User:Eufalesio/EDO impressions: Difference between revisions

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My main reason to use edos is to "buy" the entire gamut and be able to do JIoid stuff in it with the most accuracy, the least amount of pitch classes, and the most conceptualization ease.

I thus value edos that have a manageable grain, approximate a lot of stuff, and allow easy chain-of-fifths frameworks; It's easier for me to think in tempered commas. I care about the 5-limit, 7-limit, 2.3.5.13, 2.3.5.7.13, and 2.3.5.7.11.13.19(.29) JI subgroups, liking my error to be balanced across primes, but the error on 3 to be minimal. I ''can't'' not have a fifth, and it can't be badly out of tune. If there is no diatonic, it's useless to me.

I thus value edos that have a manageable grain, approximate a lot of stuff, and allow easy chain-of-fifths frameworks; It's easier for me to think in tempered commas along the chain of fifths. I care about the 5-limit, 7-limit, 2.3.5.13, 2.3.5.7.13, and 2.3.5.7.11.13.19(.29) JI subgroups, liking my error to be balanced across primes, but the error on 3 to be minimal so that I can work within a chain-of-fifths framework. I ''can't'' not have a fifth, and it can't be badly out of tune. If there is no diatonic, it's useless to me.

Despite the fifth inaccuracy, I do like meantone as it is arguably one of the best 5-limit temperaments, and it is obviously the theoretical backbone of Western music theory, still today.

I'm not a strict octave purist; I tolerate tempering the octave to achieve a better harmonic palette, and often do so to achieve higher consistency or better intonation, sacrificing a tiny bit of error on the octave to approximate all the harmonics I care about better. I don't mind having the subharmonics being worsely tuned, as they are not mirror images of harmonics, they are their own thing.

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=== 311edo ===

Ultimate ultra-high-limit JI. Absolute error is a smidge worse than 270edo, but it makes up by being consistent to the goddamn 41-odd-limit. Serendipity personified. Very hard to justify using anything else other than this, as the difference between edosteps from this point on is definitely nigh impossible to hear. I see it as an ultimate tuning of sorts for practicality's sake. SSS

=== 665edo ===

Ultimate pyth. It has an unfathomably perfect 2.3, and I say that in an almost literal sense. It is very much fathomable, obviously: the beat period of 665edo's fifth is 5077906.80060 s*Hz with two sawtooth waves in perfect sync, which would be around 3 hours, 12 minutes 21 seconds at f=440. 3 fucking hours. That's what it would take you to hear the beating of 665edo. It is, for all intents and purposes, unfathomable to focused human perception. Or, you could make a 3-hour track out of this.

However, this is not why you would use 665edo, as this essentially allows you to extend the precision limit of the chain of fifths from very good to ''extreme,'' by adding the mercator (+53 fifths) and an equalized qian comma (+306/-359 fifths) into the mix, also working as a schisma. Yes, it has a bad prime 11, but it is surprisingly good in the rest of primes up to the 27-odd-limit, which is very surprising for a convergent. I will likely never use this, but since I do greatly care about the chain of fifths as a theoretical construct, I care about this ''theoretically''. B

=== 1600edo ===

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=== 2460edo ===

The only reason I've put this one here is because it is a 12n edo, and that makes it ''slightly'' easier to work with, and very transposing friendly. It's astonishingly accurate, though dividing the semitone into 205ths is reasonably excessive. C+

=== 7315edo ===

Undecupling 665edo results in what I believe to be one of the potentially theoretically most robust yet precise JI-oid systems. Splitting the equalized qian comma in 11s greatly amplifies the accuracy of this edo and allows you to keep the unfathomably accurate chain of fifths as a strong backbone, and thirteenths of a qian comma serving as nanoalterations. I will likely never use this due to the insane precision it demands, but I have nothing other than respect for this behemoth of an edo. A

=== 8539edo ===

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=== 55edo and other fine very sharp meantonoid edos ===

Even worse than 43edo. In fact, it's a zeta valley edo, which means that it does a bad job at approximating JI, and that in my eyes is a failed edo. I don't know what the Mozarts were on while they suggested a meantone this sharp... it's not good at all! FF

=== 190537edo ===

This is the next edo in the list of record k-strong telicity, and it starts to get scary from this point. This is '''unadulterated cosmic horror''' disguised as math in the 3-limit, forget about the rest of primes. The beat period of this fifth is 984 572 779 224.54 s*Hz with two sawtooth waves in perfect sync, which would be around 70 years and 331 days at f=440. This edo has a fifth that is accurate to a level that is quite possibly beyond the scope of a human lifetime. Think about it. There is a chance you'll die before listening to 190537edo's fifth beat, at f=440.

If you say that you need accuracy to this precision, I am, beyond a reasonable doubt, wholly confident you are not human, or not anymore. Perhaps in a couple centuries, posthumanity will be able to comprehend this near-perfection, but as we stand right now, it is impossible to comprehend. Unrankable.

== EDOS I don't have much to talk about ==

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 My main reason to use edos is to "buy" the entire gamut and be able to do JIoid stuff in it with the most accuracy, the least amount of pitch classes, and the most conceptualization ease.
-I thus value edos that have a manageable grain, approximate a lot of stuff, and allow easy chain-of-fifths frameworks; It's easier for me to think in tempered commas. I care about the 5-limit, 7-limit, 2.3.5.13, 2.3.5.7.13, and 2.3.5.7.11.13.19(.29) JI subgroups, liking my error to be balanced across primes, but the error on 3 to be minimal. I ''can't'' not have a fifth, and it can't be badly out of tune. If there is no diatonic, it's useless to me.
+I thus value edos that have a manageable grain, approximate a lot of stuff, and allow easy chain-of-fifths frameworks; It's easier for me to think in tempered commas along the chain of fifths. I care about the 5-limit, 7-limit, 2.3.5.13, 2.3.5.7.13, and 2.3.5.7.11.13.19(.29) JI subgroups, liking my error to be balanced across primes, but the error on 3 to be minimal so that I can work within a chain-of-fifths framework. I ''can't'' not have a fifth, and it can't be badly out of tune. If there is no diatonic, it's useless to me.
+Despite the fifth inaccuracy, I do like meantone as it is arguably one of the best 5-limit temperaments, and it is obviously the theoretical backbone of Western music theory, still today.
 I'm not a strict octave purist; I tolerate tempering the octave to achieve a better harmonic palette, and often do so to achieve higher consistency or better intonation, sacrificing a tiny bit of error on the octave to approximate all the harmonics I care about better. I don't mind having the subharmonics being worsely tuned, as they are not mirror images of harmonics, they are their own thing.
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 === 311edo ===
 Ultimate ultra-high-limit JI. Absolute error is a smidge worse than 270edo, but it makes up by being consistent to the goddamn 41-odd-limit. Serendipity personified. Very hard to justify using anything else other than this, as the difference between edosteps from this point on is definitely nigh impossible to hear. I see it as an ultimate tuning of sorts for practicality's sake. SSS
+=== 665edo ===
+Ultimate pyth. It has an unfathomably perfect 2.3, and I say that in an almost literal sense. It is very much fathomable, obviously: the beat period of 665edo's fifth is 5077906.80060 s*Hz with two sawtooth waves in perfect sync, which would be around 3 hours, 12 minutes 21 seconds at f=440. 3 fucking hours. That's what it would take you to hear the beating of 665edo. It is, for all intents and purposes, unfathomable to focused human perception. Or, you could make a 3-hour track out of this.
+However, this is not why you would use 665edo, as this essentially allows you to extend the precision limit of the chain of fifths from very good to ''extreme,'' by adding the mercator (+53 fifths) and an equalized qian comma (+306/-359 fifths) into the mix, also working as a schisma. Yes, it has a bad prime 11, but it is surprisingly good in the rest of primes up to the 27-odd-limit, which is very surprising for a convergent. I will likely never use this, but since I do greatly care about the chain of fifths as a theoretical construct, I care about this ''theoretically''. B
 === 1600edo ===
@@ Line 106: / Line 113: @@
 === 2460edo ===
 The only reason I've put this one here is because it is a 12n edo, and that makes it ''slightly'' easier to work with, and very transposing friendly. It's astonishingly accurate, though dividing the semitone into 205ths is reasonably excessive. C+
+=== 7315edo ===
+Undecupling 665edo results in what I believe to be one of the potentially theoretically most robust yet precise JI-oid systems. Splitting the equalized qian comma in 11s greatly amplifies the accuracy of this edo and allows you to keep the unfathomably accurate chain of fifths as a strong backbone, and thirteenths of a qian comma serving as nanoalterations. I will likely never use this due to the insane precision it demands, but I have nothing other than respect for this behemoth of an edo. A
 === 8539edo ===
@@ Line 135: / Line 145: @@
 === 55edo and other fine very sharp meantonoid edos ===
 Even worse than 43edo. In fact, it's a zeta valley edo, which means that it does a bad job at approximating JI, and that in my eyes is a failed edo. I don't know what the Mozarts were on while they suggested a meantone this sharp... it's not good at all! FF
+=== 190537edo ===
+This is the next edo in the list of record k-strong telicity, and it starts to get scary from this point. This is '''unadulterated cosmic horror''' disguised as math in the 3-limit, forget about the rest of primes. The beat period of this fifth is 984 572 779 224.54 s*Hz with two sawtooth waves in perfect sync, which would be around 70 years and 331 days at f=440. This edo has a fifth that is accurate to a level that is quite possibly beyond the scope of a human lifetime. Think about it. There is a chance you'll die before listening to 190537edo's fifth beat, at f=440.
+If you say that you need accuracy to this precision, I am, beyond a reasonable doubt, wholly confident you are not human, or not anymore. Perhaps in a couple centuries, posthumanity will be able to comprehend this near-perfection, but as we stand right now, it is impossible to comprehend. Unrankable.
 == EDOS I don't have much to talk about ==