Misconceptions about xenharmony

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The field of microtonality is rife with colorful personalities and diverse perspectives, and there are many contradictory philosophies and approaches. However, the literature on microtonality in general seems to over-represent certain perspectives, and this page is intended specifically to represent some of the views that diverge from the more "mainstream" or traditional ideas about microtonality.[[toc]]

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=**Myths and Facts about Xenharmonics by mclaren**= 
**//<span style="font-weight: normal;">(written for this wiki)</span>//**

**Myth #1: "Everyone prefers the natural intervals of the pure perfect harmonic series."** This myth remains pervasive. It has been stated by Hermann Helmholtz, in the form "instrumentalists naturally tend to play in the intervals of just intonation." This myth was also repeatedly stated by Harry Partch, who claimed "The ear demands small integer ratios, and accepts substitutes against its will."

These myths have been debunked for well over 80 years. In the 1930s, the music psychologist Carl Seashore first investigated the actual intonation of violinists and other Western performers. He found that they played intervals which were neither just (i.e., small integer ratios) or equal divisions of the octave, but something entirely different. Typical intervals performed by trained Western symphony-caliber musicians are neither just nor equal-tempered. The intervals performed often differ wildly from the putative size of the musical intervals which should be played, yet audiences typically hear these distorted intervals as sounding "perfectly in tune." See Seashore, Carl, //[[http://books.google.com/books?id=p9gUknYfpjYC&printsec=frontcover#v=onepage&q&f=false|Psychology of Music]]//, 1936.

In 1961-2, physicist Charles Shackford published three articles in the then-new //Journal of Music Theory// examining the intervals actually performed by symphony musicians in live concerts. He found that the performed intervals typically differed by at least 10 cents from the target intervals, and often differed by up to 50 cents -- yet listeners were unable to hear any problem with these distorted intervals. To audiences, these extremely out-of-tune intervals sounded "perfectly in tune" and "entirely musical." See “Some Aspects of Perception, I: Sizes of Harmonic Intervals in Performance,” Shackford, Charles, //Journal of Music Theory//, Vol. 5, No. 1, 1961, 162–202; also “Some Aspects of Perception, II: Interval Sizes and Tonal Dynamics in Performance,” Shackford, Charles, //Journal of Music Theory//, Volume 6, No. 1, 1962, pp. 66–90, and "Some Aspects of Perception III: Remarks," Shackford, Charles, //Journal of Music Theory//, Volume 6, No. 2, 1962. Shackford's work builds on earlier studies which reached the same conclusions: see Paul C. Green, “Violin Intonation,” //Journal of the Acoustical Society of America//, IX (1937), 43–44; James F. Nickerson, “Comparison of Performances of the Same Melody in Solo and Ensemble with Reference to Equal Tempered, Just, and Pythagorean Intonations,” //Journal of the Acoustical Society of America//, XXI (1949), 462; idem, “Intonation of Solo and Ensemble Performance of the Same Melody,” //Journal of the Acoustical Society of America//, XXI (1949), 593.

This research has been confirmed by many subsequent listening experiments. Psychoacousticians have shown that listeners typically cannot hear a difference between pitches less than 15 cents larger or smaller than their nominal values in a real performance (see "Intonation precision of choir singers, "<span class="looklikelink authorname aqslistener"> Sten Ternström</span> and <span class="looklikelink authorname aqslistener">Johan Sundberg, </span>Journal of the Acoustical Society of America, Volume 84, Issue 1, 1988, pp. 59-69), and that all musical performers across all cultures (non-Western performers in India, for example, as well as Western symphonic musicians in Europe/North America) tend to perform large musical intervals of the size of a minor third or larger as bigger than they should be (often between 5 to 10 cents larger), while performing small musical intervals the size of a major second as smaller than they should be (typically compressing a whole tone which should be 200 cents to a value as small as 170 cents or smaller) and compressing semitones even more, typically by at least 30 cents (so that semitones, particularly those resolving downward from a supertonic to a tonic or moving upward from a leading tone to a tonic, are often measured with values as small as 70 cents or 60 cents or in some cases even 50 cents or less). See "Intonation Variants of Musical Intervals in Isolation and in Musical Contexts," <span class="name">[[http://pom.sagepub.com/search?author1=Andrzej+Rakowski&sortspec=date&submit=Submit|Andrzej Rakowski]]</span>[[#aff-1]], //Chopin Academy of Music//, Okolnik 2, 00-368 Warszawa, Poland; "Musical Intervals and Simple Number Ratios," Cazden, N., J. Res. Music Educ., 7, pp. 197-220; "Influence of the Time Interval on Experimentally Induced Shifts of Pitch," Christman, R. J. and Williams, W. E., J. Acoust. Soc. Am., 35, pp. 1030-1033, 1963; "Further Investigation of the Effects of Intensity Upon the Pitch of Pure Tones," Cohen, A., J. Acoust. Soc. Am., 33, pp. 1363-1376, 1961; "Pitch relations and the formation of scalar structure," Cross, I., R. West and P. Howell, Music perception, Vol. 2, No. 3, 1985, pp. 329-344; "The influence of pitch on time perception in short melodies," Crowder, Robert G. and Ian Neath, Music perception, Vol. 12, No. 4, 1994, pp. 379-386; "Grouping in pitch perception: evidence for sequential constraints," Darwin, C. J., R. W. Hukin and Batul Y. Al-Khatib, Journal of the Acoustical Society of America, Vol. 98, No. 2, part 1, 1995, pp. 880-885; "Some Observations on Pitch and Frequency," Davis, H., S. R. Silverman and D. R. McAuliffe, J. Acoust. Soc. Am., Vol. 23, pp. 40-42, 1951; "Mapping of interactions in the pitch memory store," Deutsch, Diana, Science, Vol. 175, 1972, pp. 1020-1022; "The Processing of Pitch Combinations," in D. Deutsch, (Ed.), The Psychology of Music, New York: Academic Press, 1982;
"Interference in memory between tones adjacent in the musical scale," Deutsch, Diana, Journal of Experimental Psychology, Vol. 100, No. 2, 1973, pp. 228-231; "Music perception," Deutsch, Diana, The Musical Quarterly, Vol. 66, No. 2, 1980, pp. 165-179; "Dichotic listening to musical sequences: Relationship to hemispheric specialization of function," Deutsch, Diana, Journ. Acoust. Soc. Am., Vol. 74, 1983, pp. 579-80; Dowling, W. J. "The 1215-Cent Octave: Convergence of Western and Non-Western Data on Pitch Scaling," Abstract QQ5, 84th meeting of the Acoustical Society of America, Friday, December 1, 1972, p. 101 of program, and so on.

Moreover, in 1986, Linda Roberts along with John R. Pierce and Max Mathews published a study in which they investigated the actual listening preferences of musical audiences. They found that presented with a choice, 8 out of 9 listeners preferred musical intervals which beat, while only 1 out of 9 listeners preferred musical intervals which were beatless. As in, for example, perfect fifths or major thirds, etc. Roberts, Pierce and Mathews referred to the first group who preferred musical intervals which beat as "rich listeners" because these listeners preferred tunings which made the music sound "rich" and "lively" with a plethora of active beats. The second group Roberts, Pierce and Mathews referred to as "pure listeners" because they preferred beatless major and minor thirds, beatless perfect fifths and perfect fourths, and so on. The interesting fact about this study is the lopsidedly bimodal nature of the distribution. Rich listeners far outnumber pure listeners. See "Harmony and New Scales," M. V. Mathews, J. R. Pierce and L. A. Roberts, in [[http://www.speech.kth.se/music/publications/kma/papers/kma54-ocr.pdf|Harmony and Tonality]], ed. J. Sundberg, 1987, pp. 59-84.

Notice that these studies present no aesthetic preference. They do not tell us that rich listeners are "better" or "more discerning" than pure listeners. These studies merely inform us that rich listeners outnumber pure listeners in Western musical audiences by a ratio of roughly 8 to 1. There is no indication that musical tunings which produce more beats are any better or any worse than musical tunings which produce fewer beats (just intonation with small integer ratios). As Warren Burt put it, "I don't hear small integers ratios as sounding any better than intervals which beat. I hear a difference -- I simply don't acknowledge that the difference produces any aesthetic superiority." Or, as William Schottstaedt, arguably the greatest living American composer, put it: "I like beats. Beats sound good."

**Myth #2: "The small integer ratios like 3/2 and 5/4 are __//the//__ original intervals from which all other musical intervals are derived."** Kyle Gann teaches this provably false claim in his course on microtonality. (Gann's discussion of microtonality is generally scrupulously accurate: this offers a rare exception. See Gann, <span class="wiki_link_ext">Kyle, </span>[[http://www.kylegann.com/JIreasons.html|"My Idiosyncratic Reasons for Using Just Intonation"]] for one of the best explanations of why composers may find just intonation useful.) Or, as Lou Harrison put it, "Just intonation tunings are the only real musical intervals. All other musical intervals are fake musical intervals."

The actual evidence of peer-reviewed published listening tests in the psychoacoustic literature show that there exists a wide range within which listeners recognize musical interval categories like "fifth" and "third" as sounding functional and musically effective. Once again, this has been known for more than 80 years, and documented in a wide variety of peer-reviewed scientific papers going back to 1926.

In <span class="st">"Variability of judgments of musical intervals," Moran and Pratt, //Journal of Experimental Psychology//, Vol. 9, 1926, pp. 492-500, 1926, researchers found that the range of recognizable musically effective and musically functional intervals ran from a low of 680 cents to a high of 720 cents for the perfect fifth. This conclusion has been confirmed and more supporting evidence piled up by many subsequent listening tests.</span>

Moreover, this conclusion is also supported by ethnomusicological studies which show that worldwide non-Western cultures tend to use a plethora of unequally spaced (or sometimes quasi-equal-spaced) 5- and 7-tone musical scales, with fifths ranging from roughly 680 cents on the low side to 720 cents on the high side.

This conclusion is also supported by the historical record of tempered tunings, which have used perfect fifths as low as 685 cents and as high as 705-710 cents.

More recently, in 1978 Easley Blackwood proclaimed the excellence and musical value of the 15 tone equal tuning, with its 720 cent perfect fifth. Ivor Darreg also concurred in his //Xenharmonic Bulletins// in the 1970s and 1980s, and Wendy Carlos chimed in to give her enthusiastic support to the 15 equal tuning. Blackwood, Darreg, Carlos and many others have composed notable pieces in the 15 equal tuning, and listeners have founds its 720-cent perfect fifths lively and vividly musical. Likewise, Ivor Darreg and many others have enthusiastically spoken in favor of tunings like 7 and 14 equal, with 685.4-cent perfect fifths. Ivor in particular boosted 14 equal because of its freshness combined with its memorable and impressive musical "mood."

All this evidence converges on the conclusion that within a wide range of about 20 cents lower than, to 20 cents higher than, the just 3/2, perfect fifths sound recognizable and musically effective in actual music. The claim that small integer ratios like 3/2 represent the only real musical intervals that listeners prefer is so far the opposite of the documented facts that the opposite is actually true. As Erv Wilson succinctly put it, "Musical cultures around the world tend to systematically //avoid// the intervals of the harmonic series." (Wilson, E., personal communication).

**Myth #3: "All music derives from harmony, and thus the pure prefect intervals of the 4:5:6 triad are the basis on which we must build musical tunings."** Western musical analysis reinforces this misconception by doing an analysis of music which almost entirely boils down Western music to series of harmonic progressions. The pseudo-scientific claims of Schenker reiterate this claim, stripping music down a series of //urlinie// which amount to little more than harmonic progressions.

In reality, melody proves far more important in music worldwide than harmony. Most of the world's musical cultures do not use triads and have no interest in musical harmony. Most of the world's music has nothing to do with triads, and well over 80% of the world's musicians do not think of music in terms of harmonic progressions. Indeed, the vast majority of the world's musicians and composers have no interest in harmonic progressions at all. Ancient cultures like the Greeks were well aware of the possibilities of producing triads: they simply had no interest in doing so.

The use of triadic harmony and triadic harmonic progressions, far from being a universal basis for music, in reality qualifies as a bizarre fringe case -- a rare exception. We find it only in North American/European music, and then only within a very limited time period (roughly 1490 to 1910). Before that time period, triads and triadic harmonic progressions are simply not used, even in Western music. And later than 1910, triads get used in Western music intermittantly -- tone clusters (Xenakis, Ligeti, Pendercki, Ives, Cowell, et al.) and sound-masses are used at least as much as triads after 1910, and heterophony and dense dissonant counterpoint are used at least as often as triadic chord progressions after 1910 even in Western music.

**Myth #4: "We must match the tuning to the timbres, so that harmonic series timbres play music written in the pure perfect natural intervals of the harmonic series."** The effects of acoustic roughness and smoothness do depend on the degree to which timbres match tunings. For example, as John R. Pierce and Max Mathews first showed in their article "Attaining Consonance in Arbitrarily Musical Scales," in the book //Music By Computer//s, ed., C. Beauchamp, 1969, and as was further developed by composers like James Dashow and William Sethares (see Sethares' book //Timbre, Tuning, Spectrum, Scale//," Elsevier, 1992), the familiar effects of acoustic points of rest (relatively beatless intervals) and acoustic points of tension (intervals within roughly 1/4 of the critical band which beat at the circa 30 hz rate first identified by Helmholtz as maximally disturbing) only exist when timbre approximately matches tuning. Bach played on a carillon, for example, sounds confusing, because the normal points of acoustic rest and acoustic tension fail to fall in the places we expect.

However, the experience of composers and audiences since 1969 has shown that musical audiences seem to prefer a wide range of timbres in musical compositions. Digitally modifying timbres so that they perfectly match the musical tuning tends to produce bland-sounding excessively vocoder-like timbres which leave audiences restless.

In fact, the history of modern music post-1970 shows that percussion ensembles have become increasingly prominent in contemporary music. These percussion ensembles typically use inharmonic timbres which utterly fail to match the 12-equal tuning, yet audience love the music produced by these percussion ensembles. The answer to this seeming conundrum is that audience crave variety. We like to hear compositions in which some of the timbres match the tuning, and in which some other timbres clash with the tuning. As with food, eating the same thing all the time day after day makes you sick. You get tired of it. In the same way, musical repasts which feature nothing but harmonic series timbre after harmonic series timbre perfectly matched to the musical tuning quickly grows dull. Audiences get restless. They want some variety, not the same bland vocoded-sounding hum all the time.

**Myth #5: "Mathematics forms the basis of music, and therefore mathematical music theory must guide us when we create new tunings."** As Paul Hindemith noted in 1937, "<span class="st">Theorists, basing their reasoning on acoustical phenomena, have repeatedly come to conclusions wholly at variance with those of practical musicians.</span>" (Hindemith, P., //The Craft of Musical Composition//, Vol. 1, 1937.) The human ear/brain system stands between the acoustic wavefronts of musical instruments and the music as we perceive it. Our human sensory apparatus and our cognitive processes are highly non-linear and subject to a wide range of cognitive biases. See "Judgement Under Uncertainty: Heuristics and Biases," Tversky, A. and Kahneman, D., //Science//, new series, Vol. 185, No. 4157, September 27 1974, pp. 1124-1131. Also see [[http://psychology.about.com/od/sensationandperception/ss/gestaltlaws.htm|Gestalt Laws of Perceptual Organization]] and [[http://www.musanim.com/miller1956/|"The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information," by George A. Miller, The Psychological Review, 1956, vol. 63, pp. 81-97]]

We do not hear frequency; rather, we perceive pitch. We do not hear amplitude; rather, we perceive loudness. We do not hear the wavefronts of series of atmospheric compressions or rarefaction; rather, we perceive music. And our perceptions find themselves subject to a vast multiplicity of distortions and cognitive limitations. See [[http://www.amazon.com/Music-Cognition-Computerized-Sound-Psychoacoustics/dp/0262531909|Music, Cognition and Computerized Sound: An Introduction to Psychoacoustics, MIT Press, ed. Perry Cook]]

It has been shown for more than 80 years that our perception of pitch depends on loudness, and contrariwise that our perception of loudness is greatly dependent on pitch. In the first case, it was shown by Harvey Fletcher back the early 1930s that our perception of the pitch of a sound tends to drop with its amplitude, and a louder sound in the mid-high range can be as much as a minor third lower, depending on its loudness. See Fletcher, H., "Loudness, pitch and the timbre of musical tones and their relation to the intensity, the frequency and the overtone structure," //Journal of the Acoustical Society of America//, Vol 6, 1934, pp. 59-69. In the second case, see the well -known [[http://www.webervst.com/fm.htm|Fletcher-Munson curve]], which all audio mixing engineers must take into account. (The Fletcher-Munson curve tells us that low frequency sounds must be greatly boosted in amplitude to sound as loud and mid-range to high frequency sounds. Recording engineers deal with this problem by using compression or hard limiting in musical recordings. Live concerts deal with this well-known problem by placing the bass-heavy instruments closer to the audience and the instruments with higher tessitura farther away from the audience, as a kind of physical equalization curve which decreases the apparently amplitude of high-pitched instruments while enhancing the bass of the low-pitched instruments.)

Mathematics has consistently failed to predict the musical effect or musical utility of new musical tunings. As Ivor Darreg pointed out, "It is absolutely impossible to //imagine// the sound or mood or a new tuning. You have to hear it. Only then can you imagine it."

The systematic musical failure of mathematically-based methods of musical organization, like total serialism, which refused take the characteristics of the human cognitive system and the human auditory system into account, also leads us toward the conclusion that mathematics fails as a basis for creating new tunings.

//"There has been so much theory, so much mathematical speculation about new tunings, and what they failed to take into account is that there is no such thing as a bad tuning, there is no such thing as a useless tuning. Every tuning has its musical uses."// -- Ivor Darreg, personal communication.

An overwhelming mountain of evidence from many different fields converges on the conclusion that the only valid way to explore microtonality is by means of experience-based knowledge. As music history shows, composers do weird bizarre things for years, then the theorists belatedly catch up. When theorists try to lead and predict what will prove musically effective, they typically fail.

Xenharmonics offers such a completely novel field of musical exploration that the only reasonable way to press forward involves hands-on experimentation. This is, in fact, the scientific method: the universe typically proves too complex for us to reason our way to correct conclusions sans hands-on experience. We must try things out, make observations, and then compare our observations of the real world with our mental models in order to gain useful knowledge.

**Myth #5: "Microtonality produces great theory and bad music." -- Brian Eno.**

The internet abounds with information about microtonality and xenharmonic, essentially all of it provably false. In contemporary music as in foreign affairs and economics and most other realms of daily life, those who talk don't know, while those who know don't talk.

[[http://www.jerrypournelle.com/reports/jerryp/iron.html|Pournell's Iron Law of Bureaucracy]] states that any institution will tend to harbor two kinds of the people. The first are the people who actually do the work that pushes things forward. The second group are those those who excel in the kind of bureaucratic infighting which advances their own careers and gains them publicity and renown. And Pournell's Law states that the second group will always tend to take power in an institution, write the rules, and end up marginalizing the first group.

This applies to the internet and to academic bodies and prestigious contemporary music institutions (like Wikipedia or tuning discussion groups or Ivy League tenured university professorships or institutions like Lincoln Center) as well as to other other types of bureaucracies. The people who wind up dominating Wikipedia articles about xenharmonics (as administrators with the power to delete edits they don't like) or Ivy League tenured professorships or the concert programmes or high-profile concert venues like Lincoln Center tend to be the people who excel at politicking and bureaucratic infighting...not the people who actually know or have accomplished things. A person becomes an administrator with the power to delete undesired entries in Wikipedia articles about micrtonality by spending 16 hours per day editing Wikipedia. This leaves no time to compose or perform or listen to microtonal music. As a result, the people who spend all their time composing and performing microtonal music get marginalized and written out of Wikipedia articles about microtonality. The same applies to people who attain positions of great power in institutions like Lincoln Center. Such people must spend essentially all their time running and politicking in Lincoln center and navigating the treacherous waters of funding committees and budget infighting with the City of New York, leaving no time to compose or perform music.

Consequently, there is essentially no valid information about xenharmonic on the internet. Moreover, as a general rule, the better-connected any xenharmonic commentator is to the internet, the more elaborate hi/r webpage, the more highly visible and polished hi/r YouTube videos, the less that person knows about xenharmonics. People with elaborate and impressive web pages and superb YouTube videos have attained that level of expertise by spending all their waking hours learning web design and video production. This leaves no time for composing and performing music. Contrariwise, the expert musicians who spending all their waking hours composing or performing music don't have years to take off to learn web design or high-definition video editing and production. Invariably, the expert musician who asks someone "Please design a high-quality professional looking web page for me" or "I need three hundred hours of video of performances edited and titles added and the viewpoints of three different cameras intercut, with SMPTE synchronization" gets the response: "I make my living doing web design/video editing and I charge $50 per hour -- why should I do it for you for free?" With the inevitable result that the web page never gets designed or the video never gets edited and put up on YouTube.

There exists a vast amount of superb microtonal music. Brian Eno has never heard it because it's produced by practicing musicians and composers who spend their time making vividly memorable music, not impressive websites or Lincoln Center concerts or thick gilt-edged books published by prestigious academic publishers. There is a great deal of insightful and accurate writing about microtonality, but it was produced by people like Ivor Darreg who cannot get published by conventional academic publishers. (Peer review generally offers a reliable method of academic quality control **//except//** in new fields like xenharmonics. With microtonality, peer-review encounters a vicious cycle of Catch-22: the academic to whom the book on microtonality gets sent for peer review responds "Never heard of this. Deep six it." And because of this kind of response in peer review, academic books on microtonality typically don't get published. But because academic books on microtonality don't get published, academics remain unfamiliar with the subject -- leading to a self-reinforcing closed cycle of lack of information about microtonality in academia.) Meanwhile, the books on microtonality which **//do//** get published (viz., Harry Partch's //Genesis of a Music//) contain [[http://sonic-arts.org/mclaren/partch/errors.htm|enormous amounts of misinformation about microtonality]] and ignore most of the range of xenharmonic tunings and most of the styles of xenharmonic music produced over the last 80 years.

This appears to be the case in the early part of the development of any new art. For the first few years, the people who are most prominent are those who know the least and have produced the worst music or art. Only slowly, after a period of many decades, do the obscure figures eventually become revealed as the great practititioners, and the previously unpublished writings finally get into (and stay in) print. Henry Cowell's //New Musical Resources//, for example, was written in 1919 but not published until 1930. it then fell out of print in the 1950s, and stayed out of print for well over 40 years.

Contemporary music finds itself subject to even more violent fads and fashions than bubble-gum pop music designed for teenagers. And just as pop music witnesses transient fashions like The Spice Girls (who at one time sold more records faster than any other group in music history and have now completely vanished from pop culture, never to be heard of again), in contemporary music transient fashions like total serialism gain immense fame, only to submerge into oblivion and disappear from the general consciousness, never to be heard of again. In contemporary music, as in bubblegum pop music, the transient fads and fashions are what grab peoples' attention. The work that stands the test of time only emerges gradually, over the course of many years. (Sometimes the work that stands the test of time was famous when originally produced. But sometimes not.)

**Myth #6: "Acoustics forms the basis of all music, and the acoustic laws of physics show that all vibrating objects resonate with natural modes of vibrations which form small integer ratios."**

This claim is so diametrically the opposite of mathematical and acoustical reality that it's hard to find words with which to state the sheer **//wrongness//** of this claim.

In actual fact, Weyl's Law of Acoustics states that only one-dimensional vibrational systems produce harmonic series vibrational modes. I.e., only one-dimensional vibrating strings, or tubes which exhibit only one degree of vibrational free (the cylindrical tube can be viewed as a rotational symmetry around a one-dimensional line, mathematically speaking, since the air in the cylindrical tube has only one degree of freedom--it can only move forward or back in one dimension).

This means that **//essentially all vibrating objects produce natural resonant modes of vibration which are non-just non-equal-tempered.//** If you pick up any object in your immediate vicinity and tap it, you will hear an inharmonic series of partials produced by non-just non-equal-tempered modes of natural vibration.

This tells us that "the chord of nature," if there is any such thing, is a non-just non-equal-tempered set of inharmonic vibrational modes. Essentially all objects in the circumambient universe have three dimensions, and Weyl's Law tells us that any vibrating objects which are not 1-dimensional exhibit inharmonic modes of vibration which are non-just non-equal-tempered. (Even vibrating systems which approximate 1-dimension systems, like a taut string or a cylindrical tube, exhibit slightly inharmonic partials whose inharmonicity results from the three dimensional nature of the system. A cylindrical tube has modes of vibration which depart from harmonicity due to edge effects and viscous air flow friction at the edges of the tube, while a string under tensions has partials which depart from harmonicity because of the mass and diameter of the strings and their tendency to act as vibrating metal rods to some degree, rather than as 1-dimensional string with length but no width or height.)

Ethnomusicology confirms this, showing that well over 80% of the world's musicians produce music using inharmonic instruments like gourds, metallophones, xylophones, drums, beaters, shakers, and so on, in non-just non-equal tempered tunings.

**"As to whether the interval 3:2 is common to all of the world's musical systems, as has occasionally been claimed, Fritz Kuttner asserts that the "fifth" in Chinese music is 20 to 30 cents flat. It is apparently nearly as flat in Siamese music..."** M. Joel Mandelbaum, //Multiple Division of the Octave and the Tonal Resources of 19-Tone Temperament//, PhD thesis, 1960, p. 16.

**"Two theoretical systems evolved in China, one derived from the Cyclic Pentatonic and the other from the division of string lengths. They are found combined in the highest form of Ch'in music. (..) Methods of arriving at these fifths included the use of twelve tubes... The fifths produced by these tubes were small compared to Western fifths. Various musicologiests place them between 670 and 680 cents as compared to the Just fifth of 702 cents."** [Lentz, Donald A., //The Gamelan Music of Java and Bali//, 1965, pg. 27]

**"There are...a number of musical cultures that apparently employ approximately equally tempered 5- and 7-interval scales (i.e., 240 and 171 cent step-sizes, respectively) in which the fourths and fifths are significantly mistuned form their natural values. Seven-interval scales are usually associated with Southeast Asian cultures (Malm, 1967). For example, Morton (1974) reports measurements (with a Stroboconn) of the tuning of a Thai xylophone that `varied only + or - 5 cents' from an equally tempered 7-interval tuning. (In ethnomusicological studies measurement variability, if reported at all, is generally reported without definition.) Haddon reported (1952) another example of a xylophone tuned in 171-cent steps from the Chopi tribe in Uganda. The 240-cent step-size, 5-interval scales are typically associated with the `gamelan' (tuned gongs and xylophone-type instruments) orchestras of Java and Bali (e., Kunst, 1949). However, measurements of gamelan tuning by Hood (1966) and McPhee (1966) show extremely large variations, so much so that McPhee states: `Deviations in what is considered the same scale are so large that one might with reason state that there are as many scales as there are gamelans.' Another example of a 5-interval, 24--cent step tuning (measured by a stroboconn, 'variations' of 15 cents) was reported by Wachsmann (1950) for a Ugandan harp. Other examples of equally tempered scales are often reported for pre-instrumental cultures... For example, Boiles (1969) reports measurements (with a Stroboconn, `+ or - 5 cents accuracy') of a South American Indian scale with equal intervals of 175 cents, which results in a progressive octave stretch. Ellis (1963), in extensive measurements in Australian aboriginal pre-instrumental cultures, reports pitch distributions that apparently follow arithmetic scales (i.e., equal separation in Hz).**

**"Thus there seems to be a propensity for scales that do not utilize perfect consonances and that are in many cases highly variable, in cultures that either are pre-instrumental or whose main instruments are of the xylophone type. Instruments of this type produce tones who partials are largely inharmonic (see Rossing, 1976) and whose pitches are often ambiguous (see de Boer, 1976)."** [Burns, E. M. and Ward, W. D., "Intervals, Scales and Tuning," in //The Psychology of Music//, 1982, ed. Diana Deutsch, pg. 258]

One-dimensional vibrational systems do not appear in nature. (All objects in our universe have three dimensions.) 1-dimensional vibrational systems are not natural, and objects like stretched strings or perfectly cylindrical hollow tubes which approximate to some degree a 1-dimensional vibrational system must be produced artificially. This means that just intonation is the most artificial and least natural possible tuning, while the most natural tuning would be some form of non-just non-equal-tempered tuning with highly inharmonic partials, like the natural vibrational modes of a struck wooden block or a metal bar or a drumhead.

Musical instruments which produce harmonic series timbres are so rare and so unusual that, to a first approximation, essentially all the world's musical instruments avoid this kind of construction. There is nothing new about this conclusion: A. J. Ellis first stated in 1885 that his survey of world music showed that "The music of most of the world's cultures is not based on mathematics nor or integer ratios, but is very contingent, and arbitrary, and entirely unique to its own society." (Ellis, A. J., "On the Musical Scales Of Various Nations," //Journal of the Royal Society of the Arts//, Vol. 3, 1885, pg. 536). The mathematical acoustics of most vibrating bodies have been known to be nonlinear and to produce inharmonic partials for most vibrating objects for well over 100 years: see Lord Rayleigh's two-volume //Acoustics//, 1895, for details.

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<html><head><title>misconceptions about xenharmony</title></head><body>The field of microtonality is rife with colorful personalities and diverse perspectives, and there are many contradictory philosophies and approaches. However, the literature on microtonality in general seems to over-represent certain perspectives, and this page is intended specifically to represent some of the views that diverge from the more &quot;mainstream&quot; or traditional ideas about microtonality.<!-- ws:start:WikiTextTocRule:4:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:4 --><!-- ws:start:WikiTextTocRule:5: --><div style="margin-left: 1em;"><a href="#toc0"> </a></div>
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 <strong><em><span style="font-weight: normal;">(written for this wiki)</span></em></strong><br />
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<strong>Myth #1: &quot;Everyone prefers the natural intervals of the pure perfect harmonic series.&quot;</strong> This myth remains pervasive. It has been stated by Hermann Helmholtz, in the form &quot;instrumentalists naturally tend to play in the intervals of just intonation.&quot; This myth was also repeatedly stated by Harry Partch, who claimed &quot;The ear demands small integer ratios, and accepts substitutes against its will.&quot;<br />
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These myths have been debunked for well over 80 years. In the 1930s, the music psychologist Carl Seashore first investigated the actual intonation of violinists and other Western performers. He found that they played intervals which were neither just (i.e., small integer ratios) or equal divisions of the octave, but something entirely different. Typical intervals performed by trained Western symphony-caliber musicians are neither just nor equal-tempered. The intervals performed often differ wildly from the putative size of the musical intervals which should be played, yet audiences typically hear these distorted intervals as sounding &quot;perfectly in tune.&quot; See Seashore, Carl, <em><a class="wiki_link_ext" href="http://books.google.com/books?id=p9gUknYfpjYC&amp;printsec=frontcover#v=onepage&amp;q&amp;f=false" rel="nofollow">Psychology of Music</a></em>, 1936.<br />
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In 1961-2, physicist Charles Shackford published three articles in the then-new <em>Journal of Music Theory</em> examining the intervals actually performed by symphony musicians in live concerts. He found that the performed intervals typically differed by at least 10 cents from the target intervals, and often differed by up to 50 cents -- yet listeners were unable to hear any problem with these distorted intervals. To audiences, these extremely out-of-tune intervals sounded &quot;perfectly in tune&quot; and &quot;entirely musical.&quot; See “Some Aspects of Perception, I: Sizes of Harmonic Intervals in Performance,” Shackford, Charles, <em>Journal of Music Theory</em>, Vol. 5, No. 1, 1961, 162–202; also “Some Aspects of Perception, II: Interval Sizes and Tonal Dynamics in Performance,” Shackford, Charles, <em>Journal of Music Theory</em>, Volume 6, No. 1, 1962, pp. 66–90, and &quot;Some Aspects of Perception III: Remarks,&quot; Shackford, Charles, <em>Journal of Music Theory</em>, Volume 6, No. 2, 1962. Shackford's work builds on earlier studies which reached the same conclusions: see Paul C. Green, “Violin Intonation,” <em>Journal of the Acoustical Society of America</em>, IX (1937), 43–44; James F. Nickerson, “Comparison of Performances of the Same Melody in Solo and Ensemble with Reference to Equal Tempered, Just, and Pythagorean Intonations,” <em>Journal of the Acoustical Society of America</em>, XXI (1949), 462; idem, “Intonation of Solo and Ensemble Performance of the Same Melody,” <em>Journal of the Acoustical Society of America</em>, XXI (1949), 593.<br />
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This research has been confirmed by many subsequent listening experiments. Psychoacousticians have shown that listeners typically cannot hear a difference between pitches less than 15 cents larger or smaller than their nominal values in a real performance (see &quot;Intonation precision of choir singers, &quot;<span class="looklikelink authorname aqslistener"> Sten Ternström</span> and <span class="looklikelink authorname aqslistener">Johan Sundberg, </span>Journal of the Acoustical Society of America, Volume 84, Issue 1, 1988, pp. 59-69), and that all musical performers across all cultures (non-Western performers in India, for example, as well as Western symphonic musicians in Europe/North America) tend to perform large musical intervals of the size of a minor third or larger as bigger than they should be (often between 5 to 10 cents larger), while performing small musical intervals the size of a major second as smaller than they should be (typically compressing a whole tone which should be 200 cents to a value as small as 170 cents or smaller) and compressing semitones even more, typically by at least 30 cents (so that semitones, particularly those resolving downward from a supertonic to a tonic or moving upward from a leading tone to a tonic, are often measured with values as small as 70 cents or 60 cents or in some cases even 50 cents or less). See &quot;Intonation Variants of Musical Intervals in Isolation and in Musical Contexts,&quot; <span class="name"><a class="wiki_link_ext" href="http://pom.sagepub.com/search?author1=Andrzej+Rakowski&amp;sortspec=date&amp;submit=Submit" rel="nofollow">Andrzej Rakowski</a></span><!-- ws:start:WikiTextAnchorRule:8:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@aff-1&quot; title=&quot;Anchor: aff-1&quot;/&gt; --><a name="aff-1"></a><!-- ws:end:WikiTextAnchorRule:8 -->, <em>Chopin Academy of Music</em>, Okolnik 2, 00-368 Warszawa, Poland; &quot;Musical Intervals and Simple Number Ratios,&quot; Cazden, N., J. Res. Music Educ., 7, pp. 197-220; &quot;Influence of the Time Interval on Experimentally Induced Shifts of Pitch,&quot; Christman, R. J. and Williams, W. E., J. Acoust. Soc. Am., 35, pp. 1030-1033, 1963; &quot;Further Investigation of the Effects of Intensity Upon the Pitch of Pure Tones,&quot; Cohen, A., J. Acoust. Soc. Am., 33, pp. 1363-1376, 1961; &quot;Pitch relations and the formation of scalar structure,&quot; Cross, I., R. West and P. Howell, Music perception, Vol. 2, No. 3, 1985, pp. 329-344; &quot;The influence of pitch on time perception in short melodies,&quot; Crowder, Robert G. and Ian Neath, Music perception, Vol. 12, No. 4, 1994, pp. 379-386; &quot;Grouping in pitch perception: evidence for sequential constraints,&quot; Darwin, C. J., R. W. Hukin and Batul Y. Al-Khatib, Journal of the Acoustical Society of America, Vol. 98, No. 2, part 1, 1995, pp. 880-885; &quot;Some Observations on Pitch and Frequency,&quot; Davis, H., S. R. Silverman and D. R. McAuliffe, J. Acoust. Soc. Am., Vol. 23, pp. 40-42, 1951; &quot;Mapping of interactions in the pitch memory store,&quot; Deutsch, Diana, Science, Vol. 175, 1972, pp. 1020-1022; &quot;The Processing of Pitch Combinations,&quot; in D. Deutsch, (Ed.), The Psychology of Music, New York: Academic Press, 1982;<br />
&quot;Interference in memory between tones adjacent in the musical scale,&quot; Deutsch, Diana, Journal of Experimental Psychology, Vol. 100, No. 2, 1973, pp. 228-231; &quot;Music perception,&quot; Deutsch, Diana, The Musical Quarterly, Vol. 66, No. 2, 1980, pp. 165-179; &quot;Dichotic listening to musical sequences: Relationship to hemispheric specialization of function,&quot; Deutsch, Diana, Journ. Acoust. Soc. Am., Vol. 74, 1983, pp. 579-80; Dowling, W. J. &quot;The 1215-Cent Octave: Convergence of Western and Non-Western Data on Pitch Scaling,&quot; Abstract QQ5, 84th meeting of the Acoustical Society of America, Friday, December 1, 1972, p. 101 of program, and so on.<br />
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Moreover, in 1986, Linda Roberts along with John R. Pierce and Max Mathews published a study in which they investigated the actual listening preferences of musical audiences. They found that presented with a choice, 8 out of 9 listeners preferred musical intervals which beat, while only 1 out of 9 listeners preferred musical intervals which were beatless. As in, for example, perfect fifths or major thirds, etc. Roberts, Pierce and Mathews referred to the first group who preferred musical intervals which beat as &quot;rich listeners&quot; because these listeners preferred tunings which made the music sound &quot;rich&quot; and &quot;lively&quot; with a plethora of active beats. The second group Roberts, Pierce and Mathews referred to as &quot;pure listeners&quot; because they preferred beatless major and minor thirds, beatless perfect fifths and perfect fourths, and so on. The interesting fact about this study is the lopsidedly bimodal nature of the distribution. Rich listeners far outnumber pure listeners. See &quot;Harmony and New Scales,&quot; M. V. Mathews, J. R. Pierce and L. A. Roberts, in <a class="wiki_link_ext" href="http://www.speech.kth.se/music/publications/kma/papers/kma54-ocr.pdf" rel="nofollow">Harmony and Tonality</a>, ed. J. Sundberg, 1987, pp. 59-84.<br />
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Notice that these studies present no aesthetic preference. They do not tell us that rich listeners are &quot;better&quot; or &quot;more discerning&quot; than pure listeners. These studies merely inform us that rich listeners outnumber pure listeners in Western musical audiences by a ratio of roughly 8 to 1. There is no indication that musical tunings which produce more beats are any better or any worse than musical tunings which produce fewer beats (just intonation with small integer ratios). As Warren Burt put it, &quot;I don't hear small integers ratios as sounding any better than intervals which beat. I hear a difference -- I simply don't acknowledge that the difference produces any aesthetic superiority.&quot; Or, as William Schottstaedt, arguably the greatest living American composer, put it: &quot;I like beats. Beats sound good.&quot;<br />
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<strong>Myth #2: &quot;The small integer ratios like 3/2 and 5/4 are <u><em>the</em></u> original intervals from which all other musical intervals are derived.&quot;</strong> Kyle Gann teaches this provably false claim in his course on microtonality. (Gann's discussion of microtonality is generally scrupulously accurate: this offers a rare exception. See Gann, <span class="wiki_link_ext">Kyle, </span><a class="wiki_link_ext" href="http://www.kylegann.com/JIreasons.html" rel="nofollow">&quot;My Idiosyncratic Reasons for Using Just Intonation&quot;</a> for one of the best explanations of why composers may find just intonation useful.) Or, as Lou Harrison put it, &quot;Just intonation tunings are the only real musical intervals. All other musical intervals are fake musical intervals.&quot;<br />
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The actual evidence of peer-reviewed published listening tests in the psychoacoustic literature show that there exists a wide range within which listeners recognize musical interval categories like &quot;fifth&quot; and &quot;third&quot; as sounding functional and musically effective. Once again, this has been known for more than 80 years, and documented in a wide variety of peer-reviewed scientific papers going back to 1926.<br />
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In <span class="st">&quot;Variability of judgments of musical intervals,&quot; Moran and Pratt, <em>Journal of Experimental Psychology</em>, Vol. 9, 1926, pp. 492-500, 1926, researchers found that the range of recognizable musically effective and musically functional intervals ran from a low of 680 cents to a high of 720 cents for the perfect fifth. This conclusion has been confirmed and more supporting evidence piled up by many subsequent listening tests.</span><br />
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Moreover, this conclusion is also supported by ethnomusicological studies which show that worldwide non-Western cultures tend to use a plethora of unequally spaced (or sometimes quasi-equal-spaced) 5- and 7-tone musical scales, with fifths ranging from roughly 680 cents on the low side to 720 cents on the high side.<br />
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This conclusion is also supported by the historical record of tempered tunings, which have used perfect fifths as low as 685 cents and as high as 705-710 cents.<br />
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More recently, in 1978 Easley Blackwood proclaimed the excellence and musical value of the 15 tone equal tuning, with its 720 cent perfect fifth. Ivor Darreg also concurred in his <em>Xenharmonic Bulletins</em> in the 1970s and 1980s, and Wendy Carlos chimed in to give her enthusiastic support to the 15 equal tuning. Blackwood, Darreg, Carlos and many others have composed notable pieces in the 15 equal tuning, and listeners have founds its 720-cent perfect fifths lively and vividly musical. Likewise, Ivor Darreg and many others have enthusiastically spoken in favor of tunings like 7 and 14 equal, with 685.4-cent perfect fifths. Ivor in particular boosted 14 equal because of its freshness combined with its memorable and impressive musical &quot;mood.&quot;<br />
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All this evidence converges on the conclusion that within a wide range of about 20 cents lower than, to 20 cents higher than, the just 3/2, perfect fifths sound recognizable and musically effective in actual music. The claim that small integer ratios like 3/2 represent the only real musical intervals that listeners prefer is so far the opposite of the documented facts that the opposite is actually true. As Erv Wilson succinctly put it, &quot;Musical cultures around the world tend to systematically <em>avoid</em> the intervals of the harmonic series.&quot; (Wilson, E., personal communication).<br />
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<strong>Myth #3: &quot;All music derives from harmony, and thus the pure prefect intervals of the 4:5:6 triad are the basis on which we must build musical tunings.&quot;</strong> Western musical analysis reinforces this misconception by doing an analysis of music which almost entirely boils down Western music to series of harmonic progressions. The pseudo-scientific claims of Schenker reiterate this claim, stripping music down a series of <em>urlinie</em> which amount to little more than harmonic progressions.<br />
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In reality, melody proves far more important in music worldwide than harmony. Most of the world's musical cultures do not use triads and have no interest in musical harmony. Most of the world's music has nothing to do with triads, and well over 80% of the world's musicians do not think of music in terms of harmonic progressions. Indeed, the vast majority of the world's musicians and composers have no interest in harmonic progressions at all. Ancient cultures like the Greeks were well aware of the possibilities of producing triads: they simply had no interest in doing so.<br />
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The use of triadic harmony and triadic harmonic progressions, far from being a universal basis for music, in reality qualifies as a bizarre fringe case -- a rare exception. We find it only in North American/European music, and then only within a very limited time period (roughly 1490 to 1910). Before that time period, triads and triadic harmonic progressions are simply not used, even in Western music. And later than 1910, triads get used in Western music intermittantly -- tone clusters (Xenakis, Ligeti, Pendercki, Ives, Cowell, et al.) and sound-masses are used at least as much as triads after 1910, and heterophony and dense dissonant counterpoint are used at least as often as triadic chord progressions after 1910 even in Western music.<br />
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<strong>Myth #4: &quot;We must match the tuning to the timbres, so that harmonic series timbres play music written in the pure perfect natural intervals of the harmonic series.&quot;</strong> The effects of acoustic roughness and smoothness do depend on the degree to which timbres match tunings. For example, as John R. Pierce and Max Mathews first showed in their article &quot;Attaining Consonance in Arbitrarily Musical Scales,&quot; in the book <em>Music By Computer</em>s, ed., C. Beauchamp, 1969, and as was further developed by composers like James Dashow and William Sethares (see Sethares' book <em>Timbre, Tuning, Spectrum, Scale</em>,&quot; Elsevier, 1992), the familiar effects of acoustic points of rest (relatively beatless intervals) and acoustic points of tension (intervals within roughly 1/4 of the critical band which beat at the circa 30 hz rate first identified by Helmholtz as maximally disturbing) only exist when timbre approximately matches tuning. Bach played on a carillon, for example, sounds confusing, because the normal points of acoustic rest and acoustic tension fail to fall in the places we expect.<br />
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However, the experience of composers and audiences since 1969 has shown that musical audiences seem to prefer a wide range of timbres in musical compositions. Digitally modifying timbres so that they perfectly match the musical tuning tends to produce bland-sounding excessively vocoder-like timbres which leave audiences restless.<br />
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In fact, the history of modern music post-1970 shows that percussion ensembles have become increasingly prominent in contemporary music. These percussion ensembles typically use inharmonic timbres which utterly fail to match the 12-equal tuning, yet audience love the music produced by these percussion ensembles. The answer to this seeming conundrum is that audience crave variety. We like to hear compositions in which some of the timbres match the tuning, and in which some other timbres clash with the tuning. As with food, eating the same thing all the time day after day makes you sick. You get tired of it. In the same way, musical repasts which feature nothing but harmonic series timbre after harmonic series timbre perfectly matched to the musical tuning quickly grows dull. Audiences get restless. They want some variety, not the same bland vocoded-sounding hum all the time.<br />
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<strong>Myth #5: &quot;Mathematics forms the basis of music, and therefore mathematical music theory must guide us when we create new tunings.&quot;</strong> As Paul Hindemith noted in 1937, &quot;<span class="st">Theorists, basing their reasoning on acoustical phenomena, have repeatedly come to conclusions wholly at variance with those of practical musicians.</span>&quot; (Hindemith, P., <em>The Craft of Musical Composition</em>, Vol. 1, 1937.) The human ear/brain system stands between the acoustic wavefronts of musical instruments and the music as we perceive it. Our human sensory apparatus and our cognitive processes are highly non-linear and subject to a wide range of cognitive biases. See &quot;Judgement Under Uncertainty: Heuristics and Biases,&quot; Tversky, A. and Kahneman, D., <em>Science</em>, new series, Vol. 185, No. 4157, September 27 1974, pp. 1124-1131. Also see <a class="wiki_link_ext" href="http://psychology.about.com/od/sensationandperception/ss/gestaltlaws.htm" rel="nofollow">Gestalt Laws of Perceptual Organization</a> and <a class="wiki_link_ext" href="http://www.musanim.com/miller1956/" rel="nofollow">&quot;The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information,&quot; by George A. Miller, The Psychological Review, 1956, vol. 63, pp. 81-97</a><br />
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We do not hear frequency; rather, we perceive pitch. We do not hear amplitude; rather, we perceive loudness. We do not hear the wavefronts of series of atmospheric compressions or rarefaction; rather, we perceive music. And our perceptions find themselves subject to a vast multiplicity of distortions and cognitive limitations. See <a class="wiki_link_ext" href="http://www.amazon.com/Music-Cognition-Computerized-Sound-Psychoacoustics/dp/0262531909" rel="nofollow">Music, Cognition and Computerized Sound: An Introduction to Psychoacoustics, MIT Press, ed. Perry Cook</a><br />
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It has been shown for more than 80 years that our perception of pitch depends on loudness, and contrariwise that our perception of loudness is greatly dependent on pitch. In the first case, it was shown by Harvey Fletcher back the early 1930s that our perception of the pitch of a sound tends to drop with its amplitude, and a louder sound in the mid-high range can be as much as a minor third lower, depending on its loudness. See Fletcher, H., &quot;Loudness, pitch and the timbre of musical tones and their relation to the intensity, the frequency and the overtone structure,&quot; <em>Journal of the Acoustical Society of America</em>, Vol 6, 1934, pp. 59-69. In the second case, see the well -known <a class="wiki_link_ext" href="http://www.webervst.com/fm.htm" rel="nofollow">Fletcher-Munson curve</a>, which all audio mixing engineers must take into account. (The Fletcher-Munson curve tells us that low frequency sounds must be greatly boosted in amplitude to sound as loud and mid-range to high frequency sounds. Recording engineers deal with this problem by using compression or hard limiting in musical recordings. Live concerts deal with this well-known problem by placing the bass-heavy instruments closer to the audience and the instruments with higher tessitura farther away from the audience, as a kind of physical equalization curve which decreases the apparently amplitude of high-pitched instruments while enhancing the bass of the low-pitched instruments.)<br />
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Mathematics has consistently failed to predict the musical effect or musical utility of new musical tunings. As Ivor Darreg pointed out, &quot;It is absolutely impossible to <em>imagine</em> the sound or mood or a new tuning. You have to hear it. Only then can you imagine it.&quot;<br />
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The systematic musical failure of mathematically-based methods of musical organization, like total serialism, which refused take the characteristics of the human cognitive system and the human auditory system into account, also leads us toward the conclusion that mathematics fails as a basis for creating new tunings.<br />
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<em>&quot;There has been so much theory, so much mathematical speculation about new tunings, and what they failed to take into account is that there is no such thing as a bad tuning, there is no such thing as a useless tuning. Every tuning has its musical uses.&quot;</em> -- Ivor Darreg, personal communication.<br />
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An overwhelming mountain of evidence from many different fields converges on the conclusion that the only valid way to explore microtonality is by means of experience-based knowledge. As music history shows, composers do weird bizarre things for years, then the theorists belatedly catch up. When theorists try to lead and predict what will prove musically effective, they typically fail.<br />
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Xenharmonics offers such a completely novel field of musical exploration that the only reasonable way to press forward involves hands-on experimentation. This is, in fact, the scientific method: the universe typically proves too complex for us to reason our way to correct conclusions sans hands-on experience. We must try things out, make observations, and then compare our observations of the real world with our mental models in order to gain useful knowledge.<br />
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<strong>Myth #5: &quot;Microtonality produces great theory and bad music.&quot; -- Brian Eno.</strong><br />
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The internet abounds with information about microtonality and xenharmonic, essentially all of it provably false. In contemporary music as in foreign affairs and economics and most other realms of daily life, those who talk don't know, while those who know don't talk.<br />
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<a class="wiki_link_ext" href="http://www.jerrypournelle.com/reports/jerryp/iron.html" rel="nofollow">Pournell's Iron Law of Bureaucracy</a> states that any institution will tend to harbor two kinds of the people. The first are the people who actually do the work that pushes things forward. The second group are those those who excel in the kind of bureaucratic infighting which advances their own careers and gains them publicity and renown. And Pournell's Law states that the second group will always tend to take power in an institution, write the rules, and end up marginalizing the first group.<br />
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This applies to the internet and to academic bodies and prestigious contemporary music institutions (like Wikipedia or tuning discussion groups or Ivy League tenured university professorships or institutions like Lincoln Center) as well as to other other types of bureaucracies. The people who wind up dominating Wikipedia articles about xenharmonics (as administrators with the power to delete edits they don't like) or Ivy League tenured professorships or the concert programmes or high-profile concert venues like Lincoln Center tend to be the people who excel at politicking and bureaucratic infighting...not the people who actually know or have accomplished things. A person becomes an administrator with the power to delete undesired entries in Wikipedia articles about micrtonality by spending 16 hours per day editing Wikipedia. This leaves no time to compose or perform or listen to microtonal music. As a result, the people who spend all their time composing and performing microtonal music get marginalized and written out of Wikipedia articles about microtonality. The same applies to people who attain positions of great power in institutions like Lincoln Center. Such people must spend essentially all their time running and politicking in Lincoln center and navigating the treacherous waters of funding committees and budget infighting with the City of New York, leaving no time to compose or perform music.<br />
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Consequently, there is essentially no valid information about xenharmonic on the internet. Moreover, as a general rule, the better-connected any xenharmonic commentator is to the internet, the more elaborate hi/r webpage, the more highly visible and polished hi/r YouTube videos, the less that person knows about xenharmonics. People with elaborate and impressive web pages and superb YouTube videos have attained that level of expertise by spending all their waking hours learning web design and video production. This leaves no time for composing and performing music. Contrariwise, the expert musicians who spending all their waking hours composing or performing music don't have years to take off to learn web design or high-definition video editing and production. Invariably, the expert musician who asks someone &quot;Please design a high-quality professional looking web page for me&quot; or &quot;I need three hundred hours of video of performances edited and titles added and the viewpoints of three different cameras intercut, with SMPTE synchronization&quot; gets the response: &quot;I make my living doing web design/video editing and I charge $50 per hour -- why should I do it for you for free?&quot; With the inevitable result that the web page never gets designed or the video never gets edited and put up on YouTube.<br />
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There exists a vast amount of superb microtonal music. Brian Eno has never heard it because it's produced by practicing musicians and composers who spend their time making vividly memorable music, not impressive websites or Lincoln Center concerts or thick gilt-edged books published by prestigious academic publishers. There is a great deal of insightful and accurate writing about microtonality, but it was produced by people like Ivor Darreg who cannot get published by conventional academic publishers. (Peer review generally offers a reliable method of academic quality control <strong><em>except</em></strong> in new fields like xenharmonics. With microtonality, peer-review encounters a vicious cycle of Catch-22: the academic to whom the book on microtonality gets sent for peer review responds &quot;Never heard of this. Deep six it.&quot; And because of this kind of response in peer review, academic books on microtonality typically don't get published. But because academic books on microtonality don't get published, academics remain unfamiliar with the subject -- leading to a self-reinforcing closed cycle of lack of information about microtonality in academia.) Meanwhile, the books on microtonality which <strong><em>do</em></strong> get published (viz., Harry Partch's <em>Genesis of a Music</em>) contain <a class="wiki_link_ext" href="http://sonic-arts.org/mclaren/partch/errors.htm" rel="nofollow">enormous amounts of misinformation about microtonality</a> and ignore most of the range of xenharmonic tunings and most of the styles of xenharmonic music produced over the last 80 years.<br />
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This appears to be the case in the early part of the development of any new art. For the first few years, the people who are most prominent are those who know the least and have produced the worst music or art. Only slowly, after a period of many decades, do the obscure figures eventually become revealed as the great practititioners, and the previously unpublished writings finally get into (and stay in) print. Henry Cowell's <em>New Musical Resources</em>, for example, was written in 1919 but not published until 1930. it then fell out of print in the 1950s, and stayed out of print for well over 40 years.<br />
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Contemporary music finds itself subject to even more violent fads and fashions than bubble-gum pop music designed for teenagers. And just as pop music witnesses transient fashions like The Spice Girls (who at one time sold more records faster than any other group in music history and have now completely vanished from pop culture, never to be heard of again), in contemporary music transient fashions like total serialism gain immense fame, only to submerge into oblivion and disappear from the general consciousness, never to be heard of again. In contemporary music, as in bubblegum pop music, the transient fads and fashions are what grab peoples' attention. The work that stands the test of time only emerges gradually, over the course of many years. (Sometimes the work that stands the test of time was famous when originally produced. But sometimes not.)<br />
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<strong>Myth #6: &quot;Acoustics forms the basis of all music, and the acoustic laws of physics show that all vibrating objects resonate with natural modes of vibrations which form small integer ratios.&quot;</strong><br />
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This claim is so diametrically the opposite of mathematical and acoustical reality that it's hard to find words with which to state the sheer <strong><em>wrongness</em></strong> of this claim.<br />
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In actual fact, Weyl's Law of Acoustics states that only one-dimensional vibrational systems produce harmonic series vibrational modes. I.e., only one-dimensional vibrating strings, or tubes which exhibit only one degree of vibrational free (the cylindrical tube can be viewed as a rotational symmetry around a one-dimensional line, mathematically speaking, since the air in the cylindrical tube has only one degree of freedom--it can only move forward or back in one dimension).<br />
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This means that <strong><em>essentially all vibrating objects produce natural resonant modes of vibration which are non-just non-equal-tempered.</em></strong> If you pick up any object in your immediate vicinity and tap it, you will hear an inharmonic series of partials produced by non-just non-equal-tempered modes of natural vibration.<br />
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This tells us that &quot;the chord of nature,&quot; if there is any such thing, is a non-just non-equal-tempered set of inharmonic vibrational modes. Essentially all objects in the circumambient universe have three dimensions, and Weyl's Law tells us that any vibrating objects which are not 1-dimensional exhibit inharmonic modes of vibration which are non-just non-equal-tempered. (Even vibrating systems which approximate 1-dimension systems, like a taut string or a cylindrical tube, exhibit slightly inharmonic partials whose inharmonicity results from the three dimensional nature of the system. A cylindrical tube has modes of vibration which depart from harmonicity due to edge effects and viscous air flow friction at the edges of the tube, while a string under tensions has partials which depart from harmonicity because of the mass and diameter of the strings and their tendency to act as vibrating metal rods to some degree, rather than as 1-dimensional string with length but no width or height.)<br />
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Ethnomusicology confirms this, showing that well over 80% of the world's musicians produce music using inharmonic instruments like gourds, metallophones, xylophones, drums, beaters, shakers, and so on, in non-just non-equal tempered tunings.<br />
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<strong>&quot;As to whether the interval 3:2 is common to all of the world's musical systems, as has occasionally been claimed, Fritz Kuttner asserts that the &quot;fifth&quot; in Chinese music is 20 to 30 cents flat. It is apparently nearly as flat in Siamese music...&quot;</strong> M. Joel Mandelbaum, <em>Multiple Division of the Octave and the Tonal Resources of 19-Tone Temperament</em>, PhD thesis, 1960, p. 16.<br />
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<strong>&quot;Two theoretical systems evolved in China, one derived from the Cyclic Pentatonic and the other from the division of string lengths. They are found combined in the highest form of Ch'in music. (..) Methods of arriving at these fifths included the use of twelve tubes... The fifths produced by these tubes were small compared to Western fifths. Various musicologiests place them between 670 and 680 cents as compared to the Just fifth of 702 cents.&quot;</strong> [Lentz, Donald A., <em>The Gamelan Music of Java and Bali</em>, 1965, pg. 27]<br />
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<strong>&quot;There are...a number of musical cultures that apparently employ approximately equally tempered 5- and 7-interval scales (i.e., 240 and 171 cent step-sizes, respectively) in which the fourths and fifths are significantly mistuned form their natural values. Seven-interval scales are usually associated with Southeast Asian cultures (Malm, 1967). For example, Morton (1974) reports measurements (with a Stroboconn) of the tuning of a Thai xylophone that `varied only + or - 5 cents' from an equally tempered 7-interval tuning. (In ethnomusicological studies measurement variability, if reported at all, is generally reported without definition.) Haddon reported (1952) another example of a xylophone tuned in 171-cent steps from the Chopi tribe in Uganda. The 240-cent step-size, 5-interval scales are typically associated with the `gamelan' (tuned gongs and xylophone-type instruments) orchestras of Java and Bali (e., Kunst, 1949). However, measurements of gamelan tuning by Hood (1966) and McPhee (1966) show extremely large variations, so much so that McPhee states: `Deviations in what is considered the same scale are so large that one might with reason state that there are as many scales as there are gamelans.' Another example of a 5-interval, 24--cent step tuning (measured by a stroboconn, 'variations' of 15 cents) was reported by Wachsmann (1950) for a Ugandan harp. Other examples of equally tempered scales are often reported for pre-instrumental cultures... For example, Boiles (1969) reports measurements (with a Stroboconn, `+ or - 5 cents accuracy') of a South American Indian scale with equal intervals of 175 cents, which results in a progressive octave stretch. Ellis (1963), in extensive measurements in Australian aboriginal pre-instrumental cultures, reports pitch distributions that apparently follow arithmetic scales (i.e., equal separation in Hz).</strong><br />
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<strong>&quot;Thus there seems to be a propensity for scales that do not utilize perfect consonances and that are in many cases highly variable, in cultures that either are pre-instrumental or whose main instruments are of the xylophone type. Instruments of this type produce tones who partials are largely inharmonic (see Rossing, 1976) and whose pitches are often ambiguous (see de Boer, 1976).&quot;</strong> [Burns, E. M. and Ward, W. D., &quot;Intervals, Scales and Tuning,&quot; in <em>The Psychology of Music</em>, 1982, ed. Diana Deutsch, pg. 258]<br />
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One-dimensional vibrational systems do not appear in nature. (All objects in our universe have three dimensions.) 1-dimensional vibrational systems are not natural, and objects like stretched strings or perfectly cylindrical hollow tubes which approximate to some degree a 1-dimensional vibrational system must be produced artificially. This means that just intonation is the most artificial and least natural possible tuning, while the most natural tuning would be some form of non-just non-equal-tempered tuning with highly inharmonic partials, like the natural vibrational modes of a struck wooden block or a metal bar or a drumhead.<br />
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Musical instruments which produce harmonic series timbres are so rare and so unusual that, to a first approximation, essentially all the world's musical instruments avoid this kind of construction. There is nothing new about this conclusion: A. J. Ellis first stated in 1885 that his survey of world music showed that &quot;The music of most of the world's cultures is not based on mathematics nor or integer ratios, but is very contingent, and arbitrary, and entirely unique to its own society.&quot; (Ellis, A. J., &quot;On the Musical Scales Of Various Nations,&quot; <em>Journal of the Royal Society of the Arts</em>, Vol. 3, 1885, pg. 536). The mathematical acoustics of most vibrating bodies have been known to be nonlinear and to produce inharmonic partials for most vibrating objects for well over 100 years: see Lord Rayleigh's two-volume <em>Acoustics</em>, 1895, for details.</body></html>