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Emile

Good sound via harmonics

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 Question about "good sound" and harmonics. Had a problem with a set of Forte I's I picked up; believed my problem was in the mid-range ... primary tones; but (after installing Crites tweeter diaphragms)  now think the 2nd, 3rd, etc harmonics come through via the tweeters and produce the richness in sound that I was missing. Would very much like to hear some comments on this (or links to explanations). (Added note to the "some of the" experts on this forum; Yes, tried searching this site for many hours ... but probably missed page 78 on thread # 12643. Sorry :( Some of us "newbies" are still trying to learn :) )

Many thanks, Emile

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On 10/20/2017 at 4:19 PM, Emile said:

 Question about "good sound" and harmonics. Had a problem with a set of Forte I's I picked up; believed my problem was in the mid-range ... primary tones; but (after installing Crites tweeter diaphragms)  now think the 2nd, 3rd, etc harmonics come through via the tweeters and produce the richness in sound that I was missing. Would very much like to hear some comments on this (or links to explanations). (Added note to the "some of the" experts on this forum; Yes, tried searching this site for many hours ... but probably missed page 78 on thread # 12643. Sorry :( Some of us "newbies" are still trying to learn :) )

Many thanks, Emile

 

The overtones of both music and noise are [obviously] very important in transmitting the character of the sound.   The difference in the sound of "tuning A" (440 Hz) on a piano, a violin, a human voice, and an oboe is largely due to the relative magnitude (intensity, amplitude) of each of the harmonics produced.  There may be other differences such as "attack" and overall SPL (sound pressure level, commonly called "volume") of the note played.  "Timbre" is another way to refer to the difference in sound between instruments playing the same note at the same SPL.   The overtones include fricative (and other) sounds as well, such as the un-tuned sound of a bow scraping across a string (other than the note and its harmonics), which some of us who sit close, cherish, or the rattle of the snares on a snare drum.  An overtone qualifies as a harmonic if it is a whole number multiple of the fundamental tone.  So, all harmonics are overtones, but not all overtones are  harmonics.  

 

Noise, too, has important overtones.  Listen to any poorly transferred, or too elderly, movie with jingling keys, or clinking glasses, etc.  They will sound very dull, but those in a well transferred newer movie will sound, clear, clean and, perhaps, exciting, thanks to overtones.

 

You refer to "richness."  I think of overtones as producing richness and detail, and facilitate producing what PWK was fond of referring to as "the inner voices of the orchestra."   I tend to think of overtones as being 1,000 Hz and over, but the piano has its highest fundamental at 4,186 Hz, which is getting up there. Turning up and down a tweeter tells the tale.  I have had other systems that used the same tweeter that is in my Klipschorns, but with a 12 dB/ octave crossover at 3,500 Hz, rather than the 36 dB/octave crossover at 4,500 Hz in my AK4 Klipschorns.  The 3,500 Xover ones have a tweeter level control (an L-pad).  Turning the L-pad all the way down, thus nearly disconnecting the tweeter, robs the music of much richness, detail, and clarity.  I'm guessing that what you are looking for resides above 3,500 Hz.  I don't know where the Forte I  crosses over to the tweeter.   

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garyrc,

 

Thank you SIR! As a scientist and engineer, I am (a bit) familiar with harmonics from systems ... but terribly unfamiliar with "audio harmonics." Your response cleared up a lot for me. Many thanks! PS; Forte I crossover to tweeters is a 6 kHZ.

Regards, Emile 

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There are probably a large number of musical and non-musical sounds that determine the sonic character of an instrument, like a bow scraping on a string, flute breath tones, etc., in addition to the essential character that comes from the overtone balance.

 

Overtones can be much lower than 1,000 Hz,  e.g., 200 Hz from a 100-Hz note, as well as 300 Hz, 400 Hz, etc. etc.  At the same time, even low notes have overtones that go above the 4K highest note of the piano.  The "tingle" of triangles and  cymbals are non-harmonic sounds that definitely higher than 4K.  So, there can be a vast frequency range of tones from bass, middle, and high notes.

 

The Crites tweeter provided increased output and clarity of overtones above 4 KHz, which (in my opinion artificially) increased the clarity of EVEN DEEP BASS NOTES, showing how important overtones are that reach several octaves above the fundamental to the definition and character of those deep bass tones.  They definitely increase clarity, but are capable of exaggerating that clarity if the overtones are exaggerated.  I wonder if that has been part of the appeal of non-Klipsch tweeters.

 

Richness may be a different issue, and could be impaired if the overall balance is tilted up too far, making it sound too thin.

 

A complicated area!

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31 minutes ago, LarryC said:

 

Overtones can be much lower than 1,000 Hz,  e.g., 200 Hz from a 100-Hz note, as well as 300 Hz, 400 Hz, etc. etc.  At the same time, even low notes have overtones that go above the 4K highest note of the piano.

 

A complicated area!

LarryC,

Yes, complicated indeed. But, if we take your 100 Hz note, we "know" it has harmonics in the 6 KHz+ area (my Forte I tweeters) ... but ... these harmonics are so far up the scale that their strength/volume/dB is so much reduced that they are virtually "gone." However, a high piano note (say 4 kHZ) has a first complimentary frequency at 8 kHz which certainly can be heard. Anyone have a sense of the power drop off in these harmonics? (Meaning 100%, 30%, 10%, etc??) 

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There was a bromide around many decades ago: "You'd be surprised at how much the addition of a tweeter will improve the performance of a woofer."

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OK; revisited some old physics textbooks :)  In a "perfect system," the harmonics are obviously multiples of the fundamantal wave with frequency f1, i.e. f1=2*f2=3*f3...=n*fn. The peak sound level ( A=amplitude ) has the same linear relation, i.e. A1=2*A2=3*A3 ... =n*An. For example ... fundamental is 100%, harmonics are 50%, 33%, 25%, 20% etc. A lot LOUDER than I thought :) So if we hear the highest A8 piano note at about 5kHz, we will hear the first harmonic at 10kHZ (at 50% sound level), and the second at 15kHz (at 33.3%) - and anyone should be able to hear these. If we take the "middle" A8 on a piano and look for the 13th harmonic, we get it at 6.16kHz (starting range of my tweeter) at 7% of the original sound pressure. Should be able to hear these (and a lot more) also. Just my 2 cents ... correct me if I'm wrong :) 

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Gosh, I wish I could find the nifty spreadsheet I made up in DOS Lotus 1-2--3 re Fourier series of a square wave.  

 

Let me challenge, in a friendly way, your last statement.

 

A preliminary matter is that we're talking the fundamental period as being a square wave.  While a piano and other musical instruments do created overtones (harmonics) I don't think their fundamental gets as harsh as a square wave.  Therefore the harmonics would not follow the Fourier square wave reconstruction.  The harmonics would be much weaker.

 

Even if a square wave, I think something is wrong about about the 13th harmonic being 7 percent.  This wiki article shows the 10th harmonic as being 30 dB down.  Wouldn't that be 1/1000 th?  The 13th would be even lower.

 

https://en.wikipedia.org/wiki/Square_wave

 

WMcD

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7 minutes ago, WMcD said:

Even if a square wave, I think something is wrong about about the 13th harmonic being 7 percent.  This wiki article shows the 10th harmonic as being 30 dB down.  Wouldn't that be 1/1000 th?  The 13th would be even lower.

 

https://en.wikipedia.org/wiki/Square_wave

Hi WMcD,

Yeah, found my result rather surprising also ... and the last time I did Fourier analysis was when Lotus 1-2-3 was popular (over 30 years ago?) so I'm a little "rusty" on the subject :) Will do some more digging to see if I can correct it.

Cheers, Emile

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2 hours ago, WMcD said:

Even if a square wave, I think something is wrong about about the 13th harmonic being 7 percent.  This wiki article shows the 10th harmonic as being 30 dB down.  Wouldn't that be 1/1000 th?  The 13th would be even lower.

 

https://en.wikipedia.org/wiki/Square_wave

WMcD,

Still puzzled, but ... if we try to make a SQUARE wave from sine harmonics, we "only" use the "odd" harmonics. So ... your "tenth" harmonic is actually the "twentieth." (Triangle waves are "made" from "even" harmonics. :) But, still cannot explain the major dB drop. If we take a string ... and "pluck it" ... we do get the fundamental frequency and ALL harmonics with frequencies f1 through n*fn and amplitutes A1 through n*An (i.e. sound levels 1.0, 0.5, 0.33, etc). The resulting "tone" is the sum off all these frequencies (and their corresponding 1.0/0.5/0.33/etc amplitudes). Maybe I have no clue of the actual waves that make up music :( 

OK; what am I missing  :) 

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8 hours ago, LarryC said:

Overtones can be much lower than 1,000 Hz,  e.g., 200 Hz from a 100-Hz note, as well as 300 Hz, 400 Hz, etc. etc.  At the same time, even low notes have overtones that go above the 4K highest note of the piano.  The "tingle" of triangles and  cymbals are non-harmonic sounds that definitely higher than 4K.  So, there can be a vast frequency range of tones from bass, middle, and high notes.

 

I wrote a pretty terrible sentence.  I agree with LarryC's statement, quoted above.   My unfortunate sentence was: "I tend to think of overtones as being 1,000 Hz and over, but the piano has its highest fundamental at 4,186 Hz, which is getting up there."   I can't seem to stop, so here is another terrible sentence: I guess what I meant was two things,  1)"Overtones I am used to being able to manipulate by using a speaker's balance control are generally 1,000 Hz and above, because these speakers with L-pads or switches (unlike the Klipsches in question), crossover about there, like my old ADC, crossing over at about 1,000 Hz, or my old two-way EVs, which crossed over at 3,500 Hz, therefore, I tend to think of overtones as being in the tweeter range, as did the OP in his OP," and 2) "Even fundamentals (as on the piano), can extend to above 4K, so their overtones go even higher (some charts show overtones going to the top (often pictured as 16K Hz or 20 Khz, but in reality what ... infinity, but at an infinitesimal amplitude?)"  That will teach me to proofread, but clarity and simplicity may be a little too much to expect from me with a subject this complex. 

 

As to the overtones of low notes, the timpani at the bottom of their range produce the some low fundamentals, overtones of high enough SPL to be heard clearly quite a ways up, and some noise involving the smack or splat sound when the beater hits the head, complete with noise overtones.

 

I love cymbals!

 

Note: the range of fundamentals of the piano in the nifty chart below (source unknown; it's been floating around for years) is much wider than in reality, I guess to show where certain notes would be, if they existed on standard pianos.  The lowest note on the 88 key version is 27.5 Hz, but I heard "it" clearly when Bernstein demonstrated it on my old TV with a 4" open back speaker that probably wouldn't think of going below about 60 Hz..  I guess I was hearing the overtones only, plus the speaker "doubling" and distortion.

 

As to the human voice, a Basso Profundo can go down to about 40 Hz, I think, so the chart may be wrong in that regard.

 

image.png.508c9ef32e47368e914c0fa385e2638b.png

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Below is an interesting website discussion of overtones and harmonics:  The first paragraph suggests how different combinations of overtones ("partials") come up with distinctively different sound qualities -- partly how we can distinguish clarinets from horns or flutes:

 

Although any one apparent sound to our ears, the following applies:  Human ears tend to group phase-coherent, harmonically-related frequency components into a single sensation. Rather than perceiving the individual partials–harmonic and inharmonic, of a musical tone, humans perceive them together as a tone color or timbre, and the overall pitch is heard as the fundamental of the harmonic series being experienced. If a sound is heard that is made up of even just a few simultaneous sine tones, and if the intervals among those tones form part of a harmonic series, the brain tends to group this input into a sensation of the pitch of the fundamental of that series, even if the fundamental is not present.

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We need a clean sheet of paper.

I think I misread the graph, and the actual peaks are a bit unclear.  (More later I hope.)

But to my thinking, middle A is A4 which is 440 Hz

A8 is 7040 Hz (meaning 4 octaves above or 4 doublings of freq or 16 times the 440 fundamental).

getting up to about 6000 Hz:

13 x 440 = 5720 Hz

14 x 440 = 6160 Hz

15 x 440 = 6600 Hz

16 x 440 = 7040 Hz

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Partial from https://electronics.stackexchange.com/questions/32310/what-exactly-are-harmonics-and-how-do-they-appear 

 

27down voteaccepted

Sinusoidal waves don't have harmonics because it's exactly sine waves which combined can construct other waveforms. The fundamental wave is a sine, so you don't need to add anything to make it the sinusoidal signal.

About the oscilloscope. Many signals have a large number of harmonics, some, like a square wave, in theory infinite.

enter image description here

This is a partial construction of a square wave. The blue sine which shows 1 period is the fundamental. Then there's the third harmonic (square waves don't have even harmonics), the purple one. Its amplitude is 1/3 of the fundamental, and you can see it's three times the fundamental's frequency, because it shows 3 periods. Same for the fifth harmonic (brown). Amplitude is 1/5 of the fundamental and it shows 5 periods. Adding these gives the green curve. This is not yet a good square wave, but you already see the steep edges, and the wavy horizontal line will ultimately become completely horizontal if we add more harmonics. So this is how you will see a square wave on the scope if only up to the fifth harmonic are shown. This is really the minimum, for a better reconstruction you'll need more harmonics.

 

So ... still believe the harmonics have a HUGE effect ... and actually the sum of the harmonics (50% + 33.3% + 25% + etc.) is "stronger" than the fundamental component :) 

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Add-on ...

 

The above shows the (odd) harmonics for a square wave. Triangle waves have even harmonics. Assume my amp outputs any combination, but :( really have no clue. Help :) 

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Errr, I dunno about the sum of harmonics of a square wave being greater than a pure side wave.

 

The RMS voltage value of a sine is 0.707 of its peak.  So Power = V*V/r or 0.5 /r

 

The RMS voltage of  square wave is 1 or its peak.  So Power = V*V/r or 1/r.

 

Therefore, speaking of power the harmonics in the square wave contain half the power.  I think, at least right now.

 

Above is edited.

 

WMcD

 

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