TAMNAMS: Difference between revisions

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'''Paucitonic''': L/s = 1/0 = infinity (trivial/pathological)

=== Terminology and final notes ===

A ratio of L/s = k/1 can be called ''k-hard'' and a ratio of L/s = k/(k-1) can analogously be called ''k-soft'', so the simplest ultrasoft tuning is 5-soft or "pentasoft", the simplest hyperhard tuning is 5-hard or "pentahard", the simplest clustered tuning is 7-hard or "heptahard", 8-hard is "octahard", 9-hard is "nonahard", and finally, the characteristic simple ultrahard tuning is 6-hard or "extrahard", as previously discussed, which can be seen to be similar to "hexahard" - hopefully helping with memorisation.

A perhaps useful (or otherwise mildly amusing) mnemonic is "2-soft is too soft to be hard and 2-hard is too hard to be soft", representing that 2-soft = 2-hard = 2/1 = '''basic'''.

Note that often the central spectrum will be sufficient for exploring a MOS pattern-period combination, and the extended spectrum is intended more for (literally) edge cases where it may be useful. Often if a temperament interpretation doesn't seem to show up for a MOS pattern-period combination, it just means the temperament needs a more complex MOS pattern to narrow down the generator range. An example of this phenomena is the highly complex MOS pattern of [[12L 17s]] represents near-Pythagorean tunings well due to having a generator of a fourth or a fifth bounded between those of [[12edo]] and those of [[29edo]], which are roughly equally off but in opposite directions, and many important near-Pythagorean systems show up in just the ratios of the central spectrum alone.

[[Category:MOS]]

@@ Line 281: / Line 281: @@
 '''Paucitonic''': L/s = 1/0 = infinity (trivial/pathological)
+=== Terminology and final notes ===
+A ratio of L/s = k/1 can be called ''k-hard'' and a ratio of L/s = k/(k-1) can analogously be called ''k-soft'', so the simplest ultrasoft tuning is 5-soft or "pentasoft", the simplest hyperhard tuning is 5-hard or "pentahard", the simplest clustered tuning is 7-hard or "heptahard", 8-hard is "octahard", 9-hard is "nonahard", and finally, the characteristic simple ultrahard tuning is 6-hard or "extrahard", as previously discussed, which can be seen to be similar to "hexahard" - hopefully helping with memorisation.
+A perhaps useful (or otherwise mildly amusing) mnemonic is "2-soft is too soft to be hard and 2-hard is too hard to be soft", representing that 2-soft = 2-hard = 2/1 = '''basic'''.
+Note that often the central spectrum will be sufficient for exploring a MOS pattern-period combination, and the extended spectrum is intended more for (literally) edge cases where it may be useful. Often if a temperament interpretation doesn't seem to show up for a MOS  pattern-period combination, it just means the temperament needs a more complex MOS pattern to narrow down the generator range. An example of this phenomena is the highly complex MOS pattern of [[12L 17s]] represents near-Pythagorean tunings well due to having a generator of a fourth or a fifth bounded between those of [[12edo]] and those of [[29edo]], which are roughly equally off but in opposite directions, and many important near-Pythagorean systems show up in just the ratios of the central spectrum alone.
 [[Category:MOS]]