153edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
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. | 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. | ||
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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). | 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). | ||
== Intervals == | |||
{{Interval table}} | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 153 | |||
| num = 3 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 153 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||