Peterson AutoStrobe 490 - Manual (Page 25)

Page 27
APPENDIX B:
WHY BE CONCERNED ABOUT UNEQUAL TEMPERAMENTS?
Temperament refers to the specific frequency (pitch) intervals placed between notes in a musical scale. With 12 notes per
octave (the most prevalent case but, by no means, the only case), there are an infinite number of ways to set the audio
frequencies of these notes relative to one another. Through the centuries, many have wrestled with the challenge of creating
the most pleasing, yet universally flexible, temperament of these 12 intervals. It turns out that it is mathematically impossible
to achieve both completely, that is, if by "pleasing", one means smooth beat-free intervals, and, if by "flexible", one means
satisfactory harmony in all possible key signatures.
Since compromise is the only option, it should come as no surprise that there exists about as many different well-defined
temperaments as there are people who have attempted to create them. The fact is: both of these goals—pleasing and
flexible—are moving targets. The requirements of harmonicity and key signature flexibility have changed greatly over the
centuries in general and vary just as greatly from person to person. For example, a piece in the 18th-century baroque style
might never modulate from a single key signature (or perhaps just to the very similar "5th" key). A temperament which is
functional in just a handful of keys might be (and was) satisfactory. In 20th-century western music, all keys and scale notes
are fair game, sometimes even within a single piece. Moreover, through the years, people have become more accepting of
complex and "closer" simultaneously sounded harmonic intervals. Harmonies that would have been considered unbearably
dissonant 150 years ago are now considered "colorful"—even beautiful—by many today. With such complex harmony and
effects like parallel harmonic movement, it is generally better to have harmonic relationships that are moderately imperfect,
but equally imperfect over all key signatures. Thus, Equal Temperament

has generally won out in modern music. You may
never have considered before that it is the adherence to this temperament that allows one to unthinkingly transpose a musical
piece to any key on a piano with no ill effects.
So, why worry about altered temperaments if equal temperament is so pervasive? The reasons are many and varied. Because
equal temperament lands so squarely in favor of flexibility, some of the intervals are, well, not very pleasing. For example,
major thirds are about 14 cents sharp from the "perfect" non-beating interval...and how often do you play a piece of music
with no major thirds anywhere? In some music, on some instruments, this is bearable. (We certainly have had a lot of
opportunity to get used to it!) But play a major third interval using a brass or reed sound (with no chorusing or other effects)
on a standard equally-tempered synthesizer, and you will understand something about why people still want to hear "live"
horn sections. No matter how good the actual timbre

of the synthesized sound is, there is something very "unhorn-like"
and disturbing about that simple harmony. Good brass and reed players constantly, and sometimes unconsciously, "lip" the
notes they play to minimize intervalic beating with notes played by others in their section.
Players of other types of instruments are not so lucky. There can be no adjusting of strings on-the-fly while playing a fretted
string instrument like a guitar; there is no "lipping" possible while playing several hundred pipes in a pipe organ. If one is
playing a program which includes classical period pieces, he will simply never achieve on an equally-tempered instrument
the beautiful effect that the composer had envisioned when composing the piece for a Just or Mean-Tone tempered
instrument. Similarly, because of their unique use of certain musical intervals, instruments like the steel slide guitar can
benefit by purposely tuning to un-equal temperaments.
Sometimes unequal temperament can be used to help correct inherent deficiencies in certain types of instruments. Fretted
instruments like the guitar are designed to be equally-tempered but it turns out that slightly altered tunings of the open strings
and harmonics relative to the fretted notes can improve the overall sound of the instrument. This is because real strings do
not act quite the same as the theoretical models that must be assumed when designing musical instruments around them.
Similarly, makers of musical instruments (such as the steel drum, bells, xylophone, etc.) which have very inharmonic timbres
can benefit from a tuner with altered temperament capabilities by using the note offsets to mimic the desired "harmonics"
(or, more accurately, partial frequencies) inherent in a given sounded tone. The programmable nature of temperaments in
the Model 490 means less work compared to constantly "dialing in" different harmonic offsets.
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