198edt: Difference between revisions
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{{ED intro}} | {{ED intro}} | ||
== Harmonics == | == Theory == | ||
{{Harmonics in equal | 198edt is related to [[125edo]], but with the [[3/1|perfect twelfth]] rather than the [[2/1|octave]] being just. The octave is [[stretched and compressed tuning|stretched]] by about 0.729 cents. Unlike 125edo, which is only [[consistent]] to the [[integer limit|10-integer-limit]], 198edt is consistent to the 12-integer-limit. In particular, it significantly improves the approximated [[prime harmonic]]s [[5/1|5]], [[11/1|11]] and [[13/1|13]] over 125edo, though the [[7/1|7]], [[17/1|17]] and [[19/1|19]], which are sharp to start with, are tuned worse here. | ||
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| | === Harmonics === | ||
| | {{Harmonics in equal|198|3|1|intervals=integer|columns=11}} | ||
}} | {{Harmonics in equal|198|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 198edt (continued)}} | ||
{{Harmonics in equal | |||
| | === Subsets and supersets === | ||
| | Since 198 factors into primes as {{nowrap| 2 × 3<sup>2</sup> × 11 }}, 198edt contains subset edts {{EDs|equave=t| 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99 }}. | ||
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| start = 12 | == See also == | ||
| collapsed = | * [[125edo]] – relative edo | ||
}} | * [[323ed6]] – relative ed6 | ||