The title was supposed to be a pun on the fact that this song uses an
alternate temperament: it doesn't. What it does use is an alternate "tuning".
Since the time that I wrote the song, I got smarter about
All notes in the scale are tuned to harmonics of the
fundamental, up through the 25th (only the 23rd is not used). This is
either really cool or really geeky. I'm not sure, but I think both.
The drone section was played by a BASIC program (which I wrote) running
on my trusty C-128 with its powerful 1MHz 6502-style processor. (Maybe
more geeky than cool after all). I seem
to like this kind of stuff, but as a public service, I only put about
three minutes of droning on the album. You're welcome.
To finally go over the geeky fence, here are the ratios of all of the
notes in the key of C (the song is in D and C and uses different tunings
for each key):
|Note ||Ratio ||Fraction (exact)
|C ||1:1 ||1.0
|C# ||17:16 ||1.0625
|D ||9:8 ||1.125
|Eb ||19:16 ||1.1875
|E ||5:4 ||1.25
|F ||21:16 ||1.3125
|F# ||11:8 ||1.375
|G ||3:2 ||1.5
|Ab ||25:16 ||1.5625
|A ||13:8 ||1.625
|Bb ||7:4 ||1.75
|B ||15:8 ||1.875
|C ||2:1 ||2.0
If you're interested in more on alternate tunings: you can check
out the alternate tuning mailing list. Send an e-mail message to:
with a blank line followed by:
SUBSCRIBE TUNING < your e-mail address >
and you'll be added to the Alternate Tuning mailing list.
In case you're interested, temperament refers to scales that are
not based directly on simple ratios. The twelve tone scale typically
used in western music is based on a ratio of the twelfth root of two
(really). This is an irrational number. Thus western music uses a
"tempered" scale, rather than a "just" scale. The scale described
above is a 12-tone, 19-limit just scale (19 refers to the largest
prime number that appears in any of the ratios).
Tempered scales are to Just scales as Irrational numbers are to
Rational numbers. If that helps.
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