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Rastmic rank three clan: Difference between revisions

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{{Mapping|legend=1| 1 1 0 -3 2 | 0 2 0 4 5 | 0 0 1 2 0 }}
{{Mapping|legend=1| 1 1 0 -3 2 | 0 2 0 4 5 | 0 0 1 2 0 }}


: Mapping generators: ~2, ~11/9, ~5
: mapping generators: ~2, ~11/9, ~5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 350.377, ~5/4 = 384.370
* [[CTE]]: ~2 = 1200.000, ~11/9 = 350.377, ~5/4 = 384.370
* [[CWE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 350.176, ~5/4 = 384.095
* [[CWE]]: ~2 = 1200.000, ~11/9 = 350.176, ~5/4 = 384.095


[[Minimax tuning]]:
[[Minimax tuning]]:
* [[11-odd-limit]]: ~2 = {{monzo| 1 0 0 0 0 }}, ~11/9 = {{monzo| -2/5 0 0 0 1/5 }}, ~5 = {{monzo| 2/5 -2 1 0 4/5 }}
* [[11-odd-limit]]: ~2 = {{monzo| 1 0 0 0 0 }}, ~11/9 = {{monzo| -2/5 0 0 0 1/5 }}, ~5 = {{monzo| 2/5 -2 1 0 4/5 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5.11
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.11


{{Optimal ET sequence|legend=1| 31, 41, 72, 247c, 281, 353c, 425bc, 497bc }}
{{Optimal ET sequence|legend=1| 31, 41, 72, 247c, 281, 353c, 425bc, 497bc }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 350.239, ~5/4 = 384.998
* CTE: ~2 = 1200.000, ~11/9 = 350.239, ~5/4 = 384.998
* CWE: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 350.039, ~5/4 = 384.587
* CWE: ~2 = 1200.000, ~11/9 = 350.039, ~5/4 = 384.587


{{Optimal ET sequence|legend=0| 31, 72, 103, 175f }} <nowiki>*</nowiki>
{{Optimal ET sequence|legend=0| 31, 72, 103, 175f }} <nowiki>*</nowiki>
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{{Mapping|legend=1| 1 1 0 -3 2 | 0 2 0 -4 5 | 0 0 1 3 0 }}
{{Mapping|legend=1| 1 1 0 -3 2 | 0 2 0 -4 5 | 0 0 1 3 0 }}


: Mapping generators: ~2, ~11/9, ~5
: mapping generators: ~2, ~11/9, ~5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 350.355, ~5/4 = 389.555
* [[CTE]]: ~2 = 1200.000, ~11/9 = 350.355, ~5/4 = 389.555
* [[CWE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 350.421, ~5/4 = 389.731
* [[CWE]]: ~2 = 1200.000, ~11/9 = 350.421, ~5/4 = 389.731


{{Optimal ET sequence|legend=1| 24d, 27e, 31, 58, 89, 154, 185 }}
{{Optimal ET sequence|legend=1| 24d, 27e, 31, 58, 89, 154, 185 }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 350.585, ~5/4 = 389.302
* CTE: ~2 = 1200.000, ~11/9 = 350.585, ~5/4 = 389.302
* CWE: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 350.568, ~5/4 = 389.610
* CWE: ~2 = 1200.000, ~11/9 = 350.568, ~5/4 = 389.610


{{Optimal ET sequence|legend=0| 27e, 31, 58, 96d, 154 }}
{{Optimal ET sequence|legend=0| 27e, 31, 58, 96d, 154 }}
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{{Mapping|legend=1| 1 1 0 6 | 0 2 0 -3 | 0 0 1 -1 }}
{{Mapping|legend=1| 1 1 0 6 | 0 2 0 -3 | 0 0 1 -1 }}


: Mapping generators: ~2, ~128/105, ~5
: mapping generators: ~2, ~128/105, ~5


[[Optimal tuning]] ([[CTE]]): ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~128/105 = 350.174, ~5/4 = 384.014
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~128/105 = 350.174, ~5/4 = 384.014


{{Optimal ET sequence|legend=1| 17, 21, 24, 31, 41, 72, 281d }}
{{Optimal ET sequence|legend=1| 17, 21, 24, 31, 41, 72, 281d }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 350.217, ~5/4 = 383.962
* [[CTE]]: ~2 = 1200.000, ~11/9 = 350.217, ~5/4 = 383.962
* [[CWE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 350.003, ~5/4 = 384.078
* [[CWE]]: ~2 = 1200.000, ~11/9 = 350.003, ~5/4 = 384.078


{{Optimal ET sequence|legend=1| 17, 24, 31, 41, 72, 312bd, 384bcd, 456bcde, 528bcde, 631bcde }}
{{Optimal ET sequence|legend=1| 17, 24, 31, 41, 72, 312bd, 384bcd, 456bcde, 528bcde, 631bcde }}
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{{Mapping|legend=1| 1 1 3 3 2 0 | 0 6 -7 -2 15 0 | 0 0 0 0 0 1 }}
{{Mapping|legend=1| 1 1 3 3 2 0 | 0 6 -7 -2 15 0 | 0 0 0 0 0 1 }}


: Mapping generators: ~2, ~15/14, ~13
: mapping generators: ~2, ~15/14, ~13


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~15/14 = 116.711, ~13/8 = 840.528
* [[CTE]]: ~2 = 1200.000, ~15/14 = 116.711, ~13/8 = 840.528
* [[CWE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~15/14 = 116.647, ~13/8 = 838.212
* [[CWE]]: ~2 = 1200.000, ~15/14 = 116.647, ~13/8 = 838.212


{{Optimal ET sequence|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}
{{Optimal ET sequence|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~15/14 = 116.704, ~13/8 = 839.452
* CTE: ~2 = 1200.000, ~15/14 = 116.704, ~13/8 = 839.452
* CWE: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~15/14 = 116.640, ~13/8 = 837.142
* CWE: ~2 = 1200.000, ~15/14 = 116.640, ~13/8 = 837.142


{{Optimal ET sequence|legend=0| 10, 31, 41, 62, 72, 103, 175f }}
{{Optimal ET sequence|legend=0| 10, 31, 41, 62, 72, 103, 175f }}
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{{Mapping|legend=1| 1 1 0 6 2 | 0 2 0 5 5 | 0 0 1 -2 0 }}
{{Mapping|legend=1| 1 1 0 6 2 | 0 2 0 5 5 | 0 0 1 -2 0 }}


: Mapping generators: ~2, ~11/9, ~5
: mapping generators: ~2, ~11/9, ~5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 350.145, ~5/4 = 389.708
* [[CTE]]: ~2 = 1200.000, ~11/9 = 350.145, ~5/4 = 389.708
* [[CWE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 350.555, ~5/4 = 390.269
* [[CWE]]: ~2 = 1200.000, ~11/9 = 350.555, ~5/4 = 390.269


{{Optimal ET sequence|legend=1| 7, 24, 31, 58, 89 }}
{{Optimal ET sequence|legend=1| 7, 24, 31, 58, 89 }}
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 350.293, ~5/4 = 389.979
* CTE: ~2 = 1200.000, ~11/9 = 350.293, ~5/4 = 389.979
* CWE: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 351.155, ~5/4 = 391.123
* CWE: ~2 = 1200.000, ~11/9 = 351.155, ~5/4 = 391.123


{{Optimal ET sequence|legend=0| 7, 24, 31, 58 }}
{{Optimal ET sequence|legend=0| 7, 24, 31, 58 }}
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{{Mapping|legend=1| 1 1 0 -1 | 0 2 0 13 | 0 0 1 0 }}
{{Mapping|legend=1| 1 1 0 -1 | 0 2 0 13 | 0 0 1 0 }}


: Mapping generators: ~2, ~896/729, ~5
: mapping generators: ~2, ~896/729, ~5


[[Optimal tuning]] ([[CTE]]): ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~896/729 = 351.416, ~5/4 = 386.314
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~896/729 = 351.416, ~5/4 = 386.314


{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99, 239, 338 }}
{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99, 239, 338 }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 351.320, ~5/4 = 386.314
* [[CTE]]: ~2 = 1200.000, ~11/9 = 351.320, ~5/4 = 386.314
* [[CWE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 351.459, ~5/4 = 387.423
* [[CWE]]: ~2 = 1200.000, ~11/9 = 351.459, ~5/4 = 387.423


{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99e }} *
{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99e }} *
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 351.343, ~5/4 = 386.314  
* CTE: ~2 = 1200.000, ~11/9 = 351.343, ~5/4 = 386.314  
* CWE: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 351.604, ~5/4 = 388.472
* CWE: ~2 = 1200.000, ~11/9 = 351.604, ~5/4 = 388.472


{{Optimal ET sequence|legend=0| 17c, 24, 34d, 41, 58, 99ef, 157eff, 290cdeeefff }}
{{Optimal ET sequence|legend=0| 17c, 24, 34d, 41, 58, 99ef, 157eff, 290cdeeefff }}
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 348.830, ~7/4 = 968.826
* [[CTE]]: ~2 = 1200.000, ~11/9 = 348.830, ~7/4 = 968.826
* [[CWE]]: ~2 = 1<span style="font-family:'Arial', sans-serif">\</span>1, ~11/9 = 348.379, ~7/4 = 965.630
* [[CWE]]: ~2 = 1200.000, ~11/9 = 348.379, ~7/4 = 965.630


{{Optimal ET sequence|legend=1| 7, 14c, 17c, 24, 31, 100de, 131bde, 162bde }}
{{Optimal ET sequence|legend=1| 7, 14c, 17c, 24, 31, 100de, 131bde, 162bde }}
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[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Pages with mostly numerical content]]
[[Category:Rastmic rank-3 clan| ]] <!-- main article -->
[[Category:Rastmic rank-3 clan| ]] <!-- main article -->
[[Category:Rastmic| ]] <!-- key article -->
[[Category:Rastmic| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Rastmic_rank_three_clan"