Schismic: Difference between revisions
m linked comma in infobox |
revised minimax error and target scale size |
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| Generator tuning = 701.731 | | Generator tuning = 701.731 | ||
| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]], [[12L 5s]] | | MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]], [[12L 5s]] | ||
| Odd limit 1 = 5 | Mistuning 1 = 0.217 | Complexity 1 = | | Odd limit 1 = 5 | Mistuning 1 = 0.217 | Complexity 1 = 12 | ||
| Odd limit 2 = (5-limit) | | Odd limit 2 = (5-limit) 125 | Mistuning 2 = 0.837 | Complexity 2 = 29 | ||
}} | }} | ||
'''Schismic''', '''schismatic''', or '''helmholtz''' is a [[5-limit]] [[regular temperament|temperament]] which takes a roughly justly tuned [[3/2|perfect fifth]] and stacks it eight times to reach [[8/5]], thus finding the 5th harmonic at the diminished fourth (e.g. C–F♭) and [[tempering out]] the [[schisma]], 32805/32768. [[5/4]] can be respelled as a major third flattened by one [[Pythagorean comma]], and thus, the Pythagorean and [[syntonic comma]]s are equated into a generalized "comma", and the octave can be split into two diatonic major thirds and one downmajor third representing 5/4. It is one of the most basic examples of a [[microtemperament]], as the fifth generator can be detuned by a fraction of a cent from just, or left untouched entirely (as the difference between [[8192/6561]] and 5/4, the schisma being tempered out, is approximately 2 cents, which is [[just-noticeable difference|unnoticeable]] to most people). Technically, the best tuning in the 5-limit is to flatten the fifth by a fraction of a cent, though tunings on both sides of the just interval work fine. | '''Schismic''', '''schismatic''', or '''helmholtz''' is a [[5-limit]] [[regular temperament|temperament]] which takes a roughly justly tuned [[3/2|perfect fifth]] and stacks it eight times to reach [[8/5]], thus finding the 5th harmonic at the diminished fourth (e.g. C–F♭) and [[tempering out]] the [[schisma]], 32805/32768. [[5/4]] can be respelled as a major third flattened by one [[Pythagorean comma]], and thus, the Pythagorean and [[syntonic comma]]s are equated into a generalized "comma", and the octave can be split into two diatonic major thirds and one downmajor third representing 5/4. It is one of the most basic examples of a [[microtemperament]], as the fifth generator can be detuned by a fraction of a cent from just, or left untouched entirely (as the difference between [[8192/6561]] and 5/4, the schisma being tempered out, is approximately 2 cents, which is [[just-noticeable difference|unnoticeable]] to most people). Technically, the best tuning in the 5-limit is to flatten the fifth by a fraction of a cent, though tunings on both sides of the just interval work fine. | ||