User:UnbihexiumFan/Temperaments: Difference between revisions

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 '''Bolded''' ratios are octave-reduced harmonics up to 21.
-=== 2.3.7.11.13 extension ===
+=== No-5's 19-limit extension ===
-One extension to the 2.3.7.11.13 subgroup is to temper [[28/27]] to be equal to [[27/26]], tempering out [[729/728]]. This maps the 13th harmonic, [[13/8]], to the sesqui-augmented second, D{{sesquisharp}}.
+While the major third is too sharp to be seen as [[5/4]], it can be seen as [[24/19]] or [[64/51]]. Treating it equal to both tempers out [[513/512]] and [[4131/4096]], providing a comma basis of [[2057/2052]], [[513/512]], [[154/153]], and [[243/242]]. The 17th harmonic is mapped to the minor second (-8 generators, D{{flat}} on C) and the 19th harmonic is mapped to the minor third (-6 generators, E{{flat}} on C). The 13th harmonic can be added by setting [[28/27]] equal to [[27/26]], tempering out [[729/728]]. This maps the 13th harmonic, [[13/8]], to the sesqui-augmented second (D{{sesquisharp}} on C).
-.3.7.11.17.19 extension: [[2057/2052]], [[513/512]], [[154/153]], [[243/242]]