HATTEN’S THEORY OF MUSICAL GESTURE
AN A P P L I E D L O GICO- DEDUCTIVE ANALYSIS OF MOZART’S FLUTE QUARTET IN D, K.285
by
DOUGLAS WALTER SCOTT
submitted in partial fulfilment of the requirements
for the degree of
MASTER OF MUSICOLOGY
a t t h e
UNIVERSITY OF SOUTH AFRICA
Supervisor: Dr. Michael Blake
J u n e 2 0 0 9
HATTEN’S THEORY OF MUSICAL GESTURE
AN A P P L I E D LOGICO - DEDUCTIVE ANALYSIS OF MOZART’S FLUTE QUARTET IN D, K.285
This study investigates the possibility of applying Hatten’s theory of m us ical gesture to a fo rmal system of musical analysis. Using historical antecedents and established mu sicological practice as a gui de, a range of musical parameters in a motive length span of music are incorporated into a s ingle gesture. This gesture forms the basi c semantic unit upon which an analytical tableau structure is built , and a syntax is developed to allow derivation s of new gestures ; a large scale structure displaying fractal -li ke s elf -similarity is then proposed. The completed system is applied to the an alysis of the ‘Adagi o ’ of M ozart’s Fl ut e Quartet K.285 to test whether it can consistently be implemented and whether it produces falsifiable results while maintaining predictive power. It is found that these requirements are indeed met and that a s et of i nference rules can be derived suggesting that the proposed system has ample scope for further development.
HATTEN’S THEORY OF MUSICAL GESTURE
AN A P P L I E D LOGICO - D E D U T I V E ANALYSIS OF MOZART’S FLUTE QUARTET IN D, K.285
K E Y T E R M S :
M U S I C A L ANALYSIS; MUSICAL GESTURE ; MOZART; HATTEN; ANALYTICAL TABLEAU X ; M U S I C A L MEANING; MUSICAL PARAMETER S ; FORMAL SYSTEM ; AURAL SONOLOGY; GRAPHICAL N O T A T I O N ; FRACTAL GEOMETRY ; L O G I C
i
CONTENTS
List of Tables iii
List of Figures iv
Chapter 1: Introduction 1
1.1 Preface 1
1.2 General Introduction 1
1.3 Hypothesis and Objective s 2
1.4 Logic and Meaning in Music 3
Chapter 2: Musical Gesture as Defined by Hatten 9
2.1 Introduction 9
2.2 Issues of D i s c o v e r y 9
2.3 The Nature of Analytical Gestu r e s 13
2 . 4 T h e M eaning of Gestures 17
2.5 Gestural A n a l y s i s 19
Chapter 3: Methodology 20
3.1 S yntax and Semantics 20
3 . 1 . 1 S y n t a x 20
3 . 1 . 2 S e m a n t i c s 23
3.2 The Analytical Algorithm 34
3.3 Final Methodological Remarks 37
ii
Chapter 4: Analysis 39
4.1. Introduction 39
4.1.1 A note on the Selection of Music for Analysis 40
4.2 Overview 40
4 . 2 . 1 M a j o r S u b - d i v i s i o n s 40
4.2 .2 T e m p o 41
4.3 Section I, phrase A 41
4.2 . 1 H a r m o n y 41
4.2 . 2 L i n e s 41
4.2 . 3 D e r i v a t i o n 42
4.2 . 4 Structural D i a g r a m 42
4.4 Adding the Second Phrase 50
4.3.1 Discussion 50
4.5 Completing the Second Movement 54
4.4.1 D i s c u s s i o n 54
Chapter 5: Conclusion 71
5 . 1 T h e H y p o t h e s i s 71
5 . 1 . 1 M e t a - systematic analysis 72
5.2 Suggestions f o r F urther Study a n d Application 75
5 . 2 . 1 Suggestions f o r F urther Study 75
5.2.2 Application 77
List of Sources 80
A p p e n d i x A - A Definition of Formal T h e o r i e s viii
A p p e n d i x B - A Sample List of P a r a m e t e r s ix
A p p e n d i x C - R e c o r d i n g [see back cover inset] iii
List of Tables
T a b l e 1 . Conditions for accepting the hypothesis 2
T a b l e 2 . T h e Secondary o b j e c t i v e s 2
T a b l e 3 . Hatten’s twelve points 10
T a b l e 4 . Hatten on the nature of gestures 1 5
T a b l e 5 . Hatten on the relation of gestures 1 6
T a b l e 6 . White’s parameters for analysis 21
T a b l e 7 . Truth Table 35
T a b l e 8 . Some compound rules 71
T a b l e 9 . Par a m e t e r s ix
T a b l e 1 0 . [A] x
T a b l e 1 1 . [B] xi
T a b l e 1 2 . [C] x ii
T a b l e 1 3 . [G] xiii
T a b l e 1 4 . [H] xiv
T a b l e 1 5 . [ x ] xv
T a b l e 1 6 . [ y ] x v i
T a b l e 1 7 . [ z ] xvii
iv
List of Figures
Figure 1. Hin demith’s system of verticalities 2 5
F i g u r e 2 . Truslit’s ‘Festgestelte bewegung’ 2 6
Figure 3. Hindemith’s ‘Act ual design of harmonic 2 7 t e n s i o n ’
F i g u r e 4. Persichetti’s tension graphs 2 8
Figure 5. White’s graphical notation 2 9
Figure 6. Hindemit h’s units of degree progression 30
Figure 7. Th o r e s s e n ’s formbuilding transformations 31
Figure 8. Lerdahl and Jackendoff’s time - span analysis 32
Figure 9. An analy tical tableau by Letz and Stenz 33
F i g u r e 10. Another example of an analytical tableau 33
F i g u r e 1 1. An axiom schema for the g e s t u r al analysis 36 s y s t e m in the form of an analytical tableau
Figure 12. A gestural philosophy of mind 38 . F i g u r e 1 3 . The second movement ‘Adagio’ o f M o z a r t ’ s 43- 44 F l u t e Q u artet in D KV285
F i g u r e 1 4 . Structural outline 45- 46
F i g u r e 1 5 . P h r a s e A 47
F i g u r e 1 6 . Gestural subdivision for phrase A 47
F i g u r e 1 7 . Gestural assignations for phrase A 47
F i g u r e 1 8 . Tableau index for phrase A 4 8
F i g u r e 1 9 . Consecutive and meta - gestures for phrase A 4 8
F i g u r e 2 0 . Resultant and combinatorial gestures for 4 9 p h r a s e A v
F i g u r e 2 1 . Completed tableaux for phrase A 4 9
F i g u r e 2 2 . Harmonic analysis for phrase B 51
F i g u r e 2 3 . Gestural subdivision for phrase B 51
F i g u r e 2 4 . Gestural assignations for phrase B 51
F i g u r e 2 5 . Tableau index for phrase B 52
F i g u r e 2 6 . Completed tableau for phrase B 52
F i g u r e 2 7 . Combined tableau for phrases A a n d B 53
F i g u r e 2 8 . Gestural subdivision for p h r a s e A ' 54
F i g u r e 2 9 . Gestural assignations f o r p h r a s e A ' 54
F i g u r e 3 0 . Gestural subdivision for p h r a s e C 55
F i g u r e 31. Gestural assignations f o r p h r a s e C 55
F i g u r e 3 2 . Tableau index for phrases A ' a n d C 56
F i g u r e 3 3 . Completed tableau for phrases A ' a n d C 57
F i g u r e 3 4 . Analytical tableau for s e c t i o n I 58
F i g u r e 3 5 . Gestural sub division for phrase D 59
F i g u r e 36. Gestural assignations for phrase D 59
F i g u r e 3 7 . Tableau index for phrase D 60
F i g u r e 3 8 . Gestural subdivision for phrase E 61
F i g u r e 3 9 . Gestural assignations for phrase E 61
F i g u r e 4 0 . Tableau index for phrase E 62
F i g u r e 4 1 . Tableau index f o r s e c t i o n I I 63
F i g u r e 4 2 . Analytical tableau for s e c t i o n I I 64
F i g u r e 4 3 . Gestural subdivision for phrase A '' 65 vi
F i g u r e 4 4 . Gestural assignations for phrase A '' 6 5
F i g u r e 4 5 . Tableaux index for phrase A '' 6 5
F i g u r e 4 6 . Gestural subdivision fo r p h r a s e B ' 6 6
F i g u r e 4 7 . Gestural assignations for phrase B ' 6 6
F i g u r e 4 8 . Tableau index for phrase B ' 6 6
F i g u r e 4 9 . Gestural subdivision for C o d a 6 7
F i g u r e 5 0 . G e s t u r e s assignations f o r C o d a 6 7
F i g u r e 5 1 . Tableau index for C o d a 6 7
F i g u r e 5 2 . Tableau index for S e c t i o n I I I 6 8
F i g u r e 5 3 . C o mpleted Tableau for Section III 6 9
F i g u r e 5 4 . The complete gestural t ableau for the second 70 movement ‘Adagio’ of Mozart’s Flute Quartet in D KV 285
F i g u r e 5 5 . The Mandelbrot set 7 9
1
C h a p t e r 1
I ntroduction
1.1 P r e f a c e
“ The result of our human outlook is the interweaving of apparent order with apparent accident. The order appears as necessity suffused with accident, the accident appears as accident suffused with necessity. The n e c e s s i t y is, in a sense, static, but it is the static form of functional process. The process is what it is by reason of its form, and the form exists as the essence of process. ” (Whitehead 1936:186)
When we listen to a piece of music, even one which we have not heard befor e, it can often be observed that it ‘sounds right’ or ‘makes sense’. Is there a way to codify this sense of correctness that accompanies listening, or is it a purely subjective p h e n o m e non with no discernable pattern?
The problem of meaning and logic in mu sic is a vexed one with fairly entrenched view s on either side of the debate. T he nature of this dissertation forces me to enter the debate, but although I will broach the t o p i c I c a n n o t hope to settle the matter in such a short space. N e v e r t h eless, I beli eve that a robust defence of the case f o r l o g i c and meaning in music is essential for the present topic. This is especially true given that simply providing a formally descriptive system of the musical surface could be accused of being a trivial and irrele vant undertaking without showing a connection to phenomenal understanding of music.
I will not try here to prove any particul ar system as an absolute answer to all questions , but rather show that it is possible to construct a system with which we can test various ideas about what is logical in music.
1.2 General Intr o d u c t i o n
T h e b r o a d aim of this dissertation is t o apply Hatten’s theory of musical gestures, as expounded in his book Interpreting Musi c a l Gestures, Topics and Tropes (2004), to a l o g i c o - d e d u c t i v e analysis of t h e second movement of M o z a r t ’ s F lute Quartet i n D M a j o r KV 285 using existing analytical tools as models .
2
1.3 H y p o t h e s i s and Objectives
Following from Diana Raffman’s ( 1 9 8 8 : 6 9 0 - 6 9 1 ) claim that music h a s a syntax i.e. ‘...a rule driven sy stem of discrete and repeatable elements type - identifiable exclusively by physical s h a p e ’ I will attempt to prove the hypothesis that:
It is possible to use the concept of gesture as an elemental unit in a l o g i cal system for musical analysis.
T he hypothes is will be taken as proven if and only if I c a n :
1) Develop a formal analytical system to analyse music using gestures as basic elements (See Appendix A).
2) S how that we can make both predictive and falsifiable (i.e. able to be proven false) claims about mu s i c al gestures using such a s y s t e m .
Table 1. Conditions for accepting the hypothesis
I n t h e c o u r s e of the dissertation I will address four specific secondary objectives pertaining to such a treatment of music:
1) Show that it is reasonable to assume that music has meaning of any kind, and more specifically a meaning which can be abstracted from the apparent musical surface.
2) Show that some problems in musical analysis may be solved by assuming that music has meaning, or that meaning is a useful a s s u m p t i o n for the analyst to make.
3) Investigate Hatten’s interpretation of how gestures capture and communicate musical meaning , in relation to and in conjunction w i t h ideas put forth by other authors.
4) Show that it is possible to adapt existing musical a n d l o g i c a l analytical tools to gestural analysis.
Table 2. The s e c o n d a r y o b j e c t i v e s
3
1.4 Logic and Meaning in Music
In his article e n t i t l e d ‘Mind: The Gap’ from the book S e l e c t e d Theories of Music Expression (19 9 6 : 7 3 - 96) Fiske argues that musical notes do no t have any meaning apart from ‘music noise’ ( i b i d . : 84). This view is not uncommon and echoes the opinions of authors such a s Davies (1994), citing He r m e r é n and Kivy; and Mithen (2005:18), who says: ‘Middle C is middle C and nothing else: it has n o r e f e r e nt; it is not a symbol’. An in - d e p t h discussion of the historical aspect of this argument, including Stravinsky’s famous statement to this effect, can be found in D e r y c k C o o k e ’ s b o o k The Language of Music ( 1 9 5 9 ) .
F i s k e ( 1 9 9 6 : 85) uses this assertion to ar gue that music e x e r t s n o compulsion u p o n t h e composer to do one thing rather than another. He concludes therefore that ‘...logical forms h a v e nothing to do with musical composition and thus nothing to do with music cognition. ’ ( i b i d . : 85) Somewhat later in the passage he uses the terms ‘alogical’ and ‘avalid’ ( i b i d . : 86) to show that music has such a non - logical nature.
This line of reasoning is highly problematic because of the nature of logic itself. It should, firstly, be noted that logic is not to be confused with the formal syste m of first order symbolic logic; they are related but not identical. If Fiske’s intention is to show that music is not first order logic he is indeed justified, but that is a very narrow conclusion, given that first order logic is but one instance of a far larger class of formal logics. An interesting discussion on the origin of this conception of the meaning of the t e r m ‘ l o g i c’ can be found in José Ferreirό s’ article ‘The Road to Modern Logic - An Interpretation’ ( 2 0 0 1 : 4 4 1 - 4 8 4 ) . Fiske’s apparent acceptance of natural language as logical, as opposed to music’s alogicality (1996:83 - 8 4 ) , s e e m s to argue against this interpretation t h o u g h .
If, h o w e v e r , logic is taken to me a n ‘ ... the compulsion of a t h i n g ...’ , according to one defini t i o n i n T he Concise Oxford D i c t i o n a r y ( A l l e n : 1 9 9 0 ) , as Fiske indeed seems to do ( 1 9 9 6 : 8 5 ) , it is diffic ult to see how anything can be c l a s s i f i e d a s a l o g i c a l : A random set of events is externally c o m p e l l e d to not follow any o r d e r a n d , c o n v e r s e l y , a n o n - random set of events is internally c o m p e l l e d t o follow an order by definition . So, whether music is random or non - random it must be logical , and since e v e r y t h i n g m u s t b e e ither random or non - r a n d o m i t does not appear that t h e term alogical has any m e r i t to begin with . Fiske in fact mak e s i t 4 clear (1996: 83) that he does not believe music to b e random, or in fact illogical, but specifically alogical.
W h a t F i s k e suggests is that an argument of the form “If X, then Y; X; Therefore Y” cannot be applied to musi c , arguing that there is nothing to compel a composer to follow s u c h a f o r m ( i b i d . : 8 5 ) . This is of course correct, but does not speak to the logicality of the music since there is no logical compulsion to believe “If X then Y” either: Any particular causal arrangement is contingent on the beliefs it represents . The correct compulsion is to believe “If (If X then Y) and X then Y”, which is a f o r m a composer is compelled to follow in music as much as in any other sphere . What Fiske seems to be arguing is that even though the music can be interpreted logically, the fact that i t is not rend ers it alogical. The argument thus appears to be circular: He is saying that m u s i c is alogical because it is not interpreted logically.
T o s e e w h y this is problematic , imagine a piece of music written in such a way as to deliberately follow each musical event X with a musical event Y. In this case we have artificially stipulated t h a t these events are musical and we can further stipulat e that they be interpreted as su ch, at the same time we have stipulated that the music follows a particular logical sequence . If we discover this logical sequence ex post facto do we have to stop con sidering the music as mu sic in order t o consider it as logical? Surely we have here an instance of something which is both musical and logical at the same time. For Fiske to be correct the conception of music must be a wholly separate and exclusive c o n c e p t ion from the conception of logic.
L e t u s take another piece of music where the composer for each instance of a particular musical event (e.g. the note ‘A’) follows that event with another musical event (e.g. the note ‘B’). Again we stipulate that the music be intended and interpreted a s m u s i c . However this time the final instance of ‘A’ is fol l o w e d b y something other than ‘B ’ (e.g. the note ‘C’). Now suppos e that the composer intended this relation (“If ‘A’ then ‘B’”) to exist and the listener consciously o r s u b - consciously comes to expect an ‘A’ to be followed by a ‘B’ and then reacts with shock when the apparently illogical ‘C’ is heard . ( a version of C.S. Pierce and John Dewey’s argument, s e e Spearshott and Cumming 2009) .
How should one categorise this r e a c t i o n ? Is the listener responding to the ‘C’ as a musical event or a logical event? Would the listener have been shocked if s/he had not been 5 expecting ‘C’ and is that expectation not derived from the purported logical sequence suggested by the composer? C l e a r l y the musical affect is intimately related in this case to the logical e f f e c t . An argument along similar lines is invoked by R o b e r t Y a n a l ( 2 0 0 6 : 2 6 2 - 263), albeit with a slightly different aim.
Thus far my defence of the logical ity of music appears t o h a v e l e d u s t o a strong form of Leonar d B . M e y e r ’s expectation theory as he developed i t most notably in Explaining Music ( M e y e r 1973) . For Meyer, the meaning of an event is related to the expectation aroused by it ( Spearshott and Cumming 2009 ) b u t h e d i d n o t extend his ideas explicitly to the logicality of m u s i c , t h u s c o n f l a t i n g meaning and logic . Fiske in fact deals w i t h a n argument of similar form in the chapter “Meyer’s theory of music expectancy” from another article in the same book (Fiske 1996: 106 - 120) and his refutations are quite effective , b u t t h e y r e v o l v e a r o u n d a cultural definition of meaning in relation to information t h e o r y (Fiske 1996: 113 - 114), a definition which I do not adopt .
T h e n o t i on of meaning that I do a d o p t i s closer to Ludwig Wittgenstein’s version of the same argument (Pojman 2003:1150 - 1151). According to him, meaning is a game played by two participants who try to guess one another’s intention in communicating and ascribe intention to apparent patterns ( w h i c h includes music al patterns as well as speech patterns) . Drawing on the above example, the composer of our hypothetical music may have meant to draw the listener’s attention to the particular section by inserting an illogical ‘C’ rather than the expected ‘B’. The listener m ay correctly or incorrectly deduce that this oddity indicates that the composer is trying to tell him/her something, maybe that the piece is coming to an end. Importantly, the listener need not be correct and the ‘C’ may have simply been an error by the pe rformer but t he listener nevertheless ascribed m e a n i n g t o the event. Meaning can therefore be described as the a s c ription of intention to pattern , or to express it in terms of semiology: Meaning resides i n t h e c o n n o t a t ion of a symbol. Another formulation w ould be: Inten s ion is present if and only if i n t e n t ion is ascribed. According to Barthes “ denotation is not the first meaning, but pretends to be so; under this illusion, it is ultimately no more than the last of the connotation s ” ( B a r t h e s 1 9 7 4 ) . D e n o t a t i o n then is that special case of intension where intention is ascribed to the use of a symbol rather than to the symbol as an abstract entity, i.e. what an author means by using a word, rather than what the word means (see Chandler 2008) . 6
While a disciplined approach may result in a hearing of a succession of musical events as being thoroughly unrelated and any perceived musical pattern as being completely u nintentional and devoid of any connotation , it is hard to see how this mode of listening can be the usu al or even a common occurrence. Human beings, after all, are pattern generating machines, f a m o u s l y attributing patterns and causality to random or unrelated sequences of events , and wrongly attributing randomness to sequences of events with no perceivable p a t t e r n . This phenomenon was termed ‘apophenia’ b y K . C o n r a d i n 1 9 5 8 ( B r u g g e r 2001) b u t it was known well befor e, as can be seen by how often the p o s t hoc ergo propter hoc fallacy has been invoked in argument through the ages. Indeed, a growing body of res e a r c h i n d i c a t e s that this kind of pattern finding phenomenon is critical to human decision making, through the action of the dopamine system, and therefore a central feature of the human psyche ( e . g . L e h r e r 2 0 1 0 ) .
T h e f a c t t h a t p a t t e r n is so readily ascrib ed even when no consistent pattern is present suggests that not s e n s i n g p a t t e r n s i s something which can be, through great effort, acquired as a skill rather than being a normal mode of understanding. S i m i l a r l y human being s readily and consistently ascribe intention to things a n d patterns of events even when they are fully aware that no intention is possible. Insofar as understa nding music is a normal m o d e o f understanding then, it would quite naturally involve ascription of m e a n i n g through assumed intention ality of perceived p a t t e r n s .
The second part of Fiske’s argument revolves around the contention t h a t the alogicality of m u s i c stems from the fact that it refers to nothing outside of itself “...music noise is a b o u t o t h e r m u s i c noise.” (au t h o r ’ s i t a l i c s , F i s k e 1 9 9 6 : 8 3 - 84) The problem here is that, strictly speaking, logical symbols are also about n o t h i n g o t her than other logical symbols. When we translate a statement such as “there is a cat in the tree” into the language of s y m b o l i c l ogic it becomes a simpl e s y m b o l : let us use ‘A’. Now this symbol cannot be said to symbo lise “there is a cat in a tree”; if it were to symbolise anything at a l l it can only be a statemen t . Crucially, that statement must not be any particular statement, in fact the statement is j ust ‘A’, it is a statement of a statement . O f c o u r s e ‘ A ’ continues to refer to the feline in the mind of t h e person doing the logic, but it ceases to be of consequence in the operation of logic and does not have any further bearing i n t h a t 7 mode of thought. T he information is lost and irrelevant from a purely logical perspective.
Perhaps Wittgenstein again captures the idea best wi th proposition 2.0233 from his Tracto Logico - Philosophicus : “If two objects have the same logical form, apart from their externa l properties, the only distinction between them is that they are different.” (Wittgenstein 2003:1153) . The notion is also supported by Ayer in the preface to his Language, Truth and Logic : “...the a priori propositions of logic...cannot be confuted [becaus e ] they do not m a k e any assertions about the empirical world , but simply record our determination to use symbols in a certain fashion.” [ m y i t a l i c s ] (Ayer 2003:1226). If we were to accept Fiske’s position on music then, we would be forced into the position of having to accept that logic itself is alogical, which is absurd.
Conversely it may be argued that music is alogical p r e c i s e l y b e c a u s e it refers to something . Herein lies some g r a i n o f t r u t h : musical events , as we have seen, are not the same thing as lo g i c a l symbols in that they refer to other musical events and hence are not logical events. This position strikes me as an extremely strong one though, because it leaves us in the position of also calling language alogical, a position which Fiske does not t a k e u p . I n f a c t the statement used by Fiske “If X then Y” does not express what the linguistic relationship , which looks and sounds exactly the s a m e d o e s . I n l o g i c , it only expresses a relationship between the truth states of X and Y, a relationship which (contrary to the linguistic conditional) is true wh enever X is false . Unless one is prepared to argue for a strict mutually exclusive relationship between connotation an d denotation, I cannot see this argument as having any validity.
In other words , l o g i c is a special case of meaning where n o t h i n g is denoted and language is the special case where anything can be d e n o t e d ( w h i l e b e i n g tightly bound to cultural influences) . M u s i c then can be defined as a form of communication where denotation i s s e l f - r e f e r e n t ial (i.e a musical idea denotes only itself) . T h i s recursive character is very important and will be discussed further i n l a t e r c h a p t e r s . T h i s working definition has three f u r t h e r important features: 1) It makes no mention of sound, the musical conception b e i n g defined as a purely mental construct which may or may not be audibly reified; 2) It allows for multiple simultaneous interpretations of the same symbol , resolving the dichotomy between logical thought and musical thought ; and 3) It 8 allows elemental i deas to mean anything (i.e. they do not restrict connotation) .
Having shown that music cannot be a l o g i c a l , by r e d u c t i o a d a b s u r d u m , i t i s necessary that it is l o g i c a l . Furthermore, s i n c e logic can be formalised it is reasonable to suppose that music, b e i ng logical, can also be formalised . But if logic is taken to be the compulsion of a thing, as per our earlier definition, what is it in music that is compelled? W h a t s h o u l d be the elements of musical syllogism? Clearly there must be some ascribed quality w hich we are logically compelled to believe when we believe something about some other ascribed qualities.
The candidates for the r o l e of t h i s ascribed quality i n m u s i c a r e m a n i f o l d . If one were to simply treat each musical idea as a logical statement and then proceed to read the music as if it were a logical argument of some sort it would most likely end up reading as nothing more than a succession of unrelated statements, a little like trying to understand Shakespeare by finding the ratio between the inst ances of the letter ‘ e ’ a n d t h e l e t t e r ‘ d ’ in the text. If, however we use a pattern of notes (by analogy to a word being a pattern of letters) we can abstract a range of standardised patterns which will constitute the required quality and which can consis tently be applied to all forms of music and yet have some claim to being meaningful in the sense of revealing or having ascribed to it an intention to communicate. This is the basic conceptualisation of a ge s t u r e .
G estures are i n d e e d often ascribed to musi c not only through d a n c e a n d a conductor’s m o v e m e n t s , but also by trained and untrained listeners asked to ‘draw’ music, as demonstrated b y T a n a n d K e l ly (2004:196) and by philosoph e r s of music dating ba c k a t least as far as Hanslick’s ‘ T ö n e n d b e w e g t e F o rmen’ according to Küh l ( 2 0 0 9 ) .
T h i s last concept, one of m u s i c a s a shaped pattern , i s adopted by Hatten in his Interpreting Musical G e s t ures, Topics and Tropes ( 2 0 0 4 ) . A gesture, t h e n , i s the act of one set of musical e v e n t s (i.e. events with no outside denotation) being c o n s i d e r e d i n r e l a t i o n to another s et of musical events .
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C h a p t e r 2
Musical gesture, as defined by Hatten
2.1 Introduction
Even though the term gesture has started to become quite widely used in the musical literature of late, the r e i s still no g e n e r a l l y a c c e p t e d c o n s e n s u s definition for it. One author who has devoted considerable effort to the gestural interpretation of music is R o b e r t Hatten, who in his Interpreting Music al Gestures, Topics a n d T r o p e s ( 2 0 0 4 : 9 3 - 96) gives us a very bro ad and comprehensive definition consisting of twelve points which I will use a s a foundation for understan ding precisely what gestures may be.
The definition may be divided into three parts dealing respectively with the issues of discove ry, the nature of , a n d t h e m e a n i n g of gestures. The points, in a red u c e d a n d p araphrased form, are given in table 3 below. It is important to note h o w e v e r that the goal is not s i m p l y t o discuss Hatten’s gestures, but to develop them into a form that is useable in the course of proving the hypothesis.
2.2 Issues of D i s c o v e r y
In this section Hatten establishes gestures as an abstraction from musical phenomenon in general, including the sound p r o d u c e d , t h e score from which they are produced and the actions performed by p r o d u c i ng it. Presumabl y one could, without harming Hatten’s central thesis, add in other elements of the musical phenomenon, such as the the atre of the performance itself, including the expectations of the listeners and the atti tude of the ticket sales - p e r s o n , a s Small does in M u s i c k i n g ( 1 9 9 8 ) ; this is an important concept which will b e further developed in Chapter 3.3 . I n a n y event, once the act o f abstraction has taken place information loss has occurred, meaning that we cannot recover the original object o f a n alysis from the list o f gestures produced by the analysis. In this respect gestures are like any analytical tool, from notation itself through Riemann’s functional harmonic symbols to Schenkerian graphs, and as such we must answer some fundamental question s raised about analysis before proceeding.
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1. Gestures are not the actions used to generate sound; r a t h e r , t h e y a r e the meaningful shaping of sounds. 2. Gestures communicate on a separate level of meaning from the notated score; their m eaning cannot be found in the notation. D i s c o v e r y 3. ‘Gestures may be inferred from the musical notation...’ By reading the notation sensitively we may infer which gesture was intended by a composer. 4. A listener can infer the intended gesture with access to only the sounds produced by a performer. 5. This point is basi cally a restatement of points 2, 3 a n d 4 : ‘Gestures may be comprised of any of the elements of music, although they are not reducible to t h e m . . . ’
6. Two defining characteristics are given here: g estures are units of the ‘perceptual present’, which may be thought of as around two seconds [ this rule is N a t u r e a contingent one, which may be related to the limits of short term memory ; as such it should be regarded as an indication of the order of magnitude, rather than a stopwatch timing - ed. see Hatten 2004:101 ] ; a n d gestures are built around ‘nuclear points of emphasis’. 7. Gestures provide continuity, even when there is none in the musical sound. 8. ‘Gestures may be hierarchically organised, i n t h a t larger gestures can be comprised of smaller ones’.
9. Gestures are motivic in nature and may serve thematic functions. 10. ‘Gestures may encompass, and help express, rhetorical action...’ and so relate to extra - m u s i c a l M e a n i n g movement or ev en verbal dialogue, without being linguistic in themselves. 11. Gestures may point to, or refer to other gestures in order to draw attention to a significant part of the m u s i c . 12. Gestures ‘...reveal the intentions and modalities of emotion and action...’
Table 3. Hatten’s twelve points
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In an article called ‘The paradox of musical analysis’ ( 1 9 9 9 ) M a r k D e B e l l i s outlines the first problem: If analysis is more meaningful or ins ightful than the original subject, is t h a t additional meaning n o t attributable to the analysis itself and a product of the analyst ’ s mind rather than that of the musician? My answer to this is in the affirmative, the analyst is indeed superimposing his interpretation, as represented by the abstraction of gestures and must do so beca use of the different role that this kind of analysis plays to the normal, notational v a r i e t y (i.e. we are not analysing anything that can normally be notated or abstracted directly from normal notation) . W h e n a piece of music is notated , the aim of the com poser is first and foremost to stipulate the physical character of the music (i.e. the specific sounds s/he wishes to use) but the thing which s/ he ultimately wishes to express are the gestures produced by the sounds. This creates a problem, because stipul ating the gestures precisely as logical objects would leave us with no specific details about the actual work we are performing ( s e e C h a p t e r 1 . 4 ) while stipulating the work p r e c i s e l y does not inform us of the gestures to be used (i.e. it would be a direct copy of the d i r e c t l y apparent qualities of the w o r k ) . The solution is to notate the ‘sound’ as accurately as possible while leaving the interpretation up to the knowledge and stylistic skills of the performer. The act of analysis is therefore an integral p art of every step of the musical process from the composer to the performer to the l i s t e n e r , and the task of t he analyst is to select an abstraction s/he can reasonably expect each of those participants to have formed themselves. It is fair to say, therefo re, that the notation and product of performance (sounds) are symbolic of the music itself as represented by gestures.
But how then can we justify using one interpretation instead of another? This is basically the questio n raised by Kofi Agawu in ‘ T h e C hallenge of Semiotics’ ( 2 0 0 0 : 1 3 8 - 160). Agawu effectively nullifies the notion of correct interpretation by pointing out that the number of ‘taxonomic - empirical’ rules which may be applied to a given musical extract are, in fact, infinite and because of this we cannot justify using any one rule, or indeed any set of rules as a basis. Here I must concede the point: A listener may use the quality of his breakfast to decide which gesture the performer was expressing, a performer can fluff a note and in so doing a l t e r t h e meaning of an entire movement, while a composer may simply have glossed over a section without thinking of any particular interpretation, or hi s handwriting may have been misread by a 12 careless editor. It is for this reason that the analyst must a s s u m e a set of gestures, justified by the score or performance , of course, and start his or her analysis from that point. Gestures are therefore axi omatic parts of the analysis which may nevertheless be loosely derivable .
If these strictures are admitted, though, we are faced with the further problem identified by Nicholas Cook in ‘Analysing Performance and Performing Analysis’ ( 2 0 0 0 : 2 3 9 - 261): If musical analysis is to have any function at all, it must in some sense be prescriptive, or suggest one performan ce over another. Does this m e a n t h a t an analyst can tell a composer what to write, or select good performance over bad ones by checking for compliance with his or her decisions? Can an analyst tell a listener what should be heard when the music is heard ‘c orrectly’? Certainly, given the above objections, such a prescriptive approach cannot be justified. What role remains for the analyst then?
My answer to this is to suggest analysis as a study of the decisions involved in music making and perception. Put a n o t h e r way, if the composer decides which gestures to symbolise with notation, the performer decides which set of gestures to implement and the listener decides the gestures which are heard, the analyst can analyse the way that gestures interact with one a nother, whether they are used in the same way by different role players or whether interpretations follow any discoverable rule, all without fear of infringing on the domains of the other role players. This is similar to the way that a philosoph er will dea l with logic, saying, ‘Apples are fruit and fruit are tasty, therefore apples are tasty’ does not inform us of anything more than th e statement is saying. I t d o e s n o t compel a speaker to make this particular inference or even to agree with its components , b u t b y studying statements of this form we can come to know the syllogism, a particularly useful piece of information about the nature of knowledge itself. According to Frege: “ To discover truths is the task of all sciences; it falls to logic to discern th e laws of being true” (in Ferreirόs 2001:450). The task of gestural analysis is then not to discover gestures, but to discover the laws of being a gesture.
T h u s t he notated score is a symbolic representation of the gestures of music and the specific gestures used are treated a s axioms for the study of gestures and their interrelationship.
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2.3 The Nature of Analytical G e s t u r e s
In this section Hatten makes several p oints, each of which s t i p u l a t e s key requirement s for creating a system for analysing with gestures. The first of th ese points is the statement that gestures are found ‘in the perceptual present ’. When analysing music there are many possible st arting points which may be used: w e can start at the level of wave forms, as does Alexander Truslit in ‘Gestaltung und Bewegung in der Musik’ of 1938 (in Repp 1 9 9 3 : 4 8 - 72, see Fig. 2 ); at the level of notes themselves, as does any analysis which is based primarily on notation; at the level of motifs, half phrases, phrases, sentences, sections, movements, whole works, bodies of works or indeed the entire musical enterprise itself. By stipulating ‘the perceptual present’ and qualifying that with the statement ‘typically within two seconds’ , Hatten simply guides us as to what should be our starting point, indicating gestures , a s o b j e c t s on the scale of motifs. Since we are not analysing motives themselves but their function as gestures I will designate this analysis a functional motivic a n a l y s i s . The ‘perceptual present’ is useful because of the psychological concept of procedural or sho rt- term memory; since we know that this kind of memory can, in a typical individual, hold fairly accurately around five to nine items for this space of time (Miller in Weiten 1995:263 - 2 6 4 ) . W e can refine our definition further by saying: The functional mot ivic analysis of the musical parameters an individual attends to in t h e perceptual p r e s e n t .
The problem of how to differentiate the function of gestures then a r i s e s . B e c a u s e the number of g estures which can be imagined is i n f i n i t e , s u r e l y i f an analyst att empts to identify e ach gesture individually s/ he would arrive very quickly a t a n i m m ense number of different types. I ndeed the total number would most likel y b e a larger order of infinity if the distinction between gestures had an infinitely fine grain (to s e e h o w , refer to Cantor in Hawking 2 0 0 5 : 9 7 1 - 1 0 3 9 ) . While investigating this typology may be of considerable interest were we to undertake a purely gestural analysis, it is wholly destructive to any attempt to perform a f u n ctional analysis using gestures , s i n c e w e a r e investigating the interaction between like and unlike gestures. In other words, we need a method to pare down the plethora of possible gesture types to a very small usable number. Here Hatten provides a useful clue to the solution by mentio ning ‘nuclear points of emphasis’ . B u t i f we know that there are points of emphasis, how can we identify 14 them? The problem is that if we identify this emphatic moment with any given parameter (such as pitch, volume, rhythm, timbre etc.) we cannot reliably te ll beforehand whether it will be the highest note or the lowest, the loudest or softest, which provides that emphasis, s o this leaves us no better off than when we started. If, however, we identify the nuclear point separately, that is, not by rigorous exa mination but by intuitive investigation into each separate parameter, it is possible to i n d i c a t e the relative location of the nuclear point within the gesture. Some gestures will have an emphasis near the beginning of the gesture, and some more toward the end, while yet others may have a central point of emphasis or be expressly without any significant nucleation (when a singer word - paints the word ‘stillness’ for example). I propose therefore that a very small set of functions are differentiated for t h e c u rrent application, and that they are differentiated by the position of this emphatic moment, being either forward, with the emphasis toward the end; backward, emphasis toward the start; or neutral, with no emphasis or emphasis toward the middle. The d e f i n ition of gestural analysis the n grows to: The functional motivic analysis of the musical parameters an individual attends t o i n t h e perceptual present , differentiated b y t h e location of e m p h a s i s amongst them .
At this point in the discussion it is necessary to deviate somewhat from the course set out thus far by introducing another list of characteristics outlined by Hatten . This list is given verbatim but not in the original order in table 4 ( 2004: 1 2 4 ) . T h i s n e w l i s t c a n be divided into two parts , e a c h d e a l ing with a separate feature, t he first part o f w h i c h is largely a revision of some of t h e i s s u e s raised earlier . The process Hatten outlines can be interpreted a s follows: Discrete musical parameters coalesce t o f o r m a n a l o g u e gestures wh ich are in turn fix ed into well - defined shapes a n d w h i c h m a y t h e n , in turn, be analysed. This gives an outline o f a s y n t a x f o r the analytical process which I w ill propose in the next c h a p t e r . B u t what then of the semantics, the way that these discrete gestures are related to one another? The issue is dealt w i t h in the next set of quotations shown in table 5 ( i b i d . : 1 2 4 ) .
Using this new information we further extend our definition. Gestural analysis is : The formal and functional motivic analysis of the musical parameters an in dividual attends to in the perceptual present, differentiated by the location of e m p h a s i s amongst them .
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Hatten’s Comment O r i g i n a l Discussion and Designation I nterpretation
‘ Contextually f. W e d e r i v e the gestures constrained and from the musical and e n r i c h e d , b o t h social parameters relating stylistically and to the specific work under strategically ’ investigation.
‘ A n a l o g , as opposed to a. T he entire gamut of digital or discrete’ parameters is potentially under investigation, rather t h a n a w ell defined subset.
‘ H e n c e , continuous i n a b. Meaning that any digital p r o d u ctive sense of (or discrete) input gets continuity (i.e. n o t converted into the necessarily continuous a n a l o g u e (or continuous) sound, but continuity of output of gestures. shape, curve, motion across silence, etc.)’
‘ Beyond precise h. Information is lost in the n o t a t i o n o r e x a c t transition from musical reproducibility’ parameters to musical g e s t u r e s .
‘Typically g. W hen we listen to music, foregrounded ’ we are not hearing musical parameters, but the gestures formed by them.
‘Possessing articulate c. Here the ges t u r e s s h a p e ’ themselves are made d i g i t a l , i . e . t h e y a r e conceived of as discrete (See Dewey 1936:172, p o i n t 5 ) .
Table 4. Hatten, on the nature of g e s t u r e s
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Hatten’s comment O r i g i n a l Discussion and Designation Interpretation
‘Amenable to type - t o k e n i. relationships via cognitive categorisation or even conceptualisation, and t h u s ’ . . .
‘Potentially systematic to j. Statements i and j the extent of being suggest that Hatten o r g a n i z e d oppositionally by believes that type, as in gestural formalising gestures “languages” or ritual may be possible. m o v e m e n t s ’
‘Possessing hierarchical d. Hatten uses this term p o t e n t i a l ’ in a Schenkerian s e n se (see page 126 - 127), so that different levels of analysis each produce gestures and different levels of gestures are related to one another in some way. Successive, repeated abstraction can be carried out.
‘Possessing a significant e. Gestures cannot be e n v e l o p e ( p r e - and interpreted in postmovement c a n isolation, but are substantially affect the related to quality of the sounding neighbouring g e s t u r e ) ’ g e s t u r e s .
Table 5. How gestures relate to one a n o t h e r
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2.4 The Meaning of G e s t u r e s
I n t h i s s ection I will briefly elaborate on my , and Hatten’s, assumption that music has meaning. It is important to note that it is not required that this justification is accept e d a s , a g a i n , I d o not hope to resolve the vexed problem of musical me aning in such a s hort space. I merely aim here to justify t h e p r i o r a s s u m p t i o n o f musical meaning in relation to gestures , w h i c h i s a n important one for the present project. The views expressed here should not be directly attributed to Hatten (see the meaning section in ta b l e 3 ) . Instead they represent a development from those views in light of the discussion in chapter 1.4.
If music is taken to mean something through the vehicle of gestures, how do gestures mean? Are they physical analogues or is the physical motion associ ated with the word an analogue of a cognitive process?
Some authors, such as Davies (2001:23 - 44) and Langer (as discussed by Osbourne 1979:16) employ an approach to answering t h i s similar to Darwin’s physiognomy, outlined in ‘The Expression of Emotion in Man and Animals’ (1998: 94 - 9 5 ) , t h e idea being that since human beings attribute shapes to music and also attribute meaning or expression to shapes it is reasonable to assume that meaning is attached to musical ‘shapes’ or gestures. Alternatively, a strong interpretation may be adopted, whereby meaning is assigned directly to g estures in the manner of words in a n a p p r o a c h similar to one followed (though not in terms of g e s t u r e s ) by Cooke in The Language of M u s i c ( C o o k e 1 9 5 9 ) . H a t t e n follows a hybrid approac h i n Interpreting Musical G e s t u r es, Topics and Tropes (2004), one where gestures convey meaning first by being a mental analogue of a physical action, and then by that analogue having an outside meaning , an idea possibly first found in Coker (1972:139).
I will, for the purposes of this dissertation, slightly adjust Hatten’s reductionist position and instead give precedence to the relational content which informs the physical gesture. I n o t h e r words, the physical gesture is iconic of a purely mental p h e n o m e n o n . Support for this approach is found in the fact that the concept of gesture is not confined to the musicological discourse, but extends to a wide range of different fields. Corballis and Gentilucci (2006:949 - 960) argue that language itself developed fro m manual (i.e. hand) gestures, in what appears to be a large and growing field in the study of language. 18
P s y c h o l o gists such as Susan G o l d i n - M e a d o w s at the University of Chicago are meanwhile studying the connection between gestu r e s and arithmetic ability ( Anonymous 2009 :77). In the musical field gestures have been linked to geometrical concepts, through the analogy of a climber (Tymoczko in Rehmeyer:2008), to mathematical functions (Mazzola and Andreatta 2007:23 - 4 6 ) , t o dance (Scruton 1997:340) and to physi cal forces and processes (Larson 2006:61 - 7 4 ) . This far from exhaustive list suggests to me that gestures are in fact a way of thinking, a kind of ‘thought - space’ where different concepts can freely intermingle , a concept similar to what Brower refers to as ‘ c r o s s - domain mapping’ ( 2 0 0 8 : 5 1 - 106) in relation to t h e idea of ‘image schemas’ which can be related to gestures (ibid. 60 and 96). E ven though music does not function as language there is still a very strong correspondence between the two modalities of t hinking in a ‘gestural’ or ‘image schematic’ thought s p a c e .
My own interpretation , t h e n , i s t h at gestures are context neutral. T h e y can denote forms of thought and may be treated as linguistic, p hysical, mathematical, logical, musical or any type of i d e a depending on how they themselves denote. So that a gesture which denotes itself is a musical gesture, and a gesture which denotes nothing is a logical gesture. At the same time, gestures qua gestures always have a musical type of denotation in that it d e n o tes itself as the signified. At the same time, a gesture can have an extra - musical connotation, a second order connotation of what the signifier intends to signify by being inten s i o n a l l y gestural in a particular way. So having establish ed the motion as g e s tural in that it denotes a movement of a certain type, the movement itself as opposed to another movement can separately and severally denote something outside of itself.
But how does a single gesture denote both itself and something e l s e ? Consider an ana logy with language to clarify the relationship: A person sees an inscri ption ‘FISH’ which s/he k n o w s in the English speaking culture is intended to denote a certain type of creature. That denotation has several connotations, including the types of creature themselves, a foodstuff, an odour or the religion associated with the word when the word is taken to also denote an English translation of the Greek word ‘Ichtus’, which itself denotes a phrase. Each time the connotation/denotation dichotomy is reso l v e d t hrough ascribed intention: “ W h a t was intended by the use of a given s i g n f r o m t h e list of connotations of that sign” and “What was intended by the 19 u s e o f a given sign as opposed another sign with similar connotations”.
T h u s a purely musical gesture which has itself as i t s f i r s t d e n o t a t i o n in what the gesture refers to , can also, at the same t i m e , d e n o t e something external as its last denotation in what the actual form of the gesture is (compare to Barthes 19 7 4 a s discussed in chapter 1.4). Seen this way, g estures become an embodiment of Frege’s solution to the paradox of analysis discussed earlier in this chapter : a gesture has a musical “Sinn”, but can have an extra - musical “Bedeutung” ( s e e S a l m o n : 1 9 9 3 ) .
It is this extra - musical musical second order den o t a tion through the vehicle of gesture which allows us to freely speak of musical m e a n i n g . Gestures can, in this interpretation, transcend the boundaries between the diffe rent modes of thought and allow u s t o develop a systemic and standardised way of thinkin g about not only music, but also the relationship between music and language (or other modes of thought) without blurring the boundaries between them. What I, as a musician, find particularly intriguing about this concept is that it seems to me ideally sui ted to the musical mode of discourse. In other words, gestures may represent a way for music to fruitfully and formally engage with other disciplines in a way analogous to mathematics, language and l o g i c .
2.5 Gestural A n a l y s i s
We are now in a position to f i n a l i s e the definition of gestures in a form which can be applied in the analysis to follow. Gestural analysis is : The formal and functional motivic analysis of m u s i c a l meaning as defined by musical parameters an individual attends t o i n t h e perceptual pre s e n t , differentiated by the location emphasis amongst them.
The analytical system which I will present in the following chapters should then be interpreted as that special case of gestural analysis where gestures which have a musical first order d e n o t a t i o n (i.e. they denote their own shape) but do not denote a n y t h i ng in the second order. That is: the musical g e s t u r e s a s t h e y are employed logically disregarding any outside meaning.
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C h a p t e r 3
Methodology
3.1 Syntax and S e m a n t i c s
We have seen that musical ideas denote nothing but other musical ideas, and that the combination of musical ideas denote s a gesture. A musical gesture is then the case when that gesture denotes only itself. But two musical gestures treated in opposition to one another denote a ges ture again. That means that a formal system of gestures has a recursive quality which is directly analogous to the recursive quality seen in musical denotation i t s e l f .
This characteristic has some very important implications, some of which will b e d e a l t w i th at the end of this chapter. For now though, the important implication is that the syntax of the system is the same as the semantics , i.e. the syntax is the relation between things and the semantics is the relation between those things, which are of the s a m e t y p e . It is as if i n s t e a d of saying “If A then B”, one were to say “If AND then OR ” . Nevertheless , I will maintain the traditional separation of syntax and semantics, dealing first with types of symbols used and how they are arrived at and then with h ow they interact .
3.1.1 Syntax
I t i s p e r h a p s not surprising that the first systematic use of the concept of force or energy in musical analysis , in the work of H i n d e m i t h ( 1 9 4 1 , see Fig. 1), should appear not too long after t h e immense popularising of the idea of energy brought about by E i n s t e i n . The basic concept is that we can define each part of the apparent musical surface according to its intensity or energy, both melodically and harmon i c a l l y , instead of defining them a c c o r d i n g to their functional rela tion to a central tone, or tonic (as in Riemann analysis) or by simply mapping the flo w of one or more parameters (as T r u s l i t d o e s with his waveform analyses, 1938; 1993, see Fig. 2 ). The result is a te nsion graph as c a n b e s e e n i n f i g u r e 3 below. This pro cess was also employed a nd developed by Persichetti in T w e ntieth Century Harmony (1962), adding the concepts of melodic line, texture tension, mass re gister and root 21 direction to those used by Hindemith (see F ig. 4 ). More recently John D. White ( 1 9 9 4 ) has used the idea as part of his C o m p r e h e n sive Musical A n a l y s i s ( F i g . 5 ). White also provides a list of musical parameters which can conceivably be so analysed, s h o w n i n t a b l e 6 .
- Details of rhythm at the motivic l e v e l . R h y t h m - Harmonic rhythm - D e n s i t y - Relationship of rhythm to text
- Melodic intervals - C o n j u n c t versus disjunct motion - T e s s i t u r a - R a n g e M e l o d y - Pitch profile - C a d e n c e s - D e n s i t y - Rel a tionship of text to melody
- Details of harmony - Consonance and Dissonance - C a d e n c e s H a r m o n y - C o n t rapuntal or polyphonic t e c h n i q u e s - Relationship of text to harmony
- Details of orchestration or instrumentation . - T e x t u r e S o u n d - D y n a m i c s - Relationship of voices - Relationship of text to sound
Table 6. White’s list of p a r a m e t e r s ( 1 9 9 4 : 25)
F o r u s e in tension analysis the text of many of these parameters simply need s t o b e a l t e r e d t o r e a d : ‘Change in X ’ where X is a p a r a m e t e r . Clearly this list is not complete, and indeed cannot be made complete since the list of possible parameters is potentially infinite, as was shown above ( f o r m y list of what I consider to be 22 key parameters see A p p e n d i x B ) . In addition to this, it is not conceivable that any listener can heed all, or even a substantial subset of even this limited list in one hearing. The analyst m u s t therefore choose a set of parameters at a given moment which a listener is most likely to be attending to, which should not be an overly difficult task given that, for the sake of clarity, most composers would not attempt to have overlarge differential s a c r o s s a v a s t set of parameters, if only because this would make understanding a work virtually impossible . ( I a m i g n o r i n g o f course the many mostly 20th c e n t u r y composers who did and do precisely that for e ffect or as a stylistic feature and I would arg u e t h a t t h e y are the exceptions which prove t h e r u l e ) .
The above examples use a continuous figure to represent the flow of tension, whereas what is required i s a set of individual g e s t u r e s . Hindemith again provides us with a useful ex a m p l e o f how this may be done (Fig.6 , ibid. 184). Hindemith uses the concept of degree progression as the defining feature of such units whereas I will be using Hatten’s definition of gestures as discussed in the previous chapter. The other difference that I would impose on thi s way of dividing the musical surface w o u l d be to apply Lerdahl and Jackendoff’s injunction again s t overlapping units (1977:118 ), because this makes analysis much simpler, meaning that two overlapping units (or groups in Lerdahl and Jackendoff ’ s terminolog y) are treated as sequential. Lars Thoressen uses a symbolic representation of such gestural unit s i n his analytical technique, called ‘Aural Sonology’ (2007), although h e l i m i t s his analysis to melodic and textural complexity, allowing him to us e a m u c h r icher symbology (see Fig. 7 ) t h a n would be possible here (I will use only three symbols b e c a u s e I only wish to investigate the formal relationship between different classes of gestures rather than the transformation of gestures t h e m s e l v e s ).
It is important to note at this point that any method of deriving gestures in this fashion is somewhat a d h o c . This is because ultimately gestures are defined by how they are perceived, and specifically where the marked element is perceived to be i n t h e perceptual presen t according to Hatten ’s s c h e m e . The derivation of gestures must be somewhat abductive as a result , a s i t u a t i o n similar to that of mathematics, where the statement 1+1=2 cannot be proven mathematically even though it is true analyticall y . 1+1=2 is true by d erivation from definition, but that definition cannot itself be mathematically derived. In the same way we can 23 use gestures analytically even though they ca nnot be analytically arrived at: we simply assume a certain gesture to be true on the basis of a ‘be st guess’, in the same way as a physicist assigns a number to a physical entity, and proceed deductively from that point onwards.
3.1.2 Semantics
Having seen how gestural analysis based on discrete symbolic representations of tension flow may be achieved, we can move on to the issue of treating these symbols syntactically. The main source of inspiration for this function is again Lerdahl and J a c k e n d o f f ’s analytical method (see Fig. 8 , as discussed in the a r t i c l e T o w a r d a Formal Theory of Tonal Music 1 9 7 7 : 1 11- 1 7 1 ) . The main thrust of their m e t h o d is the establishme nt of a set of w e l l - formedness r u l e s (this should be understood as an attempt to establish a syntax) for interpreting the hierarchical organisation of metrical points ( o r b e a t s ) in the music. The n otation depicts a ‘“right branch” ( ) ...[as something which] denotes the subordination of an event to the preceding event within that region at that level ; a “left branch” ( )...[as something which] denotes the subordination of an event to the following event within that region at that lev e l ’ ( t h i s is very simila r t o t h e semantic features discussed above, ibid.: 129). This kind of analysis does not aim t o present a logical structure and does not, at the level of the tree structure itself, have the ability to provide predictions for the furt her development of the tree; that is: for each left branch there must be a corresponding right branch - b u t this does not tell us exactly where each branch would be ; f o r t h i s information we can only refer back to the source music. Furthermore, and for roug hly the same reason, it is not falsifiable; that is: We cannot disprove the fact that any particular branch is either left or right by investigating earlier branches. The Lerdahl and Jackendoff m e t h o d i s t herefore not a strictly logico - deductive analytical s y s t e m .
There is, however , a logical system which shares many features with the above system and yet has the desired characteristics of predictiveness and falsifiability. This method is called ‘Analytical Tableau’, and i t is a common technique for dealing with modal logic, or logics dealing with relations such as X believes that Y , o r X thinks that Y , o r X is possibly Y . E x a m p l e s o f t h i s can be seen in figures 9 and 10 . The only real differenc e 24 between this procedure and Le rdahl and Jackendoff ’ s is that ea c h node is now a logical symbol, or semantic unit, and the tree represents the relation between the nodes themselves, rather than the concepts symbolised at each. In the present application this means simply that each node will hold a gesture, and the stru c t u r e will encode the relationships which hold between those gestures.
O n e f u rther addition to the standard analytical t ableau will be r e q u i r ed before we can proceed. Hatten stipulates that gestures have both ‘hierarchical potential’ and a ‘significant en v e l o p e ’ (p.126), which a r e related to Rosch’s dimensions of horizontality and verticality (1978). Ros c h ’ s horizontal boundary being h o w t h e two categories are situated with respect to one another, while the vertical dimension is the intrinsic differentiatio n. This means that each set of gestures is related to one another not only in the way t h a t t h e y relate to one another qua g e s t u r e s - so that, for example, a forward gesture with another forward gesture produces a combinatorial forward gesture (this is Rosc h’s basic level) - b u t also in that o ne gesture can be subordinated to the following one, p r o d u c i n g a forward moving ‘meta - g e s t u r e ’ . ‘Subordination’ here i s Lerdahl and Jackendoff ’ s terminology a n d the same term is employed in a similar fashion by Rosch. ‘ M e t a - gesture’ is m y o w n t e r m , but one which corresponds to Rosch’s super - ordinal level . The system I will expound in the following section will therefore treat any two gestures as combining in both of these manners to produce a third ‘resultant’ gesture wh ich then interacts with the following gesture, as indentified beforehand by our semiotic a n a l y s i s . An added dimension is therefore required over the two in a standard tableaux and this will be done by distinguishing horizontal rel ations from vertical ones ( s e e F i g . 1 1 ) .
25
Figure 1. Hindemith’s system of ordering verticalities ( h a r m o n i e s ) according to their tension, or energy, rather than their function.
26
F i g u r e 2 . Truslit’s experiment, published in 193 8 (in Repp 1 9 9 3 : 4 8 - 7 2 ) , involving one participant drawing a curve and writing a musical passage which is thought to correspond to it (Urbewegung [original motion] ). The second participant then attempts to reconstruct the original curve by listening to the music (Festgestellte Beweg [ e s t a b l i s h e d m o t i o n ] ). Because both participants were familiar with the procedure and theory i n t h i s e x p e r i m e n t (p.58) it is not possible to exc l u d e m e t a - m u s i c a l symbolisation but it is nevertheless instructive to note that this kind of gestural communication is pos s i b l e . 27
F i g u r e 3 . Hindemith’s categorisation syst em for harmonic a n a l y s i s ( 1941:158) can be seen in the line called ‘Harmonic Fluctuation’. The graphic representation of it is the ‘Actual Design of Harmonic Tension’.
28
‘ [ Although register placem ent of the entire tonal mass does affect the direction of sound, ] harmony with a strong downward pull can resist a register climb.’
F i g u r e 4 . A very similar process to that seen in Figure 2 is followed here, except that the parameters graphically notated n o w include the melodic line, texture tension, bass line, implied roots, mass register and root direction (Persichetti 1962:183) .
29
Figure 5. White’s graphical notation ( 1 9 9 4 : 2 6 2 ) is much more digital in style than either Hindemith ’s or Persichetti ’s. L o o k i n g at the line ‘A. Dynamics of texture’ one can fairly easily separate the flow into two forward gestures followed by a reversal and then three more advances.
30
F i g u r e 6 . Hindemith defines units in the music accordi n g t o degree progress i o n ( 1 9 4 1 :184). Notice that the length of these units is around t h e t w o - second ‘perceptual present’ mark a l s o associated with motives . Again, the two - seconds should not be regarded as a stopwatch timing guide, but as an indication of order of magnitude.
31
F i g u r e 7 . T h o r e s s en uses symbolic representations of gestural units to analyse ‘formbuilding transformation’ (2007). While this system does not formalise a gestural theory, it does offer an example of using symbolic musical gestures and their relations h i p to one another systematically.
32
F i g u r e 8 . L e r d a hl and Jackendoff’s ‘Grouping, metrical and time - s pan analyses’ of Schumman’s “Wehmut” from Liederkreis. The s u b - ordination tree structure is prominently displayed at the top.
33
F i g u r e 9 . A n analytical tableau with symbolic units at each node, from Letz and Stenz (2006:83). The uppercase letters represent predicates and the lowercase letters the variables. This is similar to Lerdahl and Jackendoff’s predication of a left or right branch ( or ) to a particular set of notes.
F i g u r e 1 0 . Another example of an analytical tableau . ‘ T h e e l e c t i o n ’ ( N u t e a n d E r k 1 9 9 6 : 1 7 ) u s i n g Donald Nute’s defeasible l o g i c . The arrows indicate different relationship (namely st r i c t , defeasible and defeaters). The nod es may be either satisfied or failed (as opposed to the true or false connotations of first order l o g i c ) . 34
3.2 The Analytical A l g o r i t h m
S t e p 1 : T h e m u s i c a l extract is divided into large - scale structure such as movements, sections and phrases.
S t e p 2 : T h e tempo is established. Since the gestures are temporally defined, i.e. they are roughly two seconds in length according to Hatten’s rule of thumb, this must be completed before we can continue to isolate each gesture.
S t e p 3 : The broader harmonic structure is also analysed beforehand since it may cut across gestures which occur simultaneously and so is not properly analysed at the gestural l e v e l .
S t e p 4 : A portion is selected and further divided into separate independent lines and each line is divided into gestures according to Hatten’s ‘two second’ rule of thumb.
S t e p 5 : Each gesture is analysed according to a set of indicative parameters, i.e. those prominent and likely to be noticed for that section. This is also related to parameters which have been i n d i cative in earlier gesture.
S t e p 6 : The gestures, having been ascribed a value of either forward/advancing (/), backward/retreating ( \ ), or stable/holding (^), are listed for each line in turn.
S t e p 7 : The first two g e s t u r e s of the first order or consecuti ve gestures are placed next to each other ([A] and [B] in Fig. 11 ) a n d above them is placed the gesture produced by their combination ( [ C ] i n F i g . 1 1 ) according to the truth table shown in table 7.
S t e p 8 : T h e m e t a - gestures, defined by the relationship bet w e e n each gesture and the next at the level of musical parameters ( i . e . each gesture is considered as a musical idea rather than a logical i d e a ) , are analysed and listed above ( [ D ] i n F i g . 1 1 ).
S t e p 9 : T h e m e t a - g e s t u r e ( [ D ] ) and the combination gesture ( [ C ] ) are again combined, using the sam e truth table as given in table 7 . This forms the next, resultant gesture to the side ( [ E ] i n F i g . 1 1 ).
S t e p 1 0 : The next first order gesture is appended to the side of this resultant gesture and t he process continues fr o m s t e p 7 .
S t e p 1 1 : After all the gestures for a particular section have been used in this manner, ending in a final resultant gesture, the final gesture can be used in combination with the resultant gesture of 35 other lines in the same section, with resulta nt gestures of other s e c t i o n s or with further consecutive gestures to form a new r e s u l t a n t .
S t e p 1 2 : This final resultant can now be used together with the resultant for the next part carrying on the same process at the next hierarchical level.
G e s t u r e 1 G e s t u r e 2 Combinatorial or resultant gesture
/ / /
/ \ ^
/ ^ /
\ / ^
\ \ \
\ ^ \
^ / /
^ \ \
^ ^ ^
Table 7. The truth table which will be applied in the a n a l y s i s . It is important to note that, since the prese nt method is a f o r m o f modal logic these values are not truth values ( S t a n f o r d Encyclopedia of Philosophy 2 0 0 9 ).
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D E C D E A B C
E E D E C D E B C A B
F i g u r e 11. A n axiom schema for the gestural analysis system i n the form of an analytical t a b l e a u . [ A ] a n d [ B ] represents c onsecutive g e s t u r e s , [ C ] is their combination , w h i l e [ D ] i s t h e m e t a - gesture and [ E ] is the resultant. The final resultant gesture is underlined for clarity. T h e s u p e r - structure is decided by the perceived structural units of the music being analys e d . A w e ll formed formula (wff) in this system is 1 ) a single gesture , i n s o f a r as it represents the resultant of a resolved pair , where a resolved pair consists of the base gestures with their combination considered with the meta - gesture to form a resultant; 2) a resolved pair of gestures or 3) two simultaneous gestures resolving onto a resultant . 37
3.3 Final M ethodological R e m a r k s
What may be observe d here is the fractal like self - similarity of this structural system as displayed in figure 11 (see also F ig. 5 5 ) , meaning that it looks roughly the same regardless of the scale i t is viewed at (Mandelbrot 1982) . This means that whether we use s m a l l - s cale (like wave - forms) or large - scale (like sociographic features) as fundamental units , the analysis will look a p p r o x i m a t ely the same.
An important feature of fractals is that they are bounded at some p o i n t ; u s u a l l y a fractal is a single object when viewed from the macro level. This feature is a function of the recursive nature of t h e derivation of these structures, s t a r t i n g from a simple idea, such as a triangle in the case of the Koch curve, which submitted to a simple operation infinitely many times. The fractal generated in this analysis is somewhat unique t h o u g h , in that it starts from a simple idea (the gesture attribu ted to Hatten’s ‘perceptual present’) which is infinitely expanded outwards, rather than i n w a r d s , i.e. fractals are apparently infinitely divisible, while gesture tableaux are apparently infinitely extensible . This is why Small’s idea (1998) of the meaning of music expanding into the cultural sphere averred to at the start of Chapter 2 was such a crucial one: i t s u g g e s t s that the sphere of thought can expand outwards this way to an arbitrarily large scale . The formal system of gestures, then, is in fact a f o r m a l p h i l o s o p h y of mind, with a web of denotation at different levels of the fractal, a theory depicted in figure 12.
It is in this then t h a t gestural analysis is differentiated from analysis aimed at an a posteriori investigation of an acoustic p h e n o m e n o n. Broadly speaking, musical analysis is highly systematic in analysing the score. A plethora of very potent tools c a n b e brought to bear on a score to form axioms of music or statements of musical fact, such as note names, function name or a Schenkerian U r t e x t . I t is often assumed that because of the nature of musical denotation we must stop there, we cannot proceed further because then we would be analysing some other form of thought. What the present technique offers is a way to systematise that which de notes musical ideas as they relate to one another, without f orcing the musical axioms to denote anything other than themselves and be thus transformed. In fact, at any level, any gesture can be interpreted as multiple kinds of ideas simultaneously or conve rted from one kind to another simply by changing the type of denotation. 38
M Li G P L Ma M M
- Denotation function M - Musical idea G - G e s t u r e L - Logical idea P - Pictorial idea or physical gesture (denotes a mental or physical object or physical gesture ) Li - Linguistic idea (with a culturally prescribed definition) Ma - Mathematical idea (with the number concept)
F i g u r e 1 2 . A g e s t u r a l p h i l o s o p h y of mind. The two musical ideas at the initiation point become logical id eas when they are combined to f o r m the combinatorial logical idea. The same process happens when the meta - gesture is combined with the combinatorial gesture .
In this view, the elemental ideas are initially logical and are transformed into musical i d e a s when considered in combination, a n otion indirectly suppo rted by Hanslick when he says: “ T h e f o r m s which construc t themselves out of tones are not empty but filled: they are not mere contours of a vacuum but mind giv ing shape to itself from within” (1986:30) and then refers to the “ b o n d s a n d affinities” of “ musical elements ” being without “ ... concept as its criterion or tertium comparationis ” ( i b i d . : 3 1 , author’s italics ) , a notion which identifies it as a logical idea (i.e. without denotation). The combination in turn becomes a gesture when combined with the meta - g e s t u r e .
39
C h a p t e r 4
A n a l y s i s
4.1.1 Introduction
This chapter will present a sample analysis of a piece of music which will demonstrate the formal system in use. In order to do this the information on t h e score needs to be translate d into the s y n t a x of the system (/, \ and ^). As with first order logic this translation is an intuitive process with certain rules of thumb applied. In logic this translation is not a formal process and it may be argued that it is also not formalisable.
T he assignation of variables in this way is a subject of intense study in music, and a wide array of very potent tools can be brought to bear on the problem. However, e ven with this facility, v a r i a b l e s a r e not deductively proven, but rather i n d u c t i v e l y i n t u i t e d . Once they are assigned however, they should be treated as axiomatic.
The methodology deployed for the purpose may be disputed on several grounds, not least in the method of breaking the music into significant units of the perceptual present. While th e s e reservations must be taken into account, the purpose of this dissertation is to show how such elemental units can be used i n formal analysis as opposed to showing how they can be systematically derived. As such, a principle of simplicity and c l a r i t y i s adopted which may produce musical results t h a t c o u l d seem counterintuitive , depending on precisely how o n e w o u l d reify a gesture in performance.
While the problem is acknowledged, it in no way impacts on the validity of the method, since the goal is not t o s t a n dardise the derivation of axioms , but merely to show how this could b e d o n e . The axioms are entirely a p r i o r i for the purposes of th is a n a l y s i s , despite my attempts to show how one may go about justifying t h e m a posteriori .
That being said, every at tempt has been made to represent a possible reading that a performer may make. This may be compared to the decisions that the author of the present study d i d in fact make in performance as given in Appendix C. It should be noted that the reading here is no t intended to reflect that performance and should be regarded as a wholly separate interpretation . 40
4.1.2 A Note on the Selection of Music for Analysis
The music an alysed here (the second movement of Mozart’s F l u t e Q u a r t e t in D major KV 285) was chosen l a r gely to satisfy the departmental regulation stipulating the need for a connection between the final recital and dissertation of the candidate (i.e. myself). There is however an additional reason why Mozart’s music may be particularly susceptible to this ki nd of gestural analysis and must therefore be taken into consideration when the success or failure of the investigation project is determined. It is my belief that Mozart’s music, including his purely instrumental music, can be understood as a product of h is operatic sensibility, and that his style therefore has an innate physicality in its nature which when combined with the clarity of the textures he employs makes it an ideal candidate for this kind of analysis. Whether this motive impulse is as strong in other composers, or some other element of Mozart’s style lends itself particularly to gestures is important to understanding the role of gestures in music generally, but will remain an open question for the purposes of this dissertation.
4.2 Overview
4.2 . 1 M a j o r S ubd i v i s i o n s
I n Mozart’s Flute Q u a r t e t KV 285 the major sub divisions are the three movements. Because the second movement ends on an interrupted cadence and moves a t t a c c a into the final movement, these two can also be grouped together. The second m ovement has what can be described as a modified ternary structure ( w h e r e Aʹ indicates a modified A ):
I II III A A ʹ B A ( C o d a )
o r a proto sonata form structure:
I II III A B A ʹ C D E A ʹʹ B ʹ ( C o d a )
For the sake of clarity I will assume the secon d option so that the first phrase will be called A , and the second B and so forth i n t h e following analysis (See Fig. 13 ). 41
4.2 . 2 T e m p o
The tempo indication is A d a g i o which, according to the practice of the time ( F a l l o w s : 2 0 0 9 ) , can be assumed to be in t h e r a n g e o f 50- 70 c r o t c h e t beats per minute. We can further suppose that, because of the strong melody/accompaniment division, th e dominant paradigm is that of song. Furthermore the lightness of the texture and dynamic level s u g g e s t s t hat it is not very dark i n m o o d ; perhaps a good description would be ‘nostalgic ’ . T h e s e factors therefore s u g g e s t a tempo in the upper end of the Adagio r a n g e , or approx imately 60bpm, which will be my w o r k i n g assumption.
4.3 S e c t i o n I , P h r a s e A
4.3 .1 H a r m o n y
The harmonic progress ion is fairly simple, in ke eping with the s o n g - like nature of the music [b: I - V6- V - I ] the only major non- harmonic note being the E# appoggiatura at bar 2.1.2.2 and the corresponding one at 4.2.
4.3 .2 L i n e s
T he accompan iment lines (violin, viola and c e l l o ) are fairly clearly delineated in s y n c h r o n y with the bar - lines because of their m o t i o n. These lines could arguably be sub divided with the violin having gestures on each beat while the viola has gestures the s a m e length as the bar and the cello has gestures each two bars long. F o r the sake of clarity and space , h o w e v e r , I will treat the accompaniment as a s ingle gesture encompassing the whole bar .
The melody is more difficult t o s u b d i v i d e because two interpretations are possible. The first possible solution i s t o s e g m e n t it as with the accompaniment into two sections of two gestures corresponding to the bars. Alternatively it is possible to interpret it as two sets of three gestures each two beats long ( s e e F i g . 16) . There does not seem to be an obvious rati onale to decide between the two as the first interpretation is fairly obvious i n accordance with t h e b a r - lines and the accompanying figures while the second is supported by the motion of the melody and the f a c t that the first crotchet B at 1.2 would be mor e naturally per f o r m e d with a semi - s t a c c a t o to match the articulation of the other parts. T h i s interpretation would group the first two beat s t o g e t h e r t o t h e e x c lusion of the third .
42
4.3 .3 D e r i v a t i o n
Although the derivation of the gestural symbols is key to t h i s p r o c e s s , it does not strictly fall within the ambit of the present study. I will however include such a breakdown of the first half of this part as A p p e n d i x B for the sake of completeness and by way of example for analyses which follow. It may be not i c e d t h a t while gestures are defined by the position of a nuclear point of emphasis, the sub - gestural parameters cannot be so defined (or they would be gestures themselves). The inference from parameter to gesture may be impossible to make deterministicall y s i n c e gestures are also defined as perceptual objects, i.e. they are only what they are perceived to be, and since we cannot accurately determine what an individual actually perceives we cannot purely deductively infer the nature of gestures . Nevertheles s i t i s possible to compile a n inventory making an i n f o r m e d j u d g e m e n t on the presumed information available to that individual.
4.3 .4 Structural Diagram
After placing the gestures into the structural diagram (see Fig. 18) t h e m e t a - gestures can be simila rly derived, with the same caveats as d i s c u s s e d above. Here it may be observed that while the combinatorial gesture - as represented on the vertical axis - i s the result of the previous resultant (where there is one) , t h e n e x t gesture, the meta - gesture is always derived from the gestures themselves (i.e. one gesture and the next). It can also be seen that although sequent gestures have meta - gestures, simultaneous ones do not; this omission is conscious, because gestures are defined temporally and the meta - g esture of the horizontal relation seems to me to be captured, albeit indir ectly, by the vertical relation.
43
44
F i g u r e 1 3 . The second movement ‘ A d a g i o ’ of WA Mozart’s Flute Quartet in D major KV285.
45
I: A
B
A'
C
II: D
46
E
III: A''
B'
Coda
F i g u r e 1 4 . T h e s tructural outline, showin g the grouping lines for (from outermost to innermost) t he work as a whole, the second and third movements, the second movement, sections and phrases.
47
1 2 3 4
b: i V₆ V i F i g u r e 1 5 . P h r a s e A , the first pa rt of the second movement, b a r s 1 - 4
F i g u r e 1 6 . T h e g estural sub division for p h r a s e A
F i g u r e 1 7 . T h e l a b e l s assigned to the gestures and the associated g e s t u r e s . The importance of the subdivision can b e seen from the gesture labelled A which would most likely have been read as a d v a n c i n g ( / ) if the gesture was taken to encompass the whole first bar instead of only the first two beats.
48
y
x F C
A B D E
z
G H I J
F i g u r e 1 8 . The analytical tableaux showing the position o f t h e g e s t u r e s [ A ] t o [ H ] and the meta - gestures [x] to [z] .
\ /
/ \ \ \
\ \ / \
\ /
/ \ / \
F i g u r e 19. The gestures are filled in according to the information from Fig.16 and the meta - g e s t u r e s as suggested by A p p e n d i x B .
49
\ / \ ^ \ \ / \ ^ \ \ \ \ ^
\ \ / \
\ / \ \ ^ ^ / \ / \
F i g u r e 20. The resultant and combinator i a l g e s t u r es, calculated according to Table 7, are added.
\ / \ ^ \ \ / \ ^ \ \ \ \ ^ / \ \ \
\ / \ \ ^ ^
/ \ / \ \ /
^ ^ ^
F i g u r e 2 1 . The completed tableaux for p h r a s e A . The gestures in the middle of the diagram are formed by combining the final resultants of the upper and lower lines of the first and secon d half of the phrase .
50
4.4 Adding the Second P h r a s e
4.4 .1 Discussion
This phrase immediately follows the one in the above analysis, what was determined to be p h r a s e B ( s e e F i g . 2 2 ) .
There is no apparent change in tempo here, but owing to the slightly contr asting nature of this phrase, i . e . there are fewer leaps, one could say that it is a more lyrical p h r a s e t h a n A , w h i c h perhaps suggests a fractionally slower tempo but not so much as to substantially affect interpretation.
While the melodic tension r e s u l t i n g f r o m the large leaps in A m a y have relaxed somewhat , the harmonic tension has become much more acute [D: I - - I - - v i i ° - b : v i i ° - i - v i i ° / V - - V - i] and the non - harmonic ornamentation is both more frequent and chromatic than was the case in A .
The grouping is l e s s c l e a r cut here. I have opted for a structure resembling that used in the first phrase , since a listener would m o s t likely opt for a listening stra tegy which requires as little d e v i a t i o n as possible from what is expected. Mozart also p l a c e s the tonic chord of the new (relative major) key at the start of bar 6 , which strongly indicates the bar as a major structural divi s i o n in this phrase. The melody meanwhile divides the bar in h a l f . T h e s u d d e n m o d u l a t i o n (through the use of diminished sevenths) back to the tonic of the original b minor key interrupts this flow and leads to a slightly more complex final group .
The figures 23 to 26 show the rest of the process from the structural divisions through to the construction of the tableaux.
The final figure in this series (Fig. 27), shows the combined gesture for the phrases A a n d B w i t h a final resultant gesture [^].
51
5 6 7 8
D:ii I vii° - b:vii°- i - vii°/V V i
F i g u r e 2 2 . P h r a s e B with harmonic analysis
F i g u r e 2 3 . The gestural sub division for p h r a s e B
F i g u r e 2 4 . Gestural assignation for phrase B 52
P Q
O
T U V
K L M N
R S
F i g u r e 2 5 . The analytical tableaux for p h r a s e B showing the positions of the gestures indicated in figure 21 .
/ \ ^ \ \ \ \ \ \ \ \ \ ^ \ \ \ \ \ ^ \ \ \ \ \ ^
^ / \ ^ \ \ \ ^ \ \
^ ^
F i g u r e 2 6 . The completed tableaux for phrase B 53
/ ^ \ \
\ \ \ \ ^ \ / / \ ^ \ \
\ \ / \ ^ \ / \ \ ^
/ \ /
\ / ^ \ / ^ \ ^ ^ \ \ ^ \ \ \ \ \ \ \ ^ \ \ \ \ \ ^ \ \ \ \ \ ^
^ / \ ^ \ \
\ ^ \ \
^ ^
F i g u r e 2 7 . The combined t a b l e a u f o r p h r a s e s A a n d B , t h e f i n a l resultant gesture bolded for clarity.
54
4.5 Completing the S e c o n d M o v e m e n t
4.5 .1 Discussion
By way of illustration I will conclude this chapter with an abridged derivation of the rema ining sections. This part is intended to show how the technique can be applied to larger scale structures such as whole movements and pieces. Each section will be divided into gestural units, have gestures assigned to them (with no justification given at t h i s point) and then displayed as t a b l e a u x .
F i g u r e 2 8 . Gestural sub d i v i s i o n f o r s e c t i o n I p h r a s e A '
F i g u r e 2 9 . G e s t u r a l assignations for s e c t i o n A '
55
F i g u r e 3 0 . Gestural sub d i v i s i o n f o r s e c t i o n I p h r a s e C
F i g u r e 3 1 . Gestural assignations for s e c t i o n I p h r a s e C
56
C F
A B D E
G H I J
P
O
N
M
K L
F i g u r e 3 2 . T a b l e a u i n d e x f o r p h r a s e s A ' a n d C
57
\ \ \ \ \ \ / / ^ \ ^ \ \ \ \ \ \ \
/ \ / \ ^ \ / \ ^ \ ^ \
\ \ \ \ \ \ \ \ \ \ \ ^ \ \ \ / ^ / / \ / / / / ^ / \
F i g u r e 3 3 . Completed tableau for p h r a s e s A ' a n d C
58
^ \ \
F i g u r e 3 4 . The analy tical tableau f o r s e c t i o n I
59
F i g u r e 3 5 . Gestural su b d i v i s i o n f o r p h r a s e D
F i g u r e 3 6 . G e s t u r al assignations for phrase D . The gesture names here start from A again and will do so for each new section to a v o i d o v e r long labels. It may however be considered preferable to keep the labels running continuously.
60
D
L C A J K
B
M N
E
F
G
H
I
F i g u r e 3 7 . T a b l e a u i n d e x f o r p h r a s e D . Where space is insufficient an arrow shows where the resultant appears. In the area where gesture [ F ] appears the resultant gesture of [ G ] , [ H ] and [ I ] appears as a separate box underneath the simultaneously o c c u r r i n g [ F ] , since simply stacking them would wrongly indicate a combinatorial and meta - gesture without any underlying gestures. The resultant of [ F ] w i t h [ G ] , [ H ] a n d [ I ] is placed at the head of the arrow originating at their centre.
61
F i g u r e 3 8 . Gestural sub d i v i s i o n p h r a s e E
F i g u r e 3 9 . G e s t u r al assignations for phrase E
62
O P Q
U V W X
R S
T
AA Y Z
F i g u r e 4 0 . Tableau i n d e x f o r p h r a s e E
63
O P Q
R S U V W X
Y Z T
AA
D
C A
B F L
J K
E G
H M N
I
F i g u r e 4 1 . The completed t a b l e a u index for s e c t i o n I I
64
/ / ^
^ / \
/ / / / ^ / / ^ / / \ \ / ^ /
/ / \ \ / ^ ^ / / ^ ^ / \ / \ / \ ^ ^ \ ^ \ \ / \ \ / \ \ \ ^ / / \ / / ^ / \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \
\ / / ^ / \ ^ / \ \
F i g u r e 4 2 . Analytical tableau for s e c t i o n I I
65
F i g u r e 4 3 . Gestural subdivision for phrase A ''
F i g u r e 4 4 . G e s t u r a l assignations for phrase A ''
D
C G
A B E F
H I J K
F i g u r e 4 5 . T a b l e a u index for phrase A '' 66
F i g u r e 4 6 . Gestural subdivision for phrase B '
F i g u r e 4 7 . Gestural assignation f o r p h r a s e B '
P Q
T
L M N O
R S
F i g u r e 4 8 .Tablea index for phrase B ' 67
F i g u r e 49. Gestural sub - division for s ection III C o d a
F i g u r e 50. Gestural assignation for s ection III C o d a
X
W
U V
F i g u r e 5 1 . T a b l e a u i n d e x f o r s ection III C o d a
68
G
E F
D
C
A B J K
H I
X
W
U V
P Q
T
L M N O
R S
F i g u r e 5 2 . The complete d t a b l e a u index for s e c t i o n I I I 69
\ \ / ^ / / ^ / \ / ^ / \ / ^ / \ ^ / \
/ \
/ /
\ ^ \ \ / \ \ \ / ^ / / / / / ^ 6 / ^ ^ / ^ \ \ / ^ \ \ \ / ^ ^ / ^ ^ ^ \ / ^ \ \ / \ \ \ \
/ \ \
\ \ \ \ \ \
\ ^ ^ \
^ ^
F i g u r e 5 3 . Analytical tableau for s e c t i o n I I I 6
70
Aʹʹ E
II
Coda
III Bʹ D
\ ^ / / / / ^ ^ \ / \
Aʹ A
I I B C
F i g u r e 54. T he complete gestural tableau for the second m o v e m e n t ‘ A d a g i o ’ of Mozart’s Flute Quartet in D major KV 285.
71
C h a p t e r 5
C o n c l u s i o n
5 . 1 T h e H y p o t h e s i s
The hypothesis which I set out to t e s t i n this dissertation was that it is possible for gestures to be used as a fundamental unit of a logical system which can be applied to musical analysis. By p r o ducing the analytical tableaux of the previous chapters this first objective has been met , it therefore remains for the second objective to be answered which means that this system needs to be shown to be predictive and falsifiable.
In the limited sense of predictability it is cl ear that the analytical t a b l e a u by its very nature has a predictive function, so that given a set of gestures and their meta - gestures we can always work out the resultant gesture. The converse is also true - given a resultant g e s t u r e and a meta - gesture, we can deduce what the combinatorial gesture is, and given a combinatorial gesture and one gesture we can deduce the nature of the other. Furthermore, it is possible to derive a set of compound rules such as the following:
I f t w o c o nsecutive gestures are forward the resultant must be either neutral or forward.
If two consecutive gestures are backward the resultant must be either neutral or backward.
In any series of gestures (that is gestures, combinatorial g e s t u r e s a n d m e t a - gestures), if the number of forward and backward g e s t u r e s i s equal, even or zero the resultant must be neutral.
If a resultant gesture is not neutral there must be at least one consecutive or meta - g e s t u r e t h a t is also not neutral.
T a b l e 8 . S o m e c o m p o u n d r u l e s .
72
The system is also falsifiable, so that given a combinatorial gesture and a meta - gesture we are constrained to one resultant interpretation and given a different resultant interpretation we must conclude that the derivation of the gesture wa s i n e r r o r , thereby falsifying the c o n c l u s i o n . This feature is crucial to the testability and applicability of the system because without i t, o n e cannot have any justification for discarding the system if it proves to not correspond accurately to observatio n and therefore does not truly add to the sum of knowledge. T his applies only to t h e syllogistic aspects of the system. T he structural, grouping and assignation decision s are based pu rely on intuition at this stage; they are not falsifiable in the present s t u d y even while they are crucial to any su ccessful analysis of this type.
5 . 1 . 1 M e t a - systematic analysis
These concepts can be formalised by noting that the system as p r e s e n t e d here can be wholly reduced to zeroth order (i.e. propositional) logical terms by assigning symbols to each gesture in the following manner:
Combinatorial Gesture
/ \ ^ A B C
M e t a - G e s t u r e
/ \ ^ D E F
R e s u l t a n t
/ \ ^ G H I
Each unit of the analytical tableau can then be reduced to either a single symbol (G, H or I) or a syllo g i s t i c construction (If A then if D then G). In all then, the system describes a closed universe of discourse comprising eighty one such syllogisms and a further three freestanding resultants.
Given that it can b e reduced to zeroth order logic the system i s consistent, meaning that a single gesture cannot be both of one kind and another; and sound, meaning that only valid formulas can 73 b e d e r i v e d . T h i s i s in accordance with Gödel’s completeness theorem of 1929. It may appear that neutral gestures are in effe c t gestures which are forward and backward, but they are not so defined. The proper negation of a forward gesture is [ e i t h e r a backward or neutral gesture ] .
The system can be said to be syntactically complete because, for each gesture, eith er the gesture i s forward or i t i s [ backward or n e u t r a l ] , w hich is the negation of forward . Similarly, the n e g a t i o n s of backward or neutral are also theorems. In terms of this interpretation the symbol ‘/’ means not only ‘f orward’ but a l s o [ n o t n e u t r al and not backward], i.e. not [neutral or backward] in terms of DeMorgan’s law .
It may also be noted that g iven a certain resolution of analysis applied to the musical work under consideration , i.e. a certain fixed average number of gestures per unit of time, there is a fixed and enumerable set of valid tableau constructions. Furthermore, given an enumerable set of tableau x and the fact that for each tableau there is an enumerable set of valid gestural solutions it can be asserted that the set of valid interpretations under the present system is finite , given a ‘two second’ rule . In other words, the problem presented by the fact that there is an infinite number of interpretations for any given gesture is removed when we consider that gesture in a tableau of fixed average resolut i o n . N o w , t h e r e a r e an infinite number of valid resolutions, but we can circumvent th is problem by asserting the axiom of choice , w e assert that there is some (unspecified) function which we can u s e to pick the appropriate resolution.
The system is e x p r e s s i v e l y complete over the universe of discourse of Hatten’s musical gestures themselves, that is: Every gesture, when it is perceived as a gesture must be perceived as f o r w a r d , backward or neutral. Here it is important to note that this completeness does not preclude more complex constructions, but only stipulates that there is no conceivable complex construction which does not satisfy the criteria for being f o r w a r d , backward or neutral.
I would furthermore assert that in terms of the second order connotation al interpretation of Hatten’s gestural theory , o u t l i n e d at the end of the second chapter of the present work, the system i s e x p r e s s i v e ly complete over every universe of discourse (an interpretation which may be thought of as strong gestural theory). 74
O n t h e basis of the above analysis it can be affirmed that the s y s t e m which was presented here is formally re l a t e d to a Peano (or Zermelo - Fraenkel) type axiomatization of mathem atical logic, i n t h a t it is a second order logical system. In terms of Gödel’s i n c o m p leteness theorem the system is sound and complete (as shown above) but it is not effective at the level of gesture and tableau derivation , t h a t i s : there is no way to establish within the system itself whether that tableau is a v a l i d interpretation of the music it derives from . I t accepts the axiom of choice , as discussed a b o v e , b u t it d e n i e s the axiom of induction in the sense that given an immanent musical experience from which a certain tableau is derived we cannot assert that all similar experien c e s w i l l y i e l d the same tableau. I n other words there is no single function which can be used to derive all tableaux . Alternatively the axiom of induction can b e thought of in this context to represent the statement: “Given that musical pattern X is a gesture at t i m e T , X will be the same gesture at time T+1”. A stronger form of this s t a t e m e n t , equally denied in t h e m u s i c c o n t e x t , is: “Given that X at time T is a gesture, X at time T+1 is also a gesture”.
This denial of mathematical induction is required to accou n t f o r the fact that in musical interpretation every predicate which can be applied to a musical extract must be considered to decide which gesture is assigned, or even whether the extract is interpreted as a gesture at all, rather the simple successorship that suffices in set theory. This is not meant to imply that the axiom of induct ion cannot be invoked in music at all though , indeed cadences may be e x a m p l e s where an inductive axiom is a s s u m e d , in that a composer w h o w r i t e s V - I a t t h e end of a piece c a n be taken to expect it to b e interpreted to signal the end of a p i e c e every time he does so . A formulation may take the form “If p a t t e r n X in context Y is taken to be cadence Z , t h e n pattern X in context Y+1 is also taken to be cadence Z” where context Y+1 i s taken to refer to the next time the same set events occurs. R a t h e r , the situation may be analogous to the way that mathematics may accept the axiom of choice, but may also reject i t ; t he assumption is independent of the system. In fact, the case of cade n c e s ( a s well as any number of tropes) may well be regarded as linguistic e l e m e n t s superimposed on top of music, rather than p u r e l y musical phenomen a .
This line of r e a s o n i n g s u g g e s t s that any attempt to completely ( i n the logical sense) formalise a distinc tion between language, music and other modes of thought is ultimately a doomed enterprise. 75
5 .2 Suggestions for Further Study and Application
T h e t e c h n i q u e o f analytical tableaux e m p l o y i n g gestures as fundamental units display s all the important hallmarks of a useful analytical system. But what applications could such a device be put to, or is this simply an exercise in creativ e analysis, and what weaknesses d o e s this system display which may be m i t i g a t e d through further investigation?
5 .2.1 Suggestions f o r F u r t h e r S t u d y
The most immediate objection which may be raised against the analytical tableaux is that the gesture assignation is fairly weakly supported and is based largely on intuition and ‘feel’. One way to overcome this may be to suggest a different system to perform these derivations, such as the system I propose in A p p e n d i x B o r some variant of Lerdahl and Jackendoff’s sub - ordination tree structure applied to a lower level . The advantage of this is to a llow a separate study of what are perceived to be gestures by individuals across different educational and social backgrounds. The kind of question w hich may be asked includes : ‘ D o a l l societies experience a rise in pitch as a rise in tension?’ a n d ‘How does the flow of tension within a gesture affect t h e selection of the emphasised point?’
The decisions pertaining to the structural features may also benefit from the above treatment, but I suspect that they would be much harder to ‘pin down’ , as it were, to a set of clear rules , without imposing exogeno u s s t r u c t u r e s ( c f . R o s e n : 1 9 8 8 ) on works which may or may not be so structured. One possible solution to this would be t o s h o w that some structures are innately favoured, such as the golden ratio often found in nature, but even then it would be hard to prov e that the structure is of the music itself and not simply an imposition from the analyst. Perhaps another solution may be to apply the ‘Aural Sonology’ approach of Thoressen (2007) where , rather than analysing the score as fundamental text , t h e a c t u a l s o u nds of a performance are analysed. This may be done at two levels, either by an alysing the perceived structure or the structures as heard, although this may be subject to varying interpretation; or to analyse the wave - f o r m level and see if any mathematical q u a l i t ies hint at structural division. I t is far from clear that this is in any sense achievable, since implied intention may be very far removed from any physical features of the sound and yet has a much greater impact on the perceptions of a listener . 76
I have included (as Appendix C ) a r e c o r d i n g of this movement as performed by the author at the final exam i n a t i o n concert for this degree at the UNISA Sunnyside Campus Conference H a l l i n J u l y 2007. Although I have not referred to this performance at all duri n g t h e c r e a t i o n o f t h i s t e x t , it may nevertheless be a matter of interest to see whether some of the conclusions I have reached here correspond to the performance decisions made on that o c c a s i o n . A study conducted by Ir ne Del ge ( 1 9 9 6 : 1 3 1 - 1 5 6 ) h a s indeed undertaken an investigation of this type and further work in this direction may y ield useful results .
The other feature which may be empirically tested is the syntax rules that I proposed i n T a b l e 7 : Given an individual who ascribes gestures in the expected manner (i.e. i f w e know which gestures a n d m e t a - gestures have been ascribed), are the combinatorial and resultant gestures as we have predicted them to be? Is this the case across different cultures and stylistic practices?
It is also possible to question the structural properties of the system I have laid out. Is it really the best solution to have each gestural or structural unit only affect the very next unit directly, or is it possible to devise a system where similar ideas are t r e a t e d a s b eing more conjunct s u c h a s i n Nicholas Ruwet’s ‘Methods of A nalysis in Musicology’ ( in Everist 1987:3 - 36) I have also arbitrarily imposed some restrictions which, to me at least, seem commonsensical: This includes the breakdown of gestures s o a s t o n e v e r h ave more than two simultaneous gestures , a n d a l s o restrictions on the number of consecutive gestures that can be seen as one unit. These decisions are largely aesthetic, both aurally and visually, but it is conceivable that empirical testing may illuminate whether this sensibility is generally shared amongst listeners and whether there is any way to codify it.
Finally we can ask and investigate two questions about gestures themselves: How common is it for participants in the musical process to organise thei r aural experience around discrete gestures as I have proposed? And i s it possible to further distinguish between gestures, e . g . can we expand the system to include gestures which have ‘nuclear points of emphasis’ n e a r t h e end as opposed to at the end, or to distinguish those gestures which have a peak in pitch from those with a peak in volume? Any such expansion of the properties of the fundamental units would very quickly add to the overall complexity of an analytical system, so that if w e perfectly ident ify each possible musical pattern with its own unique gesture the system would be 77 c o m p l e t e l y useless. The interpretive quality of this system comes largely from the abstraction of the gesture from the originating musical parameters; eliminating that proces s also eliminates the general nature of the insights which may be gained from it. Having said this, it may be more appropriate to have a little more c omplexity than the extremely pa red down version I have p r e s e n t e d ; presumably there is a level of complexit y which ideally captures the nature of the piece being analysed while maximising the interpretive power provided.
5 .2.2 Application
Given that this system of analytical tableaux is accepted, even with the above reservations, it remains for me to suggest s o m e useful aspects of this method of analysis.
Any analysis is always a useful tool for pedagogy and this kind may be especially so, since a student can ass ign an overall gesture w h i c h s / he wishes to achieve in a performance and work backwards through ea ch preceding phrase to obtain clues as to their interpretation. Given a particular set of resultant, combinatorial, meta - and basic gestures it is possible to work out some elements of confusing parts of music in a way which may just satisfy the ‘but why’ response of a student. The system may a l s o be useful to engage in comparative exercises between different cultural and stylistic practices, so that we can answer questions like: Does this practice favour using the same kind of gesture repeatedly and differ e n t i a t e t h e m using only meta - gestures? Or h o w d o e s this particular culture structure their music in contrast to a neighbouring one? An example of such an application may be the contrast between the minimalist music of a composer such as P h i l ip Glass with t he gamelan music of Java: These may sound very similar at the level of individual gestures but may display completely dissimilar properties at larger levels.
A system of notating gestures may also be of use for performers where a conductor or guest artist wishes to communicate how s/he wishes a particular work to be performed since traditional notation does not necessarily eliminate one reading or another. O f course, gestures may be enacted in multiple differing ways, so it does not offer a positive solutio n to the problem (if indeed it is considered a problem). Even so, exotic applications are frequently adopted for novel techniques beyond the original intended scope. 78
Mathematical applications can also include im proving the quality of computer - generated mus ical performances. The same kind of approach may also be used to analyse any of the fields discussed in the Meaning section of Chapter 2: If other fields of human endeavour are related to a gestural concept , they should be equally amenable to gestural a n a l y s i s . O t h e r mundane applications which can follow from this kind of mathematical approach may include fields w h ere important decisions need to be made rationally on the basis of incomplete information, such as in the field of financial risk management.
T h e reason why I see Hatten’s concept of gesture as an important musicological concept is precisely because it manages to capture the way in which musical ideas, what Scruton would term to n e s a s opposed to sounds (1997:14 - 1 8 ) , relate to one another . It is thi s relation which finds an analogue in similar relationships between other kinds of ideas and it is in that analogy that gestures have m e a n i n g . I t is the author’s hope that sufficient grounds have b e e n provided to defend a gainst Steven Pinker’s speculation that music is mere “evoluti onary cheesecake” (1997:528 - 5 3 8 ) .
My c l o s i n g contention, on the basis of the preceding study, i s t h a t m u s i c al thinking has a fundamental role in the process of h u m a n c o g n i t i o n a n d should, as such, play a central role in the stud y t h e r e o f .
79
F i g u r e 5 5 . The Mandelbrot set (Beyer: 2009) , arguably the most famous fractal, which displays the property o f self similarity also seen in the preceding analyses. The bottom image is an enlargement of a portion of the upper image. Notice that there is a w e l l - defined starting point (i.e. where the whole structure is visible in the upper image) which corresponds to the starting point offered by gestures . Self similarity need not be exact (Mandelbrot:1982), and shou ld not be confused with the more precise scale invariance possessed by some fractals.
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Yanal, Robert J. 2006. Hanslick’s Third Thesis. British journal of Aesthetics. Vol. 46, No.3 pp. 259 - 2 6 6 .
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A p p e n d i x A
For the purpo ses of this dissertation I will use the following definition of a formal theory:
A formal theory T consists of:
(1) A countable set of s y m b o l s . (A finite sequence of symbols of T is called an e x p r e s s i o n o f T . )
(2) A subset of the expressions, called the w e l l - f o r m e d f o r m u l a s (abbreviated wffs) of T. The wffs are the legal sentences of the theory.
(3) A subset of the wffs called the a x i o m s o f T .
(4) A finite set of relations R1, ..., Rn on wffs, called r u l e s o f i n f e r e n c e . For each Ri there is a unique po sitive integer j such that for every j wffs and each wff A one can effectively decide whether the given j wffs are in the relation Ri to A; if so, A is c a l l e d a direct consequence of the given wffs by virtue of Ri. For example, the rule modus ponens is a r elation on three wffs, A, A - > B, and B, by which B is a direct consequence of A and A - > B .
Since the set of axioms is often infinite, this set is often specified by providing a finite set of axiom schemata . A schema is a statement form; it provides a te mplate showing the form of a wff while leaving some pieces unspecified through the use of metavariables. In the above example A and B are metavariables which stand for wffs of the theory. An instance of a schema is a wff obtained from the statement form by substitution.
(Davis: 1989)
ix
A p p e n d i x B
D i m e n s i o n Explanation
P i t c h The higher the pitch the higher the tension. / is low to high, \ is high to l o w .
Tonal value of The order of tension is assumed to be: p i t c h e s T o n i c : s u b dominant:do m i n a n t : s u b - mediant:mediant:super tonic:leading note although this is largely a matter of feeling as well as the mode involved.
Melodic tension L arger leaps are generally taken t o c r e a t e higher tension.
V o l u m e Louder = Higher tension.
T i m b r e D a r k e r sounds, more complex waveforms may be considered more intense. Chord density is a related concept.
H a r m o n y As for tonal value of pitches.
H a r m o n i c Using Hindemith’s classification, f o r t e n s i o n which see f i g u r e 1 .
R h y t h m i c More complex rhythms are assumed to d e n s i t y have more tension .
Textural density Close counterpoint is taken as higher t e n s i o n .
Integrated An averaged out gesture taken from the G e s t u r e above parameters.
T a b l e 9 . A list of parameters and their implementation. x
D i m e n s i o n G e s t u r e N o t e s
P i t c h / The G’ at bar 1.2.2.1 is non - e s s e n t i a l .
Tonal value of / The B at bar 1.2 is the tonic. p i t c h e s
Melodic tension / A s a b o v e .
V o l u m e \ As suggested by the placement of strong b e a t s .
T i m b r e \ No clear in dication, derived from v o l u m e .
H a r m o n y / The B’ is the root of the chord.
H a r m o n i c ^ The G’ momentarily produces a chord of t e n s i o n t y p e I I I (in Hindemith’s typology) . T h e resolution of this dissonance will tend amplify the decrease in volume to w a r d the end of the gesture.
R h y t h m i c \ Suggested by the placement of the d e n s i t y ornament slightly before the middle of the gesture.
Textural density \ As for the rhythm.
Integrated \ Mostly due to the volume and the G e s t u r e resolution a nd the slightly dissonance of t h e n o n - harmony note in the first half.
T a b l e 10. The gesture r eferred to as [ A ] in figures 16 and 17 a b o v e . xi
D i m e n s i o n G e s t u r e N o t e s
P i t c h \
The E#’ at 2.1.2.2 is the leading note of T o n a l v a l u e o f / the dominant key whose harmony is p i t c h e s found in this bar.
Melodic tension \ The leap at the end of the gesture is large and fairly large and unexpected.
V o l u m e / In line with the beats
T i m b r e / Flautists will tend to darken the tone at the C#’ (bar 2.1) because it is an intrinsically weak note o n t h e instrument; this may serve to accent the n o t e because of the attention paid to it .
H a r m o n y \ The progression is from third to fifth to a raised seventh.
H a r m o n i c / Starting as type I.1 it moves to type I.2 t e n s i o n and then to II.2 at the very end.
R h y t h m i c / d e n s i t y
Textural density /
Integrated \ The forward i nclination is much stronger G e s t u r e here than in [A]
T a b l e 1 1 . [ B ]
xii
D i m e n s i o n G e s t u r e N o t e s
P i t c h /
T o n a l value of \ The E#’ at 2.2 is the raised fourth p i t c h e s degree of b minor.
Melodic tension \ T h e s e m i tone step is of low melodic t e n s i o n .
V o l u m e \ T w o - note slurs have a strong tendency to go from strong to weak.
T i m b r e \
H a r m o n y \ From leading - note of the dominant key (F# minor/major) to its tonic.
Harmonic tension \ From type II.2 to type I.2
Rhythmic density ^ The appoggiatura is presumed to be of crotchet length.
Textural density ^ As for the rhy t h m .
I n t e g r a t e d G e s t u r e \ A strong withdrawal.
T a b l e 1 2 . [ C ]
xiii
D i m e n s i o n G e s t u r e N o t e s
P i t c h / All the lines follow the same motion, except for the minor reversals in the violin part.
Tonal value of ^ No outstanding moments. p i t h e s
Melodic tension \ The large leap in the t w o l o w e r p a r t s i s h i g h in tension, after which the melody becomes more still.
V o l u m e / Following the pitch lines
T i m b r e ^
H a r m o n y ^ A slight increase in tension in the middle of the bar can be assumed because the v iolin outlines a second inversion chord.
Harmonic tension ^ A s a b o v e .
Rhythmic density ^
Textural density ^
/ There are three successive points of tension here, corresponding to each Integrated Gesture beat, each arising from a differ e n t source but following the line of pitch u p w a r d s .
T a b l e 1 3 . [ G ]
xiv
D i m e n s i o n G e s t u r e N o t e s
As for the previous gesture. P i t c h \
Tonal value of ^ p i t c h e s
As for the previous gesture Melodic tension \
Following the line of p i t c h V o l u m e \
T i m b r e ^
\ Because the outlined second inversion chord in the violin is now right at the end of the bar and in a very weak H a r m o n y position the implication is effectively avoided. The first inversion chord implication, again in the violin, i s stronger than the root pos i tion chord on the second beat.
H a r m o n i c \ A s a b o v e t e n s i o n
R h y t h m i c ^ d e n s i t y
Textural density ^
Integrated \ This gesture is effectively a mirror G e s t u r e i m a g e o f gesture [H]
T a b l e 1 4 . [ H ] xv
D i m e n s i o n G e s t u r e N o t e s
P i t c h / The whole of the second gesture is h i g h e r .
The main pitches in L1G1 are the tonic Tonal value of / and the dominant of b minor while L 1 G 2 p i t c h e s has the mediant and super tonic of D m a j o r . The second gesture has a falling major Melodic tension \ second while the first has a rising third.
No substantial motion. V o l u m e ^
T i m b r e /
From b:i to b:V . H a r m o n y /
From a chord of type I.1 to II.2 . H a r m o n i c / t e n s i o n
R h y t h m i c \ d e n s i t y
Textural density \ Textural density matches the rhythmic density here.
I n t e g r a t e d / G e s t u r e
T a b l e 1 5 . M e t a - gesture [x], derived from gestures [A] and [B], and seen in figure 17 above.
xvi
D i m e n s i o n G e s t u r e N o t e s
P i t c h \
Tonal value of ^ T h e E # i n the middle of the gesture is p i t c h e s the focal point.
Melodic tension \ M a x i m u m tension also occurs at the l e a p f r o m t h e C # to the E#.
V o l u m e \ As above, although some perform ers may accentuate the c# instead making the gesture ‘ \ ’ .
T i m b r e \ A s a b o v e .
/ Even though the harmony is most dense H a r m o n i c a t 2 . 1 . 2 . 2 , the release of tension happens soon after.
H a r m o n i c / A s a b o v e . t e n s i o n
R h y t h m i c \ d e n s i t y
Textural density \ Texture becomes more intense at 2 . 1 . 2 . 2 .
Integrated \ More intense bot h in advance and G e s t u r e withdrawal than [ x ] .
T a b l e 1 6 . M e t a - gesture [y] (derived from gestures [B] and [C])
xvii
D i m e n s i o n G e s t u r e N o t e s
P i t c h \ The fall is slightly greater than the r i s e .
\ Because of the change of harmony from Tonal value of b : I t o b : V , a n d b e c a u s e t h e p i t c h e s accompaniment outlines the full h a r m o n y , the tonal values rise.
^ The variation in melodic tension Melodic tension effectively cancels out any strong m o t i o n .
V o l u m e ^ In line with the pitch .
T i m b r e ^
H a r m o n y \ b : I t o b : V
H a r m o n i c ^ Both chords are t y p e I . 1 ( w i t h o u t t e n s i o n seconds, sevenths or t r i t o n e s, e a c h w i t h the bass note the same as the root ) .
R h y t h m i c ^ d e n s i t y
Textural density ^
Integrated \ A v ery slight advance which may be G e s t u r e compensated for by the strength of the withdrawal in the second gesture .
T a b l e 1 7 . M e t a - gesture [z] (derived from gestures [G] and [H])