Ray Tomes's scale

perlich@acadian-asset.co writes
>Ray Tomes wrote,
>
>>> C D Eb E F G A Bb B
>>>24 27 28 30 32 36 40 42 45
>
>Ken Moore wrote,
>
>>Very reasonable scale,
[...]
>If you're going to demand a logical notation here, start by noticing that
>the fifth from D to A is flatter than just.

But any complete just scale of C major needs two As. This one is the
major third above F. Two major tones (which is what four perfect fifths
generate) is different.

--
Ken Moore
ken@hpsl.demon.co.uk
Web site: http://www.hpsl.demon.co.uk/

Ken Moore [TD227.13]

>>Ray Tomes wrote,
>>>> C D Eb E F G A Bb B
>>>>24 27 28 30 32 36 40 42 45

>But any complete just scale of C major needs two As. This one is the
>major third above F. Two major tones (which is what four perfect fifths
>generate) is different.

The above is the usual standard JI scale plus two extra black notes.
The standard has only one A. Of course the other A is also desirable
but not absolutely essential. The same applies to a second D etc.

The origin of this scale can be seen in my post TD 202.15 which I won't
quote here as it is too long. The essence of that post is that is shows
a complete pattern of development from unity to the most complex scales.
The pattern that I list above is the part from 48 to 96 (the beginning
of that post). By two octaves later (192 to 384) the numbers 320 and
324 (i.e 4 times 80 and 81) are roughly equal as Ken says, but in the 48
to 96 octave 81 is very weak (unimportant) by comparison to 80 (I am
taking liberties with powers of 2 here).

I would say that this scale has the maximum possible 7 limit
relationships for the number of notes but very limited ability for
modulation to nearby keys. If some section is selected from further up
the harmonic series in TD 202.15 then greater modulation capability
exists but a larger number of notes are also required.

-- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
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