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Very low accuracy temperaments: Difference between revisions

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Below are listed some '''very low accuracy temperaments'''. Temperaments with exceedingly low accuracy such as these tend to temper out very large “commas” such as 9/8, 32/27, or 15/14, equating wildly different interval sizes. All temperaments listed temper out an interval of at least size 15/14. As a result, every temperament here is an [[exotemperament]].
Below are listed some '''very low accuracy temperaments'''. Temperaments with exceedingly low accuracy such as these tend to temper out very large "commas" such as 9/8, 32/27, or 15/14, equating wildly different interval sizes. All temperaments listed temper out an interval of at least size 15/14. As a result, every temperament here is an [[exotemperament]].


== Antitonic ==
== Antitonic ==
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[[Comma list]]: [[32/27]]
[[Comma list]]: [[32/27]]


{{Mapping|legend=1| 3 5 7 | 0 0 1 }}
{{Mapping|legend=1| 3 5 0 | 0 0 1 }}
 
: mapping generators: ~4/3, ~5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~4/3 = 400.000, ~10/9 = 59.935
* [[POTE]]: ~4/3 = 400.000, ~5/4 = 459.935 (~10/9 = 59.935)


{{Optimal ET sequence|legend=1| 3, 12bcc, 15bbcc, 18bbcc }}
{{Optimal ET sequence|legend=1| 3, 12bcc, 15bbcc, 18bbcc }}
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Optimal tunings:  
Optimal tunings:  
* POTE: ~2 = 1200.000, ~3/2 = 782.604 (or ~15/14 = 182.604)
* POTE: ~2 = 1200.000, ~3/2 = 782.604 (~15/14 = 182.604)


Optimal ET sequence: {{optimal ET sequence| 6, 14bc, 20bb }}
Optimal ET sequence: {{optimal ET sequence| 6, 14bc, 20bb }}
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[[Comma list]]: 4096/3645
[[Comma list]]: 4096/3645


{{Mapping|legend=1| 1 1 6 | 0 1 -6 }}
{{Mapping|legend=1| 1 0 12 | 0 1 -6 }}
 
: mapping generators: ~2, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CWE]]): ~2 = 1200.000, ~3/2 = 731.732
* [[CWE]]: ~2 = 1200.000, ~3/2 = 731.732


Supporting ETs: [[5edo|5]], [[8edo|8c]], [[13edo|13]], [[18edo|18]], [[23edo|23bc]], [[28edo|28bc]], [[33edo|33bcc]], [[41edo|41bbc]], [[51edo|51bbccc]]
{{Optimal ET sequence|legend=1| 5, 13, 18, 23bc }}


[[Badness]] (Sintel): 6.332
[[Badness]] (Sintel): 6.332
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[[Comma list]]: [[45/32]]
[[Comma list]]: [[45/32]]


{{Mapping|legend=1| 1 1 3 | 0 1 -2 }}
{{Mapping|legend=1| 1 0 5 | 0 1 -2 }}
 
: mapping generators: ~2, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 509.892
* [[CTE]]: ~2 = 1200.000, ~3/2 = 509.892


[[Optimal ET sequence]]: None aside from extremely absurd alternative ETs
{{Optimal ET sequence|legend=1| 2c, 5bc, 7bbcc }}


[[Badness]]: 0.133021
[[Badness]]: 0.133021
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Comma list: 8/7, 45/28
Comma list: 8/7, 45/28


Mapping: {{mapping| 1 1 3 3 | 0 1 -2 0 }}
Mapping: {{mapping| 1 0 5 3 | 0 1 -2 0 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~3/2 = 509.892
* CTE: ~2 = 1200.000, ~3/2 = 509.892


Optimal ET sequence: None aside from extremely absurd alternative ETs
Optimal ET sequence: none


Badness: 0.118764
Badness: 0.118764
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[[Comma list]]: [[35/27]]
[[Comma list]]: [[35/27]]


{{Mapping|legend=1| 1 1 2 | 0 1 -1 }}
{{Mapping|legend=1| 1 0 3 | 0 1 -1 }}
 
: mapping generators: ~3, ~5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~5/3 = 701.863
* [[CTE]]: ~3 = 1901.955, ~5/3 = 701.863


{{Optimal ET sequence|legend=1| 8cdd }}, otherwise none aside from extremely absurd alternative ETs
[[Optimal ET sequence]]: [[3edt|b3]], [[8edt|b8cdd]]


[[Badness]] (Sintel): 0.751
[[Badness]] (Sintel): 0.751
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 1\2, ~5/3 = 935.289
* [[CTE]]: ~7/5 = 600.000, ~5/3 = 935.289


{{Optimal ET sequence|legend=1| 10cd, 14d }}
{{Optimal ET sequence|legend=1| 10cd, 14d }}
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