How does phase of merging sines affect overall periodic tones?

[Crimadella]

TL;DR Summary

How does angular velocity of merging frequencies affect the overall sound of a periodic tone and to what degree?

I know this is an extremely complex matter thus I'm just keeping it very simple, as in sticking with only two to a few, known, pure sins. I'm curious as to how much, and in what ways, can merely altering the phase relationships of the 'same set of' individual merging frequencies impact the overall sound of periodic tone?

How does angular velocity of merging frequencies affect the overall sound of a periodic tone and to what degree?

I know this is an extremely complex matter thus I'm just keeping it very simple, as in sticking with only two to a few, known, pure sins. I'm curious as to how much, and in what ways, can merely altering the phase relationships of the 'same set of' individual merging frequencies impact the overall sound of periodic tone?

I would imagine you would interpert this phrasing as intended but I'm Autistic so if not I wouldn't know anyway thus for extra clarity...

Say you have 4 pure sins(not the religious kind), you alter phase relationships of selected frequencies and the resulting periodic tone was changed in what ways and to what degree then repeat with variable alterations of phase relationships only, as best as possible to explain at least.

If you know of a free tool that would allow my to explore this that would be a dream come true, at least for this curiosity.

I'm not there yet on the math so adding it would be a waste of your time, at least for the moment.

 

[Baluncore]

I'm curious as to how much, and in what ways, can merely altering the phase relationships of the 'same set of' individual merging frequencies impact the overall sound of periodic tone?

Your ear hears sound movement with hair cells arranged along the edges of the tapered cochlea in your ear. In effect, the cochlea is doing a frequency analysis of the periodic sound. For that reason, the phase of the individual components is irrelevant to what you believe you are hearing. You will be unable to identify the phase difference between two harmonically related sine waves, which will be separated by one octave or more.

 

[Crimadella]

Hmm, I'm just digging for deeper understanding and at least the appearance of contradiction, though this can merely be a failure to correctly interpert some relevant articles.

So, the phase relationships of internal frequencies of a periodic tone have little to no impact on the overall tone?

I'm going to see if I can locate the article, it suggested that phase relationships had somewhat significant impact on overall tone. Maybe that was an error in interpretation or much worse, a professional written article about physics related material that's inaccurate.

I've been reading about Fourier Theorem for a couple of days, from how I interpreted it, at least, naturally occurring periodic tones are loaded/filled with various harmonics at decreasing amplitude past the fundamental. While this doesn't really affect the question I was thinking more from the construction side of periodic tones, thus the frequencies within, and their amplitudes, are individually selected and aren't bound to any limitations outside of what's possible.

Well that's disappointing that a contradiction arose because now I have to resolve that, which means I have to go digging back through what I've read to find how the conflict arose, it seems from memory(Which I have bad ADHD so my memory is somewhat randomly inaccurate) that the author put emphasis on how impactful just the phase relationships were on the resulting tone. So, I have to find where I read this.

While I wouldn't imagine this would be too impactful being it's science but realistically our science is a body of knowledge controlled by humans thus bound to contain errors for various reasons from accidental intentional(for example I can show you articles frome medical research institutions, various independent ones via the last decade, nearly yearly, discovering that the CDC "Prescription" Opioid Crisis is a fabricated government scandal in which, on average and consistent via all years on record, Chronic Pain Patients whom are alleged to make up nearly 100% of their "Prescription Opioid Deaths" only actually make up 0.1~0.3% of the list, pretty significant scandal with very inhumane results expanding all the way out to impacting the medical care of most people due to doctors having unrealistic fears of addiction(which stable people aren't at virtually any risk for) thus stay far away from any medication that could remotely be abused thus relying on more risky, less tested and less effective medications.


Anyway, I wouldn't think it would have too much of an impact but is your knowledge coming from science of human biology? I ask because I'm coming at this from this, first of all with no official education in anything relevant and learning disabilities I have to push through, from the electrical engineering/audio signal processing side, if that matters(I can see the potential).

Anyway, I'll check back periodically as I seek that material I read, and if it does say what I remember I will present a link so you(or anyone else) can inspect it yourself, if you desire, so confusion on my part can be resolved.

Anyway, I will return.

 

[sophiecentaur]

How does angular velocity of merging frequencies affect the overall sound of a periodic tone and to what degree?

As you say, it's a very complicated business; your hearing system is very sophisticated and can drag out a lot of information about a source of sound and also your environment. Your hearing involves both frequency detection and timing difference between what the two ears receive. For continuous tones, your ear just detects the frequency and a mixture of sine waves may be perceived as just that. But it is often difficult / impossible to tell what those frequencies are, unless there is a dominant, identifiable tone with any added tones having a harmonic or near harmonic relationship. (i.e. multiples of one particular frequency) This can give 'colour' to a fundamental tone and allow us to identify a particular instrumental sound.

I've been reading about Fourier Theorem for a couple of days

You need to be careful with Fourier. People bring it into many situations where it doesn't apply. As you have read about it you will have found that a repetitive waveform can be analysed in terms of a number of harmonics. The relative phases of these harmonics can affect the shape of the waveform (on a scope) but it can be hard to distinguish between the actual sounds. (Evolution did not call for this ability so it never developed for us) If you hear a combination of 'any old' frequencies then it will sound just like a jumble (and the trace on a scope will have an ever changing pattern.
Search for spectrum of musical instruments and you will see that most instruments produce a dominant pattern with other sinusoids crawling along it, showing frequencies that are not actual harmonics.

Keep reading.

 

[Baluncore]

... is your knowledge coming from science of human biology?

Yes, from medical science, auditory research, and from signal processing.

Consider a repeating waveform from a musical instrument, or that generated by Fourier synthesis. When seen on an oscilloscope, the "shape" of that waveform, in the time domain, is highly dependent on the phase of the sinusoidal components.

Unfortunately, your ear cannot detect the phase detail of the waveform components. That is due to two reasons.

Firstly, the path taken by the sound vibration along the cochlea to the hair cells has different phase delays for different frequencies.

Secondly, the nerve bundle from the cochlea to the brain, has separate fibres from different hair cells. So high frequency sound signals travel at the centre of the bundle, with the lower frequency nerve fibres wrapped around that. Since the frequencies are separated into different nerve fibres, and delivered to different synapses in the brain, phase detection is not combinatorially simple.

 

[Crimadella]

How does that mesh with phase cancelation, where two opposite but equal signals being sent to a loud speaker results in nearly to complete silence? Which is also a technique used in signal noise reduction, to cancel out unwanted accumulated external signals after transmission.

Is it a completely different kind of "phase" when discussing acoustics compared to audible electrical signals?

Is it a different kind of phase when discussing components of musical tones compared to electrical signals?

IDK, I'm close to just giving up, this is the third time that asking a question results in answers in which I have no idea of what questions to ask to understand the answers and is in ways contradictory to what I've read and I'm more inclined to assume that's because while it may seem I understand what I'm reading it's obviously not the case.

I appreciate the attempts to help, truly. Thank you.

 

[DaveE]

Khan Academy has some good tutorials about waves and such. But...

I'm not there yet on the math so adding it would be a waste of your time, at least for the moment.

You'll need to get there to make much progress, I think.

 

[hutchphd]

You'll need to get there to make much progress, I think.

Absolutely . You need to be able to really understand and manipute Fourier synthesis to be conversant in this subject. In that sense the phase is a well defined entity and is "the same" for every circumstance. For instance an acoustic phase shift proportional to frequency will simply shift the fime of arrival of a sound but without distortion. Hence "phase linear"acoustic amplifiers are much desired and became a brand name. This same manipulation in Quantum Theory generates translation of the wavefunction in a line in space: there are only afew problems we know now to solve and when you have a hammer everything starts to look like a nail. You should learn them all

 

[sophiecentaur]

Consider a repeating waveform from a musical instrument,

'Repeating'? Probably not because musical instruments (except Hammond Organs) do not produce simple harmonic sounds. If you take a few hundred cycles of the note from a musical instrument, you will probably see a fairly stable waveform but not across adjacent sub patterns.

I'm just digging for deeper understanding and at least the appearance of contradiction,

Contradictions are not within the basic science; they occur between over simplified models and real sounds. I already warned against relying Fourier treatment of music.

 

[DaveE]

Also, recognize that from the propagation of sound into your ears (two of them), the mechanics of the inner ear and cochlea, nerve conduction, neural audio processing in your brain, and your cognitive interpretation of the result, this is an extremely difficult subject. No, you won't understand it all. No one does.

 

[Crimadella]

https://dsokolovskiy.com/blog/all/phase-cancellation-explained/

I'm not relying on Fourier, I literally just learned and read 'some' of the basics of Fourier. I'm relying on literally most of what I have read for around a year, when first learning of impeadance, everything I have read has been revolving around electrical circuits, primarily Audio circuitry, amplifiers and audio processing effects, even some Audio Mixing, where they literally all say the same thing about phase cancelation and even provide examples of it occurring in audio formats.

So, no one claiming that opposite but equal signals cancel themselves out? All Fourier did..while I learned that complex sounds are filled with individual sinusoidal summed together in a massive spectrum, where they the stated that just like phase cancelation works in electric signals, noise cancelation, etc it also applies to the individual frequencies that sum up to create a complex periodic tone. You would figure, regardless of the type out sound, that the core confirmed observation of phase cancelation would apply to any frequencies out of phase.

IDK, I'm now trying to figure out what exactly is going on here, I find it incredibly unlikely that electrical engineers use, in practice, physics that don't work. Same with composers via DAW's, they literally have to pay attention to phase of different tracks due to phase cancelation, as provided in the link above.

What is going on here? Misinterpretation between me and everyone else, that's definitely a possibility. There is no way for you to know everything I know, granted. I already know, and have for a long time, that complex sounds made by real world instruments do not 'perfectly repeat. As mentioned in the question, my focus was on a handful of frequencies. Obviously you can't just throw random frequencies together and expect that to suffice as a tone used in music, the entire point of focusing on a few frequencies was to observe of phase cancelation, alone, affects the resulting tone. You can take literally one frequencies and repeat it fast and that makes a busing sound at whatever pure frequency you chose(in the audible range)

Let's take a step back, does Phase Cancelation, something I've "known" about for over a year, doesn't exist? Because it will absolutely affect a resulting tone if it does exist because if you changed the phase of different frequencies the result would be lowering amplitude to canceling various different frequencies.

The very odd thing is I was merely looking go deeper into what they only mention in passing, how much and in what ways these phase relationships can change the resulting tone. If you wanted to do this you would most certainly not start with a tone resulting from basicly an infinite amount of summed frequencies.

Now, it was very confusing as to why people were bringing up how we hear, because the analysis in the audio world is what signals are going to be sent to the speaker, those are the phase relationships they are focusing on.

From what I can calculate from the replies is the implication that your hearing can't detect phase relationships or independent frequencies summed(a given, that's the purpose of Fourier, Scaligrams, etc, because of course you can't hear the individual millions of frequencies out of a summed tone, techniques were created to explore the structure of these sounds literally to find what frequencies and at what amplitudes go into making up that sound), thus when you send to equal but opposite phase signals while the speaker only produces silence, somehow the human ear can't detect phase relationships so you'll still hear sound.

 

[pbuk]

That's a very long post, so to sum up:

Misinterpretation between me and everyone else, that's definitely a possibility.

Yes that is what is going on here.

Let's take a step back, does Phase Cancelation, something I've "known" about for over a year, doesn't exist?

Nobody is saying that: obviously phase cancellation does exist.

Because it will absolutely affect a resulting tone if it does exist because if you changed the phase of different frequencies the result would be lowering amplitude to canceling various different frequencies.

No, phase cancellation only applies to the interaction between sources of the SAME frequency (or more generally, the same waveform). It says nothing about mixing sources of different frequencies.

From what I can calculate from the replies is the implication that your hearing can't detect phase relationships or independent frequencies summed

Correct.

But when two sources of the same frequency are summed something different happens, which does depend on their phase. You have already learned about this and seem to understand it, but what you need to understand is that it does not apply when combining different frequencies.

 

[hutchphd]

when you send to equal but opposite phase signals while the speaker only produces silence, somehow the human ear can't detect phase relationships so you'll still hear sound.

What is the sound of one hand clapping ?​

You need to ask the Zen forum. Here folks do math.
The concept of "phase" refers to each harmonic componenti ndividually. Unless and until you understand the math of Fourier analysis, youe will be confused. and stay confused. What you are saying is simply that (x-x)=0. That does not require discussions of "phase"

IDK, I'm now trying to figure out what exactly is going on here

Then you need to actually understand the math. There is no Royal road.
Many of the "explanations" online in this area are written by people who also do not understand. Therefore your confusion is to be expected! Enlightenment (IMHO) is always preceded by confusion and hard work.

 

[pbuk]

I'm going to see if I can locate the article, it suggested that phase relationships had somewhat significant impact on overall tone. Maybe that was an error in interpretation...

Yes, that was almost certainly the case.

or much worse, a professional written article about physics related material that's inaccurate.

That is unlikely, but even if that were the case how does that help you?

Well that's disappointing that a contradiction arose because now I have to resolve that, which means I have to go digging back through what I've read to find how the conflict arose... I have to find where I read this.

Why? People misunderstand things all the time - I do, you do, everyone does, it is part of learning.

Now you have learned what is correct, forget about it and move on.

 

[Averagesupernova]

This doesn't need to go very deep to explain that the phase relationship between two signals of different frequencies will never cause cancellation no matter how hard you try.
-
Here's a little advice for you: When something does not make sense to you and contradicts mainstream accepted science take a step back and ask yourself what you are doing wrong or how you are misapplying what you know or think you know. This applies to more than just signals and systems. ;)

 

[Crimadella]

Here's a little advice for you: When something does not make sense to you and contradicts mainstream accepted science take a step back and ask yourself what you are doing wrong or how you are misapplying what you know or think you know. This applies to more than just signals and systems. ;)

I completely agree, it this applies well beyond science. It's something I do.

Different frequencies do not cancel eachother, I was curious about that, thanks for clarifying. Do complex sounds not contain multiples of any frequencies?

 

[Averagesupernova]

I completely agree, it this applies well beyond science. It's something I do.

Different frequencies do not cancel eachother, I was curious about that, thanks for clarifying. Do complex sounds not contain multiples of any frequencies?

Of course complex sounds contain multiples. What's the point?

 

[berkeman]

Thread closed temporarily for Moderation...

 

[berkeman]

After several off-topic posts by the OP in this thread have been edited/deleted, this thread will remain closed. The OP seems less interested in the main question they asked to start the thread, and more interested in veering into off-topic subjects that are not appropriate for PF.

Thanks to all who tried to help the OP with their original technical question.