I recently had a discussion with a friend via email about this:

http://upload.wikimedia.org/wikipedia/commons/f/fb/Scriabin-Circle.svg

For those who don't know, Scriabin was a contemporary classical composer who claimed to have synesthsia. He apparently either saw colors while playing music or just had a really strong association with them.

There used to be an enormous wall of text here, but I figured it'd be more polite to organize everything into a much easier to read .pdf:

https://dl.dropboxusercontent.com/u/3154503/thoughts.pdf

Just wanted to share my thoughts with anyone who might be interested.

Interesting text indeed, Gyms :) I've always thought this myself, that different key sigs can be linked to different characteristics, though not necessarily literal colours. I've never really done any extended reading into it, though (I probably will at some point).

A fun thing I do after I finish writing music (tracked music that is) is to transpose it up or down a semitone; I find the character of the piece often changes to become "brighter" or "darker." In a lot of cases, I actually prefer the sound of the key i've transposed into.

I'm sure this kind of thing varies from person to person. I often find Ab Major (and F minor) to be a pretty bright/uplifting key signature (this is probably why a lot of the time I write music in Ab Major ;P ). F major and Bb Major are also pretty "bright" to me, though F major sounds "perkier." On the contrary, D major to me has always sounded "dark" ie. less happy. Interestingly, D and Ab are on opposite ends of the circle-of-fifth's.. er.. circle, so in my case this sorta makes sense? I don't see colours when I hear these key signatures; I'm just talking about the general impression I get from them.

I've had discussions where the concept of synesthesia has been mentioned. It's great to read a little more about it though, and hear someone else's opinions. To me, it's also been a question-mark of a concept. Also, I've always wondered what people can see when they hear non-tonal pieces of music, or pieces of music where the tonality is more vague/gets disguised (ie. through whole-tone scales, modes, lack of resolutions etc).

It seems to me what ultimately determines the relative brightness or darkness of a key is where the melody ranges and arrangement naturally fall while instinctively searching for the spectral balance within our work. I think anyone naturally tries to balance their melodies with their arrangement and working within different keys does have an effect on how generally high or low that balance sits.

Like transposing things in trackers a semitone or two gives you an immediate appreciation of what your piece sounds like a bit brighter or a bit darker, but going any further than a whole tone usually throws the established balance off.

And I think this may be demonstrating what Scriabin was alluding to, that working within certain keys will naturally give you a certain 'color'. And 'color' is a good concept to correlate with keys because both colors and keys can be respectively compared by how relatively bright they are and how similar they are with each other. Red>Orange>Yellow are similar colors in the same way C>G>D are similar keys.

oh yea, FoD I think the perception of Ab and D being opposites might have something to do with them being a tritone apart. Tritone modulations are fun, it's like making a transition from day to night or something.

For historical perceptions of a key's character, temperament plays a big role too. True equal temperament wasn't really attained until the late 19th century (i.e. Helmholtz). Prior to this any consistent tuning method necessarily left differences between the keys. Some will have a more solid, just major third, some will have a noticably detuned fifth, etc. In any uneven system of tuning the keys do have an individual character, and it could be identified on hearing by someone sufficiently familiar with them.

Aside from the theoretical and practical issue of tunning a true equal temperament, which Scriabin probably never experienced anyway, any particular tuning on a particular instrument has its own discrepancies from the model tuning, and of course they go out of tune as they're played. So, any particular person's favourite instrument may very well have its own set of key-feels.

Bach's Well Tempered Clavier was written for a very specific and newly developed form of keyboard tuning which was not equal temperament. It tours all the keys, major and minor, exposing their differences. It is rarely performed this way now.


Tuning is probably not even the biggest factor, though. It's just one I think it interesting. The thing about temperaments and key-feel is that ideally to compare them you need a homogenous instrument. The harpsichord is more homogeneous than most, the piano less so but still up there. Most instruments are not, however. The sound of an open C on a viola/cello vs. notes that have to be fingered was probably a big factor in Beethoven's obsession with C minor. A horn has pitches along its harmonic series, and pitches that are deviations from it, and any horn player can tell you which is which by sound. Even a modern piano has a split from 3-stringed to fatter 2-stringed keys, and very fat 1-stringed keys in the lowest part of the range.


When I was younger I used to think particular keys had particular feels, but eventually this was broken for me by being able to play with tuning and temperament in an idealized (i.e. synthesized / etc.) setting. I used to listen to a lot of albums on a walkman, which would lower its pitch slightly as the battery decayed. I have absolute pitch, so I tend to remember the exact pitch I listened to things at, and I'd be surprised that on changing batteries, after the initial contrast of bumping up a semitone wore off, the music had the exact same "feel" to me.

So, at this point I think temperaments can have particular feelings (though most musicians don't work with tuning this way, so it's a fairly marginalized way of doing it), and keys can have particular feelings that are bound to their specific instrument (or combination thereof), but I do not believe that in the ideal sense, any particular absolute pitch/key has an inherent feel at all that is different from the others.

Also, I always thought it was bizarre how much space Scriabin gives to blue/purple.

428Thz may not alway be perceived as Red to someone who is red-green colorblind :D

Also, when you say "...why he perceives A Maj to be red", I don't think you quite grasp what a synesthete experiences. We don't consciously choose what color something is any more than an image of the number 4 pops into your head when you read "f o u r" (neat tidbit about numbers existing in our brain's wordspace https://www.youtube.com/watch?v=n3x8fIdsla4 )
I think it's as much bullshit to say that Rachiminoff gravitated towards a golden D as it is to claim there is a right and wrong art. I wholly believe it's subjective. The fact that his colorwheel is so organized can be explained by either one of two things: either he forced himself/lied about what he perceives such that everythin looks neat and organized, or he was blessed to have such a color/key set.

The are no absolutes in synaesthesia. There are certainly popular trends, but each person will perceive different things and I think any trends are purely coincidence.

FWIW, my color/keys for violin temperament, in order from most saturated to more gray)
DMaj Green
FMaj Red (favorite)
EMaj White
CMaj Blue
GMaj Green or Brown
AMaj Yellow or Red
EbMaj Gray
Others aren't so strong and are a bit ambiguous, I' ve a feeling that this is limited because my eyes themselves have a smaller colorspace than is normal.

I kinda doubt that Scriabin was colourblind, given how important colour was to him and how he described it, but running with this idea, here's an image of what that colour wheel would look like with severe protanopia, deuteranopia, or the rarer tritanopia:

https://dl.dropboxusercontent.com/u/883356/scriabin_colorblind_p_d_t.jpg

I like how the first two circles are the same.

I don't think he's colorblind either :\ Nor do I think his passion for it disproves that possibility. You don't have to perceive the world the same way everyone else does in order to be passionate about it.

I'm now caught up thinking about color as musical art, and how it's possible for our musical tastes to evolves through an acquired taste. And if such is also possible for colorchoice tastes, in that you can slowly change these colors to match something organized without having to lie about it.

Going with the idea:
Could a person be blind/deaf to a certain scale as if he or she had colorblindness? Is there a related hearing impairment?

Tone deafness would be the aural equivlent of total colorblindess, but I don't think there's any analogy for some like the more common color-deficiency (correct term)

No I mean he literally describes red and green and blue and their vivid differences in his writings. This is not something a colourblind person would do. It would be extremely unusual for the distinction between red and green to become very important to someone who could not distinguish between them.

Protanopia and deuteranopia are both deficiencies which involve the confusion of red and green, which is why the two images look similar (but they are not really the same). One is a deficiency of red, and the other is a deficiency of green. The third one is a deficiency of blue. The colours are not representative of what a colourblind person would see, but they are representative of what a colourblind person can distinguish, i.e. this image and the original image would look the same under this kind of colourblindness.

I gotta see these specific writings to really know what you're saying.
Judging from wiki, those -opias aren't only a deficiency but a total lack of the needed receptor. Someone with a deficiency should be able to distinguish _some_ of the time, depending on exact hue and saturation.
I keep trying to defend the point of "If color deficient, then no art" is false, but I'm having trouble with the math logic where the statement "if art, then not color deficient" explicitly implies that. Should've stayed in school

I'm not talking about art. I saying that his writings clearly demonstrate that he can distinguish red from green, ergo he is EXTREMELY UNLIKELY to be colourblind.

kfaraday, would you say that your synesthetic response for black keys correlate with any kind of emotional response you have? Does a dark blue key feel generally more darker and moody when transposed from a key that isn't dark synesthetically?

i feel so dum

also, @rainwarrior and xyz

I think we'd need to establish what the notes actually represent on the wheel, probably saying they represent keys is just one aspect of it. To me, they seem to overall represent tonal centers, which could refer to chords, notes and keys.

And more than associating with colors/emotions/moods/etc, notice how the gradient of change is focused around the circle of fifths. It's pointing out how fifth relationships correspond with how similar the tonal centers are to one another. He's using color to describe this relationship, but I think the real meaning behind the color is to call attention to these relationships.

And from this angle, I'd completely agree with such a suggestion. It's quite easy to put to the test and hard to argue against. Just play around with a chord progression, stringing together C, G and D chords of any quality sound quite similar and close to one another because the tonal centers are merely fifths apart.

The history of music itself a proven statement that tonal centers flow to and from the neighboring fifth tones. Since the emotional effects of music seem to rely on how we as humans compare the feeling of things over time and how the relate, it's easy to see that a tone coming 6 tones down/up the chain of fifth off of a given tonal center(C > F# for example) is very far from being related. And you can easily test this out, play a C chord followed by an F# chord of any quality and find a corresponding melody to glide over the progression. Now compare this same process with C to G, C to F or even C tp A.

And go up another fifth from F# and you get C#. Progressing C to C# has a similar effect like F#, despite C# only being a semitone away. It all come to fifth relationships. These emotional effects exist on a kind of "micro" level with chord progression and a sort of "macro" level via key modulations.

More than looking at it from a synesthetic's vision, I think the wheel is describing this idea. What do you think?

I...think you're just talking about the modulation chapter in any theory book. http://en.wikipedia.org/wiki/Closely_related_key

Also "C>F#" http://en.wikipedia.org/wiki/Petrushka_chord :D:D:D

Well, unlike traditional music theory, I'm not talking roman numerals or common tones or voice leading or parallel keys or relative major/minor. I think all these things are quite nice for analysis, but as far as opening yourself up and being creative they're just a hindrance.

I'm suggesting that there's something quite simple going underneath what theory tries so hard to analyze.

edit:

Like looking at a good old Dm > G7 > Cmaj7. Sure you could analyze this as ii V I of any degree. You could take a look at how it would be voiced and arranged and call this bit voice leading and that bit passing tones. You could call this a secondary dominant progression. But what does any of this mean? It's completely useless outside of analysis.

It seems to me that perhaps developing a personal relationship with the ebb and flow of tonal centers, and recognizing that fifths are what ties them together by nature, might be the underlying structure of musical freedom or something. And perhaps this is what Scriabin's wheel is actually describing descriabin(loool). Perhaps this is what all the similarities between musical synesthetic experiences mean.

Humans love dat 2:3 ratio
Maybe you and I just hear and experience harmony differently :|
I don't think there's anything mystic about music, it's all just applied math. As for WHY humans find such and such number pleasing and other not, that is indeed mysterious.
Are you saying that the wheel describes quite easily what you'd have to learn in 3 years of theory? Or am I missing the point still?

I doubt we experience harmony very differently, but surely try to understand using our own devices.

Are you familiar with the harmonic series and why it's musically significant?

Yes, the harmonic series is just barrrrrrrrrrrely divergent :P

Like the multiplier of an FM synth, most intervals are aesthetically pleasing, but going with rigorous Pythagorean tuning can sometimes sound a bit ugly, hence the 4th finger slide valve on trumpets/cornets.

I'm talking about how the first two overtones of ANY naturally pitched sound are a perfect octave followed by a perfect fifth. I've said "by nature" a lot in my responses and this is what I'm referring to.

This part of nature suggests an explanation toward why cadences, the staple of western harmony, have function the way they do.

Honestly, I don't find much use for any attribution of character to any absolute pitch, unless it's in reference to a specific instrument (like the open strings on a violin). In an electronic music context I think this rarely has any meaning.

If you want to talk about the colour wheel having meaning in terms of relationships... well, I'm not sure how that's useful either. It's just the standard circle of hue mapped on the standard circle of fifths. We already know the circle of fifths- putting colours on them adds nothing new. Colours have fairly arbitrary meanings themselves.

The strange distribution that spreads out the purple side of the spectrum is a little weird. I'm not sure what justification Scriabin would have had for that. Does he think that E-flat to A-flat has less contrast than E-natural to A-natural? I certainly don't buy that idea, categorically.

Synaesthesia is kind of interesting as a phenomenon. I know two people who have told me they have a limited version of absolute pitch that manifests itself synaesthetically. One of them could see the colours red or grey, but only on specific pitches. The other described a few pitches as having a particular texture, like she was touching them. This things tend to be pretty personal and arbitrary, I think. I have absolute pitch, myself, but I'm more or less completely free of synaesthetic relationships with it. I am happy to imagine extramusical relationships while listening to or working with music, but these are actively pursued, not some automatic response from my brain.

I find it interesting that Scriabin had this particular set of associations, but I don't find it useful or applicable to my own work in music. It's just some weird fact about how his brain worked.

Damn, that is hella micro hahahaha

It seems redundant if you get mathematical with it, "the second and third terms of: 1x, 2x, 3x ,4x etc... have a relationship of 2:3 and western music likes that, a lot"
[edit:]Rain hits the nail on the head.

Though the fact that there are trends in these arbitrary perceptions does hint at there being a GrandTruth to it, though I don't buy it.

@xyz, the idea is that a resonating "C" naturally contains within its timbre another "C" an octave higher, followed by a "G". This sort of demonstrates that G "belongs" to C and suggest why G resolves to C within music.

There are instruments with strange harmonics too. On the piano it gets a bit warped due to stiffness of the strings being frequency-dependent, so overtones get increasingly sharp at higher frequencies. A lot of metal percussion instruments (e.g. bells or cymbals) have very strange harmonic components that are very unlike the overtone series.

b.t.w. "Pythagorean" tuning is a tuning system using only just 5ths (3:2), and intervals related to it by the octave. The overtone series contains many more relationships than that, so it's not really correct to refer to the trumpet intonation problem as a "pythagorean" thing- it is related to pythagorean tuning for overtones that can be generated by the 3:2 and 2:1 intervals (e.g. overtones 1, 2, 3, 4, 6, 8, 9, 12, 16...) but this description is ignoring the ones that can't (5, 7, 10, 11, 13, 14, 15...). Since tertiary harmony is a fundamental component of western harmony, and also significantly out of tune in equal temperament, we must not exclude them by calling it a problem with "pythagorean" tuning. This is a problem of the overtone series, or of just intonation, or of equal temperament (if you want to shift the blame to the other side). Correcting major/minor thirds is a very important skill if you play a brass instrument.

Also, the character attributed to various keys is a topic has been written about throughout history, and you can find many, many historical lists of what associations belong with which keys. (It seems almost every music theorist made such a list.) There are always differences, but contemporaries tend to agree with each other, and across longer spans of time the differences are much greater.

Back when I was in school, we went over a long list of these, and there was a rather funny point in history where the character of F major seems to take a sudden change in everybody's opinion. Before Beethoven's 6th, nobody ever referred to it as pastoral, but after it, absolutely everybody did for a long while. This kinda highlights how these associations can be arbitrarily imposed.

rainwarrior, so what's your opinion on this suggestion that the third overtone in the series acts as sort of model, demonstrating the relationship of fifths and explaining why any given tone has the potential of "wanting" to resolve a fifth downward?

as for tuned bells, i searched around and found a decent resource on the topic: http://carillontech.org/timbre.html

the tried and true series is still present, it just seems to be a bit obscured by the material and shape of the thing. there is still an octave>perfect fifth above the fundamental. in this case, their measurements show a nonharmonic tone creeping in between the second and third overtones, which is quite interesting. but it's an exceptional case and i'd argue that the harmonic series is still present here, if just a bit disturbed.

and do you have any resources at hand that address this sharpening of overtones you mentioned? i imagine it would be the same case as the bells.

I don't think the chord motion in 5ths that is common in western music practice is derived from the overtone series. Not directly. The overtone series itself is just a consequence of physical resonances favouring simple ratios. (Or in the case of a bell, it's the result of trial and error, engineering the shape of the bell to reach more "natural" sounding resonances- poorly built bells are much less harmonic than the one considered in that article.)

Consonance is the result of simple integer (just) relationships between pitches. The simplest intervals are the unison, octave, perfect twelfth, fifth, fourth, major third, minor third, in order of increasing complexity. This in itself is the basis of major and minor chords, why they are consonant, and why we other arbitrary types of chords were less likely to appear in practice (until we went looking for them). The septimal minor seventh (i.e. just dominant seventh) also appears later, though it is usually very out of tune in modern practice. Consonance can be attained with pure sine waves too: the overtone series is not required, though it strengthens its effect greatly.

The V-I cadence is the result of the combination of tertian harmony (major/minor chords) with counterpoint. The ti-do leading tone component of this cadence appeared very early, but the so-do bass motion did not. Listen to Machaut or Dufay maybe for examples where you can hear the leading tone motion in cadences, but the preferred bass is very different-- the leading tone might make it feel like a "prototype" for the V-I to modern ears.

Well, I'm not suggesting that root motion in 5ths was directly derived from the overtone series. Like you pointed out, it was this gradual discovery over time as people's ears continued to adapt to new ideas of consonance.

But what I'm suggesting is that perhaps the overtone series might actually explain why it works. Like, besides saying, "so-do just sounds like a good resolution", there really is no way to explain why we hear it this way. You could probably chalk it up to it just being our modern ears, but do you think that so-do being such a strong resolution and the perfect twelfth being the most simple interval besides the octave are just arbitrary coincidences?

Thanks for the great responses btw, you're giving me a lot to think about.

I just think of V-I as a stylistic thing that started to become popular in the Renaissance, then institutionalized in the Baroque. In Romantic music it gets very interesting, as now V-I is so thoroughly known and anticipated that much of the expression in Romantic harmony is ways of drawing out and delaying the V-I that the listener is intended to be waiting for. (Read more about this in: Charles Rosen's The Classical Style.)

We're still living in that culture, though it's been transformed a lot since then. I really do think that V-I is primarily a cultural device. I've thought about overtones in relationship to it, but I've so far failed to put that thought to any use (e.g. why doesn't a chord motion of a major third 5:4 seem any "stronger" than a major second 9:8?).

The utility of the V-I comes, I think, from counterpoint and the familiarity of the diatonic scale. I can't bring myself to see it as "natural", when there's hundreds of years of prior music that don't embrace it at all. The transition to it is a bit gradual. It arises naturally from a collection of principles (tertian harmony, diatonic scale, etc.) but it's not universal-- it's a product that belongs distinctly to western musical culture, from about ~1500 AD.

There are also very interesting alternatives. For example, you can adopt tertian harmony, but discard the diatonic scale and emphasize parsimonious voice leading, and naturally end up with harmony like Alan Hovhaness: http://www.youtube.com/watch?v=vlXBmIjjzAc#t=1m41s

Also, nobody moves the bass in perfect 12ths, ever*. Consider that. ;)

Perfect 12th bass motion sounds like a compo idea :D

youve managed to get pretty academic here haha


speaking as someone who isnt a synthesisethesaesthetistete and doesn't have absolute pitch, i just wanna say that i know what you mean about the fitting of notes into the spectrum

because for me, E is the lowest note that sounds good (obviously a specific E not just any old E) on a lot of instruments (it's also the first note above 20Hz, the commonly stated lower bound of human hearing, in a=440)...

and i don't really colourise that, but there's a big difference between keys like E and F where the tonic has got a impact, to a key like C where you can come down a fifth and still not really be hitting it

obv it depends on the kind of music but i used to dabble in stuff like drum n bass and i would almost go as far as to say that it doesnt sound good if you don't write it in F/F#

but in other kinds of music you might want to be able to drop down that fifth

and in yet other kinds of music you might not even get within an octave of that note (SEGAAAAAA)

for me the top end hasnt got any where near as clearly defined a boundary to it wrt to where you can go. in a tracker the highest note is often B but i never get there

i doubt it really relates to scriabin's colours. for me it's easier to accept synesthesia as a completely alien experience with no relation to my own. but still i wanted to say that i agree that the bounded range of hearing has a real effect on the sounds of the keys even in 12TET to ppl without absolute pitch hearing

@rainwarrior,

The idea with the twelfth is that it's the same tone as a perfect fifth above the fundamental or a perfect fourth below, which of course both are so-do. Sure, a perfect fifth is not the same distance as a perfect twelfth, but would it really be too far a stretch to say that they're virtually the same things? Just like how we perceive two "C"s an octave apart to be the "the same notes, one's just higher than the other." There are some psychoacoustic factors going on here which need to be considered.

If I let a note resonate on the piano and wait to hear the twelfth ringing out on the tail end of the decay, depending on which note it is, I can hear both a perfect fifth and the perfect twelfth, despite that fifth not actually being there. And this happens with a lot of timbres for me. Even when I don't perceive a fifth under the twelfth, if I try to sing the twelfth, it might accidentally come out of my mouth as a fifth but it registers immediately as 'the same thing'. So does history explain this or why 440Hz and 880Hz are perceived to be 'the same notes, one's just higher than the other'? I'm not wholly satisfied with the idea that historical and cultural factors are the sole contributors to our musical perception, although you have made strong points. This probably involves way too much faith, but would you really consider the evolution of western harmony up to this point and its similarities with the overtone series just a grand coincidence?

Historical/cultural trends, physical phenomena and human perception are all things that should be considered separate and treated differently. At this point in the discussion, we're discussing a phenomenon that involves at least all three of these acting together on our senses. Which surely complicates trying to establish a true explanation.

Also: "why doesn't a chord motion of a major third 5:4 seem any "stronger" than a major second 9:8?" Good question, it does make the overtone connection seem quite arbitrary. But f there were truly any overtone series connection, I'd say the proposal of M3 vs M2 being arbitrary is so, because they're both so faint and nearly impossible to distinguish within most timbres, unlike the twelfth.

Tho I really do like the idea that V>I motion was completely formed separate from physical phenomena and that going against it is inconsequential in any natural sense. Coltrane had his whole religious experience with root motion in major thirds. And hell, why not embrace something like that, who says musical sentences had to be punctuated with western cadences(tho I still naturally process them this way)? It's a liberating idea!

@ant1

You're the only one who's caught on to what I was trying to say earlier about naturally fitting boundaries : ))

Perhaps synesthesia is a completely quirky and irrational thing that's purely whacked-out-sense driven, but I still really want to believe that there can be an explanation to why the colors 'progress' the way they do, not so much what the colors are and what they mean.

A big driving force behind this is the idea that, while we can easily say, "aww it's just whacked out synesthesia", Scriabin fully believed in this stuff. So much that he discussed, debated and extensively wrote about it. It might be less compelling if he was a completely crazy person, but this isn't the case. I'm sure he was quite intelligent and fully aware than his perceptions were possibly unique only to him.

I'm not saying the overtone series is just a coincidence, I'm saying it's a consequence of simple ratio intervals and their physics. It's not the cause of V-I harmony. V-I harmony is also somewhat a consequence of simple ratio intervals, i.e. they have a related root cause. So... they are not unrelated. They are correlated, perhaps.

Also, as an aside, tones with symmetrical waveforms (e.g. square wave, triangle wave, clarinet) are missing every even harmonic (octave, two octaves, perfect 21st, etc...). This isn't to say they don't blend well with the missing harmonics (I did say earlier that harmony still works even with sine waves), just there are some basic timbre types that are missing harmonics in a regular way like this.

I think the idea of octave equivalence is entirely learned. I do not believe this is a "natural" perception. It is nearly ubiquitous, but only because it is a very practical musical tool. The unison is the simplest interval, the octave the second simplest. A man and a woman singing together will quickly discover how easy and extremely consonant an octave is. From here it's easy to extend this idea to a practice of mostly octave equivalence, sure, but I conject that the perception itself that E4 is somehow "equal" to E5 is something you learn.

If you must deal with orchestration, the non-equivalence of octaves becomes very clear as you try different chord spacings, different bass notes, there are many places where you cannot accept it (Brahms' symphonies are a good place to look for examples of the profound impact of octave choice- he's a master of getting variety from the strings in this way). Another fun thing to try is to work with a tuning system that has no octave (look up Bohlen-Pierce, perhaps, and play with it). Writing music without the safety net of an octave can be mind-expanding.


As for scriabin being a "crazy person", he was actually quite mentally ill. He believed he was God, and that he must bring about the end of humanity. He thought he was going to accomplish this with a work he called the Mysterium (which was unfinished at the time of his death). He was known to be extremely paranoid and nervous. He's a rather strange fellow, though it's been a long while since I was reading biographies on him and I've forgotten a lot, but there were a lot of interesting things to say about his life.


Also, Ant1, 20hz isn't the lowest pitch you can hear, it's merely the lowest sine frequency. Lower tones can be heard, just your ear won't pick up the fundamental of it. If it was only a sine wave you'd hear nothing, but a saw wave, for example, has enough harmonics that your ear/brain can piece it together as a pitch despite the lack of the fundamental sine component.

"They are correlated, perhaps."

I think we at least agree on this. Despite using different methods to describe the idea, I think you understand where I'm coming from. I'm not trying to draw a causal relationship between the existence of the overtone series and the formation of V-I harmony. I'm saying that perhaps since nature goes for the path of least resistance, by extension so do our ears. And maybe this explains why(in part) V-I sounds 'good' and why the current system has ended up where it has.

also,

gyms: "It might be less compelling if he was a completely crazy person, but this isn't the case."

rainwarrior: "He believed he was God, and that he must bring about the end of humanity."

wonderful...lol

This reminds me that I am a sausage.

"Also, Ant1, 20hz isn't the lowest pitch you can hear, it's merely the lowest sine frequency. Lower tones can be heard, just your ear won't pick up the fundamental of it."

i know that. even an unmusical charlatan idiot like ant1 realises that there isnt a key on the piano below which the notes are totally inaudible. you can go two octaves below that E and it will be audible if you want it to be.

but notes where the fundamental is inaudible sound "worse" (or at least different) than notes where it is audible. especially in genres such as drum n bass. which is what i said first time LOL !

Pardon my overzealous pedantry.