User:Eufalesio/How to build edos in DAWs: Difference between revisions

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Good edos: [[217edo|217]], [[270edo|270]], [[311edo|311]], [[612edo|612]], [[1600edo|1600]], [[2460edo|2460]] - Reasoning: Very high [[consistency limit]] / ''Astonishing'' 2.3.5.7.11.13.19 approximations.

When you ~~begin to~~ use edos beyond 159, ~~absolute error starts~~ to ~~become negligible~~, and consistency is what makes a fine-grained edo great. ~~270 is special because it approximates~~ the 2.~~3.5.7.11.13.19 astonishingly well for its size. 1600edo has absolute error comparable~~ to ~~270~~, ~~and almost 43-odd-limit consistency~~.

==== About edo usage and JI approximations (my experience) ====

When you use edos beyond 159 or 217edo, the increasingly bigger gamut of pitches makes it harder to use finer and finer edos compared to the increase in precision, and consistency compared to '''distinct''' consistency becomes a better metric for what makes a fine-grained edo great; put another way: how many intervals are '''''wheat''''', and how many are '''''chaff'''''. I'll call this the '''wheat:chaff metric'''. After all, one reason to use edos instead of JI is having a quantized palette of pitches, instead of an unfathomable continuum.

612edo and 2460 ~~are~~ S-tier 12n edos, so you get transposing-friendly hyperfine microtonality. But, since their step sizes are smaller than the melodic ~~[[Just-noticeable difference]]~~, you ~~literally~~ can't tell notes ~~that are~~ edosteps apart.

It is desirable for the wheat:chaff to be maximized, thus edos with high consistency limits and smaller gamut alongside lower '''distinct''' consistency limits are the best. Of course, relative error weighted by smaller primes is still a great metric. It follows from this, that the best edos are: [[12edo|12]], [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]], [[46edo|46]], [[53edo|53]], [[58edo|58]], [[72edo|72]], [[80edo|80]], [[84edo|84]], [[94edo|94]], [[118edo|118]], [[130edo|130]], [[159edo|159]], [[217edo|217]], [[311edo|311]]. Of those, I composed things in 12, 19, 22, 31, 41, 53, 72, 94, 159, 217.

You won't need edos finer than 94edo or 159edo if you're using acoustic sounds, or sounds with some sort of natural error or detune. 217 and 311edo are logical stopping points, because they temper a lot of useful intervals into each other (reducing chaff), and because 217edo has an edostep above the melodic [[Just-noticeable difference]] (311's is barely above, or probably isn't...). 270 is special because it approximates the 2.3.5.7.11.13.19 astonishingly well for its size. 1600edo has absolute error comparable to 270, and almost 43-odd-limit consistency.

If you still want to go even finer than that... then try 612edo and 2460; S-tier 12n edos, so you get transposing-friendly hyperfine microtonality. But, since their step sizes are smaller than the melodic JND, you can't tell notes edosteps apart.

If you STILL want to go finer... you're wasting your time. Just use [[JI]] scales and forget about edos and temperaments altogether.

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 Good edos: [[217edo|217]], [[270edo|270]], [[311edo|311]], [[612edo|612]], [[1600edo|1600]], [[2460edo|2460]] - Reasoning: Very high [[consistency limit]] / ''Astonishing'' 2.3.5.7.11.13.19 approximations.
-When you begin to use edos beyond 159, absolute error starts to become negligible, and consistency is what makes a fine-grained edo great. 270 is special because it approximates the 2.3.5.7.11.13.19 astonishingly well for its size. 1600edo has absolute error comparable to 270, and almost 43-odd-limit consistency.
+==== About edo usage and JI approximations (my experience) ====
+When you use edos beyond 159 or 217edo, the increasingly bigger gamut of pitches makes it harder to use finer and finer edos compared to the increase in precision, and consistency compared to '''distinct''' consistency becomes a better metric for what makes a fine-grained edo great; put another way: how many intervals are '''''wheat''''', and how many are '''''chaff'''''. I'll call this the '''wheat:chaff metric'''. After all, one reason to use edos instead of JI is having a quantized palette of pitches, instead of an unfathomable continuum.
-edo and 2460 are S-tier 12n edos, so you get transposing-friendly hyperfine microtonality. But, since their step sizes are smaller than the melodic [[Just-noticeable difference]], you literally can't tell notes that are edosteps apart.
+It is desirable for the wheat:chaff to be maximized, thus edos with high consistency limits and smaller gamut alongside lower '''distinct''' consistency limits are the best. Of course, relative error weighted by smaller primes is still a great metric. It follows from this, that the best edos are: [[12edo|12]], [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]], [[46edo|46]], [[53edo|53]], [[58edo|58]], [[72edo|72]], [[80edo|80]], [[84edo|84]], [[94edo|94]], [[118edo|118]], [[130edo|130]], [[159edo|159]], [[217edo|217]], [[311edo|311]]. Of those, I composed things in 12, 19, 22, 31, 41, 53, 72, 94, 159, 217.
+You won't need edos finer than 94edo or 159edo if you're using acoustic sounds, or sounds with some sort of natural error or detune. 217 and 311edo are logical stopping points, because they temper a lot of useful intervals into each other (reducing chaff), and because 217edo has an edostep above the melodic [[Just-noticeable difference]] (311's is barely above, or probably isn't...). 270 is special because it approximates the 2.3.5.7.11.13.19 astonishingly well for its size. 1600edo has absolute error comparable to 270, and almost 43-odd-limit consistency.
+If you still want to go even finer than that... then try 612edo and 2460; S-tier 12n edos, so you get transposing-friendly hyperfine microtonality. But, since their step sizes are smaller than the melodic JND, you can't tell notes edosteps apart.
+If you STILL want to go finer... you're wasting your time. Just use [[JI]] scales and forget about edos and temperaments altogether.
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