# recognise an octave and a quality of tone [meaning]



## dual light

Hello,
The following is from "Dialogue : The Art of Thinking Together" and it is difficult for me to exactly understand the logical connection of the last sentence with the preceding ones, especially in the meaning of "an octave" and "a quality of tone." Could I have your kind comment on this? 

"Joachim-Ernst Berendt points out that the ear is the only sense that fuses an ability to measure with an ability to judge. We can discern different colours, but we can give a precise _number_ to different sounds. Our eyes do not let us perceive with this kind of precision. An unmusical person can recognise an octave and, perhaps once instructed, a quality of tone, that is a C or an F-sharp."


----------



## Myridon

An octave in this context is a note that are an octave above another note.  A person not particularly trained in music can recognize that a C and a C one octave higher are the same and that a C and an F# are not the same.
From the Word Reference dictionary at the top of the page.


> 1. the  interval between two musical notes one of which has twice the pitch of  the other and lies eight notes away from it counting inclusively along  the diatonic scale
> 
> *2. one of these two notes, esp the one of higher pitch*


----------



## Kevin Beach

"Octave" comes ultimately from the Latin word _Octo_, meaning "Eight". In music, an octave is a range containing eight standard notes.

The most common example is the key of C, which can be played on a piano using white notes only, with no black notes.

In English the sequence is C D E F G A B C, the last note having the same name as the first note but sounding an octave higher.

The human ear and brain have an inate sense about the relevance of musical notes to each other, which is why some combinations of notes sound beautiful to us while others sound ugly. The notes in the standard octave are the most harmonious, at least to the western ear and to others who have experienced a lot of western music.


----------



## entangledbank

A note of twice the frequency of another is an octave higher: for example, A at 440 Hz and the next A, at 880 Hz. These sound harmonious together, because if one was not an exact multiple of the other you would hear 'beats' as their frequencies got 'out of step'. Exact multiples don't get out of step, so octaves are easy for anyone to hear.


----------



## dual light

Myridon said:


> An octave in this context is a note that are an octave above another note.  A person not particularly trained in music can recognize that a C and a C one octave higher are the same and that a C and an F# are not the same.


Thanks, Myridon.
Now I understand that "can recognize an octave" means "can recognize that a C and a C one octave higher are the same.
Can I have your further explanation about "a quality of tone, that is a C?" Does it mean something like a unque frequency of a C itself?


----------



## bennymix

Adding to the excellent piece by entangled.    The point of the quote is that some precision based in numbers (the physics of sound; acoustics) is in the ear's sensory capability.   The capability of a precise "judgment" based in numbers (physics).     The ear can 'hear' the concord of middle *a *(*440*) and the octave higher* a (880)-*-i.e., the ear, so to say can hear "2 times."   In fact if the higher proposed *a* is off, by the amount 804, the ear can hear that: 4 beats per seconds.


Contrast with colors (these are analogies).   Of course we can detect hundreds of shades of green, as well as intensities, but can one say (for intensities, saturations),  "this is 2 times as green"?  Can one detect exactly '2 times,' and does that make sense.

On the spectrum, we can't exactly say, "Violet has 2 times the frequency of red," and the eye cannot pick the exact colors (here, violet and red) to match '2 times.' On the primary colors,  yellow has about 5/4  the frequency of red, and blue about 6/5 the frequency of yellow, but the eye can't 'see' the exact points.   See the colors of the spectrum and their frequencies at, e.g., http://en.wikipedia.org/wiki/Visible_spectrum

So color judgements have a qualitative element that isn't easily reduced to quantitative or physical terms.   The ear's capabilities, esp. if trained, can 'hear' the 3/2, 4/3 or 5/4 ratio (the perfect fifth, the fourth, and the major third.)  So the ear can judge in a way the eye can't, in respect of numbers.





dual light said:


> Hello,
> The following is from "Dialogue : The Art of Thinking Together" and it is difficult for me to exactly understand the logical connection of the last sentence with the preceding ones, especially in the meaning of "an octave" and "a quality of tone." Could I have your kind comment on this?
> 
> "Joachim-Ernst Berendt points out that the ear is the only sense that fuses an ability to measure with an ability to judge. We can discern different colours, but we can give a precise _number_ to different sounds. Our eyes do not let us perceive with this kind of precision. An unmusical person can recognise an octave and, perhaps once instructed, a quality of tone, that is a C or an F-sharp."


----------



## Myridon

dual light said:


> Thanks, Myridon.
> Now I understand that "can recognize an octave" means "can recognize that a C and a C one octave higher are the same.
> Can I have your further explanation about "a quality of tone, that is a C?" Does it mean something like a unque frequency of a C itself?


No, he's not saying that a non-musical person can recognize a C - that's called perfect pitch which would require a rare talent or lots of training.  There is a similarity in the sound (what other posters are explaining in terms of objective "intervals of frequency" and the author calls a subjective "quality of tone") that makes a note that is an octave away from a starting note recognizable.  If I played any two random notes, (almost) any person could tell whether they were an octave or not (C-C or D-D or ...).  It would take some training to recognize an augmented fourth (C-F# or D-G# or ...) as something other than "not an octave."


----------



## bennymix

The author's analogy is not so apt applied to a single note.   Yes, the ear can be trained to detect the 440 *a*, plus or minus a couple percent.     One can develop an ability without 'perfect pitch.'

But *a* as 440 is rather arbitrary, and used to be *a*=400.

Looking at the spectrum, here, in terms of wave length,   http://www.chm.davidson.edu/vce/coordchem/spectrum.jpg

there is a nice red at about 650 (nm).     And note that's kind of arbitrary.   Your choice for 'exact red' might not match mine.  *Maybe the eye could be trained to detect just that 650 red.  *Maybe the eye could be trained to see if the new red was 660 (tiny bit less yellow?) or 680?   I don't know.


----------



## dual light

Myridon said:


> It would take some training to recognize an augmented fourth (C-F# or D-G# or ...) as something other than "not an octave."


It seems that as I don't know well about music, it is rather difficult to understand your explanation completely. 
The meaning of "a quality of tone, that is a C or an F-sharp" is not yet clear to me. Does "a C or an F-sharp" mean "augmented fourth (C-F#)" in your comment?


----------



## dual light

bennymix said:


> The ear's capabilities, esp. if trained, can 'hear' the 3/2, 4/3 or 5/4 ratio (the perfect fifth, the fourth, and the major third.)


As I wrote in the question to Myridon, the meaning of "a quality of tone, that is a C or an F-sharp" is still unclear to me. Could I have your further explanation about what a quality of tone means and what "a C or an F-sharp" means? I am sorry for this redundant question.


----------



## Myridon

Notes, pitches, tones, frequencies are all related.  There is a quality (Word Reference dictionary: "a distinguishing characteristic, property, or attribute") related to the tone (pitch, frequency) of two notes which are an octave apart which allows a non-trained person to answer the question: Are these two notes an octave or not?


----------



## dual light

Myridon said:


> Notes, pitches, tones, frequencies are all related.  There is a quality (Word Reference dictionary: "a distinguishing characteristic, property, or attribute") related to the tone (pitch, frequency) of two notes which are an octave apart which allows a non-trained person to answer the question: Are these two notes an octave or not?


I am afraid that there is some misinterpretation on my part about the sentence "An unmusical person can recognise an octave and, perhaps once instructed, a quality of tone, that is a C or an F-sharp"

What I understood is as follows:
(1) An unmusical person can recognise an octave.
(2) An unmusical person can recognise, perhaps once instructed(or trained), a quality of tone, that is a C or an F-sharp.

But according to your explanation, it seems that a quality of tone is almost something like an octave. If so, I don't understand why "once instucted" is added. 
Could I have your further advice on this? I am sorry for the repeated questions.


----------



## bennymix

Every note, I suppose, has a quality.   As I said in post #8, though, notes, like colors don't have an absolute reading in waves/per second.   The situations are comparable.  *a* has frequency 440 is no more true or accurate that saying red's wavelength is 650 nm.

It's the relative, not the absolute positions that are hearable;  that's the core of the analogy.  I don't see why one would say '*a*' has a special quality, in absolute terms, when a couple hundred years ago, that frequency would be called *a* sharp.   Once *a *(or some note) is set as the base (tonic), then the special qualities of "2 times" and "3/2 times" (*e* above *a*) can be heard by amateurs.






dual light said:


> As I wrote in the question to Myridon, the meaning of "a quality of tone, that is a C or an F-sharp" is still unclear to me. Could I have your further explanation about what a quality of tone means and what "a C or an F-sharp" means? I am sorry for this redundant question.


----------



## bennymix

Let us not lose sight of theOP's cited author's main point. 





> the ear is the only sense that fuses an ability to measure with an ability to judge.



I tried to explain that in post #6.    Sound judgments about concondance have clear basis in math--ratios expressible in low integers.   Color judgments about concordance  "This green goes nicely with that yellow" cannot be explained so simply--e.g. the green's frequency is 6/5 that of the yellow.

So our sound perceptions have more an element of 'judging by numbers,' that is, very simple ones.  They are clearly and simply related to physics.  Color perception and 'judgements' about 'what goes together' do not accord with judgment by numbers;  color judgements while ultimately based in physics, have a subjective element, one might say.


----------



## dual light

bennymix said:


> So our sound perceptions have more an element of 'judging by numbers,' that is, very simple ones.  They are clearly and simply related to physics.  Color perception and 'judgements' about 'what goes together' do not accord with judgment by numbers;  color judgements while ultimately based in physics, have a subjective element, one might say.


I noted your comment on judgement by numbers. The concept is very new to me, so it's not very easy to follow you.
Anyway I will summarize my understanding as follows and could you tell me whether my understanding is correct or not?

(1) A note has a quality of tone, but the quality is not absolute but relative.
(2) A C has a quality of tone and an F-sharp also has a quality of tone. Their qualities are relative.
(3) If an unmusical person is trained, he can recognize the quality of tone, an F-sharp in comparison with a C.


----------



## Myridon

If one note and another note sound "nice" together in a particular way (a quality of tone), it means that there is a particular corresponding mathematical relationship between the frequencies of the two notes.  An octave is an example of one of those relationships.  The combination of the two notes in the octave has a particular quality that is related to the fact that the frequency of the higher note is twice that of the lower note.  The combination of two notes in an augmented fourth has a different quality that is related to the mathematical relationship between those two notes. The combination of two notes in a fifth has ...
If one color and another color look "nice" together in a particular way, it has nothing to do with the frequency of the two colors of light or any other objective measurement.  Vision is purely subjective.  
A C note sounds good with a C note an octave higher for everyone.  Not everyone likes sage green with lavender purple.


----------



## dual light

Thank you everyone, especially bennymix and Myridon, for the nice and long explanation.
Actually, I was a little frustrated by my musical ignorance yesterday. I studied musical terms a little further today and now it seems I understand your comments a lot more than yesterday.
What I understand now is that I need to approach the meaning of "quality of tone" with the concept of concord. 
This understanding leaves me the last question to be solved, about which I need your further assistance.

In the expression "quality of tone, that is a C or an F-sharp," I'd like know whether the "C" means something like C major, not just a C note. 
The reason I ask this question is that if the "C" means just a C note, I think it would be difficult to apply the concept of concord to "quality of tone."
I hope this will conclude this thread and thank you in advance for your further advice.


----------



## a passerby

Probably not... but "quality of tone" is not a common phrase as it's being used here. It's up to the writer to define what they mean by it.

Without the context you've provided, I would have assumed it to mean the same thing as _timbre_ (which is actually sometimes called _tone quality_); but the author isn't using it that way, and frankly I don't know what he _did_ mean. I suspect we may not have guessed what he meant by "octave", either: he might even have meant "an octave of a major scale, played in sequence"!

Ultimately, if you want details, I think you'd be better off consulting whatever work by Joachim-Ernst Berendt he's referencing (probably _Nada Brahma − die Welt ist Klang_) -- or, better yet, a modern music theory textbook. I suspect this sentence is unrelated to the author's real thesis, anyway -- it sounds to me like he's just referencing someone obscure to make himself sound more intelligent, and worse, has partially garbled the information he was trying to repeat.


----------



## Thomas Tompion

Hello Dual light,

I think your question is very difficult because I'm not certain that Mr Berendt is sure what he's saying himself.

The point is that many unmusical people can certainly recognise an octave, but no unmusical people I know could  'recognise' a C or an F-sharp.  Being able to recognise an individual note without an tonal point of reference is a gift rare even amongst musicians and is called 'perfect pitch'.  Most musicians can easily relate one note to another, but struggle unless given a starting point.  I knew a conductor who told me in confidence that if he held his nose and blew, his ears whistled a G sharp to him.  He could relate all other notes to this, and thus gave people the impression he had perfect pitch. He asked me not to tell anyone this: he died ten years ago, so I don't feel I'm betraying a confidence, and, anyway, I haven't revealed his name.

This raises questions about what Mr Berendt can mean by 'quality of tone'.  Given that he's talked about numbers in relation to sounds, and that people have understood this, probably correctly, to refer to the relationship between the number of vibrations and the musical note, I am left wondering what he can mean by 'quality of tone'.

Apart from anything else 'quality of tone' doesn't usually refer to a particular note, but to the purity or otherwise of the tones and overtones when a given note is played: an oboe has a different 'quality of tone' to a flute.

If, as you say, you are not very familiar with the language of musical analysis, I think you should at least take this last remark to be strictly meaningless, which is how I regard it, and go on to consider the relation of the other things he says to the general flow of the argument about the differences between the senses.

I hadn't seen A Passerby's excellent analysis of this when I wrote this post.  I see we give rather similar advice.


----------



## dual light

Thanks for your comment, a passerby and Thomas Tompion.
I note some discrepancy between you and other posters.
So I am rather confused but thanks for the opportunity to see from another perspective.


----------



## cyberpedant

I highly recommend Helmholtz's _On the Sensations of Tone as a Physiological Basis for the Theory of Music_.


----------



## Myridon

Thomas Tompion said:


> I am left wondering what he can mean by 'quality of tone'


As I've tried to say several times, he's referring to an attribute of the sound made by two notes played together like resonance (he's not using "tone" in the sense of "a single pitch").  An octave has a quality that sounds "clean" while a second sounds "dischordant", a minor third sounds "sad", etc.  When the ear hears that perfectly "clean" quality of the two notes, you know that they are an octave apart which incidentally means that their frequencies are related.  When the eye sees two colors that "strike a chord" , there is no corresponding relationship between their frequencies.


----------



## Thomas Tompion

Myridon said:


> As I've tried to say several times, he's referring to an attribute of the sound made by two notes played together like resonance (he's not using "tone" in the sense of "a single pitch").  An octave has a quality that sounds "clean" while a second sounds "dischordant", a minor third sounds "sad", etc.  When the ear hears that perfectly "clean" quality of the two notes, you know that they are an octave apart which incidentally means that their frequencies are related.  When the eye sees two colors that "strike a chord" , there is no corresponding relationship between their frequencies.


What's your evidence for this, Myridon?  It doesn't seem to be evident from the quotation in the OP.

I'm not saying that you are wrong, but wondering how you came to form your view.


----------



## bennymix

Hi Myr,
I don't think you've got it quite right, here.

The author cited in the OP said,


> "Joachim-Ernst Berendt points out that the ear is the only sense that fuses an ability to measure with an ability to judge. We can discern different colours, but we can give a precise number to different sounds. Our eyes do not let us perceive with this kind of precision. An unmusical person can recognise an octave and, perhaps once instructed, a quality of tone, that is a C or an F-sharp."



As I commented, in post #8,
"The author's analogy is not so apt applied to a single note. Yes, the ear can be trained to detect the 440 a, plus or minus a couple percent. One can develop an ability without 'perfect pitch.'"

---
Upon re reading, I think the author just means that some people are born with 'perfect pitch' and others can acquire a degree of it, that is recognize a particular note, e.g. a' 440, or the c" above, on the piano 523.3 cps.    

These notes do have quality, and I don't think he means 'timbre' which relates to complexity and presence of other notes, overtones, etc.

My point, above, though, is that even if some can learn, and some have this, there is no 'objective' a, the note.



> For example, a tuning fork associated with Handel, dating from 1740, is pitched at A = 422.5 Hz, (info) while a later one from 1780 is pitched at A = 409 Hz, (info) almost a semitone lower.[



http://en.wikipedia.org/wiki/Concert_pitch

The relation of a' to a" an octave higher, is objective.

Color perception is quite acute, but I'm not sure if anyone has been trained to recognize, say, a prototypical 'red' and say "Oh that's the wavelength of 650 nm."

The twelve notes in the standard scale might be recognizable for our era, but the case of colors seems more complicated.   There are more, so to say.  Even were the 12 notes divided twice as finely, that would be 24 quarter tones in the octave.  How many colors are between red and violet.

Colors have not been standardized, and when they have been, it's not by numbers.    One does say "3 primaries" but I don't see an easy numerical basis.   And if 3 is privileged, how many are there beyond 3? 6, 9, 12, 27?

There are reasons that scales have 5 (making the octave, the sixth) or 7 notes (making the octave, the eighth), and not 6 (which would make the 'octave' the seventh).    So the author's point about judgments and relations to numbers holds somewhat for individual notes, but it's not so compelling, in my opinion.   In a sentence, assessment of sounds, most esp. of their consonance are rooted in numbers,  esp low ratios, in ways that assessments of colors are not.

=======


Myridon said:


> As I've tried to say several times, he's referring to an attribute of the sound made by two notes played together like resonance (he's not using "tone" in the sense of "a single pitch").  An octave has a quality that sounds "clean" while a second sounds "dischordant", a minor third sounds "sad", etc.  When the ear hears that perfectly "clean" quality of the two notes, you know that they are an octave apart which incidentally means that their frequencies are related.  When the eye sees two colors that "strike a chord" , there is no corresponding relationship between their frequencies.


----------



## EStjarn

Can we agree that _that is_ in the topic sentence means _say_?_.
_An unmusical person can recognise an octave and, perhaps once instructed, a quality of tone, say, a C or an F-sharp.
.
​If so, I think the contextual meaning of _quality of tone _stands out clear, however unsuitable the term itself might be to produce it.


----------



## Thomas Tompion

It's not clear to me from the context, EStJ.

  What do you think it means, a note, or a chord?


----------



## EStjarn

Providing we can understand _that is_ as _say_, as proposed above, I would definitely take it to mean a note.


----------



## bennymix

Well, let's agree it doesn't sound as if the "C" passage refers to an interval.   But dual, in post #17 did raise another possibility, which, upon reflection, would make more sense.   {Sorry I did not take this suggestion more seriously when I first read it.    }Perhaps C refers to the key of C.   This is standard musical notation, with the capital  (I have been using small letters for notes).   It's a well known bit of musical lore (sometimes challenged**), that each key has a particular color  (metaphorically) or mood or spirit.   So if you're going to write a hunting song, you might pick A.

This solves the problem that lots of people cannot pick out an individual note, an a=440, though it can be trained to some extent.    

Here is what Wiki says, under 'equal temperament' (with some allusion to the controversy about 'colors' or moods for keys).


> J. S. Bach wrote The Well-Tempered Clavier to demonstrate the musical possibilities of well temperament, where in some keys the consonances are even more degraded than in equal temperament. It is reasonable to believe that when composers and theoreticians of earlier times wrote of the moods and "colors" of the keys, they each described the subtly different dissonances made available within a particular tuning method. [...]. (Correspondingly, there is a great deal of variety in the particular opinions of composers about the moods and colors of particular keys.)



I'm not sure people are interested in the details, but he's saying that, for example, the fifth might be purer(closer to the ratio of 3/2)  in some keys than another, according to the non-equal temperament chosen.   And to varying degrees of impurity correspond various 'colors' or moods.   This is consonant (!) with the general discussion of interval as perceived.   I believe the above is the correct solution to the problem. 

Listen to Bach's _Well-Tempered Clavier_ and report back!  



===
**The challenge, in part, comes from the issue of well tempering the scale, so that *every* semitone is higher in frequency by (multiplying) the twelfth root of two. * a* times 1.059... equals* a *sharp.

==

Dual light in post#17 said,


> Thank you everyone, especially bennymix and Myridon, for the nice and long explanation.
> Actually, I was a little frustrated by my musical ignorance yesterday. I  studied musical terms a little further today and now it seems I  understand your comments a lot more than yesterday.
> What I understand now is that I need to approach the meaning of "quality of tone" with the concept of concord.
> This understanding leaves me the last question to be solved, about which I need your further assistance.
> 
> In the expression "quality of tone, that is a C or an F-sharp," I'd like  know whether the "C" means something like C major, not just a C note.
> The reason I ask this question is that if the "C" means just a C note, I  think it would be difficult to apply the concept of concord to "quality  of tone."
> I hope this will conclude this thread and thank you in advance for your further advice.


----------



## Thomas Tompion

EStjarn said:


> Providing we can understand _that is_ as _say_, as proposed above, I would definitely take it to mean a note.


But anyone with a bit of musical experience knows that no unmusical person can recognise a C or an F-sharp.

We've agreed, at least a lot of us seem to have, that even some very musical people are unable to do that.

Of course, that may not mean that you've misinterpreted Dr Berendt, ESJ; the good doctor may just have been spouting pickled cabbage.


----------



## EStjarn

I like your theory in isolation, bennymix. But I don't think we can disregard the fact that neither the book (preview here) nor the chapter is about music: the chapter title is _Listening_, the section title is _The sense of hearing_. We have stumbled on a few sentences that use music to make a point about hearing. How much understanding can the author expect his readers to possess with regard to music theory? A minimal amount, I would guess. I agree with those who feel the author doesn't know much about music theory himself.


----------



## bennymix

I believe the issue of the 'colors' or 'moods' of keys, under non-equal temperament is the answer.   And it's a well known bit of musical lore that is likely known by the author cited (Berendt), and somewhat grasped by the main author, Isaacs.

I agree, Estjarn, the Isaacs book is about dialogue and understanding.    He grasped at a musical analogy, apparently, to make a point about the role of judgement in perception.   Presumably he is going to say that when A talks to B, and hears B's response, there is--according to the music analogy-- some judgment involved.   This is my shakey inference, but I imagine he is going to say that if A hears B say, (about an issue in dispute) "I will look into the matter!"  and if A perceives B's remark as hostile, that is possibly NOT objective.   A judgment is involved, and it can be a wrong one.


----------



## EStjarn

Thomas Tompion said:


> But anyone with a bit of musical experience knows that no unmusical person can recognise a C or an F-sharp.



As hinted above, I think we need to think simple here. What if _or_ is a typo_:__.
_An unmusical person can recognise an octave and, perhaps once instructed, a quality of tone, say, a C from an F-sharp.
_._​On a twelve-tone scale, C and F-sharp are about as different in pitch as two notes can be. It would not seem an insurmountable task to learn to distinguish one from another even for an unmusical person.


----------



## bennymix

Yes, ES, that is a simple possibility; sometimes the most economical one (yours) makes the most sense.  

The sentence  





> An unmusical person can recognise an octave and, perhaps once instructed, a quality of tone, that is a C or an F-sharp."



 Reconconstructing, assuming no typo, but ellipses:

_An unmusical person can recognise an octave and, perhaps once instructed, [recognize or discern] a quality of [a] tone, that is [whether it's] a C or an F-sharp."

==
_The problem is that this does not provide a *contrast* to the situation with colors.   One can tell a *c *from and* f *sharp, and can tell yellow from green.     Same kind of thing!


----------



## Thomas Tompion

dual light said:


> [...]"Joachim-Ernst Berendt points out that the ear is the only sense that  fuses an ability to measure with an ability to judge. We can discern  different colours, but we can give a precise _number_  to different sounds. Our eyes do not let us perceive with this kind of  precision. An unmusical person can recognise an octave and, perhaps once  instructed, a quality of tone, that is a C or an F-sharp."





EStjarn said:


> [...]What if _or_ is a typo_:__.
> _An unmusical person can recognise an octave and, perhaps once instructed, a quality of tone, say, a C from an F-sharp.
> _._​On a twelve-tone scale, C  and F-sharp are about as different in pitch as two notes can be. It  would not seem an insurmountable task to learn to distinguish one from  another even for an unmusical person.


I sense three problems with that:

1.  He's said we can discern different colours, which seems to me like telling the difference between one note and another.  Yet he's saying that the senses differ in this regard.
2.  He can't be so naive as not to know that different colours have different wavelengths, just as different notes have different fundamental frequencies.
3.  If you're going to say that people can tell one note from another, why talk about 'quality of tone' which A Passerby very sensibly interpreted as referring to _timbre?_

If you're going to have to rewrite as much as you seem to feel necessary, I think you should admit that the original is gibberish, and declare open season for a guessing game.


----------



## JamesM

The "or", in my opinion, excludes the possibility of an interval.  I think "quality of tone" was a poor choice of words, personally.  It has too many meanings in the context of music and none of them have to do with pitch.  I lean more towards Thomas Tompion's gibberish theory than anything else.


----------



## bennymix

Here is some material that might interest some, on coloration of keys, which I think is what Berendt refers to

http://en.wikipedia.org/wiki/Key_coloration 



> It should be noted that the key of the piece ... contributes an indefinable something to the evocative quality. This is very difficult to put into concrete terms, but slow movements in A-flat major do have something in common, as do fast movements in C minor, concerto allegros in D major, etc. There has been disagreement on this point.[...]. Many musicians, however, tend toward an empirical acceptance of specific moods associated with specific keys, regardless of changes in pitch standards and other factors.


   from White, John D. (1976) The Analysis of Music, p. 94.

==============
http://www.wmich.edu/mus-theo/courses/keys.html
from Christian Schubart's Ideen zu einer Aesthetik der Tonkunst (1806)



> *C Major*
> Completely Pure. Its character is: innocence, simplicity, naivety, children's talk.
> *C# Minor*
> Penitential lamentation, intimate conversation with God, the friend and help-meet of life; sighs of disappointed friendship and love lie in its radius.
> *D Major*
> The key of triumph, of Hallejuahs, of war-cries, of victory-rejoicing. Thus, the inviting symphonies, the marches, holiday songs and heaven-rejoicing choruses are set in this key


====
http://web.archive.org/web/20080213173415/http://www.library.yale.edu/~mkoth/keychar.htm   {much interesting mat

From Tom Douglas Jones, _The Art of Light & Color_, 1972:
p. 103: Dr. D.S. Myers, a psychologist who talked with Scriabin, said, 





> “Sriabin’s attention was first seriously drawn to his colored hearing owing to an experience at a concert in Paris, where sitting next to his fellow countryman and composer Rimsky-Korsakoff, he remarked that the piece to which they were listening (in D major) seemed to him yellow; whereupon his neighbor replied that to him, too, the color seemed golden. Scriabin has since compared with his compatriot and with other musicians the color effects of other keys, especially B, C major, and F-sharp major, and believes a general agreement to exist in this respect.



==============
From http://www.thereminvox.com/story/28?page=5

Athanasius Kircher system of correspondences between musical intervals and colors


> octave: green
> seventh: blue-violet
> major: sixth fire red
> minor: sixth red-violet
> [...]
> fifth: gold


----------



## JamesM

This is something that only appears after years and years of training, unless someone has kinaesthesia or perfect pitch.  The original statement starts with the premise that this is an _unmusical_ person.  I know graduates with degrees in music performance who couldn't identify one key's "color" over another.  In fact, I've known brilliant pianists who have accidentally started and played through an entire piece in the wrong key, only catching the error mid-performance.  If key color were an easy thing to pick up they would know in the first bar that the color was off.

This is not something an unmusical person can pick up "perhaps, once instructed".  I think the sentence is evidence of someone not being very careful in his explanation because of a lack of expertise in the area.

These are all very interesting theories and topics for discussion but I don't see any relation between them and the original post.


----------



## Thomas Tompion

I fully agree, James.

We may be dealing with a poor translation, of course.


----------



## bennymix

Hi James,
You say, 





> In  fact, I've known brilliant pianists who have accidentally started and  played through an entire piece in the wrong key, only catching the error  mid-performance.  If key color were an easy thing to pick up they would  know in the first bar that the color was off.



The problem is that you're choosing the situation most favorable to your (apparent) preference.   The equally tempered piano especially guarantees NO (classical or baroque) coloration of keys.  Further you are discussing persons likely trained on these instruments who never had choices, so to say.   The ear becomes accustomed to the compromises, and one key is pretty much like another. 

There are some nice examples on Youtube of Chopin played in unequal temperament, and discussing why he chose keys like C sharp minor.

Many people do not know that probably Bach's 'Well Tempered Klavier' pieces were NOT equal tempered by modern standards.  Hence those pieces performed on baroque tuned keyboards do have color.

In these cases, it's highly unlikely that a trained keyboardist would switch key and not notice.

If anyone wants some urls, he or she can PM me.

One would need to talk to violinists and oboists about color since their instruments don't make it impossible.   Same for singers.
The preference of violinists for Pythagorean tuning is well known.   Some nice Youtube material is available here.

The point here is not to argue so much as to make sense of a passage, the most obvious (after prolonged debate) interpretation is that first intervals are discussed, then keys, as indicated by the capital letters. (Issues depending on perfect pitch do not fit into the argument.)   As well, already mentioned is that Isaacs, the immediate author may NOT have grasped the issues as Berendt surely did, and hence imprecisely expressed himself.

I have not read Berendt, but he was a noted music theorist and musicologist, who esp. wrote about jazz.  Apparently the gist of his books such as _The World of Sound,_ and _The Third Ear _is very much in accord with the idea that the ear and hearing are special senses, especialy rich senses into which jugments (with numerical basis) are built in.   Hence it's not suprising that Isaacs latched onto Berendt, in trying to relate perception to understanding.




JamesM said:


> This is something that only appears after years and years of training, unless someone has kinaesthesia or perfect pitch.  The original statement starts with the premise that this is an _unmusical_ person.  I know graduates with degrees in music performance who couldn't identify one key's "color" over another.  In fact, I've known brilliant pianists who have accidentally started and played through an entire piece in the wrong key, only catching the error mid-performance.  If key color were an easy thing to pick up they would know in the first bar that the color was off.
> 
> This is not something an unmusical person can pick up "perhaps, once instructed".  I think the sentence is evidence of someone not being very careful in his explanation because of a lack of expertise in the area.
> 
> These are all very interesting theories and topics for discussion but I don't see any relation between them and the original post.


----------



## EStjarn

Thomas Tompion said:


> If you're going to have to rewrite as much as you seem to feel necessary, I think you should admit that the original is gibberish, and declare open season for a guessing game.



I don't feel the sentence makes sense as it stands. However, I do think the author meant something with it, and it is this something that I'm trying to discern. I am therefore looking outside the boundaries that the normal meanings of words put on an interpretation.

I notice that in the preceding part of the chapter (about 3 pages), there are two long quotations, taking up about 3/4 of a page. This might explain why the author chose not to quote but to paraphrase Berendt.1

This is from an article by Berendt (ReVISION, 1987), apparently written some four years after the publication of _Die Welt ist Klang:_.
The ability of the ear to differentiate is much more highly developed than that of the eye. [...] We are familiar with hundreds of optical illusions but so few "acoustical illusions" that the term does not exist. There are people (not only among musicians) who have absolute pitch, but nobody -- not even a Leonardo or a Picasso -- ever had "absolute hue." "The ear can measure, the eye can only guess," is a standard sentence in many physiology textbooks, but one that might be difficult to accept in our aggressive culture of overemphasis on the eye and under emphasis of the ear.
.​I think that is what the paragraph we're focusing on is about: challenging the notion that vision would be more astonishing than hearing.

What I believe now the author tries to do in the topic sentence is to make a parallel with the previous remark "the ear is the only sense that fuses an ability to measure with an ability to judge." His example seems to include first a measurement (the octave, no judgment involved), and then a judgment (C, F-sharp). Surely, with some training we can learn to distinguish those notes _providing we have a reference pitch_. (I will not assume the author is referring to perfect pitch.)

I think that's as far as we can expect this easygoing read to want to take us on its quick visit to the land of music theory.

1 The text has a misspelling of Berendt's title: it's supposed be _Nada Brahma_, not _Nada Brohmn_ (cf. Amazon.com.) This could indicate that someone else typed the manuscript for Isaacs, the author, or that he wasn't very familiar with the book.


----------



## Thomas Tompion

EStjarn said:


> [...]What I believe now the author is trying to do in the topic sentence is to make a parallel with the previous remark "the ear is the only sense that fuses an ability to measure with an ability to judge." His example seems to include first a measurement (the octave, no judgment involved), and then a judgment (C, F-sharp). Surely, with some training we can learn to distinguish those notes _providing we have a reference pitch_. (I will not assume the author is referring to perfect pitch.)


Many thanks for this, EStjarn.

I'm sorry to say that I'm none the wiser.  Here are some of my problems about it:

1.  How does recognising an octave 'include a measurement'?
2.  How does recognising a quality of tone, in contrast, 'include a judgement'?
3.  If by 'distinguish a note' you mean be able to give the note its name when you hear it, then even with a 'reference pitch' you should not expect an unmusical person to 'distinguish a note'.  Some quite musical people aren't very good at it.
4.  I've read quite a bit of musical theory, and not often come across writing so apparently nonsensical as Dr Berendt in this translation.


----------



## bennymix

One line of the Isaacs original was :"Joachim-Ernst Berendt points out  that the ear is the only sense that fuses an ability to measure with an  ability to judge. We can discern different colours, but we can give a  precise _number_ to different sounds. 

Measurement and judgment are fused for the ear.    So there is no dichotomy or contrast as your 1. and 2. imply (your reading of EStjarn, not necessarily your view.)

Hearing an octave means you say, "This is a true octave"   easy enough for most people to hear and learn to hear.
At the very moment you decided it's true, you've 'measured' in the sense that you've determined that the ratio of frequencies is 2:1.  There is some interesting material on the major third, on you tube, and how and when it sounds 'sweet.'  At the moment you say, "That's the sweetest," a judgment that is shared, by the way, you have determined that the ratio of frequencies is 4:3.  You have implicity 'measured.'




Thomas Tompion said:


> Many thanks for this, EStjarn.
> 
> I'm sorry to say that I'm none the wiser.  Here are some of my problems about it:
> 
> 1.  How does recognising an octave 'include a measurement'?
> 2.  How does recognising a quality of tone, in contrast, 'include a judgement'?
> 3.  If by 'distinguish a note' you mean be able to give the note its name when you hear it, then even with a 'reference pitch' you should not expect an unmusical person to 'distinguish a note'.  Some quite musical people aren't very good at it.
> 4.  I've read quite a bit of musical theory, and not often come across writing so apparently nonsensical as Dr Berendt in this translation.


----------



## EStjarn

Thomas Tompion said:


> 1.  How does recognising an octave 'include a measurement'?



If we are able to recognize an octave, then we are able to infer something about the frequency of one sound in relation to that of the other. That would be the measurement here.


Thomas Tompion said:


> 2.  How does recognising a quality of tone, in contrast, 'include a judgement'?



As I think we have all agreed, the phrase _a quality of tone_​ cannot be taken literally; it is apparently a misnomer. I would suppose Isaacs means _recognise a tone_. In order to do that, most of us will need to have a reference pitch. From that pitch we can assess a tone. I understand _judge_ to mean _assess _here.


Thomas Tompion said:


> 3.  If by 'distinguish a note' you mean be able to give the note its name when you hear it, then even with a 'reference pitch' you should not expect an unmusical person to 'distinguish a note'.  Some quite musical people aren't very good at it.


Well, Isaacs qualifies his statement with _perhaps once instructed_. I suppose it could be read two ways: (i) some unmusical persons need instruction to do it but most do not; (ii) some unmusical persons may be able to do it after having been instructed. I think the sentence is actually saying (i) but means (ii).


Thomas Tompion said:


> 4.  I've read quite a bit of musical theory, and not often come across writing so apparently nonsensical as Dr Berendt in this translation.



Isaacs, Senior Lecturer at MIT Sloan School of Management, is apparently paraphrasing, however ineptly, something he's read in _The World of Sound_, ie. the translated version of _Die Welt ist Klang_ (1983) by Berendt. I would not hasten to blame either Berendt or the translator for the confusion here.


----------



## Thomas Tompion

EStjarn said:


> If we are able to recognize an octave, then we are able to infer something about the frequency of one sound in relation to that of the other. That would be the measurement here.[...]


Thanks again.

I, and I'm sure I wasn't unusual in this, could recognise an octave long before I knew anything about, or would have thought of inferring anything about, frequencies of sound.

I'd have been mystified if anyone had suggested I was 'measuring' anything.

I just heard what seemed to me to be the same note at a different level.


----------



## wandle

dual light said:


> "Joachim-Ernst Berendt points out that the ear is the only sense that fuses an ability to measure with an ability to judge. We can discern different colours, but we can give a precise number to different sounds. Our eyes do not let us perceive with this kind of precision. An unmusical person can recognise an octave and, perhaps once instructed, a quality of tone, that is a C or an F-sharp."


To understand the meaning of the text as written, as a matter of interpreting the English, it seems to me that three questions matter: (1) what is the author's basic point? (2) what is the meaning of the illustration which he offers in support of that point? and (3) how is that illustration expressed in the actual wording he has chosen to use?

Let me answer these in turn, as I see it.
 (1) His basic point is that our hearing can both distinguish numerically identified perceptions and judge their quality, whereas other senses cannot combine these abilities.
 (2) In his illustration he is saying (a) that even an unmusical person can perceive the correspondence between one note and another which is an octave higher and (b) that such a person may, once instructed, be able to tell the difference between a C and an F-sharp.
(3) He expresses these two abilities by describing (a) as 'recognising an octave' and (b) as 'recognising a quality of tone'. I understand the latter as meaning that the unmusical person, once instructed, may be able to tell not only that C and F are different notes, but that F-sharp has a different quality of tone from a natural note. 

Identifying that C and F are different notes involves detecting a difference which is measurable numerically. 
Identifying the difference between F and F-sharp involves judging a quality.

Even an unmusical person (meaning presumably one with no particular musical talent) may, with training, become able to exercise both these skills in combination.


----------



## dual light

I'd like to thank you all for valuable comments, from which I've learn a lot.


----------



## bennymix

Hi Wandle,

With all due respect, some of what you say just  doesn't hold up.   It's possible that that's what Isaac's meant, but is  confused.  It's unlikely what Berendt meant, since he knew music.

Let's look at this piece in particular:


> (3) He expresses these two abilities by describing (a) as 'recognising  an octave' and (b) as 'recognising a quality of tone'. I understand the  latter as meaning that the unmusical person, once instructed, may be  able to tell not only that C and F are different notes, but that F-sharp  has a different quality of tone from a natural note.
> 
> Identifying that C and F are different notes involves detecting a difference which is measurable numerically.
> Identifying the difference between F and F-sharp involves judging a quality.



I  can't conceive the unmusical person detecting the 'sharp' quality of  F#(on a modern, standard piano).   What does that mean "not a natural  note"-- just that it's not a white key on the piano.   How in the world  would this person 'hear' such a thing?   (I'm not sure that most musical  persons, if lacking perfect pitch, and dealing with an equal  temperament, standard  20th century piano, can hear a note and say  'that's a black note [sharp or flat]') If you mean 'natural' in some  other sense, F# is as 'natural' as any other of the 12 tones in the  expanded octave.

Surely, for an unmusical person, it's *distance*  between notes that he can make out.   If EStjarn and you are correct,  then the author simply means "Once you're about four notes [C scale]  apart, the untutored can learn to make it out."    In that case the  author could equally pick F, F#, or G to make his point.    The  untrained might have trouble, on the other hand with 'close' notes like C  and C#, or C and a quarter tone 'off' version of C.

But here is  the real rub.  If the untrained can tell notes at least a fourth (C-F)  apart, yes that has a numerical basis.   *But then there is no contrast  with the color case.*   Most people can tell yellow from green;  they  are sufficiently different and the frequencies are quite different,  percentage wise.

That's why my conclusion is that keys must be  being spoken of, at least in Berendt.   *Then* the choice of F# would  make sense:  apart from modern 20th c. piano, the *key* of F sharp has a  quality, as Chopin and others (Bach) appreciated.  I wouldn't stake my  life that I can teach the unmusical that qualitative difference, but he  *might* be able to say,  "it does feel different, more poignant."




wandle said:


> To  understand the meaning of the text as written, as a matter of  interpreting the English, it seems to me that three questions matter:  (1) what is the author's basic point? (2) what is the meaning of the  illustration which he offers in support of that point? and (3) how is  that illustration expressed in the actual wording he has chosen to use?
> 
> Let me answer these in turn, as I see it.
> (1) His basic point is that our hearing can both distinguish  numerically identified perceptions and judge their quality, whereas  other senses cannot combine these abilities.
> (2) In his illustration he is saying (a) that even an unmusical person  can perceive the correspondence between one note and another which is an  octave higher and (b) that such a person may, once instructed, be able  to tell the difference between a C and an F-sharp.
> (3) He expresses these two abilities by describing (a) as 'recognising  an octave' and (b) as 'recognising a quality of tone'. I understand the  latter as meaning that the unmusical person, once instructed, may be  able to tell not only that C and F are different notes, but that F-sharp  has a different quality of tone from a natural note.
> 
> Identifying that C and F are different notes involves detecting a difference which is measurable numerically.
> Identifying the difference between F and F-sharp involves judging a quality.
> 
> Even an unmusical person (meaning presumably one with no particular  musical talent) may, with training, become able to exercise both these  skills in combination.


----------



## wandle

bennymix said:


> Hi Wandle,
> With all due respect, some of what you say just  doesn't hold up.   It's possible that that's what Isaac's meant, but is  confused.


I cannot dispute that (I felt embarrassed re-reading later). I was trying to find some sense in the text, on the assumption that the mention of C and F-sharp is intended to illustrate the ear's ability to make a judgement, and to fuse judgement with measurement.

If we drop that assumption, then the reference to making a judgement becomes a mere en-passant remark (referring to a supposedly universal and unproblematic ability of any sense-perception) and we no longer have to find anything in the text to provide evidence either of the ear's ability to make a judgement or of its ability to fuse judgement with measurement.

Once that requirement is gone, then the whole excerpt is seen to be about the ear's ability to make measurements, and nothing else.
On this basis, the distinction he is making is between recognising an octave on the one hand and recognising a C or an F-sharp on the other hand.

Thus he is saying that even an unmusical and untrained individual can recognise an octave; and the same individual may, with training, come to recognise notes such as C or F-sharp. The point of this is simply to show that we all have the ability to make measurements with our hearing (identifying an octave or an individual note means that we have recognised a sound that is defined by a measured frequency; we do not need to know the frequency: merely naming the note correctly is the proof that we have recognised that frequency).

If that is all he means, though, why does he introduce the problematic phrase 'quality of tone'? I conclude now that he is simply trying to find an alternative term to show that in referring to C and F-sharp he is talking about something different from recognising an octave.


----------

