Above: 43,ooo-82,ooo-year old Cave Bear femur bone segment with 4 holes.
(2 complete holes, and 2 confirmed partial holes, one at each broken end of bone.)
 
NEANDERTHAL FLUTE
Oldest Musical Instrument's 4 Notes
Matches 4 of Do, Re, Mi Scale
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.EVIDENCE OF NATURAL FOUNDATION TO DIATONIC SCALE
See also webpage on Scale's Basis
 
LIBRARY ORDERS OF ESSAY -- HARD-COPY
Accompanying music:
Click title: The Joy of Counterpoint by Bob Fink
[For more new midis in classical styles, click here]
 
Updated Mar 2003 -- Two New Books on Music Origins & Music Archaeology
Updated Mar 2002-- Chinese playable flutes found --9,ooo yrs old!!
Updated Jan 2003 -- Evidence that flute was made by Neanderthals
Updated Jan 2004 -- Lacking clear taphonomic evidence,
how else could we tell artifact from accident?
Updated Oct 2003 -- Replies to Nowell & Chase, D'Errico et al
 
Musicological Analysis
by Bob Fink
Related information on this analysis: April 5 '97 Times of London; April 12 Globe & Mail; April 11 Science magazine, p.203; Discovery Channel 5/7/97; Western Report 5/5/'97 (Cover story); Scientific-American (Sept.,'97)
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"The hallmark of great science is that it reduces complexity into simplicity"
-- Bruce Stillman, director: Cold Spring Harbor (molecular biology) Laboratory, N. Y.

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Note: Discussion, debate & letters about this essay begin at this link.
 
INTRODUCTION
and SUMMARY of ESSAY
 An ancient bone flute segment, estimated at about 43,ooo up to 82,ooo years old, was found recently at a Neanderthal campsite by Dr. Ivan Turk, a paleontologist at the Slovenian Academy of Sciences in Ljubljana. It's the first flute ever to be associated with Neanderthals and its confirmed age makes it the oldest known musical instrument.
The find is also important for its implications regarding the evolution of musical scales. It's to this latter issue my analysis in this article is addressed. (See full "ESSAY" below.)
 
* * * *
Holes 2, 3 & 4 on the bone (as shown, from left to right) stand in a significant relationship to each other: The distance between holes 2 and 3 is virtually twice that between holes 3 and 4. The line-up of the holes indicate that it is a flute.
This means we are looking at a whole-tone and a half-tone somewhere within a scale. Such a combination of whole-tone and half-tone is the heart and soul of what makes up 7-note diatonic scales. Without making even one more measurement beyond this, we can already conclude: These three notes on the Neanderthal bone flute are inescapably diatonic and will sound like a near-perfect fit within ANY kind of standard diatonic scale, modern or antique. We simply cannot conceive of it being otherwise, unless we deny it is a flute at all.
In essence, the whole story is simply that.
Sometimes the simplicity of a situation, as outlined just above, is so simple that we are unnecessarily suspicious of the obvious -- that it's just "too easy" to accept it at first glance, and we tend to over-complicate things to avoid appearing hasty. Therefore, many experiments and other approaches were tried, but the simplicity of the issue remained intact.
This is the most powerful practical evidence ever in support of there being a natural foundation to the diatonic scale. It is in line with University of California's (Berkeley) Prof. Anne D. Kilmer's deciphering of the clay tablets, 4,000 years old, from Ur, indicating, in this world's oldest known song, the use of harmony and of the diatonic scale. It is also confirming of recent psychological studies by Trehub (U. of Toronto), Schellenberg (U. of Windsor), and Kagan (Harvard) of infants. These studies (Vol. 7 #5 Sept '96 of Psychological Science) showed musically untutored infants preferred natural (acoustic) intervals over dissonant intervals.
All of this recent evidence confirms the predictions and views in my 1970 book on the Origin of Music, which outlines the natural forces pushing the diatonic scale into existence.
The remaining hole (left-most first hole in the picture) is the only clue we have to answer the remaining questions, which is really the bulk of the essay's subject. To those questions, as one can read, we have come up with a fit to the Mi, Fa, Sol, La part of a minor scale, which includes a flatted La and a "neutral" third for Mi, widely used in many cultures, sometimes called a "blue" note (match no. 2 in the paper). Another match was also considered viable (no. 1)
 
To summarize the remaining questions taken up in the essay:
a) Is this remaining hole able to produce yet another diatonic note consistent with the other 3? Within variations of our permitted tolerances, and with clear parallels to human musical history, the answer is yes for any of the matches considered. (See the appendix, quotes & notes for what are acceptable dimensions needed to claim a fit.)
b) Where in the scale will the bone's set of 4 notes fit? We have assumed that the flute plays a larger scale, as it is most unlikely you'd have a scale of only 4 notes without a keynote, or with the first note being the keynote. Since a flute's keynote and its octave-up can already be played without drilling any holes at all, it is safe to assume that the 4 holes made in the bone segment would likely be for additional notes (as in match no. 2). Only two notes would then remain missing to complete the full scale. One would only drill a separate keynote hole into the marrow if no other exit from the internal hollow of the bone existed (which is remotely possible in the case of match no. 1, if this hole is at the knobby-end of the femur).
c) Which way do the 4 notes run relative to the blow-in end? Is it from the left to right (as is assumed in the paper's drawing), or right to left? (Note: If we had assumed it was the opposite direction from what's shown in the bone drawing, then we'd get the best of all matches so far (which would be a match that is the reverse of match no. 2), namely: Mi(major), Fa, Sol, and La (major) -- all holes measuring within about 1/16 of a tone tolerance. But this reverse match depends upon whether bone length in that direction would be sufficient to reach the necessary distance to the blow-in end.
d) How long was the original flute? 37 centimeters (+1 / -5cm) -- is our present estimate based on empirical measurements of commercial flute-lengths and interpolating these to the bone segment, which may have been extended to reach the required length.. There is a difference between air-column length needed to produce musical notes and the actual (shorter) flute length needed to sustain this oscillating air-column. Our empirical results indicate the flute need be about 87% of the functionally operating air-column of the fundamental keynote.
 
OTHER FACTORS NEGLIGIBLE
 
Other factors, such as flute wall thickness, material, hole diameter, interior diameter, interior obstacles and bumps -- all have been cited as able to affect pitch . But the extent of their effect on pitch in the case of this Neanderthal flute seems likely to be nil to very small , and would be only noticeable to a discerning ear.
Also, since there are so many of these factors, then by the normal operation of chance, some would tend to cancel each other out, rather than all working in the same direction to alter a note's pitch all upward or all downward. Experiments with several commercial flutes, by enlarging holes, blocking them partially, etc., tended to indicate that these changes would [regarding the range of dimensions of the artifact] be virtually inconsequential to its pitch, and well within our tolerances.
One effect of changing the flute's length (by increasing or decreasing it near the blow-in end) had only a small effect on pitch. E.g., after large length reductions -- up to two hole diameters or more -- the result was the entire scale was raised as a whole, by a tone or by a half-tone, but without throwing any of its notes appreciably out of tune with each other. It was still clearly recognizable as the scale -- it was just in a different key and a bit out of tune. On the other hand, changes of length at the open escape end made big differences. So, if you got the escape-end right, all the other matters above allow very forgiving tolerances.
Further, considering the extent of the capacity of Neanderthals to take factors other than length and distances between holes into account, and considering the range of workmanship error that we'd expect from their tools, I suspect these would have a greater effect on pitch than any of these other factors, thereby rendering these other factors negligible.
On those grounds, we took length as the deciding measure for pitch, and I built a flute into which I incorporated the same proportional spacings as is found between the 4 Neanderthal flute holes.
The resulting sound more than confirmed the analyses we've made. The findings were checked and supported by the C.U.N.Y. earth scientist who announced the find and worked on dating it . [SEE DEBATE & UPDATES BELOW]
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ESSAY
 
1.
UNEQUALLY-SPACED HOLES
 
 
The flute's holes are clearly unequally spaced, and it's very unlikely, judging from the compared distances between them, that these would have been done from poor measurements or sloppy punching or drilling. A flute-maker could be off a bit due to that kind of error, but not a lot off. The holes are a lot off from being equidistantly spaced. So this is assumption #1 -- but a likely one: The unequalness is deliberate.
The next assumption is also extremely likely to be true: 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. We also use 5's and l0's and symmetry a lot (as we have 5+5 fingers and toes).
One of the infrequent exceptions to this mental penchant is the historical 5 and 7-note musical scales. One look at a piano keyboard shows that our inclination for equal spacings for intervals between things (musical notes in this case) has been ignored or was over-ridden. Not only in Western music, but even throughout history and by widely differing musical cultures. Prof Anne D. Kilmer, head of Dept of Assyriology at U. of Cal., Berkeley, who corresponded with me about this and visited me here some years ago, had deciphered 4,000-year-old cuneiform tablets as being a song in the do, re, mi (diatonic) scale, and it was a song that had harmony (of thirds) to boot!1
This kind of growing evidence of the utter universality of the unequal-interval pentatonic and/or diatonic scales has upset many musicological apple-carts, but not mine.
Since the distance between fingertips from one tip to another is more or less equal, then the holes in this Neanderthal flute (if Neanderthals have the same mental penchant for easy arithmetic and equidistant repetitions as we do) should have been equidistant -- if for no other reason than to fit the convenience of the finger widths.

INITIAL CONCLUSIONS

To again see this predilection for equality get over-ridden in the making of these holes, therefore, is significant, and leads, even before we make further measurements, to the following (likely) conclusions:
* Firstly, as to the obvious, the Neanderthal flute-maker didn't want a single tone or a sliding "siren-like" kind of sound; so he/she put in holes so that step-wise discreet or separate notes could be created. That's the dividing of the continuum of sound into scales, just like us.
* But the holes were not acceptable to this Neanderthal if they produced just any old notes (as equidistant holes would produce). When we look at history, such a scale would be, and it seems, was felt, to be "out of tune" in most human musical cultures. [See note 5 below] The reasons for this are profusely examined in my book on music's origins (The Origin of Music). Therefore, the holes (likely) were made with the goal in mind of producing some kind of non-equal scale or set of notes.
* A large number of different scales made from such non-equally divided hole-spacings are possible -- but earlier research that I and others have published over the years indicates that there are reasons based in acoustics and ratios (of vibrations) to conclude that the likeliest scales to be "sought" with such unequal hole-spacings are pentatonic or diatonic scales. Suffice it to say these scales are overwhelmingly parallel to the acoustic "overtone series" and several other acoustic properties2 -- yet the scales were produced by ancient people with no knowledge of acoustic facts or properties -- other than the responses of their ears. So, therefore, if the Neanderthal is going to go for an unequal scale, it "probably" would be one of those two types (pentatonic and/or diatonic).
 
Using negative logic, the question arises: If the Neanderthals weren't seeking an unequal scale, why not make the holes equally-spaced?
There are "probably's" and "likely's" in the above, but I think "very" and "extremely" will be supportable adjectives once we look at accepted conclusions in other disciplines (e.g., as above: psychology, history, artifacts, physiology, musicology and acoustics -- to name a few that we will bring to bear on this anthropological-archeological flute find.
 
WHAT NOTES WERE PLAYED ON THE FLUTE?
 
Regarding the actual notes that might have come from the flute: Unless we can know the full original length of the flute, and the placement of holes on it, we cannot know for certain the notes that were played on it. But all is not lost.
Readers may be aware of all, some or none of the following, so excuse me if I assume none.
If you take a length of violin or piano string, and press down in the center (creating what is called a "node" in the string), then each half of the string when played will produce an octave up, of the note of the entire string. A division into thirds makes notes that are called 5ths, and so on.
Similarly, a column of air (inside a wind instrument) can be divided, and each lesser length of air-column can produce other notes, as well. In order to take a long musical horn and get it to produce other notes, we have seen history roll up the horn, and add valves (trumpet) or a slide (trombone) to force into existence differing lengths of columns of vibrating air inside the instrument -- hence creating the different notes in the scale.
The holes in a flute can likewise create these changing lengths of air-columns (and produce different notes). But clearly, if you don't know the full length of the flute, then the holes, representing different columns of air, can't be assigned as being, for example, at the "halfway" point of the full length of the flute (producing an octave up); or at the 1/3rd location, and so on. We might have the last 3 or 4 holes, or the middle 4, of the whole flute.
The unequal spacings would be our best clue as to which holes they were (again "assuming" we are looking for a diatonic or pentatonic scale). If we assume the scale is there (reasonable to do, I think, just from the unequalness of the hole spacings), then the hole spacings might possibly lead to the reconstruction of the full-length flute.
Again, we are left with the question above: If the Neanderthals weren't seeking an unequal scale, why didn't they make the holes equally-spaced?
(On the other hand, if we don't assume a particular scale was sought after by the hole-maker, then we cannot reconstruct anything further than the fragment as found.)
 
2.
RECONSTRUCTION OF THE WHOLE FLUTE
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First, disregarding for the moment the actual "key" or absolute pitch of notes, the general way in which a flute is made to produce a pentatonic or major diatonic scale is as follows:
Whatever the length of the flute (bone, bamboo, metal, whatever), that length (called L) is divided as follows:
From the blow-end, if no holes are punched, then the flute will produce its fundamental note (and its octave), namely, Do (from the Do, Re, Mi scale).
If you make a hole 8/9ths of the length of the effective air column, measuring from the blow end (where the slit, reed or mouthpiece is), then you will get the second note, Re, in a rising scale.
If you make another hole 4/5ths from the mouthpiece, the 3rd note, Mi (in the major scale) is formed.
And so on, until you have produced notes up to Ti.3 More holes after that would begin repeating the scale an octave higher.
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Illus: MODEL FLUTE

 

 
We can label the distances between the holes (which will be necessarily unequally-spaced) as z, y, x, w, v, u, as many as are needed to suit the number of holes. For our purposes, only six holes (plus the two Do's able to be made with all holes closed) will give us the full scale. There is the possibility of an end hole made on the face of the flute rather than made by the exiting of the hollow bore, and the possibility of a flute with 8 holes playing both Do notes.
The distances between holes are listed as percentages of the previous hole distance.
(Of course, the Neanderthal bone flute would have been made "by ear," and could not have been made using this kind of mathematical approach. We are here simply creating a comparative "model.")
Each set of any consecutive set of holes (say 4 holes in this example) will exhibit a pattern of relative spacings between them that is unique to those 4. If, after trying to account for errors in construction techniques -- a difficult matter to define, we can match the set of holes in the Neanderthal flute to one or another set of consecutive holes in our theoretical or mathematically perfect model of a flute, then we can say the bone flute fragment is part of a flute that plays, for ex., the mi, fa, sol, la part of the do, re, mi scale, or the like.
(If the Mi part of the scale was missing, or the Fa note is missing, then we would have the pentatonic scale.)
After reaching this point, the actual measurements will come into play: Picking a distance between holes in actual centimeters, we can use that to find a multiplying factor that will give us the full length of the original flute. Using other distances between holes and re-doing that calculation, and averaging the results, may compensate somewhat for any errors. The result will be approximate, but still very close to what the length would have to have been.
So the above, then, is the methodology we have put in place. (A friend, Mike Finley, very knowledgeable in science and math, is now working with me on this).
We don't want to go into such great refinements of this method as to be exceeding the accuracy possible for the Neanderthal flute-makers of that time. However, the flute, because it was found connected to being used in the cave camp-site, was probably not a throw-away (one they made but didn't like) but was one which played acceptable sounds in a scale for them. On this basis, I would expect the holes, if they are meant to reproduce a scale they desired, would have measurements close to what was wanted.
 
 
3.
RESULTS and CONCLUSIONS
 
The measurements we made produced two matches, one fair (with problems); one excellent (within about .5cm and usually much less than that), to a 4-hole pattern found (above) in the model's set of holes. The odds are great against getting any match to one of the 4-hole patterns on the model due to chance alone. As to those odds, I believe most statisticians could check them out. (See appendix .)
The relationship between the holes in the model flute is expressed as a percentage of the previous hole. This creates a pattern, e.g: From the notes re, mi, fa, sol (shown above), the pattern is as follows: Dimension e is measured from the escape end of the flute. Dim.z equals .79 of dim.e; followed by y (equal to .57 of z); then x (equal to 1.67y) and so on. If the model scale is a minor scale, then the Mi note is flatted and dimensions z2 (equal to .49e) and y2(=1.51z2) are used, along with w2and v2, to account for a minor 6th 
When we measured the bone flute, we compared its distances between holes the same way: each as a percentage of the dimension of the previous hole. In this way, we could easily see which hole patterns, if any, were alike or similar.
 
 

 

 
The holes on the ends were not as well defined as the 2 holes in the middle. So we used the distance between the middle holes as a given or standard. The end hole on the left above is so broken as to suggest two possible locations (or even no hole at all?).
It could be an end hole. Hole "a" seems better defined, but hole "b" has its claim because it lines up better with the other 3 holes.
 
MATCH-UP
 
Without regard to the overall length of the original Neanderthal bone flute, here are the possible matches: First: Do, Re, Mi, Fa: This match assigns distance "Q" on the bone flute as corresponding to distance "z" on the model flute.
 
  
MATCH # 1
Note & Dim.
Note & Dim.
Note & Dim.
Note & Dim.
On Model (Major):
from left end: 
(Do) + "c"
.
Re + "z" =
.
Mi + "y" =
.
Fa + "x"
% of previous hole:
n/a for P 
Q = .79 of dim P 
R =.57 of dim. Q
broken off
Expected dimension:
For P: 4.39cm
Given: Q=3.45cm
For R: 1.96cm
n/a
Actual dimension:
P = 2.6--3.0cm?
Q = 3.45cm 
R = 1.75cm
broken off
 
The second match is for the minor scale segment Mi, Fa, Sol, La., as follows ("Q" corresponds to "x" dim. on the model):
  
MATCH # 2
Note & Dim.
Note & Dim.
Note & Dim.
Note & Dim.
On Model (Minor):
Mi + "y2"
Fa + "x" =
Sol + "w2" =
La + "v2"
% of previous hole:
n/a 
Q = P 
R =.5 of dim. Q
broken off
Expected dimension:
For P: 3.45cm
Given: Q=3.45cm
For R: 1.72cm
n/a
Actual dimension:
P = 2.6--3.0cm?
Q = 3.45cm 
R = 1.75cm
broken off
 
This second match is to a four-note pattern; the first match is to a 3-note pattern plus a possible (and problematical) "end hole." Match #2, in the minor key, is a closer match to the expected or predicted dimensions.
The minor key has been just slightly less popular or prevalent in human musical history, but very popular nonetheless. (Being second, you could say it tries harder) Most instruments are made to play the major scale, But the "relative" minor can be obtained from the major scale by starting on note La (2 steps below Do) rather than starting on Do, provided the instrument has enough of a note-span to embrace the lower La.
The Neanderthal flute could be flipped over, thereby running the distances between holes the opposite way, and the patterns would run the opposite way and differently. But this would require that the location on the entire femur of this bone segment would need enough room on the opposite side to continue on to account for an air column up to 16 inches (411/2cm). The orientation we chose is the one where the remainder of the flute is clearly suggestive of continuing on. Even if the paleontologists say there is length enough in the opposite direction, that would give us a "Match #3" and it would be the best match (of Mi, Fa, Sol, La in the major scale).
The calculation of this reconstructed length is based on the locations of the holes from the blow-in end. If the Fa note is 3/4ths of the whole effective air column length (measured from the blow-end), and the Sol note is 2/3rds, then the distance between those holes (in the model) flute represents .083 of the whole length. The reciprocal of .083 is 12.05. Taking the distance on the bone flute (in match #two) between those holes, (3.45cm), times 12.05, equals 41.6cm (plus some kind of mouthpiece or reed at the blow-end) as the hypothetical overall length of the flute's operating air-column. As most flutes need 10-15% less actual length to account for the operating air-column (which extends out past the escape end of the flute), then the range for length would be 36-39cm of bone based on dimension "Q" being correct.
NOTE: We have no idea, however, how long a mouthpiece would have been. It could have been any significant length --especially if the femur was too short to support lower, richer tones.
Experiments we made with a bamboo flute (with equally spaced holes) and with three tin whistles (similar to simple flutes), indicated that changing the size of the hole made little difference to the pitch; nor did lumps and obstructions within the hollow bore; and pitch changes were not significantly noticeable when location errors (of hole distances to each other) were less than half the diameter of a hole (about .3 or .4 cm). Errors greater than this could no longer be classified as simply "out of tune," but would actually begin to represent, as a whole, a totally different scale, alien in virtually all respects from a major or minor series of note-steps.
In match#2, the area where we have the greatest error, it is important to note that this concerns the Mi (minor 3rd) and it parallels the recorded tendency to, and the expectation of finding, wider variations of tunings of thirds all through music history.4 The third is the keystone note determining whether a scale is minor or major; it is one of the areas in which "blue notes" are tuned; and when removed altogether from the scale (along with the 7th, Ti), it leaves us with the pentatonic scale. The Blue Note is closer to a "neutral third" (one of these was introduced -- or reintroduced -- to the scale 1100 years ago by the Arabian musician Zalzal).
The reason for historic uncertainty concerning tuning of thirds is because the influence of acoustic pressures is weak concerning this note and two other notes. We see this is possibly reflected here in the bone flute tuning as well.
Our conclusion then is this: The notes on the Neanderthal flute, if possible for it to reach the total air-column length of about 42cm (in match #two), are consistent with 4 notes of the minor diatonic scale (flatted 3rd and flatted 6th included). All the notes, even in the lesser match #1, are still within the general pitch range able to be considered as notes within the diatonic scale. ( See also * in "Notes")
-- Bob Fink Feb/97
 

A P P E N D I X
REPORT on the PROBABILITY
of the PATTERN OF HOLES in the NEANDERTHAL FLUTE
MATCHING PART of the DIATONIC SCALE
 
 
The correlation between the model and the actual pattern of holes in the Neanderthal flute is close (in Match #2). For the following material and work I thank my friend Mike Finley.
We will take the first hole on the flute as an arbitrarily fixed base point, and assume** that shifting the position of a hole by +/- .225cm will produce a noticeable difference in tone.
The remainder of the flute's available length can be divided into .45 cm sections, each corresponding to a just-noticeable different and distinct tone. To calculate a conservative estimate of the order of magnitude regarding the number of distinctive scales possible, the full remaining 7.7 cm span of the flute is available for the placement of holes in these .45cm sections. This allows for approximately 17 tones. Using a standard permutation formula, the three holes allowed to vary in position could be distributed between the available span in 17!/(14! 3!) ways, e.g., 680 ways. Therefore, the order of magnitude against getting a close match is in the hundreds.
 
Thus, it appears unlikely that a close match with the minor diatonic scale could occur as a matter of chance. (See also odds for flute itself to arise by chance)
 _________________________________
 
** In arriving at this assumption, it is first reasonable to ask what displacement of a hole is necessary to make the sound produced by the flute be objectionably out of tune. A physical criterion may be relevant in assessing whether the flute can be regarded as an example of an instrument playing a minor scale "acceptably" in tune.
Some deviations from the mathematically correct placement of holes will not produce a flute that is objectionably out of tune. For example, a full Pythagorean comma is the deviation from perfect pitch which will occur when an instrument perfectly tuned in one key is used to play in another key. To avoid this, a compromise is required to allow playing in different keys. To construct modern instruments that can transpose and play in other keys, tones are adjusted so that no note differs from perfect pitch by more than ½ comma in any key, and this produces a tempered scale (such as found on keyboard instruments).
However, what is "objectionable" is, at the margin of acceptability, subjective: To some trained vocalists, even a properly-tuned tempered scale always sounds out of tune. But to most people, it is acceptable.5
Thus, the deviation that can be deemed acceptable for present purposes must include an element of subjective judgment. Experiment with a simple bamboo flute suggests that an error of less than approximately .21 cm is acceptable. (This is similar to a half-comma.) At least, such a deviation did not sound objectionable to one of us (Bob Fink), a trained musician, but who does not have perfect pitch.
Shifting the tone of the first note above the fundamental by a Pythagorean comma would shift the position of the hole: by .45 cm, and a half-comma change in tone would shift the hole by .225 cm. Two of the three intervals between the holes in the Neanderthal flute deviate from assumed perfect pitch by .03 cm or less, well within the criteria discussed above. The third interval deviates by an average of .64cm, a bit more than a whole comma. This interval is, however, the most difficult to measure due to deterioration of the bone about the terminal hole. If this hole lies 3.0cm from the 2nd hole, as suggested by a dotted line circle (for hole "b" on the flute), then the deviation is only .45, approximately one comma. If it lies 2.6cm from the 2nd hole, (hole "a" on the flute) then the deviation from the model flute of expected locations is .84cm.
There is, of course, no attempt to imply that any of the criteria discussed here would have been applied by a musician in the Neanderthal group that used the flute. Nevertheless, the criteria provide rough limits for calculation.
 

 
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N O T E S
 
1. Anne Draffkorn Kilmer, Richard L. Crocker and Robert R. Brown, Sounds from Silence (Berkeley, California: Bit Enki Publications, 1976) and Bob Fink, "The Oldest Song in the World," in Archaeologia Musicalis (Study Group on Music Archaeology, Feb., 1988), pp. 98-100.
These describe the nature of the song as diatonic and using harmony.
 
2. J. T. Howard & J. Lyons, Modern Music (New American Library, 1958).
On page 36 and 38, Howard & Lyons write: "The art of music and the practice of harmony have been developed according to what has pleased human ears; they have been evolved by musicians, not by scientists. Nevertheless, as one compares the growth of the art of music and the extension of its basic principles with the laws of acoustics, he finds an interesting parallel between the two. In other words, men have found most pleasing to their ears the combination of those tones that bear certain mathematical relationships to one another, even though they may not have been aware that those relationships existed.... It is impossible...to ignore the parallel between two, one a science and the other an art, and fail to observe that the tones which have been accepted...as producing agreeable...sounds in combination with other given tones have corresponded roughly with the natural overtones of those given tones. Moreover, the historic order in which these tones have come into the musical vocabulary forms an almost identical pattern with the harmonic series (of overtones)." See: Natural Forces Bringing Do Re Mi Scale into Existence on line.
 
3. Hermann C. F. Helmholtz, On the Sensations of Tone (2nd English Ed.; New York: Dover Publications, Inc., 1954), p. 17, passim.
In this work, Helmholtz also cites other ratios for the tunings of the third, sixth, seventh and the second. These tunings are close to each other, but have had wide historical usage. Some of these older standard tunings, if we used them, would actually make our findings even closer. It was long experience and scientific intervention (mathematics and acoustics) that led to the most prevalent standard ratios for notes of the scale, which we used in our "model" scale. Needless to say, Neanderthals had no benefit of this kind of reckoning.
 
4. Alan P. Merriam, "African Music," in Continuity and Change In African Cultures, ed. By Wm. R. Bascomb & Melville J. Herskovits (Chicago: University of Chicago Press, 1959).
On page 72., A. M. Jones is quoted by Merriam: "I have lived in Central Africa for over twenty years, but to my knowledge I have never heard an African sing the 3rd and 7th degrees of a major scale in tune." Merriam notes pp. 71-72): "There has been some discussion of an African scale in which the third and seventh degrees are flatted or, more specifically, neutral between a major and minor interval. This concept has been advanced especially by those concerned with analysis of jazz music, since in jazz usage, these two degrees of the scale -- called 'blue' notes -- are commonly flatted and since the third degree, especially, is frequently given a variety of pitches in any single jazz performance." Helmholtz (op.cit., p.255) notes that the "history of musical systems shows that there was much and long hesitation as to the tuning of the Thirds...."
 
5. Curt Sachs, The Rise of Music in the Ancient World, East & West (N.Y.: W. W. Norton & Co., 1943) and Bruno Nettl, Music in Primitive Culture (Cambridge: Harvard University Press, 1956) and Marius Schneider, "Primitive Music," in Ancient & Oriental Music, ed. By Egon Wellesz, Vol. I of The New Oxford History of Music (London: Oxford University Press, 1957) each writing about a different culture:
On p. 133, Sachs describes a phenomenon in which conflicting tendencies (toward and away from equal divisions of the scale) may be combined. "Singers do not pay much heed to this temperament." He adds one aria "in almost Western intervals alternates with orchestral ritornelli in Siamese tuning." That is, singers sang the unequal steps, but the instruments were tuned to the tempered or equal steps.
Nettl confirms this idea. He writes: "...the instrumental scales rarely correspond exactly with the vocal scales occurring in the same tribe." (p. 60.)
Schneider writes (p.14-15): "When the same song is performed simultaneously...by voices and instruments, the melody proceeds in two different tunings. The instruments...on their own scale, the voices in theirs..." He says we must suppose "that the vocal tone-system has been evolved in a natural and specifically musical fashion, whereas in the tuning of instruments...quite different principles were applied --such as, for example, the breadth of the thumb as the standard for the space between flute holes," or such as when a need on the same instrument arises to transpose melodies into higher or lower keys, the notes are adjusted toward greater equality (tempered) so that each key will remain tolerable, if not perfect. Thus we have developed from this kind of typical behavior an expectation not to find perfect pitch tunings on an instrument.
The operative word here, relative to criteria for what is "acceptable" is that these instruments are tolerated, but when perfect pitch is available (voice, strings) then musicians choose the perfect intervals. In practical terms of instrument-making, the tolerable amounts have been in the neighborhood of up to a Pythagorean comma, and that is approximately the greatest amount of error (occurring only once) in our measurements of the Neanderthal flute. This is especially significant in light of the fact that this deviation from predicted occurs on the Mi, the third note of the scale, already with a reputation for wider tunings, as much as a quarter-tone (2 commas).
 
*Finally, this should be noted: On the bone flute, if we suppose that the key is C-minor (just for example), then the flute's notes would be Eb, F, G, Ab. These 4 notes only sound minor if you start playing the C-minor scale to which they belong from C. However, they will sound major if you start on Eb (Mi). This is because Eb is the relative major of the key of C-minor. Just playing those 4 notes alone will sound like you are playing the major notes of do, re, mi, fa (in the key of Eb major) if you don't hear anything prior to them.
   
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ACKNOWLEDGEMENTS: Bel Canto magazine (UK) Hannah Lambert, editor; Prof Bonnie Blackwell, Geology Dept. Queens College CUNY, Flushing, NY, USA; Birmingham Zoo (Alabama); Mike Finley, Saskatoon; Numerous flute-makers (on the net); Treasures of the Earth Co.; Prof Ernie Walker, archaeologist, U. of Sask, Saskatoon.
Note: The concepts of evolution in this essay have nothing in common with so-called "Creationism"
 
 
UPDATE NOTES
UPDATE, MARCH, 1998.... Some information in the Ivan Turk monograph helps considerably to narrow down the speculation regarding the notes producible by the Neanderthal flute bone.
First of all, the flute is made from a much younger bear cub (yearling) than I hoped. We had originally thought the femur was possibly from a juvenile cub old enough so that the full femur would be long enough on its own to account for the required air column length. But because we were not originally informed of the actual cub's age -- we earlier also allowed that a mouthpiece could have extended the length of the Neanderthal flute. But this was an assumption that I didn't want to be forced to make.
The new information means the flute, as a whole femur bone, would have been shorter and forces us now to rely on that assumption of an extension: If there is a match at all to diatonic scale tones -- then the bone had to be somehow extended in length by another bone or mouthpiece.
If this extension was provided at that ancient time, then the notes that could be played would be very close to do, re, mi and fa in the diatonic scale. The original match of hole spacings (match #2), which we originally chose to be the likeliest simply because of the arithmetic closeness of the match, is now a less likely match, but still viable. On the other hand, Match #1 becomes more likely (if it was a closed-end flute). And a third match, also mentioned in my original essay, which is obtained if the flute is flipped and the hole-notes are ascending in the opposite direction, is now also more likely than first thought. This is because the bone, now needing to be extended anyway if a match is to be closely in tune, could have been extended from either end of the bone artifact. Again, this 3rd match*** would provide an excellent match to the do, re, mi, fa sounds.
There is no direct ancient evidence available for or against the bone having had such an extension, regarding the oldest flutes. However, later homo sapiens history does provide examples of flutes that commonly had inserts of various lengths for mouthpieces or changes of pitch.
Of course, any hypothesis is weakened when additional assumptions must be made. As we never offered our conclusion as being proof, the weakening is one only of degree rather than of fundamental significance.
The alternative conclusions that would still be necessary if there was no assumed extension to the bone would remain difficult to justify or explain: These conclusions would be:
* That we would have a scale virtually unique to that flute (possibly matching some other obscure scale in some parts of the world, but not matching any known historically widespread scale in use). The problem with this non-conclusion is that since the hole-spacings discussed in this essay have only a one-in-hundreds chance to match a pattern of 4 notes in the diatonic major/minor scales, then this conclusion would require accepting a remarkable against-the-odds coincidence of spacings.
* That the unequal spacing (rather than equal spacings of the holes to gratify an easy fit to the fingers) would remain inexplicable.
* That we have a flute whose mouth-end would be large and uncomfortable in the mouth unless it's assumed it had to be cross-blown as in a modern flute (or -- assumed to have had an extension).
* Finally, the independent corroborative evidence that indicates, from acoustics and the ear, that there likely is a natural foundation (or impetus) toward evolution of the diatonic scale, would no longer be relevant to this bone. The "ring of likelihood" that acoustic influences offer (and that is offered by evidence from other disciplines) because this evidence integrates nicely (and as expected) toward explaining this find, would have to be abandoned in relation to the artifact.
See again: http://www.greenwych.ca/natbasis.htm and http://www.greenwych.ca/evidence.htm.
Of course, just because these alternative points, given the hole spacings, may be hard to accept, they may nevertheless be true. But instead, for me, these alternatives and the current information reported in the Turk monograph which helps narrow certain ambiguities, points me to sustain the original conclusion in the essay that the four notes are -- and remain as we concluded -- "consistent with 4 notes of the diatonic scale."
Indeed, other illustrations that super-impose the bone artifact's holes over diatonic hole patterns (similar to the illustration for match #2, which is to a minor diatonic flute) could be made for match #1, and illustrated for a third match (in reverse, to a major scale flute). All these matches would be clearly -- even you have eye problems -- very good visual matches; they're unlikely by chance, and the matches really do not require much of an acoustical "analysis." Unfortunately, we cannot get further than our current conclusion at the present time.
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