Yahoo Tuning Groups Ultimate Backup tuning Colors and sounds, our visual range is an octave!

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> In a message dated 1/19/2005 11:22:03 AM Eastern Standard Time,
> gdsecor@y... writes:
> But why would you choose red for C? Is it not obvious that A-flat
is
> red, C is green, and E is blue? :-)
>
> --George
> I believe George is emphasizing that any linkage between pitch and
color is
> arbitrary. ...
>
> best, Johnny Reinhard

That's not at all what I meant. The frequency for middle C is
~261.63 Hz (in 12-ET, with A=440). Transpose this pitch 41 octaves
up and you get ~5.753*10^14 Hz, which electromagnetic frequency is
near the middle of the visible range. This converts to a wavelength
of ~521.08 nanometers, which is very definitely green! Likewise, the
A-flat below and E above middle C will give you wavelengths
corresponding to red and blue, respectively.

However, these aren't exact -- a 30-cent drop in pitch (corresponding
to A=432.4) would give you wavelengths much closer to the RGB
profile. (In fact, C=256 transposed up 41 octaves would give you a
green wavelength of 532.54 nm, which is between the value for the RGB
and XYZ color profiles given here:
http://www.mathpages.com/home/kmath578/kmath578.htm
so perhaps there's something to be said for a "scientific" pitch
standard of C=256.

Anyway, as long as we accept octave equivalence, there's nothing
arbitrary about this at all.

--George

🔗Ozan Yarman <ozanyarman@superonline.com>

I respectfully disagree with some points here dear George:

1. An optimal palette that appeals to the eye should certainly be a scale that is composed of `conconant` elements. Not all scales are optimal or pleasing to the eye... much the same as in music.

2. Our perception of color distinctly allows us to differentiate universal color categories which have been ascertained as 11 by Berlin and Kay. These are: WHITE, BLACK, BROWN, RED, YELLOW, GREEN, BLUE, PURPLE, PINK, ORANGE and GREY. Every color will eventually fall into these categories.

3. We are able to perceive many colors in a small region though, such as a tight sequence of red, green and blue. This could be considered a color-chord, much the same as a musical chord. But such concepts as hue, contrast, brightness and saturation have other parallels in regards to sound waves.

Regards,
Ozan
----- Original Message -----
From: George D. Secor
To: tuning@yahoogroups.com
Sent: 19 Ocak 2005 Çarşamba 0:07
Subject: [tuning] Re: Colors and sounds, our visual range is an octave!

--- In tuning@yahoogroups.com, Can Akkoc <can193849@y...> wrote:
> George,
>
> Could one talk about *consonance* of colors with small frequency or
wave length ratios?

No, because:
1) Beating harmonics allow us to hear mistuned consonances, whereas
harmonics of visual frequencies are beyond our range of seeing;

2) Virtually all colored light that we see is an asynchronous
conglomeration of frequencies (the exception being that which is
laser-generated);

3) We hear distinct pitches even when they are combined in a single
electrical signal, whereas colors must originate from separate
locations or directions in order for us to perceive them separately.

> If that model flies, then could *color chords* be a plausible
concept for color *polyphony*?

You could make an limited analogy using hues for a central octave of
pitches and use successively darker shades for lower octaves and
lighter tints for higher octaves. But that analogy quickly breaks
down, because sonic consonance and dissonance does not translate
meaningfully to colored light, nor does timbre (or tone-color) have
any parallel.

--George

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> I respectfully disagree with some points here dear George:
>
> 1. An optimal palette that appeals to the eye should certainly be a
scale that is composed of `conconant` elements. Not all scales are
optimal or pleasing to the eye... much the same as in music.

True, but do those combinations of colors that are pleasing to the
eye have very much to do with "small frequency or wave length ratios?"

> --- In tuning@yahoogroups.com, Can Akkoc <can193849@y...> wrote:
> > George,
> >
> > Could one talk about *consonance* of colors with small
frequency or
> > wave length ratios?

Ozan, if you really think that this is so, then perhaps you should
demonstrate this by preparing examples of major and minor triads as
color analogies. It would be an interesting approach to harmony
and/or graphic design.

> 2. Our perception of color distinctly allows us to differentiate
universal color categories which have been ascertained as 11 by
Berlin and Kay. These are: WHITE, BLACK, BROWN, RED, YELLOW, GREEN,
BLUE, PURPLE, PINK, ORANGE and GREY. Every color will eventually fall
into these categories.

And which category does CYAN fall into? IMO cyan is as distinct from
blue as orange is from red. And no matter how many or few categories
you have, there will always be colors just on the boundary of two of
these about which category two different observers will disagree. Is
beige "white" or "brown"? Is a night sky "blue" or "black"? (I
realize that these are not *your* categories, but I can't help
thinking that this can't be as "universal" as it's cracked up to be.)

We get into the same situation with pitch (or intervals): are A-flat
(or a minor 6th) and G-sharp (or an autmented 5th) in the same pitch-
(interval-)class or are they different? It depends on what you've
been trained to hear. (Just a little something to keep this message
on-topic. :-)

> 3. We are able to perceive many colors in a small region though,
such as a tight sequence of red, green and blue. This could be
considered a color-chord, much the same as a musical chord.

Yes, of course. But do simple frequency or wavelength ratios
correlate to "consonant" color combinations? Would a slight
adjustment of hue away from these simple ratios cause these color
combinations to become more "dissonant?"

> But such concepts as hue, contrast, brightness and saturation have
other parallels in regards to sound waves.

Yes, to some extent.

Ozan, now that I've gotten my latest generalized keyboard design for
Iglashion out on MMM, I hope to have a reply to your last message
(56547) about Spectral vs. Sagittal notation soon.

Best,

--George

🔗amcmechan <amcmechan@donerus.com>

Good morning all - new to the group, but you're onto a topic that
interests me greatly, since I pursue both composition and painting.

Remember, light and sound can never be completely analogous, because
light is both a wave and a particle based phenomenon. And light also
acts differenly whether it is "additive" or "subtractive." Meaning,
whether it is a color due to the addition of individual light waves
(clouds look white because the water particles refract more light
waves of different frequencies, therefore adding to white) or the
subtraction, usually of particles. I'm not a scientist by any
stretch, but I am fascinated by the concept of why an object appears
a certain color. Plants are green, for example, not because they
have any innate property of greenness, but because the molecules that
ultimately perform photosynthesis "eat" red and blue light particles
to process to create energy, reflecting those particles that in
combination create a sense of green. Just the concept of light
eaters - cool, yet kind of creepy.

There is an excellent book on many aspects of color and culture,
called - appropriately - "Color and Culture" by John Gage (not C), of
Cambridge U. Inside is a chapter on the Colour of Sound, where he
surveys various attempts to attach the two over time, from the Greeks
forward. I'll try and summarize in a later post if anyone is
interested.

Thanks.

Andrew
amcmechan@donerus.com

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:
> Exactly Hans, thanks for the thought.
>
> Cordially,
> Ozan
> ----- Original Message -----
> From: hstraub64
> To: tuning@yahoogroups.com
> Sent: 18 Ocak 2005 Salý 19:33
> Subject: [tuning] Re: Colors and sounds, our visual range is an
octave!
>
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...>
wrote:
> > http://www.mathpages.com/home/kmath578/kmath578.htm
> >
> > The last paragraph intrugued me. I recommend this article for
those
> interested in the correlation of pitch with color.
> >
>
> Interesting! I have always thought it strange that purple and read
> look so similar although they are on opposite sides of the visible
> spectrum... The argument stated in the paragraph raises a funny
> thought in this aspect...
> --
> Hans Straub

🔗George D. Secor <gdsecor@yahoo.com>

Paul Erlich responded off-list to a couple of my messages:

--- wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:
> [GS:]
> > Anyway, as long as we accept octave equivalence, there's nothing
> > arbitrary about this at all.
> >
> > --George
>
> Hi George,
>
> Sure there is. There's no connection, or even similarity, between
how
> we perceive pitch and how we perceive color.

So what does that matter? I'm simply trying to establish a
relationship between frequencies of drastically different magnitude
using the principle of octave equivalence as the "connection." The
fact that we perceive these two groups of frequencies very
differently is, in one sense, beside the point, yet in another sense,
the whole point in making that connection apart from those
considerations.

> There isn't even a
> relationship between rhythm and pitch, even though both are audible
> frequencies (in different ways).

True.

I posed the question before about an alleged connection between C and
green shortly after I showed up on the tuning list (near the end of
this message):

/tuning/topicId_12590.html#33561

The last paragraph mentions someone else who came up with the same
conclusion as I (perhaps by coincidence), but for an entirely
different reason (a sense of absolute pitch), which I explained in a
follow-up message (my mention of 43 octaves was in error -- should
have been 41):

/tuning/topicId_33566.html#33660

Coincidence or not, at least there is a way to relate pitch to color
that doesn't depend on anyone's subjectivity.

--- wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:
[GS:]
> > And no matter how many or few categories
> > you have, there will always be colors just on the boundary of two
of
> > these about which category two different observers will
disagree. Is
> > beige "white" or "brown"? Is a night sky "blue" or "black"? (I
> > realize that these are not *your* categories, but I can't help
> > thinking that this can't be as "universal" as it's cracked up to
be.)
>
> George, the categories are much more universal than you would
think.
> May I recommend a book for you: _The Language Instinct_ by Steven
> Pinker. Color boundaries are amazingly stable (where they continue
to
> exist at all) across cultures.

Point taken. Thanks, Paul.

--George

🔗George D. Secor <gdsecor@yahoo.com>

🔗Ozan Yarman <ozanyarman@superonline.com>

Ouch! I said something which I have neither enough information on nor the time to pursue. Forgive me dear George, It is only that I have the `feeling` that color harmony practiced by such artists as Rembrant and Van Gogh have some bearing to spectral intervals much the same as intervals in music. But I don't know how they may be `contonent` or `distonent`.

Cyan... I am not sure which category it may fall into other than my feeling that it is definately bluer in tint. Perhaps Berlin and Kay should be held accountable for that categorization. Don't shoot the messenger!

It just occured to me, that the CRT tubes we stare at are actually producing the illusion of colors on the screen by mixing Red Green and Blue rays in the desired amount. This could be analogous to polyphony in music, with one exception being the contraint of vision to mono-tony (pun intended).

As to color-chords, I can only suggest that Red, Green and Yellow as in a triadic scale could be considered a major chord, while Yellow replaced by Blue could be a minor chord. It's just a feeling, but who knows?

At this point, I ask the readers' forgiveness for the barrage of messages... I hope to make up by celebrating the eid of everyone harboring a common distate for evil and a common attachment to our Lord, with the hopes for a healthier, better, happier future.

Cordially,
Ozan
----- Original Message -----
From: George D. Secor
To: tuning@yahoogroups.com
Sent: 20 Ocak 2005 Perşembe 0:26
Subject: [tuning] Re: Colors and sounds, our visual range is an octave!

Ozan, now that I've gotten my latest generalized keyboard design for
Iglashion out on MMM, I hope to have a reply to your last message
(56547) about Spectral vs. Sagittal notation soon.

Best,

--George

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗amcmechan <amcmechan@donerus.com>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Hi all,

Further to this topic - some languages have very few colour names at all,
not having developed a need for the corresponding distinctions. Even
Malay - a language spoken by hundreds of millions - until recent historical
times had names only for "light", "dark", "red" and "green". Terms for
"blue" and "yellow" are imports from other cultures, taken on when those
colours became culturally significant. Contrast this with the hundreds of
colour names that were in use in English even in Victorian times. It
certainly makes it hard to know which name to choose, when you have, not
only "purple" and "blue", but also "violet", "lavender" and "mauve".
Whatever your personal preference, there's no objective way of saying that
one colour naming system is instrinsically better for all time and cultures.
You can say that a given system fits the needs of its users ill or well.

Many of the ardent microtonalists on this list, are, of course, people
seeking new musical languages. It makes sense to me that they may make new
connections betwen artforms and new distinctions within them ...

As to how fixed the boundaries are, once we have developed specific
categories: My wife and I (both artists) very often disagree over whether a
particular hue is a "green" or a "blue". To me, it's probably an
almost-blue cyan with only a hint of green, so I call it "blue", whereas to
her it's clearly "green". Of course, she wins ... :-) What's in a name?

Regards,
Yahya
-----Original Message-----
From: George D. Secor [mailto:gdsecor@yahoo.com]
Sent: Friday 21 January 2005 5:14 am
To: tuning@yahoogroups.com
Subject: [tuning] Re: Colors and sounds, our visual range is an octave!

Paul Erlich responded off-list to a couple of my messages:

> There isn't even a
> relationship between rhythm and pitch, even though both are audible
> frequencies (in different ways).

True.

I posed the question before about an alleged connection between C and
green shortly after I showed up on the tuning list (near the end of
this message):

/tuning/topicId_12590.html#33561

/tuning/topicId_33566.html#33660

Coincidence or not, at least there is a way to relate pitch to color
that doesn't depend on anyone's subjectivity.

Point taken. Thanks, Paul.

--George

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🔗Dave Keenan <d.keenan@bigpond.net.au>

George,

Given that you're mapping pitch to hue on the basis of
octave-equivalence between acoustic frequencies and electromagnetic
frequencies, I find that while your calculations are quite correct, E
would in fact be violet and so would F (and the two would be quite
indistinguishable in hue).

See
http://en.wikipedia.org/wiki/Image:Cie_chromaticity_diagram_wavelength.png

And while Ab would indeed be red, so would A, G and F#, although you
might be able to detect the ever-so-slight orangeness of A. And while
C would indeed be green, so would B, although you might be able to
detect the ever-so-slight yellowing of B.

Eb and D would both be blue although D might be noticeably lighter
(closer to cyan).

The only really distinct hues would be Bb (orange) and C# (cyan). Note
that yellow only occurs in a narrow band somewhere between B and Bb
and the various purple hues are completely unavailable since they are
not spectral (not elicited by a single EM frequency, but requiring at
least two).

So this is a very poor mapping for most practical purposes. If we want
maximum distinctness we'd do better to map instead to a
psycho-physically-based _hue_ specification, i.e. the angle from the
white spot on the above chromaticity diagram.

In that case I'd tend to put the zero (red) point at G#/Ab so that hue
order corresponds to alphabetical order. Something like

Ab/G# red
A orange
Bb yellow
B yellow-green
C green
C# cyan-green
D cyan
Eb cyan-blue
E blue
F violet
F# purple
G red-purple

But yes, we're back to it being fairly arbitrary.

-- Dave Keenan

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> George,
>
> Given that you're mapping pitch to hue on the basis of
> octave-equivalence between acoustic frequencies and electromagnetic
> frequencies, I find that while your calculations are quite correct,
E
> would in fact be violet and so would F (and the two would be quite
> indistinguishable in hue).
>
> See
>
http://en.wikipedia.org/wiki/Image:Cie_chromaticity_diagram_wavelength
.png
>
> And while Ab would indeed be red, so would A, G and F#, although you
> might be able to detect the ever-so-slight orangeness of A. And
while
> C would indeed be green, so would B, although you might be able to
> detect the ever-so-slight yellowing of B.
>
> Eb and D would both be blue although D might be noticeably lighter
> (closer to cyan).
>
> The only really distinct hues would be Bb (orange) and C# (cyan).
Note
> that yellow only occurs in a narrow band somewhere between B and Bb

In the diagram I find yellow more sharply defined (at ~574 nm) than
either orange or cyan. Wouldn't you also consider that a distinct
hue? Taking A=440, yellow would correspond to a pitch of ~237.5 Hz,
which would be Bb|) in 72-ET. (See, I found a way to get us back on-
topic. ;-)

A quick way to convert wavelength (in nm) to pitch frequency (in Hz,
shifted 41 octaves) or vice versa is to divide 136330 by one number
to get the other.

IMO, the best orange is at 590 nm, or Bb\!, while cyan (488 or 489
nm) is C#/| -- but I think that orange could be interpreted as
anything from 580 to 595 nm, or Bb/| to Bb!) in 72-ET.

Unfortunately, both orange and yellow are close to Bb, but if you
reckon these in meantone temperament or 31-ET, then you get:

A# orange
Bb yellow
Db cyan

> and the various purple hues are completely unavailable since they
are
> not spectral (not elicited by a single EM frequency, but requiring
at
> least two).

I'm was at first a little confused by your distinction between violet
and purple, which I've always considered to be more or less
synonomous. But I can accept that violet is bluer, with purple
tending toward plum. From your table below, what you seem to be
referring to as purple (midway between blue and red) I would call
magenta (which also is not spectral). I've read somewhere that
purple (or was it violet?; I don't remember which, but I had the
impression that both were included) isn't spectral, but that the
shortest visible frequency is actually a deep blue -- conforming to
what I see at the lower corner of the chromaticity diagram in the
above link. My own experience is at variance with this. On several
occasions I've carefully examined sunlight passed through a prism and
readily observed a color at the "blue" end that one might call violet
or purple -- to see what I'm referring to, locate a point in the
diagram corresponding to 0.24 on the x-axis and go directly upward
until you encounter color; that's what I would put at the bottom end
of the hue-curve (would you call it violet or purple?).

I'm wondering how accurate the color is in that figure. Or am I
seeing something at the short end of the spectrum that most people
don't see? (Yes, I really did see a color with that much warmth,
which I would be inclined to call violet.)

Whatever the case, the non-spectral purple and magenta hues would
have to be extrapolated from both ends of the spectrum, which I
don't.think poses much of a problem.

> So this is a very poor mapping for most practical purposes.

Yes, I agree.

> If we want
> maximum distinctness we'd do better to map instead to a
> psycho-physically-based _hue_ specification, i.e. the angle from the
> white spot on the above chromaticity diagram.

Yes, we encounter problems with hue because of such factors as:

1) Our hue acuity (sensitivity to small changes in hue) varies widely
over the visible range of electromagnetic frequencies, and

2) Our eyes are more sensitive to hues near the middle of the
visible "octave", so the notion that white light is an "equal" mix of
all visible wavelengths has to be taken with a handful of salt (also
to take into account such things as color fatigue).

If our eyes were sensitive to a full octave of hue, I think we might
find appearances somewhat different.

> In that case I'd tend to put the zero (red) point at G#/Ab so that
hue
> order corresponds to alphabetical order. Something like
>
> Ab/G# red
> A orange
> Bb yellow
> B yellow-green
> C green
> C# cyan-green
> D cyan
> Eb cyan-blue
> E blue
> F violet
> F# purple
> G red-purple

It's a little ironic that, after all the alternate tunings we've
dealt with, our attempt to correlate color (using 3 additive
primaries) with pitch keeps taking us back to 12-ET. :-)

In the above table, I would substitute "magenta" for "purple".
Otherwise I would have to say that's pretty much what I had in mind.

> But yes, we're back to it being fairly arbitrary.

Actually not very much, when you think about it. C is still a green
of some sort (and definitely not red or blue), which is no worse than
the variation in frequency that the musical pitch "C" has had over
the past several centuries.

--George

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> > The only really distinct hues would be Bb (orange) and C# (cyan).
> Note
> > that yellow only occurs in a narrow band somewhere between B and Bb
>
> In the diagram I find yellow more sharply defined (at ~574 nm) than
> either orange or cyan. Wouldn't you also consider that a distinct
> hue?

Yes. Sorry. I meant "the only really distinct hues in 12-equal ...",
and it wouldn't be too much different for 12 of meantone or
Pythagorean either.

> Taking A=440, yellow would correspond to a pitch of ~237.5 Hz,
> which would be Bb|) in 72-ET.

Yes.

> A quick way to convert wavelength (in nm) to pitch frequency (in Hz,
> shifted 41 octaves) or vice versa is to divide 136330 by one number
> to get the other.
>
> IMO, the best orange is at 590 nm, or Bb\!, while cyan (488 or 489
> nm) is C#/| -- but I think that orange could be interpreted as
> anything from 580 to 595 nm, or Bb/| to Bb!) in 72-ET.
>
> Unfortunately, both orange and yellow are close to Bb, but if you
> reckon these in meantone temperament or 31-ET, then you get:
>
> A# orange
> Bb yellow
> Db cyan
>
> > and the various purple hues are completely unavailable since they
> are
> > not spectral (not elicited by a single EM frequency, but requiring
> at
> > least two).
>
> I'm was at first a little confused by your distinction between violet
> and purple, which I've always considered to be more or less
> synonomous. But I can accept that violet is bluer, with purple
> tending toward plum. From your table below, what you seem to be
> referring to as purple (midway between blue and red) I would call
> magenta (which also is not spectral).

Yes. I should have used the term magenta for the hue midway between
red and blue. And "red-magenta" instead of "red-purple". But the line
between red and blue seems to be often called "the purple line".

"blue-magenta" could be an alternative name for the hue I called
"violet". As a colour, not merely a hue, spectral violet differs from
blue-magenta, for most people, mainly by being more saturated
(stronger, less diluted with white). But the fine details of colour
are tricky and vary between people and with context, just like just
intonation. ;-)

So violet, blue-magenta, magenta and red-magenta can all be considered
varieties of purple. Purple is a less well-defined term than violet or
magenta.

However this chromaticity diagram uses "bluish-purple" as a synonym
for violet.
http://www.siggraph.org/education/materials/HyperGraph/color/images/cie.jpg
I think you can safely ignore the colours you see on this one, but it
is useful for the named regions.

> I've read somewhere that
> purple (or was it violet?; I don't remember which, but I had the
> impression that both were included) isn't spectral, but that the
> shortest visible frequency is actually a deep blue -- conforming to
> what I see at the lower corner of the chromaticity diagram in the
> above link. My own experience is at variance with this. On several
> occasions I've carefully examined sunlight passed through a prism and
> readily observed a color at the "blue" end that one might call violet
> or purple -- to see what I'm referring to, locate a point in the
> diagram corresponding to 0.24 on the x-axis and go directly upward
> until you encounter color; that's what I would put at the bottom end
> of the hue-curve (would you call it violet or purple?).

You can't trust what you see on the computer screen (LCDs are
particularly bad, changing with viewing angle) because all colours are
produced as a combination of only red, green and blue phosphors.

The printed page is no better, where cyan, magenta and yellow inks are
used.

But the shortest visible wavelength is definitely violet, by
definition. Consider that the slightly shorter invisible wavelengths
are universally called "ultra-violet".

One website suggested that to see spectral violet, take a CD (not a
CD/R) and look at the reflection of a flourescent light in it. When I
do so, it definitely doesn't look blue, and it is definitely on the
"other" side of blue from cyan, but it doesn't look as saturated as
the violet I remember in some lines on a screen in a darkened physics lab.

But either way, the best approximation to them on a computer screen is
obtained by adding a small amount of red to blue.

> I'm wondering how accurate the color is in that figure. Or am I
> seeing something at the short end of the spectrum that most people
> don't see? (Yes, I really did see a color with that much warmth,
> which I would be inclined to call violet.)

The figure is inaccurate. Your experience sounds the same as mine and
probably all "normally sighted" humans.

> If our eyes were sensitive to a full octave of hue, I think we might
> find appearances somewhat different.

As you probably know, octaves (and harmonics generally) are fairly
irrelevant to colour perception, involving as it does, the particle
nature of light, rather than the wave nature. There is no special
reason that the human range is near an octave, actually it's more like
a subminor seventh. Other animals have wider and narrower ranges.

What gives hue perception it's apparent circularity is the posession
of exactly three different colour receptors. Other animals have more
or less, and many humans have less. With only two receptors, hue is
binary (i.e. there are exactly two hues, no continuous ranges at all).
With four receptors, hue maps to the surface of a sphere.

> It's a little ironic that, after all the alternate tunings we've
> dealt with, our attempt to correlate color (using 3 additive
> primaries) with pitch keeps taking us back to 12-ET. :-)

Yes. Of course it's a natural since 12 = 4 * 3. We have the three
subtractive primaries too.

cyan

green C# D Eb blue
C E
B F
Bb F#
yellow A Ab/G# G magenta

red

> In the above table, I would substitute "magenta" for "purple".

Agreed.

> Otherwise I would have to say that's pretty much what I had in mind.

OK. But you have to admit, it bears little resemblance to what direct
"octave equivalence" would give. There's some powerful compression of
some parts of the spectrum (particularly the green and red regions)
and stretching of others (particularly orange, yellow, blue and
violet), and the addition of non-spectral hues, to get to the above.

But it's nice that both alphabetical order and "octave-equivalence"
give the same centre point.

-- Dave Keenan

🔗Dave Keenan <d.keenan@bigpond.net.au>

The reason for the "warmth" of spectral violet and the reason it is
best approximated in an RGB system by adding a small amount of red to
blue, is not due to any sort of "octave equivalence". It seems to be
due to the fact that the response curve of the red cones happens to
have an inflection in it at around what we call the blue/violet
transition, and this leads to the red cones being slightly more
sensitive than the green cones again in the violet region of the
spectrum, as they are in the green to red part.

See the logarithmic response curves about 1/3 of the way through
http://www.handprint.com/HP/WCL/color1.html

The likely reason that violet doesn't look the way I remember it from
the physics lab is that my corneas and lenses have yellowed with age
and pass less of the shorter wavelengths than they used to.

In case you were hoping that if humans could see into the near
ultraviolet they would report it as magenta due to "octave
equivalence" I must report that people who have had their lenses
removed report that UV-A appears as an unsaturated (i.e. whitish or
greyish) blue.
http://starklab.slu.edu/humanUV.htm

So presumably the red cone sensitivity falls back to nearer that of
the green in this region, and the blue cone sensitivity falls off more
rapidly than both red and green.

Putting it another way, relative to green and blue cone sensitivities,
red cone sensitivity has a little hump in the violet region in
addition to its big hump in the green to red region.

-- Dave

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
> Dave,
>
> You wrote:
>
> "What gives hue perception it's apparent circularity is the posession
> of exactly three different colour receptors. Other animals have more
> or less, and many humans have less. With only two receptors, hue is
> binary (i.e. there are exactly two hues, no continuous ranges at all).
> With four receptors, hue maps to the surface of a sphere."
>
> I don't get it. Why should hue be binary with only two kinds of
> colour receptors? If, like most cetaceans, you had only two kinds,
> and can't see blue, that means that deep water is effectively black
> to you, rather than the deep blue that human deep-sea divers see.
> (See? :-) ) But that doesn't mean you can't distinguish between
> different proportions of red and green. Dolphins, for example,
> can certainly see yellow fish - which is interesting, because most
> fish can't!

The references I have looked at say that cetaceans have only one kind
of cone receptor.

"And because there is only one type of cone,
they are essentially colorblind (although in theory it is
possible that there is a very limited form of colorvision
in some light conditions, when both the rods and the cones
are active)"

It seems uncontoversial to claim that a true monochromat can have no
experience of hue or saturation (white/grey-ness, tinted-ness,
pastel-ness), but only intensity (lightness, brightness).

But consider human dichromats who are missing the "red" receptor
(whose sensitivity peak, by the way, is actually in the yellow-green
part of the spectrum, very close to that of the "green" receptor).

Now you _could_ argue that it is the saturation that they are missing
out on, rather than the continuous range of hues. You could say that
when they look at a solar spectrum they see a continous change in hue
from one end to the other. But doesn't this seem a little unnatural,
since it is clear that somewhere near the middle of that spectrum,
possibly where trichromats would see cyan, they would experience a
"hue" that is indistinguishable from the original unseparated white
(or grey), and white and greys and black are normally considered to be
of indeterminate hue (but zero saturation).

So it makes more sense to me to say that what they see when going from
one end of the spectrum to the other is one hue (say blue) that starts
out saturated and decreases in saturation until it reaches white, and
then increases in saturation again with a different hue, call it
yellow (or red, or green). Or maybe it would be better to call these
two hues "cool" and "warm".

But of course I'd love to hear from an english-speaking true dichromat
as to whether this makes any sense to them. And of course there is
potentially all kinds of stuff about philosophy of language and
meaning, and neuro-anatomy mixed up in this. Way off-topic.

> Anyway, with respect to music, I rather like the idea of
> contemplating a green C ...

As we live a life of ease
everyone of us has all we need
skyE of blue and C of green
in our yellow suBbmarine

-- Dave Keenan

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > ...
> > I'm was at first a little confused by your distinction between
violet
> > and purple, which I've always considered to be more or less
> > synonomous. ...
> ...
> But the shortest visible wavelength is definitely violet, by
> definition. Consider that the slightly shorter invisible wavelengths
> are universally called "ultra-violet".

Yes, good point.

> One website suggested that to see spectral violet, take a CD (not a
> CD/R) and look at the reflection of a flourescent light in it. When
I
> do so, it definitely doesn't look blue, and it is definitely on the
> "other" side of blue from cyan, but it doesn't look as saturated as
> the violet I remember in some lines on a screen in a darkened
physics lab.

Yes, I've also tried that previously. A similar thing I experienced
recently was when I was wearing a pair of glasses (actually flat
plastic) with diffraction lines. Looking at a fluorescent light
source, I saw multiple images clearly separated from one another, one
of the images was a pure yellow, and the image at the short end of
the spectrum was definitely violet (not blue).

> But either way, the best approximation to them on a computer screen
is
> obtained by adding a small amount of red to blue.

Yes. I'm just disappointed that the blue color in the lower left
part of the figure doesn't seem to contain any appreciable amount of
red.

> > If our eyes were sensitive to a full octave of hue, I think we
might
> > find appearances somewhat different.
>
> As you probably know, octaves (and harmonics generally) are fairly
> irrelevant to colour perception, involving as it does, the particle
> nature of light, rather than the wave nature. There is no special
> reason that the human range is near an octave, actually it's more
like
> a subminor seventh. Other animals have wider and narrower ranges.
>
> What gives hue perception it's apparent circularity is the posession
> of exactly three different colour receptors. ...

Yes, especially taken in combination with this observation you
mentioned in your next message:

> The reason for the "warmth" of spectral violet and the reason it is
> best approximated in an RGB system by adding a small amount of red
to
> blue, is not due to any sort of "octave equivalence". It seems to
be
> due to the fact that the response curve of the red cones happens to
> have an inflection in it at around what we call the blue/violet
> transition, and this leads to the red cones being slightly more
> sensitive than the green cones again in the violet region of the
> spectrum, as they are in the green to red part.
>
> See the logarithmic response curves about 1/3 of the way through
> http://www.handprint.com/HP/WCL/color1.html

Wow, that's the most comprehensive explanation of color vision I've
ever seen! I'm especially intruigued by the "opponent processing of
color" section beginning about halfway through, and ending with the
revelation that, because the retina reprocesses the trichromatic data
gathered by the cones into w/k, r/g, and y/b channels, "the mind
never 'sees' the trichromatic outputs." 8-O

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...>
wrote:
> ...
> > Anyway, with respect to music, I rather like the idea of
> > contemplating a green C ...
>
> As we live a life of ease
> everyone of us has all we need
> skyE of blue and C of green
> in our yellow suBbmarine

Cute! But why not make that second line something like this:

Each hears notes in all (s)he sees.

--George

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> > But either way, the best approximation to them on a computer
> > screen is obtained by adding a small amount of red to blue.
>
> Yes. I'm just disappointed that the blue color in the lower left
> part of the figure doesn't seem to contain any appreciable amount of
> red.

There seems to be a lot of confusion about what the spectrum line
should do at the violet end, on the chromaticity diagram. This has
only become clear to me in the last few days, based on the aphakic's
description of UV-A as unsaturated blue.

The short wavelength end of the spectral line on the chromaticity
diagram should actually have a small right-hand hook, going first to
the right (towards red) and then (for aphakics) it continues to curve
back up again (towards green). There is no contradiction in having the
spectral curve finish in the _interior_ of the chromaticity diagram
(i.e. on an unsaturated colour). The set of possible hues is simply
the convex hull of the spectrum, on the chromaticity diagram. So the
purple line goes from the extreme red point to meet the "violet hook"
at a tangent.

The violet hook is the result of that little extra relative hump in
the "red" cone response at the short wave end.

That Wikipedia chromaticity diagram is pretty good in that regard
http://upload.wikimedia.org/wikipedia/en/4/40/Cie_chromaticity_diagram_wavelength.png
but I must agree with you that the 380 nm point ought to be a little
more obviously "around the corner" towards red.

It would seem a curious coincidence if the cutoff caused by the UV
opacity of our lenses coincided exactly with the tangent point of the
chroma closure line (the purple-line) on the spectrum curve.

> > What gives hue perception it's apparent circularity is the posession
> > of exactly three different colour receptors. ...
>
> Yes, especially taken in combination with ["the red cones become
> slightly more sensitive than the green cones again in the violet
> region of the spectrum"].

It's a common misconception that this extra "violet hump" in the red
cone response is necessary for the circularity of hue. But if you
think about it, it should be clear that this is not the case. Imagine
if we had evolved with the same three cone response curves but with
our lenses having a short wavelength cutoff at around 460 nm instead
of 380 nm. The extra red "hump" would then be irrelevant and there
would be no spectral violet. But what do you think you would see when
you mixed various amounts of spectral red and spectral blue light?

Surely you don't think that all such combinations would be black (or
white, or shades of grey). Surely a blue with a little red is going to
appear "redish-blue" and red with a little blue is going to appear
"blueish red" or at least it must produce _some_ kind of smooth
continuum of hues from blue to red, that is quite different from the
spectral ones that go around the "other side" via green.

The red cones' "violet hump" isn't necessarily an evolutionary
adaptation, it may simply be that the simplest way to evolve a
suitable protein for a red receptor happens to give it this "hump",
and since it is not detrimental it stays.

I put "hump" in scare quotes to remind you that in absolute terms
there is no hump, only a region where the response falls off with a
slope less than that of the green cones.

> I'm especially intruigued by the "opponent processing of
> color" section beginning about halfway through, and ending with the
> revelation that, because the retina reprocesses the trichromatic data
> gathered by the cones into w/k, r/g, and y/b channels, "the mind
> never 'sees' the trichromatic outputs." 8-O

Yes. But that's kind of a funny way of putting it. Why should the last
layer of retinal neurons be considered any less a part of the "mind"
than the first layer of cortical ones they transmit to? I find that a
combination of buddhist psychology (e.g. Ken Wilber's "No Boundary")
and materialist philosophy (Daniel Dennett's "Consciousness
Explained") helps me to understand this. But now I'm getting way off
topic.

> Cute! But why not make that second line something like this:
>
> Each hears notes in all (s)he sees.

Good idea.

As we live a life of ease
we hear music in all we see
skyE of blue and C of green
in our yellow suBbmarine

Thanks Paul McCartney.

-- Dave Keenan

Colors and sounds, our visual range is an octave!

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗hstraub64 <hstraub64@telesonique.net>

🔗George D. Secor <gdsecor@yahoo.com>

🔗Can Akkoc <can193849@yahoo.com>

🔗George D. Secor <gdsecor@yahoo.com>

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗George D. Secor <gdsecor@yahoo.com>

🔗Afmmjr@aol.com

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗George D. Secor <gdsecor@yahoo.com>

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗George D. Secor <gdsecor@yahoo.com>

🔗amcmechan <amcmechan@donerus.com>

🔗George D. Secor <gdsecor@yahoo.com>

🔗George D. Secor <gdsecor@yahoo.com>

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗amcmechan <amcmechan@donerus.com>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗George D. Secor <gdsecor@yahoo.com>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗George D. Secor <gdsecor@yahoo.com>

🔗Dave Keenan <d.keenan@bigpond.net.au>