Misconceptions about xenharmony: Difference between revisions

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

'''Misconception 2: "Consonance is Rare",'''

'''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 ~~[[Tel:~~0-150-300-450-600~~|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. 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 0-1-2-3-4-5-~~13 from 13~~ (~~equal~~) ~~divisions of anything~~. 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.

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.

~~'''Misconception 3: "Tunings Related to~~ the ~~Familiar~~ are ~~Easier to Learn"~~, ~~Misconception 4: "Tunings Related to~~ the ~~Familiar~~ are ~~More Appealing to the 'Average' Listener"'''~~

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.

~~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.~~

'''Misconception 3: "Tunings Related to the Familiar are Easier to Learn"'''

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.

'''Misconception 4: "Tunings Related to the Familiar are More Appealing to the 'Average' Listener"'''

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.

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

~~[[Category:about]]~~

[[Category:~~starting_point~~]]

[[Category:Overview]]

[[Category:~~xenharmony~~]]

[[Category:Essays]]

@@ Line 11: / Line 11: @@
 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",'''
+'''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 [[Tel:0-150-300-450-600|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. 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 0-1-2-3-4-5-13 from 13 (equal) divisions of anything. 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.
+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.
-'''Misconception 3: "Tunings Related to the Familiar are Easier to Learn", Misconception 4: "Tunings Related to the Familiar are More Appealing to the 'Average' Listener"'''
+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.
-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.
+'''Misconception 3: "Tunings Related to the Familiar are Easier to Learn"'''
 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.
+'''Misconception 4: "Tunings Related to the Familiar are More Appealing to the 'Average' Listener"'''
 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.
@@ Line 149: / Line 151: @@
 Musical instruments which produce harmonic series timbres are so rare and so unusual that, to a first approximation, essentially all the world's musical instruments avoid this kind of construction. There is nothing new about this conclusion: A. J. Ellis first stated in 1885 that his survey of world music showed that "The music of most of the world's cultures is not based on mathematics nor or integer ratios, but is very contingent, and arbitrary, and entirely unique to its own society." (Ellis, A. J., "On the Musical Scales Of Various Nations," ''Journal of the Royal Society of the Arts'', Vol. 3, 1885, pg. 536). The mathematical acoustics of most vibrating bodies have been known to be nonlinear and to produce inharmonic partials for most vibrating objects for well over 100 years: see Lord Rayleigh's two-volume ''Acoustics'', 1895, for details.
-[[Category:about]]
-[[Category:starting_point]]
+[[Category:Overview]]
-[[Category:xenharmony]]
+[[Category:Essays]]