Schismic: Difference between revisions

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: ''This page is about a regular temperament sometimes known as "helmholtz". For the music theorist, see [[Hermann von Helmholtz]].''

{{Infobox regtemp

| Title = Schismic

| Subgroups = 2.3.5

| Comma basis = 32805/32768

| Generator = 3/2

| Mapping = 1; 1 -8

| Pergen = (P8, P5)

| Color name = Layo

| Edo join 1 = 12 | Edo join 2 = 41

| Optimization method = CWE

| Generator tuning = 701.731

| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]], [[12L 5s]]

| Odd limit 1 = 5 | Mistuning 1 = 0.217 | Complexity 1 = 29

| Odd limit 2 = (5-limit) 75 | Mistuning 2 = 0.651 | Complexity 2 = 41

}}

'''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.

@@ Line 1: / Line 1: @@
 : ''This page is about a regular temperament sometimes known as "helmholtz". For the music theorist, see [[Hermann von Helmholtz]].''
+{{Infobox regtemp
+| Title = Schismic
+| Subgroups = 2.3.5
+| Comma basis = 32805/32768
+| Generator = 3/2
+| Mapping = 1; 1 -8
+| Pergen = (P8, P5)
+| Color name = Layo
+| Edo join 1 = 12 | Edo join 2 = 41
+| Optimization method = CWE
+| Generator tuning = 701.731
+| MOS scales = [[2L&nbsp;3s]], [[5L&nbsp;2s]], [[5L&nbsp;7s]], [[12L&nbsp;5s]]
+| Odd limit 1 = 5 | Mistuning 1 = 0.217 | Complexity 1 = 29
+| Odd limit 2 = (5-limit) 75 | Mistuning 2 = 0.651 | Complexity 2 = 41
+}}
 '''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.