Prolegomena to Music Semantics

Abstract

We argue that a formal semantics for music can be developed, although it will be based on very different principles from linguistic semantics and will yield less precise inferences. Our framework has the following tenets: (i) Music cognition is continuous with normal auditory cognition. (ii) In both cases, the semantic content derived from an auditory percept can be identified with the set of inferences it licenses on its causal sources, analyzed in appropriately abstract ways (e.g. as ‘voices’ in some Western music). (iii) What is special about music semantics is that it aggregates inferences based on normal auditory cognition with further inferences drawn on the basis of the behavior of voices in tonal pitch space (through more or less stable positions, for instance). (iv) This makes it possible to define an inferential semantics but also a truth-conditional semantics for music. In particular, a voice undergoing a musical movement m is true of an object undergoing a series of events e just in case there is a certain structure-preserving map between m and e. (v) Aspects of musical syntax (notably Lerdahl and Jackendoff’s ‘time-span reductions’) might be derivable on semantic grounds from an event mereology (‘partology’), which also explains some cases in which tree structures are inadequate for music (overlap, ellipsis). (vi) Intentions and emotions may be attributed at several levels (the source, the musical narrator, the musician), and we speculate on possible explanations of the special relation between music and emotions.

Appendices

Appendix I. Varieties of internal semantics

This Appendix discusses in greater detail the notion of an ‘internal semantics’ for music, briefly mentioned in Section 2.2.

Before we say a word about the ‘internal’ semantics in music, we consider how such a semantics can be constructed for a system as simple as the la li lu example of the Section 2.1. The key is that a syntactic system that has no semantics relating it to the external world can still be endowed with a semantics that pertains to the form of the expressions themselves. In (54), we have done so for the context-free grammar defined in the main text in (1)b. Just as is standard for human language, each step in a derivation tree is interpreted by a semantic step. The result is not exciting: each syllable denotes itself, and each sequence denotes itself as well, with the proviso that the interpretation procedure adds pauses between groups of 2 syllables.⁴⁶ Some simple examples are given in (55).

(54) a. Lexical semantics:

• [[la]] = la

• [[lu]] = lu

• [[li]] = li

• b. Compositional semantics

Notation: ˆ is used to represent concatenation of expressions; for strings s and s’, sˆ_ˆs’ denotes the concatenation of s and s’ with a pause in between.

For any words w, w’ of the lexicon Lex and for any sequences l and s of categories L and S respectively,

[[[_L w w’]]] = [[w]] ˆ [[w’]].

[[l s]] = [[l]] ˆ_ˆ[[s]]

(55) Examples

• [[[_L la lu]]] = [[la]] ˆ [[lu]] = laˆlu.

• [[[_L la lu] [_L la li]]] = [[[_L la lu]]] ˆ_ˆ[[[_L la li]]] = laˆluˆ_ˆlaˆli

Now this semantics adds very little to the syntax. But one could develop a more subtle variety of this internal semantics, one that only keeps track of certain properties of the form of our syllable sequences. For example, in (56) we define a semantics that keeps track of the vowels that appear at the end of our 2-syllable groups. Thus la lu will ‘denote’ u, while la li will ‘denote’ i, and the sequence la lu la li will denote the sequence iˆu, i.e. the concatenation of the vowels i and u.

(56) Semantics based on vocalic paths.

• [[[_L la lu]]] = u.

• [[[_L la li]]] = i

For any sequences l and s of categories L and S respectively,

[[l s]] = [[l]] ˆ[[s]].

(57) Examples

• [[[_L la lu]]] = u.

• [[[_L la lu] [_L la li]]] = [[[_L la lu]]] ˆ[[[_L la li]]] = uˆi

We can think of this semantics as associating with some strings a ‘vocalic path’ that tracks the sequence of some particularly important phonemes that appear in it – here they are the non-predictable vowels of each 2-syllable group.

While no interesting analysis would postulate that music has the kind of semantics exemplified by (54), there are prominent examples of music semantics that develop more sophisticated versions of (56). Thus Granroth-Wilding and Steedman 2014 endow their formal syntax for jazz chord sequences with a semantics that encodes paths in a tonal pitch space whose structure is depicted in (59). In their analysis (framed within Combinatory Categorial Grammar), surface chords can be assigned syntactic categories that give rise to derivation trees. Each derivational step in the syntax goes hand in hand with a semantic step. And the semantics encodes movements in tonal pitch space.

A minimal example is given in (58), which provides the semantics of a sequence V⁷-I within a tonal pitch space whose structure is displayed in (59). The final I denotes a location in tonal pitch space, with coordinates <0, 0>. The penultimate V⁷ denotes a function from x to a position that ensures a 1-step leftward movement towards x, written as: λx. leftonto(x). Taking the location <0, 0 > as an argument, the result is: leftonto(<0, 0>). Assuming the tonic (i.e. <0, 0>) is a C (circled in (59)), this would correspond to a movement from a G (also circled in (59)) to that C.

(58) Example of a syntactic and semantic derivation in Granroth-Wilding and Steedeman’s (Granroth-Wilding and Steedman 2014) framework (fragment of their Fig. 19)

(59) Structure of the tonal pitch space assumed in Granroth-Wilding and Steedman 2014 (following Longuet-Higgins 1962a, 1962b)

We believe that this analysis is close to an intuition developed in some of Lerdahl’s work (Lerdahl 2001), in which the meaning of music is essentially likened to a journey through tonal pitch space.

Importantly, this semantics is ‘internal’ – and thus not a ‘real’ semantics, from our perspective – because it does not draw a connection between music and the (music-)external reality, unlike the semantics developed in this piece.

1.1 Appendix II. Music semantics vs. logical semantics

This Appendix compares in greater detail music semantics with the simple logical semantics sketched in Section 7.1.

In order to bring the comparison into sharper focus, we define a non-standard but particularly simple logic that shares some properties with our music semantics; the main differences will become easier to grasp within this shared background. In a nutshell, this logic is defined for a language made solely of propositional letters, and conjunctions. Since the only way to combine propositional letters is by way of conjunction, we don’t need an explicit conjunction sign and thus we will solely investigate sentences of the form: p_i, p_ip_k, p_ip_kp_r, etc., as is specified by the syntax in (60)a. Each propositional letter is taken to hold true of events,⁴⁷ and concatenation is interpreted as conjunction, as shown by the semantics in (60)b.

(60) A purely conjunctive logic

• a. Syntax

• Atomic propositions: for every i ≥ 0, p_i is an atomic proposition.

• If p_i is an atomic proposition and F is a proposition, p_iF is a proposition.

• b. Semantics

• Let I be a function such that for every i ≥ 0, I(p_i) is a set of events.

• For any propositional letter p_i, p_i is true of event e just in case e is in I(p_i).

• If p_i is an atomic proposition and F is a proposition (whether atomic or not), p_iF is true of event e just in case p_i is true of e and F is true of e.

Let us immediately illustrate with the examples in (61). If p₂ holds true of events e, e’ and e", while p₃ holds true of events e' and e", the (implicit) conjunction p₂p₃ holds true of e’ and e”, as does p₃p₂. If in addition p₁ holds true of e and e’, p₁p₂p₃ holds true of e’.

(61) Examples

• I(p₁) = {e, e’}

• I(p₂) = {e, e’, e”}

• I(p₃) = {e’, e”}

• a. For any event f, p₂p₃ is true of f iff p₂ is true of f and p₃ is true of f, iff f is in {e, e’, e”} and {e’, e”}, iff f is in {e’, e"}, iff f = e' or f = e".

• b. For any event f, p₃p₂ is true of f iff p₃ is true of f and p₂ is true of f, iff f = e’ or f = e” (by a.).

• c. For any event f, p₁p₂p₃ is true of f iff p₁ is true of f and p₂p₃ is true of f, iff f is in {e, e’} and f is in {e’, e”} (by a.), iff f = e’.

We note that our rules are designed in such a way that a string is always semantically analyzed from beginning to end: a string p₁p₂p₂ is analyzed by the semantics (in (60)b(ii)) as having the structure [p₁[p₂p₃]]. Nothing deep hinges on this: given our conjunctive semantics, whether a string p₁p₂p₃ is analyzed as [p₁[p₂p₃]] (as we do) or as [[p₁p₂] p₃] won’t affect the truth conditions, since the end result will just be the conjunction of p₁, p₂ and p₃.

One could think of p₁p₂p₃ as a series of musical events, which may be true of some events such as e, e’, e”, etc. But as noted in the text, the similarities with our music semantics end there: the conjunctive logic above has no counterparts of our preservation principles (Time, Loudness, Harmonic stability); and in that logic, p₁p₂ denotes events that satisfy both p₁ and p₂ (order irrelevant), rather than pairs of events <e₁, e₂ > that satisfy p₁ and p₂ (in that order), as in our music semantics.

Appendix III. Complements on the syntax/semantics interface

This Appendix provides some complements to the discussion of the syntax/semantics interface in Section 8. Part A gives details about exceptions to tree structure in Lerdahl and Jackendoff’s analysis, as alluded to in Section 8.3.1. Part B formulates some questions raised for the present analysis by Lerdahl and Jackendoff’s prolongational reductions.

1.1 A. Exceptions to tree structure in Lerdahl and Jackendoff’s analysis of grouping

We argued in Section 8.3.1 that a mereology-based reconstruction of musical structure leads one to expect that two musical groups could have a part in common (as in (36)e in the main text) in two types of cases: when the denoted events are best analyzed as having a part in common (overlap); and when two distinct events share the same auditory trace (occlusion).

Lerdahl and Jackendoff 1983 emphasize that such cases do arise in music. Since they take grouping structure to result from principles of perception rather than from syntactic rules, they do not take these ‘exceptions’ to refute their account. On the contrary, they explain these exceptions by appealing to analogous cases in visual perception. The exceptions they list are of the two types we expect: in case of overlap, the denoted events are construed as sharing a part; in cases of occlusion, the auditory trace of an event occludes that of another event.

1.1.1 ❒ Overlap

Lerdahl and Jackendoff 1983 illustrate visual overlap by the case in which a single line serves as the boundary between two objects, and is thus best seen as belonging to both, as in (62)a, which is preferably analyzed as (62)b rather than as (62)c,d. In our terms, this is a case in which the optimal mereological decomposition of the underlying object should not be minimal – although an alternative possibility is that we are dealing with two different lines that have a unique visual trace.

(62) Lerdahl and Jackendoff’s visual analogue of overlap (Lerdahl and Jackendoff 1983 p. 59)

Cases of overlap are probably pervasive in event decomposition as well. A person’s walk is a succession of cycles in which a foot touches ground, goes up, and touches ground again. Each subevent in which the foot touches ground is both the completion of a cycle and the beginning of the next one – an event counterpart of the object perception case in (62).

Lerdahl and Jackendoff 1983 cite the very beginning of Mozart’s K. 279 sonata as an example of auditory overlap, as seen in (63). The I chord at the beginning of bar 3 seems both to conclude the first group and to initiate the second, hence it can be taken as the trace of an event that plays a dual role as the end of one event and at the beginning of another. Alternatively, and less plausibly perhaps, this could be a case in which two distinct events have the same auditory trace (this is precisely the uncertainty we had in our discussion of the visual example in (62)).

(63) An example of overlap: the beginning of Mozart’s K. 279 sonata (Lerdahl and Jackendoff 1983 p. 56) [AV46http://bit.ly/2D9Xioe]

1.1.2 ❒ Occlusion

The second case involves an object that partly occludes another object, as in (64). Here the most natural interpretation of (64)a is as (64)b, which involves occlusion, rather than as (64)c and (64)d, which don’t.

(64) Lerdahl and Jackendoff’s visual analogue of elision (Lerdahl and Jackendoff p. 59)

Here too, an event counterpart of object occlusion is not hard to find: a train passing by will visually, and sometimes auditorily, occlude numerous other events.

In music, this case is illustrated by what Lerdahl and Jackendoff call ‘elision’. Their description (as well as the visual analogy they draw) makes clear that these are really cases of auditory occlusion, as in their discussion of the beginning of the allegro of Haydn’s Symphony 104, given in a reduction in (65). As they write:

“One’s sense is not that the downbeat of measure 16 is shared (...); a more accurate description of the intuition is that the last event [of the first group] is elided by the fortissimo.”

(65) An example of elision: the beginning of the allegro of the First movement of Haydn’s Symphony 104 (Lerdahl and Jackendoff 1983 p. 57) [AV 47http://bit.ly/2DvixNW].

In sum, in several cases grouping structure departs from a simple tree structure, in ways that can be explained if musical groups are perceived as the auditory traces of events, whose mereological structure is reflected on the musical surface. In particular, there are cases of overlap in which a part is best seen as belonging to two events, and cases of occlusion in which the auditory trace of one event occludes that of another event.

1.2 B. A note on prolongational reductions

Lerdahl and Jackendoff 1983 and Lerdahl 2001 take another notion of structure, prolongational reductions, to play a central role in music perception.⁴⁸ Specifically, prolongational reductions provide a hierarchy of events "in terms of perceived patterns of tension and relaxation" (Lerdahl 2001, cited above). To make things concrete, consider again the time-span structure in (39) in the main text. Lerdahl and Jackendoff argue that it is incapable of representing the intuitive patterns of tension and relaxation represented in (66):

One might say that the phrase begins in relative repose, increases in tension (second half of measure 1 to the downbeat of measure 3), stretches the tension in a kind of dynamic reversal to the opening (downbeat of measure 3 to downbeat of measure 4), and then relaxes the tension (the rest of measure 4). It would be highly desirable for a reduction to express this kind of musical ebb and flow. Time-span reduction cannot do this, not only because in such cases as this it derives a sequence of events incompatible with such an interpretation ([(39)] as opposed to [(66)]), but because the kind of information it conveys, while essential, is couched in completely different terms. It says that particular pitch—events are heard in relation to a particular beat, within a particular group, but it says nothing about how music flows across these segments. (Lerdahl and Jackendoff 1983 p. 122).

(66) Prolongation of the initial I chord at the beginning of of Mozart’s K. 331 piano sonata (Lerdahl and Jackendoff 1983) [AV48http://bit.ly/2DamRom]

In the time-span structure in (39), the last bar forms a group, but it is headed by the V chord, which is harmonically essential (as it marks a half-cadence). As a result, the I chord at the beginning of the last bar plays a subordinate role. But intuitively it corresponds to the end of a tensing and relaxing motion that started on the same I chord, but at the beginning of bar 1. In Lerdahl and Jackendoff’s analysis, prolongational structures are derived top-down from time-span structures in such a way that subordinate time-span events can be ‘promoted’ to a higher hierarchical level if they play a key role in patterns of tension and relaxation.

From the present perspective, two main questions arise about prolongational reductions. First, could they have a counterpart in other areas of perception? In particular, if we could find visual scenes with (i) ‘headed’ events’ (in order to have a counterpart of time-span structures), and (ii) a natural notion of tension (e.g. in terms of more or less stable physical situation), could we also elicit intuitions about an equivalent of prolongational structures? This is what one would expect if the difference between these two kinds of structures derives from the kind of semantic information they seek to capture: event mereology for time-span structures, properties of the path of events in a certain space for prolongational structures.

Second, if prolongational reductions trace the ‘harmonic path’ followed by virtual sources in tonal pitch space, could one also investigate other types of paths, such as those defined by the melodic line or even the evolution of loudness? A key insight of Lerdahl and Jackendoff’s analysis of prolongational structure is that two harmonic events that are not linearly contiguous may still have a direct structural connection, as is the case of the two highlighted I chords in (66). But in the classic analysis of Schenker, the melodic line (and in particular a gradually descending melodic line called the ‘Urlinie’) has related properties: certain melodic elements can be ignored when tracing the general melodic line of a piece because they are structurally subordinate (Forte 1959; Pankhurst 2008). Could one develop a general theory in which Lerdahl and Jackendoff’s prologongational reductions and Schenker’s Urlinie are part of a broader typology? This and other questions pertaining to the interaction between prolongational reductions and music semantics must be left for future research.

Appendix IV. Extensions and further questions

This Appendix sketches some possible extensions of our analysis, and lays out further questions for future research.

1.1 ❒ Context and granularity

In these Prolegomena, we only attempted to sketch the general form of a music semantics. One important issue in actual analyses will lie in determining the level of granularity of the interpretation. One may decide to take each and every musical event corresponds to a world event. But often one may want to have a less fine-grained interpretation. The same issue arises when determining under what conditions a pictorial representation is compatible (i.e. could denote) a real world situation, as is illustrated with the coarse-grained picture in (67).

(67) Coarse-grained pictorial representation of Barack Obama.

Two mechanisms are crucial if we are to ensure that these pictures represent their intended denotations.

• (i) First, we should make sure that the set of possible denotations is small enough – it may be restricted to the set of salient politicians in the situation.

• (ii) Second, we should make sure that not all details of the pictures are required to correspond to something in the intended denotation. For instance, in a pixelized representation, some edges are due to the requirement that squares are used to represent shapes, and must be in part disregarded.

Both mechanisms should prove important in music semantics.

• (i) First, semantic intuitions that would otherwise be very unclear can be sharpened by reducing the set of possible denotations. One way to do this is by way of titles or of explicit (linguistic) descriptions. This is an important device in ‘program music’, and we saw striking instances of this mechanism in Saint-Saëns’s Carnival.

• (ii) Second, when analyzing a piece, one may decide to interpret each and every note as corresponding to a world event, or one may adopt a more coarse-grained interpretation. For instance, if we were to ask of a given movement of a swan whether it makes true the beginning of Saint-Saëns’s piece discussed in (20) in the main text, one may answer in the positive if there is a series of two movements, the second of which leads into a new spatial area (thus interpreting the modulation). Or one may wish to find a much more precise correspondence between the piece – e.g. its precise melodic movement – and the scene it is purportedly true of. Of course a coarse-grained interpretation will make the piece true in many more situations than a fine-grained one.

1.2 ❒ Interpreting a piece

If our analysis is on the right track, a musician interpreting a piece may make musical decisions that further specify the semantic interpretation of the musical score. Ending a piece fortissimo may produce the impression that the source is intentional and is reaching a goal. Ending a piece diminuendo and rallentando may yield the impression that the source is gradually losing energy and dying out. Ending diminuendo without much altering the speed may yield the impression that the source is moving away. These are of course simplifications, but the general point is that the musical interpreter may and sometimes must make semantic decisions that are left open by the score. Even after these decisions are made, there will be a plurality of situations that the music is compatible with (true of), but the musician’s interpretation will usually reduce the set of situations that are compatible with the score.

1.3 ❒ Aesthetic considerations

We have been silent on aesthetic considerations – simply because it is one thing to set up a music semantics, and quite another to assess the aesthetic value of music. If successful, music semantics should come to explain why bad and good music alike produce semantic effects: it is not its goal to offer a music aesthetics. Still, one might hope that some aesthetic considerations might in the end build on insights gained from music semantics. But nothing at all in the present enterprise suggests that the aesthetic effects of music (or for that matter its psychological effects) reduce to its semantics. This would be as absurd as claiming that the aesthetic or psychological effects of poetry are exhausted by its semantics.

1.4 ❒ Semantic effects beyond music

The key idea of our semantic analysis of music is that denotational inferences may be drawn both from normal cognition and from the tonal properties of music. This idea could in principle be applied to other areas as well.

First, one could ask whether a kind of visual counterpart of music could be devised. It would be based on animations that convey information by way of a combination of standard representational properties and ones that are internal to a more abstract system. A very simple example can be found in animated heat maps [AV49http://bit.ly/2DzS6He]: while not quite direct, the geographical content of the map is based on standard principles of visual perception, modulo some simplifications (as a first approximation, a country is seen on a map as if it were perceived from very high up, say from space); simultaneously, there is a color code which is based on natural properties of colors: ‘warm’ colors (e.g. red) represent high degrees of the relevant property, and ‘cool’ colors represent low degrees. But of course the structure of colors is entirely different from the structure of tonal pitch space, and thus it is only at a conceptual level that a correspondence between the auditory and the visual domain can be found.⁴⁹

Second, one could ask whether related ideas could be applied to the analysis of abstract painting. Certainly some standard principles of visual perception are at play in abstract painting – which is the reason we usually don’t just see shapes on a canvas, but (possibly very abstract) objects – something that already played an important role in Heider and Simmel’s abstract animations. It remains to be seen whether certain non-natural properties of the paintings could be interpreted in a way that is comparable to the tonal properties of music.

Finally, one might attempt to apply related ideas to dance, for two reasons: like music, it triggers referential and emotional inferences on the basis of natural and more abstract properties of perception; and in addition, it is often coordinated with music – and hence one might ask how the two mediums are combined (do they give rise to a single semantic representation?). For relevant work, see Charnavel 2016; Napoli and Kraus to appear, and Patel-Grosz et al. 2017.

1.5 ❒ Further questions

Two types of further questions could be asked. One pertains to the nature of semantic inferences in music. The other concerns the nature of the theory we have proposed.

One could ask whether semantic inferences in music are always conscious.⁵⁰ This need not be the case: we had to create minimal pairs and to ask appropriately abstract questions about the virtual sources in order to bring these inferences to consciousness. Certainly this is a matter of degree: some semantic effects are more subtle than others. It might be that, quite generally, inferences that are abstract and hard to put in words tend to be less conscious than more concrete and easily articulable ones (one could explore this question in other cognitive domains, such as visual cognition or the recognition of tastes and odors). Be that as it may, we believe that even when semantic inferences are unconscious, they are crucial to explain some of the psychological effects of music, as well as interpretive choices made by performers.

Turning to the nature of the theory we have proposed, one could ask whether we have not overly stretched the extension of the term ‘semantics’.⁵¹ Our source-based semantics is in part based on our ability to draw inferences on the causal sources of a sound. One could object that the term ‘semantics’ is properly used only if it pertains to an intention to mean something, perhaps along the lines of Grice’s notion of ‘utterer’s meaning’ (Grice 1957). Without taking a position on this issue, we note that our final account does have a place for the equivalent of a kind of utterer’s meaning, since the existence of a music semantics makes it possible to reconstruct the intentions of a musical narrator that attempts to convey a certain (highly abstract) message. The situation is in this respect no different from that of a narrator expressing herself in gestures or by way of drawings or visual animations.

1.5.1 Audiovisual examples

The audiovisual examples can be downloaded at the following URL: http://bit.ly/2DBhNH6

Credits for audiovisual examples.

AV00 Kominsky, J.F., Strickland, B., Wertz, A.E., Elsner, C., Wynn, K., & Keil, F.C.: 2017, Categories and constraints in causal perception. Psychological Science 28,11: 1649–1662. Video of the ‘violation’ condition (of laws of elastic collision). (Thanks to B. Strickland for providing this video.)

AV01 Musicnet materials, retrieved online on January 7, 2018 at https://www.youtube.com/watch?v=UH3IULiXo24.

AV02 Il con, Stanley Kubrick, 2001: A Space Odyssey. Retrieved online on January 7, 2018 at https://www.youtube.com/watch?v=e-QFj59PON4.

AV05, AV06, AV07, AV08, AV09 Musicanth materials, retrieved online on January 9, 2018 at https://www.youtube.com/watch?v=5LOFhsksAYw. Pianists: Vivian Troon, Roderick Elms. Conductor: Andrea Licata Royal Philharmonic Orchestra.

AV13 Video cited in: Honing, H.: 2003, The final ritard: On music, motion, and kinematic models. Computer Music Journal, 27(3), 66–72.

AV17 Kurt Masur: Leipzig Gewandhaus Orchestra.

AV18 Musicanth materials, retrieved online on January 9, 2018 at https://www.youtube.com/watch?v=5LOFhsksAYw. Pianists: Vivian Troon, Roderick Elms. Conductor: Andrea Licata Royal Philharmonic Orchestra.

AV20 Mozart, Don Giovanni, Metropolitan Opera, 1990, directed by Brian Large, stage production Franco Zeffirelli, conductor James Levine, with Kurt Moll as the Commendatore.

AV23 Tchaikovsky Ouverture solennelle “1812”, Op.49, by Berliner Philharmoniker. Conductor Claudio Abbado. Retrieved online on January 9, 2018 at https://www.youtube.com/watch?v=lDIVz9r3q3s.

AV24 Puccini, Madama Butterfly. Asheville Lyric Opera. Pinkerton - Brian Cheney; Sharpless - Mark Owen Davis. Retrieved online on January 9, 2018 at https://www.youtube.com/watch?v=YgLQ3p6hSOI.

AV25, AV28 Musicanth materials, retrieved online on January 9, 2018 at https://www.youtube.com/watch?v=5LOFhsksAYw. Pianists: Vivian Troon, Roderick Elms. Conductor: Andrea Licata. Royal Philharmonic Orchestra.

AV31 Mary Ellen Bute (visuals) and Edwin Gerschefski (piano accompaniment), 1940, Tarantella (excerpt starting at 1:09). Retrieved online on January 13, 2018 at https://www.dailymotion.com/video/xgd0wn.

AV32 Daniel Barenboim, Mozart: Complete Piano Sonatas and Variations, Piano Sonata No. 1 in C, K.279: I. Allegro.

AV36 Leonard Bernstein: Young People’s Concerts Vol. 2. Charles Ives American Pioneer (excerpt starting at 44:33). Retrieved online on January 14, 2018 at https://www.youtube.com/watch?v=tsbaSwhtx9E.

AV37 Charles Ives, The Unanswered Question. James Sinclair, Conductor. Northern Sinfonia (exceprt starting at 1:00). Retrieved online on January 14, 2018 at https://www.youtube.com/watch?v=kkaOz48cq2g.

AV38 Verdi, Simon Boccanegra, Teatro La Fenice 2014–2015, conductor Myung-Whun Chung, RAI, with Simone Piazzola as Simon.

AV42Psycho, 1960. Film directed and produced by Alfred Hitchcock, and written by Joseph Stefano. Music by Bernard Herrmann.

AV44 Verdi, Simon Boccanegra, Teatro La Fenice 2014–2015, conductor Myung-Whun Chung, RAI, with Simone Piazzola as Simon.

AV46 Daniel Barenboim, Mozart: Complete Piano Sonatas and Variations, Piano Sonata No. 1 in C, K.279: I. Allegro.

AV47 Haydn: Symphony #104 In D, H 1/104, “London” - 1. Adagio - Allegro. Adam Fischer: Austro-Hungarian Haydn Orchestra (starting at 2:29).

AV48 Margarete Babinsky. Piano Sonata in A, K.331: I. Andante Grazioso. Mozart Piano Sonatas.

AV49 Todd Mostak, Twitter Heatmapper. Retrieved online on January 14, 2018 from https://www.youtube.com/watch?v=4_v2EZGiA7w.

AV50 Musicanim, graphical score generated for Stravinsky’s The Rite of Spring, on the basis of Jay Bacal’s synthetic MIDI recording. Retrieved online on January 14, 2018 from https://www.youtube.com/watch?v=5IXMpUhuBMs.