14. On Microtonal Music (Extra Bits)
Here are two extra bits to talk about that were out of scope for my previous post about microtonal music, but which I still think are valuable to read.
First, some music I recommend, if you want to try listening to microtonal/xenharmonic/untwelvish music. If you like guitar-driven rock, Brendan Byrnes is a surprisingly prolific musician who’s done a lot with sharp-fifth tunings like 22edo and 27edo; I recommend starting with the albums “Realism” and “Holocene Dream”. (“Neutral Paradise” is one of my favorites, and “Micropangaea” is his older and most varied album.) For a better-known option, King Gizzard and the Lizard Wizard has done plenty of music in 24edo, mostly emulating Anatolian, traditional Arabic, and Jewish scales; “Flying Microtonal Banana” is the starring example among albums, and the two-part album “K. G.”/”L. W.” presents another excellent example. For jazz, go looking for the sweetened thirds and flat fifths of 31edo; Hear Between the Lines has published some excellent covers and some strong new songs as well. Zheanna Erose isn’t jazz, but shares the same tuning, and you might prefer them. Finally, if you prefer electronic music, especially DnB or psytrance, give Sevish a try! His tuning choices are much more varied but even some of the weirder ones can be interesting; for a first album I recommend “Harmony Hacker” - especially the songs “Gleam”, in 22edo, and “Orbital”, in the octave-shunning tritave-favoring Bohlen-Pierce scale which is outside the scope of this post to describe in depth - or “Horixens”, off which I particularly like “Baobaoshuijiaojiao”, in a carefully picked just-intonation subset, and “In the Zoon”, which is in a particularly strange stretched-octave 23-tone scale even more outside the scope of this post to describe. For a particularly lovely example of what you can do with voice in free intonation, have a look at Jacob Collier’s “In The Bleak Midwinter”. You could also ask to listen to my 22edo rendition of the “Price is Right” theme, my 22edo reconstruction of a long-dead alarm clock tune, or my adaptation of “I’m Pressing On the Upward Way” into 31edo as made for Grandma Kim. (It’s her favorite hymn.) In any event, happy listening!
For the other topic, I want to describe a sketch of an adaptation to the ruleset for classical-style counterpoint to make it suitable for use with microtonal or xenharmonic scales. Sadly, you probably won’t understand this well if you don’t know how classical counterpoint works, but the basic idea is that you have some base melody, and then you have to pick notes to match against that base melody with the same rhythm such that you never make a dissonant interval, never move two voices in parallel consonance, and never make jumps that are too large, among other constraints. Recall that in classical counterpoint, the so-named perfect consonances are the octave, unison, perfect fourths, and perfect fifths, while the imperfect consonances are the major and minor thirds and the major and minor sixths; all other intervals are dissonances. One way of categorizing scales is by the prime limit of the harmonies they represent well; the familiar 12edo is generally considered a 5-limit scale, since it fails to capture 7-limit or larger prime harmonics well, as previously mentioned. On the other hand, 31edo is often considered a 13-limit scale, because it provides fairly good approximations of ratios with prime factors up to 13, while 22edo is similarly considered 11-limit; naturally, just-intonation scales can be constructed to have any limit. We might notice that the perfect consonances of 12edo as described classically match most closely to 3-limit harmonies, with the imperfect consonances corresponding to the strict 5-limit harmonies, and all other intervals being considered dissonant - unsurprising, given the lack of a good harmonic seventh in 12edo. My proposed fix is a simple one: extend the notion of perfect and imperfect consonance as naturally as possible, picking the primes with the best approximations to be perfect consonances and the rest with good approximations to be imperfect consonances; we may set the error threshold between perfect and imperfect to taste, but should be consistent. For 31edo, for example, we could pick {2, 5, 7} as the perfect primes and {3, 11, 13, 17} as imperfect - or we might drop 13 and 17, or treat 3 as among the perfect primes. Then, if an interval of the scale approximates a ratio using only perfect-consonance primes, treat it as a perfect consonance; if it uses primes from the imperfect set, treat them as imperfect consonances, even if error-cancellation makes them nearly just. All other intervals are then dissonant.
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First, some music I recommend, if you want to try listening to microtonal/xenharmonic/untwelvish music. If you like guitar-driven rock, Brendan Byrnes is a surprisingly prolific musician who’s done a lot with sharp-fifth tunings like 22edo and 27edo; I recommend starting with the albums “Realism” and “Holocene Dream”. (“Neutral Paradise” is one of my favorites, and “Micropangaea” is his older and most varied album.) For a better-known option, King Gizzard and the Lizard Wizard has done plenty of music in 24edo, mostly emulating Anatolian, traditional Arabic, and Jewish scales; “Flying Microtonal Banana” is the starring example among albums, and the two-part album “K. G.”/”L. W.” presents another excellent example. For jazz, go looking for the sweetened thirds and flat fifths of 31edo; Hear Between the Lines has published some excellent covers and some strong new songs as well. Zheanna Erose isn’t jazz, but shares the same tuning, and you might prefer them. Finally, if you prefer electronic music, especially DnB or psytrance, give Sevish a try! His tuning choices are much more varied but even some of the weirder ones can be interesting; for a first album I recommend “Harmony Hacker” - especially the songs “Gleam”, in 22edo, and “Orbital”, in the octave-shunning tritave-favoring Bohlen-Pierce scale which is outside the scope of this post to describe in depth - or “Horixens”, off which I particularly like “Baobaoshuijiaojiao”, in a carefully picked just-intonation subset, and “In the Zoon”, which is in a particularly strange stretched-octave 23-tone scale even more outside the scope of this post to describe. For a particularly lovely example of what you can do with voice in free intonation, have a look at Jacob Collier’s “In The Bleak Midwinter”. You could also ask to listen to my 22edo rendition of the “Price is Right” theme, my 22edo reconstruction of a long-dead alarm clock tune, or my adaptation of “I’m Pressing On the Upward Way” into 31edo as made for Grandma Kim. (It’s her favorite hymn.) In any event, happy listening!
For the other topic, I want to describe a sketch of an adaptation to the ruleset for classical-style counterpoint to make it suitable for use with microtonal or xenharmonic scales. Sadly, you probably won’t understand this well if you don’t know how classical counterpoint works, but the basic idea is that you have some base melody, and then you have to pick notes to match against that base melody with the same rhythm such that you never make a dissonant interval, never move two voices in parallel consonance, and never make jumps that are too large, among other constraints. Recall that in classical counterpoint, the so-named perfect consonances are the octave, unison, perfect fourths, and perfect fifths, while the imperfect consonances are the major and minor thirds and the major and minor sixths; all other intervals are dissonances. One way of categorizing scales is by the prime limit of the harmonies they represent well; the familiar 12edo is generally considered a 5-limit scale, since it fails to capture 7-limit or larger prime harmonics well, as previously mentioned. On the other hand, 31edo is often considered a 13-limit scale, because it provides fairly good approximations of ratios with prime factors up to 13, while 22edo is similarly considered 11-limit; naturally, just-intonation scales can be constructed to have any limit. We might notice that the perfect consonances of 12edo as described classically match most closely to 3-limit harmonies, with the imperfect consonances corresponding to the strict 5-limit harmonies, and all other intervals being considered dissonant - unsurprising, given the lack of a good harmonic seventh in 12edo. My proposed fix is a simple one: extend the notion of perfect and imperfect consonance as naturally as possible, picking the primes with the best approximations to be perfect consonances and the rest with good approximations to be imperfect consonances; we may set the error threshold between perfect and imperfect to taste, but should be consistent. For 31edo, for example, we could pick {2, 5, 7} as the perfect primes and {3, 11, 13, 17} as imperfect - or we might drop 13 and 17, or treat 3 as among the perfect primes. Then, if an interval of the scale approximates a ratio using only perfect-consonance primes, treat it as a perfect consonance; if it uses primes from the imperfect set, treat them as imperfect consonances, even if error-cancellation makes them nearly just. All other intervals are then dissonant.
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