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In Reply to: Re: Another way to calculate THD posted by Scott Frankland on May 16, 2003 at 11:53:50:
Hi,I made a spreadsheet of all the harmonics that shows what note
they produce, what relationship it is (ie. fifth, major 3rd, etc),
and how out of tune it is with the well tempered scale. Anybody
that wants it can request via email.Ignoring masking effects for now that Cheever and Hiraga
take up in an absolute terms. This really complicates things as
I've learned before. I'm still trying to understand how to work
with this concept.Anyway, one step at a time. First...
It looks like you might be able to take a normal THD calc:
sqrt(N2*N2 + N3*N3 + ...)
and apply a weighting factor to each harmonic. I know this has
been proposed many times before, but I'm looking at it as how
consonant or discordant the harmonics are in order to set the
weighting factor.sqrt(W2*N2*N2 + W3*N3*N3 + ...)
Accounting for the 2nd, 3rd, 4th, 5th, 6th, 8th, 10th, 12th
harmonics being consonant and the 7th, 9th, 11th, 13th harmonics
being discordant, and the 7th, 11th, and 13th being out of tune
with the piano. These are somewhat based on Helmholtz Sensation
of Tone in order to adjust the extremes.W2 = 0.1 (1 octave)
W3 = 0.3 (1 octave + fifth) (.1 + .2)
W4 = 0.2 (2 octaves) (.1 + .1)
W5 = 0.5 (2 octaves + major 3rd) (.1 + .1 + .3)
W6 = 0.4 (2 octaves + fifth) (.1 + .1 + .2)
W7 = 7.0 (2 octaves + out of tune dominant seventh)
W8 = 0.3 (3 octaves) (.1 + .1 + .1)
W9 = 9.0 (3 octaves + in tune second)
W10 = 0.6 (3 octaves + major 3rd) (.1 + .1 + .1 + .3)
W11 = 11.0 (3 octaves + way out of tune 4th)
W12 = 0.5 (3 octaves + fifth) (.1 + .1 + .1 + .2)
W13 = 13.0 (3 octaves + way out of tune 6th)I wonder if the W7-W13 are strong enough?
Follow Ups:
Mike, I'm not a believer in the usefulness of THD. IMO it accomplishes little to relate the harmonic spectrum to THD because THD is a blender; it is a whitewash; it has no specificity. A THD figure doesn't tell us anything about the *character* of an amplifier. A harmonic weighting system is only a little better. It at least has the virtue of giving the lie to a conventional THD spec and serves to show how far it is from inaudible. But this is a dubious value. The harmonic spectrum OTOH tells far more.While THD itself is a homogenized figure of merit with no inherent utility, we can nonetheless convert it to something useful by Fourier transforming the THD *residue*. We do this by connecting the residue to a spectrum analyzer. The spectrum, however, can only hint at the general character of the sound. We can of course *listen* to the amplified residue to better understand the effect of different harmonics on the sonic character of the sinewave. This is of course the most elementary and general case of harmonic synthesis.
For example, a sinewave devoid of harmonics sounds colorless. Adding virtually any harmonic lends interest and spice to the sound. Add too many, however, or in the wrong proportions, and we get something worse than colorless. The distorted sound becomes ugly or dissonant. But now we have an art form.
Turn up the input (or load down the output) and we hear the character of the distortion change (for the worse usually). Make an appropriate adjustment to the circuit and we can also hear the distortion change (for better or worse). We can both see and hear the influence of the harmonics on the character of the sinewave.
If we can see correlations, we can measure them. As Western Electric learned all too well by 1916, if we can truly measure something we gain the power of prediction. We can design a circuit and tell in advance what it will (largely) sound like. And that, in the Western Electric worldview, is engineering.
Hi again,Ran an experiment where all harmonics where set to the
same value of .001 (-60db) of the fundamental. Simulating
a flat distortion pattern like you get from SS.THD calculated = .35%
Using previously describe weighting factors:
Weighted THD = .65%
Next I weighted the harmonics like this instead:
sqrt( W2*W2*N2*N2 + W3*W3*N3*N3 + ...)
Actually squaring the weighting factor as well as
the harmonic value.Using weighting values described previously
Square Weighted THD = 2.05%
Seems reasonable. I like this result better.
Still doesn't accomodate Cheever or Hiraga's Null result.
Maybe take a stab at this next.
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