Addenda:

As far as perception of harmony goes, it may help to recognize that even a single note is an oscillation, that is, a (regularly) changing thing, and that an harmonic relation is essentially a rhythmic relation:

If I tap my left hand on the desk in front of me in a regular manner, tape the tapping, and speed the recording sufficiently, when I play back the tape I'll hear a pitch (a pitch with pulse wave harmonic content). If I tap my right hand three times for every left hand tap, tape the tapping, and speed the recording sufficiently, when I play back the tape I'll hear an harmonic perfect fifth interval.

The recorded "performance" on the old bone flute is a performance by a modern performer. He or she plays a tune with the lowest tone as the tonal center. Because of the intervallic structure of the tones, it might sound like modern diatonic tonality to some. And there is absolutely no "harmony" involved.

But it isn't diatonic tonality! We can project all we like. We simply have no idea what the music and mode were like 35,000 years ago for this instrument. If archaeologists now find a perfectly preserved frozen body next to the flute and somehow are able to revive that person, perhaps she/he could play the flute and let us know what its music sounded like.

Until then, it's pure speculation -- and perhaps wishful thinking.

I'm sorry, but that sounds very silly to me. As far as I can tell, you're deliberately trying to make this much more complicated than it is. Sure, the ancient musicians in question may have used a bit of forked fingering, but if we have a set of holes in a very basic wind instrument, we can reasonably assume them to represent a scale played by successively lifting fingers.

A "diatonic" scale, by definition, has precisely seven pitches per octave, and it doesn't look to me as if the flute in question has enough holes for that.

Scotch, we agree. I was simply responding to the original poster, who implied that the recorded sample played on this instrument was in a modern tuning and played modern 'harmony' as we know it today.

Judging anything about 'scales' and harmony from a modern recording is not valid. That was my conclusion. Is it yours also?

Judging anything about 'scales' and harmony from a modern recording is not valid. That was my conclusion. Is it yours also?

That would depend on the recording. If this recording, which I'm sorry to report I still haven't heard, simply demonstrates what pitches you get by successively lifting fingers on a faithful reproduction of the ancient flute, then I think that could tell us quite a bit about ancient scales, or at least one ancient scale, and I regard a scale as an harmonic entity. If, on the other hand, the recording were to use all sorts of tricky and false fingering and were accompanied by a modern orchestra playing pitches this flute cannot produce, then I would consider it pretty misleading.

I was simply responding to the original poster, who implied that the recorded sample played on this instrument was in a modern tuning and played modern 'harmony' as we know it today.

I took you to be responding to both of us. From what you say above, I now take you to be responding to the following remark (please correct me if I'm wrong):

The most important fact for me is that the musical scale some 35,000 years ago was already more or less the same scale that is still used today in some parts of the world. This could be a proof that the sense of basic harmony is not culturally acquired but is something deeply built-in our brains and it has been there since a very, very long time.

My best guess is that "more or less the same scale that is still used today in some parts of the world" refers to the anhemitonic pentatonic scale, because that scale is virtually ubiquitous--the late Lou Harrison used to call it "the human song"--in contradistinction to the more sophisticated diatonic scale, which is derivationally Pythagorean, and thus an extension of the procedure that produces the anhemitonic pentatonic scale.

I agree that if indeed the flute in question is disposed so as to play this scale that this is evidence (although not necessarily "proof") that the scale is not culturally relative. I disagree that it says something about what is "[built into] our brains]", and I also think the use of the scale in disparate and autonomous more modern cultures already provided sufficient evidence. We could, however, probably do with more evidence of the evolution from pentatonic to diatonic.

I was indeed responding to the following text:

The most important fact for me is that the musical scale some 35,000 years ago was already more or less the same scale that is still used today in some parts of the world. This could be a proof that the sense of basic harmony is not culturally acquired but is something deeply built-in our brains and it has been there since a very, very long time.

But I strongly doubt that the poster of that remark was referring to pentatonic tuning systems. By including the phrase "sense of basic harmony," the poster was implying a great deal more than simple pitch sets. The recording also implies a favored type of "scale" and tonality that is not at all universal: it is bound to Western European notions of tonality.

The flute player in the recording was not merely playing the possible pitches on that old flute. Indeed, the player was doing much more.

Sorry I stopped following this thread for some time. The automatic messaging system (that signals a post has been added to a thread) did not work this time.

A few clarifications:

When I said:
"The most important fact for me is that the musical scale some 35,000 years ago was already more or less the same scale that is still used today in some parts of the world. This could be a proof that the sense of basic harmony is not culturally acquired but is something deeply built-in our brains and it has been there since a very, very long time."

It was more philosophical that hard sciences talk. I wanted to stress that the capability of enjoying (by producing or listening to) a melody seemed to be something acquired in the remote human past, probably not culturally acquired however and so remote that I could find no interest for the emergence of such a capability that was not directly related to group survival.

I believe the example tune in the link is based on the pentatonic scale, as for the pitch I still have to listen more carefully or reproduce it on my flute, but I have no time for it at this moment.

I acknowledge that I used "harmony" a little hastily as these instruments cannot produce true harmony by playing several notes at the same time. But I believe that such harmony exists in our mind/brain even if perceived as a sequence of notes. In other words, we identify a melody built out of a particular scale as being correct or beautiful -or not. And we base our decision on the harmonic relationship of the notes we are hearing (the "good or bad" intervals used).

The scale I was referring to was the pentatonic scale; it is not so much a western world scale but is shared by oriental people and by other people of the Andean area (Inca and other similar cultures) and their tunes are still played today.

Now as for the production of overtones and particularly the fifths that were so well and thoroughly explained by Scotch (thank you), I still cannot see how a third harmonic can be calculated by an integer power of two, which we all know give a series of pairs + "1": 1, 2, 4, 8, 16...

Integer powers of two provide all the even harmonics of a basic tone; for odd harmonics we have to use integer powers of three.

As I understood, if we have our modern A=440, then its fifth would be E (though we have a semitone included) and the frequency would be 1320 Hz. But no way to relate both by a single integer power of two. Or am I calculating wrong?

I find the foot-tapping analogy interesting; I see however a rather simple explanation for this phenomenon and I doubt for this reason that it proves a direct relationship between pitch and rhythm:

(I am not explaining what comes next to you two, as you obviously are acquainted with this subject, but for others that may be following the thread, though I doubt a little as it became so technically oriented):

Any pure tone sound is transmitted by a sinusoidal pressure waveform that has peaks and valleys (the number of this pairs of peaks (+ and -), measured in a second is defined as its frequency --> pitch for us musicians)

For the foot tapping, when sped-up sufficiently, we also have a series of peaks (though not part of a sinusoidal waveform this time) which our brains also perceive as a pitch.

Whatever the actual waveform of each "tap", we could apply Fourier analysis and obtain the harmonic components. Each harmonic is a pure tone by definition, though for complex waveforms, there may be tens of significant harmonics involved. It is straightly done by spectrum analysers, that nowadays are fairly common.

The Fourier transform (and Fourier series), provides a simple math tool to pass from the time domain of a waveform to its frequency domain (and back).

It may be that we have some sort of built-in Fourier analyser in our brains (or internal ear) that we use to differentiate the instruments (or any other sound producing devices) by its harmonic components. This "analyser" would also be the basis of our perception (and enjoyment) of harmony (this last word in the wide sense I used initially)


<Added>

Sorry I misused the word "pair" in this context (my Spanish tongue influence):
give a series of pairs + "1": 1, 2, 4, 8, 16. --> give a series of even numbers plus the "one": 1, 2, 4, 8,...

[Travel2165] By including the phrase "sense of basic harmony," the poster was implying a great deal more than simple pitch sets.

Well, I'm not telepathic, but it seems to me the operative term here is basic, and the anhemitonic pentatonic scale is certainly not the sort of arbitrary "pitch set" extolled by Allen Forte, for example, in his The Structure of Atonal Music; it's a true harmonic entity.

The recording also implies a favored type of "scale" and tonality that is not at all universal: it is bound to Western European notions of tonality.

How, specifically? (Note, by the way, that the flute was found in Western Europe.) I suspect you have this precisely backward, by the way: "Western European notions of tonality" developed from basic scale construction.

The flute player in the recording was not merely playing the possible pitches on that old flute. Indeed, the player was doing much more.

Yeah? What?

[Jose-Luis] I still cannot see how a third harmonic can be calculated by an integer power of two, which we all know give a series of pairs + "1": 1, 2, 4, 8, 16...

Um...I said integer powers of three: 1, 3, 9, 27, 81. Integer powers of two are considered equivalent for normal scale construction, thus a perfect twelfth, 3:1, is considered harmonically equivalent to a perfect fifth, 3:2. I said that too.

I find the foot-tapping analogy interesting; I see however a rather simple explanation for this phenomenon and I doubt for this reason that it proves a direct relationship between pitch and rhythm:

That was hand-tapping, actually. My feet are not so articulate. Anyway, I don't know what "reason" you're invoking here. That the explanation is "simple"? It's "simple" in the same sense that it and the "relationship" are "direct". The relationship is undoubtably there; how we perceive it is another matter. I would say that harmony is Gestalt perception of rhythmic relations.

Whatever the actual waveform of each "tap", we could apply Fourier analysis and obtain the harmonic components.

The waveform of the tap is irrelevant (as, for that matter, is the pulse wave produced by the silence alternating with the tap).

It may be that we have some sort of built-in Fourier analyser in our brains (or internal ear) that we use to differentiate the instruments (or any other sound producing devices) by its harmonic components.

I've already explained that it's been proved that we don't. We register the individual harmonics independently and learn to group them as we become more musically sophisticated.




<Added>

Scotch quips, "Yeah? What?"

I guess you haven't yet listened to the recorded excerpt, right? It is clear that the (European) player has decided notions about where to place the tonal center. And it's just one of five tonal centers that could have been chosen for the anhemitonic pentatonic tuning of that flute. I wonder why she/he chose that particular one?

A sense of harmony is implicit in this particular collection of five tones? Surely you jest.

I guess you haven't yet listened to the recorded excerpt, right?

That would be a pretty reasonable assumption.

It is clear that the (European) player has decided notions about where to place the tonal center. And it's just one of five tonal centers that could have been chosen for the anhemitonic pentatonic tuning of that flute. I wonder why she/he chose that particular one?

So you now admit that the flute plays an anhemitonic pentatonic scale? What was all that "diatonic" business? Does our flautist first just play the scale before he (homo, not vir) starts clowning? Why can't you describe specifically what you're hearing?

Yes, each of the five pitches can be made to sound as a "tonal center", more or less--maybe modal center would be a better term--, but if the scale is C, D, E, G, A--or any permutation of this (D, E, G, A, C, for example)--, then C is the progenitor (as I've shown). The tradition around these parts is to favor "major" and "minor" pentatonics, making, C and A, respectively, the centers, and this is analogously what the Javanese and Balinese traditionally do with pelog (hemitonic) scales.

A sense of harmony is implicit in this particular collection of five tones? Surely you jest.

The term harmony, its Greek and Latin cognates, was in constant use by music theorists long before the invention of "chords", long before homophony, long before polyphony, centuries before the first experiments in organum. My only quibble is with the qualification "a sense": Not "a sense", but harmony itself is both "implicit" and explicit is this scale, which is far from an arbitrary "collection".

Scotch, a bit petulantly, writes:

"So you now admit that the flute plays an anhemitonic pentatonic scale? What was all that "diatonic" business?"

Scotch now needs to quote me where I said that there was indeed actual "diatonic business" going on in the flute recording.

It has been a pleasant and very interesting thread so far. Please guys, keep it cool. We should all make enough efforts to adapt to each writing style, without falling in disqualifications. Please....

Scotch, you are right about the power of three. I did not understand your post at first reading and I only remembered you mentioned the integer powers of two a little bit later in the same post (referring to octaves). Sorry for my misunderstanding.

I accept that my "theory" of a "Fourier transform" biolgical "device" in our ear or brain sounds a little far-fetched. But then, how do you explain that we are able to differentiate easily among instruments and we can identify voices or singers without(much) problem? I attribute this human capability to our in-born ability to evaluate the contents of overtones in a sound. There are other important features such as attack, decay and the wave envelope, etc., but for a continuous sound they are not relevant. We can however, easily tell whether a sustained note comes from a flute, an organ, a whistle, a singer or other instruments.

How do we achieve this, in your opinion? If we have no "device" to evaluate the contents of overtones, we could perhaps, have a set of adaptative high pass filters or something similar. But everything seems to be highly speculative there is probably not known answer.

I cannot agree that the overtone contents of a single pulse (a tap, for instance) depends on the pulse + the rest that comes after it. If we apply the Fourier transform to a single pulse, we get its overtone contents, to the point this content completely define the pulse. We could synthesize such a pulse by adding all the overtones in due amplitude and phase. But for single pulses we get a continuous spectrum and we need in theory infinite components, though in practice there is a limit after which additional components can be neglected.

If we have a repetitive waveform instead, we get a discrete overtones spectrum and the calculus is rather simple when the original waveform is also simple. The Fourier series is used in sucha a case.

I have been away from this techniques for some 30 years and it is quite possible I have forgotten some or many things. But it was quite a simple math excercise as I recall it now.

Now we get to your specific example: a repeated tap. You said you could speed the tap sequence up by recording it and playing it at higher speed. In such a case it would result in a discrete spectrum, containing the necessary overtones.

Does this prove a relationship between rhythm and pitch? I would say that this assumption could be a little far-fetched too.

As I said before, there are two ways of examining a waveform: the time domain and the frequency domain. Both are related by Fourier analysis and this tool is widely available. Practical applications are also widely used, such as modern synthesizers to go from frequency domain ---> time domain and spectrum analysers to go from frequency domain ---> time domain.

This was the "simple" reason I was referring to. Not so simple for people not acquainted with these techniques, unfortunately (I am not referring to you, of course).

To summarize what I consider to be the main question:

How can we tell that a flute is a flute or a horn is a horn, just with our ears?

Scotch writes:

".. this is analogously what the Javanese and Balinese traditionally do with pelog (hemitonic) scales."

You will have to demonstrate that much more clearly to me. What exactly is "this"? And which particular Indonesian modes are you talking about? All of them?

<Added>

By "all of them," I meant all the pelog modes.

[Jose-Luis] To summarize what I consider to be the main question: How can we tell that a flute is a flute or a horn is a horn, just with our ears?

It’s difficult for me to see how that got to be the main question. In any case, the short answer, which I’ve given twice before, is that we CAN’T—that is, not until we’ve learned to. Different regions of cilia in the cochlea of our inner ear respond to different frequencies whether or not these frequencies represent different fundamentals or overtones of the same fundamental. As we mature we taken into account various attributes, presumably the amplitude envelope, the initial transient, the inferred spatial source, and so on, and gradually learn to group sets of harmonics with given fundamentals. (It probably helps especially to memorize the sounds of the instruments when played solo.) If anything this is re-synthesis, not “analysis”.

I cannot agree that the overtone contents of a single pulse (a tap, for instance) depends on the pulse + the rest that comes after it.

The waveform of the tap would modulate the overall pulse wave (a minor effect), but this has nothing to do with why a fast enough oscillation (be it a pulse oscillation or any other regular oscillation) is perceived as a gestalt pitch.

Now we get to your specific example: a repeated tap. You said you could speed the tap sequence up by recording it and playing it at higher speed. In such a case it would result in a discrete spectrum, containing the necessary overtones. Does this prove a relationship between rhythm and pitch? I would say that this assumption could be a little far-fetched too.

Again: the “overtones” have NOTHING whatsoever to do with this. The point is simply that precisely the same ratios are involved in both cases. The “relationship” doesn’t need to be proved; it’s simply there. The only difference in perception is the gestalt.

Maybe a few homely analogies will help you: When I was a child my friend Danny liked to clothespin playing cards to the spokes of his bicycle so that he would hear them flapping as he rode. The faster he rode, the faster they flapped, and when he got to a certain speed he was able to produce in this way the aural illusion that he had a motorcycle between his thighs. Sometimes we would lay our bicycles down in the grass and spin their wheels as hard as we could. We could scarcely discern the individual spokes then, and we produced in this way the visual illusion that our bicycles had hubcaps.

What happens is that we are still processing the earlier tap as we began to register the later tap: they blur together.