Octaves and farewell

On the question of casting out 2s from ratios, I think that the
strongest evidence that I can give that this is a significant thing is
to compare the two chords 8:15 and 15:16. The former is more pleasant
to hear than the latter.

Also, with a series like 1:2:4:8 the addition of notes at ratios of 5/4
(or 9/8 or similar) to the tonic is much more pleasant at the high end
than the low (i.e adding 5 or 10 above rather than 5/4 or 5/2).
Generally this is practiced in music, with much tighter chords in the
treble than in the base.

Therefore the octave in which a note appears is always important.

Shortly I will be unsubscribing from the list for a while at least.
I would like to thank everyone for lots of stimulating ideas and
conversation. This is without a doubt the most noise free part of
internet that I have ever found and you are to be congratulated.

My reason for departing is that tuning as such is more of a sideline
interest of mine and I have just started a cycles list myself which will
keep me busy for a while. That list can be joined by sending a message
to cycles-request@esosoft.com with subscribe in the body of the message.

I would welome email from anyone here on the wider aspects of tuning as
found in nature and the universe at large. See you around, Ray.

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