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Old 09-17-2015, 12:42 PM
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Terezian Analysis: (tuh REE zhun)

The consistent and rigorous analysis of pieces of music as abstract objects using the various metrics developed by Terez and other Theorylanders. Terezian analysis is often used to precisely describe various aspects of music in quantitative terms, and was the first such discipline to allow definitive comparisons between various pieces of music.


I think it would be so cool if we could get a respectable method together in time to be included as an appendix in Terez's Chopin book (though, obviously, only if it is up to Terez's standards).

In any case, I have some thoughts on both the structure and the metrics, based largely on the info Terez provided in the other thread. I started this one because that thread was quickly becoming unwieldy.

I do have some questions though:
Are there degrees of consonance and dissonance? Is there a consensus on whether or not two different 'points' of music are more or less dissonant?

What if two instruments are playing dissonantly, while two singers are singing harmoniously/consonantly (forgot the specific jargon)? They don't cancel each other out, right? They play off each other?

Can we ignore lyrics, and just treat vocals as another kind of instrument? Because rigorous analysis of lyrics or poetry seems counterproductive to me (and calls to mind that scene from Dead Poets Society).

Can we use some statistical methods, provided that the results they provide are consistent and repeatable?


In any case, finding the metrics to rigorously describe the properties you listed seems very doable to me.
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Old 09-17-2015, 01:31 PM
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Well we can't really ignore lyrics or at least not completely. It's the passion aspect. It will not be easy to define or measure, but ignoring the passion in music would be like comparing a pair of corpses and making conclusions on who was the better person. For the most part we can reduce the lyrics to a collection of syllables and ignore the meaning of the words, but in many cases it is the message of the song that the performers and composers are passionate about and the meaning of the lyrics is an important part of that message. The poetry part shouldn't be ignored and nor should it be given extra attention.

On the question on harmony. It's important to devise a method for measuring this, but the results must always be valued in context. Sometimes dissonance is intentional.

At this point I think the evaluation should be in two parts. First the vision or idea behind the musical piece and second how well it is executed. The motive and the act as it were.
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Old 09-17-2015, 05:13 PM
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Well we can't really ignore lyrics or at least not completely. It's the passion aspect. It will not be easy to define or measure, but ignoring the passion in music would be like comparing a pair of corpses and making conclusions on who was the better person. For the most part we can reduce the lyrics to a collection of syllables and ignore the meaning of the words, but in many cases it is the message of the song that the performers and composers are passionate about and the meaning of the lyrics is an important part of that message. The poetry part shouldn't be ignored and nor should it be given extra attention.
Presumably the fields of poetry and music theory already have tools to provide some sort of qualitative analysis on lyrics. What Terez wants is some quantitative tools to supplement (not replace) current evaluation methods.

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On the question on harmony. It's important to devise a method for measuring this, but the results must always be valued in context. Sometimes dissonance is intentional.
I don't doubt it. And I'm not advocating imposing qualitative judgments on the results our metrics might provide. I'm just saying we give academic musicians a way to assign a value (or list of values) to describe how harmonic (or otherwise) a particular bit of music is. Think of it like giving art professors a tool to measure how 'green' something in a painting is. How they apply that information will be up to them, we'll just give them a reliable tool to get that info.
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At this point I think the evaluation should be in two parts. First the vision or idea behind the musical piece and second how well it is executed. The motive and the act as it were.
When you say executed, do you mean as in a specific performance? My general idea for describing the 'skeleton' of some piece of music would include a few parameters (and a few results). Basically, I'd want to take some given 'error' value and find the smallest group of curves (with regression analysis) that describes some music with variance less than or equal to the given error value. So, you could take two pieces of music and a relatively low tolerance for error to get two groups of curves that describe their corresponding music with the same level of precision. You could compare the number of curves, and find out what song is more 'complex' in a sense. You could compare the curves themselves, to get some other information.

New metrics (questions and answers) will be added on later by people as needed, but if we can give them the basic rules and structures, we will help Terez revolutionize music theory.
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Old 09-17-2015, 05:28 PM
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When you say executed, do you mean as in a specific performance?
Call it the ideal performance. The one every performance aims to be. How well that matches the intended message or vision.
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Old 09-18-2015, 12:04 AM
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Terezian Analysis: (tuh REE zhun)...
The 'rez' part rhymes with the first syllable of "resident" etc.

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I think it would be so cool if we could get a respectable method together in time to be included as an appendix in Terez's Chopin book (though, obviously, only if it is up to Terez's standards).
An appendix is already the plan, though I'm not sure I will settle on anything by the time this book is written. I could certainly weave this into the narrative of my book, and for now the outline of the book assumes that course, but the topic of the book is almost completely separate.

I have to ask, though: what makes you think that, as a non(-trained)-musician, you could help me figure it out? It's very difficult for me to explain this stuff to non-musicians. I will try, but we're barely scratching the surface here.

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I do have some questions though:
Are there degrees of consonance and dissonance?
Yes, according to the interaction of the notes' frequencies. In a historical sense, however, it depends on how consonance and dissonance are defined, and this history informs the modern understanding of music theory. Now, for a very brief history of music:

Our modern understanding of music derives in large part from the Ancient Greek understanding of music. The Greeks had their own system of writing music. It was not passed down through the Dark Ages, but we can decipher it, in the very rare instances when notated music survives, because many musico-theoretical treatises and commentaries survive.

Only a few pieces survived in any form, often fragmentary like the Delphic Hymns. The Epitaph of Seikilos is the oldest surviving complete piece of music. What you hear at the beginning of the video—the melody—is all that was written down (along with lyrics). The arrangement and accompaniment are interpretations, ideas about how the song might have actually been performed, informed by research.

It was apparently the Greeks who discovered the ratios of "perfect" intervals (the octave, the fifth, and the fourth) as measured on a string. The circle of fifths (F-C-G-D-A-E-B-F#-C#-G#-D#-A#/Bb-F) gives the 12 tones we still use today. (The reverse gives you the circle of 4ths; as intervals, they are inversions of one another, supplementary parts of the octave.) The Greek modes are the basis for the scales we use today.

The only problem is that the perfect 3:2 ratio extrapolated this way does not quite reach the F seven octaves above the first. This discrepancy is called the Pythagorean Comma. Historically this has been compensated for in various ways.

We have no written music from the Dark Ages. Modern written music was born in the Roman Catholic Church during the Carolingian Renaissance. The monks and scribes of the church were the ones who kept the ancient Roman and Greek philosophers and historians alive, and therefore Church music was based on ancient Greek musico-theoretical writings. They did not have the Delphic Hymns or the Epitaph of Seikilos. They only had the theoretical writings.

Since Church people tend to view everything in terms of divinity, they had a special affection for the "perfect" intervals, but they also used their own interpretation of the Greek modes. For hundreds of years, they only sang unaccompanied plainchant in Church modes. (This video even shows how it was written with early neumatic notation, but after Guido d'Arezzo invented the four-line staff. Before that, they used heightened neumes, a very relative and inexact form of notation.)

When they began to experiment with polyphony in the late Middle Ages, they treated "perfect" intervals as consonances, and other intervals as dissonances. This thinking began to change (though, last in the Church itself, as always) when the Contenance angloise infected the European continent. English music incorporated the 3rd and the 6th as consonances, which has more to do with the overtone series (a physical phenomenon) than the mathematical theoretical basis of Greek music ("perfect" ratios). However, with small adjustments to the Pythagorean comma, the overtone series and the Greek modes/modern scales work together perfectly.

The ability to tolerate dissonance in music is seen, in academic music, as a progressive phenomenon. Like many notions of progress, I am not sure this one is veritable in the simple way it is often interpreted. It assumes that music will become ever more dissonant, and that the ability to enjoy ever increasing dissonance is a musically enlightened state. Hence modern academic music.

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Is there a consensus on whether or not two different 'points' of music are more or less dissonant?
In academic music, yes. That last link, for example...no one would argue it lacked constant, unrelenting and unresolved dissonance. It's just a question of whether or not one enjoys listening to it.

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What if two instruments are playing dissonantly, while two singers are singing harmoniously/consonantly (forgot the specific jargon)? They don't cancel each other out, right? They play off each other?
Dissonance can certainly be contextualized. I mentioned before that the tritone, incidentally the halfway point of the octave—the farthest apart two tones can be—is an unambiguously dissonant interval. This is the interval the violin plays at the beginning of la Danse macabre de Saint-SaŽns, in alternation with a perfect 5th. The dissonance is resolved with a V-i tutti going into the flute melody. The V-I progression is by and far the most common musical cadence, or resolution, in Western music. Almost every song ends with it. One relatively common exception (still rare) is the plagal cadence, also called the "Amen cadence" (IV-I). It is the chords the choir sings at the end of a hymn that ends with "Amen".

The common 7th chord, however, incorporates the tritone. For example, a G7 chord is spelled G-B-D-F. The interval between B and F is a tritone (a perfect 5th would be Bb-F or B-F#). By itself, it sounds grating (another example is in the South Park theme song, where the guitar plays dissonant minor 2nds and tritones throughout). In the context of the dominant 7 chord, it doesn't sound so grating, but it is still considered a dissonant chord that must be resolved.

Chopin's F-major prelude is often remarked-upon because it ends on a dominant 7 chord (I7), which causes a musician to think that it will continue in the key of Bb (which is where an F7 chord would typically resolve). (This is probably because Chopin intended it to be played as a prelude to a piece in Bb; another mystery of Chopin is why he called his preludes "preludes". Preludes to what? Well, the answer appears to be, to whatever you want, assuming a logical key relationship.)

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Can we ignore lyrics, and just treat vocals as another kind of instrument?
Yes. The relationship between lyrics and music will always be fairly abstract.

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Can we use some statistical methods, provided that the results they provide are consistent and repeatable?
Yes.

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In any case, finding the metrics to rigorously describe the properties you listed seems very doable to me.
Doable, but perhaps not as simple as you expect.
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Old 09-20-2015, 08:48 PM
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I'll reply in more detail later, but if you're asking for a sort of pre-mortem (to judge my grasp of the viability of this thing), I foresee three serious issues:

First is a sort of institutional arrogance may hinder any kind of serious adoption. I don't know the community here, but when people brought serious math into baseball, it took a while to catch on. Same thing with Wall Street. People who pride themselves on their 'gut' or intuition have not traditionally offered these kinds of things any kind of a warm reception.

Second is utility. If there already is a consensus on the answers to the questions you are after, there may not be much perceived need for these metrics. Not to mention the fact that this will be a discipline of mathematics that only one person in the world (you) will really 'get' at first.

Third is computing power. This discipline still has a somewhat vague shape in my mind, but I can see the basic structure, and you will need weeks of computing time on even a reasonably fast (personal) computer to get the numbers on even a small selection of musical works. Now, certain variables are still up in the air, and it may be that certain speedups are possible. But it's also possible that these 'unknowns' push the computing time into a realm that is largely 'unfeasible'.
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Old 09-21-2015, 07:02 AM
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I'll reply in more detail later, but if you're asking for a sort of pre-mortem (to judge my grasp of the viability of this thing), I foresee three serious issues:

First is a sort of institutional arrogance may hinder any kind of serious adoption. I don't know the community here, but when people brought serious math into baseball, it took a while to catch on. Same thing with Wall Street. People who pride themselves on their 'gut' or intuition have not traditionally offered these kinds of things any kind of a warm reception.
I think institutional arrogance goes with the territory in academia. It's not really a consideration for me in terms of viability; it's only something to consider in the approach.

I assume you are talking about stats with baseball, but I often use an analogy to the physics of baseball when describing musical talent. Good pitchers are rarely physicists, and they don't have to have a mathematical understanding of the physics to utilize natural laws and pitch well. But their talent can be analyzed scientifically. And it's also an art form, because every good pitch has measurable differences.

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Second is utility. If there already is a consensus on the answers to the questions you are after, there may not be much perceived need for these metrics.
I don't believe this will be the case. An example: most music students are expected to be able to write a fugue. This is indescribably difficult for most of us. The tools we are given to aid us in this ambition are woefully inadequate, and students who do complete the assignment invariably write bad fugues. The rubric is generally pretty forgiving.

I mentioned earlier that in the 20th century music academia came to elevate highly dissonant music as an enlightened art form. That's an oversimplification, though; specifically they came to reject functional harmony as a lingua franca of music. An oft-repeated argument is that functional harmony is predictable.

I don't believe this is quite true. In my counterpoint class, we were given fugue subjects written by Bach. Our final project was to extrapolate a fugue from one of those subjects. I assure you, none of us were able to "predict" a fugue based on those subjects, and it's not because we weren't a good class. My professor couldn't have done it. No one alive could have done it.

Bach himself composed a work called The Art of the Fugue, in which extrapolates 14 fugues and 4 canons from the same subject. And it was left unfinished when he died. Functional harmony is not predictable simply because there are rules.

Fugues are like a logic puzzle where there are several paths one can take at each juncture, and several junctures. There are an infinite number of ways to do it wrong, and a finite (yet vast) number of ways to do it right.

Atonal music dispenses with the rules, such that anyone with a basic understanding of music could write a fugue.

These strict contrapuntal forms are mostly just intellectual exercises, though. If anything, it makes the music more obscure and less likely to be enjoyed by someone without musical training. I say "mostly" because repetition is part of what makes music enjoyable, so it's possible to use that to your advantage. Bach was more successful in doing that with strict counterpoint than any other composer, but many believe his free forms (still using the rules of functional harmony, of course) are in general more enjoyable to listen to.

There are certainly exceptions among Bach's fugues. For example, it's hard to see how this fugue is hampered in any way for being a fugue. Anaiya, who is a violinist, does not care for this girl's "Romantic" performance. She recommended this guy. I would personally prefer something in between.

Anyway, the utility of being able to write a fugue is that it exposes the limits of one's understanding of functional harmony, pushes one's own limits. I think all of us would prefer to understand it better, with less headache.

I didn't finish my final project for Counterpoint. I didn't want to write a bad fugue, and I felt it was a violation of my musical principles to be forced to do so. And I developed a real mental block about it. However, my prof was a nice guy and he allowed me to substitue a graduate Bach seminar I had taken. I barely finished my final project in that class, too, because I chose the above-linked fugue as my analysis project, and right before it was due I discovered the structure of the piece was defined largely by continuous descending lines (in one voice at all times). So I had to completely redo it, and I left out a lot of little things he had asked for. I adapted Schenkerian analysis to describe the phenomenon of the descending lines, and in doing so I broke a bunch of Schenker's rules, which cost me points because I didn't understand Schenker.

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Not to mention the fact that this will be a discipline of mathematics that only one person in the world (you) will really 'get' at first.
It is my hope that I will be able to explain it in simple terms. That is the whole point.

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Third is computing power. This discipline still has a somewhat vague shape in my mind, but I can see the basic structure, and you will need weeks of computing time on even a reasonably fast (personal) computer to get the numbers on even a small selection of musical works.
I don't think so. There are a lot of variables, but the processes should be relatively simple once I figure out the shorthand.
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Old 09-21-2015, 07:08 AM
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Fugues are like a logic puzzle where there are several paths one can take at each juncture, and several junctures. There are an infinite number of ways to do it wrong, and a finite (yet vast) number of ways to do it right.
So a quantum computer could easily produce all possible good fugues in an hour or so. Now if only anyone ever managed to build an actual working quantum computer ...
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Old 09-21-2015, 02:19 PM
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So a quantum computer could easily produce all possible good fugues in an hour or so. Now if only anyone ever managed to build an actual working quantum computer ...
It actually sounds beyond a QC tbh, it sounds like an NP-Complete problem (since music is closer to a natural language than something with a lot of algebraic structure).

Of course, to show that it's in NP (and not PSPACE), recognizing a fugue has to be relatively straightforward.

In any case, my expectation is that we can get the metrics in sub-exponential time (and once Terez looks over the first batch and gives us some idea which are worth computing and which are not, we can cut the computing time down a bit more, though only by a constant factor). Still, sub-exponential is a pretty big hurdle, and I'm not sure what you mean by shorthand. If you mean something like (d/dx)f(x) (iow, writing the expression for something like dissonance variance and period in resolution epsilon without actually computing the value), that's doable. But I was under the impression that the specific values of the results were what was going to be used (in fact my idea for the appendix would mostly be akin to the log tables of old).
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Old 09-25-2015, 11:07 AM
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Sorry if this is raining on the parade, but I'm a natural skeptic and this is not clicking for me. My fundamental problem with this idea is probably something you've (Terez) heard before: how to quantify or put quantifiable parameters for purely subjective evaluations of music. I don't know anything about music theory, but I'm a lifelong fan of music and a musician (I play the drums, so I use the term "musician" loosely ). I'm really struggling with the concept of applying rigorous methods to something as squishy and subjective as the quality of a piece of music.

There was a comparison made to using Terezian Analysis versus sabermetrics in baseball. I don't mean to be patronizing here, but the difference is that sabermetrics are purely objective and statistical. There's nothing qualitative about it. Each "advanced statistic" is calculated by a formula. Formulas are underpinned with certain assumptions, i.e. a "quality start" means a pitcher completed six innings and gave up three or fewer earned runs. I personally think the value of sabermetrics/"advanced statistics" in sports is questionable, but at least they're quantitative measures being applied to objective performance. Unless there's some aspect of them that I'm missing, I should say. I don't claim to be an expert at them.

Personally, I think the intersection of applying quantitative tools and rigorous analysis to subjective/qualitative outcomes is one where academics really has fertile ground to develop some interesting techniques. Maybe this is one of those. But unless I'm really missing the point here, this seems like a misapplication of various approaches. I'm not saying it can't be done, nor am I saying that you shouldn't pursue it. I'm open to being convinced. There's just something missing here as far as I can tell.
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Old 09-25-2015, 11:22 AM
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Sorry if this is raining on the parade, but I'm a natural skeptic and this is not clicking for me.
It's not surprising, so no worries.

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My fundamental problem with this idea is probably something you've (Terez) heard before: how to quantify or put quantifiable parameters for purely subjective evaluations of music.
That's not my mission.
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Old 09-25-2015, 11:38 AM
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Wouldn't it make more sense to set up a purely objective evaluation anyway?

A first quantity that could be measured accurate enough would be the loudness of the sound.
Now that you have a start, I'm sure you can do the rest easily; after all, it is always the beginning that is hardest.
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Old 09-25-2015, 11:48 AM
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Originally Posted by GonzoTheGreat View Post
Wouldn't it make more sense to set up a purely objective evaluation anyway?
That is my mission, to codify what can be objectively codified. Perhaps it will help academic musicians explain why they have judged their music the height of their art, but musical taste will always be subjective (though I suspect there would be some correlation between musical taste and musical ability, which can be measured even in people who have no musical training). And, as stated before, that's only one consideration for why I want to do this; another consideration is what implications the physics of music might have for our understanding of natural laws.
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Old 09-25-2015, 11:51 AM
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... though I suspect there would be some correlation between musical taste and musical ability ...
If true, then I would have no musical taste whatsoever.
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Old 09-25-2015, 12:23 PM
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If true, then I would have no musical taste whatsoever.
It seems to me that people without musical ability have other primary reasons for liking the music they do. But it's possible that the physics of music affects even people without much ability. Study would be required to make any real determinations to that effect, a vast survey of musicians and non-musicians on their musical tastes, along with a test of their ability. It wouldn't even need to be blind.
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Old 09-25-2015, 08:28 PM
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Exactly what is "ability" here, terez?
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Old 09-25-2015, 08:55 PM
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That is my mission, to codify what can be objectively codified. Perhaps it will help academic musicians explain why they have judged their music the height of their art, but musical taste will always be subjective (though I suspect there would be some correlation between musical taste and musical ability, which can be measured even in people who have no musical training). And, as stated before, that's only one consideration for why I want to do this; another consideration is what implications the physics of music might have for our understanding of natural laws.
Not sure how similar linguistics would be to what you are studying, but have you ever heard of Gorgias, Terez? Gorgias was convinced that the sounds of words could be used to hypnotize the audience and thus to persuade them. He was apparently so skilled at this that he was blamed with being the father of sophistry. His writing definitely had a musical quality to it which apparently won him great fame in antiquity, though to be honest, I found it somewhat unpleasant to the ear when we read him in grad school. His Encomium of Helen was interesting though. This also calls to mind the concept of the Golden Line.
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Old 09-25-2015, 10:12 PM
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Exactly what is "ability" here, terez?
Put simply, the ability to distinguish musical tones from one another. Also, the ability to sing in tune (not necessarily with a pretty voice), the ability to sing by ear (copy a tune), the ability to play by ear if one has facility with an instrument, on up to the ability to write music from ear (dictation) and sight-sing (for the musically literate). In other words, there are various ways to measure it depending on how much training the person has.

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Not sure how similar linguistics would be to what you are studying, but have you ever heard of Gorgias, Terez? Gorgias was convinced that the sounds of words could be used to hypnotize the audience and thus to persuade them. He was apparently so skilled at this that he was blamed with being the father of sophistry. His writing definitely had a musical quality to it which apparently won him great fame in antiquity, though to be honest, I found it somewhat unpleasant to the ear when we read him in grad school. His Encomium of Helen was interesting though. This also calls to mind the concept of the Golden Line.
I am familiar with the name, but I don't remember where I encountered it. Perhaps in the short study of ancient rhetoric which we covered in music history classes, but that feels wrong to me. I think his name might have been mentioned in some kind of song or choral work. I remember learning the pronunciation (like Gorgeous, right).

PS: I found it. I accompanied a voice student who had to sing this for his juries:

https://www.youtube.com/watch?v=34r4a1O3McI
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Old 09-25-2015, 10:43 PM
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Originally Posted by Terez View Post
Put simply, the ability to distinguish musical tones from one another. Also, the ability to sing in tune (not necessarily with a pretty voice), the ability to sing by ear (copy a tune), the ability to play by ear if one has facility with an instrument, on up to the ability to write music from ear (dictation) and sight-sing (for the musically literate). In other words, there are various ways to measure it depending on how much training the person has.


I am familiar with the name, but I don't remember where I encountered it. Perhaps in the short study of ancient rhetoric which we covered in music history classes, but that feels wrong to me. I think his name might have been mentioned in some kind of song or choral work. I remember learning the pronunciation (like Gorgeous, right).

PS: I found it. I accompanied a voice student who had to sing this for his juries:

https://www.youtube.com/watch?v=34r4a1O3McI
The pronunciation by that opera singer is odd. It isn't like gorgeous. Both "g"s need to be hard, like in gorgon. Think Gorg - e - as, or almost like Gorg - e -ass, but not quite as long of an s sound as that. Plato really disliked him, but his style was very influential. Not sure how helpful he would really be for you, but he was trying to do something similar in linguistics. His style also somewhat calls to mind a similarity to symmetry studies on beauty.
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Old 09-25-2015, 10:47 PM
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It appears to be a different Gorgias anyway.
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