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Propeller Head Plaza Technical and scientific discussion of amps, cables and other topics. |
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Propeller Head Plaza Technical and scientific discussion of amps, cables and other topics. |
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In Reply to: Re: Cheever's Fundamental Misconception posted by Scott Frankland on May 21, 2003 at 09:55:21:
Hi Scott,The nice thing about using the property of an even harmonic to
"neutralize" an odd harmonic, means that the Null condition can be
attained solely by using the local properties of frequencies. As you
say in your message, I think this means that a wider range of
harmonic patterns will be acceptable to give a Null condition.In addition, what do you think of combining this neutralizing
notion with the relative dissonance of an odd harmonic? The
Figure 4 that appeared in part I of Hiraga's article in the
Feb 2002 audioXpress for instance?The way these two concepts could be combined is this...
since a 2nd and 3rd are very consonant, then it would make sense
that a slightly stronger 2nd would eliminate most of the problems
with the 3rd. Same goes for 4th and 5th.The higher in harmonics we go, the more dissonance there is. This
shifts the relative balance of strengths to neutralize between even
and odd harmonics shifts. As we have seen, the odd harmonics between
the 7th-13th are very dissonant. For the 6th to neutralize the 7th,
it would take a much larger amount of 6th to "neutralize" the 7th.
This in contrast to the relative equal ratio of 2nd to "neutralize"
the 3rd. Between the 7th-13th, I could see the amount being
proportional to the harmonic number. So a 6th would need to be at
least 6-7 times stronger to neutralize the 7th. Same goes for 10th,
etc...Once you get out to the 14th and beyond, the distinction between
dissonance and non-disonnance of even and odd harmonics is lost.
The 14th corresponds to a way out of tune dominant 7th, which is
more akin to what we would associate with an odd harmonic. This
means that the simple rule of using an even harmonic to "neutralize"
an odd harmonic is lost out in this range.At the 16th, we are back in tune (4 octaves), so this is a viable
"neutralizer". Then on beyond 16th, the harmonics drift progressively
more dissonant and out of tune, back in tune again and consonant at
the 24th, and again degenerate into behaving mostly like odd
harmonics beyond that until we reach the 32nd.So a simplifying assumption for anything beyond the 13th might be
that they should simply be as far down under the noise floor as
possible. Perhaps some of these "Super amps" with their ultra low
distortion fiugres might actually be getting into trouble with
some of these "Super" harmonics (> 13) since they are so dissonant.
It would take relatively little amounts of them, and they would not
be easily masked, since there are relatively few consonant neighbor
harmonics to mask them.
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Follow Ups
- Re: Cheever's Fundamental Misconception - mfc 05/22/0319:10:27 05/22/03 (1)
- Re: Cheever's Fundamental Misconception - Scott Frankland 22:19:27 05/22/03 (0)
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