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Ntiscifer: Difference between revisions

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The circle of 16 fifths with the flat 675-cent fifths shares some properties with the 12edo [[circle of fifths]], namely that the note a tritone from any given note can be found by going halfway around it (8 steps), and that adjacent to that (9 and 7 steps) are the sharpened and flattened version of that note, respectively.  
The circle of 16 fifths with the flat 675-cent fifths shares some properties with the 12edo [[circle of fifths]], namely that the note a tritone from any given note can be found by going halfway around it (8 steps), and that adjacent to that (9 and 7 steps) are the sharpened and flattened version of that note, respectively.  


=== 5-limit ntiscifer ===
See [[16th-octave temperaments #Ntiscifer]] for technical data.  
Equivalent to the 16edo circle of fifths with an added dimension for 5/4. In 16edo, this maps 5/4 to 375 cents, as in mavila temperament. Tunings with a separate, more accurate third include 64edo, 80edo, and 96edo; 96edo is a particularly accurate tuning, though 64edo might be considered more practical.  


[[Subgroup]]: 2.3.5
[[Category:Temperaments]]
 
[[Category:Ntiscifer| ]] <!-- main article -->
[[Comma list]]: [[43046721/33554432]]
 
{{Mapping|legend=1| 16 25 0 | 0 0 1 }}
 
[[Optimal tuning]]s:  
* [[CTE]]: ~2048/2187 = 1\16, ~5/4 = 386.3137 (~135/128 = 11.3137)
* [[CWE]]: ~2048/2187 = 1\16, ~5/4 = 373.1508 (~128/135 = 1.8492)
 
{{Optimal ET sequence|legend=1| 16 }}
 
[[Badness]]: 3.05
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