> > -Carl
> >
> >
> > ____________ _________ _________ __
> > Get the name you always wanted with the new y7mail email address.
> >
>
>

Get the name you always wanted with the new y7mail email address.
www.yahoo7.com.au/mail

Sorry for the delay. Yes i heard that this might happen! thank your friend for me. i will hopefully be able to hustle up some more shows soon!

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

rick ballan wrote:
> Hi Kraig,
>
> Did you hear the good news? A close friend of mine (John Wardle) has > been working closely with the NSW state gov't to repeal all these laws > (called POPE laws) which have been blocking musical performance in > public places. These have to do with liquor licensing, safety, and > noise pollution, and they effectively destroyed whole musical careers > since 96'. For instance, before it cost $65000 for a small restaurant > to have a jazz guitarist and serve alcohol, while having a DJ and TV > screen was a tax incentive. Now it has been reduced to $500 per year > and having a DJ or TV screen costs hefty performing rights fees. Also > these "noise" laws were being used by fierce lobbyist property > developers to close venues and buy them up for development at a cheap > price. We argued that music is by definition not noise so the law > doesn't apply (if it is noise, then this is an educational issue).
>
> Anyway, I've been invited to play for the state premier at lunchtime > today as a symbolic thank you. Bit nerve racking as I was only invited > last night at 1am and I haven't touched the guitar for weeks.
>
> ----- Original Message ----
> From: Kraig Grady <kraiggrady@...>
> To: tuning@yahoogroups.com
> Sent: Wednesday, 28 May, 2008 7:28:54 AM
> Subject: Re: [tuning] Re: Hi!
>
> having heard JI in a various degrees of accuracy, the closer and more
> you get to perfect, there is a logarithmic sweep toward various
> phenomenon. It seems in the real non electrically guided sound world,
> there does not seem to be any real attraction toward periodic. We know
> that pendulum clocks will move toward synchronization, so maybe we need
> to hold the tones longer.
>
> How can such things be measured though.
> what if the wave is a million years
> to pick a short one
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria. com/ > <http://anaphoria.com/>>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. > com/ <http://anaphoriasouth.blogspot.com/>>
>
> ',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,
>
> Mike Battaglia wrote:
> >
> > I never thought I'd see this in a tuning forum, but that is a very,
> > very, very deep and interesting question that I think everyone has
> > considered in some form or another.
> >
> > Although I usually consider the counter-question -- if two frequencies
> > are in a 2/1 ratio, and they can't be physically tuned to that
> > precision, are they actually periodic at all?
> >
> > Or if two lines on a blackboard are supposed to be an inch apart, but
> > they aren't really an inch apart, how many inches apart are they? Will
> > the ratio of actual distance to one inch be rational or irrational?
> >
> > So the question is, is ANYTHING in nature perfectly periodic/rational?
> > You say yes, but to an extremely fine degree, if I understand
> > correctly.
> >
> > I am interested in seeing your proof of this.
> >
> > -Mike
> >
> > On Tue, May 27, 2008 at 3:36 AM, rick ballan <rick_ballan@ > yahoo.com. au <mailto:rick_ballan%40yahoo.com.au>
> > <mailto:rick_ ballan%40yahoo. com.au>> wrote:
> > > Thanks Carl. Yes I suppose that's one way of stating the question. > More
> > > precisely this gap between the abstract real numbers and those > which are
> > > actually tuned or performed is not only one between the ideal and
> > reality,
> > > but more importantly between periodicity and aperiodicity. As you no
> > doubt
> > > know, given a ratio between two frequencies a/b where a and b are > whole,
> > > then the resultant wave will be periodic, the frequency being the
> > highest
> > > common factor between the two. Extending this to all possible
> > combinations,
> > > then the class of these represents both the number of "instruments"
> > which
> > > could play this frequency (note) and also the basis of harmonic
> > > intervals/chords i.e. tonality. But if the waves bear an irrational
> > > relation, then a and b do not exist and no periodic wave is produced
> > (e.g.
> > > Pythagoras' proof that no ratio a/b corresponds to the sq root of 2,
> > which
> > > is the flat-fifth interval).
> > >
> > > Now the reason I ask is not in my capacity as a jazz guitarist but
> > because
> > > I've written a theoretical physics paper on general wave theory that
> > applies
> > > to electro-magnetics and quantum waves as well, and which is
> > currently being
> > > reviewed at Sydney uni. If all waves are in reality periodic, then
> > they are
> > > also harmonic. In fact my paper shows many mathematical proof to this
> > > effect. It does this by showing that it always leads into
> > self-contradiction
> > > otherwise. It also debunks much of the experimental evidence used as
> > "proof"
> > > that light and matter waves are irrational. So you see that to
> > answer this
> > > question precisely will have repercussions throughout all of
> > physics. Bill
> > > Sethares suggested that I get you guys onto the problem because you
> > are the
> > > ones to do it and the more experimental proof the better.
> > >
> > > Thanks again Carl
> > >
> > > Rick
> > >
> > > ----- Original Message ----
> > > From: Carl Lumma <carl@... <mailto:carl%40lumma.org> > <mailto:carl% 40lumma.org> >
> > > To: tuning@yahoogroups. com <mailto:tuning%40yahoogroups.com> > <mailto:tuning% 40yahoogroups. com>
> > > Sent: Tuesday, 27 May, 2008 2:33:31 AM
> > > Subject: [tuning] Re: Hi!
> > >
> > > Hi Rick,
> > >
> > >> Now my question is: are our tempered intervals truly irrational,
> > >> which would make them aperiodic and non-tonal by definition, or
> > >> is it really the case that they approximate these or other ratios
> > >> in the rarefied upper realms of the harmonic series? In other
> > >> words, perhaps there is a limit to what we can do in the physical
> > >> world and we can only create (and/or hear) to a few decimal places?
> > >
> > > The intervals exist abstractly with infinite precision but
> > > of course can never be tuned or performed with infinite
> > > precision. It's equivalent to whether you believe in
> > > real numbers. Is that your question?
> > >
> > > -Carl
> > >
> > >
> > > ____________ _________ _________ __
> > > Get the name you always wanted with the new y7mail email address.
> > >
> >
> >
>
>
> ------------------------------------------------------------------------
> Get the name you always wanted with the new y7mail email address > <http://au.rd.yahoo.com/mail/taglines/au/y7mail/default/*http://au.mail.yahoo.com/?p1=ni&p2=general&p3=tagline&p4=other>. >
>

sorry this should be offlist!

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Kraig Grady wrote:
>
> Sorry for the delay. Yes i heard that this might happen! thank your
> friend for me. i will hopefully be able to hustle up some more shows soon!
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> rick ballan wrote:
> > Hi Kraig,
> >
> > Did you hear the good news? A close friend of mine (John Wardle) has
> > been working closely with the NSW state gov't to repeal all these laws
> > (called POPE laws) which have been blocking musical performance in
> > public places. These have to do with liquor licensing, safety, and
> > noise pollution, and they effectively destroyed whole musical careers
> > since 96'. For instance, before it cost $65000 for a small restaurant
> > to have a jazz guitarist and serve alcohol, while having a DJ and TV
> > screen was a tax incentive. Now it has been reduced to $500 per year
> > and having a DJ or TV screen costs hefty performing rights fees. Also
> > these "noise" laws were being used by fierce lobbyist property
> > developers to close venues and buy them up for development at a cheap
> > price. We argued that music is by definition not noise so the law
> > doesn't apply (if it is noise, then this is an educational issue).
> >
> > Anyway, I've been invited to play for the state premier at lunchtime
> > today as a symbolic thank you. Bit nerve racking as I was only invited
> > last night at 1am and I haven't touched the guitar for weeks.
> >
> > ----- Original Message ----
> > From: Kraig Grady <kraiggrady@... > <mailto:kraiggrady%40anaphoria.com>>
> > To: tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>
> > Sent: Wednesday, 28 May, 2008 7:28:54 AM
> > Subject: Re: [tuning] Re: Hi!
> >
> > having heard JI in a various degrees of accuracy, the closer and more
> > you get to perfect, there is a logarithmic sweep toward various
> > phenomenon. It seems in the real non electrically guided sound world,
> > there does not seem to be any real attraction toward periodic. We know
> > that pendulum clocks will move toward synchronization, so maybe we need
> > to hold the tones longer.
> >
> > How can such things be measured though.
> > what if the wave is a million years
> > to pick a short one
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria. com/
> > <http://anaphoria.com/ <http://anaphoria.com/>>>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot.
> > com/ <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>>
> >
> > ',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,
> >
> > Mike Battaglia wrote:
> > >
> > > I never thought I'd see this in a tuning forum, but that is a very,
> > > very, very deep and interesting question that I think everyone has
> > > considered in some form or another.
> > >
> > > Although I usually consider the counter-question -- if two frequencies
> > > are in a 2/1 ratio, and they can't be physically tuned to that
> > > precision, are they actually periodic at all?
> > >
> > > Or if two lines on a blackboard are supposed to be an inch apart, but
> > > they aren't really an inch apart, how many inches apart are they? Will
> > > the ratio of actual distance to one inch be rational or irrational?
> > >
> > > So the question is, is ANYTHING in nature perfectly periodic/rational?
> > > You say yes, but to an extremely fine degree, if I understand
> > > correctly.
> > >
> > > I am interested in seeing your proof of this.
> > >
> > > -Mike
> > >
> > > On Tue, May 27, 2008 at 3:36 AM, rick ballan <rick_ballan@
> > yahoo.com. au <mailto:rick_ballan%40yahoo.com.au>
> > > <mailto:rick_ ballan%40yahoo. com.au>> wrote:
> > > > Thanks Carl. Yes I suppose that's one way of stating the question.
> > More
> > > > precisely this gap between the abstract real numbers and those
> > which are
> > > > actually tuned or performed is not only one between the ideal and
> > > reality,
> > > > but more importantly between periodicity and aperiodicity. As you no
> > > doubt
> > > > know, given a ratio between two frequencies a/b where a and b are
> > whole,
> > > > then the resultant wave will be periodic, the frequency being the
> > > highest
> > > > common factor between the two. Extending this to all possible
> > > combinations,
> > > > then the class of these represents both the number of "instruments"
> > > which
> > > > could play this frequency (note) and also the basis of harmonic
> > > > intervals/chords i.e. tonality. But if the waves bear an irrational
> > > > relation, then a and b do not exist and no periodic wave is produced
> > > (e.g.
> > > > Pythagoras' proof that no ratio a/b corresponds to the sq root of 2,
> > > which
> > > > is the flat-fifth interval).
> > > >
> > > > Now the reason I ask is not in my capacity as a jazz guitarist but
> > > because
> > > > I've written a theoretical physics paper on general wave theory that
> > > applies
> > > > to electro-magnetics and quantum waves as well, and which is
> > > currently being
> > > > reviewed at Sydney uni. If all waves are in reality periodic, then
> > > they are
> > > > also harmonic. In fact my paper shows many mathematical proof to > this
> > > > effect. It does this by showing that it always leads into
> > > self-contradiction
> > > > otherwise. It also debunks much of the experimental evidence used as
> > > "proof"
> > > > that light and matter waves are irrational. So you see that to
> > > answer this
> > > > question precisely will have repercussions throughout all of
> > > physics. Bill
> > > > Sethares suggested that I get you guys onto the problem because you
> > > are the
> > > > ones to do it and the more experimental proof the better.
> > > >
> > > > Thanks again Carl
> > > >
> > > > Rick
> > > >
> > > > ----- Original Message ----
> > > > From: Carl Lumma <carl@... <mailto:carl%40lumma.org> > <mailto:carl%40lumma.org>
> > <mailto:carl% 40lumma.org> >
> > > > To: tuning@yahoogroups. com <mailto:tuning%40yahoogroups.com>
> > <mailto:tuning% 40yahoogroups. com>
> > > > Sent: Tuesday, 27 May, 2008 2:33:31 AM
> > > > Subject: [tuning] Re: Hi!
> > > >
> > > > Hi Rick,
> > > >
> > > >> Now my question is: are our tempered intervals truly irrational,
> > > >> which would make them aperiodic and non-tonal by definition, or
> > > >> is it really the case that they approximate these or other ratios
> > > >> in the rarefied upper realms of the harmonic series? In other
> > > >> words, perhaps there is a limit to what we can do in the physical
> > > >> world and we can only create (and/or hear) to a few decimal places?
> > > >
> > > > The intervals exist abstractly with infinite precision but
> > > > of course can never be tuned or performed with infinite
> > > > precision. It's equivalent to whether you believe in
> > > > real numbers. Is that your question?
> > > >
> > > > -Carl
> > > >
> > > >
> > > > ____________ _________ _________ __
> > > > Get the name you always wanted with the new y7mail email address.
> > > >
> > >
> > >
> >
> >
> > ----------------------------------------------------------
> > Get the name you always wanted with the new y7mail email address
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