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In Reply to: The paper can't be that good and here's why... posted by clarkjohnsen on May 01, 2003 at 13:19:44:
I can't deny that, but I think that he is on the right track, within his listening exprience. For me, it is the higher order harmonics that I MUST eliminate in order to make good sounding amps and preamps. Next, it's negative feedback. He addresses these two issues very well.
Follow Ups:
Hiraga states in his paper that eliminating the high order harmonics
makes for a dull or soft sounding amp.I think this paper also implies that high order harmonics must
be smoothly decreasing, because the equation dictates a fourier
series that is monotonic as well as terms that smoothly decrease
in amplitude with increasing harmonic number.I'd be interested in your thoughts on this. Should high order
harmonics be simply eliminated or should they follow a prescribed
decay pattern. It seems like two philosophies emerge toward getting
a good sounding amp. One that is 0% distortion, the other that is
get a distortion pattern to follow a prescribed pattern (same as
non-linearity of the ear???). Maybe combos of the two are best?
It is almost impossible to remove ALL higher order distortion with solid state equipment. All I can do it reduce it to below the level that it can be easily detected. I think that another factor is also important, besides masking by the ear, and this is the dissonance created by higher order odd harmonics because they do not follow the musical scale very well. This would lead me to eliminate ANY higher order odd components if possible.
Looked around and found some interesting (to me anyway) graphs
showing how (some) harmonics of a note will differ slightly from
the notes on a standard piano.Before I assumed that the problems were the 7th, 9th, 11th, etc.
intervals themselves were the problems because these intervals
are dissonant. Now I understand that (some) of the harmonics
themselves can be out of tune. The diagram shows the 7th, 11th,
13th, and *14th*, etc. as being slightly out of tune.I suppose everyone else new this but me :), very interesting.
Thanks again.
Here are some interesting fun facts about the differences
between harmonics and notes. Looking at the 7th harmonic...Take all 12 notes starting at C1 (32.703 Hz) up to C2 (65.406 Hz).
Multiply the note frequency by 7 to get the 7th Harmonic. This
gives a frequency of 228.921 thru 457.842 Hz. The dominant 7th of
the C is Bb and this is the note closest in frequency to the 7th
harmonic as well. It has a frequency of 233.082, and 466.164 Hz
respectively. The corresponds to a delta of 4.161 - 8.322 Hz.Do the same for notes starting at C3, and the delta between note
and harmonic varies from 16.637 - 33.273 Hz.In other words the higher the octave, the worse (much worse) and
out of tune the harmonics get from their corresponding note. It
looks like it doubles every time you go up an octave.Hi order harmonics are bad!
I did not know this either. Thanks for your post.
Great input mfc. Your reference removes a lot of 'head scratching' about the problem of higher order harmonics.
Let me quote from 'Science and Music' Sir James Jeans 1937 , p87: "... all these (first) six harmonics form parts of the common chord of the fundamental note, and so are concordant with this note and with one another. The seventh harmonic, however, introduces an element of discord; if the fundamental tone is c', its pitch is approximately b (flat)''', which forms a dissonance with c. The same is true with the ninth, eleventh, thirteenth, and all higher odd-numbered harmonics; these add dissonance as well as SHRILLNESS (caps mine) to the fundamental tone, and so introduce a roughness or harsheness into the composite sound. The resultant quality of tone is often described as 'metallic' , since a piece of metal, when struck, emits a sound which is rich in discordant high tones. "
Does this sound like some audio equipment that you have heard? ;-)
Hi,In the process of looking at how harmonics match notes I stumbled
on another big misconception I had.The 5th harmonic does *not* correspond to a major 5th in an octave.
The 4th harmonic does *not* correspond to the 4th in an octave.
The 3rd harmonic does *not* correspond to a major 3rd in an octave.
etc...In fact it goes like this:
7th Harmonic > 2 octaves + dominant 7th
6th Harmonic > 2 octaves + major 5th
5th Harmonic > 2 octaves + major 3rd
4th Harmonic > 2 octaves
3rd Harmonic > 1 octave + major 5th
2nd Harmonic > 1 octaveSeeing it this way makes it easy to see that the 2nd - 6th are
very consonant intervals. The 7th is nasty and also out of tune.
I'd make sure an amp had no trace of anything above the 6th.
Seeing it this way makes it easy to see that the 2nd - 6th are
very consonant intervals. The 7th is nasty and also out of tune.
I'd make sure an amp had no trace of anything above the 6th.Isn't this attempting to relate amplifier distortion to the western musical scale just a little bit silly? This line of reasoning reduces music down to nothing but a collection of pure tones as it's written on the page.
I don't know about the rest of you, but virtually all of the music I listen to is made using musical instruments, both acoustic and electric/electronic, all of which produce an abundance of harmonics when playing just a single note. Because if they didn't, they'd all jsut be producing pure tones and would all sound the same.
So unless y'all are listening to music produced on an old computer sound card that only spits out a single pure tone for each note, or are a really big fan of the theramin music, instead of asking yourselves how the 6th harmonic resulting from amplifier distortion relates to the musical scale, you should be asking yourselves how that 6th harmonic relates to the 6th harmonic being produced by the actual instrument(s) used to perform those pure tones written on the page.
se
I got into that briefly in my Stereophile article (Jan '97, p. 131). I show how a typical *flute* spectrum approximates the uniformly converging series of harmonics generated by a *SET amplifier* (or the human ear). I also show how a typical *clarinet* spectrum approximates the odd-order pattern of harmonics generated by a *PP amp*. From these two charts, and other considerations such as blending and masking, I develop the notion of composite consonance.
I got into that briefly in my Stereophile article (Jan '97, p. 131). I show how a typical *flute* spectrum approximates the uniformly converging series of harmonics generated by a *SET amplifier* (or the human ear). I also show how a typical *clarinet* spectrum approximates the odd-order pattern of harmonics generated by a *PP amp*. From these two charts, and other considerations such as blending and masking, I develop the notion of composite consonance.I'm sure I must have read it but can't recall it specifically. I've only saved back issues to October '97 and the article's not in the archives on the Stereophile site.
Oddly enough I've been working on a little low powered (a whopping 4 watts) amplifier employing passive voltage gain via a transformer, whose nonlinearities are largely odd-order, driving an active single-ended current gain stage whose nonlinearities are largely even-order.
I wonder how that would work into your notion of composite consonance.
se
Basically, this pattern of odd-order distortion will tend to behave as a filter or synthesizer, causing everything that passes through it to take on a clarinet-like "reedy" coloration. This is only approximately true, and is based on the additive effect of the odd-order harmonics to the input signal. This superposition of harmonics is complicated by the possible phase differences among the harmonics. To quote myself: “The typical instrumental timbre...contains so many harmonics that we cannot ordinarily distinguish their individuality. What we hear from instruments is the resultant blend of the harmonic intervals; that is, the composite tone.” This is true for tones passing through amplifiers as well.The problem is that it is very difficult to predict what the audible result of all these complicated additions will be. To quote myself again: “The blending effect can be easily tested with a guitar. For example, playing F (below open E) together with open E causes objectionable beating. Adding an A intermediate to the two tones smoothes out the subjective effect considerably. The interval of F with E is a major seventh (8:15). Adding the A, however, creates two new intervals: a major third (4:5) and a perfect fifth (2:3). The two consonant intervals then "swamp out" the one dissonant interval to create an overall composite consonance. The critical parameter for composite consonance is thus not masking, but blending.”
This simple little experiment that anyone can make shows the complexity of human hearing, and the resulting difficulty that arises when we try to make formulaic judgments about its action.
Silly? Don't think so. Not if your amp produces a lot of
7th, 11th, 13th harmonic.The point is the input source material contains harmonics
and fundamentals. The brain locks all these together and
produces an instrument out of it. Each recipe of harmonics and
fundamental defines an instrument that the brain somehow
recognizes as such.Now an amp comes along and alters the recipe(s). The high
order harmonics are more like spices than basic ingredients
(a little goes a long way). Throw some 7th into the mix, but
only a pinch. Too much spoils the batch. The 11th even worse,
13th... worse than that.
Silly? Don't think so. Not if your amp produces a lot of
7th, 11th, 13th harmonic.Depends where you define "a lot." If the 7th, 11th, and 13th harmonics are up anywhere near the level of the fundamental, I wouldn't call it an amp. I'd call it a broken pile of parts.
The point is the input source material contains harmonics
and fundamentals. The brain locks all these together and
produces an instrument out of it. Each recipe of harmonics and
fundamental defines an instrument that the brain somehow
recognizes as such.Sure.
Now an amp comes along and alters the recipe(s). The high
order harmonics are more like spices than basic ingredients
(a little goes a long way). Throw some 7th into the mix, but
only a pinch. Too much spoils the batch. The 11th even worse,
13th... worse than that.Yes.
I wasn't saying that higher order harmonics should simply be ignored. Only that it's rather silly to relate them to the music scale itself. Rather it's how the harmonics effect the tones of the instruments. Particularly given that the western, even-tempered scale you're relating them to isn't universal.
se
Hi Steve,"Only that it's rather silly to relate them to the music scale
itself." ... "Particularly given that the western, even-tempered
scale you're relating them to isn't universal."This particular phenomena is one that clicks with me so I
have to disagree. One of the phenomena I hear with too much
distortion is that things sound out of tune. When John Curl
mentioned that harmonics are out of tune with the piano, it
was an AHA moment. If you've ever tuned a ham radio receiver
thru a station playing music, and listened to the splatter
of side bands...that's the same effect magnified 100x."Rather it's how the harmonics effect the tones of the instruments."
I agree with this, and am thinking of the violin or clarinet makers
who looked for just the right recipe of varnishes and woods to make
their particular instrument sound just right. A couple hundred years
of development to get it just right. Subtle to say the least. Passing
those beautifully constructed tones thru an amp, and what comes out
the other side? Can we say that those tones will be treated with the
same care that they were originally produced? ... Can you say don't
cast your pearls before swine.
Mfc, I'm glad that you saw the significance of this. For decades, I have tried to understand why audio components sound the way that they do, and higher order odd harmonics have been noted as a big problem for the last 70 years or more. In recent years, because of design constraints, higher order distortion has creeped in, and is hidden by the 'artificial' noise floor created by THD testing. It is artificial, because we would not hear the vast majority of the noise added into the THD measurement. Today, I measure wires that have almost as much 7th harmonic distortion as the residual third harmonic distortion in my test setup, which means that they generate MORE 7th harmonic distortion than third harmonic. Could it be important? Maybe.
The book that I mentioned is available at Amazon.com for $10 or less, used.
Hi,I'm thinking of using a 16-bit Soundcard, some sort of differential
preamp to null out the crud, and software like Audiotester to
investigate these low level harmonics.Can you see things like capacitor and resistor distortion with a
setup like this?Thanks
You need more. First, you have to have some sort of fundamental tone nulling circuit in order to increase your dynamic range. No spectrum analyser that I have used can see this distortion directly. I use a Sound Technology THD analyser, but a great set of articles appeared in 'Electronics World' from July 2002-Dec2002, describing a good circuit and a good digital spectrum analysis program for a PC. This is what I would recommend first. However, almost any good THD analyser would work as well, and they can be sometimes found on E-bay at a good price, especially if your time has any value. I would look for an HP339 or a ST1700A.
Hang in there, mfc. Did you know that many musical instruments are designed to minimize 7th and higher order harmonics? From 'Science & Music', Sir James Jeans , 1937, Dover reprint 1968. Get it used if you can.
p 91 "In the piano the wire is struck with a hammer covered with soft felt. The felt prolongs the duration of the impact, so that, by the time that the hammer finally breaks its contact with the string, a substantial length of the string has already been set in motion. this reduces the energy which goes into the higher harmonics, and so avoids the harsh jangle of sound ... As we have seen that discord begins with the seventh harmonic, the hammer should be sufficiently felted to reduce the seventh and higher discordant harmonics (ninth, eleventh,etc) to small proportions."
p92 "Even if the hammer were perfectly hard, the seventh harmonic could be eliminated entirely by allowing the hammer to strike the string at a point a seventh of its length from one end, this being a node for the vibration in question. ..."
See how higher order vibrations are addressed, in musical instruments? Thanks SE for getting me back to my books, to look this up.
Hang in there, mfc. Did you know that many musical instruments are designed to minimize 7th and higher order harmonics? From 'Science & Music', Sir James Jeans , 1937, Dover reprint 1968. Get it used if you can.
p 91 "In the piano the wire is struck with a hammer covered with soft felt. The felt prolongs the duration of the impact, so that, by the time that the hammer finally breaks its contact with the string, a substantial length of the string has already been set in motion. this reduces the energy which goes into the higher harmonics, and so avoids the harsh jangle of sound ... As we have seen that discord begins with the seventh harmonic, the hammer should be sufficiently felted to reduce the seventh and higher discordant harmonics (ninth, eleventh,etc) to small proportions."Which is perhaps why harpsicords sound so "jangly."
It's also worth noting that the piano produces not just harmonic components, but also non-harmonic components, i.e. components which are not harmonically related to the fundamental, presumably due to the piano string also behaving like a rod, rather than just a string.
This is why the additive synthesis folks (such as Wendy Carlos of Switched On Bach fame) found it so difficult to replicate the sound of the piano. They'd always approached the problem by using harmonic components (additive synthesis involves creating the sound by building it up with pure tones forming the fundamental and harmonic components as opposed to subtractive synthesis where you start out with a harmonically rich waveform such as square, triangular and sawtooth, and apply filtering to change the harmonic content). Without the non-harmonic components, the results were disappointing.
So if one wants to replicate the sound of a piano, you have to think outside the harmonic box so to speak.
In any case, my point is still the same. If you want to relate amplifier distortion to the reproduction of music, it should be in the context of the sound produced by the various instruments (not just piano) rather than the music scale (and by the way, not all cultures use the western music scale that this discussion has centered around).
se
Please, SE read a book about it, rather than tell us what you already 'know'. The piano is only one example. There are many others such as the violin in the book. It is obvious that they try to minimize higher order odd harmonics, if they can.
Anyone who deliberately designs in, or neglects 7th and higher order harmonics into their amps and preamps are welcome to compete with me in the audio marketplace.
nt
That is a real cool reference...On a different note :), I know a clarinet produces some odd
harmonics. But these must be balanced, and allow the instrument to
produce its beautiful piercing sound.Another observation about Western music and source material...
A lot of rock music uses 7th, 9th, 13ths. These are actual notes
however. Therefore, at least the intervals would be in tune.
OTOH, the guitar amps themselves generate a lot of harmonics. I doubt
rock music gets mangled to much in an amp - just as long as the amp
is BIG and LOUD.
"...higher order odd harmonics because they do not follow the
musical scale very well"Are you saying (for example) the 9th harmonic of 100hz (900Hz)
doesn't match a note?If this is so, it all makes a lot of sense as to why such
small amounts of hi-order harmonics would be so objectionable.I remember playing in band in high school...people playing out
of tune stuck out like sore thumbs.Thanks
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