Misconceptions about xenharmony: Difference between revisions

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=Igliashon's "Six Misconceptions of Novice Microtonalists"=  

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 probably sound terrible, and you will probably 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 immediately 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 difficult and confusing (and therefore disappointing) 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. As far as I have seen, nobody in this century who has begun with 31-EDO has been satisfied enough with it to stop their exploration right there and spend the rest of their life in that one tuning; 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, thinking that if the "best" system didn't work out for them, what hope is there?

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. The sky's the limit once you get your sea-legs, but you **must** get those sea-legs first!

**Misconception 2: "Consonance is Rare"**

Consonance is //not// rare at all. In fact it is omnipresent. Especially in the higher ETs, maybe 24-EDO and above, it is almost impossible to find a tuning that is not at least as capable of consonance as 12-TET. Even among the smaller EDOs, it is almost universally true that each one 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 tastes 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 0-10-20-30-40-50-1300 cents repeating every 1300 cents (or something). The strength and quality of consonance may vary from tuning to tuning, but there is nearly //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 almost //always// there to be found if you know how to look.

It is true that accurate approximations of the 5-limit (let alone the 7, 11, or 13-limit) are rare among small tunings. This should not be surprising, considering that the octave-equivalent 13-odd-limit tonality diamond contains 42 intervals. But consonance does not require the full 13-limit, and subgroups of the 13-limit are plentiful.

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. The truth is, the familiar diatonic scale is about the sweetest-sounding thing in music, as are the familiar 5-limit consonances. When an instrument gives you the choice between familiar and sweet or unfamiliar and sour, it is hard to make yourself choose the latter. Odds are you will keep coming back to those familiar patterns, because they sound nicer and are easier to play--it's as if the instrument is rewarding you for being conservative and punishing you for trying new things.

On the other hand, if you begin with a tuning that lacks the familiar diatonic structure and the familiar 5-limit consonances, you will have no choice but to find something new. At first it may seem that the learning curve is steeper, because your old habits are being thwarted at every turn, but what is actually happening is that the tuning is teaching itself to you. When you don't find sweet sounds in the old familiar places, you have to look in new places, and they are more rewarding when you find them; being "rewarded" helps you stay motivated to continue learning. Eventually the old habits will die, new ones will take their place, and you will be effortlessly making music that sounds new and good.  

I know how it feels at first. You've gotten your first taste of microtonality and you think it's the greatest thing since sliced bread, but your friends, family, and fellow musicians are totally NOT sharing your enthusiasm. They are utterly failing to grasp why in the hell you would want to split off from the rest of the civilized 12-equal world and play music that "only aliens would like". So you start to have your doubts, and you start thinking that maaaaaybe instead of starting out with something wildly unfamiliar like Miracle temperament or 16-EDO, maybe you should be "easing people into it" with something like extended 7-limit Meantone or 19-EDO, even though what really got your motor running for microtonality in the first place was the really crazy-sounding new stuff. You think that if you can show people, "look, I can still play 'Smoke on the Water' or 'Moonlight Sonata', microtonality doesn't have to sound like alien music!" that this will turn their aversion into fascination and then they will eagerly join your cause.

Guess again, grasshopper. There's a big and obvious problem with this way of thinking. The truth is that people who want to listen to and/or make familiar-sounding music are not going to find anything very compelling about microtonality, because if you are going to make a new and more complicated tuning sound totally normal...what's the point of switching? It's like trying to sell ice-makers to the Inuits--why would they want to spend money for a machine that makes ice cubes when there's //snow// all around them? It's all cost and no benefit, because all they want is stuff that sounds familiar...and there's nothing more familiar than what they already have.

 

The truth is that lots and lots of people don't give two turds about microtonality, no matter what form it's in. The only way to win them over is to make music they like that is impossible to approximate with something familiar, and even then the odds of them actually becoming "converts" is practically non-existent. On the other hand, the people who //are// interested in microtonality want to hear music that sounds, well, microtonal. Sure, there are lots of ways to sound microtonal and not all microtonalists like all forms of microtonal music, but none of them want to hear music that sounds like 12-TET if you promise them something microtonal. There's nothing at all wrong with playing in 12-TET, and most microtonalists still listen to tons and tons of music in 12-TET (it's hard not to!), but you've really got to ask yourself if it's worth the trouble of refretting a guitar, or buying a retunable synth, or learning new fingerings on the bassoon (etc.), if what you really want to do is make music that doesn't actually sound much different.

If one looks to the meditative traditions of the world that use sound to help enhance meditation, the most common sounds are gongs, bells, and group chants (usually monophonic or even monotonic). The clear trend between all of these is "harmonic impurity", i.e. beating. Most bells produce inharmonic spectra where the overtones actually beat with one another, as do most gongs, and a room full of people chanting the same mantra or hymn will //never// be in perfect tune--there will always be some amount of beating. In modern times, the phenomenon of "binaural beating" is well-known and quite popular as a method of inducing relaxed states. One thing that is conspicuously absent from all meditative or trance-inducing sounds is beatless harmony played by pure harmonic timbres. Try this experiment for yourself: listen to 10 minutes of a Justly-tuned pipe organ sustaining a 4:5:6:7:9:11 hexad, and see just how relaxed it makes you feel! The truth is, given a static sustained harmony, one that beats is more relaxing than one that doesn't.

 

 

 

 

 

<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;misconceptions about xenharmony&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The field of microtonality is rife with colorful personalities and diverse perspectives, and there are many contradictory philosophies and approaches. However, the literature on microtonality in general seems to over-represent certain perspectives, and this page is intended specifically to represent some of the views that diverge from the more &amp;quot;mainstream&amp;quot; or traditional ideas about microtonality.&lt;!-- ws:start:WikiTextTocRule:4:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:4 --&gt;&lt;!-- ws:start:WikiTextTocRule:5: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Igliashon's &amp;quot;Six Misconceptions of Novice Microtonalists&amp;quot;"&gt;Igliashon's &amp;quot;Six Misconceptions of Novice Microtonalists&amp;quot;&lt;/a&gt;&lt;/div&gt;

&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Igliashon's &amp;quot;Six Misconceptions of Novice Microtonalists&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Igliashon's &amp;quot;Six Misconceptions of Novice Microtonalists&amp;quot;&lt;/h1&gt;

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 probably sound terrible, and you will probably 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 immediately 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 difficult and confusing (and therefore disappointing) 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. As far as I have seen, nobody in this century who has begun with 31-EDO has been satisfied enough with it to stop their exploration right there and spend the rest of their life in that one tuning; 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, thinking that if the &amp;quot;best&amp;quot; system didn't work out for them, what hope is there?&lt;br /&gt;

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. The sky's the limit once you get your sea-legs, but you &lt;strong&gt;must&lt;/strong&gt; get those sea-legs first!&lt;br /&gt;

&lt;strong&gt;Misconception 2: &amp;quot;Consonance is Rare&amp;quot;&lt;/strong&gt;&lt;br /&gt;

Consonance is &lt;em&gt;not&lt;/em&gt; rare at all. In fact it is omnipresent. Especially in the higher ETs, maybe 24-EDO and above, it is almost impossible to find a tuning that is not at least as capable of consonance as 12-TET. Even among the smaller EDOs, it is almost universally true that each one 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 tastes 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;

No, consonance is ubiquitous, practically inescapable unless you insist on using ridiculous scales like 0-10-20-30-40-50-1300 cents repeating every 1300 cents (or something). The strength and quality of consonance may vary from tuning to tuning, but there is nearly &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 almost &lt;em&gt;always&lt;/em&gt; there to be found if you know how to look.&lt;br /&gt;

It is true that accurate approximations of the 5-limit (let alone the 7, 11, or 13-limit) are rare among small tunings. This should not be surprising, considering that the octave-equivalent 13-odd-limit tonality diamond contains 42 intervals. But consonance does not require the full 13-limit, and subgroups of the 13-limit are plentiful.&lt;br /&gt;

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. The truth is, the familiar diatonic scale is about the sweetest-sounding thing in music, as are the familiar 5-limit consonances. When an instrument gives you the choice between familiar and sweet or unfamiliar and sour, it is hard to make yourself choose the latter. Odds are you will keep coming back to those familiar patterns, because they sound nicer and are easier to play--it's as if the instrument is rewarding you for being conservative and punishing you for trying new things.&lt;br /&gt;

On the other hand, if you begin with a tuning that lacks the familiar diatonic structure and the familiar 5-limit consonances, you will have no choice but to find something new. At first it may seem that the learning curve is steeper, because your old habits are being thwarted at every turn, but what is actually happening is that the tuning is teaching itself to you. When you don't find sweet sounds in the old familiar places, you have to look in new places, and they are more rewarding when you find them; being &amp;quot;rewarded&amp;quot; helps you stay motivated to continue learning. Eventually the old habits will die, new ones will take their place, and you will be effortlessly making music that sounds new and good. &lt;br /&gt;

I know how it feels at first. You've gotten your first taste of microtonality and you think it's the greatest thing since sliced bread, but your friends, family, and fellow musicians are totally NOT sharing your enthusiasm. They are utterly failing to grasp why in the hell you would want to split off from the rest of the civilized 12-equal world and play music that &amp;quot;only aliens would like&amp;quot;. So you start to have your doubts, and you start thinking that maaaaaybe instead of starting out with something wildly unfamiliar like Miracle temperament or 16-EDO, maybe you should be &amp;quot;easing people into it&amp;quot; with something like extended 7-limit Meantone or 19-EDO, even though what really got your motor running for microtonality in the first place was the really crazy-sounding new stuff. You think that if you can show people, &amp;quot;look, I can still play 'Smoke on the Water' or 'Moonlight Sonata', microtonality doesn't have to sound like alien music!&amp;quot; that this will turn their aversion into fascination and then they will eagerly join your cause.&lt;br /&gt;

Guess again, grasshopper. There's a big and obvious problem with this way of thinking. The truth is that people who want to listen to and/or make familiar-sounding music are not going to find anything very compelling about microtonality, because if you are going to make a new and more complicated tuning sound totally normal...what's the point of switching? It's like trying to sell ice-makers to the Inuits--why would they want to spend money for a machine that makes ice cubes when there's &lt;em&gt;snow&lt;/em&gt; all around them? It's all cost and no benefit, because all they want is stuff that sounds familiar...and there's nothing more familiar than what they already have.&lt;br /&gt;

The truth is that lots and lots of people don't give two turds about microtonality, no matter what form it's in. The only way to win them over is to make music they like that is impossible to approximate with something familiar, and even then the odds of them actually becoming &amp;quot;converts&amp;quot; is practically non-existent. On the other hand, the people who &lt;em&gt;are&lt;/em&gt; interested in microtonality want to hear music that sounds, well, microtonal. Sure, there are lots of ways to sound microtonal and not all microtonalists like all forms of microtonal music, but none of them want to hear music that sounds like 12-TET if you promise them something microtonal. There's nothing at all wrong with playing in 12-TET, and most microtonalists still listen to tons and tons of music in 12-TET (it's hard not to!), but you've really got to ask yourself if it's worth the trouble of refretting a guitar, or buying a retunable synth, or learning new fingerings on the bassoon (etc.), if what you really want to do is make music that doesn't actually sound much different.&lt;br /&gt;

If one looks to the meditative traditions of the world that use sound to help enhance meditation, the most common sounds are gongs, bells, and group chants (usually monophonic or even monotonic). The clear trend between all of these is &amp;quot;harmonic impurity&amp;quot;, i.e. beating. Most bells produce inharmonic spectra where the overtones actually beat with one another, as do most gongs, and a room full of people chanting the same mantra or hymn will &lt;em&gt;never&lt;/em&gt; be in perfect tune--there will always be some amount of beating. In modern times, the phenomenon of &amp;quot;binaural beating&amp;quot; is well-known and quite popular as a method of inducing relaxed states. One thing that is conspicuously absent from all meditative or trance-inducing sounds is beatless harmony played by pure harmonic timbres. Try this experiment for yourself: listen to 10 minutes of a Justly-tuned pipe organ sustaining a 4:5:6:7:9:11 hexad, and see just how relaxed it makes you feel! The truth is, given a static sustained harmony, one that beats is more relaxing than one that doesn't.&lt;br /&gt;

Now go forth, make mistakes, and learn from them!&lt;br /&gt;