Escapade family: Difference between revisions
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The '''escapade family''' tempers out the [[escapade comma]], {{monzo|32 -7 -9}}, of size 9.492 [[cent]]s. The defining feature of this comma is splitting [[5/3]] into sixteen quartertones of which [[5/4]] makes up seven and [[4/3]] makes up nine; therefore [[16/15]] is two generator steps. It most naturally manifests as a [[2.3.5.11 subgroup]] temperament, tempering out [[4000/3993]] and [[5632/5625]]. | The '''escapade family''' tempers out the [[escapade comma]], {{monzo|32 -7 -9}}, of size 9.492 [[cent]]s. The defining feature of this comma is splitting [[5/3]] into sixteen quartertones of which [[5/4]] makes up seven and [[4/3]] makes up nine; therefore [[16/15]] is two generator steps. It most naturally manifests as a [[2.3.5.11 subgroup]] temperament, tempering out [[4000/3993]] and [[5632/5625]]. | ||
Extensions of escapade to incorporate prime 7 (and therefore the full [[11-limit]]) include escapist {{nowrap|(21 & 22)}}, tempering out [[225/224]] and mapping 7 to −4 generators; escaped {{nowrap|( | Extensions of escapade to incorporate prime 7 (and therefore the full [[11-limit]]) include escapist {{nowrap|(21 & 22)}}, tempering out [[225/224]] and mapping 7 to −4 generators; escaped {{nowrap|(22 & 87)}}, tempering out [[245/243]] and mapping 7 to −26 generators; alphaquarter {{nowrap|(65d & 87)}}, tempering out [[5120/5103]] and mapping 7 to 61 generators; septisuperfourth (aka biscapade) {{nowrap|(22 & 86)}}, tempering out [[6144/6125]], splitting the octave in half and mapping 7 to −15 generators; and arch {{nowrap|(43 & 87)}}, tempering out [[3136/3125]] and splitting the generator into two [[64/63]] intervals; all are considered below. | ||
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