Where F + f = O

A (factitious) "two and only two sizes" for every 1 - ? EDO�

If "d" = division (any so defined equidistant {d}ivision of the octave), "F"
= 7 (a {F}ifth), "f" = 5 (a {f}ourth), and "O" = 12 (an {O}ctave), and you
take the arithmetic means of f[d] and F[d] and use them as a �median� F/f @
7.1/35 and 4.34/35: (f � O x F) + (F � O x F)/(f � O x f) + (F � O x f)�

And if d = (d � O) X F/(d � O) X f, (d � O) X F = {[(d � O) X F] � (O X
F)}/ {[(d � O) X F] � (O X f ), and (d � O) X f = {[(d � O) X f ] � (O X
F)}/{[(d � O) X f ] � (O X f )}, you could use ({[(d � O) X F] � (O X F)} +
{[(d � O) X F] � (O X f )) and ([(d � O) X f ] + {[(d � O) X f ] � (O X f )}
as {H}orizontal and {v}ertical {c}oordinates on a I�IV�V triad square where
the first (root), third and fifth of the I, IV and V, delineate the
1st�3rd�5th, 4th�6th�8th, and 5th�7th�(9th - 7) of a + w + w + h + w + w + w
+ h diatonic heptad�

And if Hc 1, 2 and vc 1, 2 are �literally� represented as decimal
fractions/mixed decimals where:

0 = the one of the tonic (the d 1st)
0 + {[(d � O) X F] � (O X F)} = the third of the tonic (the d 3rd)
0 + {[(d � O) X F] � (O X F)} + {[(d � O) X f] � (O X F)} = the fifth of the
tonic (the d H5th)

0 + [(d � O) X f ] = the one of the subdominant (the d 4th)
0 + [(d � O) X f ] + {[(d � O) X F] � (O X F)} and {[(d � O) X F] � (O X F)}
+ [(d � O) X f ] = the third of the subdominant (the d 6th)
0 + [(d � O) X f ] + {[(d � O) X F] � (O X F)} + {[(d � O) X f] � (O X F)}
and {[(d � O) X F] � (O X F)} + {[(d � O) X f] � (O X F)} + [(d � O) X f ] =
the fifth of the subdominant (the d 8th)

0 + [(d � O) X f ] + {[(d � O) X f] � (O X f )} = the one of the dominant
(the d v5th)
0 + [(d � O) X f ] + {[(d � O) X f] � (O X f )} + {[(d � O) X F] � (O X F)}
and {[(d � O) X F] � (O X F)} + [(d � O) X f ] + {[(d � O) X f] � (O X f )}
= the third of the dominant (the d 7th)
0 + [(d � O) X f ] + {[(d � O) X f] � (O X f )} + {[(d � O) X F] � (O X F)}
+ {[(d � O) X f] � (O X F)} - d and {[(d � O) X F] � (O X F)} + [(d � O) X
f] � {(O X F) + [(d � O) X f ]} + {[(d � O) X f] � (O X f )} - d = the fifth
of the dominant (the d 2nd)

Then an internally consistent representation (representation being the key
word here, least this all be some manner of numeric sophistry) of diatonic
seconds should be achieved from rounding off the decimal fractions/mixed
decimals of �w�w�h�w�w�w�h�* to the nearest integer.

Respectfully,
Dan Stearns

*Actually this should be: + Lw + Sw + Lh + Sw + Lw + Lw + Sh. As there would
be both a {L}arge and {S}mall diatonic �half-step�, and a {L}arge and
{S}mall diatonic �whole-step� derived from a sort of �ordinal� interval
where the arithmetic mean of F + f squared = [(+ Lw + Sw + Lh + Sw + Lw + Lw
+ Sh) � (v5 - H5)], and d is always comprised of mF + mf squared (4,900
�ordinal� intervals) arranged + 841 + 840 + 349 + 840 + 841 + 841 + 348�
Eventually the integer representations of the w and h diatonic seconds will
round L and S up and down by one digit; when�? I don�t know� But I suspect
it would be well beyond any 'utilitarian' representation of d. (3 is the
first equidistant division of the octave to demarcate the integers of w and
h.)