User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning: Difference between revisions
m →How to choose a type: “Why different sized EDOs have different procedures” |
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== How to choose a type == | == How to choose a type == | ||
Remember: All of these rules are made to be broken. Bend the rules to fit the EDO. Don't bend the EDO to fit the rules. | Remember: All of these rules are made to be broken. Bend the rules to fit the EDO. Don't bend the EDO to fit the rules. | ||
=== Why different sized EDOs have different procedures === | |||
As EDOs get bigger and their step size gets smaller, their step size gets closer and closer to the [[just-noticeable difference]]. This means that if a smaller EDO has high relative error on a prime, it will sound like the prime is not there at all (no-no), but if a larger EDO has high relative error on a prime, especially a small prime, it will sound like there are two versions of the prime (dual). Different approaches are needed for different EDO sizes to reflect this. | |||
Also, as EDOs get bigger, more notes per octave need to be labelled with a JI approximation, so more basics elements are needed to produce those labels. Whereas, as EDOs get smaller, too many basis elements just make it needlessly complicated to navigate them, and fewer basis elements are better. So this is another reason for differing approaches at different EDO sizes. | |||
=== EDOs with 1 to 6 tones/octave === | === EDOs with 1 to 6 tones/octave === | ||
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# If there are aren't enough of those to fill all 3 spots, then allow primes, composites or taxicab intervals of any size which the edo approximates within 15 cents, giving preference to ones with lower primes | # If there are aren't enough of those to fill all 3 spots, then allow primes, composites or taxicab intervals of any size which the edo approximates within 15 cents, giving preference to ones with lower primes | ||
=== EDOs with 7 to | === EDOs with 7 to 27 tones/octave === | ||
# The subgroup should have 5 basis elements | # The subgroup should have 5 basis elements if the EDO has 7-12 tones, or 6 basis elements if the EDO has 13-27 tones | ||
# Add prime 2 to the subgroup | # Add prime 2 to the subgroup | ||
# If 3 is approximated within 15 cents, add 3 to the subgroup | # If 3 is approximated within 15 cents, add 3 to the subgroup | ||
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# Primes 2, 3, 5, 7 and 11 must be added to the subgroup | # Primes 2, 3, 5, 7 and 11 must be added to the subgroup | ||
# If any primes 3, 5, 7 or 11 have more than 40% relative error, then they should be made a dual prime | # If any primes 3, 5, 7 or 11 have more than 40% relative error, then they should be made a dual prime | ||
# If there are more than 2 dual-primes, then only the | # If there are more than 2 dual-primes, then only the 2 lowest dual-primes should be kept dual, and the rest made single again | ||
# If there are still spots left open, then they should be filled by every prime 13 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled | # If there are still spots left open, then they should be filled by every prime 13 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled | ||
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# Primes 2, 3, 5, 7 and 11 must be added to the subgroup | # Primes 2, 3, 5, 7 and 11 must be added to the subgroup | ||
# If any primes 3, 5, 7 or 11 have more than 40% relative error, then they should be made a dual prime | # If any primes 3, 5, 7 or 11 have more than 40% relative error, then they should be made a dual prime | ||
# If there are more than 3 dual-primes, then only the | # If there are more than 3 dual-primes, then only the 3 lowest dual-primes should be kept dual, and the rest made single again | ||
# If there are still spots left open, then they should be filled by every prime 13 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled | # If there are still spots left open, then they should be filled by every prime 13 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled | ||
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# Primes 2, 3, 5, 7, 11 and 13 must be added to the subgroup | # Primes 2, 3, 5, 7, 11 and 13 must be added to the subgroup | ||
# If any primes 3, 5, 7, 11 or 13 have more than 40% relative error, then they should be made a dual prime | # If any primes 3, 5, 7, 11 or 13 have more than 40% relative error, then they should be made a dual prime | ||
# If there are more than 4 dual-primes, then only the | # If there are more than 4 dual-primes, then only the 4 lowest dual-primes should be kept dual, and the rest made single again | ||
# If there are still spots left open, then they should be filled by every prime 17 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled | # If there are still spots left open, then they should be filled by every prime 17 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled | ||