Request for Assistance on a Scale

I am working on a project that requires prehistoric music.

I found this article in wikipedia
http://en.wikipedia.org/wiki/Prehistoric_music

and was wondering if anyone knew the correct scale interpretation of
this sentence:

The bone flute plays both the five- or seven-note scale of Xia Zhi and
six-note scale of Qing Shang of the ancient Chinese musical system.

Neither of the scales are listed in this reference on Chinese music:

http://upload.wikimedia.org/wikipedia/en/2/29/Modality.gif

If you have another suggestion that is non-Chinese it would be welcome
also.

Thanks!

Chris

i can't imagine that ethnomusicologist would not rip this page to threads. I think i will send it to their list! the idea that music relate to literacy is absurd. India is much more classical music and much older than the puny few hundred years Europe has climbed out of its beastly existence ( of human sacrifice BTW which we can debate has ended there [ Srebrenica <http://english.aljazeera.net/news/europe/2008/06/2008619125525418575.html>] <http://english.aljazeera.net/news/europe/2008/06/2008619125525418575.html> or by its colonies elsewhere [Iraq])

Jim French convinced me that the bones were used for reed instruments not flutes. try and make a bone flute. The spacing of equally placed holes leads to the subharmonic series of which Kathleen Schlesinger knew the most. Her book- The Greek Aulos- should be in every microtonal library IMHO :).
since it is hard to get i will mention that she site examples of where the exit hole is tuned to a perfect fifth below various notes in the subharmonic series. you can play as you which keeping in mind sub 7, 9,10 or 11.
Because of the times and her sexual persuasion, her book and work where attacked on the most trivial of grounds, yet appeared to be successful . Within the first few pages she shows the common tone modulations of the subharmonic series which gives you- the diamond! Which she argues was the basis of the Greek system. Her references to other indigenous music. the relation to Patch is uncanny in this regard and maybe his meeting with her made Mayer's work even more clear, or not.

/^_,',',',_ //^ /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/>

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

vaisvil wrote:
>
> I am working on a project that requires prehistoric music.
>
> I found this article in wikipedia
> http://en.wikipedia.org/wiki/Prehistoric_music > <http://en.wikipedia.org/wiki/Prehistoric_music>
>
> and was wondering if anyone knew the correct scale interpretation of
> this sentence:
>
> The bone flute plays both the five- or seven-note scale of Xia Zhi and
> six-note scale of Qing Shang of the ancient Chinese musical system.
>
> Neither of the scales are listed in this reference on Chinese music:
>
> http://upload.wikimedia.org/wikipedia/en/2/29/Modality.gif > <http://upload.wikimedia.org/wikipedia/en/2/29/Modality.gif>
>
> If you have another suggestion that is non-Chinese it would be welcome
> also.
>
> Thanks!
>
> Chris
>
>

[ Attachment content not displayed ]

Chris Vaisvil wrote:
> What is the "sub-harmonic" series?
> > I have not heard of that before.

http://dictionary.reference.com/search?r=2&q=subharmonic

[ Attachment content not displayed ]

It is the same intervals as the harmonic series except going down instead of up. if you divide a string into equal parts, usually done at the midpoint of the string or equally spaced wholes you will end up with this series.
A practical application would be in having a high drone and you sounded just intervals below.

It is much less explored than the harmonic series these days, but is just as musically viable. there is a certain depth it has that the harmonic series can lack.

on page 3 of
http://anaphoria.com/tres.PDF
there are some interesting subharmonic based scales using two different series instead of one.
But this is a little developed over the prehistoric idea. yet people where little different than us biologically so they might have taken to music way more than we give them credit for. I mean did birds have to learn monosyllable songs first? i doubt it!
i have notes on other scales that i will have to put up at some point. twist my arm if really urgent.
but i go to Japan on Friday

/^_,',',',_ //^ /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/>

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

Chris Vaisvil wrote:
>
> What is the "sub-harmonic" series?
>
> I have not heard of that before.
>
> Familyographer Zone
>
> .
>
>

--- In tuning@yahoogroups.com, "vaisvil" <chrisvaisvil@...> wrote:

>
> If you have another suggestion that is non-Chinese it would be welcome
> also.
>

I would vote for the sort of pentatonic used by the Tuvans, which is
straight out of the overtone series. Not only do they use these scales
for singing (where they essentially have no choice unless they alter
the base note, which they sometimes do), but they also use them when
playing their bowed string instrument. Thus you've got tonic, pure
major second, pure major third, the jump to the pure fifth (funny how
they mostly avoid the sharp fourth), and the last note can have a dual
identity, either be the natural sixth when it occurs above the fifth
or the natural 7th when it occurs below the tonic. I have some
recordings of aboriginal music using similar scales. Can't get a whole
lot more "natural" than that.

But then, maybe it doesn't sound "primitive" enough for your purposes.

;-)

Ciao,

P

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> It is the same intervals as the harmonic series except going down
> instead of up. if you divide a string into equal parts, usually done at
> the midpoint of the string or equally spaced wholes you will end up
with
> this series.

Say what?! If you divide a string into equal parts, you get the normal
harmonic series. Shorter length = higher pitch. Or does Anaphoria
represent a "Mystery Spot" outside the normal laws of physics?

In order to reproduce a subharmonic series acoustically, you will need
to multiply the lengths of a string or tube by whole numbers, not divide.

Ciao,

P

Paul Poletti wrote:
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>> It is the same intervals as the harmonic series except going down >> instead of up. if you divide a string into equal parts, usually done at >> the midpoint of the string or equally spaced wholes you will end up
> with >> this series.
> > Say what?! If you divide a string into equal parts, you get the normal
> harmonic series. Shorter length = higher pitch. Or does Anaphoria
> represent a "Mystery Spot" outside the normal laws of physics?

Anaphoria's with the rest of the world on this one.

> In order to reproduce a subharmonic series acoustically, you will need
> to multiply the lengths of a string or tube by whole numbers, not divide.

He said divide into equal parts, not divide by whole numbers. What happens if you multiply the smallest of the equal parts by whole numbers?

Graham

no i am afraid not. take a guitar and place the frets equally spaced apart and you will have the subharmonic series ( mixed with the distortion of string bending.)
there has been a few subharmonic guitars made and this is what you have

/^_,',',',_ //^ /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/>

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

Paul Poletti wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > It is the same intervals as the harmonic series except going down
> > instead of up. if you divide a string into equal parts, usually done at
> > the midpoint of the string or equally spaced wholes you will end up
> with
> > this series.
>
> Say what?! If you divide a string into equal parts, you get the normal
> harmonic series. Shorter length = higher pitch. Or does Anaphoria
> represent a "Mystery Spot" outside the normal laws of physics?
>
> In order to reproduce a subharmonic series acoustically, you will need
> to multiply the lengths of a string or tube by whole numbers, not divide.
>
> Ciao,
>
> P
>
>

--- In tuning@yahoogroups.com, "Chris Vaisvil" <chrisvaisvil@...> wrote:
>

> > Jim French convinced me that the bones were used for reed instruments
> > not flutes. try and make a bone flute. The spacing of equally placed
> > holes leads to the subharmonic series of which Kathleen
Schlesinger knew
> > the most.

Another miracle! No matter how you slice it, frequency is inversely
proportional to length. ANY series of equally spaced holes will
produce a linear progression of length, thus a linear progression of
pitch. Both harmonic and subharmonic series are log progressions...
and last time I checked, linear and log were like night and day, cat
and dog, hot and cold, etc etc etc. in other words, never the two
shall meet.

I would also be very interested in the evidence which supports the
conclusion that bone instruments were always excited by a reed. A tube
is a tube, and I'm sure an experience kuval player (especially an
Iranian) cold pick up a clarinet without the mouthpiece and play it no
prob. No how is someone in 10,000 year who finds one of the joints of
a clarinet going to divine how the instruent was excited? Do tell!

Ciao,

P

all i know as that i have played many flutes with equally spaced holes and they gave me the subharmonic series except for the exit hole which, more often than not a fifth or fourth against one of the other notes. Schlesinger's critic by the way did not disagree with her math or measurements, just her history. French actually duplicated many of these by pulling them right out of the book.
i will leave it to Graham or the more mathematically inclined to explain the subharmonic series in terms you have a problem with. perhaps if you have a monochord you can plot out where the subharmonic series 8-16 is and observe the distance

/^_,',',',_ //^ /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/>

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

Paul Poletti wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, > "Chris Vaisvil" <chrisvaisvil@...> wrote:
> >
>
> > > Jim French convinced me that the bones were used for reed instruments
> > > not flutes. try and make a bone flute. The spacing of equally placed
> > > holes leads to the subharmonic series of which Kathleen
> Schlesinger knew
> > > the most.
>
> Another miracle! No matter how you slice it, frequency is inversely
> proportional to length. ANY series of equally spaced holes will
> produce a linear progression of length, thus a linear progression of
> pitch. Both harmonic and subharmonic series are log progressions...
> and last time I checked, linear and log were like night and day, cat
> and dog, hot and cold, etc etc etc. in other words, never the two
> shall meet.
>
> I would also be very interested in the evidence which supports the
> conclusion that bone instruments were always excited by a reed. A tube
> is a tube, and I'm sure an experience kuval player (especially an
> Iranian) cold pick up a clarinet without the mouthpiece and play it no
> prob. No how is someone in 10,000 year who finds one of the joints of
> a clarinet going to divine how the instruent was excited? Do tell!
>
> Ciao,
>
> P
>
>

On Tue, Jun 24, 2008 at 3:06 AM, Paul Poletti <paul@...> wrote:
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>>
>> It is the same intervals as the harmonic series except going down
>> instead of up. if you divide a string into equal parts, usually done at
>> the midpoint of the string or equally spaced wholes you will end up
> with
>> this series.
>
> Say what?! If you divide a string into equal parts, you get the normal
> harmonic series. Shorter length = higher pitch. Or does Anaphoria
> represent a "Mystery Spot" outside the normal laws of physics?
>
> In order to reproduce a subharmonic series acoustically, you will need
> to multiply the lengths of a string or tube by whole numbers, not divide.

Well, you have the write idea, but you're misinterpreting Kraig's
statements. Think of it this way:

If I take a guitar string, and I put 7 evenly spaced frets in it: one
halfway through the length of the string, one halfway between each of
those segments, and one halfway between each of THOSE segments, I will
have eight evenly spaced "positions" on the string. Not
logarithmically placed, but linearly placed.

I'll have the open string,

I'll have a string length which is 7/8 of that, so the frequency will
be 8/7 times that of the open string,

I'll have a string length which is 3/4 of that, so the frequency will
be 4/3 times that of the open string,

and so on. The full pattern is that the frequencies will be in this
ratio, where s represents the frequency of the open string:

s, (8/7)s, (4/3)s, (8/5)s, (2/1)s, (8/3)s, (4/1)s, (8/1)s

Now, if we recenter our perspective on this series, so that we call
the TOP frequency the fundamental frequency -- let's call it "f" --
we'll get this perspective:

(1/8)f, (1/7)f, (1/6)f, (1/5)f, (1/4)f, (1/3)f, (1/2)f, f

Which is a subharmonic series. Neat, eh?

-Mike

> Well, you have the write idea, but you're misinterpreting Kraig's
> statements. Think of it this way:

Of course, what I meant to say was that you have the ryte idea.

Just out of curiosity, what does the fretting pattern look like for a
guitar that has frets placed at each harmonic from 8 to 32 or
something? How would that diverge from a 12-equal logarithmic looking
fretting pattern? Would the pattern still look logarithmic in nature,
but have even more of a "curve" to it or something? Maybe an
exponential looking curve rather than a logarithmic one?

-Mike

here is a
diagram
http://www.chrysalis-foundation.org/origins_of_length_ratios.htm

/^_,',',',_ //^ /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:
>
> all i know as that i have played many flutes with equally spaced holes
> and they gave me the subharmonic series except for the exit hole which,
> more often than not a fifth or fourth against one of the other notes.
> Schlesinger's critic by the way did not disagree with her math or
> measurements, just her history. French actually duplicated many of these
> by pulling them right out of the book.
> i will leave it to Graham or the more mathematically inclined to
> explain the subharmonic series in terms you have a problem with. perhaps
> if you have a monochord you can plot out where the subharmonic series
> 8-16 is and observe the distance
>
> /^_,',',',_ //^ /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/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Paul Poletti wrote:
> >
> > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> > <mailto:tuning%40yahoogroups.com>,
> > "Chris Vaisvil" <chrisvaisvil@...> wrote:
> > >
> >
> > > > Jim French convinced me that the bones were used for reed > instruments
> > > > not flutes. try and make a bone flute. The spacing of equally placed
> > > > holes leads to the subharmonic series of which Kathleen
> > Schlesinger knew
> > > > the most.
> >
> > Another miracle! No matter how you slice it, frequency is inversely
> > proportional to length. ANY series of equally spaced holes will
> > produce a linear progression of length, thus a linear progression of
> > pitch. Both harmonic and subharmonic series are log progressions...
> > and last time I checked, linear and log were like night and day, cat
> > and dog, hot and cold, etc etc etc. in other words, never the two
> > shall meet.
> >
> > I would also be very interested in the evidence which supports the
> > conclusion that bone instruments were always excited by a reed. A tube
> > is a tube, and I'm sure an experience kuval player (especially an
> > Iranian) cold pick up a clarinet without the mouthpiece and play it no
> > prob. No how is someone in 10,000 year who finds one of the joints of
> > a clarinet going to divine how the instruent was excited? Do tell!
> >
> > Ciao,
> >
> > P
> >
> >
>
>

the frets are equally (close to- to deal with bend correction) spaced apart !

/^_,',',',_ //^ /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/>

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

Mike Battaglia wrote:
>
> > Well, you have the write idea, but you're misinterpreting Kraig's
> > statements. Think of it this way:
>
> Of course, what I meant to say was that you have the ryte idea.
>
> Just out of curiosity, what does the fretting pattern look like for a
> guitar that has frets placed at each harmonic from 8 to 32 or
> something? How would that diverge from a 12-equal logarithmic looking
> fretting pattern? Would the pattern still look logarithmic in nature,
> but have even more of a "curve" to it or something? Maybe an
> exponential looking curve rather than a logarithmic one?
>
> -Mike
>
>

Paul Poletti wrote:

> Both harmonic and subharmonic series are log progressions

If you say this then each of us probably uses different terminology for different things. For one thing, I find harmonic series to be "linear" because one of the most important properties of a period is its frequency -- i.e. either relative (in form of a ratio) or absolute (in Hz). As the tones in the harmonic series are equally spaced in terms of frequency (i.e. the differences between consecutive frequencies are the same), then I would call the harmonic series "linear" and the subharmonic series "inversely linear". A series of intervals of equal sizes (like a chromatic scale in 12-EDO, for example) is exponential because instead of keeping the differences the same, here the factors are the same (i.e. ~1.05946 for 12-EDO).

For another thing, how could equally spaced holes produce the steps you call "linear" if you mean equally sized intervals by that? You yourself said that length is inversely proportional to frequency, which, however, contradicts your second statement that a linear progression of length is a linear progression of pitch. Equally spaced holes would result in frequencies of 1/f, 2/f, 3/f and so on -- approximately, of course, because of the end effect.

Petr

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

>
> He said divide into equal parts, not divide by whole
> numbers.

Now, THAT'S a difference without a distinction. I defy you divide a
string into equal parts without using whole numbers. If you have a
string divide into 10 segments of equal length, then I'm pretty sure
that each segment will be equal to the total length divide by uh, um,
er, well...10, for example. Now, last time I checked, 10 was indeed a
whole number.

> What happens if you ->multiply<- the smallest of the
> equal parts by whole numbers? [emphasis added]

Then it is no longer "division", is it. By your own words...

You guys are describing the precisely the same mountain, except seen
from the top down rather than the bottom up. Still the same old mountain.

A rose by any other name...

Ciao,

P

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
I agree completely! Here the crux of the issue:

>
> Now, if we recenter our perspective on this series, so that we call
> the TOP frequency the fundamental frequency -- let's call it "f" --
> we'll get this perspective:

This is not just a shift of emphasis, this is a fundamental reversal
of the process; you are no longer "dividing" a *long* string length,
you are multiplying a *short* string length. The simple fact that you
started with a longer string in order to arrive at the generating
string length is of no consequence.
>
> (1/8)f, (1/7)f, (1/6)f, (1/5)f, (1/4)f, (1/3)f, (1/2)f, f
>
> Which is a subharmonic series. Neat, eh?

As I said, you must "multiply". A subharmonic series is, by
definition, "sub", below. You cannot descend in pitch by division of
dimensions of the string or tube. I'm not misinterpreting Kraig's
description, he is simply using the wrong words. If he had used the
right terms, I would have had no trouble.

Ciao,

P

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> no i am afraid not. take a guitar and place the frets equally spaced
> apart and you will have the subharmonic series ( mixed with the
> distortion of string bending.)
> there has been a few subharmonic guitars made and this is what you have

I see my mistake in thinking, now. I was thinking a linear division of
the *octave*, since all modern wind instruments work on that
principle, as do all descriptions of the construction of sclaes using
string lengths. It is the space between the full tube length and the
half tube length which is divided into x parts by whatever scheme. It
didn't occur to me to think of dividing the *entire* tube length into
equal bits. Ditto with strings.

But my basic objection to the descriptions so far remains. The term
"subharmonic" means going down in frequency. Acoustically, you are
multiplying lengths, not dividing. The critical difference is which
length do you consider to be the generating length: the full length,
of the smallest segment. If it is the full length and you are
dividing, then it cannot be the subharmonic series. If it IS the
smallest length, and you are multiplying, then it IS the subharmonic
series.

The critical difference of course is that the one way allows infinite
progression through the appropriate series while the other is a
limited series. You can *divide* a length into however many equal
parts you want, and rise as far as you want through the harmonic
series. However, if you play the slight of hand you guys are playing
and take a short segment of a longer object as the generating length,
you can only descend through the subharmonic series to the longest
multiple of the generating length allowed for by the maximum length of
the object.

Anyway, in a much broader sense, and much more interesting, the whole
crux of the issue revolves around how primitive man approached the
issue. Did he first listen and then construct instruments in such a
way that the imitated what he heard, or did he just make things and
accept the sounds as they came? I suspect a some of both, but they
represent a fundamental difference in approach. Do we control the
sound we make, or do we simply make sounds? Does the ape simply pick
up any old stick to bash in the head of the ape from the other tribe,
or does he, after a spell, start seeking sticks which are heavier at
one end, or perhaps with pointy protrusions, or does he figure out a
way to wedge a stone into the split stick, or ...

Getting back to music, it is impossible to argue which approach is
more "natural", for the moment you CONSTRUCT something, you have
already made a quantum leap. In this sense, even something which seems
as simple as "equal division" is already an intellectual construct of
fairly advanced proportions. Thus any argument that the one or the
other solution is more "primitive", i.e. "less advanced", "less
developed", whatever terminology you want to pin on it, this argument
is bogus. As soon as we start to MAKE things, the genie is out of the
bottle, and we are free to design the object according to our
expectations. And one thing I am sure of, prehistoric man did a good
bit o' singin' long before he started to make melody producing objects.

Granted, the foreign sound of a scale using a subharmonic series would
perhaps present the dramatic effect of being "something different"
which may be advantageous to the ultimate goals of the "project" at
hand, whatever it may be (documentary film? theatre play? Hollywood
pseudo-historical narrative?). In that case, the possible veracity
(which cannot but be suspect in all cases) of the approach is of no
consequence, so one may as well grab whatever scale one wants.

Maybe we have a bone flute (or was it a reed? still waiting for that
explanation) with equally spaced holes precisely because the guy who
made it played it and thought, "Yuk! This thing doesn't sound good at
all!" and threw it promptly into the beat bog.

Who knows?

Ciao,

P

> > Which is a subharmonic series. Neat, eh?
>
> As I said, you must "multiply". A subharmonic series is, by
> definition, "sub", below. You cannot descend in pitch by division of
> dimensions of the string or tube. I'm not misinterpreting Kraig's
> description, he is simply using the wrong words. If he had used the
> right terms, I would have had no trouble.
>
> Ciao,
>
> P

Don't weasel out of it dude. He didn't use the wrong words.

-Carl

> > > Which is a subharmonic series. Neat, eh?
> >
> > As I said, you must "multiply". A subharmonic series is, by
> > definition, "sub", below. You cannot descend in pitch by
> > division of dimensions of the string or tube. I'm not
> > misinterpreting Kraig's description, he is simply using the
> > wrong words. If he had used the right terms, I would have
> > had no trouble.
> >
> > Ciao,
> >
> > P
>
> Don't weasel out of it dude. He didn't use the wrong words.

On the other hand, posts like these

/tuning/topicId_77364.html#77478
/tuning/topicId_77364.html#77440

have been right on the money and were very much appreciated.
Thanks,

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > > Which is a subharmonic series. Neat, eh?
> >
> > As I said, you must "multiply". A subharmonic series is, by
> > definition, "sub", below. You cannot descend in pitch by division of
> > dimensions of the string or tube. I'm not misinterpreting Kraig's
> > description, he is simply using the wrong words. If he had used the
> > right terms, I would have had no trouble.
> >
> > Ciao,
> >
> > P
>
> Don't weasel out of it dude. He didn't use the wrong words.

What he said was this:

> > It is the same intervals as the harmonic series except going down
> > instead of up. if you divide a string into equal parts, usually
done at
> > the midpoint of the string or equally spaced wholes you will end up
> with
> > this series.

Now, "dividing a string into equal parts" (which is what he said, need
i stress again) is EXACTLY what I and the other 2 professors teach the
students of acoustics at ESMUC in order to produce the HARMONIC (not
the lack of the prefix "sub") series. It might appear that we are in
good company in this practice:

http://www.music.sc.edu/fs/bain/atmi02/hs/index-audio.html

http://www.cartage.org.lb/en/themes/arts/music/elements/generalities/harmonic/harmonic.htm

http://graham.main.nc.us/~bhammel/MUSIC/ovrtns.html

http://www.answers.com/topic/harmonic-series?cat=technology

http://www.guitar-vacation-retreats.com/resources/overtone_series.html

(I could go on and on listing literally hundreds, but I hope you get
the point)

ALL of which talk about DIVIDING the string up into equal parts to
produce the HARMONIC series.

Now, practically speaking, you CAN arrive at a limited subharmonic
series by FRETTING a string using any ONE set of equal division points
and then considering the SHORTEST FRET to be the fundamental position,
, but this represents a significant divergence from the normal state
of affairs and the normal approach when designing or talking about
string instrument construction. Somebody who doesn't know what you are
on about can't get it, precisely because you have properly described
neither the theory (i.e. multiplication of the generating length) nor
exactly what you are doing (fretting)... especially if the are used to
the normal description of how to produce the harmonic series.

It's not weaseling, it's just trying to keep the terminology straight.
If I were to teach my students exactly what a "subharmonic series" is
(and I think I will next year, it's an interesting idea!) I would
start by STRESSING that it is the reverse of the harmonic series in
EVERY aspect, involving multiplication instead of division,
frequencies going DOWN instead of up from the generating tone, and a
real world a short tube or string made progressively longer.

BTW, I DID get the whole business about linear and log totally messed
up, thanks to trying to recover from a "contact" hangover and almost
no sleep when I wrote the message, due to the biggest party night of
the year in Catalunya, said partying of which I did not partake but
the constant din of thousands upon thousands of exploding firecrackers
and rockets until almost daybreak DID deprive me of a normal night's
sleep. The harmonic series IS a linear progression of frequency, no
matter which direction you move through it, up or down, but the
subharmonic series is NOT a linear progression of frequencies, not in
any normal sense of the word. Perhaps it is derived by a "reverse
linear" process (though the only references to "reverse linear" I
could find was complex stuff about data analysis), the series of
descending frequencies which a subharmonic series describes is NOT linear.

Glad you liked the other posts, anyway.

;-)

Ciao,

P

BTW I am still REALLY interested in hearing why bones flutes weren't
never no bone flutes but only always bone oboes or clarinets or duduks
or whatever...

Dividing a string into equal parts won't produce a harmonic series.
How could it? The distance along the string from the 2nd harmonic to
the third harmonic is obviously not equal to the length from the 1st
harmonic to the second, if we're counting the first harmonic as the
open string. Dividing a string into equal parts will produce a
subharmonic series from the perspective of the shortest length used in
the string.

-Mike

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> Dividing a string into equal parts won't produce a harmonic series.
> How could it? The distance along the string from the 2nd harmonic to
> the third harmonic is obviously not equal to the length from the 1st
> harmonic to the second, if we're counting the first harmonic as the
> open string. Dividing a string into equal parts will produce a
> subharmonic series from the perspective of the shortest length used in
> the string.
>
> -Mike
>
The crux of the matter, and the original source of confusion in
Kraig's post, is what you mean by "dividing". In acoustics, when
talking about the harmonic series in regards to tubes or strings, it
means that the string vibrates in segments which divide its length
into equal parts; 2 equal parts for the second harmonic, 3 equal parts
for the third harmonic, 4 equal parts for the fourth harmonic, etc,
the rule being that in order to produce harmonic X, the tube or string
must be divided into X equal parts, ALL of which are simultaneously
vibrating. You can, of course, physically produce these frequencies by
touching your finger lightly against the string at any one of the
division points for the mode in particular, or in the case of wind
instruments, opening a very small vent hole at any one of these
division points, though in the case with even-numbered modes, some
points may produce more than one harmonic mode of vibration.

Now, if for you "dividing" means placing frets at points which
represent a series of equal divisions of the total string length, or
in the case of a tube, boring holes at these points, then the series
of notes produced when the tube or string is redimensioned by the act
of placing a finger on the fret or opening a large tone hole
(essentially changing the length of the tube), it cam be considered as
a means to produce a subharmonic series IF and ONLY if you consider
the shortest segment thereby produced to be the fundamental length,
i.e. the length which generates the whole series. Note also that you
are not "dividing" the vibrating object in any acoustical sense, but
rather what you are "dividing" equally is only the measurement of the
object's initial length in order to define a series of different
sublengths.

So the former is an acoustic interpretation of the word "divide", i.e.
literally dividing the vibrating object into smaller units, all of
which are vibrating, and the latter is a completely practical "get out
the ruler" and figure out where to put the elements that will alter
the functional acoustical length of the object. The former literally
produces the harmonic series, the later produces a SCALE which, when
played in a descending direction, follows a limited subharmonic
progression. While the latter may suffice in the instrument workshop,
it won't garner you a passing mark in any acoustics or physics class.

Ciao,

p

Ah, I see what you're saying now. Kraig was referring to putting
evenly-spaced frets down, you're referring to putting unevenly-spaced
frets down at places where the string would be divided into 2 equal
parts, 3 equal, 4 equal, etc.

-Mike

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i was talking about a string, a physical object.
there is nothing in your original description that says you have to do the process for each harmonic so i am afraid your own definition lacks clarity being incomplete. fail.

why anyone would assume that if i said divide in equal parts, that this would be a process you would repeat over and over again for each harmonic. only if you already knew this. So the confusion is in just how you are used to thinking of harmonics on a string.

if i said divide this paper in equal parts starting at the halfway point. what would most people do.

/^_,',',',_ //^ /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/>

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

Paul Poletti wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, "Mike > Battaglia" <battaglia01@...> wrote:
> >
> > Dividing a string into equal parts won't produce a harmonic series.
> > How could it? The distance along the string from the 2nd harmonic to
> > the third harmonic is obviously not equal to the length from the 1st
> > harmonic to the second, if we're counting the first harmonic as the
> > open string. Dividing a string into equal parts will produce a
> > subharmonic series from the perspective of the shortest length used in
> > the string.
> >
> > -Mike
> >
> The crux of the matter, and the original source of confusion in
> Kraig's post, is what you mean by "dividing". In acoustics, when
> talking about the harmonic series in regards to tubes or strings, it
> means that the string vibrates in segments which divide its length
> into equal parts; 2 equal parts for the second harmonic, 3 equal parts
> for the third harmonic, 4 equal parts for the fourth harmonic, etc,
> the rule being that in order to produce harmonic X, the tube or string
> must be divided into X equal parts, ALL of which are simultaneously
> vibrating. You can, of course, physically produce these frequencies by
> touching your finger lightly against the string at any one of the
> division points for the mode in particular, or in the case of wind
> instruments, opening a very small vent hole at any one of these
> division points, though in the case with even-numbered modes, some
> points may produce more than one harmonic mode of vibration.
>
> Now, if for you "dividing" means placing frets at points which
> represent a series of equal divisions of the total string length, or
> in the case of a tube, boring holes at these points, then the series
> of notes produced when the tube or string is redimensioned by the act
> of placing a finger on the fret or opening a large tone hole
> (essentially changing the length of the tube), it cam be considered as
> a means to produce a subharmonic series IF and ONLY if you consider
> the shortest segment thereby produced to be the fundamental length,
> i.e. the length which generates the whole series. Note also that you
> are not "dividing" the vibrating object in any acoustical sense, but
> rather what you are "dividing" equally is only the measurement of the
> object's initial length in order to define a series of different
> sublengths.
>
> So the former is an acoustic interpretation of the word "divide", i.e.
> literally dividing the vibrating object into smaller units, all of
> which are vibrating, and the latter is a completely practical "get out
> the ruler" and figure out where to put the elements that will alter
> the functional acoustical length of the object. The former literally
> produces the harmonic series, the later produces a SCALE which, when
> played in a descending direction, follows a limited subharmonic
> progression. While the latter may suffice in the instrument workshop,
> it won't garner you a passing mark in any acoustics or physics class.
>
> Ciao,
>
> p
>
>

This is another use of the term used by improv and other instrumentalist. pulling extreme pressure on the string producing lower tones than the fundamental. it is a may or may not be a different thing all together. i don't know enough about what is actually going on.

/^_,',',',_ //^ /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/>

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

Chris Vaisvil wrote:
>
> It is neat but does not explain how the lady violinist can generate a > G one octave below the string.
>
> O

There may be an easier way to think about and conceptualise the frequency and ratios of the sub/harmonics..

Sub harmonics ratios may be considered as the reciprocals of the harmonics ratios.

e.g. harmonics 3/2, 4/3, 5/3 ..... etc.
sub harmonics 2/3, 3/4, 3/5 ..... etc.

The what, which, why, where, when and how exactly of the sub/harmonics are other questions.

I shall resist the temptation to comment further;-)

>On 24 Jun 2008, at 23:29, Kraig Grady wrote:

> i was talking about a string, a physical object.
> there is nothing in your original description that says you have to do
> the process for each harmonic so i am afraid your own definition lacks
> clarity being incomplete. fail.
>
> why anyone would assume that if i said divide in equal parts, that > this
> would be a process you would repeat over and over again for each
> harmonic. only if you already knew this. So the confusion is in just > how
> you are used to thinking of harmonics on a string.
>
> if i said divide this paper in equal parts starting at the halfway
> point. what would most people do.
>

> ._,___

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

[ Attachment content not displayed ]

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musically it is found most often when the drone is higher and the melodic lines are below.
but it should be understood that if you have a subharmonic scale, you could use any tone as the tonic; any of it modes.

/^_,',',',_ //^ /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/>

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

Chris Vaisvil wrote:
>
> One consequence of this seems to be that the fundamental is determined > by relative amplitude... only?
>
> my previous definition, the fundamental is the lowest tone, has no > meaning in the sub-harmonic world.
>
> On Tue, Jun 24, 2008 at 6:49 PM, Charles Lucy <lucy@... > <mailto:lucy@...>> wrote:
>
> There may be an easier way to think about and conceptualise the
> frequency and ratios of the sub/harmonics..
>
>
> Sub harmonics ratios may be considered as the reciprocals of the
> harmonics ratios.
>
> e.g. harmonics 3/2, 4/3, 5/3 ..... etc.
> sub harmonics 2/3, 3/4, 3/5 ..... etc.
>
> The what, which, why, where, when and how exactly of the
> sub/harmonics are other questions.
>
> I shall resist the temptation to comment further;-)
>
>
>
>
> >On 24 Jun 2008, at 23:29, Kraig Grady wrote:
>
>> i was talking about a string, a physical object.
>> there is nothing in your original description that says you have
>> to do >> the process for each harmonic so i am afraid your own definition
>> lacks >> clarity being incomplete. fail.
>>
>> why anyone would assume that if i said divide in equal parts,
>> that this >> would be a process you would repeat over and over again for each >> harmonic. only if you already knew this. So the confusion is in
>> just how >> you are used to thinking of harmonics on a string.
>>
>> if i said divide this paper in equal parts starting at the halfway >> point. what would most people do.
>>
>
>
>
>
>
>
>
>
>
>
>
>
>
>> ._,___
>
> 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>
>
>
>
>
>

I imagine someone on this list knows more about this particular bowing technique.
i can say little here without someone finding issue with it.
it does not occur in nature acoustically ( or possibly rarely depending on the above)

think of a string half the length
as done with a fret, you will have the octave. let say this distance is 16 inches,
if you put a fret every inch between this octave point and the nut and play this series
you will have the subharmonic series 16 through 32.

/^_,',',',_ //^ /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/>

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

Chris Vaisvil wrote:
>
> then if it is bowed.... it is a forced vibration? like a speaker?
>
> I guess I'm trapped by the illustrations in my physics book of a > standing wave in a pipe.
>
> I'm having a hard time visualizing a string vibrating at a half wavelength
>
> On Tue, Jun 24, 2008 at 6:39 PM, Kraig Grady <kraiggrady@... > <mailto:kraiggrady@...>> wrote:
>
>
> This is another use of the term used by improv and other
> instrumentalist. pulling extreme pressure on the string producing
> lower
> tones than the fundamental. it is a may or may not be a different
> thing
> all together. i don't know enough about what is actually going on.
>
>
>
> /^_,',',',_ //^ /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/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Chris Vaisvil wrote:
> >
> > It is neat but does not explain how the lady violinist can
> generate a
> > G one octave below the string.
> >
> > O
>
>
>

On 25 Jun 2008, at 00:12, Kraig Grady wrote:

> I imagine someone on this list knows more about this particular bowing
> technique.
>
> it does not occur in nature acoustically ( or possibly rarely > depending
> on the above)
>

>

Just a thought?

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

[ Attachment content not displayed ]

As high as their sounds are, they appear to be lower than their size would imply, so you are probably right and a good example!

/^_,',',',_ //^ /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/>

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

Charles Lucy wrote:
>
>
> On 25 Jun 2008, at 00:12, Kraig Grady wrote:
>
>> I imagine someone on this list knows more about this particular bowing >> technique.
>>
>> it does not occur in nature acoustically ( or possibly rarely depending >> on the above)
>>
>
>
>
>
>
>
>>
>
> Just a thought?
>
>
> 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>
>
>
>
>

[ Attachment content not displayed ]

[ Attachment content not displayed ]

well then let me say you can use the relationships found in the harmonic series to make a scale. and likewise the inversion.
The music of Ben Johnston commonly does just this.

Since the subharmonic series is not found in nature (for the most part) i felt no reason to qualify.

8-10-11-12-14-16 in terms of harmonic or subharmonic relations is just one of many examples. personally i prefer examples.

/^_,',',',_ //^ /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/>

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

Chris Vaisvil wrote:
>
> to me a scale and melody is different from the harmonic series.
>
> the harmonic series, to me, is what determines the timbre of an instrument
>
> we can conceptualize and generalize what the harmonic series is
>
> but it does not, to me, include notes of a melody by definition > because harmonics are not perceived a distinct notes.
>
> perhaps I'm being picky - I understand things by having clear > definitions in order to examine relationships.
>
> On Tue, Jun 24, 2008 at 7:10 PM, Kraig Grady <kraiggrady@... > <mailto:kraiggrady@...>> wrote:
>
> musically it is found most often when the drone is higher and the
> melodic lines are below.
> but it should be understood that if you have a subharmonic scale, you
> could use any tone as the tonic; any of it modes.
>
> /^_,',',',_ //^ /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/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
> Chris Vaisvil wrote:
> >
> > One consequence of this seems to be that the fundamental is
> determined
> > by relative amplitude... only?
> >
> > my previous definition, the fundamental is the lowest tone, has no
> > meaning in the sub-harmonic world.
> >
> > On Tue, Jun 24, 2008 at 6:49 PM, Charles Lucy
> <lucy@... <mailto:lucy%40harmonics.com>
> > <mailto:lucy@... <mailto:lucy%40harmonics.com>>> wrote:
> >
> > There may be an easier way to think about and conceptualise the
> > frequency and ratios of the sub/harmonics..
> >
> >
> > Sub harmonics ratios may be considered as the reciprocals of the
> > harmonics ratios.
> >
> > e.g. harmonics 3/2, 4/3, 5/3 ..... etc.
> > sub harmonics 2/3, 3/4, 3/5 ..... etc.
> >
> > The what, which, why, where, when and how exactly of the
> > sub/harmonics are other questions.
> >
> > I shall resist the temptation to comment further;-)
> >
> >
> >
> >
> > >On 24 Jun 2008, at 23:29, Kraig Grady wrote:
> >
> >> i was talking about a string, a physical object.
> >> there is nothing in your original description that says you have
> >> to do
> >> the process for each harmonic so i am afraid your own definition
> >> lacks
> >> clarity being incomplete. fail.
> >>
> >> why anyone would assume that if i said divide in equal parts,
> >> that this
> >> would be a process you would repeat over and over again for each
> >> harmonic. only if you already knew this. So the confusion is in
> >> just how
> >> you are used to thinking of harmonics on a string.
> >>
> >> if i said divide this paper in equal parts starting at the halfway
> >> point. what would most people do.
> >>
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >> ._,___
> >
> > 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>>
> >
> >
> >
> >
> >
>
>
>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> i was talking about a string, a physical object.

No, you are talking about the measurement of the space on the neck of
the instrument underneath the string. You do not divide the string
itself, you simply stop it at different lengths which represents
division of its MEASUREMENT. NOT the same thing.

> there is nothing in your original description that says you have to do
> the process for each harmonic so i am afraid your own definition lacks
> clarity being incomplete. fail.

Hmmm. I'll try to communicate this to the entire acoustics community
world wide, that our standard definition lacks clarity. It's a huge
task, maybe you can help? You take all the physics/acoustics teachers,
writers, theorists on your side of the world, I'll take all those on
mine. Ready? Go!
>
> why anyone would assume that if i said divide in equal parts, that this
> would be a process you would repeat over and over again for each
> harmonic. only if you already knew this.

That's precisely the point. Saying "divide the string into equal
parts" already IS something thousands of people say in a certain
context, so it is YOU who is pissing against the wind here.

> So the confusion is in just how
> you are used to thinking of harmonics on a string.

So many of us used to thinking in this confused way!
>
> if i said divide this paper in equal parts starting at the halfway
> point. what would most people do.

Which paper would that be? The imaginary one that a computer screen
represents in the minds of some people? Sort of like the imaginary
length of the string (not the string itself) that you are dividing?

And besides, what you actually said was:

> > It is the same intervals as the harmonic series except going down
> > instead of up. if you divide a string into equal parts, usually
done at
> > the midpoint of the string or equally spaced wholes you will end up
> with
> > this series.

Now the "or" in this sentence implies multiple solutions to the
problem. Obviously the option of starting at the center implies
progressive halving, but the "equally spaced wholes" option would seem
to imply the other possibility, which is of course dividing the length
of the string (again, not the string itself) into any odd number of
equally spaced wholes, i.e. divided by whole numbers, or dividing the
length by multiples of 6, which have a division point at the center
but are not derivable by further progressive halving. So yeah, your
sentence implies multiple solutions, not just the one of progressive
halving you now seem to wish to have said in hindsight.

Ciao,

P

the series goes from 16 at the top (highest) down to 32, so it is going down and lower.
sorry i left that out

/^_,',',',_ //^ /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/>

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

Chris Vaisvil wrote:
>
> wouldn't that give you shorter string lengths and therefore higher, > not lower, pitches?
>
> there is something I'm not getting here....
>
> On Tue, Jun 24, 2008 at 7:12 PM, Kraig Grady <kraiggrady@... > <mailto:kraiggrady@...>> wrote:
>
> I imagine someone on this list knows more about this particular
> bowing
> technique.
> i can say little here without someone finding issue with it.
>
> it does not occur in nature acoustically ( or possibly rarely
> depending
> on the above)
>
> think of a string half the length
> as done with a fret, you will have the octave. let say this
> distance is
> 16 inches,
> if you put a fret every inch between this octave point and the nut
> and
> play this series
> you will have the subharmonic series 16 through 32.
>
>
>
> /^_,',',',_ //^ /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/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Chris Vaisvil wrote:
> >
> > then if it is bowed.... it is a forced vibration? like a speaker?
> >
> > I guess I'm trapped by the illustrations in my physics book of a
> > standing wave in a pipe.
> >
> > I'm having a hard time visualizing a string vibrating at a half
> wavelength
> >
> > On Tue, Jun 24, 2008 at 6:39 PM, Kraig Grady
> <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> > <mailto:kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>>> wrote:
> >
> >
> > This is another use of the term used by improv and other
> > instrumentalist. pulling extreme pressure on the string producing
> > lower
> > tones than the fundamental. it is a may or may not be a different
> > thing
> > all together. i don't know enough about what is actually going on.
> >
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > 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/>>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > Chris Vaisvil wrote:
> > >
> > > It is neat but does not explain how the lady violinist can
> > generate a
> > > G one octave below the string.
> > >
> > > O
> >
> >
> >
>
>
>

fine thanks for clearing that up, although we don't know if it is being over driven or not.
It does not appear to be so.
So no relation to the subharmonic series at all.

/^_,',',',_ //^ /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/>

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

Chris Vaisvil wrote:
>
> Male cicadas have loud noisemakers called "timbals > <http://en.wikipedia.org/wiki/Timbal_%28biology%29>" on the sides of > the abdominal <http://en.wikipedia.org/wiki/Abdomen> base. Their > "singing" is not the stridulation > <http://en.wikipedia.org/wiki/Stridulation> (where two structures are > rubbed against one another) of many other familiar sound-producing > insects like crickets > <http://en.wikipedia.org/wiki/Cricket_%28insect%29>: the timbals are > regions of the exoskeleton <http://en.wikipedia.org/wiki/Exoskeleton> > that are modified to form a complex membrane with thin, membranous > portions and thickened "ribs". Contracting the internal timbal muscles > produces a clicking sound as the timbals buckle inwards. As these > muscles relax, the timbals return to their original position producing > another click. The interior of the male abdomen is substantially > hollow to amplify the resonance of the sound. A cicada rapidly > vibrates these membranes, and enlarged chambers derived from the > tracheae <http://en.wikipedia.org/wiki/Invertebrate_trachea> make its > body serve as a resonance <http://en.wikipedia.org/wiki/Resonance> > chamber, greatly amplifying the sound. They modulate their noise by > wiggling their abdomens toward and away from the tree that they are > on. Additionally, each species has its own distinctive /song./^[1] > <http://en.wikipedia.org/wiki/Cicada#cite_note-milne-0>
>
> from wikipedia
>
>
> sounds like a speaker to me - driven by muscles.
>
>
> On Tue, Jun 24, 2008 at 7:20 PM, Charles Lucy <lucy@... > <mailto:lucy@...>> wrote:
>
>
> On 25 Jun 2008, at 00:12, Kraig Grady wrote:
>
>> I imagine someone on this list knows more about this particular
>> bowing >> technique.
>>
>> it does not occur in nature acoustically ( or possibly rarely
>> depending >> on the above)
>>
>
>
>
>
>
>
>>
>
> Just a thought?
>
>
> 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>
>
>
>
>
>

On Tue, Jun 24, 2008 at 6:52 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> One consequence of this seems to be that the fundamental is determined by relative amplitude... only?
>
> my previous definition, the fundamental is the lowest tone, has no meaning in the sub-harmonic world.

Well, if you're looking at a subharmonic series, the fundamental is
usually considered to be the highest tone.

-Mike

--- In tuning@yahoogroups.com, "Chris Vaisvil" <chrisvaisvil@...> wrote:
>
> to me a scale and melody is different from the harmonic series.
>
> the harmonic series, to me, is what determines the timbre of an
instrument
>
> we can conceptualize and generalize what the harmonic series is
>
> but it does not, to me, include notes of a melody by definition because
> harmonics are not perceived a distinct notes.

The word "harmonic" simply means that the elements of the set are all
multiples of the generating element. So if all of the frequencies of a
scale are multiples of the lowest tone, then the scale is a harmonic
series. That said, generally speaking a scale is usually imagined as
existing within the confines of an octave, so by definition a harmonic
series cannot be a scale and vice versa.

However, it IS possible and quite common that real harmonics of a
fundamental frequency are used as a musical scale. Examples abound,
from natural horns and trumpets to tromba marina to Tuvan singing:

http://www.sciam.com/article.cfm?id=the-throat-singers-of-tuv

>
> perhaps I'm being picky - I understand things by having clear
definitions in
> order to examine relationships.

I generally agree completely with that approach. That's exactly why I
choke on the idea of a subharmonic series being created by reducing
the length of a long string. It's putting the cart before the horse.

Ciao,

P

like the last thread we could go on.
we have both made our points.
we now know what we mean which is i hope the important thing.
.
/^_,',',',_ //^ /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/>

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

Paul Poletti wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > i was talking about a string, a physical object.
>
> No, you are talking about the measurement of the space on the neck of
> the instrument underneath the string. You do not divide the string
> itself, you simply stop it at different lengths which represents
> division of its MEASUREMENT. NOT the same thing.
>
> > there is nothing in your original description that says you have to do
> > the process for each harmonic so i am afraid your own definition lacks
> > clarity being incomplete. fail.
>
> Hmmm. I'll try to communicate this to the entire acoustics community
> world wide, that our standard definition lacks clarity. It's a huge
> task, maybe you can help? You take all the physics/acoustics teachers,
> writers, theorists on your side of the world, I'll take all those on
> mine. Ready? Go!
> >
> > why anyone would assume that if i said divide in equal parts, that this
> > would be a process you would repeat over and over again for each
> > harmonic. only if you already knew this.
>
> That's precisely the point. Saying "divide the string into equal
> parts" already IS something thousands of people say in a certain
> context, so it is YOU who is pissing against the wind here.
>
> > So the confusion is in just how
> > you are used to thinking of harmonics on a string.
>
> So many of us used to thinking in this confused way!
> >
> > if i said divide this paper in equal parts starting at the halfway
> > point. what would most people do.
>
> Which paper would that be? The imaginary one that a computer screen
> represents in the minds of some people? Sort of like the imaginary
> length of the string (not the string itself) that you are dividing?
>
> And besides, what you actually said was:
>
> > > It is the same intervals as the harmonic series except going down
> > > instead of up. if you divide a string into equal parts, usually
> done at
> > > the midpoint of the string or equally spaced wholes you will end up
> > with
> > > this series.
>
> Now the "or" in this sentence implies multiple solutions to the
> problem. Obviously the option of starting at the center implies
> progressive halving, but the "equally spaced wholes" option would seem
> to imply the other possibility, which is of course dividing the length
> of the string (again, not the string itself) into any odd number of
> equally spaced wholes, i.e. divided by whole numbers, or dividing the
> length by multiples of 6, which have a division point at the center
> but are not derivable by further progressive halving. So yeah, your
> sentence implies multiple solutions, not just the one of progressive
> halving you now seem to wish to have said in hindsight.
>
> Ciao,
>
> P
>
>

[ Attachment content not displayed ]

On Tue, Jun 24, 2008 at 6:49 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
> then if it is bowed.... it is a forced vibration? like a speaker?
>
> I guess I'm trapped by the illustrations in my physics book of a standing
> wave in a pipe.
>
> I'm having a hard time visualizing a string vibrating at a half wavelength

Ah. That's an interesting question. You're referring to string
"crunching", as it were.

I'm not sure how that works any more than I'm sure how a speaker can
produce f/2, to be honest.

-Mike

[ Attachment content not displayed ]

It would seem that what would be important is whether it is musically viable or not.
In regard to prehistoric music, i do not envisions strings being the first instruments.
Tuvan music is very beautiful, yet harmonic singing appears to limited around the world to a few places . (Angola is another locale although difficult to find recordings)
Still it could be quite old or not. We have no reason to assume that prehistoric music was the same the world over.

/^_,',',',_ //^ /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/>

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

Paul Poletti wrote:
>
> -
>
> I generally agree completely with that approach. That's exactly why I
> choke on the idea of a subharmonic series being created by reducing
> the length of a long string. It's putting the cart before the horse.
>
> Ciao,
>
> P
>
>

>> perhaps I'm being picky - I understand things by having clear
> definitions in
>> order to examine relationships.
>
> I generally agree completely with that approach. That's exactly why I
> choke on the idea of a subharmonic series being created by reducing
> the length of a long string. It's putting the cart before the horse.

A subharmonic series WILL be created relative to the frequency
corresponding to the shortest division of the string. Why do you
insist that the center frequency of any series of harmonic
relationships has to be viewed as that corresponding to the open
string?

-Mike

i don't know .
Isn't it by the harmonics implying the bass?
I think it is a question of the same word being used to describe related phenomenon.

/^_,',',',_ //^ /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/>

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

Chris Vaisvil wrote:
>
> does being over driven a necessity for subharmonics?
>
> in the music theory speaker example bass notes were being reproduced > by a speaker w/o distortion.
>
> or am I not seeing something here?
>
> On Tue, Jun 24, 2008 at 7:41 PM, Kraig Grady <kraiggrady@... > <mailto:kraiggrady@...>> wrote:
>
> fine thanks for clearing that up, although we don't know if it is
> being
> over driven or not.
> It does not appear to be so.
> So no relation to the subharmonic series at all.
>
>
>
> /^_,',',',_ //^ /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/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Chris Vaisvil wrote:
> >
> > Male cicadas have loud noisemakers called "timbals
> > <http://en.wikipedia.org/wiki/Timbal_%28biology%29
> <http://en.wikipedia.org/wiki/Timbal_%28biology%29>>" on the sides of
> > the abdominal <http://en.wikipedia.org/wiki/Abdomen
> <http://en.wikipedia.org/wiki/Abdomen>> base. Their
> > "singing" is not the stridulation
> > <http://en.wikipedia.org/wiki/Stridulation
> <http://en.wikipedia.org/wiki/Stridulation>> (where two structures
> are
> > rubbed against one another) of many other familiar sound-producing
> > insects like crickets
> > <http://en.wikipedia.org/wiki/Cricket_%28insect%29
> <http://en.wikipedia.org/wiki/Cricket_%28insect%29>>: the timbals are
> > regions of the exoskeleton
> <http://en.wikipedia.org/wiki/Exoskeleton
> <http://en.wikipedia.org/wiki/Exoskeleton>>
> > that are modified to form a complex membrane with thin, membranous
> > portions and thickened "ribs". Contracting the internal timbal
> muscles
> > produces a clicking sound as the timbals buckle inwards. As these
> > muscles relax, the timbals return to their original position
> producing
> > another click. The interior of the male abdomen is substantially
> > hollow to amplify the resonance of the sound. A cicada rapidly
> > vibrates these membranes, and enlarged chambers derived from the
> > tracheae <http://en.wikipedia.org/wiki/Invertebrate_trachea
> <http://en.wikipedia.org/wiki/Invertebrate_trachea>> make its
> > body serve as a resonance
> <http://en.wikipedia.org/wiki/Resonance
> <http://en.wikipedia.org/wiki/Resonance>>
> > chamber, greatly amplifying the sound. They modulate their noise by
> > wiggling their abdomens toward and away from the tree that they are
> > on. Additionally, each species has its own distinctive /song./^[1]
> > <http://en.wikipedia.org/wiki/Cicada#cite_note-milne-0
> <http://en.wikipedia.org/wiki/Cicada#cite_note-milne-0>>
>
> >
> > from wikipedia
> >
> >
> > sounds like a speaker to me - driven by muscles.
> >
> >
> > On Tue, Jun 24, 2008 at 7:20 PM, Charles Lucy
> <lucy@... <mailto:lucy%40harmonics.com>
> > <mailto:lucy@... <mailto:lucy%40harmonics.com>>> wrote:
> >
> >
> > On 25 Jun 2008, at 00:12, Kraig Grady wrote:
> >
> >> I imagine someone on this list knows more about this particular
> >> bowing
> >> technique.
> >>
> >> it does not occur in nature acoustically ( or possibly rarely
> >> depending
> >> on the above)
> >>
> >
> >
> >
> >
> >
> >
> >>
> >
> > Just a thought?
> >
> >
> > 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>>
> >
> >
> >
> >
> >
>
>
>

--- In tuning@yahoogroups.com, "Chris Vaisvil" <chrisvaisvil@...> wrote:
>
> I'm a little puzzled....
>
> I forgot my physics and didn't put two and two together....
>
> An pipe can vibrate at 1/3 or 1/2 or 1/4 of the wavelength true....

Pipes vibrate at either 1/2 (open at both ends) or 1/4 (closed at one
end) of the wavelength in the open air. I think what you mean is that
waves can form internally which have half lengths which are equal to
divisions of the total length.
>
> A speaker can be driven to reproduce frequencies lower than the
width of the
> speaker

Yeah, but that is with fancy designs like ducted ports.
>
> But in music theory class that was explained as the mind fooling the
> listener into reproducing the fundamental via the harmonics.

That's a different thing altogether, the mind filling in the missing
fundamental. And then there are Tartinni tones, which is another thing
yet.
>
> I'm not sure about that any more....

A quick google of the terms would perform the required refresh cycle.
>
> But.... how can a string vibrate at half the fundamental frequency
when it
> is held at both ends?

It can't, not under normal conditions. The description of increase
pressure with slower bow speed makes me suspect she is mucking with
the Helmholtz motion, maybe causing the normal wave to be rereflected
once sending it back around the loop where it is again reflected from
the bow and then when it finally comes around again it creates enough
displacement to overcome the increase friction caused by the extra
pressure? Don't know, just an idea. But this has nothing to do with a
subharmonic series per se, since her audio samples make it obvious
that the first subtone produced is NOT the octave, followed by a fifth
down followed by a fourth down, which would be the case in a real
subharmonic series.

Ciao,

p

[ Attachment content not displayed ]

[ Attachment content not displayed ]

> It can't, not under normal conditions. The description of increase
> pressure with slower bow speed makes me suspect she is mucking with
> the Helmholtz motion, maybe causing the normal wave to be rereflected
> once sending it back around the loop where it is again reflected from
> the bow and then when it finally comes around again it creates enough
> displacement to overcome the increase friction caused by the extra
> pressure? Don't know, just an idea. But this has nothing to do with a
> subharmonic series per se, since her audio samples make it obvious
> that the first subtone produced is NOT the octave, followed by a fifth
> down followed by a fourth down, which would be the case in a real
> subharmonic series.

What audio samples are these? I'd like to hear.

-Mike

these are harmonics of the tube. not subharmonics.
and this series will produce what Paul had pointed out.
We cannot find the subharmonic series in nature or in a tube. you have to drill equidistant holes in it to force it to sound this series.

One can base a scale on anything and people do.
The point is that it appeared people used these subharmonic scales quite far back, and they stuck with them. We still find flutes/winds of this construction the world over.

/^_,',',',_ //^ /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/>

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

Chris Vaisvil wrote:
>
> sure... but one can base a scale on anything so that wasn't clear to me.
>
> is not a pipe vibrating with a standing wave at a quarter or half > wavelength natural in some sense?
>
> This looks interesting - a virtual pipe
>
> http://www.physics.smu.edu/~olness/www/03fall1320/applet/pipe-waves.html > <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html>
>
>
> Thanks!
>
> On Tue, Jun 24, 2008 at 7:33 PM, Kraig Grady <kraiggrady@... > <mailto:kraiggrady@...>> wrote:
>
> well then let me say you can use the relationships found in the
> harmonic
> series to make a scale. and likewise the inversion.
> The music of Ben Johnston commonly does just this.
>
> Since the subharmonic series is not found in nature (for the most
> part)
> i felt no reason to qualify.
>
> 8-10-11-12-14-16 in terms of harmonic or subharmonic relations is
> just
> one of many examples. personally i prefer examples.
>
>
>
> /^_,',',',_ //^ /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/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Chris Vaisvil wrote:
> >
> > to me a scale and melody is different from the harmonic series.
> >
> > the harmonic series, to me, is what determines the timbre of an
> instrument
> >
> > we can conceptualize and generalize what the harmonic series is
> >
> > but it does not, to me, include notes of a melody by definition
> > because harmonics are not perceived a distinct notes.
> >
> > perhaps I'm being picky - I understand things by having clear
> > definitions in order to examine relationships.
> >
> > On Tue, Jun 24, 2008 at 7:10 PM, Kraig Grady
> <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> > <mailto:kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>>> wrote:
> >
> > musically it is found most often when the drone is higher and the
> > melodic lines are below.
> > but it should be understood that if you have a subharmonic
> scale, you
> > could use any tone as the tonic; any of it modes.
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > 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/>>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> >
> >
> > Chris Vaisvil wrote:
> > >
> > > One consequence of this seems to be that the fundamental is
> > determined
> > > by relative amplitude... only?
> > >
> > > my previous definition, the fundamental is the lowest tone, has no
> > > meaning in the sub-harmonic world.
> > >
> > > On Tue, Jun 24, 2008 at 6:49 PM, Charles Lucy
> > <lucy@... <mailto:lucy%40harmonics.com>
> <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>>
>
> > > <mailto:lucy@... <mailto:lucy%40harmonics.com>
> <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>>>> wrote:
> > >
> > > There may be an easier way to think about and conceptualise the
> > > frequency and ratios of the sub/harmonics..
> > >
> > >
> > > Sub harmonics ratios may be considered as the reciprocals of the
> > > harmonics ratios.
> > >
> > > e.g. harmonics 3/2, 4/3, 5/3 ..... etc.
> > > sub harmonics 2/3, 3/4, 3/5 ..... etc.
> > >
> > > The what, which, why, where, when and how exactly of the
> > > sub/harmonics are other questions.
> > >
> > > I shall resist the temptation to comment further;-)
> > >
> > >
> > >
> > >
> > > >On 24 Jun 2008, at 23:29, Kraig Grady wrote:
> > >
> > >> i was talking about a string, a physical object.
> > >> there is nothing in your original description that says you have
> > >> to do
> > >> the process for each harmonic so i am afraid your own definition
> > >> lacks
> > >> clarity being incomplete. fail.
> > >>
> > >> why anyone would assume that if i said divide in equal parts,
> > >> that this
> > >> would be a process you would repeat over and over again for each
> > >> harmonic. only if you already knew this. So the confusion is in
> > >> just how
> > >> you are used to thinking of harmonics on a string.
> > >>
> > >> if i said divide this paper in equal parts starting at the
> halfway
> > >> point. what would most people do.
> > >>
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >> ._,___
> > >
> > > Charles Lucy
> > > lucy@... <mailto:lucy%40lucytune.com>
> <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>>
> > <mailto:lucy@... <mailto:lucy%40lucytune.com>
> <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.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>>
> > <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>>
> > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>>
> > >
> > >
> > >
> > >
> > >
> >
> >
> >
>
>
>

On Tue, Jun 24, 2008 at 8:09 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
> It seems that the speaker example could be a genuine
> subharmonic phenomena - it was explained that speakers physically can't
> reproduce wavelengths larger the their physical size and therefore it was
> the brain filling in the fundamental.
>
> but. come to think of it.. how would that work with something metallic that
> does not follow the "normal" harmonic series?

Then the question is, how does the speaker produce (3/2)f, 2f, (5/2)f,
3f, (7/2)f, and so on, so that we perceive (1/2)f as the fundamental?

On Tue, Jun 24, 2008 at 8:06 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
> Why do you
> insist that the center frequency of any series of harmonic
> relationships has to be viewed as that corresponding to the open
> string?
>
> physics seems to talk to the traditional harmonic series page 7
>
> page 9 is the closed end pipe
>
> http://www.swarthmore.edu/NatSci/echeeve1/Class/e12/E12Asn06/PhysicsOfSound.pdf
>
> But... it appears that I was wrong - that quarter wavelength is actually the
> fundamental
> according to this text.
>
> I still can not conceptualize how a string can do this.

Wait, I'm confused... Are you talking about the equally spaced frets
or the subtone crunching of a violin?

I missed the link to the sample, but thanks for clearing up that these subharmonics are different than the ones we are referring to.

/^_,',',',_ //^ /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/>

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

Paul Poletti wrote:
>
> -
> It can't, not under normal conditions. The description of increase
> pressure with slower bow speed makes me suspect she is mucking with
> the Helmholtz motion, maybe causing the normal wave to be rereflected
> once sending it back around the loop where it is again reflected from
> the bow and then when it finally comes around again it creates enough
> displacement to overcome the increase friction caused by the extra
> pressure? Don't know, just an idea. But this has nothing to do with a
> subharmonic series per se, since her audio samples make it obvious
> that the first subtone produced is NOT the octave, followed by a fifth
> down followed by a fourth down, which would be the case in a real
> subharmonic series.
>
> Ciao,
>
> p
>
>

this is a good perception question.
i imagine with a gong or more with a tam tam the brain might fill in a bass based on the cues it is presented which might not coincide with the actual source. i don't know

/^_,',',',_ //^ /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/>

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

Chris Vaisvil wrote:
>
> It seems that the speaker example could be a genuine
> subharmonic phenomena - it was explained that speakers physically > can't reproduce wavelengths larger the their physical size and > therefore it was the brain filling in the fundamental.
>
> but. come to think of it.. how would that work with something metallic > that does not follow the "normal" harmonic series?
>
> On Tue, Jun 24, 2008 at 8:00 PM, Kraig Grady <kraiggrady@... > <mailto:kraiggrady@...>> wrote:
>
> i don't know .
> Isn't it by the harmonics implying the bass?
> I think it is a question of the same word being used to describe
> related
> phenomenon.
>
>
>
> /^_,',',',_ //^ /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/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Chris Vaisvil wrote:
> >
> > does being over driven a necessity for subharmonics?
> >
> > in the music theory speaker example bass notes were being
> reproduced
> > by a speaker w/o distortion.
> >
> > or am I not seeing something here?
> >
> > On Tue, Jun 24, 2008 at 7:41 PM, Kraig Grady
> <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> > <mailto:kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>>> wrote:
> >
> > fine thanks for clearing that up, although we don't know if it is
> > being
> > over driven or not.
> > It does not appear to be so.
> > So no relation to the subharmonic series at all.
> >
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > 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/>>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > Chris Vaisvil wrote:
> > >
> > > Male cicadas have loud noisemakers called "timbals
> > > <http://en.wikipedia.org/wiki/Timbal_%28biology%29
> <http://en.wikipedia.org/wiki/Timbal_%28biology%29>
> > <http://en.wikipedia.org/wiki/Timbal_%28biology%29
> <http://en.wikipedia.org/wiki/Timbal_%28biology%29>>>" on the sides of
> > > the abdominal <http://en.wikipedia.org/wiki/Abdomen
> <http://en.wikipedia.org/wiki/Abdomen>
> > <http://en.wikipedia.org/wiki/Abdomen
> <http://en.wikipedia.org/wiki/Abdomen>>> base. Their
> > > "singing" is not the stridulation
> > > <http://en.wikipedia.org/wiki/Stridulation
> <http://en.wikipedia.org/wiki/Stridulation>
> > <http://en.wikipedia.org/wiki/Stridulation
> <http://en.wikipedia.org/wiki/Stridulation>>> (where two structures
> > are
> > > rubbed against one another) of many other familiar sound-producing
> > > insects like crickets
> > > <http://en.wikipedia.org/wiki/Cricket_%28insect%29
> <http://en.wikipedia.org/wiki/Cricket_%28insect%29>
> > <http://en.wikipedia.org/wiki/Cricket_%28insect%29
> <http://en.wikipedia.org/wiki/Cricket_%28insect%29>>>: the timbals are
> > > regions of the exoskeleton
> > <http://en.wikipedia.org/wiki/Exoskeleton
> <http://en.wikipedia.org/wiki/Exoskeleton>
> > <http://en.wikipedia.org/wiki/Exoskeleton
> <http://en.wikipedia.org/wiki/Exoskeleton>>>
> > > that are modified to form a complex membrane with thin, membranous
> > > portions and thickened "ribs". Contracting the internal timbal
> > muscles
> > > produces a clicking sound as the timbals buckle inwards. As these
> > > muscles relax, the timbals return to their original position
> > producing
> > > another click. The interior of the male abdomen is substantially
> > > hollow to amplify the resonance of the sound. A cicada rapidly
> > > vibrates these membranes, and enlarged chambers derived from the
> > > tracheae <http://en.wikipedia.org/wiki/Invertebrate_trachea
> <http://en.wikipedia.org/wiki/Invertebrate_trachea>
> > <http://en.wikipedia.org/wiki/Invertebrate_trachea
> <http://en.wikipedia.org/wiki/Invertebrate_trachea>>> make its
> > > body serve as a resonance
> > <http://en.wikipedia.org/wiki/Resonance
> <http://en.wikipedia.org/wiki/Resonance>
> > <http://en.wikipedia.org/wiki/Resonance
> <http://en.wikipedia.org/wiki/Resonance>>>
> > > chamber, greatly amplifying the sound. They modulate their
> noise by
> > > wiggling their abdomens toward and away from the tree that
> they are
> > > on. Additionally, each species has its own distinctive /song./^[1]
> > > <http://en.wikipedia.org/wiki/Cicada#cite_note-milne-0
> <http://en.wikipedia.org/wiki/Cicada#cite_note-milne-0>
> > <http://en.wikipedia.org/wiki/Cicada#cite_note-milne-0
> <http://en.wikipedia.org/wiki/Cicada#cite_note-milne-0>>>
> >
> > >
> > > from wikipedia
> > >
> > >
> > > sounds like a speaker to me - driven by muscles.
> > >
> > >
> > > On Tue, Jun 24, 2008 at 7:20 PM, Charles Lucy
> > <lucy@... <mailto:lucy%40harmonics.com>
> <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>>
>
> > > <mailto:lucy@... <mailto:lucy%40harmonics.com>
> <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>>>> wrote:
> > >
> > >
> > > On 25 Jun 2008, at 00:12, Kraig Grady wrote:
> > >
> > >> I imagine someone on this list knows more about this particular
> > >> bowing
> > >> technique.
> > >>
> > >> it does not occur in nature acoustically ( or possibly rarely
> > >> depending
> > >> on the above)
> > >>
> > >
> > >
> > >
> > >
> > >
> > >
> > >>
> > >
> > > Just a thought?
> > >
> > >
> > > Charles Lucy
> > > lucy@... <mailto:lucy%40lucytune.com>
> <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>>
> > <mailto:lucy@... <mailto:lucy%40lucytune.com>
> <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.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>>
> > <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>>
> > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>>
> > >
> > >
> > >
> > >
> > >
> >
> >
> >
>
>
>

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Kraig & Paul --

you are writing past one another by confusing two ways of producing subharmonic relationships: the first is a division of a string into equal parts, which are then related subharmonically with the shortest part the "fundamental" (/1 or, better, perhaps, Wilson's term "guiding tone") or tones which are related as subharmonically to the whole length of a given string (each successive string then 2x, 3x, 4x... the length of the first, sounding, respectively, at 1/2, 1/3, 1/4 etc. the frequency of the first).

One can, in fact, drive a bowed string into oscillation at the first one or two subharmonic modes by bowing with increased pressure, a technique I use in my 2nd Quartet. I heard this first in Crumb's quartet _Black Angels_. The violinist/composer Mari Kimura has become rather proficient at this technque, and samples of her playing and research can be found online.

--
Dr. Daniel Wolf
Composer
Frankfurt

a flute without holes will produce a harmonic series.
but if you drill holes randomly and play this it will not be harmonics of this tube.

i am not sure what you are asking a reference to.

/^_,',',',_ //^ /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/>

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

Chris Vaisvil wrote:
>
> please explain... these statements seem contradictory
>
> We cannot find the subharmonic series in nature or in a tube. you have
> to drill equidistant holes in it to force it to sound this series.
>
> The point is that it appeared people used these subharmonic scales quite
> far back, and they stuck with them. We still find flutes/winds of this
> construction the world over.
>
> isn't a flute based on the "traditional" harmonic series?
>
> do you have a reference?
>
> On Tue, Jun 24, 2008 at 8:10 PM, Kraig Grady <kraiggrady@... > <mailto:kraiggrady@...>> wrote:
>
> these are harmonics of the tube. not subharmonics.
> and this series will produce what Paul had pointed out.
> We cannot find the subharmonic series in nature or in a tube. you
> have
> to drill equidistant holes in it to force it to sound this series.
>
> One can base a scale on anything and people do.
> The point is that it appeared people used these subharmonic scales
> quite
> far back, and they stuck with them. We still find flutes/winds of
> this
> construction the world over.
>
>
>
> /^_,',',',_ //^ /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/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Chris Vaisvil wrote:
> >
> > sure... but one can base a scale on anything so that wasn't
> clear to me.
> >
> > is not a pipe vibrating with a standing wave at a quarter or half
> > wavelength natural in some sense?
> >
> > This looks interesting - a virtual pipe
> >
> >
> http://www.physics.smu.edu/~olness/www/03fall1320/applet/pipe-waves.html
> <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html>
>
> >
> <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html
> <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html>>
>
>
> >
> >
> > Thanks!
> >
> > On Tue, Jun 24, 2008 at 7:33 PM, Kraig Grady
> <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> > <mailto:kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>>> wrote:
> >
> > well then let me say you can use the relationships found in the
> > harmonic
> > series to make a scale. and likewise the inversion.
> > The music of Ben Johnston commonly does just this.
> >
> > Since the subharmonic series is not found in nature (for the most
> > part)
> > i felt no reason to qualify.
> >
> > 8-10-11-12-14-16 in terms of harmonic or subharmonic relations is
> > just
> > one of many examples. personally i prefer examples.
> >
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > 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/>>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > Chris Vaisvil wrote:
> > >
> > > to me a scale and melody is different from the harmonic series.
> > >
> > > the harmonic series, to me, is what determines the timbre of an
> > instrument
> > >
> > > we can conceptualize and generalize what the harmonic series is
> > >
> > > but it does not, to me, include notes of a melody by definition
> > > because harmonics are not perceived a distinct notes.
> > >
> > > perhaps I'm being picky - I understand things by having clear
> > > definitions in order to examine relationships.
> > >
> > > On Tue, Jun 24, 2008 at 7:10 PM, Kraig Grady
> > <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> <mailto:kraiggrady%40anaphoria.com
> <mailto:kraiggrady%2540anaphoria.com>>
> > > <mailto:kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>
>
> > <mailto:kraiggrady%40anaphoria.com
> <mailto:kraiggrady%2540anaphoria.com>>>> wrote:
> > >
> > > musically it is found most often when the drone is higher and the
> > > melodic lines are below.
> > > but it should be understood that if you have a subharmonic
> > scale, you
> > > could use any tone as the tonic; any of it modes.
> > >
> > > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > > Mesotonal Music from:
> > > _'''''''_ ^North/Western Hemisphere:
> > > North American Embassy of Anaphoria Island
> > <http://anaphoria.com/ <http://anaphoria.com/>
> <http://anaphoria.com/ <http://anaphoria.com/>>
> > > <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/>>
> > > <http://anaphoriasouth.blogspot.com/
> <http://anaphoriasouth.blogspot.com/>
> > <http://anaphoriasouth.blogspot.com/
> <http://anaphoriasouth.blogspot.com/>>>>
> > >
> > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > >
> > >
> > >
> > > Chris Vaisvil wrote:
> > > >
> > > > One consequence of this seems to be that the fundamental is
> > > determined
> > > > by relative amplitude... only?
> > > >
> > > > my previous definition, the fundamental is the lowest tone,
> has no
> > > > meaning in the sub-harmonic world.
> > > >
> > > > On Tue, Jun 24, 2008 at 6:49 PM, Charles Lucy
> > > <lucy@... <mailto:lucy%40harmonics.com>
> <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>>
> > <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>
> <mailto:lucy%2540harmonics.com <mailto:lucy%252540harmonics.com>>>
>
> >
> > > > <mailto:lucy@... <mailto:lucy%40harmonics.com>
> <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>>
> > <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>
> <mailto:lucy%2540harmonics.com
> <mailto:lucy%252540harmonics.com>>>>> wrote:
> > > >
> > > > There may be an easier way to think about and conceptualise the
> > > > frequency and ratios of the sub/harmonics..
> > > >
> > > >
> > > > Sub harmonics ratios may be considered as the reciprocals of the
> > > > harmonics ratios.
> > > >
> > > > e.g. harmonics 3/2, 4/3, 5/3 ..... etc.
> > > > sub harmonics 2/3, 3/4, 3/5 ..... etc.
> > > >
> > > > The what, which, why, where, when and how exactly of the
> > > > sub/harmonics are other questions.
> > > >
> > > > I shall resist the temptation to comment further;-)
> > > >
> > > >
> > > >
> > > >
> > > > >On 24 Jun 2008, at 23:29, Kraig Grady wrote:
> > > >
> > > >> i was talking about a string, a physical object.
> > > >> there is nothing in your original description that says you
> have
> > > >> to do
> > > >> the process for each harmonic so i am afraid your own
> definition
> > > >> lacks
> > > >> clarity being incomplete. fail.
> > > >>
> > > >> why anyone would assume that if i said divide in equal parts,
> > > >> that this
> > > >> would be a process you would repeat over and over again for
> each
> > > >> harmonic. only if you already knew this. So the confusion is in
> > > >> just how
> > > >> you are used to thinking of harmonics on a string.
> > > >>
> > > >> if i said divide this paper in equal parts starting at the
> > halfway
> > > >> point. what would most people do.
> > > >>
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >> ._,___
> > > >
> > > > Charles Lucy
> > > > lucy@... <mailto:lucy%40lucytune.com>
> <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>>
> > <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>
> <mailto:lucy%2540lucytune.com <mailto:lucy%252540lucytune.com>>>
>
> > > <mailto:lucy@... <mailto:lucy%40lucytune.com>
> <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>>
> > <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>
> <mailto:lucy%2540lucytune.com <mailto:lucy%252540lucytune.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>>
> > <http://www.lucytune.com <http://www.lucytune.com>
> <http://www.lucytune.com <http://www.lucytune.com>>>
> > > <http://www.lucytune.com <http://www.lucytune.com>
> <http://www.lucytune.com <http://www.lucytune.com>>
> > <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>>
> > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>>
> > > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>
> > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>>>
> > > >
> > > >
> > > >
> > > >
> > > >
> > >
> > >
> > >
> >
> >
> >
>
>
>

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I'm not really a string player, but this is one of the tricks I can
do with a fiddle. The first mode of playing with increased pressure
is indeed an octave below the fundamental and, by further increasing
pressure, on a good day, you can get the twelfth below, thus the
subharmonic relationships. Kimura is now able, by varying pressure
very subtly to play pitches in-between these modes. I can't
duplicate that, but, as a trombonist, I believe that what she is
doing is exactly like brass players playing "falsett tones" between
the lowest ordinary pitch and the highest pedal tone, thus playing a
pitch continuum although theory says there should be an unplayable
tritone gap between the two. Falsett tones are produced by the lips
vibrating at an intermediate mode (i.e. 1.5 x the pedal tone
frequency) with, of course, considerable adjustment by slide and
lipping up or downward.

djw

But this has nothing to do with a
> > subharmonic series per se, since her audio samples make it obvious
> > that the first subtone produced is NOT the octave, followed by a
fifth
> > down followed by a fourth down, which would be the case in a real
> > subharmonic series.
> >
>

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
> Just out of curiosity, what does the fretting pattern look like for a
> guitar that has frets placed at each harmonic from 8 to 32 or
> something? How would that diverge from a 12-equal logarithmic looking
> fretting pattern? Would the pattern still look logarithmic in nature,
> but have even more of a "curve" to it or something? Maybe an
> exponential looking curve rather than a logarithmic one?

That's right, except 12-equal string lengths (and hence fret positions
as measured from the nominal bridge position) aren't proportional to
the logarithm but inversely proportional to the exponential.
Subharmonic is proportional (linear). Harmonic is inversely
proportional which is also called hyperbolic (with an offset in this
case).

For fret number n, the relative string lengths (full string = 1) are:
12-EDO: 1/(2^(n/12))
Subharmonic: (32-n)/32
Harmonic: 8/(n+8)

If measuring from the nominal nut position the relative distances become.
12-EDO: 1 - 1/(2^(n/12))
Subharmonic: n/32
Harmonic: n/(n+8)

But you either already knew that, or didn't really want to know
because this isn't tuning-math. Sorry.

And I say "nominal" because the real nut position is set forward from
its theoretical position by about 0.5 mm (shortening the strings) to
compensate for the increase in tension when strings are fretted as
opposed to open, and the bridge or saddle-pieces are set back between
about 1 mm for treble string and 5 mm for bass string (lengthening the
strings) to compensate for end-effects due to string stiffness.

-- Dave Keenan

the subharmonic is the inverse, the mirror, the reciprocal, of the harmonic series. Like how the minor is to the major. or the major scale to the Phrygian.

/^_,',',',_ //^ /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/>

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

Chris Vaisvil wrote:
>
> http://astro.pas.rochester.edu/~aquillen/phy103/Lectures/I_Flute.ppt > <http://astro.pas.rochester.edu/%7Eaquillen/phy103/Lectures/I_Flute.ppt>
>
> seems to be a reference but.... I don't see the relationship to > subharmonics.
>
> Is the series of notes different for the sub harmonic vs harmonic series?
>
> in normal cases each series seem to be based on dividing by half or > doubling an octave.
>
> On Tue, Jun 24, 2008 at 8:20 PM, Chris Vaisvil <chrisvaisvil@... > <mailto:chrisvaisvil@...>> wrote:
>
> please explain... these statements seem contradictory
>
>
> We cannot find the subharmonic series in nature or in a tube. you
> have
> to drill equidistant holes in it to force it to sound this series.
>
> The point is that it appeared people used these subharmonic scales
> quite
> far back, and they stuck with them. We still find flutes/winds of
> this
> construction the world over.
>
> isn't a flute based on the "traditional" harmonic series?
>
> do you have a reference?
>
>
> On Tue, Jun 24, 2008 at 8:10 PM, Kraig Grady
> <kraiggrady@... <mailto:kraiggrady@...>> wrote:
>
> these are harmonics of the tube. not subharmonics.
> and this series will produce what Paul had pointed out.
> We cannot find the subharmonic series in nature or in a tube.
> you have
> to drill equidistant holes in it to force it to sound this series.
>
> One can base a scale on anything and people do.
> The point is that it appeared people used these subharmonic
> scales quite
> far back, and they stuck with them. We still find flutes/winds
> of this
> construction the world over.
>
>
>
> /^_,',',',_ //^ /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/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Chris Vaisvil wrote:
> >
> > sure... but one can base a scale on anything so that wasn't
> clear to me.
> >
> > is not a pipe vibrating with a standing wave at a quarter or
> half
> > wavelength natural in some sense?
> >
> > This looks interesting - a virtual pipe
> >
> >
> http://www.physics.smu.edu/~olness/www/03fall1320/applet/pipe-waves.html
> <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html>
>
> >
> <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html
> <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html>>
>
>
> >
> >
> > Thanks!
> >
> > On Tue, Jun 24, 2008 at 7:33 PM, Kraig Grady
> <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> > <mailto:kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>>> wrote:
> >
> > well then let me say you can use the relationships found in the
> > harmonic
> > series to make a scale. and likewise the inversion.
> > The music of Ben Johnston commonly does just this.
> >
> > Since the subharmonic series is not found in nature (for the
> most
> > part)
> > i felt no reason to qualify.
> >
> > 8-10-11-12-14-16 in terms of harmonic or subharmonic
> relations is
> > just
> > one of many examples. personally i prefer examples.
> >
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > 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/>>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > Chris Vaisvil wrote:
> > >
> > > to me a scale and melody is different from the harmonic
> series.
> > >
> > > the harmonic series, to me, is what determines the timbre
> of an
> > instrument
> > >
> > > we can conceptualize and generalize what the harmonic
> series is
> > >
> > > but it does not, to me, include notes of a melody by
> definition
> > > because harmonics are not perceived a distinct notes.
> > >
> > > perhaps I'm being picky - I understand things by having clear
> > > definitions in order to examine relationships.
> > >
> > > On Tue, Jun 24, 2008 at 7:10 PM, Kraig Grady
> > <kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>
> <mailto:kraiggrady%40anaphoria.com
> <mailto:kraiggrady%2540anaphoria.com>>
> > > <mailto:kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>
>
> > <mailto:kraiggrady%40anaphoria.com
> <mailto:kraiggrady%2540anaphoria.com>>>> wrote:
> > >
> > > musically it is found most often when the drone is higher
> and the
> > > melodic lines are below.
> > > but it should be understood that if you have a subharmonic
> > scale, you
> > > could use any tone as the tonic; any of it modes.
> > >
> > > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > > Mesotonal Music from:
> > > _'''''''_ ^North/Western Hemisphere:
> > > North American Embassy of Anaphoria Island
> > <http://anaphoria.com/ <http://anaphoria.com/>
> <http://anaphoria.com/ <http://anaphoria.com/>>
> > > <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/>>
> > > <http://anaphoriasouth.blogspot.com/
> <http://anaphoriasouth.blogspot.com/>
> > <http://anaphoriasouth.blogspot.com/
> <http://anaphoriasouth.blogspot.com/>>>>
> > >
> > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > >
> > >
> > >
> > > Chris Vaisvil wrote:
> > > >
> > > > One consequence of this seems to be that the fundamental is
> > > determined
> > > > by relative amplitude... only?
> > > >
> > > > my previous definition, the fundamental is the lowest
> tone, has no
> > > > meaning in the sub-harmonic world.
> > > >
> > > > On Tue, Jun 24, 2008 at 6:49 PM, Charles Lucy
> > > <lucy@... <mailto:lucy%40harmonics.com>
> <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>>
> > <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>
> <mailto:lucy%2540harmonics.com
> <mailto:lucy%252540harmonics.com>>>
>
> >
> > > > <mailto:lucy@... <mailto:lucy%40harmonics.com>
> <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>>
> > <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>
> <mailto:lucy%2540harmonics.com
> <mailto:lucy%252540harmonics.com>>>>> wrote:
> > > >
> > > > There may be an easier way to think about and
> conceptualise the
> > > > frequency and ratios of the sub/harmonics..
> > > >
> > > >
> > > > Sub harmonics ratios may be considered as the
> reciprocals of the
> > > > harmonics ratios.
> > > >
> > > > e.g. harmonics 3/2, 4/3, 5/3 ..... etc.
> > > > sub harmonics 2/3, 3/4, 3/5 ..... etc.
> > > >
> > > > The what, which, why, where, when and how exactly of the
> > > > sub/harmonics are other questions.
> > > >
> > > > I shall resist the temptation to comment further;-)
> > > >
> > > >
> > > >
> > > >
> > > > >On 24 Jun 2008, at 23:29, Kraig Grady wrote:
> > > >
> > > >> i was talking about a string, a physical object.
> > > >> there is nothing in your original description that says
> you have
> > > >> to do
> > > >> the process for each harmonic so i am afraid your own
> definition
> > > >> lacks
> > > >> clarity being incomplete. fail.
> > > >>
> > > >> why anyone would assume that if i said divide in equal
> parts,
> > > >> that this
> > > >> would be a process you would repeat over and over again
> for each
> > > >> harmonic. only if you already knew this. So the
> confusion is in
> > > >> just how
> > > >> you are used to thinking of harmonics on a string.
> > > >>
> > > >> if i said divide this paper in equal parts starting at the
> > halfway
> > > >> point. what would most people do.
> > > >>
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >> ._,___
> > > >
> > > > Charles Lucy
> > > > lucy@... <mailto:lucy%40lucytune.com>
> <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>>
> > <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>
> <mailto:lucy%2540lucytune.com <mailto:lucy%252540lucytune.com>>>
>
> > > <mailto:lucy@... <mailto:lucy%40lucytune.com>
> <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>>
> > <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>
> <mailto:lucy%2540lucytune.com <mailto:lucy%252540lucytune.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>>
> > <http://www.lucytune.com <http://www.lucytune.com>
> <http://www.lucytune.com <http://www.lucytune.com>>>
> > > <http://www.lucytune.com <http://www.lucytune.com>
> <http://www.lucytune.com <http://www.lucytune.com>>
> > <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>>
> > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>>
> > > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>
> > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>>>
> > > >
> > > >
> > > >
> > > >
> > > >
> > >
> > >
> > >
> >
> >
> >
>
>
>
>

yes. it is more involved as to the size of the hole and where you start your series of holes. i can't help you with that i am afraid.

/^_,',',',_ //^ /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/>

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

Chris Vaisvil wrote:
>
> I need to find the physics of this
>
> but if you drill holes randomly and play this it will not be harmonics
> of this tube.
>
> thanks - that effectively changes the tube length.... right?
>
> On Tue, Jun 24, 2008 at 8:26 PM, Kraig Grady <kraiggrady@... > <mailto:kraiggrady@...>> wrote:
>
> a flute without holes will produce a harmonic series.
> but if you drill holes randomly and play this it will not be
> harmonics
> of this tube.
>
> i am not sure what you are asking a reference to.
>
>
>
> /^_,',',',_ //^ /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/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Chris Vaisvil wrote:
> >
> > please explain... these statements seem contradictory
> >
> > We cannot find the subharmonic series in nature or in a tube.
> you have
> > to drill equidistant holes in it to force it to sound this series.
> >
> > The point is that it appeared people used these subharmonic
> scales quite
> > far back, and they stuck with them. We still find flutes/winds
> of this
> > construction the world over.
> >
> > isn't a flute based on the "traditional" harmonic series?
> >
> > do you have a reference?
> >
> > On Tue, Jun 24, 2008 at 8:10 PM, Kraig Grady
> <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> > <mailto:kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>>> wrote:
> >
> > these are harmonics of the tube. not subharmonics.
> > and this series will produce what Paul had pointed out.
> > We cannot find the subharmonic series in nature or in a tube. you
> > have
> > to drill equidistant holes in it to force it to sound this series.
> >
> > One can base a scale on anything and people do.
> > The point is that it appeared people used these subharmonic scales
> > quite
> > far back, and they stuck with them. We still find flutes/winds of
> > this
> > construction the world over.
> >
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > 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/>>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > Chris Vaisvil wrote:
> > >
> > > sure... but one can base a scale on anything so that wasn't
> > clear to me.
> > >
> > > is not a pipe vibrating with a standing wave at a quarter or half
> > > wavelength natural in some sense?
> > >
> > > This looks interesting - a virtual pipe
> > >
> > >
> >
> http://www.physics.smu.edu/~olness/www/03fall1320/applet/pipe-waves.html
> <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html>
> >
> <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html
> <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html>>
> >
> > >
> >
> <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html
> <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html>
> >
> <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html
> <http://www.physics.smu.edu/%7Eolness/www/03fall1320/applet/pipe-waves.html>>>
> >
> >
> > >
> > >
> > > Thanks!
> > >
> > > On Tue, Jun 24, 2008 at 7:33 PM, Kraig Grady
> > <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> <mailto:kraiggrady%40anaphoria.com
> <mailto:kraiggrady%2540anaphoria.com>>
> > > <mailto:kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>
> > <mailto:kraiggrady%40anaphoria.com
> <mailto:kraiggrady%2540anaphoria.com>>>> wrote:
> > >
> > > well then let me say you can use the relationships found in the
> > > harmonic
> > > series to make a scale. and likewise the inversion.
> > > The music of Ben Johnston commonly does just this.
> > >
> > > Since the subharmonic series is not found in nature (for the most
> > > part)
> > > i felt no reason to qualify.
> > >
> > > 8-10-11-12-14-16 in terms of harmonic or subharmonic relations is
> > > just
> > > one of many examples. personally i prefer examples.
> > >
> > >
> > >
> > > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > > Mesotonal Music from:
> > > _'''''''_ ^North/Western Hemisphere:
> > > North American Embassy of Anaphoria Island
> > <http://anaphoria.com/ <http://anaphoria.com/>
> <http://anaphoria.com/ <http://anaphoria.com/>>
> > > <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/>>
> > > <http://anaphoriasouth.blogspot.com/
> <http://anaphoriasouth.blogspot.com/>
> > <http://anaphoriasouth.blogspot.com/
> <http://anaphoriasouth.blogspot.com/>>>>
> > >
> > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > >
> > > Chris Vaisvil wrote:
> > > >
> > > > to me a scale and melody is different from the harmonic series.
> > > >
> > > > the harmonic series, to me, is what determines the timbre of an
> > > instrument
> > > >
> > > > we can conceptualize and generalize what the harmonic series is
> > > >
> > > > but it does not, to me, include notes of a melody by definition
> > > > because harmonics are not perceived a distinct notes.
> > > >
> > > > perhaps I'm being picky - I understand things by having clear
> > > > definitions in order to examine relationships.
> > > >
> > > > On Tue, Jun 24, 2008 at 7:10 PM, Kraig Grady
> > > <kraiggrady@... <mailto:kraiggrady%40anaphoria.com>
> <mailto:kraiggrady%40anaphoria.com
> <mailto:kraiggrady%2540anaphoria.com>>
> > <mailto:kraiggrady%40anaphoria.com
> <mailto:kraiggrady%2540anaphoria.com>
> > <mailto:kraiggrady%2540anaphoria.com
> <mailto:kraiggrady%252540anaphoria.com>>>
>
> > > > <mailto:kraiggrady@...
> <mailto:kraiggrady%40anaphoria.com>
> > <mailto:kraiggrady%40anaphoria.com
> <mailto:kraiggrady%2540anaphoria.com>>
> >
> > > <mailto:kraiggrady%40anaphoria.com
> <mailto:kraiggrady%2540anaphoria.com>
> > <mailto:kraiggrady%2540anaphoria.com
> <mailto:kraiggrady%252540anaphoria.com>>>>> wrote:
> > > >
> > > > musically it is found most often when the drone is higher
> and the
> > > > melodic lines are below.
> > > > but it should be understood that if you have a subharmonic
> > > scale, you
> > > > could use any tone as the tonic; any of it modes.
> > > >
> > > > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > > > Mesotonal Music from:
> > > > _'''''''_ ^North/Western Hemisphere:
> > > > North American Embassy of Anaphoria Island
> > > <http://anaphoria.com/ <http://anaphoria.com/>
> <http://anaphoria.com/ <http://anaphoria.com/>>
> > <http://anaphoria.com/ <http://anaphoria.com/>
> <http://anaphoria.com/ <http://anaphoria.com/>>>
> > > > <http://anaphoria.com/ <http://anaphoria.com/>
> <http://anaphoria.com/ <http://anaphoria.com/>>
> > <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/>>
> > > <http://anaphoriasouth.blogspot.com/
> <http://anaphoriasouth.blogspot.com/>
> > <http://anaphoriasouth.blogspot.com/
> <http://anaphoriasouth.blogspot.com/>>>
> > > > <http://anaphoriasouth.blogspot.com/
> <http://anaphoriasouth.blogspot.com/>
> > <http://anaphoriasouth.blogspot.com/
> <http://anaphoriasouth.blogspot.com/>>
> > > <http://anaphoriasouth.blogspot.com/
> <http://anaphoriasouth.blogspot.com/>
> > <http://anaphoriasouth.blogspot.com/
> <http://anaphoriasouth.blogspot.com/>>>>>
> > > >
> > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > >
> > > >
> > > >
> > > > Chris Vaisvil wrote:
> > > > >
> > > > > One consequence of this seems to be that the fundamental is
> > > > determined
> > > > > by relative amplitude... only?
> > > > >
> > > > > my previous definition, the fundamental is the lowest tone,
> > has no
> > > > > meaning in the sub-harmonic world.
> > > > >
> > > > > On Tue, Jun 24, 2008 at 6:49 PM, Charles Lucy
> > > > <lucy@... <mailto:lucy%40harmonics.com>
> <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>>
> > <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>
> <mailto:lucy%2540harmonics.com <mailto:lucy%252540harmonics.com>>>
> > > <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>
> <mailto:lucy%2540harmonics.com <mailto:lucy%252540harmonics.com>>
> > <mailto:lucy%2540harmonics.com <mailto:lucy%252540harmonics.com>
> <mailto:lucy%252540harmonics.com
> <mailto:lucy%25252540harmonics.com>>>>
>
> >
> > >
> > > > > <mailto:lucy@... <mailto:lucy%40harmonics.com>
> <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>>
> > <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>
> <mailto:lucy%2540harmonics.com <mailto:lucy%252540harmonics.com>>>
> > > <mailto:lucy%40harmonics.com <mailto:lucy%2540harmonics.com>
> <mailto:lucy%2540harmonics.com <mailto:lucy%252540harmonics.com>>
> > <mailto:lucy%2540harmonics.com <mailto:lucy%252540harmonics.com>
>
> > <mailto:lucy%252540harmonics.com
> <mailto:lucy%25252540harmonics.com>>>>>> wrote:
> > > > >
> > > > > There may be an easier way to think about and
> conceptualise the
> > > > > frequency and ratios of the sub/harmonics..
> > > > >
> > > > >
> > > > > Sub harmonics ratios may be considered as the reciprocals
> of the
> > > > > harmonics ratios.
> > > > >
> > > > > e.g. harmonics 3/2, 4/3, 5/3 ..... etc.
> > > > > sub harmonics 2/3, 3/4, 3/5 ..... etc.
> > > > >
> > > > > The what, which, why, where, when and how exactly of the
> > > > > sub/harmonics are other questions.
> > > > >
> > > > > I shall resist the temptation to comment further;-)
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > >On 24 Jun 2008, at 23:29, Kraig Grady wrote:
> > > > >
> > > > >> i was talking about a string, a physical object.
> > > > >> there is nothing in your original description that says you
> > have
> > > > >> to do
> > > > >> the process for each harmonic so i am afraid your own
> > definition
> > > > >> lacks
> > > > >> clarity being incomplete. fail.
> > > > >>
> > > > >> why anyone would assume that if i said divide in equal parts,
> > > > >> that this
> > > > >> would be a process you would repeat over and over again for
> > each
> > > > >> harmonic. only if you already knew this. So the confusion
> is in
> > > > >> just how
> > > > >> you are used to thinking of harmonics on a string.
> > > > >>
> > > > >> if i said divide this paper in equal parts starting at the
> > > halfway
> > > > >> point. what would most people do.
> > > > >>
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >> ._,___
> > > > >
> > > > > Charles Lucy
> > > > > lucy@... <mailto:lucy%40lucytune.com>
> <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>>
> > <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>
> <mailto:lucy%2540lucytune.com <mailto:lucy%252540lucytune.com>>>
> > > <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>
> <mailto:lucy%2540lucytune.com <mailto:lucy%252540lucytune.com>>
> > <mailto:lucy%2540lucytune.com <mailto:lucy%252540lucytune.com>
> <mailto:lucy%252540lucytune.com <mailto:lucy%25252540lucytune.com>>>>
>
> >
> > > > <mailto:lucy@... <mailto:lucy%40lucytune.com>
> <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>>
> > <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>
> <mailto:lucy%2540lucytune.com <mailto:lucy%252540lucytune.com>>>
> > > <mailto:lucy%40lucytune.com <mailto:lucy%2540lucytune.com>
> <mailto:lucy%2540lucytune.com <mailto:lucy%252540lucytune.com>>
> > <mailto:lucy%2540lucytune.com <mailto:lucy%252540lucytune.com>
> <mailto:lucy%252540lucytune.com
> <mailto:lucy%25252540lucytune.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>>
> > <http://www.lucytune.com <http://www.lucytune.com>
> <http://www.lucytune.com <http://www.lucytune.com>>>
> > > <http://www.lucytune.com <http://www.lucytune.com>
> <http://www.lucytune.com <http://www.lucytune.com>>
> > <http://www.lucytune.com <http://www.lucytune.com>
> <http://www.lucytune.com <http://www.lucytune.com>>>>
> > > > <http://www.lucytune.com <http://www.lucytune.com>
> <http://www.lucytune.com <http://www.lucytune.com>>
> > <http://www.lucytune.com <http://www.lucytune.com>
> <http://www.lucytune.com <http://www.lucytune.com>>>
> > > <http://www.lucytune.com <http://www.lucytune.com>
> <http://www.lucytune.com <http://www.lucytune.com>>
> > <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>>
> > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>>
> > > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>
> > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>>>
> > > > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>
> > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>>
> > > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>
> > <http://www.lullabies.co.uk <http://www.lullabies.co.uk>
> <http://www.lullabies.co.uk <http://www.lullabies.co.uk>>>>>
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > >
> > > >
> > > >
> > >
> > >
> > >
> >
> >
> >
>
>
>

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Chris wrote:
> A speaker can be driven to reproduce frequencies lower than the
> width of the speaker

This is in fact desirable, since when the wavelength is shorter
than the diameter of the driver, the sound becomes highly
directional, which means you need to stand directly in front of
the speakers to hear it. This is a principle reason for tweeters
being small, and, existing at all.

> But in music theory class that was explained as the mind fooling
> the listener into reproducing the fundamental via the harmonics.

It was explained wrongly then. Since sound is a longitudinal
wave, it is the *throw* of the driver, not its diameter, that
is important to low frequency reproduction.

-Carl

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Chris wrote:
> and therefore it was the brain filling in the fundamental.

This does happen to some extent, and in fact there's a
company that sells a DSP to add in harmonics to boost the
perceived bass (often used with NXT-type speakers, which
lack real bass). It was also important in the phone
system, where for decades (still?) the system couldn't
carry frequencies as low as the fundamentals of typical
male speaking voices.

> but. come to think of it.. how would that work with
> something metallic that does not follow the "normal"
> harmonic series?

If one partial is louder than the others, especially in
the all-important 100-800 Hz. range, you may hear that
out and not notice the other partials as much. The brain
is very aggressive with pitch extraction. Not until we
get to stuff like snare drums does the thing give up the
ghost. Sometimes they can be ranked higher or lower that
some pitch, but you'd be hard-pressed to say exactly what
the pitch is.

-Carl

--- In tuning@yahoogroups.com, "Chris Vaisvil" <chrisvaisvil@...> wrote:
>
> It was explained wrongly then. Since sound is a longitudinal
> wave, it is the *throw* of the driver, not its diameter, that
> is important to low frequency reproduction.
>
> Still the same problem exists though doesn't it?
>
> What is the wavelength of 60 Hz?
>
> like 500,000 meters... http://www.csgnetwork.com/freqwavelengthcalc.html

Uh, that looks like an RF calculator. Wavelength is
speed/frequency. Light travels through air significantly
more quickly than sound. :)

-Carl

--- In tuning@yahoogroups.com, "Chris Vaisvil" wrote:
> *
> *speed of sound at sea level = 340.29 m / s*still - much
> more than the throw of a normal speaker....

I didn't say the throw of the driver had to match the
wavelength. Rather, it has an impact on the efficiency
of the low-frequency sound that can be produced.

http://en.wikipedia.org/wiki/Thiele/Small

-Carl

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On Tue, Jun 24, 2008 at 8:29 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Then the question is, how does the speaker produce (3/2)f, 2f, (5/2)f,
> 3f, (7/2)f, and so on, so that we perceive (1/2)f as the fundamental?
>
> Isn't that the odd frequencies in the harmonic series? a sawtooth.
>
> I'm not sure I see the point of encoding in units of 0.5f because it doesn't
> make a difference.
>
> I fail to see your point entirely.

It makes a difference because if f is the actual frequency, and you're
saying that we want to get the harmonic series of f/2 so that the
brain can "hear" that phantom fundamental in there, we're going to
need the harmonic series of THAT frequency, not the harmonic series of
f Putting a harmonic series over f will cause the brain to hear f as
the phantom fundamental, and we want to hear f/2.

So the harmonic series we want is (2/2)f, (3/2)f, (4/2)f, (5/2)f,
(6/2)f, (7/2)f, etc. and then the brain will hear (1/2)f as the
phantom fundamental. How does the speaker generate (3/2)f and (5/2)f
and such?

-Mike

> That's right, except 12-equal string lengths (and hence fret positions
> as measured from the nominal bridge position) aren't proportional to
> the logarithm but inversely proportional to the exponential.
> Subharmonic is proportional (linear). Harmonic is inversely
> proportional which is also called hyperbolic (with an offset in this
> case).

So what is proportional to the logarithm? Nothing?

> For fret number n, the relative string lengths (full string = 1) are:
> 12-EDO: 1/(2^(n/12))
> Subharmonic: (32-n)/32
> Harmonic: 8/(n+8)
>
> If measuring from the nominal nut position the relative distances become.
> 12-EDO: 1 - 1/(2^(n/12))
> Subharmonic: n/32
> Harmonic: n/(n+8)
>
> But you either already knew that, or didn't really want to know
> because this isn't tuning-math. Sorry.
>
> And I say "nominal" because the real nut position is set forward from
> its theoretical position by about 0.5 mm (shortening the strings) to
> compensate for the increase in tension when strings are fretted as
> opposed to open, and the bridge or saddle-pieces are set back between
> about 1 mm for treble string and 5 mm for bass string (lengthening the
> strings) to compensate for end-effects due to string stiffness.

Interesting. So if I was actually refretting a guitar, would I measure
these lengths from the actual nut position, or from 0.5 mm down past
where the nut lies? I just defretted this guitar, and I was going to
make it fretless; but I might do 19-tet instead, or even 31-tet if
it's a viable option.

-Mike

Mike;

Since you have defretted a guitar, before refretting it, may I make a suggestion.

Instead of cutting the new grooves for a permanent refret, fill the old grooves with plastic wood and sand the surface..
By tying nylon first or second strings around the neck at various positions you will be able to experiment before deciding which fretting system to go for.
It is easiest to tie the nylon frets below their eventual position and then push them up the fretboard, which will tighten the knots, into the desired location.
I suggest that you make the knots in the uppermost position around the fretboard, so that you minimise the restrictions to your hand movements, although you will feel the nylon strings at the back of the fretboard.

As you know there are thousands of possibilities for the fret positions for you try.

Here are the specs for a couple which work for me:

http://www.lucytune.com/guitars_and_frets/frets.html

Doing it this way gives you the opportunity to find what works best for you without the need to be "stuck" with any particular choice.

Have fun!

On 25 Jun 2008, at 07:54, Mike Battaglia wrote:

> > That's right, except 12-equal string lengths (and hence fret > positions
> > as measured from the nominal bridge position) aren't proportional to
> > the logarithm but inversely proportional to the exponential.
> > Subharmonic is proportional (linear). Harmonic is inversely
> > proportional which is also called hyperbolic (with an offset in this
> > case).
>
> So what is proportional to the logarithm? Nothing?
>
> > For fret number n, the relative string lengths (full string = 1) > are:
> > 12-EDO: 1/(2^(n/12))
> > Subharmonic: (32-n)/32
> > Harmonic: 8/(n+8)
> >
> > If measuring from the nominal nut position the relative distances > become.
> > 12-EDO: 1 - 1/(2^(n/12))
> > Subharmonic: n/32
> > Harmonic: n/(n+8)
> >
> > But you either already knew that, or didn't really want to know
> > because this isn't tuning-math. Sorry.
> >
> > And I say "nominal" because the real nut position is set forward > from
> > its theoretical position by about 0.5 mm (shortening the strings) to
> > compensate for the increase in tension when strings are fretted as
> > opposed to open, and the bridge or saddle-pieces are set back > between
> > about 1 mm for treble string and 5 mm for bass string (lengthening > the
> > strings) to compensate for end-effects due to string stiffness.
>
> Interesting. So if I was actually refretting a guitar, would I measure
> these lengths from the actual nut position, or from 0.5 mm down past
> where the nut lies? I just defretted this guitar, and I was going to
> make it fretless; but I might do 19-tet instead, or even 31-tet if
> it's a viable option.
>
> -Mike
>
>
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

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On Wed, Jun 25, 2008 at 6:17 AM, Chris Vaisvil <chrisvaisvil@...> wrote:
> A speaker, being an analog device, should be able to reproduce any frequency
> in the input signal without regard to it relationship.
>
> I don't know if phantom tones exist right now....
> it would seem something like a bell would have a problem in this respect
> since the harmonic series is different for the typical.
>
> Since the mind is building a phantom tone, it stands to reason that it would
> need some basis for the extrapolation
>
> It makes a difference because if f is the actual frequency, and you're
> saying that we want to get the harmonic series of f/2 so that the
> brain can "hear" that phantom fundamental in there, we're going to
> need the harmonic series of THAT frequency, not the harmonic series of
> f Putting a harmonic series over f will cause the brain to hear f as
> the phantom fundamental, and we want to hear f/2.
>
> So the harmonic series we want is (2/2)f, (3/2)f, (4/2)f, (5/2)f,
> (6/2)f, (7/2)f, etc. and then the brain will hear (1/2)f as the
> phantom fundamental. How does the speaker generate (3/2)f and (5/2)f
> and such?

Alright, the the question I have is, in what sense does a speaker
generate the first subharmonic, and is it the subharmonic of the
frequencies being PLAYED, or the subharmonic corresponding to the
wavelength of the speaker?

Sounds to me as though it must be of the signal, as you can "hear" low frequencies even on tiny "ear buds".

On 25 Jun 2008, at 11:22, Mike Battaglia wrote:
>
>
> Alright, the the question I have is, in what sense does a speaker
> generate the first subharmonic, and is it the subharmonic of the
> frequencies being PLAYED, or the subharmonic corresponding to the
> wavelength of the speaker?
>
> _

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

How exactly is it that a speaker can do this, and can it generate a
whole subharmonic series, or just the first undertone?

On Wed, Jun 25, 2008 at 6:27 AM, Charles Lucy <lucy@...> wrote:
> Sounds to me as though it must be of the signal, as you can "hear" low
> frequencies even on tiny "ear buds".
>
> On 25 Jun 2008, at 11:22, Mike Battaglia wrote:
>
> Alright, the the question I have is, in what sense does a speaker
> generate the first subharmonic, and is it the subharmonic of the
> frequencies being PLAYED, or the subharmonic corresponding to the
> wavelength of the speaker?
>
> _
>
>
>
>
>
>
>
>
> 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
>
>
>

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Okay, let me rephrase: WHY does a speaker produce the first undertone
of a given signal, if that signal isn't there in the original
recording?

On Wed, Jun 25, 2008 at 6:38 AM, Chris Vaisvil <chrisvaisvil@...> wrote:
> How exactly is it that a speaker can do this, and can it generate a
> whole subharmonic series, or just the first undertone?
>
> it vibrates at the required frequency up and back
>
> I would imagine size relates to efficiency for certain ranges and nothing
> else.
>

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On Wed, Jun 25, 2008 at 6:46 AM, Chris Vaisvil <chrisvaisvil@...> wrote:
> Okay, let me rephrase: WHY does a speaker produce the first undertone
> of a given signal, if that signal isn't there in the original
> recording?
>
> does it?
>
> that would seem to be the "phantom" tone?

Man, we're going in circles! If it's a phantom tone, then the speaker
will need to produce the harmonic series of that tone. And if that
tone is f/2, then the speaker has to produce 2f/2, 3f/2, 4f/2, 5f/2,
so that the brain can fill in the f/2 phantom fundamental. And what
kind of nonlinear distortion produces 3f/2 and 5f/2 and 7f/2, for
example?

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On Wed, Jun 25, 2008 at 7:10 AM, Chris Vaisvil <chrisvaisvil@...> wrote:
> then it sounds to me that the answer is no.
>
> the speaker does not... unless it is broken in some fashion
>
> I have yet to be convinced that subharmonics exist beyond a concept
>
> each case so far has been a device driven to generate the lower tone

Do you mean whether or not subharmonics exist sounding simultaneously
in nature...? Or just the series sounding simultaneously?

On Wed, Jun 25, 2008 at 7:12 AM, Mike Battaglia <battaglia01@...> wrote:
> On Wed, Jun 25, 2008 at 7:10 AM, Chris Vaisvil <chrisvaisvil@...> wrote:
>> then it sounds to me that the answer is no.
>>
>> the speaker does not... unless it is broken in some fashion
>>
>> I have yet to be convinced that subharmonics exist beyond a concept
>>
>> each case so far has been a device driven to generate the lower tone
>
> Do you mean whether or not subharmonics exist sounding simultaneously
> in nature...? Or just the series sounding simultaneously?

Er, I mean the subharmonic series sounding simulateously, like the
harmonic series, or just the series being played out in some fashion?

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--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> > That's right, except 12-equal string lengths (and hence fret positions
> > as measured from the nominal bridge position) aren't proportional to
> > the logarithm but inversely proportional to the exponential.
> > Subharmonic is proportional (linear). Harmonic is inversely
> > proportional which is also called hyperbolic (with an offset in this
> > case).
>
> So what is proportional to the logarithm? Nothing?

I don't know of any useful meaning that could be attached to string
lengths which were proportional to the logarithm of the fret number.
But of course in the case of 12-equal the fret number is proportional
to the logarithm of the frequency.

It can also be confusing because the "inverse" in "inversely
proportional" is different from the "inverse" in "the logarithm is the
inverse of the exponential". Inversely proportional really means
_reciprocally_ proportional, i.e. proportional to 1/(whatever).

> > And I say "nominal" because the real nut position is set forward from
> > its theoretical position by about 0.5 mm (shortening the strings) to
> > compensate for the increase in tension when strings are fretted as
> > opposed to open, and the bridge or saddle-pieces are set back between
> > about 1 mm for treble string and 5 mm for bass string (lengthening the
> > strings) to compensate for end-effects due to string stiffness.
>
> Interesting. So if I was actually refretting a guitar, would I measure
> these lengths from the actual nut position, or from 0.5 mm down past
> where the nut lies?

Some manufacturers don't bother with nut-setforth and they may use
different amounts so I can't say. I suggest you measure all the
existing fret positions (at least up to the 12th) to the nearest 0.25
mm and put them in a spreadsheet. Then take your scale length
initially to be double the distance from nut to 12th fret and try
adding various amounts to all the fret distances (and twice to the
scale length) until you get the best agreement with the theoretical
formula. (You could make a spreadsheet on Google documents and invite
me or others to help you get it right).

> I just defretted this guitar, and I was going to
> make it fretless; but I might do 19-tet instead, or even 31-tet if
> it's a viable option.

Here's a paper of mine you might enjoy.
http://dkeenan.com/Music/MicroGuitar.pdf
There's an untried Blackjack design at the end.

Another method for rapid prototyping of microtonal frettings is to use
1 mm diameter nylon monofilament fishing line (hard trace or leader)
and file notches in both edges of the fingerboard (or in something you
attach to both edges of the fingerboard, like some wood, plastic or
wire) where you want the frets, then tie the fishing line under the
top strap button and just wind it around and around the neck
spiralling up through all the notches and eventually tying it off to a
tuning machine. I learnt this trick from one Charles Neville. See
http:// www.cyberferal.com/UncleBob/gallery
Click on a photo to zoom it.

We independently came up with the same idea of using one continuous
piece of fishing line for all the frets. I laced them _through_ a
hollow tube neck with holes, he wrapped them _around_ a solid neck
with notches.

-- Dave Keenan

Chris Vaisvil schrieb:
> > Then the question is, how does the speaker produce (3/2)f, 2f, (5/2)f,
> 3f, (7/2)f, and so on, so that we perceive (1/2)f as the fundamental?

The speaker ideally is not a sounding membrane, but a piston that moves the air. It shouldn't, but nevertheless may contribute its own vibrations across its diameter, but the frequency is due to the magnet behind it and its possible acceleration. I think you mix this up with an old saw about the frequencies transmitted by telephone, where the lower ones are or were simply filtered away.

klaus

On Wed, Jun 25, 2008 at 8:36 AM, Dave Keenan <d.keenan@...> wrote:
> --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>>
>> > That's right, except 12-equal string lengths (and hence fret positions
>> > as measured from the nominal bridge position) aren't proportional to
>> > the logarithm but inversely proportional to the exponential.
>> > Subharmonic is proportional (linear). Harmonic is inversely
>> > proportional which is also called hyperbolic (with an offset in this
>> > case).
>>
>> So what is proportional to the logarithm? Nothing?
>
> I don't know of any useful meaning that could be attached to string
> lengths which were proportional to the logarithm of the fret number.
> But of course in the case of 12-equal the fret number is proportional
> to the logarithm of the frequency.
>
> It can also be confusing because the "inverse" in "inversely
> proportional" is different from the "inverse" in "the logarithm is the
> inverse of the exponential". Inversely proportional really means
> _reciprocally_ proportional, i.e. proportional to 1/(whatever).
>
>> > And I say "nominal" because the real nut position is set forward from
>> > its theoretical position by about 0.5 mm (shortening the strings) to
>> > compensate for the increase in tension when strings are fretted as
>> > opposed to open, and the bridge or saddle-pieces are set back between
>> > about 1 mm for treble string and 5 mm for bass string (lengthening the
>> > strings) to compensate for end-effects due to string stiffness.
>>
>> Interesting. So if I was actually refretting a guitar, would I measure
>> these lengths from the actual nut position, or from 0.5 mm down past
>> where the nut lies?
>
> Some manufacturers don't bother with nut-setforth and they may use
> different amounts so I can't say. I suggest you measure all the
> existing fret positions (at least up to the 12th) to the nearest 0.25
> mm and put them in a spreadsheet. Then take your scale length
> initially to be double the distance from nut to 12th fret and try
> adding various amounts to all the fret distances (and twice to the
> scale length) until you get the best agreement with the theoretical
> formula. (You could make a spreadsheet on Google documents and invite
> me or others to help you get it right).
>
>> I just defretted this guitar, and I was going to
>> make it fretless; but I might do 19-tet instead, or even 31-tet if
>> it's a viable option.
>
> Here's a paper of mine you might enjoy.
> http://dkeenan.com/Music/MicroGuitar.pdf
> There's an untried Blackjack design at the end.
>
> Another method for rapid prototyping of microtonal frettings is to use
> 1 mm diameter nylon monofilament fishing line (hard trace or leader)
> and file notches in both edges of the fingerboard (or in something you
> attach to both edges of the fingerboard, like some wood, plastic or
> wire) where you want the frets, then tie the fishing line under the
> top strap button and just wind it around and around the neck
> spiralling up through all the notches and eventually tying it off to a
> tuning machine. I learnt this trick from one Charles Neville. See
> http:// www.cyberferal.com/UncleBob/gallery
> Click on a photo to zoom it.
>
> We independently came up with the same idea of using one continuous
> piece of fishing line for all the frets. I laced them _through_ a
> hollow tube neck with holes, he wrapped them _around_ a solid neck
> with notches.

Wow, that's a great idea. I might actually do just that.

On a side note, my nephew was reading my posts on this forum, and he
read these ones out loud:

> So what is proportional to the logarithm? Nothing?
> Another method for rapid prototyping of microtonal frettings is to use 1 mm diameter nylon monofilament fishing line

Do you realize that we're slowly losing all sense of how to
communicate with normal people? I don't know what to say.

-Mike