4L 5s (3/1-equivalent): Difference between revisions

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{{Scale tree|depth=7|Comments=9/4:BPS is in this region}}
{{Scale tree|depth=7|Comments=9/4:BPS is in this region}}


Schism, by which I<sup>[''who?'']</sup> mean, the most accurate value for 5/3 and-or 7/3 is found outside the 4L 5s MOS.
Analogously to how the diatonic scale equalizes approaching [[7edo]] and its small steps collapse to 0 in [[5edo]], this scale equalizes approaching [[9edt]] and its small steps collapse in [[4edt]]; therefore, temperaments setting the 7/3 generator to precisely 7\9edt and to precisely 3\4edt are analogs of [[whitewood]] and [[blackwood]] respectively; however, unlike for the diatonic scale, the just point is not close to the center of the tuning range, but approximately 1/4 of the way between 9edt and 4edt, being closely approximated by 37\[[48edt]] and extremely closely approximated by 118\[[153edt]].
 
Also, the way I see it, as 4edt and 9edt are comparable to 5edo and 7edo, then the "counterparts" of Blackwood and Whitewood would be found in multiples therein and would be octatonic and octadecatonic, e.g. 12edt and 27edt.{{clarify}}