Misconceptions about xenharmony: Difference between revisions

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The more correct conclusion suggested by this observation is that what determines the amount of "restlessness" a musical stimulus will induce in a normal listener is the sheer volume of psychoacoustic and musical information present. A little bit of information is boring but not unpleasant--think the single drone of a tambura or the hum of a refrigerator--and an overload causes the cognitive faculty to shut down and let the stimuli blur into pure noise--which is also, coincidentally, soothing, at least if it's near pink or brown noise. So at either extreme of the spectrum--monophonic drone vs. noise--we have a sort of soothing "dullness". As we edge away from the drone, the informational content increases, and we develop **interest**; this can take many forms, be it monophonic melody or subtly shifting overtones or harmonic textures and what not. At some point--a point which is very much listener-dependent--interest (and thus pleasure) peaks, and further increasing the informational content becomes confusing and decreases pleasure. At some point (also very listener-dependent), pleasure becomes negative; this is usually the point where the information is as high as it can get before it becomes totally unintelligible, i.e. before it comes to be heard as pure noise.  

**//&lt;span style="font-weight: normal;"&gt;From a post on the [[http://nonoctave.com/forum/|nonoctave.com forum]]&lt;/span&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 "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.

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;

**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.

**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.

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.)

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.

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.

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.

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.)

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.

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.

The more correct conclusion suggested by this observation is that what determines the amount of &amp;quot;restlessness&amp;quot; a musical stimulus will induce in a normal listener is the sheer volume of psychoacoustic and musical information present. A little bit of information is boring but not unpleasant--think the single drone of a tambura or the hum of a refrigerator--and an overload causes the cognitive faculty to shut down and let the stimuli blur into pure noise--which is also, coincidentally, soothing, at least if it's near pink or brown noise. So at either extreme of the spectrum--monophonic drone vs. noise--we have a sort of soothing &amp;quot;dullness&amp;quot;. As we edge away from the drone, the informational content increases, and we develop &lt;strong&gt;interest&lt;/strong&gt;; this can take many forms, be it monophonic melody or subtly shifting overtones or harmonic textures and what not. At some point--a point which is very much listener-dependent--interest (and thus pleasure) peaks, and further increasing the informational content becomes confusing and decreases pleasure. At some point (also very listener-dependent), pleasure becomes negative; this is usually the point where the information is as high as it can get before it becomes totally unintelligible, i.e. before it comes to be heard as pure noise. &lt;br /&gt;

  &lt;strong&gt;&lt;em&gt;&lt;span style="font-weight: normal;"&gt;From a post on the &lt;a class="wiki_link_ext" href="http://nonoctave.com/forum/" rel="nofollow"&gt;nonoctave.com forum&lt;/a&gt;&lt;/span&gt;&lt;/em&gt;&lt;/strong&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;

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;

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;

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;

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;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;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;

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;

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;

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;

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;

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;

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;

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;