Missing Fundamental

[paulraphael]

I like hearing the fundamental at the bottom, so I play a P-bass into a 15" woofer and roll the tone forward or back depending on how sine-wavey or cutting I want it to be for the song. J-bass players are going to have a lot more focused overtones / mids. I see some bass players around town with rigs that aren't even capable of reproducing the fundamental with any kind of volume.
are more fragile and sensitive to tension.

It seems like a few bass speaker manufacturers are making full-range cabinets with quite flat frequency response curves down to 40hz. They're using some modern driver and design technologies. They don't necessarily use big drivers or big boxes, but they require a lot of power. Some players love the sound; others prefer the more mid-centric classic sound. I probably fall into the latter camp, but haven't tried any of these speakers in person.

 

[dasdoing]

traditionally the bass had to keep it's energy above the kick drum. things get very muddy once two instruments compete at the same frequencies.
then the synth-bass took over in many genres, and it was placed below the kick('s main energy frequencies)

 

[JustAnandaDourEyedDude]

Anharmonicity is an intrinsic part of any vibrating string that does not have zero diameter. It isn't an issue with the way the string is energised (struck, plucked, whatever) but is a problem with the harmonic structure of the vibrating string. Basically the problem is that the apparent length of the string is different for the different harmonics. Since the string has width, there isn't a simple defined end point where there is no vibration and the ideal string pivots from. Rather the point at the end of the string where it vibrates from is somewhere inside the string at a point that can move depending upon how much the string bends. This means that the fundamental can see a string that is effectively of a different length to a harmonic. This means that each harmonic is not an exact integer multiple of the fundamental, but usually a bit higher in pitch. Thus anharmonic. The very heavy wound stings in a piano are particularly subject to this issue, but it affects all strings. Shorter pianos need heavier strings, and are worse affected. The problem is that a piano is intrinsically out of tune with itself.
Managing anhamonicity is part of why pianos are tuned with a stretched tuning, and why smaller pianos need more stretch than large ones. In order to make the piano sound in tune with itself octaves are stretched so that anharmonics between octaves more closley match the next octave's fundamentals.

Multiple stings on a note in a piano is a really interesting part of its construction. The strings are not tuned identically. They are very slightly split in tuning. When struck they act as a set of coupled oscillators and they pass energy between one another, with each string in turn oscillating more than the others in a continuous dance. The coupled system acts as a whole in generating the note.

Excellent explanation of anharmonicity, thanks very much correcting my assumption about what it is! Reading it, I can see that idealizing the string as having zero diameter and having a length precisely equal to the distance between its points of contact with the wood is inadequate to describe its audible real behavior. I can understand that higher harmonics would see a shorter effective length. I follow why shorter pianos would be worse affected, owing to both the shorter string length and larger diameter needed to compensate for this (a stubbier string). I did not know about the stretched tuning or about the multiple strings coupling to produce a single tone, but they make sense. Piano construction and functioning is clearly more complex than my brief googling the other day led me to think . Thanks for the great insight your post provides. The degree of anharmonicity would stay the same as the struck note decays, unless the harmonics decay at different rates. In the former case, something else must account for what @rdenney described hearing as the note clarifying from its initial broad pitch to a purer tone as it settles down.

I have often considered that it is possible the one reason why pianos were once considered as a difficult instrument to reproduce is that excessive harmonic distortion in the reproduction chain lead to audible harmonics that were integer multiples, an these did not sound the same as the anharmonic harmonics inherent in a piano, so the instrument never sounded quite right.

Sounds quite plausible. Makes me glad we have low THD in the reproduction chain today .

 

[paulraphael]

traditionally the bass had to keep it's energy above the kick drum. things get very muddy once two instruments compete at the same frequencies.
then the synth-bass took over in many genres, and it was placed below the kick('s main energy frequencies)

Right. There's also the question of if it's more important to feel a bass track or to hear the tune it's playing. I find that an emphasis in the ribcage-rattling frequencies can hurt tonal clarity. Also the bottom octave emphasizes room problems, and requires power levels that weren't always affordable (or portable, or available at all).

I just saw that Duke from Audiokinesis is a member here. I'd love to hear his input on this. I'm not sure if his speakers are flat into the bottom octaves, but it's a topic he doubtless knows about. And I think he's friends with designers of many modern bass speakers.

 

[paulraphael]

I repeated the bass low-e spectrum, this time with eq:

I didn't have time to add sound to this or the previous recording, but you can download the audio clips here. The FFT shows the 3rd pluck.*

Filter is linear phase, 96db/octave low-pass, set at 56khz (when set lower, some of the fundamental snuck through).

The results really surprised me. I was expecting to hear a bigger difference. I suspect that many of the differences in subjective low-end performance have more to do with broader slopes in the upper bass and low mids. FWIW, I'm doing my listening with headphones that are reasonably well eq'd, so I can to hear 40hz just fine, but I'm not able to get body sensations. I don't have any full-range speakers to test.

*This is an original composition, so please venmo me royalties if you perform a cover version.

 

[StefaanE]

Hmm, that makes absolutely no sense to me. If I have absolute pitch in a naming system in which G4 = 440Hz, then I’m told that what I called G4 (440Hz) is now called A4, all I need to do is transpose each note name up one tone in order to identify it per the new naming system. This kind of transposition is trivial, and I still have absolute pitch.

I have perfect pitch. I hear notes by name, based on today’s conventions, but I cannot hear the difference between 440Hz and 442Hz when the notes are played individually. Play them together, and I am acutely aware the instruments are out of tune (more than most people I know, even my fellow brass band players).
To “hear” the key of a piece requires theoretical knowledge, and is not inherent in perfect pitch. The comment about a piece performed in the “wrong key” being akin to ”blue grass” makes no sense unless one already knows the key the piece is written in. I regularly transpose when accompanying singers on the piano, and believe you me, it’s still the same song. Musical keys were associated with moods, but that no longer applies with today’s equal temperament. But even when performing using unequal temperament, one still needs to know the key the piece was written in; there is nothing in a melody, a harmony or a harmonic progression that ties it to a particular key.

 

[Francis Vaughan]

In the former case, something else must account for what @rdenney described hearing as the note clarifying from its initial broad pitch to a purer tone as it settles down.

For that I would expect your initial thought that it is an aspect of the hammer strike is closer to the reason. Strings have lots of vibrational modes. We concentrate on the one mode when talking of the note and its harmonics, but strings can vibrate in other ways. You can have a longitudinal vibration for instance. Strings also don't just vibrate up and down in parallel to the direction of the hammer blow - they start to vibrate in changing radial directions. (The Stuart piano is designed to reduce this effect.) Lots of reasons why there will be other energy in the struck note. Some of this will die down, so you would expect the note to settle after striking.

On the subject of the Stuart, they make a 108 note piano, with a range exceededing even the Bosendörfer Imperial. They have this to say about the fundamental and its harmonics.

The lower you get in the bass, the more the fundamental disappears. In fortissimo playing, you get a great many harmonics, in which the fundamental gets completely lost. However, if you play them chromatically, you can curiously recognise the note's name with no difficulty. If the aim is not to create a sound effect, whatever it is, the best result is found in pianissimo playing. In softer playing, overtones are less present and you can easily recognise the fundamental of the very first C if you play it together with its upper octave, for instance.

 

[RayDunzl]

I have perfect pitch.

I don't, but have good "is it in tune" perception.

https://digg.com/video/perfect-pitch-prodigy-instantly-identifies-some-impossibly-complicated-chords

 

[RayDunzl]

Audio Buddy brought over a boombox tape (on CD) of his band from the 70's.

I didn't like the tuning.

My CD player has a "pitch" knob.

I tuned it to my feeling for it. A couple of steps.

We argued.

I asked, what key is it in?

"A" he said.

Where's an "A" in the tune?

Right here.

Ok, so I brought up a 440 pitch on the PC, and compared,

I was spot on.

I can do things like that, but usually only the first time (once).

After that, I'm a fail.

I wonder why I didn't win the lottery the first time I played.

 

[LTig]

Anharmonicity is an intrinsic part of any vibrating string that does not have zero diameter.
[..] The very heavy wound stings in a piano are particularly subject to this issue, but it affects all strings. Shorter pianos need heavier strings, and are worse affected. The problem is that a piano is intrinsically out of tune with itself.

Never heard of that one, many thanks! Does this mean that a digital piano needs to emulate this behaviour to sound real?

 

[StefaanE]

Never heard of that one, many thanks! Does this mean that a digital piano needs to emulate this behaviour to sound real?

AFAIK, a digital piano plays samples from a real piano. The challenge is to emulate the keyboard “feel” without having real hammers and strings.

 

[dasdoing]

The results really surprised me. I was expecting to hear a bigger difference.

Equal Loudness Contours explain this

a 41Hz tones has to have 93-ish dB to be percieved equaly loud to a 81-ish dB 82Hz tone. that means that if they both play at 81dB the 82Hz is percieved more then twice as loud (they say 10dB diference is percieved as twice as loud).
now factor in that even on a linear scale the 82Hz is louder.

 

[andreasmaaan]

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.

Yeh, sure. But even if it proves that you have some degree of absolute pitch, my comment was in response to your earlier point that:

we all have absolute pitch. it is just not trained. if we hear a song a thousand times we can say when it is in the wrong pitch.
with that beeing said, it seams that an adult can't train it to the point of identify notes.

What I'm saying is that there is in fact a very large proportion of the population who are unable to tell when a song is in the wrong key, no matter how many times they have heard it.

 

[Pio2001]

What I'm saying is that there is in fact a very large proportion of the population who are unable to tell when a song is in the wrong key, no matter how many times they have heard it.

I am definitely part of them.

Although I've got a good pitch discrimination (down to 5 cents), and I can nearly tell if a movie is playing in PAL speedup or not (speed and pitch 4 % too high) : it's quite difficult for an unknown movie, but easy for a movie that I know. This is not pitch recognition, however, the clue to tell if a movie is playing too fast is the sound of human voices.

But if I'm hearing a song played a whole tone higher or lower than usual, I won't notice at all.

The discussion about anharmonicity is interesting. I'll have to check that on my instrument (a yangqin) next time I tune it. I can hear that the treble range of the instrument sounds strangely flat although the electronic tuner says it is in tune.
I have recorded some notes and looked at them in REW's spectrum analyzer, but it is difficult to interpret what's happening : harmonics are divided into several close peaks.

 

[andreasmaaan]

The discussion about anharmonicity is interesting. I'll have to check that on my instrument (a yangqin) next time I tune it. I can hear that the treble range of the instrument sounds strangely flat although the electronic tuner says it is in tune.
I have recorded some notes and looked at them in REW's spectrum analyzer, but it is difficult to interpret what's happening : harmonics are divided into several close peaks.

Have never heard a yangqin and all now curious to hear how it sounds. You wouldn't be able to recommend some yangqin music would you?

 

[Pio2001]

Of course !
Here is my favourite composition for yangqin :

And here is a presentation of the instrument :

 

[LTig]

Of course !
Here is my favourite composition for yangqin :

Like it! Very accessible to European ears. The guy who entered the stage at the end - is this the composer?[

 

[richard12511]

I'm not sure I understand the argument here. If society as a whole decided that everything we had previously called "blue" was now going to be called "red" and vice-versa, this would not result in any change in the prevalence of colour blindness (although different words would now be used to describe the same colours).

What if the "red" I see is not the same "red" that you see? As long as our own color perceptions are consistent within themselves, we could both have totally different images in mind, yet have no way to communicate it.

 

[richard12511]

I very much doubt this is true for more than a subset of the population. Do you have any source for it?

I can do this, though I can't tell you the pitch. I was in choir in junior high and highschool.

If this is true we could all sing the first three notes of Smoke in the Water in the correct pitch. Let's all try and then compare if we got it right.

I got it right .

 

[pozz]

What if the "red" I see is not the same "red" that you see? As long as our own color perceptions are consistent within themselves, we could both have totally different images in mind, yet have no way to communicate it.

What he's talking about is the inability to distinguish or identify the object. Where there is no percept.