AW.: RE: RE: Harmonic entropy

I thought it would be useful to throw this into the discussion:

From Klarens Bharlogh(1), _Bus Journey to Parametron (all about
_Cogluotob�sisletmesi_)_ (Feedback Papers 21-23):

...It is probably clear by now that the described system of tonality
evaluation works on the basis of just intonation, and would thus seem to
preclude the use of a tempered instrument, were it not for the already
mentioned tendency of the mind's ear to bend slightly deviant pitches to an
optimal value. In order to guage the tonality of the field creatable in a
certain mode around a given tonic, one would have to know the tuning of the
scale as desired and/or interpreted by the ear. Whether the ear would be able
to succeed in fulfilling this desire would depend upon its tolerance towards
two types of aberration:
1. the deviation of the imagined pitch from the given one, and
2. the contraction or expansion of the steps in the scale resulting from the
aforesaid stretch of the imagination.
After some experimenting, I arbitrarily set the tolerance limits for these
two phenomena at +/- 25 (this value leads to the zone limits contained in
Appendix VII(2)) and +/- 18 cents, respectively (by comparison, most music
lovers are quite willing to accept a tempered 200 cent whole tone as a
substitute for the 182 cent major second between the second and third degrees
of a major scale). For example, if the ear's bent for bending causes a given
note 100 cents above the tonic to be pushed up to 111.7 (ratio 16/15) and the
next given note 200 cents above the tonic to be pulled down to 182.4 cents
(ratio 10/9), the size of the resulting halftone step imagined between them
would be a mere 182.4-117 = 70.7 cents, outside the prefixed step tolerance
limits (+/- 18 cents); this form of imaginary tuning would have to be
rejected as exaggerated, as would the mental readjustment of a tritone to
568.7 cents (ratio 25/18), outside the zonal limits (600 +/- 25).

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(1) In Clarlow's publications, the orthography of the author's name is highly
variable.
(2) Appendix VII presents the "most tonal intervals"(3) for each zone +/- 25
cents about each tone of a 24tet scale continued to a Major tenth. The
possible intervals were selected from the set of ratios where the terms of
the ratio have maximum 4 digits and maximum absolute values 2^13, 3^7, 5^3,
7^2, 11^1. Taking the single best candidate in each quartertone zone, Barlow
gets the following:
25/24, 16/15, 27/25, 9/8, 8/7, 6/5, 11/9, 5/4, 9/7, 4/3, 25/18, 7/5, 36/25,
3/2, 14/9, 8/5, 81/50, 5/3, 7/4, 16/9, 50/27, 15/8, 27/14, 2/1, 25/12, 32/15,
35/16, 9/4
(3) In more recent publications, Bahlowe uses "harmonicity" instead of
"tonality", which is now reserved for "harmonic cohesion".