Inharmonic partials
Yes, a piano, even a concert grand, has very little output at the fundamental frequency of the lowest notes, yet we still somehow perceive the fundamental.
What is also interesting is that the partials of a piano note, especially low notes, are inharmonic, that is, for a low C at c. 32Hz, the partials are not exactly at 64Hz, 96Hz, 128Hz etc., they are at slightly higher frequencies. This is caused by the stiffness of the strings, which inhibits vibration near the bridge and agraffes. It is the reason why a piano tuner "stretches" the tuning - e.g. the lower notes are tuned slightly lower than a simple mathematical harmonic model would suggest is correct. The effect is less pronounced for longer strings, which is one reason a large grand piano generally has a better sound that a smaller one.
A piano tuner will generally tune the fourth partial of the lower notes (i.e. at a nominal 4f) to the note two octaves above; in a large grand the second partial (nominally 2f) will then also be in tune with the note one octave above, or at least have a very slow and unnoticeable beat frequency. On a small piano, it is virtually impossible to get both the second and fourth partials in tune in this way, and is one of the reasons small pianos sound horrible - beat-free octaves in the bass are impossible. On a large piano the fundamentals of the lowest notes can be as much as 30 cents lower in frequency than one might expect with a simple harmonic analysis.
It strikes me this has a bearing on any system that removes a low pitch fundamental from a signal and adds back harmonic partials ("harmonics") in order to increase the perception of the fundamental. The added harmonic partials will be out of tune with the original inharmonic partials. It might be OK with synthesised sounds with harmonic partials, but for bass strung instruments, this sounds more like a recipe for mud-bass than max-bass to me. Approach with caution.
Stephen
Yes, a piano, even a concert grand, has very little output at the fundamental frequency of the lowest notes, yet we still somehow perceive the fundamental.
What is also interesting is that the partials of a piano note, especially low notes, are inharmonic, that is, for a low C at c. 32Hz, the partials are not exactly at 64Hz, 96Hz, 128Hz etc., they are at slightly higher frequencies. This is caused by the stiffness of the strings, which inhibits vibration near the bridge and agraffes. It is the reason why a piano tuner "stretches" the tuning - e.g. the lower notes are tuned slightly lower than a simple mathematical harmonic model would suggest is correct. The effect is less pronounced for longer strings, which is one reason a large grand piano generally has a better sound that a smaller one.
A piano tuner will generally tune the fourth partial of the lower notes (i.e. at a nominal 4f) to the note two octaves above; in a large grand the second partial (nominally 2f) will then also be in tune with the note one octave above, or at least have a very slow and unnoticeable beat frequency. On a small piano, it is virtually impossible to get both the second and fourth partials in tune in this way, and is one of the reasons small pianos sound horrible - beat-free octaves in the bass are impossible. On a large piano the fundamentals of the lowest notes can be as much as 30 cents lower in frequency than one might expect with a simple harmonic analysis.
It strikes me this has a bearing on any system that removes a low pitch fundamental from a signal and adds back harmonic partials ("harmonics") in order to increase the perception of the fundamental. The added harmonic partials will be out of tune with the original inharmonic partials. It might be OK with synthesised sounds with harmonic partials, but for bass strung instruments, this sounds more like a recipe for mud-bass than max-bass to me. Approach with caution.
Stephen
This is simply an "illusion". As with visual illusions, the brain takes some crude input and creates the best-bet perception that fits the cues the best. With certain harmonics lined-up like ducks in a row*, the brain inserts the fundamental. This has been known for long time. The fundamental sound is as real as any non-veridical visual illusion.
With some visual illusions, you look at a piece of the image through a small hole and the "illusion" goes away. Likewise here, you perceive the fundamental in some senses, but not in all ways.
For example, the RT60 of the illusory fundamental in your room isn't right. Your chest does not feel it. Its does not beat with other bass sounds. And so on.
Nice illusion, but just an illusion... like all hearing.
Ben
*as Ludus Tonalis implies, a generic fuzz-box distortion generator ("one size fits all") will not produce a really good fitting "ducks in a row" for all fundamentals and certainly not for all bass instruments. So you get, as Ludus Tonalis says, mud bass.
With some visual illusions, you look at a piece of the image through a small hole and the "illusion" goes away. Likewise here, you perceive the fundamental in some senses, but not in all ways.
For example, the RT60 of the illusory fundamental in your room isn't right. Your chest does not feel it. Its does not beat with other bass sounds. And so on.
Nice illusion, but just an illusion... like all hearing.
Ben
*as Ludus Tonalis implies, a generic fuzz-box distortion generator ("one size fits all") will not produce a really good fitting "ducks in a row" for all fundamentals and certainly not for all bass instruments. So you get, as Ludus Tonalis says, mud bass.
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Not much I can add to the scientific discussion here but I personally used the maxxbass car audio module about 10 years ago (I think I still have the unit somewhere in one of my closets).
For what it's worth, it just works, in some ways amazingly so. Made my 6.5 inch midrange units sound like 8 inches at the very least.
I remember some hiss from the unit itself but other than that the bass sounded as clean as a car audio setup would allow
It was mostly pooh poohed by the car audio community at the time as a 'distortion generator' though I thought it was a great unit
I'm curious to know what the audiophiles among us here think of such a technology and if they would use it themselves based on the science behind it?
For what it's worth, it just works, in some ways amazingly so. Made my 6.5 inch midrange units sound like 8 inches at the very least.
I remember some hiss from the unit itself but other than that the bass sounded as clean as a car audio setup would allow
It was mostly pooh poohed by the car audio community at the time as a 'distortion generator' though I thought it was a great unit
I'm curious to know what the audiophiles among us here think of such a technology and if they would use it themselves based on the science behind it?
Signal level and the perception of loudness are not the same thing.
A sine wave will sound less loud than a pulse wave at similar signal level.
Why?
In simplistic terms its because the hearing system has frequency bands. A sine will only stimulate 1 frequency band, a pulse will stimulate more frequency bands. The more frequency band stimulated, the higher the perceived loudness of the sound.
So if some electronic device produces an audible amount of harmonics, the sound will be perceived as louder than a transparent device, even with the same signal level.
Stuff like Vinyl, tape, some tube circuits produce harmonics AND the production of these harmonics is level dependent. The higher the signal in level, the more harmonics produced. The result is that things seem to have more low level detail and impact, but its just compression. Everyone in music production uses it, its easy to spot if you know what to listen for. In fact a compressed signal has LESS information in it than the original signal.
Higher harmonics are not "musically" related to the fundamental, so they sound "weird". See here: https://en.wikipedia.org/wiki/Harmonic#Harmonics_on_stringed_instruments
That's why clipping of most opamps circuits sound less good than clipping of most tube circuits. Tubes produce less higher harmonics than opamps when overdriven.
All this is common knowledge in psycho acoustics.
I guess it is also common knowledge on this forum ! 😉
But these effects do for sure add to the perception of the effect that is talked here: The perception of non existing lf content through the intentional controlled generation of harmonics.
Regards
Charles
But these effects do for sure add to the perception of the effect that is talked here: The perception of non existing lf content through the intentional controlled generation of harmonics.
Regards
Charles
milkshake, not what I am talking about.
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The intentional control of harmonics is one thing to produce "phantom" notes, that has been demonstrated.
I'm trying to look beyond that, to the unintentional effect(s) of higher levels of lower order harmonics.
Look, on the surface at least, an amplifier that produces "excess" lower order harmonics (for example, but not limited to,
a SE triode amp) is adding additional frequencies above whatever signal is present. Intuitively that ought to sound
"brighter" and add to things such as sibilence and "spray" (cymbals, etc...) but generally speaking this is
not what is heard. The argument that there is a 1-2dB drop at 20kHz (in some cases) doesn't fly since most of the
added energy that is heard as objectionable is below 10kHz.
So, is it possible that the additional harmonics are having an effect similar to the "missing fundamental" method??
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And 2nd,4th...etc harmonics ARE musically related, they are octaves.
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The intentional control of harmonics is one thing to produce "phantom" notes, that has been demonstrated.
I'm trying to look beyond that, to the unintentional effect(s) of higher levels of lower order harmonics.
Look, on the surface at least, an amplifier that produces "excess" lower order harmonics (for example, but not limited to,
a SE triode amp) is adding additional frequencies above whatever signal is present. Intuitively that ought to sound
"brighter" and add to things such as sibilence and "spray" (cymbals, etc...) but generally speaking this is
not what is heard. The argument that there is a 1-2dB drop at 20kHz (in some cases) doesn't fly since most of the
added energy that is heard as objectionable is below 10kHz.
So, is it possible that the additional harmonics are having an effect similar to the "missing fundamental" method??
------------------
And 2nd,4th...etc harmonics ARE musically related, they are octaves.
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Assume that this is not the case, but if you think that high output impedance can cause warmth I'd like to know what the mechanism might be? How "high" and into what load"?
Add an ohm or two series resistor to your favour subwoofer simulator to see what's going on.
The potential divider means the impedance plot is effectively imposed on the frequency response. Where there's a rise in impedance, there's a dB or two rise.
Most ported boxes will have an impedance peak in the 60-100Hz range (as well as one below tuning which doesn't matter so much), so there'll be a dB or two added there, often heard as warmth or extra bass tone.
Chris
You call it "warmth" which implies you welcome it but everybody else calls it boomy and we all try to get rid of it.
You may find that warmth just swell for your music but the rest of us dislike one-note bass.
Good to experiment.
B.
Gosh, I feel so stupid of not thinking straight about this.
I use a DSP Xover with L-R 49dB profile at 130 Hz. So when I turn off my woofs, there's nothing playing below 120 or so.
So how does the Prince of Denmark March on the giant Aeolian-Skinner organ in St John the Divine in NYC sound?
Sounds pretty good as far as the notes of the composition go. Obviously, all the ducks are lined up since the pedal that is playing on the recording is for-real. I can hear the pedal just fine. Just that the low notes have no physical impact and somethings about the sound aren't quite right.
Ben
I use a DSP Xover with L-R 49dB profile at 130 Hz. So when I turn off my woofs, there's nothing playing below 120 or so.
So how does the Prince of Denmark March on the giant Aeolian-Skinner organ in St John the Divine in NYC sound?
Sounds pretty good as far as the notes of the composition go. Obviously, all the ducks are lined up since the pedal that is playing on the recording is for-real. I can hear the pedal just fine. Just that the low notes have no physical impact and somethings about the sound aren't quite right.
Ben
I'm trying to get past bass, and DF.
My focus is now on everything other than bass - having established to concept that the ear can "hear" sound that is not actually being reproduced, given certain harmonic relationships.
Shift gears/focus.
My focus is now on everything other than bass - having established to concept that the ear can "hear" sound that is not actually being reproduced, given certain harmonic relationships.
Shift gears/focus.
No, some posters further up the page called it warmth, I was merely explaining the correlation between "warmth" and a non-zero output impedance.
FWIW I'd be interested to try and DIY one of these FX boxes. I do have a guitar multi-FX pedal and a digital mixing desk. I'm almost certain I can come up with something...
Chris
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Bear,
I think what you may be looking for is quite simple- even order harmonic distortion is always "musically relevant", that is, it adds no notes not present in the original composition.
On the other hand, odd order distortion may add notes that were not present in the original composition, which may be dissonant, or at least change the original composition.
As an example of what "sounds good", and what "sounds wrong", I did an experiment with loading woofers as push-pull (one driver reversed in direction and polarity) to reduce even order distortion.
Frequency response remained identical, while the PP pair showed reduced even-order distortion compared to the same drivers in "normal" configuration. The listening panel (myself and a college student with a good music and audio background) both could hear no difference between the two at lower drive levels.
As the speakers were driven progressively harder, the "normal" configuration simply sounded "louder" as it was driven past Xmax, (the linear operating range), while the PP pair sounded "odd", as the lack of even order distortion that would normally mask the odd order distortion made the odd order distortion "stick out".
The observation of this effect was program dependent, music already rich in odd order harmonics (like some metal/thrash genres) were not changed much, while melodies and harmonies sang or played on familiar acoustic instruments made the accentuated odd order distortion more apparent, and had a more negative effect than the "normal" driver configuration.
As a guitar player, it is obvious to me that "fuzz boxes" that add in odd-order distortion may work OK for one note at a time "lead" playing, but sound horrible for chords, while the primarily even-order tube (valve) distortion sounds good for both lead and chords.
That said, my description of odd order distortion making chords sound "horrible" is due to a musical acclimation, and a "sound" background that has avoided that type of distortion like the plague, but obviously there are many that are completely OK with that type of sound, judging by the popularity of many genres of music I find difficult to listen to for more than a short interval.
Art
Anybody can do anything they like to their music reproduction.
But for the sound to be correct... each instrument (and to some extent, each recording setting) has its characteristic harmonic signature (which to summarize, I previous called "ducks in a row").
You can add second and even-numbered harmonic distortion to across the board and maybe it will delight some listeners. But it won't delight listeners who want the sound to be acoustically or musically correct. Which for most of us is a foundational aspiration.
Ben
But for the sound to be correct... each instrument (and to some extent, each recording setting) has its characteristic harmonic signature (which to summarize, I previous called "ducks in a row").
You can add second and even-numbered harmonic distortion to across the board and maybe it will delight some listeners. But it won't delight listeners who want the sound to be acoustically or musically correct. Which for most of us is a foundational aspiration.
Ben
Well, everytime I scope the spkr output or input of PI stages of any of my tube guitar amps fed from a sine generator I see dominant odd order distortion (square waves), albeit with skewed duty cycle and differently sloped crests, but still mainly squares.
If moderate to heavy distortion (say, typical AC/DC crunch) were dominantly 2nd order it would almost look like and sound like half-wave recitified (= horrible).
A slight 2nd order signature I only see when staying at (semi-)clean gain levels.
Simple pedal fuzzes do sound bad with chords because they don't shape the frequency response before the distortion, therefore too much bass muds up the sound.
Not sure if I'm late to the discussion or taking it in a different direction, but I saw a few mentions of musical instruments creating a perceived fundamental.
In fact, with polyphonic instruments (particularly the guitar), you can take advantage of IMD by playing a perfect fifth dyad (two notes at a frequency ratio 3:2) to create a subharmonic one octave below the actual fundamental. This is used in nearly all guitar-based rock music and it is called "power chords" with either a distortion pedal or by overdriving the amp.
In fact, with polyphonic instruments (particularly the guitar), you can take advantage of IMD by playing a perfect fifth dyad (two notes at a frequency ratio 3:2) to create a subharmonic one octave below the actual fundamental. This is used in nearly all guitar-based rock music and it is called "power chords" with either a distortion pedal or by overdriving the amp.
MitchMev, please give a specific example of a "power chord" creating the illusion of a subharmonic? Maybe an ascii "tab"?
If I've not played it before and know how it sounds, I'll try it?
But the idea again is that no matter if it sounds "better" or different when there are extra harmonics, short of MitchMev's particular example, and the example of purposeful and significant % of added distortion in guitar/MI situations, I'm back at the relatively low levels of THD like 1.0% and less, more like <0.1% and lower, where there appears to be some sort of qualitative perception of difference - in some cases where the higher distortion amplification sounds better - and here's the key idea; especially in the HF and often in the lower mids... aka vocals may sound less "mechanical" and less "electronic".
I am not saying that there is a direct correlation between higher distortion and better sound.
Art's experience is interesting - it hints at a mechanism. But how does that apply to highs?
Again, with highs, harmonic distortion produces "new" energy above and not below the original signal. Beating sum+diff that fall below the original "fundamentals" (the signal) are likely to be extremely low in magnitude, aka how could they significantly change the perception and maybe even be audible??
We always "say" that things such as a SE triode amp sound euphonic because of the extra THD being low order and high 2nd order, but does that really explain? For example why would a cymbal hit appear to have MORE "richness" as in "body" and "tone" if you've added more HF information? Would that not make it brighter and thinner?? AKA, take a super clean amplifier and put a parametric or tone control and boost the higher harmonics??
Also the case I am wrestling with is where I've got two devices both with reasonable specs, reasonably low distortion, some differences, one with super low distortion specs, and the differences heard simply can not be discerned by the specs, nor predicted.
( I expect to do some bona fide electronic measurements, because this has me so confounded, but it will take time before I can set it up and get it done... in the meantime I'm hoping to elicit some others who may have insights that I am unaware of)
_-_-
If I've not played it before and know how it sounds, I'll try it?
But the idea again is that no matter if it sounds "better" or different when there are extra harmonics, short of MitchMev's particular example, and the example of purposeful and significant % of added distortion in guitar/MI situations, I'm back at the relatively low levels of THD like 1.0% and less, more like <0.1% and lower, where there appears to be some sort of qualitative perception of difference - in some cases where the higher distortion amplification sounds better - and here's the key idea; especially in the HF and often in the lower mids... aka vocals may sound less "mechanical" and less "electronic".
I am not saying that there is a direct correlation between higher distortion and better sound.
Art's experience is interesting - it hints at a mechanism. But how does that apply to highs?
Again, with highs, harmonic distortion produces "new" energy above and not below the original signal. Beating sum+diff that fall below the original "fundamentals" (the signal) are likely to be extremely low in magnitude, aka how could they significantly change the perception and maybe even be audible??
We always "say" that things such as a SE triode amp sound euphonic because of the extra THD being low order and high 2nd order, but does that really explain? For example why would a cymbal hit appear to have MORE "richness" as in "body" and "tone" if you've added more HF information? Would that not make it brighter and thinner?? AKA, take a super clean amplifier and put a parametric or tone control and boost the higher harmonics??
Also the case I am wrestling with is where I've got two devices both with reasonable specs, reasonably low distortion, some differences, one with super low distortion specs, and the differences heard simply can not be discerned by the specs, nor predicted.
( I expect to do some bona fide electronic measurements, because this has me so confounded, but it will take time before I can set it up and get it done... in the meantime I'm hoping to elicit some others who may have insights that I am unaware of)
_-_-
Well, if you take a power chord (A3 and E4 for example), you have 220 Hz and ~330 Hz. Their sum is 550 and their difference is 110. You can see that 110 is exactly an octave below 220. An interesting artifact is the C#5 (550 Hz) that is created, which makes this inherently a major chord, even though the player did not intend it to be major or minor. The C#5 is slightly flat, but due to the 12 tone equal temperament, all intervals (except the octave) are slightly out of tune anyway.
Don't ask me how this is relevant to the topic at hand, I just thought it was worth bringing up 😀
MitchMev explained the lower "implied" fundamental of a two-note dyad.
HF compression drivers, and to a lesser extent (at least in my limited testing) "full range" drivers also have a very measurable sub-harmonic content when driven hard. In other words, you can see, and hear, the difference frequency between the fundamental tones, 523 and 932 Hz signal will result in a 409 Hz output, as well as the usual upper harmonics one expects.
In the high frequency range, the harmonic distortion content can vary quite a bit between drivers as far as the ratio between even and odd order.
In testing of several HF drivers I found, (and you can hear for yourself) that when equalized flat, all the drivers sounded virtually the same, while at high drive levels the different harmonic, and sub-harmonic content made their sound quite identifiably different.
http://www.diyaudio.com/forums/multi-way/212240-high-frequency-compression-driver-evaluation.html
Note the various sub-harmonics the driver test below exhibits using 523 & 932 Hz test tones.
When driven hard at the LF end of the compression driver, my preliminary testing has found that horn loaded 3.5" "full range" drivers have far less distortion than the compression drivers we hear at most concerts. I will be building several two-way horn loaded cabinets using 3.5" and 8" cone drivers, and comparing distortion between them and 2x10"/3" diaphragm horn load cabinets in the coming months.
Although speakers have far more distortion than what would be considered "acceptable" for a "Hi-Fi" amplifier, amplifiers all have a somewhat different harmonic content when overdriven, their clipping may sound fairly benign, or incredibly bad, depending on the design topology, current limiting, input and output devices, and other design aspects that go beyond my depth.
Cheers,
Art
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