Diaschismic family: Difference between revisions
m →Shrutar |
Move srutal archagall to subgroup extensions section as it skips multiple primes. - redundant category |
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{{Mapping|legend=1| 2 0 11 | 0 1 -2 }} | {{Mapping|legend=1| 2 0 11 | 0 1 -2 }} | ||
: mapping generators: ~45/32, ~3 | : mapping generators: ~45/32, ~3 | ||
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==== Subgroup extensions ==== | ==== Subgroup extensions ==== | ||
Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', | Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', considered in [[#Subgroup extensions]]. The [[S-expression]]-based comma list of this temperament is {[[256/255|S16]], [[289/288|S17]]}. | ||
== Septimal diaschismic == | == Septimal diaschismic == | ||
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Mapping: {{mapping| 2 0 11 12 -1 | 0 2 -4 -4 5 }} | Mapping: {{mapping| 2 0 11 12 -1 | 0 2 -4 -4 5 }} | ||
: mapping generators: ~2, ~55/32 | : mapping generators: ~2, ~55/32 | ||
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{{Mapping|legend=1| 4 0 22 43 | 0 1 -2 -5 }} | {{Mapping|legend=1| 4 0 22 43 | 0 1 -2 -5 }} | ||
: mapping generators: ~25/21, ~3 | : mapping generators: ~25/21, ~3 | ||
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{{Mapping|legend=1| 2 1 9 -2 | 0 2 -4 7 }} | {{Mapping|legend=1| 2 1 9 -2 | 0 2 -4 7 }} | ||
: mapping generators: ~45/32, ~35/24 | : mapping generators: ~45/32, ~35/24 | ||
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{{Mapping|legend=1| 2 1 9 11 | 0 2 -4 -5 }} | {{Mapping|legend=1| 2 1 9 11 | 0 2 -4 -5 }} | ||
: mapping generators: ~45/32, ~10/7 | : mapping generators: ~45/32, ~10/7 | ||
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{{Mapping|legend=1| 2 0 11 -15 | 0 2 -4 13 }} | {{Mapping|legend=1| 2 0 11 -15 | 0 2 -4 13 }} | ||
: mapping generators: ~45/32, ~140/81 | : mapping generators: ~45/32, ~140/81 | ||
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{{Mapping|legend=1| 2 0 11 4 | 0 2 -4 1 }} | {{Mapping|legend=1| 2 0 11 4 | 0 2 -4 1 }} | ||
: mapping generators: ~45/32, ~7/4 | : mapping generators: ~45/32, ~7/4 | ||
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{{Mapping|legend=1| 2 1 9 2 | 0 3 -6 5 }} | {{Mapping|legend=1| 2 1 9 2 | 0 3 -6 5 }} | ||
: mapping generators: ~45/32, ~9/7 | : mapping generators: ~45/32, ~9/7 | ||
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{{Mapping|legend=1| 2 2 7 6 | 0 3 -6 -1 }} | {{Mapping|legend=1| 2 2 7 6 | 0 3 -6 -1 }} | ||
: mapping generators: ~45/32, ~8/7 | : mapping generators: ~45/32, ~8/7 | ||
| Line 1,265: | Line 1,237: | ||
{{Mapping|legend=1| 2 0 11 8 | 0 4 -8 -3 }} | {{Mapping|legend=1| 2 0 11 8 | 0 4 -8 -3 }} | ||
: mapping generators: ~45/32, ~21/16 | : mapping generators: ~45/32, ~21/16 | ||
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Badness (Sintel): 1.13 | Badness (Sintel): 1.13 | ||
== Subgroup extensions == | |||
=== Srutal archagall (2.3.5.17) === | |||
{{See also | Fiventeen }} | |||
Subgroup: 2.3.5.17 | |||
Comma list: 136/135, 256/255 | |||
Subgroup-val mapping: {{mapping| 2 0 11 5 | 0 1 -2 1 }} | |||
: mapping generators: ~17/12, ~3 | |||
Optimal tunings: | |||
* WE: ~45/32 = 599.5585{{c}}, ~3/2 = 704.6188{{c}} | |||
* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 705.1356{{c}} | |||
{{Optimal ET sequence|legend=0| 10, 12, 22, 34, 80, 114, 194bc }} | |||
Badness (Sintel): 0.212 | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Diaschismic family| ]] <!-- main article --> | [[Category:Diaschismic family| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||