Re: CHAT: conlang and alternate tuning WAS: from the ashes...

Christophe Grandsire:

> Well, I read the page, and though I understand the principle, I
> still don't
> understand the implications (the intervals must be expressed as
> ratios of whole
> numbers, but compared to what? And what is really a temperament?).
> Maybe an
> example would be welcome. Since the last conlang I created is
> accompanied with
> a conculture which has absolutely nothing to do with European
> culture, I'd like
> to come up with a musical scale which is original for them :)) .
If one applies the whole-number ratios to frequency values, one
can derive a justly tuned scale.  For example, taking the tone
A = 440 Hz and a series of intervals for a major scale:
1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2/1

gives us
Note    Ratio   Freq (Hz)
A       1/1     440.000
B       9/8     495.000
C#      5/4     550.000
D       4/3     586.667
E       3/2     660.000
F#      5/3     733.333
G#      15/8    825.000
A       2/1     880.000

The equal temperament systen divides the frequency range
into (logarithmically) equal intervals, so the same scale notes
would be somewhere like:

A               440.000
B               493.333
C#              554.365
D               587.330
E               659.255
F#              739.989
G#              830.609
A               880.000

Of course, finer interval divisions result in more tones per
"octave" (a poorly-named concept, as it turns out) than the
12 usual in Western music.

The previously-cited Just Intonation Network http://www.dnai.com/~jinetwk
has a good number of links to articles (from one of which I lifted
the above example).

-Tone generator

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