153edt: Difference between revisions

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153edt is notable for being the denominator of a convergent to log<sub>3</sub>(7/3), after [[9edt]], [[13edt]] and [[35edt]], and the last before [[3401edt]], and therefore has an extremely accurate approximation to [[7/3]]. In fact, 153edt demonstrates 11-strong 7-3 [[telicity]], due to the next term in the continued fraction expansion being large (note how much larger 3401 is than 153), although 3401edt in fact surpasses it, demonstrating 16-strong 7-3 telicity.

153edt is notable for being the denominator of a convergent to log<sub>3</sub>(7/3), after [[9edt]], [[13edt]] and [[35edt]], and the last before [[3401edt]], and therefore has an extremely accurate approximation to [[7/3]], a mere 0.0036 cents flat. In fact, 153edt demonstrates 11-strong 7-3 [[telicity]], due to the next term in the continued fraction expansion being large (note how much larger 3401 is than 153), although 3401edt in fact surpasses it, demonstrating 16-strong 7-3 telicity.

In the no-twos [[7-limit]], 153edt supports [[canopus]] temperament, which gives it a rather accurate approximation of the 5th harmonic; and it additionally is accurate in the [[11-limit]], tempering out the comma [[387420489/386683451]] in the 3.7.11 subgroup. Harmonics 19 and 29 are also notably good.

However, 153edt's approximation of [[2/1]] is close to maximally bad, meaning that it is as far from an octave-equivalent tuning that an [[EDT]] of this size can be (though by this point, it is only 6 or so cents off).

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 {{Harmonics in equal|153|3|1|intervals=prime}}
-edt is notable for being the denominator of a convergent to log<sub>3</sub>(7/3), after [[9edt]], [[13edt]] and [[35edt]], and the last before [[3401edt]], and therefore has an extremely accurate approximation to [[7/3]]. In fact, 153edt demonstrates 11-strong 7-3 [[telicity]], due to the next term in the continued fraction expansion being large (note how much larger 3401 is than 153), although 3401edt in fact surpasses it, demonstrating 16-strong 7-3 telicity.
+edt is notable for being the denominator of a convergent to log<sub>3</sub>(7/3), after [[9edt]], [[13edt]] and [[35edt]], and the last before [[3401edt]], and therefore has an extremely accurate approximation to [[7/3]], a mere 0.0036 cents flat. In fact, 153edt demonstrates 11-strong 7-3 [[telicity]], due to the next term in the continued fraction expansion being large (note how much larger 3401 is than 153), although 3401edt in fact surpasses it, demonstrating 16-strong 7-3 telicity.
 In the no-twos [[7-limit]], 153edt supports [[canopus]] temperament, which gives it a rather accurate approximation of the 5th harmonic; and it additionally is accurate in the [[11-limit]], tempering out the comma [[387420489/386683451]] in the 3.7.11 subgroup. Harmonics 19 and 29 are also notably good.
 However, 153edt's approximation of [[2/1]] is close to maximally bad, meaning that it is as far from an octave-equivalent tuning that an [[EDT]] of this size can be (though by this point, it is only 6 or so cents off).