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Reflections before the beginning of the academic year #2764964
09/12/18 12:45 PM
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This is already the 47th year in general and the 38th year in Academy and college, during which I teach the course of jazz and pop harmony . And the further the time goes, the less I am satisfied. Even more than twenty years ago it became clear that the theme of harmony of any genre-classics, blues, jazz, pop, etc. should begin from the first moment with study of the overtones system . But how does this usually happen? There are no overtones ; first, the intervals are studied by counting halftones, tones, minor thirds, major thirds, and so on. Intervals are laid in abstract training circuits, divorced from the real sound, i.e. acoustics. Then come a turn of four triads - by the same method, by adding thirds. From the very first moment the most important qualities of intervals and chords are excluded: a measure of tension and dissonance. Without this music can not make even one step, especially jazz and pop (modern)! Here is a simple question for test ; and students who finished the academic course of harmony could not answer:
what is the hierarchy of dissonance of four triads and their inversions?

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Re: Reflections before the beginning of the academic year [Re: Nahum] #2764973
09/12/18 01:34 PM
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What a huge and complicated topic! I lectured in these concepts many decades ago. I will not try to answer, yet, your question, but offer two ideas.

First, from a historical point of view, music did start off as overtones, as early as 5000 years ago, perhaps longer, if some of the bone instruments found are accurately dated. Natural horns are all overtone based. Singers prefer to sing harmony, not intervals destroyed by Equal Temperament. It is only in the 20th Century that experiments begin by dispensing with overtone-based music altogether - 12 tone music, serial music, and the like.

Why we teach music from the begining as scales and not chords is a very interesting question.

Second, the idea of tension and/or dissonance is at the very core of all music, in my opinion. The concepts I taught always made reference to ‘tension’ and ‘relaxation’ in music as the defining characteristic of a musical line, whether melodic or harmonic. As you know, the idea of intervals as consonant or dissonant has changed over the past 1000 years. The major third was once considered a dissonant interval. In modern harmonically-based music, we think of a tritone as dissonant/tense and it wants to resolve/relax to a Major or minor chord.

But, in much modern atonal music, there is still tension and relaxation. What might be considered dissonant, a tritone for example, in harmonic music now becomes the relaxation/resolution reference point, and other, much more dissonant tone clusters form the tension elements that give the music direction.

With regard to triad-based four note chords, it is possible that the movement of bottom note of whatever inversion is used from one chord to the next determines that chords tensin/dissonance.

Just a few ideas to start off the discussion.

Last edited by prout; 09/12/18 01:36 PM.
Re: Reflections before the beginning of the academic year [Re: Nahum] #2765002
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Originally Posted by prout
What a huge and complicated topic!
Yes, I heard this from teachers many times. But this is the result of an ancient mumbo jumbo, which someone interested from harmonic police introduced into the method of traditional musical education. And since then it has become a religious dogma: learning overtones is very, very difficult - Bull !!! Only it took me 30 years to understand this ...
Of course, it should start with something simple. understandable even to the beginner in theory .
Our modern life is different because we have a choice in everything: what to eat, what to dress, on whom to marry, where to go on vacation ,what kind of dog to buy - a million opportunities. There are only two areas where we have no choice: who are our parents, and where does the study of harmony begin.

Syllabus of Classical Harmony

https://www.rcmusic.com/sites/default/files/files/S44_TheorySyl_2016_ONLINE_RCM_V2_F.PDF from page 13.


Syllabus of Jazz Harmony
http://www.jamesmiley.net/new/Teaching_files/MUSC%20239%20Syllabus%20F2013.pdf from page 2

Try to find the term "overtones" or "harmonics"; because I didn't find.


Overtone Tree



[Linked Image]


There is one inaccuracy: 7 on the top right should be 7# .



Last edited by Nahum; 09/12/18 03:07 PM.
Re: Reflections before the beginning of the academic year [Re: Nahum] #2765016
09/12/18 04:01 PM
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Adtually the word ‘harmonic’ occurs once in the jazz syllabus, but only in reference to ‘transcription’.

RCM graduates, from the large number of students I have worked with over the decades, know little or nothing about overtone structure and its relationship to how we create music. They know even less about overtone structure and its effect on an instrument’s tone, and nothing at all about the piano and its effect on overtones, namely, inharmonicity.

I like your overtone tree. That is a neat way of seeing the progression. Thanks for that.

Re: Reflections before the beginning of the academic year [Re: Nahum] #2765050
09/12/18 06:40 PM
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Originally Posted by Nahum

Here is a simple question for test ; and students who finished the academic course of harmony could not answer:
what is the hierarchy of dissonance of four triads and their inversions?



I do not believe there is a good answer to this question for several reasons ….

- dissonance can only be worked out in context. A chord sounds more or less dissonant depending upon the chords and melodies that suround it.
- dissonance can only be determined relative to experience. Someone who has only ever heard Mozart is going to have a different understanding of dissonance to somebody who spends their life listening to Cecil Taylor.
- intervals are just different from each other so comparing 4ths to 3rds is like comparing apples to pears. I cannot even say whether a minor third is more dissonant than a major third even in isolation let alone in the context of real music.

I know there are several theoretical ways to determine dissonance levels in chords but I always wonder what is the point of all that when you can just listen to the chord and decide for yourself based on how the chord sounds to you given its environment. That is what ears are for.

About overtones and the harmonic series I don’t really know. All musicians should know a little about the physics of sound but what exactly this has to do with the harmony I am not too sure, not that much I would guess given that equal temperament and even a 12 note scale are arbitrary cultural creations.
Learning harmony from the first principles of the harmonic series would be a bit like learning to play tennis by studying how muscles work - how the muscles function is obviously vitally important for playing tennis but one doesn’t have to be an expert in chemical synapses to be a great tennis player. Better to study some Bach chorales really imo.

Re: Reflections before the beginning of the academic year [Re: beeboss] #2765053
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I’ll let nahum answer about the dissonance question, but harmonics and harmony I can address.

Harmonics are generated by blowing a horn, bowing a string, or singing a single note. The harmonics extend infinitely, getting weaker in general as the pitch increases. Our system of western harmony evolved from those harmonics.

Take the note C. the first harmonic of is C, the second harmonic of C is C, the third harmonic of C is G, the fourth harmonic of C is C, the fifth harmonic of C is E, the six harmonic of C is G, the seventh harmonic of C is close to Bb, the eight harmonic of C is C, the ninth harmonic of C is D, the tenth harmonic of C is E.

From these harmonics and the rest, we derive the chords CEG, CEGBb, GBbD, and so on.

The piano does not produce harmonics, because the string is struck, not bowed. The same is true of guitar. The partials (the correct word for overtones) are inharmonic. Each partial in the series is slightly sharper than the one before it. There are no pure octaves on a piano. They must be tuned as a compromise between the beating partials each note produces.

Re: Reflections before the beginning of the academic year [Re: beeboss] #2765081
09/12/18 09:20 PM
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Originally Posted by beeboss



I do not believe there is a good answer to this question for several reasons ….

- dissonance can only be worked out in context. A chord sounds more or less dissonant depending upon the chords and melodies that suround it.
Those. you actually deny one of the key concepts in jazz harmony: harmonic tensions, with what I can not agree.


Quote
- dissonance can only be determined relative to experience. Someone who has only ever heard Mozart is going to have a different understanding of dissonance to somebody who spends their life listening to Cecil Taylor.
- intervals are just different from each other so comparing 4ths to 3rds is like comparing apples to pears. I cannot even say whether a minor third is more dissonant than a major third even in isolation let alone in the context of real music.
You want to go where I did not plan at all - a discussion in the field of psychoacoustics: whether dissonance is an acoustic (natural) or cultural phenomenon.

Quote
I know there are several theoretical ways to determine dissonance levels in chords but I always wonder what is the point of all that when you can just listen to the chord and decide for yourself based on how the chord sounds to you given its environment. That is what ears are for.
.
Sense, of course there is, otherwise Hindemith would not do this; first inside the intervals :
http://www.hindemith.info/en/life-work/biography/1933-1939/work/principles-and-categories/ - series 2

It did not give me much trouble in the first lesson of the course of harmony of jazz (for beginners) in college to prove the importance of acquaintance with the physics of sound, where hiding inside ... almost the entire course of harmony ; as an answer to the question "Why do we need to know this?" But with a remark about the ears completely agree! Only I open before the student  1. the possibility of the choice of alternatives, which he/she is completely deprived of in above syllabuses and 2. permission to play with them, as with cubes, which the syllabus does not provide.
Here is a brief concept:
The overtone tree, of infinite height, consists of a central trunk consisting in its turn from the drone of lower overtones 1 - 5, and all the others are located on the branches higher and higher. The higher the new overtone is, the greater the charge of dissonance (tension) it carries within itself.
The drone is a harmonic cage (but not John smile ), which makes it possible to build from 5 to 7 variants of three- pitches structure , where each of four usual triads is only a fragment.
Thus, the student's perspective on the chord concept is immediately expanded, even earlier than he gets the corresponding chord symbols for some of them. Instead of 4 cubes for the game, the beginner gets 7.

Re: Reflections before the beginning of the academic year [Re: Nahum] #2765125
09/13/18 04:14 AM
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A preliminary knowledge of the overtone system explains in the future the following:

Which pitches are acoustically closest to the chosen one;
What is the inversion of interval and inversion of chord;
What is an open and closed position of the chord;
What is a cluster ;
What is harmonic tensions , and what is their hierarchy ;
Where did the tonic and dominant come from;
Why sound of more and more lower intervals and chords in the closed position is less and less pleasing to the ear;
Which intervals and in which register more preferable as the basis of voicings , and which to a lesser extent ;
Why the distance between the internal voices of the chord should not exceed an octave, otherwise the sound will not be homogeneous;
Why in natural hierarchy the bass is at the bottom , the melody- at the top, and the chords between them .

This is only a small part of the questions, and into the field of arrangement I have not yet invaded ...

Re: Reflections before the beginning of the academic year [Re: Nahum] #2765136
09/13/18 05:56 AM
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Thank you Nahum, all this is interesting!

And I agree the overtone/harmonic series should be taught more up front. This is a chart that was given to me on the first day with my current teachers - a single page with the instructions: "This is how we want you to start thinking musically". It's like a unifying theory for all the tones. All of a sudden I could start thinking actively & intelligently about the sounds instead of just learning things in an academic/passive way.

From Most Consonant
————————
Perfect 8
Perfect 5
Perfect 4
Major 6
Major 3
Minor 3
Minor 6
Minor 7
Major 2
Major 7
Minor 2
Tritone
————————
To Most Dissonant


We are the music makers,
And we are the dreamers of dreams.
Re: Reflections before the beginning of the academic year [Re: Nahum] #2765137
09/13/18 06:14 AM
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Groove On , this is precisely the scheme of Hindemith http://www.hindemith.info/en/life-work/biography/1933-1939/work/principles-and-categories/ . There is only one difference - for jazz ears: the tritone isn't the most dissonant interval, it is on the second place after the major seventh , in accordance with the side combinations of overtones.
My course is gradually leading to a fusion with elements of northern African music.

Last edited by Nahum; 09/13/18 06:23 AM.
Re: Reflections before the beginning of the academic year [Re: Nahum] #2765139
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Originally Posted by Nahum
[quote=beeboss]

- dissonance can only be worked out in context. A chord sounds more or less dissonant depending upon the chords and melodies that suround it.


Originally Posted by Nahum

Those. you actually deny one of the key concepts in jazz harmony: harmonic tensions, with what I can not agree.



I think you may be misunderstanding what I am saying. What I am saying is actually the opposite of what you appear to think I am saying. I am not denying harmonic tensions but rather that in order for there to be tensions there has to be release, they go together as yin and yang. Suspensions (for instance) are a dynamic process that happen over time, you need both parts - the tension and the realease, and I am saying that it only makes sense to look at the suspension and resolution together as a pair and that looking at each individually without consideration of the next (or previous) moment in time renders any analysis almost meaningless.

To extend this idea out a bit it follows that what is important is not the supposed dissonance level of each individual chord (or interval) but rather how the levels of dissonance change over time taking in the previous and later chords into account. An extremely consonant interval can be made to sound extremely dissonant if placed carefully, and vice versa. The very idea of harmonic tensions implies the movement of notes over time relative to a harmonic/tonal structure.

Originally Posted by Nahum

You want to go where I did not plan at all - a discussion in the field of psychoacoustics: whether dissonance is an acoustic (natural) or cultural phenomenon.


If dissonance is a cultural phenomenon then there is little point trying to treat it as a purely physical one, the whole approach of explaining dissonance starting from the harmonic series would be bound to fail.


Originally Posted by Nahum
[quote=beeboss]

I know there are several theoretical ways to determine dissonance levels in chords but I always wonder what is the point of all that when you can just listen to the chord and decide for yourself based on how the chord sounds to you given its environment. That is what ears are for.


Originally Posted by Nahum

Sense, of course there is, otherwise Hindemith would not do this; first inside the intervals :
http://www.hindemith.info/en/life-work/biography/1933-1939/work/principles-and-categories/ - series 2


Sure, but what does it mean if Hindermith says that a minor 3rd is more dissonant than a major 3rd, what use is this supposed to have and what justification is there for it?
If the equally tempered scale (ie the one most people consider to be in tune these days) corresponded to the harmonic series I could understand this approach better, but it doesn’t!

Last edited by beeboss; 09/13/18 06:34 AM.
Re: Reflections before the beginning of the academic year [Re: beeboss] #2765175
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Originally Posted by beeboss


I am not denying harmonic tensions but rather that in order for there to be tensions there has to be release, they go together as yin and yang. Suspensions (for instance) are a dynamic process that happen over time, you need both parts - the tension and the realease, and I am saying that it only makes sense to look at the suspension and resolution together as a pair and that looking at each individually without consideration of the next (or previous) moment in time renders any analysis almost meaningless.

That's right, but I'm surprised. that you do not see the ultimate release for any chord , which is right in front of the eyes - "tree trunk", created from a drone I -V (- VIII =I). This brings up a refined sense of the process of tensions and releases.

Re: Reflections before the beginning of the academic year [Re: Nahum] #2765190
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Originally Posted by Nahum
This is already the 47th year in general and the 38th year in Academy and college, during which I teach the course of jazz and pop harmony . And the further the time goes, the less I am satisfied. Even more than twenty years ago it became clear that the theme of harmony of any genre-classics, blues, jazz, pop, etc. should begin from the first moment with study of the overtones system . But how does this usually happen? There are no overtones ; first, the intervals are studied by counting halftones, tones, minor thirds, major thirds, and so on. Intervals are laid in abstract training circuits, divorced from the real sound, i.e. acoustics. Then come a turn of four triads - by the same method, by adding thirds. From the very first moment the most important qualities of intervals and chords are excluded: a measure of tension and dissonance. Without this music can not make even one step, especially jazz and pop (modern)!

This is patently false.

Quote
Here is a simple question for test ; and students who finished the academic course of harmony could not answer:
what is the hierarchy of dissonance of four triads and their inversions?

Perhaps it's of interest to some but I've no idea of the answer and couldn't be more certain it's something I don't need to know.

Re: Reflections before the beginning of the academic year [Re: Nahum] #2765194
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Originally Posted by dire tonic

This is patently false.
What can also be said about this reaction is the absence of any argumentation..

Quote

Perhaps it's of interest to some but I've no idea of the answer and couldn't be more certain it's something I don't need to know.
Those who are not interested in it - please do not worry!

Re: Reflections before the beginning of the academic year [Re: Nahum] #2765204
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Originally Posted by Nahum
Originally Posted by dire tonic

This is patently false.
What can also be said about this reaction is the absence of any argumentation..

I'm speaking from personal experience as a pro pop musician and what I know of my peers. We took every step without recourse to this kind of analysis.

Let me remind you of your assertion:-

"Without [this] music can not make even one step..."

Quote
Quote

Perhaps it's of interest to some but I've no idea of the answer and couldn't be more certain it's something I don't need to know.
Those who are not interested in it - please do not worry!

That's a relief.

Re: Reflections before the beginning of the academic year [Re: dire tonic] #2765217
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Originally Posted by dire tonic
Originally Posted by Nahum
Originally Posted by dire tonic

This is patently false.
What can also be said about this reaction is the absence of any argumentation..

I'm speaking from personal experience as a pro pop musician and what I know of my peers. We took every step without recourse to this kind of analysis.

Let me remind you of your assertion:-

"Without [this] music can not make even one step..."

Quote
Quote

Perhaps it's of interest to some but I've no idea of the answer and couldn't be more certain it's something I don't need to know.
Those who are not interested in it - please do not worry!

That's a relief.
My sense is that you did not read the title of this thread. It is an academic musing on the students who, presumably, are interested in this question or they wouldn’t be going to school.

There are many approaches to learning and playing music. Some people are interested in the ‘why’.

Re: Reflections before the beginning of the academic year [Re: Nahum] #2765219
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Originally Posted by prout
[
My sense is that you did not read the title of this thread.
This refers to the joint prehistory.

Re: Reflections before the beginning of the academic year [Re: prout] #2765224
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Originally Posted by prout

My sense is that you did not read the title of this thread. It is an academic musing on the students who, presumably, are interested in this question or they wouldn’t be going to school.

There are many approaches to learning and playing music. Some people are interested in the ‘why’.


I'm reading the content of the posts which I would hope reflects the title.

As the discussion has moved on I would pay attention to beeboss who has hit the nail on the head IMO.

No harm in pursuing the 'why' but if students are persuaded that they will not be able to progress (specially in pop, allegedly!) without understanding what is being proposed, as in:-

"Without [this] music can not make even one step..."

- they’ve been misinformed.

This kind of analysis is not a prerequisite.

Re: Reflections before the beginning of the academic year [Re: dire tonic] #2765241
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Originally Posted by dire tonic

"Without [this] music can not make even one step..."

- they’ve been misinformed.

This kind of analysis is not a prerequisite.

I do not understand why you are trolling here, without absolutely any argument.

Re: Reflections before the beginning of the academic year [Re: Nahum] #2765248
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Originally Posted by Nahum

I do not understand why you are trolling here, without absolutely any argument.


I object to the accusation of trolling. I'll make a complaint if you do it again.

The argument as already outlined should be self-evident.

You've made an assertion (I'm paraphrasing), that music (pop, for example) cannot take a step without understanding a set of principles - 'principles' incidentally which IMO beeboss has effectively refuted, one by one (I note you cannot challenge him on them).

However, I and others have taken all the necessary steps to advance their musicianship without understanding this set of 'principles' hence negating your assertion.

It's basic logic. If it's not clear, I can provide a parallel.

Re: Reflections before the beginning of the academic year [Re: Nahum] #2765260
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Here is my partial answer to the question what is the hierarchy of dissonance of four triads and their inversions?
Among the inversions of the major and minor triads in the middle register is the most dissonant - the first inversion, the least dissonant - the second inversion. The abundance of the first triad inversion in Elton John harmony indicates a preference for softer dissonances than say the major 7.

Last edited by Nahum; 09/13/18 03:06 PM.
Re: Reflections before the beginning of the academic year [Re: Nahum] #2765266
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"Acoustics" provides the initial role of inspiration for music, but actually understanding music requires understanding how we've abstracted those qualities and incorporated them into the human imagination. Thinking too "concretely" about the role of acoustics in music leads to all sorts of problems. I'm going to be quoting from various posts of the same writer who I believe has succinctly cut through a lot of the underlying issues in play here. All bold my emphasis.

This first quote exemplifies my point about this "too concrete" thinking without context:

Quote
The most important point I would make is that what you describe under 2.) is the way Schenkerian analysis is always supposed to work (for any piece); the idea of mechanically "reducing" according to locally-determined values of consonance and dissonance is extremely un-Schenkerian. An apparent dissonance might turn out to be "really" a consonance; and vice-versa.

(A favorite go-to example: "the tonic chord in root position" from Beethoven's Piano Concerto No. 4 that is dissonant.)

This is of course why Straus misses the point; his argument might apply to Lerdahl and Jackendoff, but certainly not to Schenker. Yet most Schenkerians (at least) would regard Lerdahl and Jackendoff as a pretty bad theory even of "tonal" music.

At the most basic level, the conceptual problem with such approaches (including, as far as I can tell, that of the OP, /u/Kalcipher) is that they are too concrete: they assume an extremely impoverished notion of context, one that misses all kinds of essential metadata. This includes, for instance, the kind of information that allows one to recognize that the situation in the Beethoven example above is "like" situations where a 6 and 4 resolve to a 5 and 3.


The overtone series as the source of meaning for consonance does play a role, but it leads to all sorts of conceptual problems when you take it too seriously. It's especially pernicious because of the particular way if causes confusion with how it interacts with "chord theory".

For example, there's a certain train of thought concerning the "emancipation of dissonance" found in both Schoenberg and Nadia Boulanger trying to ascribe the freer use of these notes to the overtone series. Which leads to an unspoken understanding that has caused loads of confusion.

Quote
Certain simultaneities occurring in music are “chords”, and others aren’t. Those that aren’t are the result of combining tones of a “chord” with other, so-called “non-harmonic”, tones, which must fall into one of a number of particular types specifying how they relate to the tones of nearby “chords”. If a certain such “non-harmonic” formation gets used sufficiently often by sufficiently prestigious composers, it may be declared a “chord”, and thereafter liberated from the restrictions governing non-harmonic tones, subject only to the rules governing the interactions of “chords” themselves – which rules it is the task of the theorist to formulate. We agree not to notice the fact that the rules for non-harmonic tones actually permit any simultaneity to arise, and thus through usage, to attain the status of a “chord”, because we prefer not to acknowledge that it is usage that determines :chord” status, and instead to maintain a fiction that “chord” status is inherently justified by supposed relationships to the overtone series.

Well, Schoenberg noticed. And, he argued that the overtone series, too, could potentially be seen to justify essentially any chord, by reference to the higher partials, whose relationships to the fundamental are more complex and suggestive of the dissonant intervals that characterize many of the simultaneities of the “modern” music of the time.

https://komponisto.tumblr.com/post/160087428485/early-webern-the-futility-of-chord-theory-and


One can certain argue this emanicpation, but it comes not from an appeal to the overtone series but actual musical context.

Quote
As is well known, Schoenberg – whose teaching synthesized the old and the new by essentially conveying a modern composer’s understanding of musical history, for like Schenker he was an artist rather than a scholar – advocated an idea he called the “emancipation of the dissonance”. This idea, which can indeed be viewed as perhaps the central generating force of the history of serious, ambitious music (and not just of the 20th century, though yes, in particular, of that period), has nevertheless been entirely misunderstood by virtually everyone, with the important and ironic exception of Schoenberg’s fierce critic, Schenker.

Properly stated, the idea in its essence is this: Because all dissonance has its conceptual origin in consonance, there is no theoretical restriction on the dissonance that may be employed in free composition, provided its relationship to some underlying consonance is comprehensible.

The history of musical progress, thus (in the so-called “harmonic” domain) is one of increasingly complex and distant relationships to consonance becoming “comprehensible”. This might be compared to the phenomenon of elliptical usage in language, the process whereby “I wish you a good morning!” becomes “Good morning!”, which, in turn, becomes “Morning!” – a process which is meaningfully similar to the musical process whereby

[Linked Image]

becomes

[Linked Image]

which becomes

[Linked Image]




To make this more relevant to this forum see how this line of thought is essentially the same to justify Jazz use of 'dissonance':
https://www.scribd.com/document/199...f-Modern-Jazz-Questions-about-Method-pdf

But what role the overtone series actually play?:

Quote
Observations are always theory-laden; but in the case of music, the theories in circulation are so bad that this staple slogan of postmodernism really comes into its own. From where I sit the idea of "interval-based dissonance studies", or "ranking triads by dissonance" etc. doesn't even make sense as a concept. It's almost gibberish. You can measure acoustical properties, and you can try to find out what kind of context listeners automatically attribute to an out-of-context sound; these are questions that at least make sense (without regard to how interesting they might be). But asking listeners to produce "dissonance rankings" doesn't; it amounts to asking them to do (a kind of) music theory on the spot, subject to weirdly circumscribed, artificial, and musically irrelevant restrictions.

What it -- posing such a question at all -- in fact looks like is a failure to absorb the music-theoretical insight that the actual properties -- the ultimately meaningful concepts -- that people were historically pointing to with the terms "consonance" and "dissonance" turn out to be matters of diatonic structure. Pythagoras in the blacksmith shop may have thought that "consonances" were the "good" sounds and "dissonances" the "bad" ones, but a few millennia later we now realize (at least, those of us who do realize it) that what he was actually getting at -- though of course he didn't realize it -- was that consonance is the stability property of non-step-related tones in a diatonic collection; and dissonance, the corresponding instability resulting from step relations and chromatic tones. The diatonic collection itself, of course, comes from the harmonic series (this being Pythagoras' contribution to the subject, and is almost the entire extent of the relevance of physical acoustics to music theory).

I simply don't think that anyone who has truly integrated the insight of the preceding paragraph into their consciousness would have any interest in asking some random experimental subject whether they think a minor third is "more dissonant" than a major third, or an augmented triad "more dissonant" than a diminished triad. The question of consonance and dissonance is a theoretical one that has been settled theoretically. Of course one expects listeners to perceive an augmented triad differently from a diminished triad, by virtue of the fact that the diminished triad fits into a single diatonic collection, and the augmented triad doesn't. There's no mystery about this.

Much more interesting than the reactions of experimental subjects (constrained to use the vocabulary of "dissonance", as if they were themselves music theorists investigating a question that hadn't been settled) to out-of-context stimuli, is the implication of the above that the diminished triad is actually a consonance. Thus, we are led to recognize the autonomy of the VII harmonic step and the Locrian mode. It is, to be sure, a special case, because there is only a single diminished triad within any diatonic collection (and thus only one mode with a diminished triad as tonic); if we need to explain a difference in "experimental perception" of the diminished triad relative to the major and minor, the explanation is here at hand. But it is of yet more relevance as an explanation of the artistically normative implication that we should perceive it differently, in accordance with its nature.

We are also led, by the realization above regarding the nature of consonance and dissonance, to distinguishing between dissonance that arises from step relationships and that which arises merely from chromaticism; the latter we may call pseudo-consonance. It is into this category that the augmented triad falls.

https://www.reddit.com/r/musictheor...onsonance_definitions/drqjcyi/?context=3


Quote
But, if the arguments purporting to found chordal practice (and thus theory) on the overtone series (and even, in Riemann’s case, on a hypothesized symmetrical “undertone series”) strike us as quaint bordering on ridiculous now, it is – or at least should be – only to the extent that our theoretical sophistication has increased enough to know that (at least until the advent of spectralism, etc.) the overtone series serves as a source of the pitch materials of Western art music only through its role in the generation of the diatonic scale. It is from the latter that we may then derive all other theoretical notions in the realm of pitch, such as consonance, dissonance, and the triad (all of which arise ultimately from the distinction between steps and skips, an essential, perhaps the essential, psychological feature of diatonic space).

Most of the reasoning leading to these conclusions can be found in Schenker, for all that he continues to view the major triad as being grounded directly in “Nature” (i.e. the overtone series); in particular, he writes that “No overtone beyond the fifth in the series has any application to our tonal system”, the heading of §11 of Harmony.https://komponisto.tumblr.com/post/160087428485/early-webern-the-futility-of-chord-theory-and


]Anyone interested on how the diatonic collection (and the twelve divisions of the octave) can be rationally reconstructed from the abstract notions of "skip" and "step" should see the Appendix to Westergaard's Introduction Tonal Theory. Strictly speaking, only the notions of "unison", "octave", and "fifth" are really truly needed as a primary source of intervals to construct the diatonic system and all other intervals.

Even the major third plays a more subordinate role. I'd probably argue that the major third plays from the overtone series in how it helps "break the tie" between Ionian/Major and Aeolian/Minor for the choice of conceptual priority. (Which is reflected in the conventional assignment of unaltered scale degrees 1234567, the notion of a Picard Third, and the alterations made to Aeolian via the melodic/harmonic minor scale constructs which are essentially "borrowings" from Major into pure Minor).]

The tumblr essay I linked, is long but really worth reading and considering. I'll conclude here by re-quoting one of the often-quoted statements by Schenker and his followers (I can already think of at least three instances):

THE DISSONANT INTERVAL IS ALWAYS A PASSING EVENT, NEVER A COMPOSITE SOUND.

The notion of "step" or "adjacency with trajectory" or "dissonance" always has a sense where it occurs and passes through an underlying consonant "stable non-adjacent" space whether this be more literal or more imaginary/spiritual/abstract. There's always a sense where you always hear these dissonances move and function "inside" of something larger even if only implicitly (hearing a note's resolution tendencies doesn't mean it actually does so).





Last edited by anamnesis; 09/13/18 03:49 PM.
Re: Reflections before the beginning of the academic year [Re: Nahum] #2765267
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Acoustic explanation: the smaller is the interval which located at the bottom of the voicing , the more dissonant is its sound - in strict accordance with the system of overtones.

Re: Reflections before the beginning of the academic year [Re: Nahum] #2765273
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Anamnesis, thanks for the materials.

Re: Reflections before the beginning of the academic year [Re: Nahum] #2765370
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As I understand it, a wide range of fundamental objections to the initiated study of overtones system in the course of harmony is based on the views of musical theorists of the past who had no connections with observations and analyzes in the field of jazz and non-European musical cultures at all . Suffice it to mention the most important Soviet musicologist Leo Mazel, who explained the phenomenon of gravity dominant in the tonic by introductory pitches of tritone , completely denying the acoustic mechanism of overtones. However, he knew nothing about setting up and using African drums (as he wrote specifically), where the main pitch is final, despite the fact that there is no tritone in pentatonic scales.
https://www.youtube.com/watch?v=ZDdN8GQQ3A8

We don't hear overtones?

About drone on tampour in Indian music already mentioned?
https://www.youtube.com/watch?v=LZ8BJfU-7t8

We don't hear overtones?

And when the didgeridoo sounds, we don't hear overtones?

https://www.youtube.com/watch?v=E5tgXbFAZwY

We do not hear the overtones in the human voice?

https://www.youtube.com/watch?v=vC9Qh709gas

I take my Tibetan cup and gently hit it; I am enveloped in a fairytale sound. If the blow is sharper, there is a sound of an octave + fifth higher.
No overtones here?

I easily clap my hands, then sharply - sometimes the sharp sound is higher by an octave, sometimes by a fifth.
Not overtone?

Who dares to say that the overtones are not at every step? Minor triad is not at every step, and the overtones - yes. So where does the study of harmony begin?

===========================================
On my desk in college, during the lessons of harmony and arrangement, there is always a large schema with this scheme, so that the students never forget it:

[Linked Image]


And in the end, only the facts decide whether this is the right approach or not:

https://yadi.sk/d/44_r3Dd23YakLz


https://soundcloud.com/you/tracks









Last edited by Nahum; 09/14/18 02:26 AM.
Re: Reflections before the beginning of the academic year [Re: Nahum] #2765371
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Overtones are sources of chords, not vice versa!

Re: Reflections before the beginning of the academic year [Re: Nahum] #2765387
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Originally Posted by Nahum

We don't hear overtones?




Nobody would deny that all (non-electronic) sounds are built up of overtones/harmonics/partials, that is a physical fact of resonating systems, but to try to use that as a justification of complex harmony is another thing entirely imo.
Humans have been playing music for thousands maybe tens of thousands of years and yet the dominant tonic harmonic relationship has been around for what 500 or so. Already dominant chords are all but abolished in pop music and classical music has moved on well beyond functional harmony ages ago. Given this it seems strange to me to say that there is a physical reason for this harmonic relationship to be essential.
When we look around the world at all the different types of music there are are there any other that have a dominant chord that resolves to a tonic? I think there is not. The 1st and 5th drone is more common but I don’t see that we can really extend this to explaining the whole harmonic system of western music and jazz.

To me classical harmony of the 18/19th century, or modal jazz harmony, is much more like a movement in painting, say expressionism for example.
It is an expression of the times which changes relatively rapidly. To me this kind of cultural explanation just seems to fit the facts we observe much better.

Ultimately though I couldn’t care less about any of this, I am only really interested in the utility of an idea. If ranking dissonance levels of triads and inversions helps somebody create something then that is great, I just can’t see the use for me.


Originally Posted by Nahum


And in the end, only the facts decide whether this is the right approach or not:

https://yadi.sk/d/44_r3Dd23YakLz



If that is one of your students you are obviously doing a splendid job of teaching harmony - some very beautiful and advanced harmony going on there, I love it. But there is more than one way to skin a cat!

Re: Reflections before the beginning of the academic year [Re: beeboss] #2765398
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Originally Posted by beeboss
When we look around the world at all the different types of music there are are there any other that have a dominant chord that resolves to a tonic? I think there is not. The 1st and 5th drone is more common but I don’t see that we can really extend this to explaining the whole harmonic system of western music and jazz. ]

Here I just disagree! Because each blow on drum causes a sound composed of the main tone and its overtones-octave and fifth , which the skilled player can select using different techniques of touch . But the ending will always be on the main pitch. In a low pitch of piano, a person with a very developed overtone hearing (possibly a color ) can hear a chord X7; a musician with an ordinary developed musical ear necessarily feels in a low drone the major triad - checked dozens of times in groups at the first lesson of harmony course y. Try it, and make sure!
Overtons are sources of stable tonic and unstable fifth stage. Equal to the dominant in all musical cultures, be it Indian swaras , or Arab maqams .

My goal: do not load the student with the rules, but open up the horizons of opportunities and alternatives for them. And you heard the result.

Last edited by Nahum; 09/14/18 07:33 AM.
Re: Reflections before the beginning of the academic year [Re: Nahum] #2765402
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So this is decidedly not restricted to prout's 'why' but a more general 'how'. I admit that's piqued my interest. Where and in what manner do the benefits accrue. The student sees this table of overtones….but then what is the process? What next?

Originally Posted by Nahum
Here I just disagree! Because each blow on drum causes a sound composed of the main tone and its overtones-octave and fifth , which the skilled player can select using different techniques of touch . But the ending will always be on the main pitch. In a low pitch of piano, a person with a very developed overtone hearing (possibly a color ) can hear a chord X7; a musician with an ordinary developed musical ear necessarily feels in a low drone the major triad - checked dozens of times in groups at the first lesson of harmony course y. Try it, and make sure!
Overtons are sources of stable tonic and unstable fifth stage. Equal to the dominant in all musical cultures, be it Indian swaras , or Arab maqams.

Will this be music for the performer's pleasure or the listener's?
Any chance of a practical demonstration? I'm hard put to see how you capitalize on the low drone major triad in such a way as to sustain interest.

Quote

My goal: do not load the student with the rules, but open up the horizons of opportunities and alternatives for them. And you heard the result.

That's pretty close to begging the question.

As is well known, each of us springs off a different starting line. Your student may already have been a gifted and able player who has inevitably improved during his time with you whether under his own steam or your pressure. On the other hand, if he transitioned from nursery rhymes to this more advanced level after an intensive course of overtoneing, I'd be interested in learning more - preferably from the student himself. Could he be invited to tell us something about his development during the overtone study phase?

Re: Reflections before the beginning of the academic year [Re: dire tonic] #2765418
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Originally Posted by Nahum
In a low pitch of piano, a person with a very developed overtone hearing (possibly a color ) can hear a chord X7; a musician with an ordinary developed musical ear necessarily feels in a low drone the major triad - checked dozens of times in groups at the first lesson of harmony course y. Try it, and make sure!
Overtons are sources of stable tonic and unstable fifth stage. Equal to the dominant in all musical cultures, be it Indian swaras , or Arab maqams.

Will this be music for the performer's pleasure or the listener's?
Any chance of a practical demonstration? I'm hard put to see how you capitalize on the low drone major triad in such a way as to sustain interest.


..unfortunately my skimming your post led to the wrong response and the edit window is too short.

Yes, the harmonics are audible up to X7, usually they unfold as the fundamental frequency fades over time although this does depend on the quality of the piano and the pitch of the note. However the instantaneous strike is highly biased to the perceived fundamental. Why are you preoccupied with the overtones here?

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