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Serial or free atonal? (Game)

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Thanks to dim7's suggestion, this is a game. Serial or free atonal?

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To me, "serial" implies a use of a method, using the full possible 12-pitch spectrum, which as a result avoids any feeling of tonality. It is therefore non-tonal.

"Free atonality" is the result of increasing chromaticism, both in voices and in root-movement of chord functions, to the point where the tonality is ambiguous, and tonality is too hard to pin down. It is still the result of tonality.

Since chromatic root movement is based on minor-second intervals, which correspond to movement by fifths via tritone substitution, freely atonal root movement is not "atonal" chromaticism (see interval projection, noting that the only two intervals which "cycle" through all 12 notes when projected, or stacked, are the minor second and the fifth).

As long as a chromatic note can be related back to a root movement, it is not truly chromatic in a free sense; it is tonal.

Therefore, we have to demonstrate the presence of root movement in order to call something "freely atonal." The root movement might be vague or ambiguous; in other words, the functions might belong to more than one possible key area, but nonetheless they are tonal because of vertical chord structure, which might be the strongest indication of tonality.

Serialism, by contrast, will not have the same degree of vertical consistency, harmonically; it will be seen as confluences of separate melodic elements, not as aggregates of chords with functions.
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Serial method does not automatically include atonality. Serial method does not automatically exclude tonality.
I think serial method does exclude tonality. That's because I developed a complete definition of tonality.

"Atonal" is a term used to denote opposition to tonality; atonality is music which has no tonal center. "Atonal" means "not tonal."

Tonal music does have a tonal center.

Serial music can be atonal, in fact, it is atonal by nature. Serial music is "not tonal."

Serial music is atonal, because it does not use the tonal hierarchical model of a fundamental tone and its harmonics.
"Tonal center" does not include localized cells of pitch clusters.

Localized tonal centers do not denote or create "true" tonality, because they make divisions within the octave.

If there is more than one tonal center within an octave of pitch-classes, it is not tonal in the true sense.

Tonality has a tonal center which covers all the relevant notes within an octave. This necessarily means that tonality deals with octave-constructed scales or pitch collections, which have starting points, and those starting points repeat in subsequent (and preceding) octaves. This means, in our 12-note system, that "true tonality" consists of a pitch center to which the other notes are subservient, however many of the eleven others are used.

True tonality is an overriding tonality, which covers all pitches used in the octave.

When we start dividing the octave, and creating localized tonal cells, this is not tonality. This smaller division of the octave is, in fact, closer to being serial or geometric, or mathematical in method (not harmonic-based).

This is because divisions of the octave which create local cells of pitch reference are not based on the intervals of the fourth or fifth, which concur with, and are derived from, the harmonic model.

Small, inner-octave divisions and intervals are based on geometric and mathematical considerations of "12-ness."
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What is a "localized tonal center" by the way?
One of the easiest ways to create a localized tone center is by using dim 7 chords.

Diminished seventh chord, C-Eb-Gb-A. Lower any of the tones, and you get a dom 7 chord.
C-Eb-Gb-(Ab) = Gb7
C-Eb-(F)-A = F7
C-(D)-Gb-A = D7
(B)-Eb-Gb-A = A7

This gives you four possible new dominant chords within the octave, which can be used independently, in a chromatic fashion, as Bartok did, or tonally, to modulate and create a new tonal center.

These diminished 7 chords consist of 4 notes, and there are 3 of them. This is 3 localized pitch centers, governing 4 notes each.

Another way:
Whole tone scales have only three intervals: maj2, maj3, and tritone. There are only two whole tone scales in the chromatic collection. That means that cross-relations between two WT scales will have a fifth, m3, or m2. These cross-relations can be used to go to new key areas, via the fifth, or chromatically, with the m2. (See Debussy and Berg).

Whole tone scales consist of 6 notes, and there are 2 different ones (2x6=12). Each interval (M2/M3/Tritone) gives a possible tonal center, plus the possibility of shifting a m2/m3/or P5 to a new scale with 3 new possible centers. This make 6 possible tone centers, within an octave.

Recursive means repeating, as a closed pattern, as in "divisible into 12" (using steps):1x12=12, 2x6=12, 3x4=12, 4x3=12.

When you reach 5 (Five half-steps/P4), 5 times what is 12? Nothing. A new "out of octave" number must be used: 5x12=60.

Likewise, 7 times what is 12? Nothing. So, a new denominator is needed: (seven half-steps/P5), 7x12=84.

Between 4 and 5, the tritone, is also recursive: 6 (six half steps) is 6x2=12 and is invertible (C-F#-C-F#) like a repeating decimal.

These examples demonstrate the nature of the smaller intervals m2, M2, m3, M3, and of tritones. They are recursive, unlike fourths & fifths, which are normally used as "go to" keys in modulations because of their inherent tendency to "travel outside the octave."
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Serialism is a method of avoiding tonality.

Atonality could be further divided into two kinds: "non-serial atonality" and "free atonality."
While I do not dispute that Wagner and Liszt and others were heading for a more chromatic territory, enabled by the inherent features of a Pythagoran 12-note octave division, their vision was still tonal, in a broad, flexible sense. Bartok I can see as being an outgrowth of this, but Schoenberg and company were actually in opposition to a sense of tonality. Yes, their 12-tone music was atonal in the fullest sense, not just an outgrowth of Late-Romantic chromaticism.

Schoenberg's music is beautiful, but it does not create an overriding sense of tonality; in fact, in that regard, it is harmonically disorienting. The 12-note system ensures that no tonal center will be emphasized, due to the ordering and cycling of all 12 notes. It is a method designed to avoid a sense of tonality.

Even serial methods are better at creating localized tonal effects. At least with serial set theory, one can use unordered sets ans smaller subsets. The 12-tone method always uses all twelve notes, and worse, it puts them in a specific order, forcing them to be melodic and "unharmonic." This was a system definitely designed to "murder" any sense of tonality.

Harmony, and a sense of tonality, however fleeting and localized, depends on the use of unordered sets; sets which are an "index" of pitches, like scales, which can be drawn from freely, and thus create, by their emphasis, an "interval vector" which creates a sense of tonality, or sonority.
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Sorry, but I still don't understand what is a "localized tonal centre". You answered how to create one, but not what is a localized tonal centre.
A "localized tone center" is when your ear is attracted to an area which it hears as being a tone center. This area is not heard as an overriding sense of tonality, but is usually more fleeting and temporary.

In traditional tonality, there is an "overall sense" of tonality which remains true to one pitch, the tone center, around which all twelve of the other pitches revolve.

If the overall, octave-spanning hierarchy gets broken up, then the tonal center can appear to shift.

The whole tone scale is the best example of tonal ambiguity; because of its interval structure, and lack of a fifth, any note of the scale is a candidate for being the key note, even though if it was, the tonal sense is still weak.

These things are self-evident upon listening.

"Localized" tone center is a term used when the "overall" tone center is not present, or is weakened. "Localized" means "partial" or not governing all twelve notes. The sense of tonality is then fragmented, not using all 12 notes, and becomes a "seed" area of tonality.

Here, Bartok is using sounds derived from the diminished scale, which creates an ambiguous sense of tonalty, because of the nature of the scale and how it is used; there is no stable fifth, for starters.
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There's a lot of loose use of the term "tonal" around this subject. I don't hear Schoenberg's Piano Concerto as being tonal in any sense of the word, and especially to my ear.

Sure, you can hear triads, and melodies which seem to suggest chords with roots, but there is no 'function' heard as they progress through time; they seem to wander, and never settle down to a tonic. That's not tonality. It could not be analyzed tonally, as is has no root function, or any harmonic goal. Whatever allusions to harmonic tonality one may hear are completely arbitrary, and are the result of Schoenberg's manipulation of the row.

The ear hears lower bass notes as roots of chords, and the higher notes as subservient members of that 'chord.' It's really not a harmonically-derived chord, though; it's a 'harmonic aggregate,' derived from the row structure, and has nothing to do with harmonic function, unless we 'imagine' it to be.

Even if Schoenberg purposely meant to suggest harmonic function, he could only do this in isolated relationships, and there is no way he could sustain this allusion/illusion for more than a 'chord' or two.

But he knew this; he knew the way our ears hear. Our ears hear "from low to high," and any stack of notes will be heard as having its 'root' on the bottom. This is not 'tonality' in any sense; this is simply the way our ears hear.
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Debussy is an easier listen, but I would not label him as 'atonal' just because he is 'not tonal' in the traditional sense. 'Atonal' means "having no tonal center," and this is not the case with Debussy.

Debussy worked freely, ignoring function, and his music was tonal or 'tone-centric' in places. However, it could suddenly shift into a different region. We might hear a 'cadence' or resting point, but these are not prepared, as they would be in tonality.

Another factor in the argument that Debussy's music is not 'atonal' (yet not functional in a tonal sense) is his use of scales, such as the pentatonic, whole-tone, diminished, and 'synthetic' scales, such as the lydian with flat-7 scale.

To use a scale implies a 'starting point' which proceeds upward through the octave, until the starting pitch is reached again in the next higher octave. This in itself implies and creates, to our ears, a sense of tonality, since scales are like "indexes of pitches" which can be drawn upon freely, in any order (unlike tone-rows), and which can have their own harmonic function by building triads and stacking thirds on top of any scale note.

Additionally, these 'synthetic functions' do not need to have arbitrarily assigned functions; the functions arise naturally as a result of their degree of dissonance in relation to the starting 'root' note. The functions will be ranked (by our ears) in terms of the most consonant being the most important or related harmonically to the tonic note, and so forth, towards the most dissonant. This is a self-evident 'harmonic truth' which applies to any scale, whether it be 'world music,' folk music, or any tone-centric music.
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There is almost always a tonic pitch to be found in Debussy and it's not too hard to find, but it also doesn't stick around for any great length before a new tonic pitch is in play.
Then it's not really a tone center in the sense of truly tone-centered music. It's weakened, or ambiguous.

Therefore, it's not really accurate to say it's 'atonal,' since it does exhibit fleeting tone-centers.

Neither is it accurate to say it is tonal music, in the sense of having an overriding sense of key, and using key signatures which apply to large sections of the composition.

It's "Impressionism," which means, among other structural stylistic practices, "has a weakened or ambiguous sense of tonality due to the use of whole-tone scales, etc."

So, I think I would describe this as 'unstable tonality' or as 'chromatic tonality', a less radical version of Schoenberg's period of 'free atonality.'
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This isn't much of a game, is it?
I never liked sports anyway.
This makes more sense to me as a comparison: Schoenberg's string quartets. These were the String Quartet No. 1 in D minor, Op. 7 (1905), String Quartet No. 2 in F sharp minor, Op. 10 (1908), String Quartet No. 3, Op. 30 (1927), and the String Quartet No. 4, Op. 37 (1936). In addition to these, he wrote several other works for string quartet which were not published. The most notable was his early String Quartet in D major (1897).

So, how do you hear them? The early D major, and No. 1, are tonal. No. 1 is said to be in D minor. Do you hear it this way? Mahler said he could not read the score, so it must have confused him.

In No. 2, the first three movements are said to be tonal, but the fourth movement has no key signature. Is it 'atonal?'

Quartet No. 3 is supposed to be totally 12-tone. How does it sound? Is the rhythmic dimension important? Do you hear rows? Is he using motives?

The Fourth Quartet is totally serial as well. Unlike No. 3, this one is melodic, not rhythmic, in its overall thrust. It has been suggested that in this movement Schoenberg's choice of the different forms of the 12-note row function in a manner 'analogous' to the different tonal areas explored in a sonata form that is written in traditional tonality. Does this 'analogy' to tonality mean that it is indeed, tonal? Or are these structural analogies?
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I heard all of Schoenberg's string quartets and based on my layman's intuition, I think of them as tonal honestly. Lack of key signatures do not signify atonality to me because tonal centers still exist although in smaller chunks.
The established view is that the String Quartet No. 1 in D minor, Op. 7 (1905), is tonal, although it stretches tonality to the limit. Also, the early String Quartet in D major (1897) is tonal, in the late-Romantic tradition.

String Quartet No. 2 in F sharp minor
, Op. 10 (1908), is tonal, although very extendedly tonal, except for the fourth movement with no key signature. It has been analyzed by experts not to be strictly 12-tone, so it is an example of 'free atonality,' written atonally, but using no strict 'system' like the 12-tone system to avoid tonality.

This movement may be structured along other lines, which, although not codified into a systematic method yet, are nonetheless examples of the use of 'atonal procedures' which might involve sets of notes (dyads, trichords, tetrads, septads, etc.) which are unordered, and are thus able to exhibit sonorous harmonic effects due to their interval content (interval vectors). This is probably why you say that these quartets sound 'tonal.'

String Quartet No. 3, Op. 30 (1927), and the String Quartet No. 4, Op. 37 (1936) are 12-tone. In other words, they are not tonal, they are atonal, and were written using the 12-tone system.

At this point in the early use of the 12-tone system, who can say how strict Schoenberg was being? He might have been using the ordered 12-tone rows as melodic and thematic material, sticking strictly to the ordered rows; and using subsets of unordered notes as his harmonic material. So, strictly speaking, Schoenberg was not being strictly 12-tone all the time; he probably was using 'atonal procedures' involving un-ordered sets, in order to create a harmonic dimension in the otherwise non-harmonic, strictly melodic/counterpoint world of the ordered 12-tone row.

It's appropriate to describe these string quartets as 'musical', 'sonorous', and, yes, even 'tonal', although this use of the term 'tonal' is not really correct, but just a descriptive convenience on the user's part. I've heard Schoenberg's music described in this way before.
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millionrainbows: You say that 12 tone music goes completely against tonality. You obviously have not heard of the 12-tone tonality idea of George Perle later taken up by Joseph Straus!
Yes, I have the Perle book. Perle was influenced by Milton Babbitt in this, as well. Thanks to them, there is emerging a comprehensive way of dealing with the harmonic aspects of serialism. To call this "tonality" is using the term very loosely and generally.

"Sonorous" and "tonal" do not mean the same thing. Tonality must be pervasive, sustained, and be a general, implicit system in its very structure and DNA. Serialism is just "a system" which has to be re-invented every time, in each composition. I'm not saying that's good or bad; I'm just pointing out the differences in these systems and in tonality.

I think it is very reasonable to argue that Schoenberg's method was an outgrowth from the increasing chromaticism of the late romantic period. Schoenberg certainly thought of it like that. Indeed, he even considered his ideas to be implicit in general contrapuntal technique.
That's because ordered rows are inherently contrapuntal. I don't think chromaticism is the same as 12-tone sets. By discarding function, and using ordered rows, a fundamental line was crossed. This is what I wish to point out; how serialism is different than tonality, not how it is similar.

If you mean common-practice tonality, then I agree that serialism is often atonal. But there are certainly some ways that the word tonal is used that 12 tone music does fit with. If you have a row, and everything else is related to that row, then the structure of the row is an important governing factor of the sound of the work. For example, in Schoenberg's Violin Fantasy it is the combinatorial nature of the two hexachords of the prime row which controls the selection of rows which are paired with each other. This means you get a set of harmonies that are dependent on an abstract structure.
Yes, but what you fail to point out is that the hexachords share content, but not order. This makes them more like scales. I can see the relation of the hexachords to the row in a general way, after the fact; but this hexachordal content, designed to squeeze harmony out of ordered rows, is not a defined or general aspect of serialism, as it is in tonality, which has an implicit harmonic aspect in its very structure.

You have a set of pitch relations that control harmonic behaviour and resultant sound. Plus, the piece goes through different 12-tone areas as described by David Lewin. That all sounds like a type of tonality to me!
Yes, it is a "type" of "tonality," but it has to be put there by somebody, and it is not functional tonality. It is very different. That's what I wish to emphasize; the difference.

Why should I have to "reconcile" serialism with tonality? I accept each one on its own terms.
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I heard all of Schoenberg's string quartets and based on my layman's intuition, I think of them as tonal honestly. Lack of key signatures do not signify atonality to me because tonal centers still exist although in smaller chunks.
I guess you can "think" of them as tonal, but that doesn't mean they are. This kind of logic could be taken to the extreme, and every note at any moment could be considered a 'tonal center' even if it only lasts a millisecond. But this kind of logic is not productive, and eventually a cogent definition must be arrived at.

Also, this 'ruins' the modernity of Schoenberg; it's like seeing unicorns and Greek figures in abstract expressionism. The Schoenberg quartets are tonal where they are tonal, and "atonal" where they are not tonal.

Come to think of it, these Schoenberg quartets are not good examples for this issue, since they are transitional and contain areas of both tonality and atonality.

Why do people keep pursuing this line of thought, to try to keep modern music in the conservative camp of tonality? I suppose it's because they hate the idea of a well-defined, precise form of music which is not tonal, called "modern", and are hesitant to cross that line; they maintain their distance from modernity by seeing Debussy, Schoenberg, and Bartok as traditional tonalists first, and radicals second.

This is a fairly easy position to maintain, as the lines between tonality and 'harmonic' non-tonal music are often blurred; and the opposing view is a tedious position to argue, for the same reason. Only in precise terms, and in-depth analysis, will the differences between atonal and other forms of tonality become apparent, and as happy-go-lucky listeners, this is irrelevant.

So, let's look up at the clouds in the sky, and see what we can see! Does that sound like fun, kiddos? Oh, look! I see a unicorn! And there's a cow! and a sheep!
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