Superkleismic: Difference between revisions
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{{Infobox regtemp | {{Infobox regtemp | ||
| Title = | | Title = Superkleismic | ||
| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.19 | | Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.19 | ||
| Comma basis = [[875/864]], [[1029/1024]] (7-limit); <br> [[100/99]], [[245/242]], [[385/384]] (11-limit); <br> [[100/99]], [[133/132]], [[190/189]], [[385/384]] (L11.19) | | Comma basis = [[875/864]], [[1029/1024]] (7-limit); <br>[[100/99]], [[245/242]], [[385/384]] (11-limit); <br>[[100/99]], [[133/132]], [[190/189]], [[385/384]] (L11.19) | ||
| Mapping = 1; 9 10 -3 2 14 | |||
| Edo join 1 = 15 | Edo join 2 = 26 | | Edo join 1 = 15 | Edo join 2 = 26 | ||
| | | Generators = 5/3 | Generators tuning = 878.2 | Optimization method = CWE | ||
| MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], [[11L 4s]], [[15L 11s]] | | MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], [[11L 4s]], [[15L 11s]] | ||
| Pergen = (P8, ccP4/9) | | Pergen = (P8, ccP4/9) | ||
| Odd limit 1 = 7 | Mistuning 1 = 6.09 | Complexity 1 = 15 | | Odd limit 1 = 7 | Mistuning 1 = 6.09 | Complexity 1 = 15 | ||
| Odd limit 2 = | | Odd limit 2 = 2.3.5.7.11.19 21 | Mistuning 2 = 8.85 | Complexity 2 = 26 | ||
}} | }} | ||
'''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit]] such that three [[6/5]] generators reach [[7/4]] (tempering out [[875/864]] ([[S-expression|S5/S6]]), the keema) and such that three [[8/7]] intervals reach [[3/2]] (tempering out [[1029/1024]] ([[S-expression|S7/S8]]), the gamelisma), making it a member of the [[gamelismic clan]] and a [[keemic temperaments|keemic temperament]]; its [[5-limit]] comma is [[1953125/1889568]], the shibboleth comma. It [[extension|extends]] extremely easily to the [[11-limit]] as well, by tempering out [[100/99]] ({{S|10}}) so that two generators reach [[16/11]], which also serves to extend the structure of [[orgone]] in the 2.7.11 subgroup. This implies [[385/384]] and [[441/440]] are tempered out as well. Furthermore, since in superkleismic, the interval [[21/20]] stands for half [[10/9]] = ([[19/18]])⋅([[20/19]]), we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out [[361/360]] ({{S|19}}) and [[400/399]] ({{S|20}}). Superkleismic can also be defined in the [[13-limit]], where two generators are identified with [[13/9]] alongside 16/11, tempering out [[144/143]] and [[325/324]], and extended to 17 to reach the full [[19-limit]], based on the equivalence (8/7)<sup>2</sup> ~ [[17/13]] (natural in slendric) and tempering out [[273/272]] and [[833/832]], in addition to [[120/119]] and [[170/169]]. | '''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit]] such that three [[6/5]] generators reach [[7/4]] (tempering out [[875/864]] ([[S-expression|S5/S6]]), the keema) and such that three [[8/7]] intervals reach [[3/2]] (tempering out [[1029/1024]] ([[S-expression|S7/S8]]), the gamelisma), making it a member of the [[gamelismic clan]] and a [[keemic temperaments|keemic temperament]]; its [[5-limit]] comma is [[1953125/1889568]], the shibboleth comma. It [[extension|extends]] extremely easily to the [[11-limit]] as well, by tempering out [[100/99]] ({{S|10}}) so that two generators reach [[16/11]], which also serves to extend the structure of [[orgone]] in the 2.7.11 subgroup. This implies [[385/384]] and [[441/440]] are tempered out as well. Furthermore, since in superkleismic, the interval [[21/20]] stands for half [[10/9]] = ([[19/18]])⋅([[20/19]]), we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out [[361/360]] ({{S|19}}) and [[400/399]] ({{S|20}}). Superkleismic can also be defined in the [[13-limit]], where two generators are identified with [[13/9]] alongside 16/11, tempering out [[144/143]] and [[325/324]], and extended to 17 to reach the full [[19-limit]], based on the equivalence (8/7)<sup>2</sup> ~ [[17/13]] (natural in slendric) and tempering out [[273/272]] and [[833/832]], in addition to [[120/119]] and [[170/169]]. | ||