Misconceptions about xenharmony: Difference between revisions

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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Igliashon's "Four Misconceptions About Xenharmony and Microtonality"=

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Igliashon's "Four Misconceptions About Xenharmony and Microtonality" (and some further myths and facts about xenharmonics by mclaren)=

This page expresses the views of [[IgliashonJones|Igliashon Jones]], and may not be representative of the xenharmonic community in general. In fact, most of what follows is in direct contradiction with much of what has been written about microtonality, as well as much of what is considered "common sense" in many parts of the community...which is, in fact, the reason the author felt compelled to bring this page into existence.

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==Misconception 2: "Consonance is Rare and Therefore Important"==

Consonance is //not// rare at all. In fact it is omnipresent. It is only specifically well-tuned 5-limit consonance that is rare, and tunings that offer good approximations of the full 13-limit are very rare, but neither the 5-limit nor the full 13-limit are necessary for consonance. Almost every EDO approximates some consonant subgroup of Just Intonation with the same or greater level of accuracy that 12-TET has in the 5-limit. With a little care, all of these EDOs can be made to sound nice enough for the general public. Yes, even 10, 11, 13, and 14-EDO. In fact, even 8-EDO does a fairly passable approximation of harmonics 10:11:12:13:14 as 0-150-300-450-600 cents; it's not //great//, but it's //awesome// for such a tiny EDO--no interval is off by more than 18 cents, which is more or less as good as 12-TET.

No, consonance is ubiquitous, practically inescapable unless you insist on using ridiculous scales like 0-10-20-30-40-50-1200 cents. The strength and quality of consonance may vary from tuning to tuning, but there is //always// enough to serve effectively as contrast to the equally-ubiquitous dissonance, if only you take the time to understand what the contrast is and how to deal with it appropriately. Sometimes the most consonant harmonies look nothing like major and minor chords in 12-TET, so they can take some searching. But they are //always// there to be found if you know how to look.

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You know what tuning is the //most// related to the familiar? 12-TET! I don't care what the psychoacousticians say, the vast majority of people accustomed to 12-TET will prefer the sound of 12-TET to tunings which approximate the same harmonies but in "better" tune. They will think the Just major third sounds flat and dull, they will think the semitones are too wide or the minor third is too sharp or the dominant 7th isn't tense enough to create an effective resolution. You don't need to take my word for it, go forth and test this! Play people two versions of a familiar piece of music (preferably NOT rendered using your PC's built-in general MIDI sound set), but don't tell them which is which, and ask them to rate which one they like best. I've done it, and I know what the answers are.

The truth is, anyone not actively seeking out microtonal music will either not be able to hear the difference, or if they can hear it, they won't like it (unless it's "ethnically correct" microtonal music, like Indian or Arabic music). The only people looking for music in some variety of meantone or 12-tone well-temperaments are looking for the words "historically informed performance", aka the "authentic" or "early" music crowd. Those who //are// actively seeking out music that is called "microtonal" couldn't care //less// about smoother and more in-tune harmonies following the same familiar patterns. As Brian McLaren once said, "they are not shrinking violets". They want stuff that will make their brain do happy back-flips, stuff that will turn their ears inside-out. There are many ways to accomplish this, and they do not all involve chucking 5-limit harmony out the window (in fact, some of the best ways are completely //centered// on 5-limit harmony in some way or another), but the point is that if you pussy-foot around microtonality mumbling quietly about how it's "just like 12-TET, but more in tune", absolutely NO ONE will take you seriously. Not average listeners, not microtonal enthusiasts, not your fellow microtonal musicians, and most //certainly// not the average Guitar Center customer or university music student. The only way to make it as a microtonalist in this world is to go for broke, whether that means 13-EDO, 13-limit JI, 900 notes of Hemiennealimmal temperament, or somewhere in between. Pull that "familiar = good" stick out of your anus and do something //new//. Smack the world in the face with something they've never heard before, and at the very least you'll attract a handful of people who will enthusiastically beg for more. If you're good at it, you might even make an international name for yourself among the underground microtonal scene, and if you're REALLY good at it (and/or really LUCKY) you might actually break out of the sub-culture and find your way into the public-at-large.</pre></div>

The truth is, anyone not actively seeking out microtonal music will either not be able to hear the difference, or if they can hear it, they won't like it (unless it's "ethnically correct" microtonal music, like Indian or Arabic music). The only people looking for music in some variety of meantone or 12-tone well-temperaments are looking for the words "historically informed performance", aka the "authentic" or "early" music crowd. Those who //are// actively seeking out music that is called "microtonal" couldn't care //less// about smoother and more in-tune harmonies following the same familiar patterns. As Brian McLaren once said, "they are not shrinking violets". They want stuff that will make their brain do happy back-flips, stuff that will turn their ears inside-out. There are many ways to accomplish this, and they do not all involve chucking 5-limit harmony out the window (in fact, some of the best ways are completely //centered// on 5-limit harmony in some way or another), but the point is that if you pussy-foot around microtonality mumbling quietly about how it's "just like 12-TET, but more in tune", absolutely NO ONE will take you seriously. Not average listeners, not microtonal enthusiasts, not your fellow microtonal musicians, and most //certainly// not the average Guitar Center customer or university music student. The only way to make it as a microtonalist in this world is to go for broke, whether that means 13-EDO, 13-limit JI, 900 notes of Hemiennealimmal temperament, or somewhere in between. Pull that "familiar = good" stick out of your anus and do something //new//. Smack the world in the face with something they've never heard before, and at the very least you'll attract a handful of people who will enthusiastically beg for more. If you're good at it, you might even make an international name for yourself among the underground microtonal scene, and if you're REALLY good at it (and/or really LUCKY) you might actually break out of the sub-culture and find your way into the public-at-large.

**Myths and Facts about Xenharmonics by mclaren**

**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."

In 1963, a physicist published several articles in the then-new Journal of Music Theory examining the intervals actually performed by symphony musicians in real performances. 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."

This research has been confirmed by many subsequent listening experiments. Psychouacousticians 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, 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).

Moreover, in 1983, 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 perferred 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.

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. 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 "Variability of judgments of musical intervals," Journal of Experimental Psychology, Vol. 9, pp. 492-500, 1926,

Moran, H., & Pratt, C.C., 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 extend by many subsequent listening tests.

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 roughy 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 tunings like 7 and 14 equal, with 685.4-cent perfect fifths. Ivor in particular boosted 14 equal because of its unfamiliarity combined with 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 thta 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 systemtically //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 will 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//, 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 compositions 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 1947, "The conclusions of mathematicians and acousticians are systematically at variance with the practice of musicians." 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.

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.

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 Fletch back in the 1920s and early 1930s that our perception of the pitch of a sound tends to rise with its amplitude, and a louder sound in the mid-high range can be as much as a minor third higher, depending on its loudness. In the second case, see the well -known 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. This is the psychoacoustic basis of the RIAA equalization curve used on LPs.)

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 failure of mathematically-based methods of musical organization, like total serialism, which failed to take the characteristics of the human cognitive system and the human auditory system into account, also converges on 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.

The evidence 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. We must try things out, make observations, and then compare our observations 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.

Pournelle's Iron Law of Bureacracy 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 excel in the kind of bureaucratic infighting which advances themselves and gains them publicity and renown. And Pournelle's Law states that the second group will always tend to take power.

This applies to the internet and to academic 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 places like 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.

Consequenly, 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.

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 thick 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 publishers. Meanwhile, the books on microtonality which do get published (viz., Harry Partch's //Genesis of a Music//) contain 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 practictitioners, 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 are now completely vanished, never to be heard of again, in contemporary music transient fashions like The New Complexity and 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 to 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 completely opposite the 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 sylindrical tube has only one degree of freedom--it can only move foward or back in one dimension).

This means that **//essentially all vibrating objects produce natural resonant mode 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, as a non-just non-equal-tempered set of inharmonic vibrational modes. Essentially all objects in the circumabient 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.

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.

One-dimensional vibrational systems do not appear in nature. They are not natural, and objects like stretched strings or perfectly cylindrical hollow tubes must be produced artificially. This means that just intontion 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, translation plus commentary on Hermann Helmholtz's //On the Sensations of Tone//). 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.</pre></div>

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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>misconceptions about xenharmony</title></head><body><h1 id="toc0"><a name="Igliashon's &quot;Four Misconceptions About Xenharmony and Microtonality&quot;"></a>Igliashon's &quot;Four Misconceptions About Xenharmony and Microtonality&quot;</h1>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>misconceptions about xenharmony</title></head><body><h1 id="toc0"><a name="Igliashon's &quot;Four Misconceptions About Xenharmony and Microtonality&quot; (and some further myths and facts about xenharmonics by mclaren)"></a>Igliashon's &quot;Four Misconceptions About Xenharmony and Microtonality&quot; (and some further myths and facts about xenharmonics by mclaren)</h1>

This page expresses the views of <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a>, and may not be representative of the xenharmonic community in general. In fact, most of what follows is in direct contradiction with much of what has been written about microtonality, as well as much of what is considered &quot;common sense&quot; in many parts of the community...which is, in fact, the reason the author felt compelled to bring this page into existence.

<h2 id="toc1"><a name="Igliashon's &quot;Four Misconceptions About Xenharmony and Microtonality&quot;-Misconception 1: &quot;More is More&quot;"></a>Misconception 1: &quot;More is More&quot;</h2>

<h2 id="toc1"><a name="Igliashon's &quot;Four Misconceptions About Xenharmony and Microtonality&quot; (and some further myths and facts about xenharmonics by mclaren)-Misconception 1: &quot;More is More&quot;"></a>Misconception 1: &quot;More is More&quot;</h2>

When you begin in microtonality, usually the first thing that happens is you discover there's a huge variety of potential new consonant intervals, which are not represented in 12-TET. It's only natural to want to try out all these new intervals, but it's a mistake to begin with a humongous tuning system that approximates as many of these new intervals as possible. If you're accustomed to (and proficient in) 12-TET, you are going to have a mental melt-down if you go straight for something like 31-EDO or 41-EDO or triple-BP or something. The sheer variety of new possibilities will short-circuit your brain. The truth is that nothing you have learned in 12-TET has prepared you to juggle such a plethora of new harmonic possibilities, and you will probably try to do a million things at once--and this will sound terrible, and you will be disappointed, and you will probably lay your shiny new microtonal instrument aside and go back to what's familiar. It is better to begin small--absolutely no more than 24 notes if an equal temperament, and definitely no more than 12 if JI (since JI is so drastically different than equal temperament). You can always expand later, and you will find the novel sounds of smaller systems more accessible and more rewarding. I speak from experience, as someone who did begin immediately in 31-EDO, and have been retreating to smaller and smaller EDOs ever since, lamenting the loss of thousands of dollars and countless hours to tuning systems that looked good on paper but were disappointing and confusing to work with. If I could do it all over again, I would start at 13-EDO or 14-EDO and not read a word of theory until thoroughly accustomed to a single new system, and I've seen too many others make the same mistakes I have. Nobody in this century who has begun with 31-EDO has been satisfied enough with it to stop their exploration right there; they either move on to JI, or down to the smaller EDOs, or up to the more accurate temperaments (41, 53, 72, etc.)...or they give up on microtonality all together.

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It's also true that a JI system can produce a drastically larger palette of intervals than an equally-sized equal temperament. If you are hell-bent on exploring all the intervals within the 15-limit tonality diamond, do not pass go, do not collect $200, do not touch 31-EDO, but go straight to the harmonic series, specifically the scale of harmonics 8-16. In one 8-note octave-repeating scale, you will find all the intervals in the 15-limit tonality diamond (which is A LOT of intervals), although most only occur at one place in the scale. You should absolutely become fluent with the sound of these intervals in this scale before you consider trying out a temperament based on them. Then bump it up to harmonics 16-32 to see what some of the even more exotic identities feel like. Then, and only then, are you ready to start looking at high-limit temperaments.

<h2 id="toc2"><a name="Igliashon's &quot;Four Misconceptions About Xenharmony and Microtonality&quot;-Misconception 2: &quot;Consonance is Rare and Therefore Important&quot;"></a>Misconception 2: &quot;Consonance is Rare and Therefore Important&quot;</h2>

<h2 id="toc2"><a name="Igliashon's &quot;Four Misconceptions About Xenharmony and Microtonality&quot; (and some further myths and facts about xenharmonics by mclaren)-Misconception 2: &quot;Consonance is Rare and Therefore Important&quot;"></a>Misconception 2: &quot;Consonance is Rare and Therefore Important&quot;</h2>

Consonance is not rare at all. In fact it is omnipresent. It is only specifically well-tuned 5-limit consonance that is rare, and tunings that offer good approximations of the full 13-limit are very rare, but neither the 5-limit nor the full 13-limit are necessary for consonance. Almost every EDO approximates some consonant subgroup of Just Intonation with the same or greater level of accuracy that 12-TET has in the 5-limit. With a little care, all of these EDOs can be made to sound nice enough for the general public. Yes, even 10, 11, 13, and 14-EDO. In fact, even 8-EDO does a fairly passable approximation of harmonics 10:11:12:13:14 as 0-150-300-450-600 cents; it's not great, but it's awesome for such a tiny EDO--no interval is off by more than 18 cents, which is more or less as good as 12-TET.

Consonance is not rare at all. In fact it is omnipresent. It is only specifically well-tuned 5-limit consonance that is rare, and tunings that offer good approximations of the full 13-limit are very rare, but neither the 5-limit nor the full 13-limit are necessary for consonance. Almost every EDO approximates some consonant subgroup of Just Intonation with the same or greater level of accuracy that 12-TET has in the 5-limit. With a little care, all of these EDOs can be made to sound nice enough for the general public. Yes, even 10, 11, 13, and 14-EDO. In fact, even 8-EDO does a fairly passable approximation of harmonics 10:11:12:13:14 as 0-150-300-450-600 cents; it's not great, but it's awesome for such a tiny EDO--no interval is off by more than 18 cents, which is more or less as good as 12-TET.

No, consonance is ubiquitous, practically inescapable unless you insist on using ridiculous scales like 0-10-20-30-40-50-1200 cents. The strength and quality of consonance may vary from tuning to tuning, but there is always enough to serve effectively as contrast to the equally-ubiquitous dissonance, if only you take the time to understand what the contrast is and how to deal with it appropriately. Sometimes the most consonant harmonies look nothing like major and minor chords in 12-TET, so they can take some searching. But they are always there to be found if you know how to look.

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I will grant that there are some people whose ears are so sensitive to the mildest bit of beating or roughness that nothing short of JI or an insanely-accurate microtemperament will do; however, a quick survey of what passes for &quot;well-received&quot; microtonal music reveals that in truth, such obsessiveness about intonation is rare in the general populace.

<h2 id="toc3"><a name="Igliashon's &quot;Four Misconceptions About Xenharmony and Microtonality&quot;-Misconception 3: &quot;Tunings Related to the Familiar are Easier to Learn&quot;"></a>Misconception 3: &quot;Tunings Related to the Familiar are Easier to Learn&quot;</h2>

<h2 id="toc3"><a name="Igliashon's &quot;Four Misconceptions About Xenharmony and Microtonality&quot; (and some further myths and facts about xenharmonics by mclaren)-Misconception 3: &quot;Tunings Related to the Familiar are Easier to Learn&quot;"></a>Misconception 3: &quot;Tunings Related to the Familiar are Easier to Learn&quot;</h2>

Tunings related to the familiar, like 17, 19, 22, 26, 27, 29, and 31-EDO, are easy to learn--if what you want to learn is how to make familiar-sounding music! These tuning all support many of the same patterns and relationships that work in 12-TET, so at first blush it is dead-simple to apply those same patterns and make nice-sounding music. The problem is that this music will not sound a whole lot different than what you're used to. If you want to make music that doesn't just sound like a mild retuning of the same old diatonic cliches, these systems are all a greater challenge than less-familiar ones, because the strong pull of the familiar is difficult to escape from. If you are a guitarist, you will probably tune the open strings of a 19-tone guitar to something nearly identical to 12-TET standard, i.e. EADGBE. This means that all your old habits translate perfectly, and you can comfortably stay in the same muscle-memory ruts you've been digging into for years. Power chords, the minor pentatonic, the major scale, I-IV-V progressions...all of these work just the same. On the other hand, if you want to explore the less-familiar scales and temperaments supported by 19, you will find that none of them fits on the instrument as simply and intuitively as the familiar diatonic stuff. In fact, many of them are a headache to learn and will make you feel like you're 12 years old again picking up the guitar for the first time. And to be honest, they won't sound as good when you play them, because you won't be very good at playing them, and because (let's face it) those familiar chords are sweeter in sound than the new ones. So you will probably go back to writing familiar-sounding stuff, because it's more fun and sounds better--in other words, the instrument will reward you for staying in your rut and punish you for trying to break it.

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Compare this to picking up a 13-tone guitar. Everything is upside down and backwards from the word &quot;go&quot;; your B string is now tuned almost a tritone above the G, rather than a major 3rd above it as usual. Two fourths now yields a wide major 6th, and three yields a flat major 9th. Familiar chord-shapes and scale-patterns don't work at all, so you can't and won't use them. You also have lots of new dissonances showing up where there used to be consonances, and vice-versa, and because of this you will get excellent and immediate &quot;feedback&quot; from the instrument as you try out new patterns. When you find a new consonant pattern, that sets off a &quot;reward&quot; response in your brain, as all of a sudden this dissonant and foreign new tuning favors you with a bit of sweetness. Your old habits will wither and die very quickly, and new patterns will all but force themselves upon you--even if you have no &quot;theoretical&quot; idea of what you're supposed to be trying to do!--and this is the precise definition of &quot;easy to learn&quot;.

<h2 id="toc4"><a name="Igliashon's &quot;Four Misconceptions About Xenharmony and Microtonality&quot;-Misconception 4: &quot;Tunings Related to the Familiar are More Appealing to the 'Average' Listener&quot;"></a>Misconception 4: &quot;Tunings Related to the Familiar are More Appealing to the 'Average' Listener&quot;</h2>

<h2 id="toc4"><a name="Igliashon's &quot;Four Misconceptions About Xenharmony and Microtonality&quot; (and some further myths and facts about xenharmonics by mclaren)-Misconception 4: &quot;Tunings Related to the Familiar are More Appealing to the 'Average' Listener&quot;"></a>Misconception 4: &quot;Tunings Related to the Familiar are More Appealing to the 'Average' Listener&quot;</h2>

You know what tuning is the most related to the familiar? 12-TET! I don't care what the psychoacousticians say, the vast majority of people accustomed to 12-TET will prefer the sound of 12-TET to tunings which approximate the same harmonies but in &quot;better&quot; tune. They will think the Just major third sounds flat and dull, they will think the semitones are too wide or the minor third is too sharp or the dominant 7th isn't tense enough to create an effective resolution. You don't need to take my word for it, go forth and test this! Play people two versions of a familiar piece of music (preferably NOT rendered using your PC's built-in general MIDI sound set), but don't tell them which is which, and ask them to rate which one they like best. I've done it, and I know what the answers are.

The truth is, anyone not actively seeking out microtonal music will either not be able to hear the difference, or if they can hear it, they won't like it (unless it's &quot;ethnically correct&quot; microtonal music, like Indian or Arabic music). The only people looking for music in some variety of meantone or 12-tone well-temperaments are looking for the words &quot;historically informed performance&quot;, aka the &quot;authentic&quot; or &quot;early&quot; music crowd. Those who are actively seeking out music that is called &quot;microtonal&quot; couldn't care less about smoother and more in-tune harmonies following the same familiar patterns. As Brian McLaren once said, &quot;they are not shrinking violets&quot;. They want stuff that will make their brain do happy back-flips, stuff that will turn their ears inside-out. There are many ways to accomplish this, and they do not all involve chucking 5-limit harmony out the window (in fact, some of the best ways are completely centered on 5-limit harmony in some way or another), but the point is that if you pussy-foot around microtonality mumbling quietly about how it's &quot;just like 12-TET, but more in tune&quot;, absolutely NO ONE will take you seriously. Not average listeners, not microtonal enthusiasts, not your fellow microtonal musicians, and most certainly not the average Guitar Center customer or university music student. The only way to make it as a microtonalist in this world is to go for broke, whether that means 13-EDO, 13-limit JI, 900 notes of Hemiennealimmal temperament, or somewhere in between. Pull that &quot;familiar = good&quot; stick out of your anus and do something new. Smack the world in the face with something they've never heard before, and at the very least you'll attract a handful of people who will enthusiastically beg for more. If you're good at it, you might even make an international name for yourself among the underground microtonal scene, and if you're REALLY good at it (and/or really LUCKY) you might actually break out of the sub-culture and find your way into the public-at-large.</body></html></pre></div>

The truth is, anyone not actively seeking out microtonal music will either not be able to hear the difference, or if they can hear it, they won't like it (unless it's &quot;ethnically correct&quot; microtonal music, like Indian or Arabic music). The only people looking for music in some variety of meantone or 12-tone well-temperaments are looking for the words &quot;historically informed performance&quot;, aka the &quot;authentic&quot; or &quot;early&quot; music crowd. Those who are actively seeking out music that is called &quot;microtonal&quot; couldn't care less about smoother and more in-tune harmonies following the same familiar patterns. As Brian McLaren once said, &quot;they are not shrinking violets&quot;. They want stuff that will make their brain do happy back-flips, stuff that will turn their ears inside-out. There are many ways to accomplish this, and they do not all involve chucking 5-limit harmony out the window (in fact, some of the best ways are completely centered on 5-limit harmony in some way or another), but the point is that if you pussy-foot around microtonality mumbling quietly about how it's &quot;just like 12-TET, but more in tune&quot;, absolutely NO ONE will take you seriously. Not average listeners, not microtonal enthusiasts, not your fellow microtonal musicians, and most certainly not the average Guitar Center customer or university music student. The only way to make it as a microtonalist in this world is to go for broke, whether that means 13-EDO, 13-limit JI, 900 notes of Hemiennealimmal temperament, or somewhere in between. Pull that &quot;familiar = good&quot; stick out of your anus and do something new. Smack the world in the face with something they've never heard before, and at the very least you'll attract a handful of people who will enthusiastically beg for more. If you're good at it, you might even make an international name for yourself among the underground microtonal scene, and if you're REALLY good at it (and/or really LUCKY) you might actually break out of the sub-culture and find your way into the public-at-large.

Myths and Facts about Xenharmonics by mclaren

Myth #1: &quot;Everyone prefers the natural intervals of the pure perfect harmonic series.&quot; 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;

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;

In 1963, a physicist published several articles in the then-new Journal of Music Theory examining the intervals actually performed by symphony musicians in real performances. 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;

This research has been confirmed by many subsequent listening experiments. Psychouacousticians 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, 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).

Moreover, in 1983, 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 perferred 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.

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;

Myth #2: &quot;The small integer ratios like 3/2 and 5/4 are the original intervals from which all other musical intervals are derived.&quot; Kyle Gann teaches this provably false claim in his course on microtonality. 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;

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.

In &quot;Variability of judgments of musical intervals,&quot; Journal of Experimental Psychology, Vol. 9, pp. 492-500, 1926,

Moran, H., &amp; Pratt, C.C., 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 extend by many subsequent listening tests.

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 roughy 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 tunings like 7 and 14 equal, with 685.4-cent perfect fifths. Ivor in particular boosted 14 equal because of its unfamiliarity combined with memorable and impressive musical &quot;mood.&quot;

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 thta 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 systemtically avoid the intervals of the harmonic series.&quot; (Wilson, E., personal communication).

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; 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 will 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: &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; 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 Music By Computer, ed., C. Beauchamp, 1969, and as was further developed by composers like James Dashow and William Sethares (see Sethares' book Timbre, Tuning, Spectrum, Scale,&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.

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 compositions 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: &quot;Mathematics forms the basis of music, and therefore mathematical music theory must guide us when we create new tunings.&quot; As Paul Hindemith noted in 1947, &quot;The conclusions of mathematicians and acousticians are systematically at variance with the practice of musicians.&quot; 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.

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.

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 Fletch back in the 1920s and early 1930s that our perception of the pitch of a sound tends to rise with its amplitude, and a louder sound in the mid-high range can be as much as a minor third higher, depending on its loudness. In the second case, see the well -known 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. This is the psychoacoustic basis of the RIAA equalization curve used on LPs.)

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 imagine the sound or mood or a new tuning. You have to hear it. Only then can you imagine it.&quot;

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

&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; -- Ivor Darreg, personal communication.

The evidence 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. We must try things out, make observations, and then compare our observations with our mental models in order to gain useful knowledge.

Myth #5: &quot;Microtonality produces great theory and bad music.&quot; -- 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.

Pournelle's Iron Law of Bureacracy 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 excel in the kind of bureaucratic infighting which advances themselves and gains them publicity and renown. And Pournelle's Law states that the second group will always tend to take power.

This applies to the internet and to academic 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 places like 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.

Consequenly, 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.

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 thick 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 publishers. Meanwhile, the books on microtonality which do get published (viz., Harry Partch's Genesis of a Music) contain 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 practictitioners, 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 are now completely vanished, never to be heard of again, in contemporary music transient fashions like The New Complexity and 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 to work that stands the test of time was famous when originally produced. But sometimes not.)

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;

This claim is so completely opposite the 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 sylindrical tube has only one degree of freedom--it can only move foward or back in one dimension).

This means that essentially all vibrating objects produce natural resonant mode 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 &quot;the chord of nature,&quot; if there is any such thing, as a non-just non-equal-tempered set of inharmonic vibrational modes. Essentially all objects in the circumabient 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.

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.

One-dimensional vibrational systems do not appear in nature. They are not natural, and objects like stretched strings or perfectly cylindrical hollow tubes must be produced artificially. This means that just intontion 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 &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, translation plus commentary on Hermann Helmholtz's On the Sensations of Tone). 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.</body></html></pre></div>

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-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Igliashon's "Four Misconceptions About Xenharmony and Microtonality"=
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Igliashon's "Four Misconceptions About Xenharmony and Microtonality" (and some further myths and facts about xenharmonics by mclaren)=
 This page expresses the views of [[IgliashonJones|Igliashon Jones]], and may not be representative of the xenharmonic community in general. In fact, most of what follows is in direct contradiction with much of what has been written about microtonality, as well as much of what is considered "common sense" in many parts of the community...which is, in fact, the reason the author felt compelled to bring this page into existence.
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 ==Misconception 2: "Consonance is Rare and Therefore Important"==
 Consonance is //not// rare at all. In fact it is omnipresent. It is only specifically well-tuned 5-limit consonance that is rare, and tunings that offer good approximations of the full 13-limit are very rare, but neither the 5-limit nor the full 13-limit are necessary for consonance. Almost every EDO approximates some consonant subgroup of Just Intonation with the same or greater level of accuracy that 12-TET has in the 5-limit. With a little care, all of these EDOs can be made to sound nice enough for the general public. Yes, even 10, 11, 13, and 14-EDO. In fact, even 8-EDO does a fairly passable approximation of harmonics 10:11:12:13:14 as 0-150-300-450-600 cents; it's not //great//, but it's //awesome// for such a tiny EDO--no interval is off by more than 18 cents, which is more or less as good as 12-TET.
 No, consonance is ubiquitous, practically inescapable unless you insist on using ridiculous scales like 0-10-20-30-40-50-1200 cents. The strength and quality of consonance may vary from tuning to tuning, but there is //always// enough to serve effectively as contrast to the equally-ubiquitous dissonance, if only you take the time to understand what the contrast is and how to deal with it appropriately. Sometimes the most consonant harmonies look nothing like major and minor chords in 12-TET, so they can take some searching. But they are //always// there to be found if you know how to look.
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 You know what tuning is the //most// related to the familiar? 12-TET! I don't care what the psychoacousticians say, the vast majority of people accustomed to 12-TET will prefer the sound of 12-TET to tunings which approximate the same harmonies but in "better" tune. They will think the Just major third sounds flat and dull, they will think the semitones are too wide or the minor third is too sharp or the dominant 7th isn't tense enough to create an effective resolution. You don't need to take my word for it, go forth and test this! Play people two versions of a familiar piece of music (preferably NOT rendered using your PC's built-in general MIDI sound set), but don't tell them which is which, and ask them to rate which one they like best. I've done it, and I know what the answers are.
-The truth is, anyone not actively seeking out microtonal music will either not be able to hear the difference, or if they can hear it, they won't like it (unless it's "ethnically correct" microtonal music, like Indian or Arabic music). The only people looking for music in some variety of meantone or 12-tone well-temperaments are looking for the words "historically informed performance", aka the "authentic" or "early" music crowd. Those who //are// actively seeking out music that is called "microtonal" couldn't care //less// about smoother and more in-tune harmonies following the same familiar patterns. As Brian McLaren once said, "they are not shrinking violets". They want stuff that will make their brain do happy back-flips, stuff that will turn their ears inside-out. There are many ways to accomplish this, and they do not all involve chucking 5-limit harmony out the window (in fact, some of the best ways are completely //centered// on 5-limit harmony in some way or another), but the point is that if you pussy-foot around microtonality mumbling quietly about how it's "just like 12-TET, but more in tune", absolutely NO ONE will take you seriously. Not average listeners, not microtonal enthusiasts, not your fellow microtonal musicians, and most //certainly// not the average Guitar Center customer or university music student. The only way to make it as a microtonalist in this world is to go for broke, whether that means 13-EDO, 13-limit JI, 900 notes of Hemiennealimmal temperament, or somewhere in between. Pull that "familiar = good" stick out of your anus and do something //new//. Smack the world in the face with something they've never heard before, and at the very least you'll attract a handful of people who will enthusiastically beg for more. If you're good at it, you might even make an international name for yourself among the underground microtonal scene, and if you're REALLY good at it (and/or really LUCKY) you might actually break out of the sub-culture and find your way into the public-at-large.</pre></div>
+The truth is, anyone not actively seeking out microtonal music will either not be able to hear the difference, or if they can hear it, they won't like it (unless it's "ethnically correct" microtonal music, like Indian or Arabic music). The only people looking for music in some variety of meantone or 12-tone well-temperaments are looking for the words "historically informed performance", aka the "authentic" or "early" music crowd. Those who //are// actively seeking out music that is called "microtonal" couldn't care //less// about smoother and more in-tune harmonies following the same familiar patterns. As Brian McLaren once said, "they are not shrinking violets". They want stuff that will make their brain do happy back-flips, stuff that will turn their ears inside-out. There are many ways to accomplish this, and they do not all involve chucking 5-limit harmony out the window (in fact, some of the best ways are completely //centered// on 5-limit harmony in some way or another), but the point is that if you pussy-foot around microtonality mumbling quietly about how it's "just like 12-TET, but more in tune", absolutely NO ONE will take you seriously. Not average listeners, not microtonal enthusiasts, not your fellow microtonal musicians, and most //certainly// not the average Guitar Center customer or university music student. The only way to make it as a microtonalist in this world is to go for broke, whether that means 13-EDO, 13-limit JI, 900 notes of Hemiennealimmal temperament, or somewhere in between. Pull that "familiar = good" stick out of your anus and do something //new//. Smack the world in the face with something they've never heard before, and at the very least you'll attract a handful of people who will enthusiastically beg for more. If you're good at it, you might even make an international name for yourself among the underground microtonal scene, and if you're REALLY good at it (and/or really LUCKY) you might actually break out of the sub-culture and find your way into the public-at-large.
+**Myths and Facts about Xenharmonics by mclaren**
+**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."
+In 1963, a physicist published several articles in the then-new Journal of Music Theory examining the intervals actually performed by symphony musicians in real performances. 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."
+This research has been confirmed by many subsequent listening experiments. Psychouacousticians 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, 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).
+Moreover, in 1983, 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 perferred 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.
+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. 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 &lt;span class="st"&gt; "Variability of judgments of musical intervals," Journal of Experimental Psychology, Vol. 9, pp. 492-500, 1926, &lt;/span&gt;
+&lt;span class="st"&gt;Moran, H., &amp; Pratt, C.C., 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 extend by many subsequent listening tests.&lt;/span&gt;
+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 roughy 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 tunings like 7 and 14 equal, with 685.4-cent perfect fifths. Ivor in particular boosted 14 equal because of its unfamiliarity combined with 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 thta 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 systemtically //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 will 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//, 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 compositions 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 1947, "The conclusions of mathematicians and acousticians are systematically at variance with the practice of musicians." 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.
+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.
+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 Fletch back in the 1920s and early 1930s that our perception of the pitch of a sound tends to rise with its amplitude, and a louder sound in the mid-high range can be as much as a minor third higher, depending on its loudness. In the second case, see the well -known 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. This is the psychoacoustic basis of the RIAA equalization curve used on LPs.)
+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 failure of mathematically-based methods of musical organization, like total serialism, which failed to take the characteristics of the human cognitive system and the human auditory system into account, also converges on 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.
+The evidence 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. We must try things out, make observations, and then compare our observations 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.
+Pournelle's Iron Law of Bureacracy 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 excel in the kind of bureaucratic infighting which advances themselves and gains them publicity and renown. And Pournelle's Law states that the second group will always tend to take power.
+This applies to the internet and to academic 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 places like 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.
+Consequenly, 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.
+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 thick 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 publishers. Meanwhile, the books on microtonality which do get published (viz., Harry Partch's //Genesis of a Music//) contain 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 practictitioners, 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 are now completely vanished, never to be heard of again, in contemporary music transient fashions like The New Complexity and 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 to 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 completely opposite the 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 sylindrical tube has only one degree of freedom--it can only move foward or back in one dimension).
+This means that **//essentially all vibrating objects produce natural resonant mode 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, as a non-just non-equal-tempered set of inharmonic vibrational modes. Essentially all objects in the circumabient 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.
+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.
+One-dimensional vibrational systems do not appear in nature. They are not natural, and objects like stretched strings or perfectly cylindrical hollow tubes must be produced artificially. This means that just intontion 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, translation plus commentary on Hermann Helmholtz's //On the Sensations of Tone//). 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.</pre></div>
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 This page expresses the views of &lt;a class="wiki_link" href="/IgliashonJones"&gt;Igliashon Jones&lt;/a&gt;, and may not be representative of the xenharmonic community in general. In fact, most of what follows is in direct contradiction with much of what has been written about microtonality, as well as much of what is considered &amp;quot;common sense&amp;quot; in many parts of the community...which is, in fact, the reason the author felt compelled to bring this page into existence.&lt;br /&gt;
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+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Igliashon's &amp;quot;Four Misconceptions About Xenharmony and Microtonality&amp;quot; (and some further myths and facts about xenharmonics by mclaren)-Misconception 1: &amp;quot;More is More&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Misconception 1: &amp;quot;More is More&amp;quot;&lt;/h2&gt;
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 When you begin in microtonality, usually the first thing that happens is you discover there's a huge variety of potential new consonant intervals, which are not represented in 12-TET. It's only natural to want to try out all these new intervals, but it's a mistake to begin with a humongous tuning system that approximates as many of these new intervals as possible. If you're accustomed to (and proficient in) 12-TET, you are going to have a mental melt-down if you go straight for something like 31-EDO or 41-EDO or triple-BP or something. The sheer variety of new possibilities will short-circuit your brain. The truth is that nothing you have learned in 12-TET has prepared you to juggle such a plethora of new harmonic possibilities, and you will probably try to do a million things at once--and this will sound terrible, and you will be disappointed, and you will probably lay your shiny new microtonal instrument aside and go back to what's familiar. It is better to begin small--absolutely no more than 24 notes if an equal temperament, and definitely no more than 12 if JI (since JI is so drastically different than equal temperament). You can always expand later, and you will find the novel sounds of smaller systems more accessible and more rewarding. I speak from experience, as someone who did begin immediately in 31-EDO, and have been retreating to smaller and smaller EDOs ever since, lamenting the loss of thousands of dollars and countless hours to tuning systems that looked good on paper but were disappointing and confusing to work with. If I could do it all over again, I would start at 13-EDO or 14-EDO and not read a word of theory until thoroughly accustomed to a single new system, and I've seen too many others make the same mistakes I have. Nobody in this century who has begun with 31-EDO has been satisfied enough with it to stop their exploration right there; they either move on to JI, or down to the smaller EDOs, or up to the more accurate temperaments (41, 53, 72, etc.)...or they give up on microtonality all together.&lt;br /&gt;
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 It's also true that a JI system can produce a drastically larger palette of intervals than an equally-sized equal temperament. If you are hell-bent on exploring all the intervals within the 15-limit tonality diamond, do not pass go, do not collect $200, do not touch 31-EDO, but go straight to the harmonic series, specifically the scale of harmonics 8-16. In one 8-note octave-repeating scale, you will find all the intervals in the 15-limit tonality diamond (which is A LOT of intervals), although most only occur at one place in the scale. You should absolutely become fluent with the sound of these intervals in this scale before you consider trying out a temperament based on them. Then bump it up to harmonics 16-32 to see what some of the even more exotic identities feel like. Then, and &lt;em&gt;only&lt;/em&gt; then, are you ready to start looking at high-limit temperaments.&lt;br /&gt;
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-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Igliashon's &amp;quot;Four Misconceptions About Xenharmony and Microtonality&amp;quot;-Misconception 2: &amp;quot;Consonance is Rare and Therefore Important&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Misconception 2: &amp;quot;Consonance is Rare and Therefore Important&amp;quot;&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Igliashon's &amp;quot;Four Misconceptions About Xenharmony and Microtonality&amp;quot; (and some further myths and facts about xenharmonics by mclaren)-Misconception 2: &amp;quot;Consonance is Rare and Therefore Important&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Misconception 2: &amp;quot;Consonance is Rare and Therefore Important&amp;quot;&lt;/h2&gt;
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-Consonance is &lt;em&gt;not&lt;/em&gt; rare at all. In fact it is omnipresent. It is only specifically well-tuned 5-limit consonance that is rare, and tunings that offer good approximations of the full 13-limit are very rare, but neither the 5-limit nor the full 13-limit are necessary for consonance. Almost every EDO approximates some consonant subgroup of Just Intonation with the same or greater level of accuracy that 12-TET has in the 5-limit. With a little care, all of these EDOs can be made to sound nice enough for the general public. Yes, even 10, 11, 13, and 14-EDO. In fact, even 8-EDO does a fairly passable approximation of harmonics 10:11:12:13:14 as 0-150-300-450-600 cents; it's not &lt;em&gt;great&lt;/em&gt;, but it's &lt;em&gt;awesome&lt;/em&gt; for such a tiny EDO--no interval is off by more than 18 cents, which is more or less as good as 12-TET. &lt;br /&gt;
+Consonance is &lt;em&gt;not&lt;/em&gt; rare at all. In fact it is omnipresent. It is only specifically well-tuned 5-limit consonance that is rare, and tunings that offer good approximations of the full 13-limit are very rare, but neither the 5-limit nor the full 13-limit are necessary for consonance. Almost every EDO approximates some consonant subgroup of Just Intonation with the same or greater level of accuracy that 12-TET has in the 5-limit. With a little care, all of these EDOs can be made to sound nice enough for the general public. Yes, even 10, 11, 13, and 14-EDO. In fact, even 8-EDO does a fairly passable approximation of harmonics 10:11:12:13:14 as 0-150-300-450-600 cents; it's not &lt;em&gt;great&lt;/em&gt;, but it's &lt;em&gt;awesome&lt;/em&gt; for such a tiny EDO--no interval is off by more than 18 cents, which is more or less as good as 12-TET.&lt;br /&gt;
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 No, consonance is ubiquitous, practically inescapable unless you insist on using ridiculous scales like 0-10-20-30-40-50-1200 cents. The strength and quality of consonance may vary from tuning to tuning, but there is &lt;em&gt;always&lt;/em&gt; enough to serve effectively as contrast to the equally-ubiquitous dissonance, if only you take the time to understand what the contrast is and how to deal with it appropriately. Sometimes the most consonant harmonies look nothing like major and minor chords in 12-TET, so they can take some searching. But they are &lt;em&gt;always&lt;/em&gt; there to be found if you know how to look.&lt;br /&gt;
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 I will grant that there are some people whose ears are so sensitive to the mildest bit of beating or roughness that nothing short of JI or an insanely-accurate microtemperament will do; however, a quick survey of what passes for &amp;quot;well-received&amp;quot; microtonal music reveals that in truth, such obsessiveness about intonation is rare in the general populace.&lt;br /&gt;
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-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Igliashon's &amp;quot;Four Misconceptions About Xenharmony and Microtonality&amp;quot;-Misconception 3: &amp;quot;Tunings Related to the Familiar are Easier to Learn&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Misconception 3: &amp;quot;Tunings Related to the Familiar are Easier to Learn&amp;quot;&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Igliashon's &amp;quot;Four Misconceptions About Xenharmony and Microtonality&amp;quot; (and some further myths and facts about xenharmonics by mclaren)-Misconception 3: &amp;quot;Tunings Related to the Familiar are Easier to Learn&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Misconception 3: &amp;quot;Tunings Related to the Familiar are Easier to Learn&amp;quot;&lt;/h2&gt;
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 Tunings related to the familiar, like 17, 19, 22, 26, 27, 29, and 31-EDO, are easy to learn--if what you want to learn is how to make familiar-sounding music! These tuning all support many of the same patterns and relationships that work in 12-TET, so at first blush it is dead-simple to apply those same patterns and make nice-sounding music. The problem is that this music will not sound a whole lot different than what you're used to. If you want to make music that doesn't just sound like a mild retuning of the same old diatonic cliches, these systems are all a greater challenge than less-familiar ones, because the strong pull of the familiar is difficult to escape from. If you are a guitarist, you will probably tune the open strings of a 19-tone guitar to something nearly identical to 12-TET standard, i.e. EADGBE. This means that all your old habits translate perfectly, and you can comfortably stay in the same muscle-memory ruts you've been digging into for years. Power chords, the minor pentatonic, the major scale, I-IV-V progressions...all of these work just the same. On the other hand, if you want to explore the less-familiar scales and temperaments supported by 19, you will find that none of them fits on the instrument as simply and intuitively as the familiar diatonic stuff. In fact, many of them are a headache to learn and will make you feel like you're 12 years old again picking up the guitar for the first time. And to be honest, they won't sound as good when you play them, because you won't be very good at playing them, and because (let's face it) those familiar chords are sweeter in sound than the new ones. So you will probably go back to writing familiar-sounding stuff, because it's more fun and sounds better--in other words, the instrument will reward you for staying in your rut and punish you for trying to break it.&lt;br /&gt;
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 Compare this to picking up a 13-tone guitar. Everything is upside down and backwards from the word &amp;quot;go&amp;quot;; your B string is now tuned almost a tritone above the G, rather than a major 3rd above it as usual. Two fourths now yields a wide major 6th, and three yields a flat major 9th. Familiar chord-shapes and scale-patterns don't work at all, so you can't and won't use them. You also have lots of new dissonances showing up where there used to be consonances, and vice-versa, and because of this you will get excellent and immediate &amp;quot;feedback&amp;quot; from the instrument as you try out new patterns. When you find a new consonant pattern, that sets off a &amp;quot;reward&amp;quot; response in your brain, as all of a sudden this dissonant and foreign new tuning favors you with a bit of sweetness. Your old habits will wither and die very quickly, and new patterns will all but force themselves upon you--even if you have no &amp;quot;theoretical&amp;quot; idea of what you're supposed to be trying to do!--and this is the precise definition of &amp;quot;easy to learn&amp;quot;.&lt;br /&gt;
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-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Igliashon's &amp;quot;Four Misconceptions About Xenharmony and Microtonality&amp;quot;-Misconception 4: &amp;quot;Tunings Related to the Familiar are More Appealing to the 'Average' Listener&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Misconception 4: &amp;quot;Tunings Related to the Familiar are More Appealing to the 'Average' Listener&amp;quot;&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Igliashon's &amp;quot;Four Misconceptions About Xenharmony and Microtonality&amp;quot; (and some further myths and facts about xenharmonics by mclaren)-Misconception 4: &amp;quot;Tunings Related to the Familiar are More Appealing to the 'Average' Listener&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Misconception 4: &amp;quot;Tunings Related to the Familiar are More Appealing to the 'Average' Listener&amp;quot;&lt;/h2&gt;
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 You know what tuning is the &lt;em&gt;most&lt;/em&gt; related to the familiar? 12-TET! I don't care what the psychoacousticians say, the vast majority of people accustomed to 12-TET will prefer the sound of 12-TET to tunings which approximate the same harmonies but in &amp;quot;better&amp;quot; tune. They will think the Just major third sounds flat and dull, they will think the semitones are too wide or the minor third is too sharp or the dominant 7th isn't tense enough to create an effective resolution. You don't need to take my word for it, go forth and test this! Play people two versions of a familiar piece of music (preferably NOT rendered using your PC's built-in general MIDI sound set), but don't tell them which is which, and ask them to rate which one they like best. I've done it, and I know what the answers are.&lt;br /&gt;
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-The truth is, anyone not actively seeking out microtonal music will either not be able to hear the difference, or if they can hear it, they won't like it (unless it's &amp;quot;ethnically correct&amp;quot; microtonal music, like Indian or Arabic music). The only people looking for music in some variety of meantone or 12-tone well-temperaments are looking for the words &amp;quot;historically informed performance&amp;quot;, aka the &amp;quot;authentic&amp;quot; or &amp;quot;early&amp;quot; music crowd. Those who &lt;em&gt;are&lt;/em&gt; actively seeking out music that is called &amp;quot;microtonal&amp;quot; couldn't care &lt;em&gt;less&lt;/em&gt; about smoother and more in-tune harmonies following the same familiar patterns. As Brian McLaren once said, &amp;quot;they are not shrinking violets&amp;quot;. They want stuff that will make their brain do happy back-flips, stuff that will turn their ears inside-out. There are many ways to accomplish this, and they do not all involve chucking 5-limit harmony out the window (in fact, some of the best ways are completely &lt;em&gt;centered&lt;/em&gt; on 5-limit harmony in some way or another), but the point is that if you pussy-foot around microtonality mumbling quietly about how it's &amp;quot;just like 12-TET, but more in tune&amp;quot;, absolutely NO ONE will take you seriously. Not average listeners, not microtonal enthusiasts, not your fellow microtonal musicians, and most &lt;em&gt;certainly&lt;/em&gt; not the average Guitar Center customer or university music student. The only way to make it as a microtonalist in this world is to go for broke, whether that means 13-EDO, 13-limit JI, 900 notes of Hemiennealimmal temperament, or somewhere in between. Pull that &amp;quot;familiar = good&amp;quot; stick out of your anus and do something &lt;em&gt;new&lt;/em&gt;. Smack the world in the face with something they've never heard before, and at the very least you'll attract a handful of people who will enthusiastically beg for more. If you're good at it, you might even make an international name for yourself among the underground microtonal scene, and if you're REALLY good at it (and/or really LUCKY) you might actually break out of the sub-culture and find your way into the public-at-large.&lt;/body&gt;&lt;/html&gt;</pre></div>
+The truth is, anyone not actively seeking out microtonal music will either not be able to hear the difference, or if they can hear it, they won't like it (unless it's &amp;quot;ethnically correct&amp;quot; microtonal music, like Indian or Arabic music). The only people looking for music in some variety of meantone or 12-tone well-temperaments are looking for the words &amp;quot;historically informed performance&amp;quot;, aka the &amp;quot;authentic&amp;quot; or &amp;quot;early&amp;quot; music crowd. Those who &lt;em&gt;are&lt;/em&gt; actively seeking out music that is called &amp;quot;microtonal&amp;quot; couldn't care &lt;em&gt;less&lt;/em&gt; about smoother and more in-tune harmonies following the same familiar patterns. As Brian McLaren once said, &amp;quot;they are not shrinking violets&amp;quot;. They want stuff that will make their brain do happy back-flips, stuff that will turn their ears inside-out. There are many ways to accomplish this, and they do not all involve chucking 5-limit harmony out the window (in fact, some of the best ways are completely &lt;em&gt;centered&lt;/em&gt; on 5-limit harmony in some way or another), but the point is that if you pussy-foot around microtonality mumbling quietly about how it's &amp;quot;just like 12-TET, but more in tune&amp;quot;, absolutely NO ONE will take you seriously. Not average listeners, not microtonal enthusiasts, not your fellow microtonal musicians, and most &lt;em&gt;certainly&lt;/em&gt; not the average Guitar Center customer or university music student. The only way to make it as a microtonalist in this world is to go for broke, whether that means 13-EDO, 13-limit JI, 900 notes of Hemiennealimmal temperament, or somewhere in between. Pull that &amp;quot;familiar = good&amp;quot; stick out of your anus and do something &lt;em&gt;new&lt;/em&gt;. Smack the world in the face with something they've never heard before, and at the very least you'll attract a handful of people who will enthusiastically beg for more. If you're good at it, you might even make an international name for yourself among the underground microtonal scene, and if you're REALLY good at it (and/or really LUCKY) you might actually break out of the sub-culture and find your way into the public-at-large.&lt;br /&gt;
+&lt;br /&gt;
+&lt;strong&gt;Myths and Facts about Xenharmonics by mclaren&lt;/strong&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;strong&gt;Myth #1: &amp;quot;Everyone prefers the natural intervals of the pure perfect harmonic series.&amp;quot;&lt;/strong&gt;  This myth remains pervasive. It has been stated by Hermann Helmholtz, in the form &amp;quot;instrumentalists naturally tend to play in the intervals of just intonation.&amp;quot; This myth was also repeatedly stated by Harry Partch, who claimed &amp;quot;The ear demands small integer ratios, and accepts substitutes against its will.&amp;quot;&lt;br /&gt;
+&lt;br /&gt;
+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 &amp;quot;perfectly in tune.&amp;quot;&lt;br /&gt;
+&lt;br /&gt;
+In 1963, a physicist published several articles in the then-new Journal of Music Theory examining the intervals actually performed by symphony musicians in real performances. 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 &amp;quot;perfectly in tune&amp;quot; and &amp;quot;entirely musical.&amp;quot;&lt;br /&gt;
+&lt;br /&gt;
+This research has been confirmed by many subsequent listening experiments. Psychouacousticians 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, 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).&lt;br /&gt;
+&lt;br /&gt;
+Moreover, in 1983, 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 &amp;quot;rich listeners&amp;quot; because these listeners perferred tunings which made the music sound &amp;quot;rich&amp;quot; and &amp;quot;lively&amp;quot; with a plethora of active beats. The second group Roberts, Pierce and Mathews referred to as &amp;quot;pure listeners&amp;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.&lt;br /&gt;
+&lt;br /&gt;
+Notice that these studies present no aesthetic preference. They do not tell us that rich listeners are &amp;quot;better&amp;quot; or &amp;quot;more discerning&amp;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, &amp;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.&amp;quot; Or, as William Schottstaedt, arguably the greatest living American composer, put it: &amp;quot;I like beats. Beats sound good.&amp;quot;&lt;br /&gt;
+&lt;br /&gt;
+&lt;strong&gt;Myth #2: &amp;quot;The small integer ratios like 3/2 and 5/4 are &lt;u&gt;&lt;em&gt;the&lt;/em&gt;&lt;/u&gt; original intervals from which all other musical intervals are derived.&amp;quot;&lt;/strong&gt;  Kyle Gann teaches this provably false claim in his course on microtonality. Or, as Lou Harrison put it, &amp;quot;Just intonation tunings are the only real musical intervals. All other musical intervals are fake musical intervals.&amp;quot; &lt;br /&gt;
+&lt;br /&gt;
+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 &amp;quot;fifth&amp;quot; and &amp;quot;third&amp;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.&lt;br /&gt;
+&lt;br /&gt;
+In &lt;span class="st"&gt; &amp;quot;Variability of judgments of musical intervals,&amp;quot; Journal of Experimental Psychology, Vol. 9, pp. 492-500, 1926, &lt;/span&gt;&lt;br /&gt;
+&lt;span class="st"&gt;Moran, H., &amp;amp; Pratt, C.C., 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 extend by many subsequent listening tests.&lt;/span&gt;&lt;br /&gt;
+&lt;br /&gt;
+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 roughy 680 cents on the low side to 720 cents on the high side.&lt;br /&gt;
+&lt;br /&gt;
+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.&lt;br /&gt;
+&lt;br /&gt;
+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 tunings like 7 and 14 equal, with 685.4-cent perfect fifths. Ivor in particular boosted 14 equal because of its unfamiliarity combined with memorable and impressive musical &amp;quot;mood.&amp;quot;&lt;br /&gt;
+&lt;br /&gt;
+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 thta listeners prefer is so far the opposite of the documented facts that the opposite is actually true. As Erv Wilson succinctly put it, &amp;quot;Musical cultures around the world tend to systemtically &lt;em&gt;avoid&lt;/em&gt; the intervals of the harmonic series.&amp;quot; (Wilson, E., personal communication).&lt;br /&gt;
+&lt;br /&gt;
+&lt;strong&gt;Myth #3: &amp;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.&amp;quot;&lt;/strong&gt; 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 will amount to little more than harmonic progressions.&lt;br /&gt;
+&lt;br /&gt;
+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. &lt;br /&gt;
+&lt;br /&gt;
+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.&lt;br /&gt;
+&lt;br /&gt;
+&lt;strong&gt;Myth #4: &amp;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.&amp;quot;&lt;/strong&gt; 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 &amp;quot;Attaining Consonance in Arbitrarily Musical Scales,&amp;quot; in the book &lt;em&gt;Music By Computer&lt;/em&gt;, ed., C. Beauchamp, 1969, and as was further developed by composers like James Dashow and William Sethares (see Sethares' book &lt;em&gt;Timbre, Tuning, Spectrum, Scale&lt;/em&gt;,&amp;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. &lt;br /&gt;
+&lt;br /&gt;
+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 compositions which leave audiences restless. &lt;br /&gt;
+&lt;br /&gt;
+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.&lt;br /&gt;
+&lt;br /&gt;
+&lt;strong&gt;Myth #5: &amp;quot;Mathematics forms the basis of music, and therefore mathematical music theory must guide us when we create new tunings.&amp;quot;&lt;/strong&gt; As Paul Hindemith noted in 1947, &amp;quot;The conclusions of mathematicians and acousticians are systematically at variance with the practice of musicians.&amp;quot; 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.&lt;br /&gt;
+&lt;br /&gt;
+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.&lt;br /&gt;
+&lt;br /&gt;
+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 Fletch back in the 1920s and early 1930s that our perception of the pitch of a sound tends to rise with its amplitude, and a louder sound in the mid-high range can be as much as a minor third higher, depending on its loudness. In the second case, see the well -known 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. This is the psychoacoustic basis of the RIAA equalization curve used on LPs.)&lt;br /&gt;
+&lt;br /&gt;
+Mathematics has consistently failed to predict the musical effect or musical utility of new musical tunings. As Ivor Darreg pointed out, &amp;quot;It is absolutely impossible to &lt;em&gt;imagine&lt;/em&gt; the sound or mood or a new tuning. You have to hear it. Only then can you imagine it.&amp;quot;&lt;br /&gt;
+&lt;br /&gt;
+The systematic failure of mathematically-based methods of musical organization, like total serialism, which failed to take the characteristics of the human cognitive system and the human auditory system into account, also converges on the conclusion that mathematics fails as a basis for creating new tunings.&lt;br /&gt;
+&lt;br /&gt;
+&lt;em&gt;&amp;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.&amp;quot;&lt;/em&gt; -- Ivor Darreg, personal communication.&lt;br /&gt;
+&lt;br /&gt;
+The evidence 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.&lt;br /&gt;
+&lt;br /&gt;
+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. We must try things out, make observations, and then compare our observations with our mental models in order to gain useful knowledge.&lt;br /&gt;
+&lt;br /&gt;
+&lt;strong&gt;Myth #5: &amp;quot;Microtonality produces great theory and bad music.&amp;quot; -- Brian Eno.&lt;/strong&gt;&lt;br /&gt;
+&lt;br /&gt;
+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.&lt;br /&gt;
+&lt;br /&gt;
+Pournelle's Iron Law of Bureacracy 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 excel in the kind of bureaucratic infighting which advances themselves and gains them publicity and renown. And Pournelle's Law states that the second group will always tend to take power.&lt;br /&gt;
+&lt;br /&gt;
+This applies to the internet and to academic 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 places like 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.&lt;br /&gt;
+&lt;br /&gt;
+Consequenly, 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.&lt;br /&gt;
+&lt;br /&gt;
+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 thick 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 publishers. Meanwhile, the books on microtonality which do get published (viz., Harry Partch's &lt;em&gt;Genesis of a Music&lt;/em&gt;) contain 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.&lt;br /&gt;
+&lt;br /&gt;
+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 practictitioners, and the previously unpublished writings finally get into (and stay in) print. Henry Cowell's &lt;em&gt;New Musical Resources&lt;/em&gt;, 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. &lt;br /&gt;
+&lt;br /&gt;
+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 are now completely vanished, never to be heard of again, in contemporary music transient fashions like The New Complexity and 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 to work that stands the test of time was famous when originally produced. But sometimes not.) &lt;br /&gt;
+&lt;br /&gt;
+&lt;strong&gt;Myth #6: &amp;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.&amp;quot;&lt;/strong&gt;&lt;br /&gt;
+&lt;br /&gt;
+This claim is so completely opposite the mathematical and acoustical reality that it's hard to find words with which to state the sheer wrongness of this claim.&lt;br /&gt;
+&lt;br /&gt;
+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 sylindrical tube has only one degree of freedom--it can only move foward or back in one dimension).&lt;br /&gt;
+&lt;br /&gt;
+This means that &lt;strong&gt;&lt;em&gt;essentially all vibrating objects produce natural resonant mode of vibration which are non-just non-equal-tempered.&lt;/em&gt;&lt;/strong&gt;  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.&lt;br /&gt;
+&lt;br /&gt;
+This tells us that &amp;quot;the chord of nature,&amp;quot; if there is any such thing, as a non-just non-equal-tempered set of inharmonic vibrational modes. Essentially all objects in the circumabient 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.&lt;br /&gt;
+&lt;br /&gt;
+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.&lt;br /&gt;
+&lt;br /&gt;
+One-dimensional vibrational systems do not appear in nature. They are not natural, and objects like stretched strings or perfectly cylindrical hollow tubes must be produced artificially. This means that just intontion 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. &lt;br /&gt;
+&lt;br /&gt;
+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 &amp;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.&amp;quot; (Ellis, translation plus commentary on Hermann Helmholtz's &lt;em&gt;On the Sensations of Tone&lt;/em&gt;). 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 &lt;em&gt;Acoustics&lt;/em&gt;, 1895, for details.&lt;/body&gt;&lt;/html&gt;</pre></div>