216edo: Difference between revisions

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216edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with many mappings possible for the 13-limit. The following four will be discussed here: {{val| 216 342 502 606 747 799 }} ([[patent val]]), {{val| 216 '''343''' 502 '''607''' '''748''' '''800''' }} (216bdef), {{val| 216 342 '''501''' 606 747 799 }} (216c), and {{val| 216 342 502 '''607''' 747 799 }} (216d).

The 216c val is [[Enfactoring|enfactored]] in the 11-limit, and it happens to be of the best accuracy. Like 72, it [[Tempering out|tempers out]] [[15625/15552]] and [[531441/524288]] in the 5-limit; [[225/224]], [[1029/1024]], and [[4375/4374]] in the 7-limit; [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]] in the 11-limit. However, it tempers out [[2200/2197]] and 2205/2197 in the 13-limit, and ~~practically corrects the approximate~~ [[13/1|13th harmonic]] ~~to as fit as it can be~~.

The 216c val is [[Enfactoring|enfactored]] in the 11-limit, and it happens to be of the best accuracy. Like [[72edo|72]], it [[Tempering out|tempers out]] [[15625/15552]] and [[531441/524288]] in the 5-limit; [[225/224]], [[1029/1024]], and [[4375/4374]] in the 7-limit; [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]] in the 11-limit. However, unlike 72, it tempers out [[2200/2197]] and 2205/2197 in the 13-limit, and is an good correction from 72edo's flat [[13/1|13th harmonic]]. This val supports [[phicordial]], a [[weak extension]] of [[miracle]].

The 216bdef val chooses the sharp mapping for each of the harmonics, so it is the opposite of 216c in terms of tuning. It tempers out [[2048/2025]] and {{monzo| 1 -46 31 }} in the 5-limit; [[3136/3125]], [[4000/3969]], and 40353607/39858075 in the 7-limit; [[2560/2541]], [[3025/3024]], [[3388/3375]], and 12005/11979 in the 11-limit; [[325/324]], [[364/363]], [[640/637]], and [[1716/1715]] in the 13-limit.

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 edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with many mappings possible for the 13-limit. The following four will be discussed here: {{val| 216 342 502 606 747 799 }} ([[patent val]]), {{val| 216 '''343''' 502 '''607''' '''748''' '''800''' }} (216bdef), {{val| 216 342 '''501''' 606 747 799 }} (216c), and {{val| 216 342 502 '''607''' 747 799 }} (216d).
-The 216c val is [[Enfactoring|enfactored]] in the 11-limit, and it happens to be of the best accuracy. Like 72, it [[Tempering out|tempers out]] [[15625/15552]] and [[531441/524288]] in the 5-limit; [[225/224]], [[1029/1024]], and [[4375/4374]] in the 7-limit; [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]] in the 11-limit. However, it tempers out [[2200/2197]] and 2205/2197 in the 13-limit, and practically corrects the approximate [[13/1|13th harmonic]] to as fit as it can be.
+The 216c val is [[Enfactoring|enfactored]] in the 11-limit, and it happens to be of the best accuracy. Like [[72edo|72]], it [[Tempering out|tempers out]] [[15625/15552]] and [[531441/524288]] in the 5-limit; [[225/224]], [[1029/1024]], and [[4375/4374]] in the 7-limit; [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]] in the 11-limit. However, unlike 72, it tempers out [[2200/2197]] and 2205/2197 in the 13-limit, and is an good correction from 72edo's flat [[13/1|13th harmonic]]. This val supports [[phicordial]], a [[weak extension]] of [[miracle]].
 The 216bdef val chooses the sharp mapping for each of the harmonics, so it is the opposite of 216c in terms of tuning. It tempers out [[2048/2025]] and {{monzo| 1 -46 31 }} in the 5-limit; [[3136/3125]], [[4000/3969]], and 40353607/39858075 in the 7-limit; [[2560/2541]], [[3025/3024]], [[3388/3375]], and 12005/11979 in the 11-limit; [[325/324]], [[364/363]], [[640/637]], and [[1716/1715]] in the 13-limit.