# From the "inverted spectrum" to the "music transposed by 12" problem?

So here's an argument for category theory in neuroscience. He presents the inverted spectrum problem and yoneda lemma as its solution. I am abridging it:

We can order colours from long wavelength light to short wavelength light. And the idea is that there are some people who for whatever reason would see that spectrum for whatever reason see that spectrum we see it flipped, we would not be able to find out...

There is no metaphysical reason that if my brain is exactly like your brain that it would be the same mental experience... There is no mathematical mapping between certain brain states and mental states. Atleast none we know yet.

Does this mean if we knew everything including about the brain, we could never infer what exactly it is conscious of?

Well the answer to that is in the early visual system because of color opponency so we have a cone circuit diagram that leads us to oppose yellow from blue and red versus green they're literally inhibiting each other and that gives us two opposing poles a yellow blue pole and a green red pole that gives rise to a two-dimensional structure so this is how we wrap that one-dimensional linear. Spectrum around in a two-dimensional spectrum and in fact this right here would only be a slice of something more complicated because we can go all the way from Black from complete darkness to White complete brightness so this is not just a two-dimensional Circle each time I'm showing you a color circle like that we're actually taking a slice through a three-dimensional structure such as a sphere and we can do psychophysics on that so ... we can psychophysically measure precisely with numbers the distances that exist between red and another color and then find out if that is a certain difference that people assign to that is the difference between this red and this this yellow

The relation between red and all the other colours uniquely define red

## Question

Now, let me pose my variation: "The music transposed by 12 problem." Basically imagine someone plays a piece of music. Again let's assume there is human A and human B. A hears it like us but B hears the same song transposed by 12. Here's what's confusing me as someone whose familiar with music: Baselines and melodies aren't the same. So basically if I play a groovy bass line solo. This individual would not headbang to it and I would know aha! This person is hearing transposed by 12.

Edit: I can play chords which when transposed to the extreme left end of the piano will no longer sound like music. I think this fact of music as a kind of universality.

For a better discussion see here. If we change the frequencies heard the whole thing can sound like a muddied mess.

Surely I must be missing out on something? Am I being silly? Are both variations of the problem equivalent? Why doesn't the yoneda lemma work now (in both cases spectrum inversion and transposition the relative relations between frequencies are preserved)?

• Reason for downvote? Commented Jun 29, 2023 at 4:33
• I think this is a super interesting question, but it needs a bit of thought. There is no doubt that we experience sounds in way that is different from our perception of colour in the sense that musical tones in our minds seem to have a definite order to them from low to high, whereas there isn't an analogous order to colours. Commented Jun 29, 2023 at 15:46
• "bass line" not "baseline". A "baseline" is a reference value, often recorded over time. A "bass line" is a sequence of notes played by a low instrument. Commented Jun 29, 2023 at 16:22
• Ironically, transposed down an octave is probably clearer than "transposed by 12". Even more clear might be every wavelength doubled or every frequency halved. Commented Jun 29, 2023 at 20:33
• A more fitting (and, I think, interesting) comparison is the difference between major and minor. Two triads with the exact same intervallic structure, but one upside down. Both are consonant. But minor is different from major, some would say sadder, or weaker, or perhaps... bluer. What if some people actually hear it as redder? Commented Jul 2, 2023 at 4:10

This question conflates the objective and subjective elements of perception. Or to put it more concretely, we don't question that the cones of the retina each respond to certain wavelengths of light, we question whether the subjective experience generated by the transmission of signals from those cones is the same for different people. If a scientist could locate precisely those electro-chemical signals that I perceive as red in my brain, and somehow — surgically, chemically, magically — impose those electro-chemical signals on your brain, would you see red? Or would you see blue, or green, or some other color?

The fact that we agree externally that this sense-experience is called 'red' does not in any way mean that we have the same subjective experience. We could have utterly different subjective experiences without realizing it, because we've all learned that whatever idiosyncratic experience we have to a common sense-object would be called 'red'.

Language is functional and use-driven. We use the word 'red' for this, and it simply doesn't matter whether this appears the same to both of us.

With respect to your music example, why would someone not hear the baseline when it's transposed by 12? The baselines and melodies may not be the same as the original, but they have the same relative relation to each other. People transpose songs into different keys all the time, and while there might be some minor issues (e.g., different keys have different moods) everyone recognizes the transposed song as 'the song', and most people will miss the fact that it's been transposed at all. That takes some musical knowledge, and a good ear.

So what exactly is the problem? The transposition clearly cannot take the music out of the range of physical human hearing (that's a biophysical phenomenon, and we are talking about subjective experience). The entire piece is transformed systematically, so your groovy baseline will still be appreciated even if the listener is not 'hearing' exactly what you're hearing. If they don't headbang to it, is that because they don't 'hear it' properly, or because they just don't 'like it' the way it appears to them subjectively, or just because they don't 'like it' even though they hear it the same way as you?

• I can play chords which when transposed to the left end of the piano will no longer sound like music Commented Jun 29, 2023 at 6:57
• Also when I say transpose by 12 I'm refering to staying in the same key just a different scale Commented Jun 29, 2023 at 7:05
• @MoreAnonymous: Ah, sorry, music theory isn't really one of my areas. But the point is that whether we're talking about sight or hearing (or any other sense) there's an objective/subjective divide. The same sensory input might produce different subjective experiences for different people. but these different subjective experiences must be mediated through language, which will connect them through the shared externally sensed object. One would not transpose the music physically; one would transpose the music cognitively Commented Jun 29, 2023 at 15:08
• @MoreAnonymous: One might do that systematically, in which the structural components of the music (while perceived differently) would still have the same effect, and still be identified linguistically as the same external music object. Or one might do that chaotically (a kind of musical dyslexia) in which the structure is lost and the external music object isn't identifiable. or even differentiable from mere noise. But the latter would be an obvious cognitive disfunction, while the former would pass without notice. Commented Jun 29, 2023 at 15:13
• the second point (music dyslexia) is exactly the point I'm making ... The proposed solution that musical notes/colours should be relational does not work. Commented Jun 29, 2023 at 15:20

The transposing operation is approached in a wrong manner.

Before, there's no "start" of the light spectrum in you example. If you start from what you see as "red", you will have "orange" at a certain distance X. Now, imagine that the "red" you see is "green" for me, and I start from it. It's the same point, with different colours but same names! In any case, I will also have what I call "orange" at the same relative distance. Even if you would see it as "cyan", if you could plug my optical system in your brain.

In general, what changes here is the whole, but internally, proportions remain. Imagine if I take my head off, and connect to my body vertically inverted (chin upside, eyes below). While I will see the world upside down, names don't change, above and below keep the same. Things will still fall to the ground, and I will call it "below".

But in case of transposition, it's not the universe what changes, but only a particular object inside, so the idea don't applies.

In order for you to perceive a +12 transposition of La (A4), you will need to sense 880 vibrations instead of 440 in the same time period. You are changing the specific object (frequency) but not the universe (time).

Now, the only way for you to perceive A5 as 440 hertz (transposed) is for your brain to work at the double of speed. This is the example you are looking for: the case where the referential point (speed of your brain) changes, which causes all objects inside to change as well.

Anyway, you cannot perceive any change, because your mind just goes faster, and the objects remain proportionally relative to the universe: you get less vibrations, but while time passes slower for you, so A4 is 440hz for you. While my brain, which goes slower, makes me feel things go faster, it gets more vibrations, but in a shorter (relative) time. So, for me, A4 is also 440hz.

You would only feel the transposition (you would feel A5, 880 hz) only if you would be able to plug part of my audition system to your brain (that is, my auditory system generates an A4, but when it reaches your brain, it becomes an A5).

• I am pretty sure that the brain does not receive and process the raw waveform of the sounds one hears, any more than it does for the light one sees. Just as each of our retinal cones responds to one of three spectral ranges and sends a signal encoding intensity, each sensory cell in the cochlear responds to one narrow frequency range and sends a signal encoding how loud it is. In both cases, the brain receives the envelope of the wave. Commented Jun 29, 2023 at 12:29

I mean the argument for the visual spectrum is essentially that "colors aren't real". Light isn't actually of a certain color it's just an electromagnetic wave of a certain frequency. Our means of perception just happen to group certain contrasts due to being perceptive in different regions of the spectrum.

So our perceptive system essentially outputs a color-by-numbers picture and the brain is a small child that paints regions of the same number in the same color, but as it is free to choose from the entire palette what numbers and colors to associate, it's possible that the pictures look completely different but people are still able to communicate what places have the same color. They can identify a common external property, but their internal visualization would be different.

It's also interesting that our grouping of red and yellow as warm and blue and purple as cold is more psychological than physical. As blue light has a higher frequency and thus more energy than red. Though in our environment it's usually red things that are hot (fire) and blue things that are cold (water). Though that's not entirely psychological either as hot objects radiate light with a certain frequency usually in the infrared domain (to slow to be visible), so when they are really hot they enter the visual range on the left side with a reddish color. Objects emitting blue light due to temperature would be way hotter but we don't usually encounter things that hot on earth.

Now the question in terms of music is whether "tones are real". So is what we're hearing in our minds really the acoustic wave or a direct analog or is our perceptive system again producing a auditory picture of numbers for our brain to apply the colors?

And languagewise we already are inapt to describe that properly because descriptions of tone and pitch are linked to the physical wave so to say hearing it an octave lower or higher doesn't work because that would change a physical property, resulting in different regions in the ear being excited and a different number being used, not a different color. For comparison if you doubled/half the frequency of visible light you leave the visible spectrum so that would be a measurable difference and not just a subjective experience.

So it would be rather something like the sound in your head being different from the sound in my head, but the proportions between sounds and the relations to physical properties being preserved. Though it's hard to even describe that, as the properties of sound, like whether it's high or low, loud or soft, are related to external physical properties and aren't just names for internal states.

• Because of the shape of the blackbody spectrum, objects glow white not blue. When stars are blue, absorption by dust is involved, & Doppler blueshift: Roses are red, roses are blue, depending on their relative velocity, to you'. It's interesting to note that there are no green stars. Commented Jun 29, 2023 at 18:33
• "Too slow to be visible" should be "too [low-energy, long wavelength, low frequency] to be visible", light traveling the same speed in any vacuum. Methane ('natural gas') burns blue, but more importantly, BBR emits a broad range of frequencies, so after orange, hot bodies emit what looks yellowish white because of all the present frequencies. If the peak were in the blue range, we'd still see white for this reason. @CriglCragl, our choice of classification means there are no green stars, but green corresponds to 4800K which is a common enough surface temperature for stars. Commented Jun 29, 2023 at 20:26
• @user121330: No visible stars look green Commented Jun 29, 2023 at 20:36

Sight and sound share some terms, but our perception of them is drastically different. First, we hear in fundamentally one angular dimension while we see in 2. In addition, our perception of color is based on a linear combination of responses from 3 different types of receptors (color-blindness means one or more receptors are missing, while there are people with 4 types of receptors), each with a different frequency response profile, while our ears have a much larger number of variously sized 'hairs' (cilia) that mechanically vibrate in response to sounds.

More to the point, we see over a very narrow range of frequencies when compared to our hearing (nearly 10 octaves for the young). As audio notes get lower, we bump into a couple problems. First, we get old and we can't hear the low notes as well - musicians and audiophiles will compensate by intuiting the note based on its overtones, but some sounds have quieter overtones and if you only hear the overtone, the actual note is lost unless you can feel it without your ears. Next, the speed we play the notes starts to matter at the bottom of the range. The lowest note on the piano is under 30 hz. If you play that low C for just 1/15th of a second, there are only about 2 cycles to figure out which note that is. If we were digital computers with 44,000 samples per second (which is enough to represent any sounds we can hear), this would be enough to determine which note, but hearing is more complicated.

It takes a little time for a sound to get a few of those cilia vibrating, and then it takes a little time for your brain to figure out what that combination means. Fundamentally, our effective sampling rate isn't high enough in the low frequency range to figure out what note is playing unless we can hear it for a while. Thus, the tubist playing flight of the bumble-bee sounds a bit "muddy". It is almost certain, given that cilia can be damaged or impeded, we each have a somewhat unique perception of sounds - especially in the low frequency range.