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OT CHAT Re: Non-Human Phonology

From: Roger Mills Monday, December 4, 2006, 21:25
```Carsten Becker wrote:
>
> An easier way to determine a tritone is to have a look at
> the cycle of fifths (I hope it'll get through correctly):
>
>                C
>          F     |     G
>        Bb      |       D
>      Eb -------+------- A
>        Ab      |       E
>          Db    Gb    B
>                F#
>
> As you can see, F and B are on opposite sites (11 and 5
> o'clock respectively), so you've got a tritone there.
>Love your little chart!! This is probably obvious to everyone, but I find it
interesting:

Any note at X o'clock, plus the note at (X +/- 6) o'clock, makes a tritone.
(At least, in standard piano tuning)

Given a tritone, if you raise the top note 1/2 step and lower the bottom
tone 1/2 step, you resolve to a major chord; this is because, of course, the
tritone contains 2 of the 4 notes of a Dom7, which of course resolves to
Tonic.

C-F# (D7)> B-G (G) // F#-C > F-C#/Db > C#/Db (and note that the new tonic
notes also make tritone: G--C#/Db, what fun)

Ab-D (Bb7) > G-Eb (Eb) // D-Ab/G#> Db/C#-A (A) etc. etc. etc.

(Had to go to the piano to be sure :-)))

I assume this is also a well-known fact:
The difference between any two consecutive perfect squares is equal to (1*)
the sum of their sq.roots (I.e. 36-25 = 11 = 6+5

The difference between the square of x^2 and (x+2)^2 is 2* (the sum of
x+x+2) ( 64-36 = 28 = 2*(8+6)

and so on up.  Not sure this is useful knowledge :-)))
```