198edt: Difference between revisions

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== Theory ==

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.

198edt is related to [[125edo]], but with the [[3/1|perfect twelfth]] rather than the [[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.

=== Harmonics ===

{{Harmonics in equal|198|3|1|intervals=integer|columns=12|start=12|collapsed=true}}

{{Harmonics in equal|198|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 198edt (continued)}}

=== Subsets and supersets ===

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 == Theory ==
-edt 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.
+edt is related to [[125edo]], but with the [[3/1|perfect twelfth]] rather than the [[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.
 === 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}}
+{{Harmonics in equal|198|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 198edt (continued)}}
 === Subsets and supersets ===