a semantic question (from a Semitic person)

Is there a specific word to describe intervals which share a particular
numerary nexus? For example, if I want to describe only 5-limit intervals
which include 5 (exclude 3/2, 4/3, etc.). Would you say it is on the
"plane of 5", or "5-plane intervals" (referring to a lattice dimension)?

-Adam

_________________
Adam B. Silverman
153 Cold Spring Street; A3
New Haven, CT 06511
(203) 782-1765

abs22@pantheon.yale.edu



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I think this is fascinating, but I echo Gary's concern about the pitch
relations since the flute is not intact. I might also add that not all
"archaeomusicologists" accept Kilmer's and Duchesne-Guillemin's
interpretation of the Hurrian cult hymn, and Babylonian notation in
general, as being polyphonic. It is hard to believe that a musical
notation could evolve which did not allow for the easy notation of
single notes, but only two-part chords.

M.L. West, author of the best book (IMO) on ancient Greek music
has written an article "The Babylonian Musical Notation and the
Hurrian Melodic Texts," Music and Letters 75(2): 161-179 (1994) in
which he/she interprets the dyads as strings to be played by the two
hands of the harpist. West does accept the cyclic principle of
tuning by 5ths, 4ths and octaves (aka Pythagorean), 7 modes and 12
"chromatic" notes in the octave. West's transcription, however,
suggests an extremely repetitive melody and a narrow range. The phrase
or line endings do make some musical sense.

By a statistical method, David Halperin has come up with a very
different transcription which involves a considerable degree of
descending scalar motion. His paper is in Musikometrika 4: 101-115
(1992). (the volume # could be 1 as my xerox copy is smeared)

The notation and nomenclature may be traced back to King Lipit-Ishtar
of Nippur (2nd millennium BCE) and even to the Sumerian ruler Shulgi
in the 22nd century BCE. I think the data are sufficient to establish
the antiquity of the "Pythagorean" tuning in the West and for that
matter the influence of Babylon on Greek math and music ("Harmonics").
Some Chinese sources claim a priority of some 500 years for the discovery
of this tuning, but most scholars believe the early Chinese dates to be
exaggerated and instead refer to the first emperor, Shih Huang Di, in
the 3rd century BCE when Chinese and Hellenic culture came into contact,
partly as a result of Alexander's conquests.

For what it's worth, West believes neutral intervals to be found on
some surviving auloi, as mentioned by Aristoxenos. West also believes
Kathleen Schlesinger ignored the unequally spaced holes of the known
auloi when she developed the theories expressed in her opus "The Greek
Aulos." Certainly neutral intervals are not rare in world music today.
The Greek hemiolic chromatic may be the relict of a neutral pentatonic
(also the spondeion scale) and neutral intervals are common in Islamic
music, Africa, etc.

--John



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I agree with the challenge to the speculation that one can infer a tuning
from an instrument that has lost its mouthpiece to time. This was the
problem with Schlesinger's Greek Aulos computations...interesting numbers,
however with no genuine relation to the double-reed instruments because
they don't take into account embouchure, reed length, etc.

On the other hand, the dating of this item and concurrent attribution to
the Neanderthal line of primates is quite significant. The debate still
rages whether we are descendents of this line, or not. I've heard some
impassioned commentary regarding unscientific distortions of Neanderthal
jaws, which are pushed out past their physiogamic relationships so that
they seem more foreign to our own.

A joke making the circles now is that early music is older than people.

Johnny Reinhard
Director
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@idt.net


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>On the other hand, the dating of this item and concurrent attribution to
>the Neanderthal line of primates is quite significant.

Definitely. It's the first clear evidence of what we call "art" outside
of our species, albeit a very closely-related species. Of course the
biggest caveat to that is the possibility that whale songs might also be
"purposeless", pure expression.



>The debate still rages whether we are descendents of this line, or not.

The most coherent answer to that question I've heard says that the
Neanderthals were the European descendents of Homo Erectus, and modern
humans are the African descendents of Homo Erectus. (The Homo Erecta (?)
that made it to Asia apparently died out comparatively quickly.) As Johnny
accurately pointed out though, that theory is by no means universally
accepted.

Along those lines, it's interesting to note that Neanderthals were very
big, burly, hearty species, living in severe cold most of the time, and in
most cases hunting with essentially hand-to-hand combat. Many of them
sustained severe injuries during hunts - far more severe than Homo Sapiens
Sapiens like us generally did. All that, and they still apparently had
time for music. Take that to the next debate on funding cuts for musical
programs!



>A joke making the circles now is that early music is older than people.

A kinda analogous question: Which came first: Computers or computer
graphics, given that Charles Babbage got the idea for storing programs for
his Differential Engine on punched cards from the Jaquard (sp?) loom, which
used them to wave intricate and visually pleasing patterns into fabrics.



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I didn't want to give my own interpretations of Fink's article before
presenting his thoughts, but now that it has started some good discussion,
I thought I'd jump in.

Fink draws most of his conclusions from the not exactly profound
observation that the holes in the flute are unequally spaced. For some
reason, he thinks that this is a momentous discovery, as most people, he
surmises, would expect primitive Neanderthals to tend to space things
equally. He adopts as one of his assumptions: "As we humans seem to show,
there is a history of a predisposition toward equality in measurements: The
distances between telephone poles; between pickets; between windows on
buildings in the architecture of all periods and cultures; between sidewalk
slabs; between inches; feet, yards, centimeters -- between ranks and files
of all types, etc. "

I don't see what any of this has to do with music. Is any Paleolithic art
symmetrical? Does any of it show equality in measurements? I see no reason
to think that Neanderthals would develop a music based on equal
measurements on flute holes even if they liked to arrange their caves or
other dwellings with the stone age equivalent of regular sidewalk slabs.

That aside, Fink seems to equate unequal with diatonic, for some reason
that I cannot quite fathom. Diatonic means to me a seven note scale with a
certain sequence of tones and semitones, the tones being about twice the
size of the semitones. Now, he has only four tones on this flute. He
postulates a sequence of tone, tone, semitone, which will fit into a
diatonic scale, sure, but also a pelog scale, the in scale of Japan,
certain non-diatonic Eastern European scales, plenty of non-diatonic ragas,
and so on. Unless one stretches one's definition of "diatonic" to include
all of these scales, I don't see any reason to suppose that Neanderthals
were or were not using diatonic melodies. Also, by admitting the
possibility of neutral thirds, he is stretching the term diatonic quite
far.

Fink apparently has another publication which I have not seen in which he
argues that the diatonic and anhemitonic pentatonic scales are the best
musical representations of the harmonic series (what he calls the "overtone
series"). I'm afraid I'm at a loss to understand why four, six, or
forty-three tones per octave can't also model the harmonic series, or how
neutral thirds fit into this scheme, but then I haven't read this other
paper.

Fink, like some other writers, argues for the historic precendence of just
intonation, based only on the beauty and naturalness of the harmonic
series. Now, I love the sounds of many JI intervals, and I use JI in my
music, but to say that it is therefore the fundamental basis for all music
is to misunderstand what art is. This is not to say that the harmonic
series plays no role in the evolution of musical systems, I believe it
plays a very powerful one, but for some cultures, so does the mystical
value of a length of pipe, the ability to transpose, the tension resulting
from temperament, and so on.

Which of these many criteria were important to the Neanderthals? I sure as
hell don't know, and I don't think one fragment of a bone flute will tell
us. Perhaps it was different for the Neanderthals in Spain, or for the
Neanderthals living a hundred or a thousand years earlier or later. It is
much easier for me to conclude that there is some researcher predisposition
here than to extrapolate from this fragment a "natural foundation to the
diatonic scale."

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)621-8360 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^




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Not to beat this bone flute thing to extinction, but I have some questions
about the acoustics of flutes as they are presented in Fink's article. He
draws the conclusion that, because of unequal spacing of the holes in the
bone, it must have played a diatonic scale.

Now I have a Balinese suling (bamboo flute) that plays a pretty reasonable
major scale if you lift up your fingers one at a time (despite the fact
that the music it plays in Bali is not diatonic). Yet the physical distance
between the second and third holes is almost the same as the distance
between the other holes. (I measure them all as within 1 millimeter of the
same distance: about 32 mm.)

According to Fink it should be half the distance because the interval is
half as large. However, in another place in his article he says that hole
placement has the same relationship to frequency as string length does.
That would seem to indicate that the holes would have to get closer
together to preserve the same interval between them.

Does anyone know more about or have any references on the acoustics of
flute hole placement? Thanks.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)621-8360 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^




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>Not to beat this bone flute thing to extinction,

Harhar.




>Now I have a Balinese suling (bamboo flute) that plays a pretty reasonable
>major scale if you lift up your fingers one at a time ...
>Yet the physical distance
>between the second and third holes is almost the same as the distance
>between the other holes.

I'd wager that they're also xdifferent diameters too. This is a bit of
an oversimplification, but the larger a tonehole is, the more it behaves
like cutting the tube off entirely. A small tonehole lets the vibration
extend farther down the tube than a larger tonehole, thereby making the
pitch flatter.




>he says that hole
>placement has the same relationship to frequency as string length does.
>That would seem to indicate that the holes would have to get closer
>together to preserve the same interval between them.

That is true. Theobald Boehm, the inventor of the modern flute, in his
book as translated and extensively commented by Dayton C. Miller (Dover
publication, if still available), characterized the placement of flute
toneholes as like frets on a string, but - essentially - with the
embouchure hole closer to the end of the tube than the bridge of the string
would be.

Back when I was in high school, I did a science fair project to study
flute acoustics and thereby design and build 10TET flutes. In that
investigation, I found that that prescription really didn't work. The
toneholes ended up having to be spread out farther apart than that.



>Does anyone know more about or have any references on the acoustics of
>flute hole placement?

The easiest way to place holes on a woodwind, I think I've concluded, is
to make a test instrument with essentially arbitrarily-placed holes, play a
scale up the tube precisely measuring the pitch of each hole. You can then
plot those as distance/pitch pairs to form a "calibration curve". That is
to say, you can connect the dots and smooth the curve to make it
continuous, and then use that curve to run the process backward: Look up
from the calibration curve, the lengths that match whatever pitches you
want, and then build an instrument of otherwise identical dimensions, with
holes where you looked them up on the curve.



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Even if we can establish that these were indeed musical instruments (and
not pasta strainers or candelabra), the list of variables to be covered
before a tuning is established is formidable:

(1) the mouthpiece is missing: how much longer was it? was it transverse
(if so, where was the blow hole placed) or vertical? If vertical, then was
it with a cut (like a quena or shakuhachi) or without a cut (like a nay)?
or was it a direct flute in the first place? A buzzed lip embrochure (like
a cornetto) is plausible, though I assume fipple flutes and reeds - both
more complex technologies - would be less likely.

(2) Has someone seen an X-ray of the instrument? Is the channel primarily
conical or cylindrical? (That makes a big difference in both overblowing
and fingerhole placement - and one in which Gary's Science Fair project
would have been seriously affected; Benade's _Horns, Strings, and Harmony_
provides a fascinating introduction to woodwind building with useful
information on fingerholes). How deep are the fingerholes? Deep walled
instruments may have fingerholes of variable length which lengths become
critical to the pitch (bassoon players know about this; serpents and
racketts took advantage of this to create more reachable fingerings).

(2) The fingerhole placement has to be considered in combination with both
size and depth of the holes. How much have the holes increased in diameter
while decreasing in depth due to wear over the years?

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>(2) Has someone seen an X-ray of the instrument? Is the channel primarily
>conical or cylindrical?

The picture on the web page shows the remaining fragment to be fairly
short, so it would be difficult to really tell. It's probably fair to say
though that presumably all they did was hollow out the marrow from the
bone, so it was probably largely cylindrical


>(That makes a big difference in both overblowing
>and fingerhole placement - and one in which Gary's Science Fair project
>would have been seriously affected

By the way, that "calibration-curve"-based procedure I described is not
how I did my science fair flutes. But it probably is one of the easiest
ways to do it. And yes, when using this procedure, the calibration tube
must have all other aspects of its essential geometry identical with the
final instrument, including the shape and size of the bore.



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>Bill Alves writes:
>Does anyone know more about or have any references on the acoustics of
>flute hole placement? Thanks.
>
>This is the second time I'm going to suggest this book as an answer, but is
>the best thing I've seen so far and relatively new. Bart Hopkin's book
>Musical Instrument Design (See Sharp Press) gives the best advice I've seen.

Thanks for reposting this reference. I'm sorry not to have taken notice of
it the first time around.

Fink, in his paper on the flute, takes note of some of complicating factors
that Gary and Dan have brought up, but essentially says that, since they
would be random, their effect on pitch would be cancelled out. This is
assuming that the Neanderthals, unlike later instrument builders, took no
notice of their hole diameter, bore, and so on, and that Fink's guess for
the overall length of the flute is close. Both are pretty tenuous
assumptions, I think.

I've played renaissance gemshorns which are also flutes made out of bones
(horns) and the diameters of the holes vary considerably from instrument to
instrument. I had assumed that the instrument maker gradually widened them
as a way to fine tune them, but I don't know. (One hole on the bass
gemshorn was too big for most people's fingers, I recall.)

The hole diameters on the Balinese suling I mentioned do not really vary as
far as I can measure. The bore seems cylindrical. However, if the pitch is
a function of the overall length of the closed tube, why, if is there such
a long distance between the last hole and the end of the tube? That is,
when all my fingers are down, I assume the air column is the length of the
whole tube, about 43.7 cm as I measure it. When I lift my finger off the
lowest hole, the vibrating length decreases to about 34 cm (measured to the
middle of the hole), but the pitch only goes up about a whole tone. When I
lift up my next finger, the length drops only to 30.8 cm, but the pitch
rises another whole tone.

I finally saw the Discovery article yesterday, and I must say that it looks
like a much more profound discovery than the one in Slovenia. As Clif
mentioned, there is a tusk "tuba" with sixteen holes (apparently equally
spaced, as Fink may be disappointed to learn), something that could have
been a bagpipe, graduated bones that could have been parts of a xylophone,
and a small bone triangle.

What was more astonishing to me is that they found a 50,000-year-old cave
painting of musicians in a procession playing these instruments! In the
photograph reproduced, the tuba is clearly played by blowing, though it's
impossible to tell if it was a flute or buzzed-lip instrument. The triangle
can clearly be seen played by another musician. Another figure is more
amorphous, but one can easily imagine it to be a bagpipe. This is the first
cave painting ever found associated with the Neanderthals, by the way.

It would be great to find out more about this discovery.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)621-8360 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^




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