I agree; I was positing a deeper processing level isomorphism. It may also be that this isomorphism only exists in anomalous individuals, or is more pronounced in them (i.e. synesthites, absolute pitchers). It’s just conjecture of course.
This is very closely analogous to the sine wave (‘pure spectral pitch’).
An experiment to test this would involve first accurately translating the pitch octave to the color octave, and then looking for ismorphisms in brain activity between perception of the matching pairs.
Anyway thanks for the elegant response. I still haven’t figured out how to convert pitch frequencies to the CIE color space, but hopefully it will click if I enter that water a few more times.
I am really not sure what you mean by a “deeper processing level isomorphism,” but, anyway, I doubt whether you will find anything like it in synesthetes. Pitch-color synesthetes may very well exist, but if they are anything like synesthetes in other domains the pitch-color associations will be completely different in different individuals. One person might experience C# as blue, and G as red, and another might experience them the other way round, or experience C# as yellowy-green and G as reddish-brown, or whatever. Synesthetes are consistent in their own cross-modal associations, but they are not consistent with other synesthetes, and there rarely seems to be much pattern to the associations.
Well, first of all you would have to establish a non-arbitrary way of doing the mapping. Given the complexities, which I outlined, of the way that colors and pitches are actually encoded by the sense organs, the mere physics of light and sound does not seem likely to provide a suitable basis for this, because the sense organs are not measuring the physical parameters in any sortof straightforward way. If there is any consistent mapping (and, frankly, I doubt it), the only way to discover it would be through psychophysical experiment: asking lots of people lots of questions, perhaps along the lines of “Does color A or color B seem to you to correspond more closely to the tone you are now hearing,” and then statistically boiling down the results to try to extract a consistent pattern. After that, even if you got one, I doubt if anyone has much idea about where in the brain you would go looking for this hypothetical “isomorphism.” (And, despite all the hype about fMRI recently, all available methods for monitoring activity in living human brains have very serious limitations.)
There has been some work done of colour and tone, I specifically remember a commercial course that proports to teach perfect pitch by getting the user to learn their personal colour to pitch associations. But that was the rub, they were personal. The claim was that most people had pretty similar associations, but not all. (For instance I have amazed a few musical associates with asking them what colour F# is, and most said orange.) The other problem with the associations is that they don’t necessarily follow the colour wheel. Whilst F# might be orange, G might be greeny blue. Indeed you could look to the classical idea of a scale’s inherent sound to get an idea of how wildly the perceptions wander.
So, not only is there little (if any) physical basis for mapping colour frequency to audible frequency as a scale extension, the is also some counterexample to the idea in that those associations to are seen do not follow the same order.
You have explained the situation very clearly and I think I have to file this one under “Pipe Dreams” for now.
I think Newton was chasing the same pipe dream for a period (or a similar one) -
“At first, Newton split his spectrum into five principal colors. But the number did not fit his conception that colors, like notes of music, expressed harmonies. A spectrum of colors, like a musical scale, he imagined, must have seven steps to make a full octave.” - http://www1.umn.edu/ships/updates/newton1.htm
“In an attempt at objectivity, Newton asked “an Assistant, whose Eyes for distinguishing Colours were more critical than mine” to draw his own colour partitions. From the agreed dividers, Newton could well have calculated each sine of refraction but, in an extraordinary leap of imagination, decided to compare them instead to the notes of a musical scale:
“…in proportion to one another, as the Numbers, 1, 8/9, 5/6, 3/4, 2/3, 3/5, 9/16, 1/2, and so to represent the Chords of the Key, and of a Tone, a third Minor, a fourth, a fifth, a sixth Major, a seventh, and an eighth above that Key…”” - http://home.vicnet.net.au/~colmusic/opticks1.htm
And here’s a little bit of confirmation for him:
I don’t know if it matters, but I noticed you said that you are calculating pitches logarithmically which suggest you are using pitches that are not really used in today’s music. We use the Well Temperament, not the Equal Temperament tuning system. Well Temperament adjusts certain pitches so they sound more in tune.
Is that quite true though? Sure, what, say, a piano is tuned to is not exactly equal temperament (note the stretched octaves, for instance), but wouldn’t it be better to say it’s a slightly modified equal temperament rather than well-tempered? To me, the latter suggests a high degree of consonance in many keys, but once you start getting into keys like D-flat or F-sharp or anything else with a lot of sharps and flats in it, they start to sound a good bit out of tune. Yes, I understand there are many types of well-tempered tuning systems, but I’ve never heard the modern tuning system described as anything but equal temperament.
I suspect he has equal temperament mixed up with pythagorean tuning. Still, he’s not entirely wrong.
Piano tuning is stretched because the natural harmonics of the strings don’t quite match up. This is less of a problem in any instrument that does not have that many tone generators (strings in this case). But, really the piano is one of the closest to equal temperament (with maybe lesser stringed instruments doing better)
Any woodwind or brass instrument does go more towards well-tempered tuning if they are playing with other similar instruments. A good band, in order to sound more in tune. will still play nearly equal tempered fifths and octaves, but will modify the third by lowering it (and, consequently the sixth by raising it.
Now, I’m not as well-versed in vocalists (odd because I was a vocal major), but I know that barbershop similarly tries to create more resonance by altering pitches. The goal is to have one harmonic from each note match the other, creating a sort of fifth voice. Based on that description, I would assume they are the closest to pythagorean tuning.
Anyways, I said all this to say that, while pop music et al is really focused on equal temperament (or at least piano temperament), other styles of music do use different tunings.
Also, since he was mapping to hz, I doubt any of it mattered. Using logarithmic scales is just because our ears notice a bigger difference between small changes in lower frequencies, and, consequently, smaller differences in small changes in higher frequencies.
For example, even most tone deaf people will notice the difference between 55hz (A) and 62hz(B), but a trained musician can have trouble hearing the difference between 3520hz (A) and 3527hz (A) unless they were played simultaneously or nearly so. That works whether I’m dealing with equal tempered tuning (62 = 61.735) or pythagorean tuning (62 = 61.875).
