# What is "harmonic music"?



## millionrainbows (Jun 23, 2012)

"Harmonic music" is music that uses a "harmonic model" to help create its effect and sense of tonality.

Harmonic music is based on an hierarchy, not like serialism, which is not.

Let's ponder the meanig of "hierarchy" first. This is a "pyramid" of relations, in which every element of the set is related to the top of the pyramid, the "key" element.

This is not true of serial methods of relation; pitches are related only to those notes immediately preceding and immediately following. In this sense, serialism is not a relation of elements, and does not deal with pitches as iodentities, but is a template of relations. It deals with the "spaces between notes," not the notes themselves. In this sense, *serialism deals in quantitative relations, not fixed identities in an hierarchy. *(see my blog "Number as identity")

This harmonic model is based on the overtones (higher pitches) heard over the fundamental note.

This fundamental may be expressed numerically as "1", with the overtones being fractional parts of this. Pythagoras demonstrated this with his monochord, which divided a single string into an octave (2:1) with its fractional divisions (2:3, 3:4, 4:5, etc.)

This division is based on the *preservation of the octave,* and the fact that *we hear octaves as being "pitch equivalences;"* a "G" is a "G", regardless of register.

Since Pythagoras was not able to get true fifths to "stack" or project into a closed octave, he closed the octave at the nearest coincidence of the spiral of projection. Thus, our 12-note division of the octave, while being modelled on perfect intervals, is in reality a compromise; an artififcial, arbitrary system of division.

Thus, our diatonic scale *emulates* a harmonic model, by relating all its scale notes, like an index, to a "key" note, which can be considered "1". Thus, each note of the scale is related to the fundamental in a certain way.

In the C major scale, "C" is 1, and the octave is 2:1. Next is G, which is 2:3, and so on (see my blogs for the complete ratios).

Harmonic models such as this can be said to create a "tonality" which places the fundamental "C" as the "key" or center of tonality, *although a sense of tonality is not totally dependent upon the presence of a harmonic hierarchy.

*Some exceptions could be cited. Schoenberg or Berg tried creating vague senses of tonality in certain places in their works, but this tonal effect is totally subjective, and is not intrinsic to the use of ordered serial rows.

Remember, to be an hierarchy, each note of the scale (or set of pitches) must be related in a fixed way to the key note (or "1"). In serial rows, there is no "1".

In fact, s_erial rows are not really pitches in their essential nature; _they are a fixed template of relations, only to each other, in an ordered manner, which insures that there is no "1" identity.

They can be transposed to any pitch; p_itch (as identity) is irrelevant. The nature of a tone-row is in its fixed quantities of relations (intervals), not the specific, local pitch identities which might be incarnate.
_
Therefore, serial rows are not harmonic by their very definition. The ordering _insures_ that there is no harmonic hierarchy.

Next, I'll discuss how Debussy's music is essentially harmonic. Also, I'll go into how Bartok's methods are a variant of the harmonic model on a smaller, more microscopic scale.


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## Mahlerian (Nov 27, 2012)

Nonsense dressed up with technical terminology is still nonsense.

This theory of yours coincides with nothing either in the music itself or in anyone else's theories.

For everyone reading this thread, ask yourself: is Erwartung inherently more tonal than Berg's Violin Concerto, simply because the latter uses an ordered series?

Perhaps then you'll realize how absurd this whole thing is...


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## GioCar (Oct 30, 2013)

^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Right or wrong you could be, this is not a post by a Moderator....just my personal opinion.


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## norman bates (Aug 18, 2010)

millionrainbows said:


> This is not true of serial methods of relation; pitches are related only to those notes immediately preceding and immediately following.
> In this sense, serialism is not a relation of elements, and does not deal with pitches as iodentities, but is a template of relations. It deals with the "spaces between notes," not the notes themselves. In this sense, *serialism deals in quantitative relations, not fixed identities in an hierarchy. *(see my blog "Number as identity")


I think it's difficult to escape completely the physical aspect of dissonance and consonance, so even if serialism try to avoid the hierarchy the hierarchy is still there, even if it's limited to "those notes immediately preceding and immediately following".


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## millionrainbows (Jun 23, 2012)

*Next* is a look at *tonality, total chromaticism ("atonality"), and serialism,* and how these are different, as well as being related.

In *traditional functional tonality,* diatonic major and minor scales are prevalent; root progressions are emphasized mainly by fifths (descending); chromatic notes are use to reinforce, or threaten the sense of tonality.

As the boundaries of tonality are approached, *total chromaticism, or so-called pre-serial "atonality" *is encountered.

Before delving into those characteristics, an exposition of what "ordering" really means. Ordered rows are only a partial aspect of the nature of serial rows vs. unordered scales. What does ordering do?

It does two main things: first, it "orders" the row _horizontally, in time,_ so that there are "melodic" or "thematic" elements created. After all, for a melody or theme to exist, it must "unfold in time" as a* succession *of pitch events.

Now, what else does ordering do?

An ordered row also implicitly insures that no note is repeated or is given undue emphasis or repetition, or is "returned" to until all other notes have been stated. This insures that a sense of tonality will be discouraged. What other reason could there be for the "non-repeating" rule?

These two characteristics of* ordered rows *are congruent in spirit & purpose to the characteristics of *"total chromaticism" or pre-serial atonality. *Let's examine those characteristics.

*"Total chromaticism" or "atonality"* is a way of avoiding tonal focus. It is usually based on the entire chromatic scale (like serial rows), and composers have used various ways of keeping all twelve notes "in circulation," which harkens to serialism's "non-repetition" requirement. Without tonality, atonality uses wide leaps to emphasize melody and avoid a chromatic "mush;" atonal sonorities are often more varied than in tonality, and more dissonant. Importantly, the texture of atonality is more often linear than chordal; and the various lines are transformed & developed through transposition, inversion, and retrograde, which is also very similar to serial methods. Check out Schoenberg's Serenade, with its imitations of Baroque dance-forms; also see, as a less extreme example, Richard Strauss' Metamorphosen for good examples of total chromaticism or "atonality."

So we can see that "total chromaticism" or "atonality" are closely related to serial methods, and how these developments at the extreme end of tonality led, inevitably, to a non-harmonic/hierarchic way of creating music which has no definite tonal focus.

Next, I'd like to go into how "tonality" and "harmonic hierarchies" are closely related, and other ways that tonality can be established, and how these concepts can differ.


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## millionrainbows (Jun 23, 2012)

norman bates said:


> I think it's difficult to escape completely the physical aspect of dissonance and consonance, so even if serialism try to avoid the hierarchy the hierarchy is still there, even if it's limited to "those notes immediately preceding and immediately following".


You have a good point there, norman. Sonance is definitely physical, and modeled with ratios which precisely reflect vibrational realities. It's hard to argue with a vibrating eardrum.

That's the experience of all music, serial or tonal: all music ends up being a "harmonic" experience, in the sense that this is the way our ears vibrate.

There's another aspect of serialism which does "degrade" or discourage the sonance factor, and this is the ordering and non-repetition. The sonance of intervals is still there, but it's been evened-out, and is not related by degree to a "key" note. Thus, Webern created "areas" of certain interval-sonorities with his tone rows and how he related them; thus, this is the way we must listen to them, not as "less or more," but as sonic entities, taken in isolation.

In other words, it's the "internal relations" of tonal scales which creates tension, sonance, and a sense of tonality. With serial tone-rows, this internal relation is different.


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## millionrainbows (Jun 23, 2012)

Now, I'd like to turn the discussion to a "transitional" work, which begins to cross the border into "free atonality," which leads on to true serialism.

This will show that tonality led to chromaticism, which led to* total *chromaticism (free atonality); and free atonality is just a step away from serialism, except that serialism "codified" those conditions of total chromaticism into a new method.

Showing this transition goes a long way in "justifying" and proving that Schoenberg's dodecaphony, and the serialism which followed, were not arbitrary developments, but grew organically out of the methods and practices of the tonal system.

It might also be of aid to any listeners out there who can identify a simple V-I progression, yet are befuddled by more modern music. If you have a decent ear, _this is the piece for you _to listen to now, in order to gain this deeper understanding.

*Alban Berg: 4 Lieder op. 2, number 2. *This short song is titled _*Schlafend tragt man mich.*_ This song uses a dominant-seventh chord (a.k.a. *V* chord) with a lowered fifth (or augmented fourth). This altered fifth makes the chord unstable, but since it's a dominant seventh with the *flatted 7th,* it wants to resolve to *"I" *anyway, just like any other* V-I* that Haydn would use in tonality. We all should know what a *V-I *is by now, I hope.

This series of V chords is derived from the whole-tone scale. About the whole tone scale: it is a 6-note scale, and there are two of them, "threaded" right next to each other, in the chromatic octave. In C, this would be C-D-E-F#-G#-A#, and the other one is C#-D#-F-G-A-B.

Each WT scale, by itself, has a "flatted fifth" or tri-tone interval, which could be considered to be a 1/b5 relation, or a "root-flat-fifth" basis for a chord, which is how Berg uses them. Also present in each WT scale is the b7, which creates the dominant sound of a V chord, which wants to resolve or move on.

The dominant "V" chord of tonality also contains the tri-tone relation of Maj 3/b 7 (in C this is E-Bb). All diatonic major scales contain this tri-tone.

Now listen to the Berg song. It begins with a V7, then to another V7, in a series of cascading, descending V7 chords. These descending fifth root movements are derived from the relation of the two whole-tone scales. Although each WT scale taken alone contains no perfect fifth, by moving chromatically to the other WT scale, a V-V root movement is accomplished. In C, this would be *C*-D-E-F#-G#-A# to C#-D#-F-*G*-A-B. Ain't that nifty?

Listening to this song is like constantly falling through a series of descending root movements, never arriving, always moving, restless, just like the late-Romantic aesthetic would have it.

This Berg song also demonstrates the ongoing struggle of Western music, between the "harmonic" or aural, visceral aspects of music and tonality, and the mechanisms which are also at play, intrinsic to the 12-note division of our octave, a.k.a. the chromatic scale, and the various symmetrical divisions of the octave which are possible, into 2, 3, 4, and 6 parts, giving rise to the escape from tonality with its outward-going 5 and 7 divisions, into smaller, symmetrical "inner octave" divisions, which, instead of heading for infinity past "1," seek the other-directed infinity: "1" headed in the opposite direction, inward from "1" towards a "zero" never to be reached; the infinity of ever-smaller fractional divisions.

Western thought turns inward, away from expansion and conquering of new territories, and outer space, into an ever shrinking introspection and exploration of inner space. It seems antithetical to our conquering, dominating Western thought-style, doesn't it?

No wonder modernism had a problem "catching on" with the general status quo...but I'm beginning to wax philosophical; I'd better stop now.


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## millionrainbows (Jun 23, 2012)

Now another transitional work, *Schoenberg's String Quartet II, op. 10 (1907-08). *It's a four-movement work, and the first three movements have key signatures of F# minor, D minor, and Eb minor; the fourth movement has no key signature. That's a nice piece of information to know, isn't it? Such are the drudgeries of listening to modern music.

As is usual with "free atonality," works written before Schoenberg had devised the "serial" method, the whole-tone scale keeps cropping up. What is it with this six-note scale?

I think its appeal lies in:

(1) its neat division of the chromatic collection into two hexads,

(2) its symmetry, being composed of whole-steps, major thirds, tri-tones (flat fifths), augmented fifths (flat sixth, or flatted sub-mediant), and flat sevenths;

(3) its "floating" sound of suspended or ambiguous tonality,

(4) its M3, b5, and b7 suggesting altered dominant chords;

(5) its tri-tone suggesting an augmented chord. This has ties with Wagner and his use of the augmented chord.

The use of a soprano in this work shows ties with Mahler, who used it in a symphonic context.

The first movement, in D minor, is tentative. The themes are easily recognizable, although as a whole it doesn't develop very far. In this sense, it is a good starting place to listen for Schoenberg as a thematic composer.

The second "scherzo" movement is rather "schizo" in the way it jumps around. Schoenberg was certainly a clever fellow, but I doubt that he had much desire to communicate in this part. This seems like an internal reverie, perhaps affected by his life-events at this time (the Gerstl affair, his wife's return, and Gerstl's subsequent suicide).

Apparently, by his association with Gerstl and other fringe artistic-types, Schoenberg is revealed to be as much of an "outsider" as any of them, but Schoenberg was essentially a survivor who, in the end, wanted to belong to the Viennese tradition. Perhaps his alienation was more from without than from within, as Gerstl's was. Although Schoenberg was frequently accused of being mentally aberrant, and still may be considered so even today by hostile listeners, I can relate to the "outsider" mentality, and of shame-based identity being foisted upon people.

In the third movement, ostensibly in Eb minor, the soprano enters. Now we are in the variation stage, and thing begin to "click" in a more profound way. It harkens back thematically to the first movement.

The fourth, final movement also features the soprano, and here is the famous line "I feel the air of other planets." We done taken off into outer space! It opens with a figure which ascends all the way from the cello to the violins. Upon close examination, the violin figure that is settled on & repeated turns out to be whole-tone related, although Schoenberg covers his tracks with ornamental notes outside the scale, and is much sneakier than Berg was in his use of the WT scale.

So, we can see from this work that "free atonality" was something that came about naturally, as a consequence of increasing chromaticism, and began to use other symmetrical divisions of the chromatic octave. As total chromaticism is reached, all 12 notes are kept in circulation, until, finally, Schoenberg saw the need for some sort of "method" which could moderate and control this total chromaticism, since tonal functions had become ambiguous to the point of being meaningless in such a chromatic environment. Thus, "twelve-ness" begins to assert itself; the geometry of 12 and its subdivisions, from resonant, harmonic hierarchy, into the geometry of Apollonian idealism.


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## millionrainbows (Jun 23, 2012)

So why examine "free-atonal" works in a discussion of "harmonic music?"

To underscore the fact that "non-harmonic mechanisms" began creeping into tonal music, even before it became "officially" serial or non-harmonic.

Scales and mechanisms such as the whole-tone scale are not based on harmonic factors of resonance as functional tonality is (although the WT scales sounds remarkably resonant since the introduction of ET tuning).

Since "free atonality" is still based on tonality, it is a good way to underscore these "intrusions" of geometric thinking, as opposed to the "givens" of harmonic tonality.

We can gain a valuable generalized idea from the above examples; of what it is that happens to tonality when it becomes more and more chromatic, and all 12 notes are in circulation; that the "mechanisms" generated by the division of the octave into twelve begin to naturally take over, in the absense of a clear tonal hierarchy.

From this, another valuable insight is gained: a sense of tonality is created by its notes, but also _just as much by what notes are left out.

_As chromaticism increases, "redundancy" of notes increases, and tonality becomes less focussed and defined.


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## millionrainbows (Jun 23, 2012)

*KINDS OF CHROMATICISM

*Chromatic notes do not in themselves constitute a state of "atonality," and can, in fact, even be overtly mono-tonal.

In order to obscure a sense of tonality, the harmonic function (the horizontal movement to new "root" stations, or "root movement") must be chromatic. This means that root movement (usually in the bass, but not always) must be constantly shifting to new root stations.

Otherwise, if the chromatic lines are in the upper voice, then it can easily be tonal, by simply placing a constant bass note under it. This is what Miles Davis does in his later jazz, like _On the Corner, Bitches Brew, The Jack Johnson Sessions, and The Cellar Door Sessions;_ he simply establishes a "groove" in the bass, usually an ostinato figure with tonal implications, puts a beat to it, and the soloists are free to play any "outside" chromatic riffs they wish, with the full confidence that the lines will be "tonal-ized" in reference to the drone underneath.


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## Mahlerian (Nov 27, 2012)

So, put a few completely arbitrary pedal points under something, and it becomes tonal?

I am not saying that Miles Davis's playing or the pedals he used are arbitrary.


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## millionrainbows (Jun 23, 2012)

Mahlerian said:


> So, put a few completely arbitrary pedal points under something, and it becomes tonal?
> 
> I am not saying that Miles Davis's playing or the pedals he used are arbitrary.


No, but it might fool your ear into hearing it tonally, because that's the way our ears hear, based on a harmonic model. Our ears tend to reference everything to a single fundamental, and according to the harmonic model, the fundamental is in the bass, with harmonics as higher-pitched derivatives, as ratios of that "1" fundamental.


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## norman bates (Aug 18, 2010)

millionrainbows said:


> Otherwise, if the chromatic lines are in the upper voice, then it can easily be tonal, by simply placing a constant bass note under it. This is what Miles Davis does in his later jazz, like _On the Corner, Bitches Brew, The Jack Johnson Sessions, and The Cellar Door Sessions;_ he simply establishes a "groove" in the bass, usually an ostinato figure with tonal implications, puts a beat to it, and the soloists are free to play any "outside" chromatic riffs they wish, with the full confidence that the lines will be "tonal-ized" in reference to the drone underneath.[/SIZE]


Isn't more correct to call that modality instead of tonality? By the way, I'd really like to see a discussion on modal music in the twentieth century.


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## millionrainbows (Jun 23, 2012)

_I'm moving this quote and reply over to this thread from the "current listening thread" to spare my fellow listeners who do not wish to engage.
_


Mahlerian said:


> Why criticize someone for something they didn't try to do?
> 
> Most of the serialists have come back around and realized that Schoenberg was right all along. Creating pieces athematically makes it difficult to maintain coherence. Why do you think _Le marteau_, a thematic/melodic work, has become the among most popular of all 50s serial pieces?


_*"The row is not a scale, nor is it necessarily a theme, but since the linear aspect of a twelve-tone piece will inevitably trace the intervals of the row again and again, that row can be easily stated as a theme if the composer chooses to use it that way."
*
-Allen Shawn, from Arnold Schoenberg's Journey

The row automatically insures coherence, because of the ordering.
_


> Schoenberg is a great composer because he wrote great music: Pierrot Lunaire, the String Quartets, Moses und Aron, the concertos, the Suite for Piano and so forth are excellent works, fully worthy of any comparison with the masters of the past or present.


_I didn't question Schoenberg's greatness, or criticize Schoenberg for being thematic, or because he made "tonal analogies" which resemble true tonality. After all, he was a traditional late-Romantic who emerged from the Viennese tradition.

It seems that I have a much more clearly defined notion of what constitutes "tonality."

It's easy to confuse "tonality" with "harmonic hearing," because the two are both based on the simple harmonic model, the way our ears hear tones.

This harmonic model consists of a fundamental tone, with higher-pitched lesser constituent pitches embedded within, called "harmonics," and these smaller constituent parts are ratios of the fundamental. Arithmetically, this can be seen as "fractions" of the fundamental ("1").

In works like Serenade, which is freely atonal, totally chromatic, and uses a 14-note "theme" or tone row, the bass clarinet figure in the last movement (Lied ohne Worte) might fool your ear into concluding that it is "tonal", because that's the way our ears hear, based on the harmonic model. 
_
_Our ears tend to reference everything to a single fundamental, and according to the harmonic model, the fundamental is in the bass, with harmonics as higher-pitched derivatives, as ratios of that "1" fundamental.

*This conclusion of "tonality" would be incorrect, though, since there is no tonal hierarchy, or tonal root movement of chords. 
*
The bass line, its movement, and all the resulting tonal implications which have been stacked on top, are the result of the ordering of the row, not a tonal hierarchy or reference. If anything, Schoenberg was making "tonal analogies" in this piece.
_


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## millionrainbows (Jun 23, 2012)

norman bates said:


> Isn't more correct to call that modality instead of tonality? By the way, I'd really like to see a discussion on modal music in the twentieth century.


_No, not in this later chromatic "outside" phase of Miles Davis. Earlier albums, like the ubiquitous "Kind of Blue" are modal, as is Coltrane's Atlantic period (My Favorite Things, Ole Coltrane). Coltrane became chromatic as well, during his late ABC/Impulse series of recordings.

It's interesting how the evolution of jazz harmonic thinking belatedly parallels the Western classical evolution into chromaticism, along with the concomitant audience rejection. Heh-heh...

_


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## norman bates (Aug 18, 2010)

millionrainbows said:


> _No, not in this later chromatic "outside" phase of Miles Davis. Earlier albums, like the ubiquitous "Kind of Blue" are modal, as is Coltrane's Atlantic period (My Favorite Things, Ole Coltrane). Coltrane became chromatic as well, during his late ABC/Impulse series of recordings. _


_

I have not the knowledge for discuss in depth this, but are you sure that modalism and chromaticism are different things? I mean, just to take an example Coltrane's India is very chromatic and still is modal (basically an improvisation over a pedal point). And the same for the music of George Russel, Andrew Hill or Wayne Shorter (and Miles Davis with the second quintet, and those pieces were way more complex than the vamps of the electric albums in the seventies).



millionrainbows said:



It's interesting how the evolution of jazz harmonic thinking belatedly parallels the Western classical evolution into chromaticism, along with the concomitant audience rejection. Heh-heh...

Click to expand...

_In jazz there are other reasons too. One for me is that the genre was "decapitated" because too much greats died very young or had other troubles, I think that the history of jazz after the sixties could have been very different if some of its most creative minds like coltrane, charlie parker, herbie nichols, booker little, dick twarzik, strayhorn, dolphy, clifford brown, fats navarro, ayler, scott la faro and many others were still alive. But it's obvious that often music that sounds more chromatic is also more difficult to decipher and it's also more difficult for the composer to built something that does not sounds just as random notes.


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## millionrainbows (Jun 23, 2012)

norman bates said:


> I have not the knowledge for discuss in depth this, but are you sure that modalism and chromaticism are different things? I mean, just to take an example Coltrane's India is very chromatic and still is modal (basically an improvisation over a pedal point). And the same for the music of George Russel, Andrew Hill or Wayne Shorter (and Miles Davis with the second quintet, and those pieces were way more complex than the vamps of the electric albums in the seventies).


I see what you mean, but it's well known that *Miles & Coltrane *took a modal approach, at least for a period. Miles'_* "So What"*_ is clearly mixolydian (major scale with b7). These more stable modes were in response to the departure from be-bop, which was much more restless, with constantly changing root movement (a new chord on every beat, at fast tempos). The modal thing was a chance to settle down and create a "mood." Miles saw that his strengths lay in this "mood" approach, rather than in the technical prowess required for be-bop and hanging with *Charlie Parker*. No easy feat, and listen to Miles' flubs in these early recordings; he was barely keeping up.

Coltrane played through Nicholas Slonimsky's Thesaurus of Scales, and you're right, the whole thing was headed for more chromaticism. But as I mentioned earlier, *chromatic activity* is very simple if it is referenced to a pedal tone in the bass.

*True chromaticism *results when the *root movement *of chords becomes so restless that it is ambiguous, or obscured by its own movement.

This is quite different from what Miles Davis was doing, and in fact, be-bop is more harmonically complex, because it involves rapidly-changing root stations. What Miles Davis did, over a monotone groove, is structurally simpler, and is more akin to "world music" or African music.

*True chromaticism is related to tonality because it involves root movement, i.e. harmonic function. *With later Miles Davis (Cellar Door Sessions), there is no "harmonic function;" all events take place over a "drone." This is a decidedly non-Western approach.....ooooooooooooooooooooooo


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## norman bates (Aug 18, 2010)

millionrainbows said:


> This is quite different from what Miles Davis was doing, and in fact, be-bop is more harmonically complex


I agree if you're talking of the electric period and kind of blue, I think that the music of the second quintet was way more complex (due to the compositions of Shorter in particular) than that. And even when they played standards in that period (like on the live at plugged nickel) they were making very complex and abstract music (so much that I've heard many times the criticism that the songs can't be recognized anymore, and it's true). Anyway we're always talking about serialism, but the thesaurus (as well as the could be a good starting point for a topic on the tonality in the twentieth century. It was an influence even on "pop" musicians like Frank Zappa and especially Allan Holdsworth (and his music harmonically is very, very interesting and original to my ears).


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