Re: Kraig Gradys questions about 3x5 (Es, Ps & Is... etc.)

0+w2+h3+w5+w7+h8

0. (wh)w(wh)
2. [hw]w[hw]
3. w(wh)(wh)
5. (wh)(wh)w
6. [hw][hw]w
8. (wh)w(wh)

>This is the pentatonic as a subset of a 7 tone scale with w=2steps and
h=1st

It�s a five note subset of eight equidistant divisions of the octave where:

"d" is eight
and d � O � F = dF
and dF is five�*

>Still don't get the Es, Ps & Is and what does it tell us

In the case of the 3x5 pentad the Es and Ps delimit the n-tETs that are
incapable of representing a 3w + 2h scale where nw=nw, nh=nh and n<0� And
the Is defines the most immediate n-tETs that will represent the 3x5
pentad - as all equidistant divisions of the octave after 3 � 5/5 � 3 will
contain a 3x5 pentad where w=w, h=h and h<0.**

Respectfully,
Dan

*For more detailed (though probably not much more profitable) explanation of
this, see Jan. 11th post "Three sets of "O".

**Again the post from the 11th allows a more detailed context (the f/F right
triangle) to illustrate the properties of the Es, Ps, and Is...