User:BudjarnLambeth/Draft related tunings section

This is a draft of what a standard "related tunings" section might look like on edo pages, using 36edo as an example.

Todo:

• Choose a more sensible set of tunings (eg remove zpis and ed255/128-type things and ads n-limit WE, n-limit TE type things)
• Make the mapping info take up less horizontal space
• Add a column for amount of stretch (maybe as a %?)
• Change error columns to use absolute error (in cents) rather than relative error (%)

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Related equal tunings

What follows is a comparison of stretched- and compressed-octave 36edo tunings.

Of the stretched-octave tunings listed, 36ed513/256, with a step size about 33.4 cents, performs best in this comparison, approximating all 11-limit primes with less than 36% relative error (< 12 cents error).

Of the compressed-octave tunings listed, 36ed511/256, with a step size about 33.25 cents, performs best in this comparison, approximating all 11-limit primes with less than 36% relative error (< 12 cents error).

The edonoi scales of 57edt and 101ed7 are almost exactly the same as 36edo. They are 36edo with the octave stretched by less than 1 ¢. Their main usage is to optimise 36edo for use as a dual-5 tuning, while also making slight improvements to 3/1 and 7/1 as well. So if one intends to use both 36edo's vals for 5/1 at once, 57edt or 101ed7 may be worth considering.

Tuning	Step size (cents)	Error (% step size)					Mapping (# steps)
		Prime 2	Prime 3	Prime 5	Prime 7	Prime 11	Prime 2	Prime 3	Prime 5	Prime 7	Prime 11
154zpi	33.547	+23	+31	-5	-41	+27	36	57	83	100	124
36ed257/128	33.521	+20	+26	-12	+50	+15	36	57	83	101	124
36ed513/256	33.427	+10	+11	-35	+23	-18	36	57	83	101	124
57edt	33.368	+4	0	+50	+5	-40	36	57	83	101	124
101ed7	33.355	+2	-2	+46	0	-46	36	57	84	101	124
155zpi	33.350	+2	-3	+45	-1	-48	36	57	84	101	124
36edo	33.333	0	-6	+40	-6	+46	36	57	84	101	125
36ed511/256	33.239	-10	-22	+18	-35	+11	36	57	84	101	125
156zpi	33.152	-20	-37	-5	+38	-23	36	57	84	102	125
36ed255/128	33.145	-21	-38	-6	+36	-25	36	57	84	102	125