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Updated Mar 2003-- Two New Books on Music Origins & Music Archaeology

 
ADDITIONAL COMMENTS
EXCERPTS FROM ETHNOMUSICOLGY CORRESPONDENCE:
Interpretation of the 9,ooo year old Chinese flutes [& of the Neanderthal flute].
UPDATED MAR., 2003
 
Click here to search this entire site
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MEDIA REPORTS AND MORE ON SCALE NOTES
.
From: Erik <info@eriktheflutemaker.com>
Subject: 2nd Jiahu crane flute is pentatonic
 
Hi Bob:
My name is Erik Sampson. I am a self taught Bamboo flutemaker, for about 30 years. I was browsing an article of yours and I thought I'd mention the New York Times article on The Jiahu Crane Flute. It stated that the playable one was almost 9 inches long, so I blew up the pix of the 6 flutes to that proportion and reproduced 3 in bamboo. The 2nd from the top with 5 holes sounded pretty out of tune and I had to do a lot of tweaking to make any sense.
Then I accidentally made the end blown notched mouthpiece (Andean Quena style) on the other side and it was a lovely pentatonic scale. I was so delighted!
I have been working with the Japanese Shquhachi flute which I was told was from the 7th century. Here was a Chinese pentatonic flute supossesedly 90 centuries old.
On a personal note. I made over 100 of these and in 3 weeks sold $1500.00 to go towards the Jiahu Crane Flute CD. You can see my work and story on my web site: eriktheflutemaker.com
Have a great day,
Erik
 
Date: Sat, 16 Oct 1999 18:35:12 -0400
From: Su Zheng:
<szheng@MAIL.WESLEYAN.EDU> or szheng@WESLEYAN.EDU
Subject: Re: 9,000-yr old flutes-- where [have] the subalterns' voices have gone?
These are some of the titles, keywords, and main contents one read in recent reports by Euro-American mainstream news on Jiahu flutes from China (some of these reports were posted on SEM-L).
-------------------------------
ASSOCIATED PRESS
By JOSEPH B. VERRENGIA AP Science Writer
When scientists from the United States and China blew gently through the mottled brown instrument's mouthpiece and fingered its holes, they produced tones unheard for millennia, yet familiar to the modern ear.
"It's a reedy, pleasant sound, a little thin, like a recorder," said Garman Harbottle, a nuclear scientist who specializes in radiocarbon dating at Brookhaven National Laboratory on New York's Long Island.
--------------------------------
Fox News by Amanda Onion:
The guy [not a woman?--BF] had obviously spent a lot of time on it," said Garman Harbottle, a chemist at the >Brookhaven National Laboratory in Long Island who wrote about the ancient flute in this week's journal, Nature.
Most significantly, Garman Harbottle says the seven notes on the instrument comprise a nearly accurate octave.
--------------------------------
FURTHER COMMENTS ON THE RECENTLY FOUND ANCIENT CHINESE FLUTE SOUNDS
By Bob Fink, author of "Neanderthal Flute Musicological Analysis"
--------------------------------
New York Times, September 28, 1999
"After 9,000 Years, Oldest Playable Flute Is Heard Again"
--------------------------------
What concerns me is that in these reports, no names of Chinese scholars were mentioned (the article on Nature was in fact co-authored by Garman Harbottle and three Chinese scientists), and no earlier scholarly publications by Chinese scholars were cited. The general impression one gets from these reports is that this was a recent discovery and analysis, and the American scientist Garman Harbottle had an important role in it.
Well, here is some information that I would like to share with my SEM colleagues:
In the 1990 book -- The Universe of Music - A History (UMH) -- China Supplementary Volume I: Instruments -- (A UNESCO / IMC Project), chief editor Zhao Feng wrote in his article "An Outline of the History of Chinese Music from the Chinese Musical Instruments Found in Archaeology Sites":
"The Jiahu flute (Pictures 4-6) is a better instrument than the Hemudu bone whistles. There are seven holes and a mouth hole on the Jiahu bone flute.
"There are conspicuous lines to mark the opening locations of the holes. This may indicate that calculation had been made in making the instrument.
"There is a small hole beside the seventh hole. The small hole was probably put there to adjust the pitch of the seventh hole. The Jiahu bone flute was a sacrificial object. There are two flutes in one grave. The grave is a relic of the early Jiahu Culture (7737 +- 123 years before present by radio carbon date).
"The length of the bone flute is 22.2 cm. The tube pitch is rested as #F5 + 44, the seventh hole A5 +8, the sixth hole B5 -25, the fifth hole C6 +24, the fourth hole D6 +16, the third hole E6 +16, the second hole G6 -40, and the first hole #A6 -42. Therefore the bone flute plays both the five or seven-notes scale of Xia Zhi and six-notes scale of Qing Shang of the ancient Chinese musical system. In the same grave wherethe bone flute was found, sacrificial tortoise shells were unearthed. There are characters carved on the tortoise shells. Some of the recognizable characters are similar to those of the Yin Dynasty (Picture 4). The Jiahu bone flute indicates that musical culture of China began to develop in the late Neolithic Age."
(P. 6, original English text from the book)
In the Chinese text on page 1 of the book, it states that the Jiahu flutes were unearthed in 1979 at the Wuyang County, Henan Province.
On pages 14 and 15, there are three photos related to Jiahu flutes:
photo no. 4, a carved tortoise shell uncovered with the Jiahu flutes;
photo no. 5, Wu Yang [county] Jiahu flute. (showing one flute only, the one still playable)
photo no. 6, a design indicating where the flutes were put in the grave (both next to the left shoulder of the dead body)
A final note: although this 1990 book reported the research on Jiahu flutes, in another book called "A Pictorial Guide to the History of Chinese Music" published in China in 1988, the Jiahu flutes were not mentioned. One could probably say that this 1990 study was one of the earliest by Chinese music scholars.
Su Zheng
Assistant Professor of Music and Women's Studies
Director of Graduate Studies in Music
Music Department
Wesleyan University
Middletown, CT 06459
------------------------------------------------------
FROM BOB FINK TO SU ZHENG
Dear Su Zheng:
Thank you for reporting the information about the Chinese scholars behind the 9,ooo year-old flutes story.
In addition, I read or was told that the discovery of the flutes had been made some years ago, and that westerners only recently prevailed upon the Chinese to release the information to the west.
I also had occasion to mention the matter of the media's quotes in private posts to a member of the list regarding the news reports. Part of what I wrote in those e-mails is as follows:
To DV:
"About surrendering to let the instrument tell me what it will:
"That's just what Harbottle at the Brookhaven Labs did!! As a result, he "heard" the "do re mi" scale -- probably because, as a musically-biased westerner, his mind [may have overly] "adjusted" the sounds toward that scale....
"That while modern flautists have skills with lip/fingerings to alter tones, the [little added hole] correction by this ancient flutemaker (whom researcher Harbottle carelessly refers to as a "guy" [which I noted in brackets when I sent the reports of the flutes to the list]) shows a desire to rely on the holes themselves to determine the pitch...." etc.
I am sorry that the media saw fit to minimize the role of the Chinese -- interviewing mostly Harbottle. Apparently like most of us in the west, the media as well as Harbottle too often forget westerners aren't the only people in the world.
At link ( http://www.greenwych.ca/fl3debat.htm#From ) I made a pictorial description of the notes played on the playable flute based on the Nature article. The list you quoted from Zhao Feng's writings differs slightly from this as follows:
The Nature article information is listed then the info you cite listed just below it:
7 ...6 ...5 ..4 ...3... 2 ...1 ..(Hole number)
A5 B5 C6 D6 E6 F#6 A6 (Nature article)
A5 B5 C6 D6 E6 G6 A#6 (Zhao Feng)
I assume the discrepancy is due to the large number of pitch cents below both the G6 and the A#6 which allow a possible labeling for these notes as F#6 and A6?
Thank you for writing.
Bob Fink
------------------------------------------------------
FROM SU ZHENG TO B0B FINK
Dear Bob,
Thank you very much for sending me further information on the Jiahu flute.
And your comparison between the two descriptions is interesting. About your question on the discrepancies between Nature's infor and Zhao's report, since I am not an expert on this matter, I could only speculate. I think you were probably right that the discrepancies might have much to do with the fact that both pitches are much lower than G6 and #A6, allowing an interpretation of #F6 and A6. Ultimately, I believe, what pitches one should hear of these two holes, and the tube pitch (#F5 + 44), would depend on how scholars want to think about the scale(s). Zhao in his article casually made a connection between the Jiahu flute and some of the later Chinese scales, I am not sure there is convincing evidence. But, again, I'm not an expert on this subject, I might be wrong.
Thanks again for your information and your message.
All the best,
Su    
 
APPRECIATION OF SMALL PITCH CHANGES
 
From my letter to ethnomusicologist KO:
If you ask me, I would define "roughly in tune" [as an adjective meaning an interval is "in-tune" with acoustic intervals]...as being within the standard average for what's called the "just noticeable increment" that physiologists use in hearing examinations (and other sciences use that measurement of threshold increment as well).
In my recollection, this amounts to about a Pythagorean comma. Naturally, individuals vary, but a scientific average has already been struck, and a normal curve exists or can be drawn that would indicate what percentage of a population of people with human ears can distinguish less: Say, half a comma; and what (an even smaller, minute) percentage could be predicted by the statistical normal [bell] curve to distinguish a quarter-comma, and so on. This is standard statistical math, long established ("proven"?) to be an effective measurement of human biological hearing capacity.
I don't have hearing-test literature still here (I never thought I'd have to defend such established matters), but there is no need for ethnomusicologists to re-invent the wheel on this. It has already been done. Cultural tests have also been done (harder to do, as instructions for testing can be harder to convey), and the differences in hearing ability (averaged, averaged, averaged), in comparing peoples, has never, so far, been considered statistically significant.
...There are always some one percent of people, or some such tiny figure, who can do quarter-tone recognitions in any given population. That, to the best of knowledge that I'm aware of, means also : "in any given culture" as well as population. --Bob Fink

SINGERS VS INSTRUMENTS (To KO) --VALID CITATIONS?

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. [The Rise of Music in the Ancient World, East & West N.Y.: W. W. Norton & Co., 1943, p. 133.]
...revisiting Sach's quote I see he did base his observation on a measured recording of the Siamese ritornelli: "Decca 20127 B" -- wherever that is. Cents would be possible to obtain, I presume.
..."Just some guy's opinion" is actually (usually) a valid thing, not as perjoritive as you put it. All scientific knowledge in some measure really ends up being some person's opinion, or some person's interpretation of a measuring device, backed up by another's revisiting the scene and giving a similar opinion, and so on. When it's important enough, you repeat the experiment / observation if possible, or, as I did, see if other independent observations are parallel to it, relying then on the "quantity of the sample" to offset error in any one citation.
[There is also] the testimony from thousands of better singers [in the west, who sing near-perfect acoustic intervals] saying they cannot stand tempered piano accompaniments. They say this because they consider, as they often said (during my 60+ years of lifetime), "the piano sounds 'out of tune,' even after the tuner tuned it!!" (Many singers haven't a clue what temperament means, although they obviously can hear it coming from a tuned piano, to their chagrin.)
You wrote: "...however, it doesn't explain why the piano became perhaps the most popular instrument, after the voice, in the 19th and early 20th century. And don't we love them "out-of-tune" pianos in Western saloons in the movies."
That's simply because the average (average, average, average -- I must stress) majority-member westerner cannot tell it's tempered!! I can't either!!
Play a perfect fifth for me, or a tempered fifth, and I think they sound identical -- my inner filia do not register the difference -- probably for a similar reason that makes some people short, others tall, still others colour-blind or partly so. (This matter is not understood biologically as to why, but it is factual. Most can't tell.) I love the piano and compose on it.
In this case, therefore, I'm saying that the average person doesn't notice. BUT HERE'S THE POINT -- Trained, ear-sensitive, experienced singers DO note it. They would be a minority in western culture (under a bell curve) -- but a significant minority. They would [consistently] sing their own idea of intervals, not the tempered version on an instrument.
Such a group would also exist as a parallel significant group in other cultures, and I recognized that as similar in the sources I ran across and sent to the list. And whether in western or other cultures, it would mean (to me anyway) a preference for acoustic-inspired intervals (i.e., subliminally suggested from overtone structures).
1. Each of the cultural (including western) populations apparently has a majority of people who biologically cannot distinguish anything much finer than a Pythagorean comma (or something close to that). (I am one of these people). Therefore, if they sing intervals that differ from the naturally occurring intervals provided to us by overtone structures, it means virtually nothing -- not in western nor in non-western cultures. And not being different...humans, likely most will sing non-acoustic intervals -- in Ghana or in New Jersey.
2. However, if you claim it does mean something -- that it reflects on the sources I used in some way, or that in Ghana no preference for acoustic intervals is shown, then you must also claim (to be consistent) that likewise it reflects against the commonly agreed view that "the west's music IS based on a preference for acoustic diatonic intervals" ..... After all, how can such a conclusion be sustained if we westerners mostly sing non-acoustic intervals? (And most of us do.) --Bob

TOO MUCH PRESENT, NOT ENOUGH PAST

To KO:
There are many disadvantages in trying to generalize a development using only a 20th century study of various present-day cultures. This of course assumes we are just answering the question: "How and why do scales develop and evolve?" That cannot be answered from over-study of the present and over-ignoring the past. Looking for how scales develop & change is hard when many of cultures exhibit very slow change; and it's unreliable to project the present as being representative of the distant past.
On the other hand, again, in looking for any scale's developmental motion, the advantages of dealing with the past (through archaeology, instruments/relics and comparing cultures to each other) is that we get many (not just current-day) "still-frames," so that they can "play back" as if a movie (flickering and haltingly, to be sure, due to sparse numbers of frames offered to us by sparse evidence). This engenders many debatable interpretations as well. This is also the fate of general evolution studies of biological life-forms: Too much present, not enough past. -- Bob
To SAS music list:
Ethnomusicologists have touted field work as the source of many of their conclusions about early or ancient music. I think that today, where there is no place left untouched by Western cultures or other neighboring cultures, the claim of people in some of these cultures that their arts haven't changed for hundreds of years is, on one hand probably true -- especially if what they refer to is some religious or ritual-connected music or art or symbolism. These "tend" to remain true to tradition [and change slowly].
But, on the other hand, you can't be sure their claim is right, and so where do you stand with this type of field work "evidence" except for it being anecdotal? However, it is still evidence to be sure, but I'd rather replace it whenever possible with any fossil or relic, or even careful deduction/induction from clues or from relevant parallel sciences (acoustics /history /archeology /paleontology /anthrop /physiology /statistical-odds/ etc.
Let me relate a story to illustrate this point:
I went to an annual "folkfest" type gathering here, and found one pavilion had a food-booth serving Phillippine food. I bought a "souvlaki or kebab" type of item -- meat and stuff on a stick, found it unique and delicious. It was also familiar, as I had tasted that unique flavour or spices and meat many years before. This had to be a true, authentic recipe of long-standing tradition! But I hadn't a clue how the unique taste was achieved. And to wait for this flavour to come back only once a year was too infrequent. I had to know how to make that taste at will!!
I offered money to the cook to tell me the recipe -- "leave out nothing, name all spices, cooking times, etc," I said.
She was happy to tell me for free.
"First," she said, "marinate the meat cubes overnight in about a half-cup of 7-up...."
See my point? (By the way, the "secret" taste-significant ingredient, I think, was cinnamon mixed into the 7-up.) Clearly, the 7-up was an easier substitute for earlier, more traditional ingredients, acceptable to her and perhaps to her sense of tradition or authenticity, but no longer exactly the same as scores of years ago.... --Bob

METHODOLOGY

From my letter to ethnomusicologist JR:
As to my own position, ... I am by philosophical or scientific bent a relativist -- believing that most things for humans are conditioned, with society & experience writing human behavior on the essentially "blank" human chalkboard.
However, that chalkboard of ours isn't totally blank. We are born with built-in responses to pain, pleasure, sour, sweet, pungent, bright, drab, rough, smooth, etc.. all of which are universal (albeit capable of being altered by further conditioning, such as "acquired tastes" in, for example, food). There are such brain "wirings" for the sense of touch, smell, taste and even sight (optical illusions among others). So why not for the sense of hearing? E.g., noisy and "musical"?
However relativist I am, I believe that music is very subject in its evolution to certain natural legacies...I took [archaeological finds] as verification evidence for the views that I wrote (in my Origin of Music writings) all before the finds .
The factual matters regarding cultural uses (or "preferences") for non-acoustic scale pitches is certainly a matter to be addressed, and I will try to address them....
As an analogy, Copernicus' view that the planets "circle" the sun certainly is oversimplified when more accurate measurements and facts come to light that indicate the orbits are elliptical, wobbly, and very complex -- and not "in tune" with a perfect circle.
The issue is whether the natural "push" is toward circular (overall, or "on average")? ... Or whether there is NO PUSH AT ALL toward circular orbits or solar-centered orbits?
That is, is Copernicus right (despite the corrupted non-circular orbits that are not [perfectly] "centered" on the Sun) -- Or was Ptolemy right, who admitted to no orbits whatsoever?
That is how I view cultural vagaries in pitch -- as true valuable facts, but smaller factors that do not disprove the essential "push" that the world of mathematics, physics (acoustics) and physiology dictate as being essentially responsible for the evolution of certain musical scale tones "overall" or on "average."
That is why I asked you about the methodology -- was it quantified? Namely, how many octaves ARE in tune, and what percent are found "off" [acoustically] in any cultural measurement? It's important to know what is "overall" or "average".) Do only instruments serve as the source for pitch-data, or do singers serve as the source (who notoriously tend toward perfect intervals? See note 5 in my essay.
[Acoustically] off-tune instruments may have many meanings: Attempts at temperament?; Due to ease of fingering (despite that kind of hole-spacing causing non-acoustic tuning)?; Miscalculation of the effects on pitch-holes from the non-cylindrical bores of bone or bamboo and other natural materials used for instrument-making?; Or instruments being blindly copied by others when producing new, additional instruments?
All these possibilities throw the meaning of vagaries of pitch-tastes often into inconclusive turmoil, in my view. I admit, the trouble with relying on singers to gauge cultural preferences or pitch-tastes rather than relying on artifacts, is that ancient singers are dead and we are stuck with the tiny "sample" of the present, which may be overly influenced by other cultural contacts -- not as pristine a source as ancient singers would be. -- Bob
From my letter to KO:
The narrower "evolution of scales and how and why they spread" is the limit of my subject. There might be a judgement about "better" [or "good"] here -- but only in this sense: Acoustic-backed tonal material has a "better" chance to spread over time outside of, or beyond, cultural contexts. But I believe "good music" is always determined within the creative/cultural contexts.
If I thought only acoustic stuff meant "good," then who could be "better" than Lawrence Welk? Uh one, uh two, uh duh!!
...[Try to] separate what can be explained by science; and what can be explained by social conditioning. For example:
Singing non-acoustic tones can be explained by the power of cultural conditioning, without claiming that intervals are [arbitrarily] all equally "consonant" or "dissonant" as conditioning dictates.
Singing and playing acoustic tones [consistently]-- especially when the same intervals occur in independent cultures with similar 5-7 note scales, can be explained as the result of acoustic pressures without resorting to cultural explanations. --Bob
 
TENDENCIES TO PREFERENCES
OF INTERVALS/SCALE STEPS
From KO to Bob:
"All that I see from listening ...is that humans often seem to use a basic collection of between perhaps 5 and 10 notes, including octave relationships, but not including slides, glisses, or other types of "microtonal" additions; and that the smallest unit between the principal notes, apart from the case of glisses, is around 100 cents; other intervals appear to be variable, although certainly, something close to what we call the "major 2nd", the "minor 3rd", the "4th" and the "5th", do appear to be preferred in our Bell curve model.
"I agree with you if what you are trying to suggest is this: that over time, more people over a broader geographic and cultural range will "buy" and like more music based on diatonic-based idioms with "just"-type intervals, than other harmonic-types. That these scale-types appear to be dominant in: 1) the West; 2) South Asia; 3) East Asia; and have important presence in 4) SE Asia; 5) Oceania; 6) the Middle East (despite competing "microtonal" and "quarter-tone" systems used in art music); and 7) Africa (among a number of competing styles), make this likely."

AGAIN: MY ACOUSTIC PARALLELS "CHART"

To KO:
It's really simpler to develop a concept of scale evolution once you leave musicology/ethnomusicology and look into acoustics. (I think my view always has been simple save for the "reading-between-lines" recoil by some writers.)
Take so-called "western" musical-scale history. It's as simple as this little chart (found in my URL: http://www.greenwych.ca/natbasis.htm). Get ready for brevity!!
I developed this little chart/diagram [below] in my research, ending in writing my book on the origin of music years ago, because I wanted to replace the earlier erroneous concept that scales were evolved from, or justified by, the "cycle of 5ths" [or the "up & down" cycle of 5ths] -- which failed to explain the minor scale, and also was simply not believable as a realistic or actual tuning method for earlier peoples. And finally, as Sachs points out, it cannot even accurately reproduce the acoustic octave, the most basic interval in music.
However, taken as a "trio" of tones, then the average overtones of [all three] -- a note, its fifth and fourth -- are all produced in the very practice of music virtually all the time, subliminally heard [and capable of being an on-going influence] -- unlike the results of a cycle of fifths, which does not happen at all in the day-to-day practice of music.
The chart is based on the three most universal intervals of human music worldwide, past & present: The octave (or a "tonic"), the 5th and the Fourth:
Note C = C, G, E, / Bb
Note G = G, D, B, / F
Note F = F, C, A, / Eb
The first line is a list of the different overtones of C, by audibility.
The second line is a list of the overtones of G, which is the 5th of C.
The third line lists overtones of F, the 4th of C.
That's it!
This chart, added up, will give us the major Diatonic; And when accounting for avoidance of half-tones in a scale, gives us the Pentatonic; And when I account for the audibly weak areas in the diatonic scale -- the major 3rd and the major 7th -- by substituting the next weakest overtones -- then that gives us the minor Eb for E, and the minor Bb for B, etc., -- i.e., the minor scale.
These weakest areas ALSO delineate the usual place where blue or "neutral" notes exist.
These now already immense "coincidence" parallels of music with acoustics can be described further -- until you have to conclude it's NO coincidence, because all these aspects of western music were developed by people without knowledge of acoustics (other than subliminally hearing its effect on them).
Why wouldn't humans in ALL cultures be likewise subject -- over time -- to the same phenomena? Unless they aren't humans? --Bob
 
[NOTE: Virtually all material in square brackets
added afterward for syntax, grammar or clarity.]
 
------------------------- Update: Nov., 2ooo ------------------------
 
Discovery and Research on Ancient Bone Flutes From Jiahu Site
 
At the Sept 20 meeting of the group, several Chinese scholars attended, and made some very interesting & important observations:
 
Juzhong Zhang pointed out that during the period from 1984 to 1987, he took charge of the excavation of the Neolithic Jiahu site in Wuyan city, Henan province. There has been wide attention and interest among academic circles brought to the bone flutes.
25 bone flutes were discovered in early May 1986. First found were two basically complete seven-hole bone pipes beside the limb bone of the master in tomb M78.
The most complete bone [M282:20] in August 1987 was examined by Xinghua Xiao. a researcher and Vice Professor of the Musical School of Chinese Art Institute. The flute player, Baosheng Ning, of the Central National Music Ensemble, first blew the scale.
In November 1987, Xinghua Xiao invited musical historians Xiangpeng Huang and Zhongliang Tong to come to Zhengzhou City, Henan Province to do sound-measurements.
It was unanimous: The Jiahu bone flutes were the earliest Chinese musical instruments, with the scale, and it could play melodies. Part of the folk song named "Xiao Bai Chai" was played by Yaoying Xu, who made the sound measurements. Mr. Huang concluded that the Jiahu bone flute [M282:20] had the complete 6-tone scale and incomplete 7-tone scale, which created a sensation in music historian circles.
 
Xinghua Xiao pointed out that the bone flutes from the early period (ca. 7000 BC) have a complete five-note scale. This discovery shows that over 9000 years ago, Chinese in the area of the Central Plains may have been the first to usher in a musical culture stage of civilization.
Four aspects of the Xiao remarks indicate:
1. The early period has five or six holes in bone flutes; There are seven holes on most flutes of the middle period; and seven or eight holes in the last period.
2. Changes in the arrangement of scales indicates the makers already had developed temperament standards.
3. Regarding the amazement concerning the accuracy of the tuning system of flute number 341:2: The hole-drilling method and the arrangement of the five-tone scale shows at that time, the practice of Chinese music had already entered a new realm.
4. Over a period of 1200 years, the music developed from a four-tone scale to a seven-tone scale in successive changes, and went from being complex to having a high level of simplicity. This progression is important in its significance for modern musical composition.
 
See pictures of the flutes.

Chinese Temperament

XU Fei questioned if any one tone in a set of 12 pitch-pipes in some kind of temperament could be used as an initial tone? This question was not solved until late 16th Century in China (by Zhu Zaiyu, 1536-1611 ) and late 19th century (by Lord Rayleigh, 1842-1919) in Europe.
Intensive research and examination of data from Zhu's original works [Zhu's invention of pitch-pipes of twelve-tones], and using modern physics, it's possible to conclude any of Zhu's pitch-pipes could be regarded as the initial tone in turn. In other words, the pitch-pipes designed by Zhu correspond exactly with modern twelve-tone equal temperament. This proved that Zhu's theory and pitch-pipes were the finest achievement in acoustics not just in ancient China but also in the world at that time.
 
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