User:Eufalesio/Harmonic tiers: Difference between revisions

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Melodically, they are both basically the same. There are pairs of 11- and 13- limit intervals that sound alike, like 39/32~11/9, 27/22~16/13. The comma that equates both pairs is 352/351, so it can be safely fudged or tempered. They work extremely well melodically, giving a nice xenharmonic punch to any music rooted in the 5- or 7- limit.

* Prime 11: It's the first truly xenharmonic prime. Good flavor, but in my opinion, it's harder to use than 13. Since it can be considered a type of "fourth", "augmented fourth" or "half-augmented fourth" (depending on how precise or pedantic you want to be), I see it as a deviation from a very consonant interval: the fourth 4/3, which is part of the reason why I don't like it as much. However, it adds a great otonal flavor from time to time.

* Prime 11: It's the first truly xenharmonic prime. Good flavor, but in my opinion, it's harder to use than 13. Since it can be considered a type of "fourth", "augmented fourth" or "half-augmented fourth" (depending on how precise or pedantic you want to be), I see it as a deviation from a very consonant interval: the fourth 4/3, which is part of the reason why I don't like it as much. However, it adds a great otonal flavor from time to time. This prime is also seemingly connected to prime 7 in a number of ways, but the most natural are either [[orgone]] or [[gary]]; gary being a better alternative in my opinion.

* Prime 13: The second xenharmonic prime. Technically less consonant than 11, but I find it easier to work with. ~~Part of this is the fact that it~~ is extremely well approximated by 10n edos, and ~~by Pythagorean tuning placing it as the triple augmented fourth. It is also~~ extremely easy to reach through the 7-limit too, connecting a chain of 5*7 to 13 through the ~~schismina~~. The fact that it is a kind of sixth means that its interval class is not perfect, so it lends itself to readily accept xenharmonic ~~(neutral)~~ values. Might be just my bias, but I just really like it. And it also appears in the 12:13:14:15:16, which I really like too.

* Prime 13: The second xenharmonic prime. Technically less consonant than 11, but I find it easier to work with. It is extremely well approximated by 10n edos and extremely easy to reach through the 7-limit too, connecting a chain of 5*7 to 13 through the minisma. The fact that it is a kind of sixth means that its interval class is not perfect, so it lends itself to readily accept xenharmonic values. Might be just my bias, but I just really like it. And it also appears in the 12:13:14:15:16, which I really like too. This prime is also seemingly connected to prime 5 in a number of ways, most notably through [[marveltwin]] or [[Wilschisma#Will|will]].

=== P-Tier IV ===

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* Prime 17: It's dissonant. It's good for lowering the complexity of wide otonal chords, but that's it. I don't like it harmonically that much on its own. Melodically, works as a 12edo-ish semitone, but I often just turn to 16/15 because I like it more.

* Prime 19: Despite being a very weak consonance, it is extremely close to a Pythagorean minor third, which automatically makes it very easy to use. It's great to build otonal minor chords and get somber feelings whilst being locked on the fundamental, and specially for ending cadences, for which 6/5 might make for a worse minor third. It combines great with 3 in the 16:19:24 chord. Melodically, it works the same as 5... so, great!

* Prime 19: Despite being a very weak consonance, it is extremely close to a Pythagorean minor third, which automatically makes it very easy to use. It's great to build otonal minor chords and get somber feelings whilst being locked on the fundamental, and specially for ending cadences, for which 6/5 might make for a worse minor third. It combines great with 3 in the 16:19:24 chord. Melodically, it works the same as 5... so, great! I only really use it for a couple intervals: 19/16, 19/12.

==== P-Tier IVb ====

It includes primes 23, 29, and 31, which sound quite xenharmonic.

From this tier onward the likelyhood of me using these is minimal. It includes primes 23, 29, and 31, which sound quite xenharmonic.

* Prime 23: It's kind of a weird prime in my opinion. Since it sounds like a very sharp augmented fourth, but shares a similar consonance level to 19, it should be in the same tier. But I don't like it that much on its own. The only time I'd use it is in a super wide otonal chord and for that it excels. Melodically, I'd treat it like a sharper 10/7, that is... a slightly sharper tritone.

* Prime 29: Despite being one of the less consonant primes, it makes for a nice supraminor flavor. Apart from that, since it is a kind of seventh, it accepts xenharmonic values more easily. It's very well approximated by 7n edos, so it also has that going for it. Melodically, I'd say it goes best when used in the tetrachord 24:26:29:32, serving as a more pungent, xenharmonic version of 15:16:18:20 (as the interval 29/24).

* Prime 29: Despite being one of the less consonant primes, it makes for a nice supraminor flavor. Apart from that, since it is a kind of seventh, it accepts xenharmonic values more easily. It's very well approximated by 7n edos, so it also has that going for it. Melodically, I'd say it goes best when used in the tetrachord 24:26:29:32, serving as a more pungent, xenharmonic version of 15:16:18:20 (as the interval 29/24). Least hard to use of the bunch.

* Prime 31: It's arguably the most dissonant of all the primes seen so far. Its octave complement, 32/31 is also incredibly close to 33/32, so by fudging or tempering 1024/1023, one can get a good approximation of 31 by reducing it to the 11-limit, which at least makes it somewhat approachable, but its integer complexity makes it a very difficult prime to digest and work with. Melodically, it's the same as 64/33, so it is incredibly jarring. Its octave complement is no better either, being a quartertone.

=== P-Tier V and beyond ===

There would theoretically be infinite tiers, each having exponentially more primes than the one before, but I really don't care for primes beyond 29. ~~They become far too complex for my ears and~~ I'm ~~sure that their sonorities can be fudged into other less complex intervals. The only way they can be reliably~~ and ~~practically explored for most cases is by using the serendipitous 311edo,~~ I~~'d say~~.

There would theoretically be infinite tiers, each having exponentially more primes than the one before, but I really don't care for primes beyond 19. I'm a fairly classical guy and I want to limit myself to a set of primes I can control.

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 Melodically, they are both basically the same. There are pairs of 11- and 13- limit intervals that sound alike, like 39/32~11/9, 27/22~16/13. The comma that equates both pairs is 352/351, so it can be safely fudged or tempered. They work extremely well melodically, giving a nice xenharmonic punch to any music rooted in the 5- or 7- limit.
-* <u>Prime 11</u>: It's the first truly xenharmonic prime. Good flavor, but in my opinion, it's harder to use than 13. Since it can be considered a type of "fourth", "augmented fourth" or "half-augmented fourth" (depending on how precise or pedantic you want to be), I see it as a deviation from a very consonant interval: the fourth 4/3, which is part of the reason why I don't like it as much. However, it adds a great otonal flavor from time to time.
+* <u>Prime 11</u>: It's the first truly xenharmonic prime. Good flavor, but in my opinion, it's harder to use than 13. Since it can be considered a type of "fourth", "augmented fourth" or "half-augmented fourth" (depending on how precise or pedantic you want to be), I see it as a deviation from a very consonant interval: the fourth 4/3, which is part of the reason why I don't like it as much. However, it adds a great otonal flavor from time to time. This prime is also seemingly connected to prime 7 in a number of ways, but the most natural are either [[orgone]] or [[gary]]; gary being a better alternative in my opinion.
-* <u>Prime 13</u>: The second xenharmonic prime. Technically less consonant than 11, but I find it easier to work with. Part of this is the fact that it is extremely well approximated by 10n edos, and by Pythagorean tuning placing it as the triple augmented fourth. It is also extremely easy to reach through the 7-limit too, connecting a chain of 5*7 to 13 through the schismina. The fact that it is a kind of sixth means that its interval class is not perfect, so it lends itself to readily accept xenharmonic (neutral) values. Might be just my bias, but I just really like it. And it also appears in the 12:13:14:15:16, which I really like too.
+* <u>Prime 13</u>: The second xenharmonic prime. Technically less consonant than 11, but I find it easier to work with. It is extremely well approximated by 10n edos and extremely easy to reach through the 7-limit too, connecting a chain of 5*7 to 13 through the minisma. The fact that it is a kind of sixth means that its interval class is not perfect, so it lends itself to readily accept xenharmonic values. Might be just my bias, but I just really like it. And it also appears in the 12:13:14:15:16, which I really like too. This prime is also seemingly connected to prime 5 in a number of ways, most notably through [[marveltwin]] or [[Wilschisma#Will|will]].
 === P-Tier IV ===
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 * <u>Prime 17</u>: It's dissonant. It's good for lowering the complexity of wide otonal chords, but that's it. I don't like it harmonically that much on its own. Melodically, works as a 12edo-ish semitone, but I often just turn to 16/15 because I like it more.
-* <u>Prime 19</u>: Despite being a very weak consonance, it is extremely close to a Pythagorean minor third, which automatically makes it very easy to use. It's great to build otonal minor chords and get somber feelings whilst being locked on the fundamental, and specially for ending cadences, for which 6/5 might make for a worse minor third. It combines great with 3 in the 16:19:24 chord. Melodically, it works the same as 5... so, great!
+* <u>Prime 19</u>: Despite being a very weak consonance, it is extremely close to a Pythagorean minor third, which automatically makes it very easy to use. It's great to build otonal minor chords and get somber feelings whilst being locked on the fundamental, and specially for ending cadences, for which 6/5 might make for a worse minor third. It combines great with 3 in the 16:19:24 chord. Melodically, it works the same as 5... so, great! I only really use it for a couple intervals: 19/16, 19/12.
 ==== P-Tier IVb ====
-It includes primes 23, 29, and 31, which sound quite xenharmonic.
+From this tier onward the likelyhood of me using these is minimal. It includes primes 23, 29, and 31, which sound quite xenharmonic.
 * <u>Prime 23</u>: It's kind of a weird prime in my opinion. Since it sounds like a very sharp augmented fourth, but shares a similar consonance level to 19, it should be in the same tier. But I don't like it that much on its own. The only time I'd use it is in a super wide otonal chord and for that it excels. Melodically, I'd treat it like a sharper 10/7, that is... a slightly sharper tritone.
-* <u>Prime 29</u>: Despite being one of the less consonant primes, it makes for a nice supraminor flavor. Apart from that, since it is a kind of seventh, it accepts xenharmonic values more easily. It's very well approximated by 7n edos, so it also has that going for it. Melodically, I'd say it goes best when used in the tetrachord 24:26:29:32, serving as a more pungent, xenharmonic version of 15:16:18:20 (as the interval 29/24).
+* <u>Prime 29</u>: Despite being one of the less consonant primes, it makes for a nice supraminor flavor. Apart from that, since it is a kind of seventh, it accepts xenharmonic values more easily. It's very well approximated by 7n edos, so it also has that going for it. Melodically, I'd say it goes best when used in the tetrachord 24:26:29:32, serving as a more pungent, xenharmonic version of 15:16:18:20 (as the interval 29/24). Least hard to use of the bunch.
 * <u>Prime 31</u>: It's arguably the most dissonant of all the primes seen so far. Its octave complement, 32/31 is also incredibly close to 33/32, so by fudging or tempering 1024/1023, one can get a good approximation of 31 by reducing it to the 11-limit, which at least makes it somewhat approachable, but its integer complexity makes it a very difficult prime to digest and work with. Melodically, it's the same as 64/33, so it is incredibly jarring. Its octave complement is no better either, being a quartertone.
 === P-Tier V and beyond ===
-There would theoretically be infinite tiers, each having exponentially more primes than the one before, but I really don't care for primes beyond 29. They become far too complex for my ears and I'm sure that their sonorities can be fudged into other less complex intervals. The only way they can be reliably and practically explored for most cases is by using the serendipitous 311edo, I'd say.
+There would theoretically be infinite tiers, each having exponentially more primes than the one before, but I really don't care for primes beyond 19. I'm a fairly classical guy and I want to limit myself to a set of primes I can control.