53edo: Difference between revisions

Many of its multiples such as [[159edo]], [[212edo]], [[742edo]], [[901edo]] and [[954edo]] have good consistency limits and are each of their own interest. The [[mercator family]] comprises rank-2 temperaments with 1/53-octave periods.

=== Ups and downs notation ===

53edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).

Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:

{{Sharpness-sharp5}}

In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.

Because the 5th is so accurate, 53edo also offers good approximations for Pythagorean thirds. In addition, the 43\53 interval is only 4.8 cents wider than 7/4, so 53edo can also be used for 7-limit harmony, in which it tempers out the [[septimal kleisma]], 225/224.

| Schismina

<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave

=== 21st century ===