Missing Fundamental

[Helicopter]

Doing what?
Telling A4 when tuned to 440 or telling A4 when supposedly tuned to 392 to discover it was G4 at 440 ?

He could sing a note. If choir director asked for C4, he sould sing C4. He was like a human tuning fork kit.

 

[infinitesymphony]

It was a discussion about the missing fundamental (a relatively simple subject by comparison but still fascinating IMHO) but I dragged it off course. Please do help us get it right. . Not being facetious here. I can see you know what you are talking about.

My comment was more along the lines of, after reading the thread and catching up with what was moved here vs. what was new, not only could I see that the discussion of the missing fundamental was talked across by people arguing different points (i.e. "pianos and acoustic instruments are in fact capable of generating deep bass" vs. "listen to this deep bass, oh wait it's only harmonics in this recording but whatever"), but that a new discussion about tuning and pitch perception had cropped up and that people were arguing that absolute pitch means you're out of luck if everything isn't perfectly tuned to your trained pitch. Every person I've ever met who had acquired "perfect pitch" had no problem adjusting to the relative pitch center of an ensemble if their instrument allowed for it. Tuning perception doesn't mean being bound by it even if you happen to know you're sharp or flat relative to A440.

 

[infinitesymphony]

Also, pull out your strobe tuners. I dare you to find me a professional ensemble musician who isn't attempting to hit just intonation by tuning their notes to the chord, or by shifting notes intentionally sharp to sweeten them in a solo context.

 

[dasdoing]

Doesn’t that prove only that you have some ability to discern between pitches?

relative pitch? I surely have that.
but I am talking about huming the notes before the song. this is not relative pitch because I had no parameter to relate too.

 

[infinitesymphony]

If anyone's interested in hearing a short example of how A440 can be used as a relative tuning rather than an absolute tuning, check out the way Jacob Collier (who has a fantastic ear for pitch) uses a chord sequence to modulate into a new key in a slightly higher tuning in order to evoke an emotion.

 

[F1308]

Clearly some one is trolling.

Piano-1 is tuned to (A440). Playing the white keys from A4-A5 results an A-minor scale.
Piano-2 is tuned to (A392). Playing the white keys from A4-A5 results in an "A-minor"* scale.

But Piano-2 played the same pitches as Piano-1's G-minor scale.

People with absolute pitch can obviously cannot tell Piano-2's "A-minor" to Piano-1's G-minor scale, because they are the same pitches.

And notice that the trolling user has derailed a thread for the second time.

Not so, sorry.
Playing white keys A4-A5 on any of those pianos will not provide you with a single clue of the scale used until you hear the missing fundamental.
It will simply be felt as more "happy" for the one with the higher pitch and more "sad" for the lower one.
But...
It could be C major.
It could be A minor.
Once you make the harmony, you will know.
Addiing the missing tones, such as CC for bass and the chord GCE, or CEG, or GCE will instantly tell us we are well away from the sadness of A minor and from now on we can hear the bass even when not played. The missing fundamental.
Yes, we are enjoying Carmina Burana. C major.
But it has to be started, at least once...

 

[rdenney]

Do you have a link or reference for this. You spiked my curiosity but I did not find evidence of this.

Thanks
Wayne

I should withdraw the comment--I can't find a reference to it, either. That's the problem with received knowledge.

I have conducted experiments, but it depends on the high frequencies being produced and then subsequently damped by absorption over distance, leaving the mixing products to continue to propagate. (Of course, low frequencies propagate more readily over distance than do high frequencies.) It works like any RF mixer, where we mix a carrier with a sideband and then filter out both to leave the baseband signal.

I wonder if the source of my knowledge misinterpreted the diagrams of the Diaphone, which used two sirens, but not for this purpose.

Rick "wishing it was true" Denney

 

[rdenney]

Also, pull out your strobe tuners. I dare you to find me a professional ensemble musician who isn't attempting to hit just intonation by tuning their notes to the chord, or by shifting notes intentionally sharp to sweeten them in a solo context.

Or the simple fact that pianos are tuned in imperfect octaves, spreading the pitch from bottom to top, which presents challenges for musicians being accompanied by pianos.

Rick "good pitch memory is not immutable, but rather a matter of training, and those so trained do often struggle when playing in groups tuned to a different pitch standard than they are used to" Denney

 

[MRC01]

I should withdraw the comment--I can't find a reference to it [foghorn difference tones], either. That's the problem with received knowledge. ...

The concept is possible because our hearing introduces intermodulation distortion when we hear pure tones. That is, if you listen to 2 pure tones, under the right conditions you can hear the absolute difference between them a 3rd tone, even when it's not actually there. There's an easy way to demonstrate this. Flutes have a pure tone especially in the top register - they have few harmonics and almost like a sin wave. Two flutes playing different notes produces difference tones in the ears of listeners. Of course this requires accurate intonation which is difficult on the flute, making it great practice. It's not uncommon for flute students to play difference tone etudes with their instructors and friends. The music is written so that the difference tones become part of the music. Of course, you can hear difference tones in any flute duet, it's part of that "buzzing" sound when they're perfectly in tune.

Foghorns could operate on the same principle, though I don't know whether they actually do.

 

[infinitesymphony]

Or the simple fact that pianos are tuned in imperfect octaves, spreading the pitch from bottom to top, which presents challenges for musicians being accompanied by pianos.

While string, wind, and vocal performers do need to adjust their tuning relative to any fixed-pitch instrument that might be playing, they are also accustomed to tuning their notes by ear in the moment, so it's not necessarily more difficult than usual. I'd argue fixed-pitch instruments have a more significant disadvantage in that if they go out of tune during a performance, there's not much that can be done about it, and they can't adjust their intervals and resulting overtones to be more "pure" on the fly.

 

[rdenney]

While string, wind, and vocal performers do need to adjust their tuning relative to any fixed-pitch instrument that might be playing, they are also accustomed to tuning their notes by ear in the moment, so it's not necessarily more difficult than usual. I'd argue fixed-pitch instruments have a more significant disadvantage in that if they go out of tune during a performance, there's not much that can be done about it, and they can't adjust their intervals and resulting overtones to be more "pure" on the fly.

Oh, yes, but then the piano and the way it is usually tuned was designed to mask all those micro-mismatches as part of its characteristic sound, much like an orchestra full of string players using vibrato. The strings use vibrato, but not the brass, because the brass is seeking a different tuning model for a different effect.

I play in a brass quintet, and when we get it right, magic happens.

Rick "struggling with tremor these days, however, making some vibrato unavoidable" Denney

 

[watchnerd]

Pianos?

I thought this thread was going to be about power chord partials and IMD creating new fundamentals.

I'll go back to my bass practice...

 

[sigbergaudio]

Very interesting thread! If I may pitch in (pun intended) from a manufacturer perspective, we did some studies on what your system should be able to reproduce based on typical frequency content in contemporary music. We did spectrum analysis of quite a lot of music, with the goal of determining the target frequency response of our music oriented subwoofers. This is not by any means a scientific study of music, and we intentionally looked at music we already knew to have a good bass fundament (that someone who owned a high quality system with a subwoofer would be inclined to play), so this is not by any means an average of all music of all time.

Anyway:

We found that even in tunes perceived as quite rich in bass content, the most powerful frequencies between 20-200hz was typically in the 50-70hz region.

Tracks with sub-40hz content was common.

Tracks with sub-30hz was less common, and this was typically found in tracks with obviously very deep bass, and most likely to be found in newer recordings with synth/electronic instruments.

Tracks with sub-25hz content was relatively rare.

Does this mean you'd be fine with a system that doesn't go below 30h-40hz? Well, based on our findings (and in our context) we concluded that you would want a system that could produce content at least down to 30hz perfectly. Thus, 30hz couldn't be at the limit of the system. In practice you'd need a system that is quite capable at least down to 20-25hz to confidently reproduce 30hz and above at moderately high levels and with low distortion. On the other hand if your taste is limited to genres with less bass, or mostly older recordings, a limit of 40hz would probably be fine most of the time, so this is also dependent upon what you listen to.

I'm obviously not objective on the topic, but I thought these findings on frequency content in a wide number of tracks might be somewhat relevant.

 

[NTK]

I found some recordings of individual piano notes at U of Iowa. They are recorded with a Steinway B, with the left mic 8" above center bass strings, and the right mic 8" above center treble strings. Here are the spectra of a few notes (A0, B0, C1, D1, E1, G1).
http://theremin.music.uiowa.edu/MISpiano.html



It is interesting to see that the fundamentals mostly only showed up on 1 channel for A0, B0 and C1, with C1 switched to right channel from left. By about E1, the volume of the channels are comparable. I think it is because the Steinway B is not of sufficient size and/or rigid enough to radiate the fundamentals of the lower notes as proper acoustic waves. The "sounds" picked up by the mics were probably either evanescent waves and/or hydrodynamic waves, which decay exponentially with distance, and would not be detected (either by ear or mics) at the typical listening distance.

 

[LeftCoastTim]

I found some recordings of individual piano notes at U of Iowa. They are recorded with a Steinway B, with the left mic 8" above center bass strings, and the right mic 8" above center treble strings. Here are the spectra of a few notes (A0, B0, C1, D1, E1, G1).
http://theremin.music.uiowa.edu/MISpiano.html

View attachment 102745 View attachment 102746 View attachment 102747 View attachment 102748 View attachment 102749 View attachment 102750

It is interesting to see that the fundamentals mostly only showed up on 1 channel for A0, B0 and C1, with C1 switched to right channel from left. By about E1, the volume of the channels are comparable. I think it is because the Steinway B is not of sufficient size and/or rigid enough to radiate the fundamentals of the lower notes as proper acoustic waves. The "sounds" picked up by the mics were probably either evanescent waves and/or hydrodynamic waves, which decay exponentially with distance, and would not be detected (either by ear or mics) at the typical listening distance.

My interpretation/theory on these plots is that the strings themselves are vibrating at the fundamental, and when the mic is close enough to it, it can be picked up. But the vibration of the strings must pass through the bridge and to the soundboard in order to be heard by the audience. I'm willing to bet that the bridge and the soundboard is unable to transmit such low frequencies.

Very interesting! Thank you.

 

[MRC01]

I found some recordings of individual piano notes at U of Iowa. They are recorded with a Steinway B, with the left mic 8" above center bass strings, and the right mic 8" above center treble strings. Here are the spectra of a few notes (A0, B0, C1, D1, E1, G1). ...

Those show the 28 Hz fundamental we discussed earlier. I've seen the same in some piano recordings in my collection. I suspect the reason it only appears in some recordings is (1) most obviously, not much piano music actually uses that note (though nearby notes may cause low level sympathetic vibration) and (2) it's a weak frequency only audible when miced at a certain position & distance.

Sometimes natural musical instruments can bend the rules. Like the spectrum for the lowest notes on a flute show the first few harmonics stronger than the fundamental (same as that A0 piano note). If we saw that measuring equipment we'd call it > 100% distortion. With a flute or other musical instrument, we call it a "fat purple" tone (or something like that).

PS: I have a harp recording that has a 25-30 Hz resonance when the player strums the lowest strings. It's low level but quite audible when listening on equipment that reproduces that range. Sounds amazing.

 

[bigjacko]

Very interesting discussion here, but I want some points to be make. Do we have some take away here? Will IMD create new notes? What is the lowest frequency that is sufficient for us?

 

[RayDunzl]

My interpretation/theory on these plots is that the strings themselves are vibrating at the fundamental, and when the mic is close enough to it, it can be picked up. But the vibration of the strings must pass through the bridge and to the soundboard in order to be heard by the audience. I'm willing to bet that the bridge and the soundboard is unable to transmit such low frequencies.

I have an electric bass guitar - which has strings - and picks up the string vibrations magnetically - so not dependent on the bridge or soundboard.

Typically, the fundamental, though strong, is weaker than the second harmonic.

I figure it is just how strings prefer to vibrate.

I (finally) intentionally produced a pluck with a higher fundamental, for the purpose of observing the harmonic series, but it wasn't easy:

I'm not sure if the electrical pickup is "flat", and it has knobs to perform some filtering, so, my observation is not scientifically rigorous.

 

[watchnerd]

I have an electric bass guitar - which has strings - and picks up the string vibrations magnetically - so not dependent on the bridge or soundboard.

Typically, the fundamental, though strong, is weaker than the second harmonic.

I figure it is just how strings prefer to vibrate.

I (finally) intentionally produced a pluck with a higher fundamental, for the purpose of observing the harmonic series, but it wasn't easy:

View attachment 102762

I'm not sure if the electrical pickup is "flat", and it has knobs to perform some filtering, so, my observation is not scientifically rigorous.

With the right amount of distortion, and the right partials, you should be able to create a new fundamental.

Caveat, I'm a bass player, not a guitar player, but it's conceptually the same for either electrified instrument.

 

[RayDunzl]

What is the lowest frequency that is sufficient for us?

30Hz for me.

Below is more tactile than tone.

https://www.stereophile.com/content/question-bass-bass-instruments-frequencies-page-3