Perception of audio harmonics - finding possible deeper meanings?

[Psalehesost]

It remains to see whether this will be meaningful - it depends on the possible answer. Feel free to join in with any thoughts.

I've experimented with audio processing - and thought about how added harmonics are perceived. What I wonder is whether, like other modes of our experience, audio harmonics could be related - by analogy - to deeper things. Gurdjieff relates musical notes to worlds (densities) and various processes; and the Ra material relates the seven colors and the color spectrum to energy gradations in several contexts.

Harmonics are multiples of the base/fundamental frequency - the number of the harmonic is the number of the multiple of frequency. (so the 1st is the base frequency, the 2nd double that, and every time it is doubled a new octave is entered)

I'll put in some quotes and notes regarding the perception of different harmonics:

The primary color characteristic of an instrument is determined by the strength of the first few harmonics. Each of the lower harmonics produces its own characteristic effect when it is dominant or it can modify the effect of another dominant harmonic if it is prominent. In the simplest classification, the lower harmonics are divided into two tonal groups. The odd harmonics (third and fifth) produce a "stopped" or "covered" sound. The even harmonics (second, fourth, and sixth) produce "choral" or "singing" sounds.

The first six harmonics are the significant ones in terms of "color" - beginning with the seventh, harmonics add "edge", perceived "loudness", and if added to (ie. it is distorted) a complete musical signal, it is "harsh".

Musically the second is an octave above the fundamental and is almost inaudible; yet it adds body to the sound, making it fuller. The third [...] produces a sound many musicians refer to as "blanketed." Instead of making the tone fuller, a strong third actually makes the tone softer. Adding a fifth to a strong third gives the sound a metallic quality [...]. A strong second with a strong third tends to open the "covered" effect. Adding the fourth and the fifth to this changes the sound to an "open
horn" like character.

Added to a musical signal (distortion), the second also makes the sound "warmer"; the third makes it "brighter" - though at a cost. The sixth wasn't mentioned in detail - added to a signal, it can give a brighter, "airier" quality.

Adding the even harmonics to a signal means making the waveform more asymmetric - it is asymmetric waveform distortion - the odd alone affect waveforms symmetrically. (and the symmetric odds when added are generally unpleasant, while the asymmetric evens can be pleasant. context - the sounds involved, the frequencies in the waveform distorted - is always important - too much evens, particularly including a strong fourth harmonic, can make the sound so "rich" and "fat" that it sounds muddy)


The sound of adding harmonics to a signal can in some ways "feel" as if the "substance" of the sound changes. (maybe I'm semi-synaesthetic in this way - though the words musicians use to describe sounds suggest to me that it is more universal) So that adding odd harmonics can make the sound feel "contracted", somewhat "plastic" and "metallic" with a sharp "brightness" on top - while adding even harmonics can make the sound feel "expanded", with a somewhat "wood-like" quality, and as if there are several "layers" of substances spread out within the same "space" at once.

Interesting in this regard is modern music recordings, given the loudness war in which signals are literally smashed, meaning bursts of noise are hidden all over the tracks, extra odd harmonics kicking in at every sound level peak. Most people don't notice, but many older (ear-trained) musicians have written that it sounds like [insert word for excrement here] - side effects of this sound processing include listening fatigue (ear and brain get tired). (in addition, there's the squashing of the dynamic range with its overcompression, causing rapid, unnatural sound level variations, and a "mushiness" - and causing the brain to interpret the sound as still "louder" and more "intense" because of the way it works - and if I listen to such at any length my brain in fact turns mushy!)


While this knowledge can be used in a creative (as well as an entropic) way in sound processing, I wonder if there's a deeper significance to how the harmonics are perceived and what they "convey" to the listener. As mentioned at the beginning, whether there's a way to relate them in some way to higher or more abstract concepts.


As an aside, if someone is curious about how harmonics "look" in relation to waveforms, you can open up a 2D graph application and play with polynomials of sin(x) - the power will give the order of the harmonic, and you can see how they combine.

 

[Risen]

I feel really stupid right now :(
Would you possibly be willing to provide a kind of diagram to help explain? I think you are on to something important but to be honest I am having trouble processing the information. MMM maybe some music samples with examples pointed out? Then again this may just be something way over my head. Maybe I will understand better after reading responses. I am very interested in this topic. Thanks for posting it.

 

[Buddy]

opossum, this may or may not be helpful to start:

Harmonics may be achieved in anything that can be fit to a wave, but most often the term is used to describe their use in music. In music, harmonics refer to the sounds which are produced at multiples of the same frequency as a base sound. This base sound is often referred to as the fundamental, or first harmonic.

An example may help demonstrate this more clearly: if the note being produced is A4, for example, it resonates at 440 Hz/second. At the second multiple of this fundamental, or 880 Hz/second, we find the second harmonic. At the third multiple of this fundamental, or 1320 Hz/second, we find the third harmonic. At the fourth multiple of this fundamental, or 1760 Hz/second, we find the fourth harmonic. This continues on well past the sound being audible to the human ear.

Musically, rather than talking about the actual frequencies of the harmonics, we would instead talk about their relationship to the fundamental in musical terms. So we can look at the second harmonic as being an octave above the fundamental. The third harmonic is then an octave and a fifth above the fundamental. The fourth harmonic is two octaves above the fundamental. And so on, with the harmonics alternating between being a major third and a minor third higher each time we go up.
_http://www.wisegeek.com/what-are-harmonics.htm

If I'm understanding correctly, essentially, the question seeks to start with the known in music theory regarding harmonics and draw one-to-one relationships to any existing cognitive counterparts comparable to the way these same musical harmonics relate to the color spectrum.

 

[Risen]

Thanks Bud, I am starting to understand a little better now. It will take time to digest. You are a very kind and considerate person. Thank you for your patience.

 

[monotonic]

I deal with this sort of idea constantly since my hobby is audio design. One thing about amplifier design is that, according to designers such a Jean Hiraga, the greatest correlation between measured specifications and good sound is a monotonically decreasing harmonic profile. This means, that when an amp DOES distort something, the distortion should take the form of harmonics, each decreasing with frequency. Amps with this characteristic are said to sound "musical".

A monotonic spectrum is easy to demonstrate. Silicon diodes and bipolar transistors both exhibit an exponential error curve. This essentially means the output is 2^X, where X is the input signal. Another interesting aspect of these devices is distortion scalability. These devices need a "bias" to "open them up" before they are useful. The input signal must modulate within this bias, and if the signal gets too strong, it will be stronger than the bias and cause clipping or severe distortion. For diodes and bipolar transistors, if you change the bias, and make sure the input signal is in proportion to that bias, the distortion amount and harmonic profile will remain the same. So if you bias a bipolar at 1V, with a .001V input signal, it will have the same distortion as the same transistor run at 2V with an input signal of .002V. Very low total distortion is achieved by running transistors at a bias which is very high in proportion to the input signal.

Other types of transistors and diodes, such as FETs and schottkeys, do not exhibit this scalability, because they exhibit square-law behavior. I am not as familiar with the math of these, but they will always produce less distortion if run at a higher bias, regardless of any proportionality to input signal.

The importance of this difference for this discussion is that bipolars and FETs distort the sound in different ways, because each effectively applies a different mathematical transform to the sound. Because bipolars are scalable, they don't seem to have prominent "sweet spots". FETs on the other hand are not scalable, and tend to sound best when biased at certain levels. While both exhibit a monotonically decreasing harmonic profile, the relation of individual harmonics to each other and their interaction with the signal is different. Hence, they each affect the character of the sound in a different way. In the DIY audio community, everyone has their preferences. Which circuits and components sound best is a very subjective/controversial issue, sometimes leading to fights. It is a VERY confused scene.

I don't have much if any insight here, but will answer questions. As I said, this is a controversial issue, people's perceptions are variable and one's preferences seem to hinge largely on one's personal philosophy/beliefs. As such I don't know how useful this could be until one has gone through a large part of the Work.

Also, plucked string instruments tend to have a monotonically decreasing harmonic profile, since they exhibit polynomial vibration modes (don't know math, but I think that's correct). Again this may regard "musicality".

 

[Turgon]

I feel really stupid right now :(
Would you possibly be willing to provide a kind of diagram to help explain? I think you are on to something important but to be honest I am having trouble processing the information. MMM maybe some music samples with examples pointed out? Then again this may just be something way over my head. Maybe I will understand better after reading responses. I am very interested in this topic. Thanks for posting it.

Hey opposum,

Here's a youtube video that discusses a bit about guitar harmonics (a good medium that a lot of people can relate to) which he explains up to the 4th harmonic on a whiteboard and gives examples on the guitar.

http://www.youtube.com/watch?v=5j2AxGGmT-g&feature=relmfu

Edit - Note, I'd listen to the guitar parts on headphones, but turn the volume down! Since harmonics can hit really high Hz/frequencies (think opera singer breaking glass), it can hurt your ears.

Interesting in this regard is modern music recordings, given the loudness war in which signals are literally smashed, meaning bursts of noise are hidden all over the tracks, extra odd harmonics kicking in at every sound level peak. Most people don't notice, but many older (ear-trained) musicians have written that it sounds like [insert word for excrement here] - side effects of this sound processing include listening fatigue (ear and brain get tired). (in addition, there's the squashing of the dynamic range with its overcompression, causing rapid, unnatural sound level variations, and a "mushiness" - and causing the brain to interpret the sound as still "louder" and more "intense" because of the way it works - and if I listen to such at any length my brain in fact turns mushy!)

 

[monotonic]

There are many factors that contribute to the listening experience aside from harmonic distortion. I've heard that tests have shown that people generally cannot perceive harmonic distortion at levels below .4%; most modern devices have distortion below .01%. My experience is that time-related distortions such as phase shift and rising distortion with frequency, have a much larger impact on the listenability of amplifiers. If you are able to manage these issues, you can move on to worrying about harmonic distortion.

It is not as easy as pointing a finger at any single cause for ear fatigue, headaches, and general bad sound. At least as long as you're not overdriving your equipment or using sound compression. There are many factors which affect listenability. Playing with amplifiers of my own design has given me a unique view of all the things that can go wrong on the analog end of the signal chain. In short, extreme gains can be had from paying attention to detail. If you really want a good system, without paying huge amounts of money, you have to build it yourself. There is a very large DIY Audio community.

 

[Psalehesost]

I feel really stupid right now :(
Would you possibly be willing to provide a kind of diagram to help explain?

Poor external considering - didn't think enough of explaining the basic concepts I have come to take for granted.

In addition to what Bud posted, the Wikipedia article ( _http://en.wikipedia.org/wiki/Harmonic ) has more info and a graph, though the graph is not of waveforms but of vibrating strings - though the concept is the same (you can count them from one to seven as each of the seven in the picture shows the next harmonic).

(note: Turgon made his contribution after the above was written - the above is kept as it may still be useful)

I think you are on to something important but to be honest I am having trouble processing the information.

Then, hard to say yet if I am on to something. But maybe we'll find out.

MMM maybe some music samples with examples pointed out?

That's a bit harder - I haven't made any, but the time could be taken to change that (coding something simple up, taking a short part of a suitable music track and creating versions with different harmonics added). Though I think it's a good idea to look at the concept and discuss a bit first to see if it that would be likely to be worthwhile.

If I'm understanding correctly, essentially, the question seeks to start with the known in music theory regarding harmonics and draw one-to-one relationships to any existing cognitive counterparts comparable to the way these same musical harmonics relate to the color spectrum.

That gets close to my thought, apart from not having directly related harmonics to the color spectrum. Musical notes could easily be related to the latter, the example of Newton having done so being mentioned in this article: ( _http://en.wikipedia.org/wiki/Visible_spectrum ). Fittingly in that case, the visible spectrum covers very nearly an octave of frequencies.

This would not be as straightforward with harmonics - maybe you could map those first significant harmonics, but in terms of frequency I think it would appear quite artificial however done, because the second harmonic is already an octave above the first, the fourth two octaves, and the sixth is 2.5 octaves above the first. (for each succeeding octave reached as you count harmonics, you have twice as many until you reach the next)

If it can be done, it would have to be based on something other than frequency - cognitive experience could come into play in that case. If this succeeded (and was based on something truly objective), then already you would have analogy between harmonics and metaphysical concepts, through extension from analogies between colors and metaphysical concepts.

But I suspect (speculate) that if harmonics can be related to something deeper, it is not exactly parallel with the relating of musical notes and colors to other things (notes and colors more or less interchangeable for this), that instead harmonics would be related to different things and/or in different ways. (ie. not to an octave of something)

If octaves are still part of the context, the most "natural" (straightforward) would be to make analogies with something that extends beyond several octaves and has twice as many points of interest within each new octave.

 

[HiThere]

Thank you for an interesting thread - in my experience sounds (music and nature and other sounds) can lead to insights and peace of mind.
When I play guitar I tend to use an old '71 amp that is highly unpredictable and prone to shut itself down without warning, but it sounds so sweet that I never have found another amp quite like it.
Its potmeters are wildly unlinear in their function, with ugly harmonics interspersed with "sweet spots". I've always found it fascinating that this amp sounds more genuine to me than newer amps, and I've never heard a transistor amp that sounds like this. It can make almost any preamp distortion sound come to life, and I can take a transistor created sound and feed it through this old amp and get a usable sound. Fascinating and fun! Well, enough rambling for now I guess. :)

 

[Al Today]

Hi Psalehesost, very interesting. :)

When I think of all the various session references to what sound may do, as well as scientific data available to sound (like the cool things it does to water), I have no doubt that sound can affect us in ways we have yet to discovered. But... What are you going to do if you discover that "brown" note?

_http://www.ask.com/wiki/Brown_note : And other interesting references.
Forgive me, i couldn't stop myself...

 

[Risen]

Hi Psalehesost, very interesting. :)

When I think of all the various session references to what sound may do, as well as scientific data available to sound (like the cool things it does to water), I have no doubt that sound can affect us in ways we have yet to discovered. But... What are you going to do if you discover that "brown" note?

_http://www.ask.com/wiki/Brown_note : And other interesting references.
Forgive me, i couldn't stop myself...

Al, you are so funny!, A possible cure for constipation?

I will be studying the links provided and try to keep my mouth shut until I have more to offer.

 

[dant]

As for Audio/Math/Physics, take a look @
_http://www.falstad.com/mathphysics.html

There are some interesting things that can generate
audio and in different conditions. Many of these java
apps support visuals & sound and allows for experimentation
given options. This site is pretty cool, if you ask me!

 

[Crystla24]

Well I hadn't intended to comment on this but I happened to be reading through some other threads and ended up following a link over to the lawofone website with the Ra material (it's so easy to get off on all kinds of interesting stuff around here). I ended up clicking on the General Tarot section just out of my own interest- _http://www.lawofone.info/results.php?category=Tarot&subcategory=General anyway, this just led to a whole new study of interest (the tarot). This link could also interest someone studying the correlations between numbers which i seen in another What's on your mind thread. But it talks about the links to Mind, Body, and Spirit through the sub-concious and keeps referring to the tarot as a melody, and having octaves that reach to each of these...then research the word Leitmotif and alot of interesting stuff comes up. I even seen a link of someone talking about the leitmotif being used in the Bible? Lol, looks like this could lead to a lifetime of study :) just thought I would share what I stumbled upon ;D