beta, Β

1. Scale / Tuning

A scale devised by Wendy Carlos, which does not have octaves, because of its equal "step size" of 63.8 ¢, with 18.809 steps per "octave".

It is "defined strictly as a local minimum of the root-mean-square error function that Wendy set up with 3/2, 5/4, 6/5, 7/4, and 11/8 as target intervals." [Paul Hahn, Onelist Tuning Digest 116]

The Carlos Beta tuning splits a tempered "perfect-4th" into two equal parts, each of which in turn are twice divided in half - thus, the perfect-4th subtends 8 equal steps of 63.8 ¢ each. The first "8ve" of this scale is covered by the following notes in descending order:

               degree  cents

                19   1212.2
                18   1148.4
                17   1084.6
                16   1020.8
                15    957
                14    893.2
                13    829.4
                12    765.6
                11    701.8
                10    638
                 9    574.2
                 8    510.4
                 7    446.6
                 6    382.8
                 5    319
                 4    255.2
                 3    191.4
                 2    127.6
                 1     63.8
                 0      0
		

Various EDOs give approximations to the Carlos beta scale:

• 19-edo is a fairly low-cardinality tuning which gives a rough approximation of the beta tuning, with 1deg19-edo giving a passable approximation to one step of beta. But its approximation of the 3/2 ratio is 11deg19-edo, which is the same narrow 5th which acts as the generator in 19-edo's role as the 19-et approximation of 1/3-comma meantone, and the error from the beta 5th is enough to be audibly noticeable.
• 94-edo gives a much better approximation of beta, at the cost of much higher cardinality, with 5deg94-edo closely approximating one step of beta, and 55deg94-edo giving a very good approximation of the beta 5th.

2. Note

Used in its lower-case form β as an additional letter-name in Erv Wilson's notations, signifying a note near "B", but with a musical function separate from "B", in whatever particular scale the notation is describing. See The Wilson Archives for examples and explanations of his notation.