303edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|303}} == Theory == 303et is only consistent to the 3-odd-limit, with three mappings possible for the 7-limit: * {{val|303 480 704 851}} (patent..." |
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== Theory == | == Theory == | ||
303edo is in[[consistent]] to the [[5-odd-limit]] with three mappings possible for the 7-limit: | |||
* {{val|303 480 704 851}} (patent val) | * {{val| 303 480 704 851 }} ([[patent val]]) | ||
* {{val|303 480 '''703''' 851}} (303c val) | * {{val| 303 480 '''703''' 851 }} (303c val) | ||
* {{val|303 480 '''703''' '''850'''}} (303cd val) | * {{val| 303 480 '''703''' '''850''' }} (303cd val) | ||
The patent val [[tempering out|tempers out]] 4294967296/4271484375 and 31381059609/30517578125 in the 5-limit; [[3136/3125]], 177147/175000 and 10616832/10504375 in the 7-limit, [[support]]ing [[gregorian leap day]]. | |||
Using the 303c val, it tempers out [[15625/15552]] and {{monzo|-83 48 3}} in the 5-limit; [[225/224]], [[4375/4374]] and {{monzo|36 -7 5 -13}} in the 7-limit | Using the 303c val, it tempers out [[15625/15552]] and {{monzo| -83 48 3 }} in the 5-limit; [[225/224]], [[4375/4374]] and {{monzo| 36 -7 5 -13 }} in the 7-limit, supporting [[catakleismic]] | ||
Using the 303cd val, it tempers out 15625/15552 and {{monzo|-83 48 3}} in the 5-limit; [[1029/1024]] | Using the 303cd val, it tempers out 15625/15552 and {{monzo| -83 48 3 }} in the 5-limit; [[1029/1024]] and [[43046721/43025920]] in the 7-limit, supporting [[tritikleismic]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo|-160 101}} | | {{monzo| -160 101 }} | ||
|{{mapping|303 480}} | | {{mapping| 303 480 }} | ||
| 0.3044 | | 0.3044 | ||
| 0.3045 | | 0.3045 | ||
| 7.69 | | 7.69 | ||
|} | |} | ||