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Encyclopedia of Microtonal Music Theory

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[Brink McGoogy, with Joe Monzo]

A small interval used to separate two mappings that occur on the traditional Halberstadt keyboard. It usually occurs between the F and the F#. Its design is to accomodate two separate mappings, one on the white keys and one on the black keys, which maintain the approximate chromatic ordering of a 1/3-tone edo such as 17-edo or 18-edo.

To date [2005] there are two species of mappings which incorporate the brinko:

  1. pyramid-of-mars symmetry (refer to its own separate Encyclopedia entry)
  2. phinnochian (5- and 7-node wheels of Enoch):

  3. Lowering the 5-note mapping by an offset of about 130 cents works well, giving a brinko of ~12.8 cents, as illustrated below:

    brink tuning: phinocchio, table of cents values and pitch-height graph

The phenomenon of the brinko was encountered in 1992 by Brink McGoogy.

The above example is one which exhibits the "asymmetrical brinko". When fitting together the two mappings (5-tone and 7-tone), the brinkos between F:F# and A#:B are mutually exclusive. Making one larger will always make the other smaller. If F and F# are made the same pitch (i.e., brinko = 0, as in a tuning created by Buzz Kimball before the brinko was discovered), A#:B is the maximum brinko size. If A# and B are the same pitch, F:F# is the maximum brinko size, and is the same as the previous case. Thus this is the full range of size of the brinko.

Brink's own preferred brinko tuning is a special case, analagous in some ways to 12-edo, and in other ways to meantone (so it's a sort of "mean-brinko"), is the symmetrical brinko tuning. Brink designed the symmetrical brinko tuning in which the brinko between F:F# is the same as the brinko between A#:B.

brink tuning: phinocchio with symmetrical brinko, table of cents values and pitch-height graph
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