7th symphony allegretto A1 motif
Having gone through everything in the previous post, we'll first return to our Beethoven (7th symphony) example to clear some things up. I want to make it clear, to avoid unnecessary confusion, that even a sequence that consists of substructures that are perceived to repeat can be a full Canonical Sequence in itself, as long as it doesn't require SGP in order to comprehend the way the theme flows or how thematic material is used in it (which is an important distinction). As such, the primary theme of the second movement of Beethoven's 7th is very much a Canonical Sequence, even thought it could be decomposed into something that could at least in part be built up with Variant Addition. It has repeating substructures within it (motifs consisting of the individual 2-bar subsections in each 8-bar theme, which I have labeled A1 above), and you could construct the theme by taking a single such subsection and extending it out with Variant Addition (similarly to what was done with the Montiverdi madrigal in the previous part), but there is still nothing preventing it from being interpreted as a single, whole Canonical Sequence in the absence of SGP. Each A1 section within it ends appropriately enough and continues to lead into the next substructure (either continuing into another A1 within the theme or ending the theme by omitting its final note), but without creating an expectation that its own structural resolution is suspended and delayed so as to be resolved through the entirety of the next substructure, (which would otherwise be a phrase extension, which I would indicate with the black, backward pointing arrows that I used in the modified versions of the Montiverdi madrigal, but which are absent in my illustration of the opening section of Beethoven's 7th in part 2). Instead, each 2 bar motif is basically sufficient in itself, as while it sets up the next part or instance of the theme, as an individual phrase, to continue by not constituting a complete structural cadence itself (except when ending each theme instance), it also doesn't create an expectation that the note immediately after should be a realization of such a cadence either. Specifically there is no need to reinterpret it with SGP or variant structures, since, unlike "Zefiro Torna", the theme does not set up an expectation of a resolution that is subverted. So each part can be perceived to flow into the next using the basic understanding of musical repetition offered by the more fundamental sense of basic metrical rhythm combined with the phrase structures that arise out of EVP (as opposed to SGP based structures).
However, what I have discussed above is not necessarily something that can be used as a general rule which tells you what is a motivic part of a Canonical Sequence or what is strictly a variant structure, or even that there has to be a hard distinction between the two if it's possible to interpret a structure as both (an issue I'll deal with shortly). I intend this as an illustration of the differences between these two specific examples (motifs from Beethoven's 7th and Montiverdi's Zefiro Torna) and consider it largely an attempt to explain why I have placed each in the category that I have using my own intuition. I expect each reader to follow along with the music in each example itself in order to discover what they feel themselves, and find out how their own experience of mental phenomena matches up with what I have described along with what each of the specific aspects subjectively feel like to them. I want to build up the phenomenological intuition of the reader by bringing attention to these things, so that they will either realize what they lack, or otherwise learn to distinguish between various ways they do perceive structure in music and how it feels to grapple with each.
So, continuing on, I will have to point out that, despite me stressing that the motif discussed doesn't require SGP to be perceived as a satisfying musical theme, there's nothing actually saying a SGPA couldn't interpret these substructures in light of something like a generalization of variant addition, and in fact, I'd say that doing so is actually the natural way that a EVN-SGA would end up hearing the theme, as being composed of many internal structures as well as also being a complete theme that is still itself a canonical sequence, as this enables a greater impression of structural richness and is likely to happen subconsciously anyway, given that it is my experience. This total sense of structure rising out of all the possibilities enabled by SGP is what I label Variant Construction, which is what this series of articles has been building up to defining. Now, I must note that I don't actually intend to define all the structural possibilities that may result from this, as I suspect those may be effectively infinite, but I do want to give people a general idea of what this does enable.
To let you picture this more clearly and finally give it some sort of definition, Variant Construction enables compositional techniques enabled by Variant Addition such as "phrase extension", "phrase elision" [4], and additionally allows certain kinds of links between phrases and uses of interpolation to enlarge structure. Variant Construction is primarily an interpretive model of total structure, a way of defining and exploring how exactly it is that structures that would otherwise be limited to the expressive power of canonical sequences can be reinterpreted using super grammatical faculties so that these additions and expansions of structural possibility can take place and make sense to the listener while enriching the experience of the music. As such, variant construction concerns itself with a totality of structural possibilities that go beyond the techniques mentioned above, and allows the exploration of things like the addition of internal structure to canonical sequences that might affect how their phrasing is interpreted. It also affects things like extra motivic grouping, like how patterns between groups can affect how they relate and form larger groups under grouping structure (which we will look at later on using the C Major Prelude analysis detailed in the GTTM[1]). Beyond this, it is also concerned with the resolution, or sublation, of ambiguities in the variant structure that may arise from all this. The rest of this article will use different pieces to illustrate these ideas.
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C Minor Fugue Example:
First I'll make use of Bach's C minor fugue from Book 1 of the WTC to illustrate what can be done with this kind of ambiguity.
Here, in this fugue, you may be tempted initially to follow along the subject as shown in this diagram, going with this grouping or some variation of it.
The key to understanding why I have called Variant Construction, lies in this potential of creating new interpretations though 'searching' through possible grouping structures in this way. I must note that I'm not specifically trying here to define the process of composing music by adding repeating or linked parts of Canonical Forms in particular ways (though this in naturally relevant to composition), but rather, to name the mental process of mentally building up the music into groups in such a way that interpretations more complex than what the canonical sequences of EVP would allow otherwise become possible. This may be important in the actual process of composition, but I wish to stress that I intend this primarily as a method of understanding how the mind can process music.
I've brought up the two different basic groupings I have for a reason. Different interpretations of grouping structure can result in different examples of such groupings feeling important if you specifically concentrate on perceiving them, but there's nothing actually saying you can't subconsciously experience each of these groupings being a meaningful part of the feel of the phrase structure simultaneously to a certain degree. It is possible that each of them is capable of being a force shaping how you understand and interpret the music if, instead on concentrating on one of them exclusively, you try to acknowledge how different groupings might each affect the music at the same time. In fact I'd say that in many cases it is ideal to be able to understand multiple grouping structures like this unconsciously (especially in complex fugal works) with the ultimate aim actually being to put aside the need to explicitly think about the structure of the music and surrendering to the sense of everything flowing smoothly, working together at the same time while you are barely aware of any conscious attempt to analyse anything. In my experience, I feel the greatest richness in the music when I'm able to move past the mindset of explicit searching for structure and manage to let everything I'm aware of influence me at once. But in this flow state, I find that explicit awareness of division into grouping structure feels superfluous. Instead, it ends up feeling like a single, almost indefinable structure shaped by forces that are beyond my explicit conscious understanding, though which are only possible by first familiarizing myself with the music and thinking about the apparent structures which are presented to me as I listen to them now that I possess both Encompassing Voice and Super Grammatical Perception.
Here, Glenn Gould describes the way that, in interpreting a piece, he may wrestle with several different forces that simultaneously influence how he feels he ought to influence his phrasing of the piece, only being satisfied when he believed that he's played well enough to capture each of them appropriately. As such, it may only be possible to really get into this state (whether listening or playing) after already spending enough time grappling with the piece.
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G Minor Fugue Example:
To continue on, lets look at examples of what Variant Construction can actually achieve on a larger, more substantial scale and how bigger phrase structures can arise by having super grammatical processes link their elements together.
But hang on, isn't the second last note still a D, falling in the same place in the only an octave higher? And couldn't this mean that there's a sense in which the final four notes are an embellishment of the A to D step in the previous bar? Try listening to the piece again and with this interpretation in mind. It's unnatural and results in a lack of resolution doesn't it? But on the whole doesn't this feel similar to what happened in the Montiverdi piece before, where the end of one section is forced to become the beginning of another, in a way that demands that your mind find some way to resolve it, but is otherwise awkward and unsatisfying if you can't? I know I was completely unable to resolve this when I lacked SGP. But now, for me, there's a sense that it acts as a structural hinge that links together different parts by making you interpret them as extensions of other material.
We only have to look further into the piece to see what the melodic structure could have done in contrast. In fact, this form of it occurs in the bass only a short time after (at around 0:55 into the linked video). Here, the part that is equivalent to the 'hinge' in the section where the material is first introduced is played out in they way you would expect it to be played in order to give it a firm resolution. The marked sections are able to parallel each other as canonical material (modified through embellishment) and resolve in parallel fashion, before continuing on into a cadential sequence resolving to D (though I guess this would be a half-cadence in this instance [2]).
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Cadential Extensions and Assorted Structures
Expansions of cadences, elongations of parts of the music that serve to hammer home the tonal center and firmly finish off a piece or section of it are common in tonal music, especially in common practice western art music. A perfectly 'generous' example of this is the finale of Beethoven's 5th.
https://youtu.be/xAQFJ1YpFaI?t=12m40s
When this occurs, variant construction is essential in enabling the feeling of continuation of post-candential expansion throughout these sections. Without it, the listener will simply desire the music to rest on the tonic as soon as possible and find the expansions past this to be excessive and pointless.
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Varied Rhythmic Examples:
Stravinsky's Le Sacre du printemps is one of the most SGP intensive works in the repertoire. The way that each musical block fragment of melody links up with other blocks across the distinct rhythms is something that SGPNs will completely fail to perceive, making the whole work feel perpetually disconnected, and the slower parts especially will feel like a slog to get through. There is very much a night and day difference on what it is like to listen to it between lacking SGP and having it. It is a strong showcase of how poetic sensibility can be used to create a separate sense of meter that carries through variations of rhythm that would otherwise break this feeling. This process is similar to what I hold allows the less rhythmical, freely structured meters of High Verse poetry to work on a poetically sensitive mind.
This John Adams composition and the way its sequences musical fragments are blared at the listener should have a similar effect, it will only feel like it has meaningful structure to SGPAs. The actual poem itself, John Donne's Batter my heart, three-person'd God, also contains meaningful structure whose effects will not be fully apparent to those without SGP, such as feeling resulting from the parallel between "knock, breathe, shine" and "break, blow, burn", and the total meaning of "Reason, your viceroy in me," which I hold contains conflicting ambiguities of meaning that SGPNs will be unable to intuitively resolve.
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Justification and relation to the Generative Theory of Tonal Music:
Part of why I am so confidant that SGPNs will be unable to comprehend variant structure is that I effectively spend years searching for structures like it in music, perplexed by my own inability to perceive anything resembling it despite expecting to be able to do so. I was told by lovers of 'well composed' [3] symphonic music that part of why they loved such music was that each each aspect of it felt like part of a well ordered machine, each section feeling like it naturally flows on from the previous, with each part having to follow on, often in ways they couldn't imagine playing out differently. Yet, despite having attained Encompassing Voice during this time and assuming that I had all the mental capabilities needed to fully appreciate all kinds of music, I didn't feel that way at all, with most art music still feeling broken, disjointed and piecemeal, with odd, abrupt changes to melodies that made no sense and unnaturally drawn out cadences. I didn't know at the time if I was lacking in any particular way, or that there was any additional state of mind of importance beyond EVP that I might need, and so I assumed that if I was perceptive enough I would 'get it' somehow and that it must somehow be my lack of sensitivity or knowledge that was holding me back. I read comments by an amateur composer explaining how the structural difficulties he would encounter in composing music were close to those of writing software, and how he could "write himself into a corner" in both cases creating structures similar in kind that extended themselves in ways that would prevent him achieving his goals. But with my experience developing software and the extent allow me to relate to this, this didn't make a lot of sense to me. Music (though still incredibly emotional) just didn't seem to have the same kind of rich structure that would allow the kinds of 'mistakes' that could have such significance on such a scale.
But encountering Fred Lerdahl and Ray Jackendoff's Generative Theory of Tonal Music (GTTM) only caused me to became even more perplexed. I wanted to make sense of it, and honestly believed I could at that point if I thought about it hard enough, but I found that even on the most basic level it described features of music that I had no experience of. The grouping of things into hierarchical structures on several levels from the smallest motif to the largest movement subsuming one another in turn, beyond that of the internal tension implied by thematic structures, was not something that I had ever felt was meaningful in any of my experience of music. Or at the least, such structure was irrelevant to the shaping of my interpretation of thematic structure. I could guess how certain patterns might arise that could give rise to this hierarchical structure, or which might be intellectually analysed as such (especially while looking at a score or graphical representation of the music and looking for similarities and parallel symmetry), but I didn't feel that any of these constructs had importance to musical structure independently of simply being part of a given theme (which I now categorize as a canonical structure) or subsequent response. It is only now that I intuitively feel how parallelism gives rise to extensions and variants of structures, beyond them simply being part of a basic thematic skeleton.
I will note though, that in the GTTM, a significant assumption is made about the nature of the listener to whom the structures described are supposed to be apparent. That is that the listener is someone who is "experienced in a musical idiom", i.e. they have somehow learned or innately possess the cognitive capability and prerequisites required in order to understand the formal structures described, whatever that implies. This suggests an awareness that not everyone will perceive music the same way, which at least is something that can account for differences of culture, and is something that agrees with my own theoretical framework and experiences. Leading on from that, I will make the suggestion that Lerdahl and Jackendoff's GTTM describes an experience of musical structure that is absolutely dependent on the possession of EVP and SGP together, and that people not in possession of both cognitive abilities will not process music in that way. This I feel will end up being a core aspect of my theory, once I have spend more time evaluating Lerdahl and Jackendoff's theories.
Conclusions and Research:
For much of this article, we've specifically looked at some of what EVA-SGAs are uniquely capable of perceiving and how I've chosen to model this with the ideas of Variant Addition (parallel structure that can extend and/or transform the flow of themes) and Variant Construction (the mental sublation/combination of the various possibilities of these grouping structures, and others, into a total, continuous whole). All this is in contrast with the musical structures that are possible to comprehend without SGP. Because of this, we can start to find ways of classifying possible grammars of music in terms of linguistic ideas
For instance, the EVA-SGN understanding of how successions of canonical themes follow each other within a given single voice is generally similar to the structure of recursive right embedding of sentences in language, with each theme running its course and then, depending on how solidly it ends in a cadence (determined by the 'strength' of the note influenced by contextual factors and how it resolved relative to the global key that has been established in the listener's mind), continuing on through the next theme instance (whether it be a variation of the same theme or other material that follows melodically). Large scale (arbitrarily large scale?) center embedded structures made up of variant transformations of (thematic) canonical sequences impossible without SGP, however, are seemingly made possible by Variant Construction. Through this, SGP also allows subsections effectively resolving into a different key to be embedded in larger structures, and all kinds of basically arbitrary musical forms to be built up using these techniques. Understanding the mental buildup of these structures is something I wish to further pursue and hopefully research can be done on this in the future that makes this possible.
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So to end it all, and provide a bit of consolation to readers who may have realized by now that they are not in possession of at least one of these perceptual abilities, I'll grant listeners a couple of pieces which I'm sure are capable of completely satisfying even those who otherwise have neither EVP or SPG.
This last one being a particular favorite of mine. Enjoy.
[1] https://en.wikipedia.org/wiki/Generative_theory_of_tonal_music
[2] http://www.music.mcgill.ca/~caplin/caplin-classical-cadence.pdf
[3] https://youtu.be/OuYY1gV8jhU?t=6m3s
[4] http://core.ecu.edu/music/jacobse/classes/analysis/PHRASES.HTM
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