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| Ratiotonic Temperament: A Proposal for the
Organization of Tones in Art Music as an Alternative to Twelve-Tone Equal Temperament Peter Lucas Hulen
In order to
accommodate a more or less equal range for all eight contonations
and the total network of tones they share, a unified temperament must
be
developed. In order to fit a suitable range of pitches onto a
commercially-available
electronic instrument capable of the necessary fine detuning, the tones
of all eight contonations must be combined and arranged in ascending
order
(a custom-made electronic instrument constructed according to this
system
remains to be created). Many instruments have a range of ten and
one-half
octaves divided into twelve tones each (128 notes in all). Figure 5
illustrates
how a hypothetical instrument with a range of C-2 to G8 (128 notes)
could
be detuned to accommodate such a range of pitches (in fact the Yamaha
TX802
FM tone generator, for example, has a range from C-2 to G8, and it will
detune to within 0.5859375 cents [1/1024 of an octave] of a specific
value
in whole cents, so this chart could be adapted to detune that
instrument
according to the overall system). The black noteheads indicate the
default
notes of the hypothetical instrument, while the white noteheads aligned
with them indicate the pitches to which they would be detuned (plus or
minus so many cents as indicated). The letter names indicate the
primary
tone(s) of the contonation(s) containing the given note. The ranges of
the contonations as given in the "Table of Contonations" in the
Appendix
correspond to this 128-note range of pitches shown in Figure 5. | View Figure 6 | Page 1 | You are on Page 2 | On to Page 3 | Page 4 | Appendix Peter Lucas Hulen is Byron K. Trippet Assistant Professor of Music at Wabash College in Crawfordsville, Indiana, USA. © 2005 Peter Hulen |
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