source file: mills2.txt
Date: Tue, 10 Sep 1996 08:54:13 -0700

Subject: Re: Babies and tuning

From: linusliu@hk.super.net (Linus Liu)

Oh, yes, it is. We first aware that listeners feels notes being in tune or
out, and then tell it. That is why there is this tuning list, right?

To explain why is another matter.

Any interval can be in tune if that interval can be and is used properly
in music. Therefore:

 do 10/9 re 10/9 me 27/25 fa 9/8 so 10/9 la 10/9 te 27/25 do

is a good scale because 1. identical tetrachords 2. same size whole tones
adjacent to each other in each tetrachord 3. tetrachords a 3/2 good fifth
apart. And:

 do 9/8 re 9/8 me 16/15 fa 10/9 so 9/8 la 9/8 te 16/15 do 

is also a good scale (Chinese scale) because of the very same reasons, plus
the fact that the interval 9/8 is only 0.3 cent away from the tempered
1221.5 cent per octave mean tone (you call it equal tempered, 101.8
cent per half-tone) scale. 9/8 = 203.9 cents vs 101.8 x 2 = 0.3 cent 
difference.

You put half each scale from each to make a new scale, then you get a
lousy scale.

When playing music FOR the Chinese scale, the intervals 81/64 (do-me),
 32/27 (me-so), and 5/4 (fa-la) are all good intervals in the same 
music.

Linus Liu.

>   I'd say that it's not so much a matter of telling when a note is out of tune
>as devising a strict mathematically rigorous definition - or even a general
>qualitative definition - of what constitutes being in-tune.  Every careful
>studies I'm aware of suggests that singers players of indefinite-pitch
>instruments don't consistently follow any one particular standard.  
>
>   And then you have to answer the question of whether an exactly perfect 9:7
>third (for example) should be considered in-tune or out-of-tune.  It's out of
>tune if 2^4/12 or 5:4 is your basis for deciding, but, by definition, it's
>exactly in-tune if 9:7 is your goal.  
>
>   We probably need a few more words or phrases to describe these new concepts.
>
>


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