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Missing fundamental for guitar low e string

pma

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Just for fun, below are three music wav files in the zip. Low e string recorded from electric guitar, the same file with fundamental frequency notched and finally a Deltawave difference file. It is an example of one of the auditory illusions how human ear is able to hear the missing fundamental in the string tone.

missing fundamental.png
 

Attachments

  • missingfundam.zip
    1.5 MB · Views: 32
I posted a note from an electric bass.

It took a lot of tries before I was able to get the fundamental level above the second harmonic.

It wasn't missing, but I needed it to be the highest level for the "distortion" measure to work correctly.

1725485838267.png
 
It took a lot of tries before I was able to get the fundamental level above the second harmonic.
Best to be played by fingers only?

e6_.png


But the goal here is not to measure distortion of electrical signal from the guitar. The goal is to show psychoacoustic phenomenon, that even if the fundamental frequency is notched out, the ear is still fooled and hears the same guitar note, wit a bit different timbre.
 
It could well be that fundamental is actually there, as a difference tone formed by the ear's own distortion,
See attached "Heerens and de Ru" paper I mention here on a regular basis, and more importantly their experiments which demonstrate a lot of interesting psychoacoustic phenomena which may actually be physical phenomena happening right in the ear, before any neuronal processing. While the paper is not truly academic source and never got peer-reviewed (AFAIK), the experiments section is absolutely brilliant, and they offer(ed) a software for it to make things easier.
 

Attachments

  • Book Heerens de Ru EN.pdf
    761.5 KB · Views: 35
It could well be that fundamental is actually there, as a difference tone formed by the ear's own distortion,
Yes, it is there as a result of human perception mechanism, though it physically does not exist. It is similar as if you create twin tones in the middle band, the ear perceives difference frequency (beats), though there is no difference tone in the spectrum. Simply put, our ear hear sounds that in fact do not exist. Psychophysics and psychoacoustics give explanation. We are often too much concentrated to engineering view point.

Please feel to try this:


The test question is which signal has higher frequencies content, based on listening and hearing the pitch.
 
I well remember a BBC TV show from around 1980 or so where they demonstrated this effect by featuring a solo double bass playing low notes and assuming that we are listening on TV set speakers that can't reproduce low frequencies, which was true for me and I guess most viewers. They pointed out that despite that the low frequencies are absent we can still recognize the instrument and perceive the notes. I was in my mid-teens and was quite impressed with the lesson and have been fascinated with the difference between sensing and measurable signals since then, and not just in audio.
 
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though it physically does not exist.
Depends one where you look at. Before the eardrum it doesn't exist, but inside the ear it is there, still on a physical level (at least that's the Heerens/deRu theory).

This distortion is why recorder flute quartets, when playing closely spaced notes, sound completely broken even live. Back in elementary school we were driven to play recorder flute in ensembles as part of basic musical education and everybody hated it, one of the reasons sure was this annoying distortion.

One also shouldn't judge tweeter distortion by letting it play alone since even with a distortionless tweeter we'll be hearing those nasty ear-IMD products. With no lower frequencies to mask, it becomes quite audible.
 
Just for fun, below are three music wav files in the zip. Low e string recorded from electric guitar, the same file with fundamental frequency notched and finally a Deltawave difference file. It is an example of one of the auditory illusions how human ear is able to hear the missing fundamental in the string tone.

View attachment 390280
I think that's also the idea with power chords. For example when we play E3 (160[*], 320, ...) and B3 (240, 480, ...) we get 160, 240, 320, ... and that's like E2 (80, 160, 240, ...) without the fundamental:
[*] I rounded the frequencies to make things easier to see
Code:
e|-----
B|-----
G|-----
D|--9--
A|--7--
E|-----
01_E3.B3.png


In this particular case, we can add the missing fundamental by playing the open E and compare. Admittedly the difference seems to me bigger than in your example but maybe I just played it wrong :)
Code:
e|-----
B|-----
G|-----
D|--9--
A|--7--
E|--0--
02_E3.B3__E2.png


We can go even further and play B2 (120, 240, ...) and we get 120, 160, ... which is like E1 without the fundamental (and without the 2nd harmonic):
Code:
e|-----
B|-----
G|-----
D|--9--
A|--7--
E|--7--
03_E3.B3__B2.png


Someone who can play :) shows it here:
 

Attachments

  • 01_E3.B3.flac.zip
    161.8 KB · Views: 18
  • 02_E3.B3__E2.flac.zip
    172.9 KB · Views: 24
  • 03_E3.B3__B2.flac.zip
    161.8 KB · Views: 22
I posted a note from an electric bass.

It took a lot of tries before I was able to get the fundamental level above the second harmonic.

It wasn't missing, but I needed it to be the highest level for the "distortion" measure to work correctly.

View attachment 390295
Low E is 41 hz. Is that live or recorded? If live, straight in or thru an amp/cab? Live bass usually has louder low freqs than recorded.
 
Low E is 41 hz. Is that live or recorded? If live, straight in or thru an amp/cab? Live bass usually has louder low freqs than recorded.

I didn't play rhe low E.

Don't know how well tuned it was, but the measurement gave a fundamental of 96.5Hz. So, open G string:

"For a 5-string bass guitar in standard tuning (B-E-A-D-G), here are the note names and their corresponding frequencies:

  1. B0: 30.87 Hz
  2. E1: 41.20 Hz
  3. A1: 55.00 Hz
  4. D2: 73.42 Hz
  5. G2: 98.00 Hz "
The signal was guitar -> TRS cable -> Focusrite Clarett 4Pre USB -> REW RTA window
 
I didn't play rhe low E.

Don't know how well tuned it was, but the measurement gave a fundamental of 96.5Hz. So, open G string:

"For a 5-string bass guitar in standard tuning (B-E-A-D-G), here are the note names and their corresponding frequencies:

  1. B0: 30.87 Hz
  2. E1: 41.20 Hz
  3. A1: 55.00 Hz
  4. D2: 73.42 Hz
  5. G2: 98.00 Hz "
The signal was guitar -> TRS cable -> Focusrite Clarett 4Pre USB -> REW RTA window
Most amps and cabs reinforce the fundamentals especially if you use the shape, contour, scoop, etc button/faders (EQs that lower the mid bass). Those low fundamentals use so much power not much ends up in recordings, they lower the overall volume a lot, which is counter to the loudness wars, and make cutting vinyl difficult. Easiest way to make a song louder is to lower those low freqs. A good mix of an electric bass in a club will make you feel those freqs. This pyschoacoustic effect of replacing those fundamentals only goes so far they do actually make a difference if there loud enough. I play a 5 string with a 15" cab and you can tweak things so you feel those low fudamentals. Why would a pipe organ builder bother with 32' pipes, the most expensive ones, if they didn't make a difference?

Aside: Traveling in Germany and visited the Berlin Cathedral today, awe inspireing, over 7,000 pipes in the organ, would have loved to hear/feel it.
 
There are many factors at work here. Three that are rarely if ever mentioned:

The neck pickup position on Gibson guitars and classic Fender designs - copied in almost all guitar and bass models in production - are 22% or less of the open string length. This attenuates the fundamentals of notes below the fifth fret 10dB or more. Some Gibson basses have pickups just below the 20th fret, and they have problems with overdriving bass guitar speakers beyond XMax, which of course accentuates the harmonics.

Classic open backed guitar cabinets roll off at least an octave above low E fundamental. Even sealed box bass cabinets roll -12dB/octave at 80Hz.. This would make them suitable for six string guitars, except spekaers intended for bass guitar usually roll off relatively smoothly above ~4.5KHz, while guitar "Musical Instrument" speakers have cone breakup peaks up to 10dB somewhere between 1.8KHz and 3.5KHz, and extend to 5.5 - 6.5KHz.

One major problem with BASS is cabinet resonance, a necessary mechanism for flat frequency response. When a bass instrument is used as a rhythm intrument, the resonance which is generally evidenced as impedance peak(s) stores energy at teh begnning of the note and releases it on the tail. Not only does this affect timing, teh energy is subtracts and added at the speaker resonance frequencies, which are anharmonic to the music. This is one reason why all commercial recordings (except organ, which can;t start and stop sounding abruptly) have a high pass at 80Hz - consumer speakers sound muddy when a bass note starts and stops quickly.

I did an experiment playing a bass guitar into an oscilloscope, and properly formed staccato notes have a rectangular modulation envelope and and integer number of half cycles. This is the best test waveform according to no less authority than Harry F. Olsen, as shown on the dust cover of his textbook "Modern Sound Reproduction". Wavform generators to produce this have not been available for decades, so I had to build my own. Hint: vented boxers and high Qms drivers produce this transient intermodulation distortion in excess.
 
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