Talk:Missing fundamental

misnomer? (title by 172.x.x.x)
How can a periodic signal be missing any fundamental frequency? If the fundamental frequency corresponds to the shortest repeating period then it has to exist for any periodic signal. For example the signal, sin(2x) + sin(3x), will repeat exactly as often as sin(x) to which they 'refer'. Even if a signal lacks a component with the same frequency as its fundamental, it still has the same fundamental frequency.


 * This is psychoacoustics, not physics. You are using the overtone series to create the illusion of a fundamental.  The real fundamental is stripped out, too low to hear, or is being simulated.  Whether a fundamental that is psychoacoustically inaudible exists or does not exist is a philosophical matter.172.151.119.150 22:21, 29 April 2007 (UTC)

see also? SRS?
Can someone expand the refered acronym (SRS)


 * Its a company name.--Light current 12:46, 7 May 2006 (UTC)

Ok, so what is it doing in the article? I've followed, the connexion is not transparent (besides being both related to audio)


 * Try this .Could you please sign your posts by typing 4 tildes ~ . Thanks.--Light current 23:58, 10 May 2006 (UTC)


 * Sorry, I don't get it, I'll quote:

( http://www.srslabs.com/home100.asp ::)


 * Welcome to SRS


 * SRS Labs develops audio, voice and surround sound technologies that enrich and enhance the audio experience of any consumer electronics product. Over 300 of the world's top consumer electronics manufacturers look to SRS Labs to provide patented audio techniques when designing their newest products.


 * Found in over 600 million products worldwide, SRS Labs is widely recognized as the mark of powerful and immersive sound. Select a category on the left to explore the company's wide range of audio technologies and see for yourself how SRS Labs makes great products sound even better. "

It looks like marketing hype, how is it related directly to the Mising fundamental page? Oyd11 17:20, 14 May 2006 (UTC)


 * Its the company web page. You have to search for the list of products in the glossary. THen you find:
 * TruBass®
 * Psychoacoustic bass enhancement for speakers and headphone systems that delivers bass up to an octave below the physical capabilities of the speaker's driver.
 * If you look at the other link, there is more detaill on the SRS system --Light current 11:35, 15 May 2006 (UTC)

Double Bass sound
I believe this phenomenon makes the DB sound lower than it actually is!--Light current 19:31, 29 August 2006 (UTC)


 * You may be right. f=73 and f=55 have peaks at the second harmonic.  f=41 has a peak at the third harmonic.  You could test your theory by looking at the overtone series and mimicking it with CoolEdit.  (source: Music, Physics, and Engineering, 2nd ed, Dover.)172.151.119.150 22:05, 29 April 2007 (UTC)

Radio stations
I think some FM stations are using this trick. The US pop stations have a heavier sound, even on cheap systems. Combined with compression, it sounds like crap.172.151.119.150 22:30, 29 April 2007 (UTC)

Misleading demonstration
It should be mentioned that the final bass note in each version is only likely to sound identical when played on small speakers (such as PC speakers) that cannot produce any real bass.

In that case, comparison of the two versions demonstrates absolutely nothing, since the sounds actually produced will be identical. 68.239.116.212 (talk) 04:53, 12 November 2009 (UTC)


 * You're right. I'm moving the content here until it can be rethought and/or reworded so that it's abundantly clear to any listener on any equipment what's being demonstrated.


 * I suggest not trying to bother with a demonstration of "phantom bass", since that depends on the listener's equipment. Instead, it would be better to focus on a demonstration for the general principle by replicating one of the experiments on the German Audio magazine test CD, where one dyad is played, then a second is played, and depending on which group you fall into, you'll think the second dyad was of a higher or lower average pitch than the first. —mjb (talk) 23:37, 10 May 2010 (UTC)


 * Agreed! No demonstration of phantom bass can be attempted when listener equipment is not known. Binksternet (talk) 13:56, 10 November 2010 (UTC)

Fix to patent ref
It took me two goes (because of my own lack of expertise) to fix a fault in a previous editor's attempt to use the Template: US patent. Their original error was to use too many pipes. By the time I had worked out it was as simple as that, I had already put a "see Discussion" in an edit summary, because the edit summary did not allow me enough characters to make sense.

As I had already put in a "see Discussion" I thought I had better put something in here.

I am just guessing at what had happened previously, but when I found it the reference was going to the US (the country), not to the relevant patent.

FrankSier (talk) 23:22, 23 January 2011 (UTC)


 * Thanks for fixing that. --Kvng (talk) 16:41, 24 January 2011 (UTC)

Heidelberg research
I just made a couple changes to make it more accurate. Also, I want to propose that this paragraph be moved to the middle of the "Explanation" section, and the "Differences in Perception" section removed; it doesn't really seem worthy as its own section if there is only one bit of information for it. I will do this in a few days if no one has any objection, or things to add to the "Differences in Perception" section. Eflatmajor7th (talk) 01:43, 22 July 2012 (UTC)


 * No objection here. Thanks for working on it! —mjb (talk) 05:43, 22 July 2012 (UTC)

Reverted by Dicklyon ? *** Non-neutral, essentially FRINGE POV; see editor's talk page. ***
'''It is important to describe the recent research and the research that has been done in the past which contributes to the questions arising today. Of significance, it is still under question the exact mechanism. It is important to inform the public of all of the hypotheses that are arising on this topic so that future researchers can be well informed with what information is still in need of explanation.''' [Akwasí Píèsíe's text bolded by Dicklyon for comparison below] To have a balanced representation of various points of view:

Akwasí Píèsíe 1967 edit *** The findings of Monahan et al., show that the listener reconstructs the fundamental or virtual pitch within roughly 100 ms after the sound signal onset, which is in accordance with earlier electrophysiological research. According to their paper it also suggests that this fundamental pitch is reconstructed at the very beginning of the auditory cortex. The experiments of Willem Chr. Heerens and J. Alexander de Ru, however, show that this reconstruction process takes place even earlier. Contrary to the conclusion that an early neural mechanism is responsible for the mystery of the inferential pitch, Heerens and de Ru show evidence that the cause for this reconstruction of the virtual or fundamental pitch is hydrodynamic in origin. For residual tone complexes – harmonic series where the first harmonic or fundamental is missing – the differentiating and squaring - (hydrodynamic) process in the cochlea reconstructs perfectly the corresponding but missing fundamental. Mathematically, this signifies that the mammalian cochlea differentiates and squares the incoming sound pressure signal. In terms of physics, it means that a sound energy signal is offered to the organ of Corti. Functioning as a Fourier analyzer, the organ of Corti subsequently converts these incoming signals into the sound energy frequency spectrum that is transferred to the auditory cortex in a frequency selective way. ***

Reverted by Dicklyon ? *** Non-neutral, essentially FRINGE POV; see editor's talk page. *** ?

Encyclopedic content must be verifiable! Well also, the experiments are very verifiable! http://www.a3ccm-apmas-eakoh.be/pcbwp/experiments.htm The experiments are as neutral, as neutral as the other examples and the other external links which are in the two sections 'Examples' and 'External links'. So the experiments and the references are very well Non-neutral. Akwasí Píèsíe 1967 (talk) 21:12, 6 January 2013 (UTC)


 * I support the inclusion of the hydrodynamic explanation. Binksternet (talk) 21:14, 6 January 2013 (UTC)


 * I have no problem with including hydrodynamic explanations, including the far-out one by Heerens, but User:Akwasí Píèsíe 1967 who just showed up today has been posting a string of very slanted POV on this and related cochlear topics at various articles. I have explained on his talk page that he needs to take a more balanced approach.  Since I have published a hydrodynamic-based explanation myself (in press; yes, the cochlea does have some second-order nonlinear distortion), and I've told Heerens in an off-wiki forum why his explanation is flawed (and others have supported me in this), I'm biased; so I'll stay away from editing on this further myself.  I encourage you to help this new editor get it right.  The weight given to Heerens might best be proportionate to the citations that his work has gotten, which as far as I can tell is zero.  The problem is that he claims his approach is physics based, but he ignores the first-order physics and invokes a second-order effect as if it were the main thing.  Dicklyon (talk) 21:47, 6 January 2013 (UTC)


 * We also have a potential WP:SOCK issue here, as the wording in the post above is pretty much identical to that of User:Caitlinmayhew at Talk:Cochlear amplifier, who said "It is important to describe the recent research and the research that has been done in the past which contributes to the questions arising today. Of significance, it is still under question the exact mechanism... It is important to inform the public of all of the hypotheses that are arising on this topic so that future researchers can be well informed with what information is still in need of explanation." a little over a year ago. At the least, a user page statement declaring and explaining the relationship between the accounts is needed.  Dicklyon (talk) 21:58, 6 January 2013 (UTC)


 * Dicklyon, you have told Heerens in an off-wiki forum why his explanation is flawed. I do not see his explanation - in the doctrine with physics - about the reversal of the physical rules with regard to traveling waves is flawed. About the reversal of the physical rules with regard to traveling waves, I support Heerens with his PhaseWave.pdf on that off-wiki forum: http://lists.mcgill.ca/scripts/wa.exe?A2=ind1208d&L=auditory&P=684 Akwasí Píèsíe 1967 (talk) 20:36, 11 January 2013 (UTC)


 * Hmmm. It would be most reassuring to see other academics review the Heerens work positively. If such a review exists I cannot locate it. Binksternet (talk) 08:45, 7 January 2013 (UTC)


 * It would be most reassuring to see non-biased academics review the Heerens explanations. Akwasí Píèsíe 1967 (talk) 20:36, 11 January 2013 (UTC)


 * The great thing about science is that you can believe one thing before an experiment, then change to believe another thing afterward. Bias should be self-correcting in the presence of experimental evidence. Binksternet (talk) 21:01, 11 January 2013 (UTC)

The fact that the missing fundamentals in a tone complex can be both systematically manipulated and calculated - perception calculations - Heerens / de Ru
Especially interesting discussion. I am mainly concerned with signal processing applied to medical problems causing this problem exciting me a bit, even a lot. I am concerned with the hearing itself and with (f)MRI where auditory stimulus is used. I must admit that this is an interesting discussion in explanations. I will also have to read the book. If Heerens - de Ru are correct, then not only must and should the theory of the operation of the hearing be re-examined, but also the methodology in which hearing aids are based. Signal processing on the basis of the energy spectrum is very different (and a pack of more complex). At this time I feel that this is analogous as in fMRI where there are two schools. A school that additivity postulates that in the traditional thought pattern fits only works well for high SNR and another school that the additivity rejects because even with fMRI especially the energy content is measured as the absolute phase can not be measured. I know Heerens by his scientific publications during the eighties and nineties regarding capacitive sensors and potential theory offering his expertise in general physics, sensor technology, potential theory, and vacuum technology. Especially interesting discussion. Peculiar, as the point of these sound fragments is to allow anyone, even those without any expertise, to simply listen and hear that these fragments exactly follow the rules as predicted by that new concept of the auditory sense. (the fact that the missing fundamentals in a tone complex can be both systematically manipulated and calculated). The expert wikipedia reader might actually consider this good offering and explanation to that effect. Aside from that, the entire concept has been carefully analysed, is in itself consistent and completely correct in making use of the laws of physics. It therefore stands to reason that it would be capable of taking an objective position. The sound fragments – that have been composed based on a differentiating and squaring auditory sense – can be predicted exactly. This can be heard by anyone without any training whatsoever. K B JANUAR ENERO GENNAIO (talk) 08:08, 7 January 2013 (UTC)


 * The explanation of such effects by 2nd-order distortion dates back at least to Helmholtz. The fact that difference frequencies can be calculated and manipulated is well known before Heerens.  But WP usually bases articles on secondary sources; it would be best to wait and see how the Heerens & Ru theory catches up, rather than use WP to promote an unusual POV from a primary source.  And is that you again with a third WP:SOCK account, new today just to say these things?  Dicklyon (talk) 08:30, 7 January 2013 (UTC)

Missing fundamental (image)



 * "The wavelength which is the least common multiple of all overtones is that of the fundamental. Thus even if it itself is missing, the frequency is still perceptible."

? Hyacinth (talk) 23:38, 17 January 2013 (UTC)


 * That's what's known as an "edit summary". It explains (if tersely) why I partially reverted you here (this is called a "diff").  There were two aspects to my partial revert; one involving wavelength, the other involving "so", which you can see by looking at the diff.  Please look and tell me how you would justify either part of what you had there.  And I see you have again put it back; that's called WP:Edit warring, and is frowned on.  Dicklyon (talk) 00:55, 18 January 2013 (UTC)
 * I also include to the right the figure that I removed, along with its caption that you had. I can't see how it's helpful at all.  Dicklyon (talk) 00:57, 18 January 2013 (UTC)


 * There is no need for your tone. If one expects courtesy one must display courtesy.
 * We have not yet reverted each other three times (I haven't), thus there is no edit warring.
 * What is counterproductive and why?
 * Why are you bringing up the word "so" with me? Hyacinth (talk) 02:33, 18 January 2013 (UTC)
 * The word "so" is part of what you restored several times with your UNDO, as it was part of my edit, as noted in my edit summary; I didn't mean to imply that it came  from you originally, but it was analogous to the "thus" in your passage about wavelength that I also took out.  And you are edit warring long before you have a WP:3RR violation.  My tone was intended to be introductory, as you seem to be a novice editor.  Did I get that wrong?  Dicklyon (talk) 06:48, 18 January 2013 (UTC)

The above image shows a very strange wave series, very much an artificial one rather than a natural one. The crests and troughs are half circles, not sine waves. I don't think the image can be used at all, ever. Binksternet (talk) 03:03, 18 January 2013 (UTC)


 * I agree with Dicklyon and Binksternet that bringing wavelength into this article, and its associated concept of least common multiple is not necessary, nor is the graphic with all the semicircles. Hyacinth was right to point out that the word "so" was not his/hers, at least not recently, although I agree that the semicolon is better there. Also, since this is an article about both pitch (music) and pitch (psychophysics), I think we could have some graphic simply illustrating the obvious common periodicity between complexes with and without the fundamental, maybe even without the first couple harmonics. If no one has any immediate objections, or of course immediate graphics of their own to contribute, I will do this in Matlab soon. Eflatmajor7th (talk) 06:08, 18 January 2013 (UTC)
 * Good idea. Dicklyon (talk) 06:48, 18 January 2013 (UTC)
 * Your new figure looks good. The caption contained "the common periodicity reflecting the fundamental is nevertheless clear", which I simplified, as it has hard to see what it meant, and it seemed to claim more than is supportable.  There is considerable subtlety in the whole missing fundamental thing, and we should be careful not to trivialize it.  In particular, removing the fundamental does not a always leave the periodicity unchanged.  And the pitch perceived does not always agree with the periodicity, whether the fundamental is present or not.  And the basic problem is similar even for sounds that aren't periodic.  There's more we could do here, but I think this is good for now.  Dicklyon (talk) 06:08, 20 January 2013 (UTC)
 * Thanks. You're absolutely right that the general issue of residue pitch is more nuanced than is addressed in this article, for instance the shift of the residue when the spectrum becomes inharmonic, as would be the case if all harmonics were shifted up or down linearly. I have been thinking about creating a separate article on pitch shift of the residue, as it is probably not appropriate to try and discuss it here. Your deletion from the caption is fine, but the reason I said "reflecting" is because, in this simple case, the periodicity does reflect the pitch for both sounds: It is 10 milliseconds, .01 seconds, the reciprocal of which is 100 Hz. I guess the point is clear enough the way it is now, but I thought some kind of clarification might be in order, like citing the simple math I just pointed out, or having arrows in the figure pointing to two consecutive peaks in both waveforms. Think anything like this is necessary? Eflatmajor7th (talk) 07:06, 20 January 2013 (UTC)
 * Probably not necessary. Might as well start the residue bit here, rather than a new article.  If it gets to be too much, then split.  Dicklyon (talk) 07:18, 20 January 2013 (UTC)
 * The proportional, subjectively observed gradual shift of the residual pitch, in case each contribution of a series of equidistant stimulus frequencies is shifted over the same frequency difference. This perceived pitch shift – clearly subjective observations that were reported by trained examiners. - The residual pitch shifts proportionally to the equidistant frequency contributions shift in a tone complex: They are subjectively observed: we should be careful. - The residual pitch shifts proportionally to the equidistant frequency contributions shift in a tone complex. According to some experiments described the pitch can, by good approximation, be perceived to be equal to the sub harmonic frequency of the center frequency of the complex, which is closest to the difference frequency. Subjectively observed: Therefore, in order to attain less subjective experimental data with regard to that which actually transpires, series of experiments are conducted showing they are not based on reality but on an illusion. Akwasí Píèsíe 1967 (talk) 15:56, 20 January 2013 (UTC)
 * Careful subjective matching experiments usually find a perceived pitch closer to a subharmonic of one of the lower components in the complex, not the middle ones. Your passive voice leaves your meaning unclear in "series of experiments are conducted".  And it's not clear what you mean by illusion, or what alternative you have in mind for subjective pitch matching experiments.  Dicklyon (talk) 18:47, 20 January 2013 (UTC)
 * The phenomenon of the occurrence of a correct pitch (pitch) with a physically missing fundamental ("case of the missing fundamental", not "case of the missing pitch"), eg occurring in a small transistor radio, has put many researchers thinking about. In summary, in the course of history, various alternative theories exist, whether or not rejected. Terhardt and Goldstein said "first effect of pitch shift" and this effect is studied by Schouten eg, de Boer and colleagues. This effect comprises that the pitch (virtual pitch, or synonym: residue pitch, musical pitch, low pitch) of a tone set (for example: triplet) consisting of, for example, 660 Hz, 860 Hz, and 1060 Hz is not equal to 200 Hz (the difference in tone from non-linear distortion) but at 215 Hz, which is harmonically related to the fundamental tone best suited to the anharmonic triplet. According to the experiments described by De Boer [De Boer E. (1956) On the “residue” in hearing. Thesis; University of Amsterdam.] the pitch can, by good approximation, be perceived to be equal to the sub harmonic frequency of the center frequency of the complex, which is closest to the difference frequency. For example: in the 1430+1630+1830+2030+2230+2430+2630 Hz tone complex, for a center frequency of 2030 Hz and a difference frequency of 200 Hz, one tenth of the 2030 Hz of the center frequency, equals 203 Hz. But if you study the recently published booklet with the following title: Applying Physics Makes Auditory Sense, with subtitle: A new paradigm in hearing: The third chapter – Methods and experiments for verification – you see that chapter 3 deals with perception experiments in which the ‘shift in pitch’, described in literature as result of a uniform frequency shift in higher ‘incomplete harmonic’ sound complexes, is found as an illusion, based on subjective perception of musically trained experimenters. Therefore, in order to attain less subjective experimental data with regard to that which actually transpires, Heerens and de Ru conducted a series of experiments. Those experiments are described in chapter 3. page 34 and page 35 see there 3.7 Is pitch shift in an enharmonic tone complex with equidistant frequencies an illusion? My passive voice leaves my meaning: "Again, it would be best to wait and see how the Heerens & de Ru theory catches up". Akwasí Píèsíe 1967 (talk) 12:06, 21 January 2013 (UTC)
 * There are no experiments in the document you are referring to. There is mention of experiments in it, but, if anything, the authors did them on themselves. There are no methods, statistics, results summaries, or anything that is included in a proper experiment. All claims are simply anecdotal; so, I repeat, there are no experiments in that paper. Also, your claims ignore the wealth of published psychophysical experiments that have existed for more than a half-century showing the effects of pitch shift, some of which you referenced. For example: de Boer 1956, Schouten et al. 1962, Patterson 1973, Gerson and Goldstein 1978, Greenberg et al. 1987, Wile and Balaban 2007. Eflatmajor7th (talk) 15:16, 21 January 2013 (UTC)

How does the image look now? Hyacinth (talk) 04:25, 16 January 2014 (UTC)
 * The wave shape is better, but I'm still not loving it. Dicklyon (talk) 05:05, 16 January 2014 (UTC)
 * It's already been mentioned that the waves in that image are not sinusoids, and they will not become sinusoids by changing the resolution of the picture. Furthermore and more importantly, there has not been any stated reason why an image like this is helpful. It still seems to me only to confuse things, so I still don't support its inclusion. If we want to add an image, let's talk what issue it should address that is not already addressed, and how it will do it. Eflatmajor7th (talk) 00:44, 17 January 2014 (UTC)

Tritone paradox
I just wanted to explain that I added tritone paradox as a "see also" because, like missing fundamental, research shows that people generally fall into one of two categories: those who hear it one way, and those who hear it the opposite way. I don't know if the phenomena are linked, but they seem similar enough to warrant a pointer. —mjb (talk) 10:12, 4 June 2014 (UTC)

incorrect section re: acoustic guitar fundamental
This section, and the web page it cites, appear to be incorrect:

"The fundamental frequency is not normally heard on acoustic guitars, classical guitars and other stringed instruments with one end of the strings anchored on a soundboard bridge which has a low profile, holding the strings close to the soundboard surface. In these cases, the lateral string vibration has no discernable effect on the bridge; instead, the bridge is excited by changes in string tension, which are twice the lateral wave frequency. On these instruments, listeners hear the first harmonic as the lowest note. Electric guitars are not like this; the fundamental frequency of each string is heard because the lateral string movement excites the electric pickups underneath the vibrating string.[15]" (citation is here: http://www.guitarmasterworks.com/about-guitar-acoustics-101.html )

It's certainly not the case that the fundamental of a plucked steel string guitar is either missing or not perceived. For some lower notes (E, A) the fundamental can be a little quieter than the first harmonic, but the note is still perceived in its correct and actual octave, not, as the web page suggests, an octave higher. This can be trivially demonstrated with any mic and a simple FFT.

I plan to remove this section unless someone can educate me as to why I'm wrong. If the point is that the lowest strings on a steel guitar have weaker fundamentals than first harmonics, that should be stated without the distracting description of tension cycles from the string excursion or citing that web page, IMO.

Chconnor (talk) 01:53, 31 October 2019 (UTC)

Adding cited materials
I plan to add my description of the topic under the lead section and some recent data from academic papers published in 2013 and 2016 under the subcategory - Explanation. Rest assured these will be cited. Please do let me know if you think the article won't benefit from my additions. Thanks. Carino, Cz (talk) 03:46, 9 February 2024 (UTC)

Redirect page
Turned this page into the Virtual Pitch search's redirect page. Carino, Cz (talk) 22:43, 26 February 2024 (UTC)

Replaced plagiarized content
Adding instead a referenced material. Carino, Cz (talk) 04:55, 22 March 2024 (UTC)