Schismic: Difference between revisions
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'''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♭). This 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 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♭). This 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 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. | ||
See [[Schismatic family # | See [[Schismatic family #Schismic, schismatic, a.k.a. helmholtz]] for technical data. | ||
== Interval chain == | == Interval chain == | ||