User:Ganaram inukshuk/5L 2s: Difference between revisions

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== Tuning ranges==

17edo and 19edo are the smallest edos that ~~requires the least amount~~ of ~~new notation, if any~~. Note that any enharmonic equivalences that 12edo has no longer hold for either 17edo or 19edo.

=== Simple tunings ===

17edo and 19edo are the smallest edos that offer more variety of pitches than 12edo. Note that any enharmonic equivalences that 12edo has no longer hold for either 17edo or 19edo.

Larger edos are described in the following subsections.

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The range of hypohard tunings can be divided into a minihard range (step ratios 2:1 to 5:2) and quasihard range (step ratios 5:2 to 3:1).

==== Minihard ====

Minihard tunings correspond to Pythagorean tuning and schismatic temperament, characterized by having a perfect 5th that is as close to just (701.96¢) as possible, resulting in 81/64 (407.8¢) for its major 3rd. Compatible edos include 41edo, and 53edo.

Minihard tunings correspond to Pythagorean tuning and schismatic temperament, characterized by having a perfect 5th that is as close to just (701.96¢) as possible, resulting in 81/64 (407.8¢) for its major 3rd. Compatible edos include 41edo and 53edo.

==== Quasihard ====

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 == Tuning ranges==
-edo and 19edo are the smallest edos that requires the least amount of new notation, if any. Note that any enharmonic equivalences that 12edo has no longer hold for either 17edo or 19edo.
+=== Simple tunings ===
+edo and 19edo are the smallest edos that offer more variety of pitches than 12edo. Note that any enharmonic equivalences that 12edo has no longer hold for either 17edo or 19edo.
 Larger edos are described in the following subsections.
@@ Line 152: / Line 154: @@
 The range of hypohard tunings can be divided into a minihard range (step ratios 2:1 to 5:2) and quasihard range (step ratios 5:2 to 3:1).
 ==== Minihard ====
-Minihard tunings correspond to Pythagorean tuning and schismatic temperament, characterized by having a perfect 5th that is as close to just (701.96¢) as possible, resulting in 81/64 (407.8¢) for its major 3rd. Compatible edos include 41edo, and 53edo.
+Minihard tunings correspond to Pythagorean tuning and schismatic temperament, characterized by having a perfect 5th that is as close to just (701.96¢) as possible, resulting in 81/64 (407.8¢) for its major 3rd. Compatible edos include 41edo and 53edo.
 {{MOS degrees|Scale Signature=5L 2s|Step Ratio=7/3; 9/4}}
 ==== Quasihard ====