212edo: Difference between revisions

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Theory: +octave stretch
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=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|212}}
{{Harmonics in equal|212}}
=== Octave stretch ===
212edo can benefit from slightly [[stretched and compressed tuning|stretching the octave]], using tunings such as [[124edf]] or [[336edt]]. This improves the approximated harmonics 5, 7, 11, 13 and brings the flat mappings of 17 and 19 closer; only the 23 becomes less accurate as it is tuned sharp already.


=== Subsets and supersets ===
=== Subsets and supersets ===
Since 212 factors into {{factorisation|212}}, 212edo has subset edos {{EDOs| 2, 4, 53, and 106 }}. As such, it can be used to tune the period-53 [[cartography]] temperament and the period-106 [[boiler]] temperment.  
Since 212 factors into {{factorisation|212}}, 212edo has subset edos {{EDOs| 2, 4, 53, and 106 }}. As such, it can be used to tune the 53rd-octave [[cartography]] temperament and the 106th-octave [[boiler]] temperment.  


A step of 212edo is exactly 50 [[türk sent]]s.
A step of 212edo is exactly 50 [[türk sent]]s.