Diminished Seventh Chord Research Articles

Revealing the Mystery of Emotions in Sounds The Theory of Musical Equilibration Explains the Impact of Ordered Sounds as the Listener’s Identification with Processes of Will

ABSTRACT Science has long been concerned with the question of how it is possible for music to elicit emotions‒so far, however, with only moderate success. The theory of musical equilibration shines a light on this problem from a new perspective. The theory was first proposed in 1997 by German music theorist, Bernd Willimek, who further developed it with his wife and fellow theorist, Daniela Willimek. Music itself, the theory goes, cannot generate emotions directly. Rather, emotions should be understood as a response to the processes of will that are encoded in music. By identifying with these processes of will, listeners experience music emotionally. This is comparable to the situation of moviegoers who identify with the protagonist on screen and thereby vicariously experience emotions. In this work, the affirmative character of the major triad and the negative character of the minor triad are substantiated. According to the theory of musical equilibration, the volume at which a minor chord is played determines whether it is perceived as sorrow or anger. Furthermore, the authors discuss issues such as why a diminished seventh chord is well suited as the score for film scenes involving fear, or how an augmented chord can convey amazement and astonishment. To show the practical application of the theory of musical equilibration, the authors carried out tests with school (K-12) and university students (basic test part A, basic test part B, Rocky test).

Äquidistanzen im zwölftönigen System. Zusammenhänge kompositorischer Verfahren im frühen und späten Klavierwerk Franz Liszts

Franz Liszt’s late piano works represent a radical change in his musical style. They stand out for their frequent use of equidistant scales and chords such as the diminished seventh chord or the augmented triad as well as the combination of different scale types such as the whole tone scale, the octatonic scale or the “gipsy scale”. While the compositional techniques in Liszt’s late works have often been described in isolation from Liszt’s earlier works and have been understood as paving the way for post-tonality, this article aims to show that they also emerge from a system of more traditional techniques that complement each other and were actually used by Liszt throughout his career as a composer. A discussion and comparison of selected techniques in Liszt’s late piano work as exemplified in La lugubre gondola I/II, Nuages gris, Unstern! and Bagatelle ohne Tonart is related to techniques in earlier works such as Funerailles. It can be shown that the “idiosyncratic” techniques in the late works are actually ultimate consequences from compositional techniques dating back to the Baroque period.

Dig That Lick (DTL): Analyzing Large-Scale Data for Melodic Patterns in Jazz Performances

Dig That Lick (DTL): Analyzing Large-Scale Data for Melodic Patterns in Jazz Performances

Microtonal Analysis of "Blue Notes" and the Blues Scale

Microtonal evaluation of blue notes in the early blues scale by empirical pitch measurement and statistical characterization has not yet been performed in existing research. To address this, fifteen recorded classic blues performances by acknowledged early masters of the blues were studied. Computer based methods were used to collect the audio frequencies of note samples from each performance. Each note had its frequency ratio with respect to the average tonic tone for the performance converted to microtonal cents format. Cluster analysis was performed on these note collections to identify individual note clusters. The fourth and fifth were clearly identified. Three principal "blue note" clusters were isolated with means of 319.1, 582.8, and 1037.9 cents. These values corresponded closely to the harmonic half diminished seventh chord (i.e. 1, ♭3, ♭5, ♭7 with harmonics 5:6:7:9). The "neutral" third was confirmed to occur in this sample. A similar blending of the perfect fourth and tritone was demonstrated in this study. The flat 7th presented as three separate clusters. Several clusters idiosyncratic to individual performers were also identified. Findings are discussed with regards to the array of theories proposed to explain the blues.

Beyond musical qualia. Reflecting on the concept of experience.

How is it that a diminished seventh chord played on a piano, or an open E string plucked on a guitar, give rise to the experiences they do? How can we explain the feeling closure evoked by a cadence in tonal music? Answers to questions like these have been sought in association with the notion quale. In its original usage, the term qualia (the plural form quale) refers to the intrinsic qualities the subjective experience associated with a given sensory event (Jackson, 1982). But its usage in current research has come to describe subjective experience more broadly (Haugeland, 1985; Nagel, 1974), including musical varieties (see Huron, 2006; Zentner, 2012). For the latter, it is common to refer to musical qualia (Dowling, 2010; Goguen, 2004). In this paper, we take a critical look at three standard notions qualia (in general) and musical qualia (in particular). Although our main goal is to contribute to a richer understanding what musical experience entails, we draw from the broader context cognitive science, philosophy mind, and Gestalt psychology, presenting arguments that go beyond the sole domain music. Indeed, because music spans such a wide range human activity, it offers a rich experiential context where theories cognition may be put to the test. For this reason, our musically oriented discussion may have implications for assessing the validity the notion qualia in general.We begin by considering three main philosophical perspectives on qualia. Here we critically discuss their explanatory power using examples drawn from musical contexts. Following this we examine the alternative proposals Daniel Dennett (1979, 1988), and Diana Raffman (1993), respectively. As we discuss, both thinkers deliver compelling eliminativist approaches to the notion qualia, with Raffman offering a critical extension Dennett's position using musical experience as a paradigmatic example. Although these two approaches are certainly fascinating, we suggest they are also problematic, as they rely on models the mind that provide only limited accounts what musical experience entails. In response to this, and the three main perspectives on qualia previously discussed, we then explore another possibility, drawing on the notion body (Gallagher & Zahavi, 2008; Jonas, 1966; Merleau-Ponty, 1945), research in Gestalt psychology, and the enactive framework to cognition originally developed by Varela, Thompson, and Rosch (1991; see also Thompson, 2007; Stewart, Gapenne, & Di Paolo, 2010). Here we suggest a richer, relational, and more holistic model music cognition that embraces the way people actually engage with and talk music in the course their lived experience. We also explore how this approach impacts the concept qualia and consider its relevance for musical research and practice. Before embarking on this, however, let us start with a brief discussion over the three most common perspectives on the notion qualia to clarify their significance for musical research.Three Perspectives on QualiaThe three most common approaches to the study qualia can be summarized as follows:(a) the nonintentional, nonrepresentationalist view (NINR)(b) the intentional, representationalist view (IR), and(c) the intentional, nonrepresentationalist view (INR)The first option (NINR) is probably the most pervasive one. It has been described in terms a quartet attributes, where qualia are understood as ineffable, intrinsic, private, and directly apprehensible [but not directly describable] in consciousness (see Dennett, 1988). In this view, qualia are not explicitly of or something (which means-in classical phenomenological terms-they are nonintentional1). They are, rather, just phenomenal properties present in the perceiver. As an example, consider the sensation being depressed. This feeling is not literally about something. …

Octatonicism and Chromatic Harmony

In this paper, the author looks at the relationship between octatonic structures and chromatic harmony. The discussion concentrates on two major aspects of late-tonal octatonicism: the use of alternative bass tones for the diminished seventh chord and the development of these sonorities into hexachordal and pentachordal combination chords. A number of late nineteenth-century and early twentieth-century chromatic passages are analyzed. Complex harmonies in chromatic passages are explained by formulating reductive models comprised of simpler, octatonic constructs.

Fidelio: Melodramas of Agency and Identity

This essay was meant to be an introductory paragraph or perhaps a page on the way to an analysis of Douglas Sirk's All That Heaven Allows (1955) and two films widely recognized as being in its orbit, Rainer Werner Fassbinder's Ali: Fear Eats the Soul (1974) and Todd Haynes's Far From Heaven (2002).1 My aim was to read these melodramas in terms of the ways in which sexual identity affected possibilities of agency. In the course of thinking about that question, it occurred to me that it also might be asked about a much earlier example of melodrama. This essay takes up that point; it stands as a prolegomenon to an investigation that would lead to Sirk and the melodramas in his debt. That future path is, at times, indicated.In the score of Beethoven's only opera, Fidelio (1814), the duet between Leonore and Rocco in the second act is introduced by what the heading for musical number 12 calls a Melodram.2 This is the appropriate technical term for this brief two-minute stretch of the opera: the two characters speak, their utterances punctuated with musical phrases. Beethoven's opera is formally a Singspiel or opera comique; everywhere else in the score, we find either speech or concerted numbers. If the orchestra is playing, the singers will be singing. If not, the singer speaks. Music and speech never interact except in this melodrama. This raises some obvious questions: Why does Beethoven introduce melodrama into his opera? Why at this point in his score does he violate the rules of composition about speech and song? In his stunning 1972 essay Tales of Sound and Fury: Observations on the Family Drama, Thomas Elsaesser has pointed to melodrama of the kind we find in Fidelio as a system of through which the emotional weight of the moment is underscored.3 For Elsaesser, this formal feature lies at the heart of all melodrama, in the work most readily associated with melodrama in the twentieth centurythe films of Douglas Sirk, most notably. What it might be doing in an opera, where, it is easy to presume, the singing voice heightens emotion, is a question that Elsaesser does not ask.Elsaesser's point is not about opera but does help to remind us how much the plot of Beethoven's opera and the moment at which it arrives at its dramatic/musical Melodram brings his score into the orbit of a family drama. Leonore is, at this moment, descending into the lowest reaches of a prison in the company of Rocco, the jailer in charge of the prison. In male disguise and bearing the name Fidelio, she has insinuated herself into Rocco's company by winning the affection of his daughter Marzelline away from her previous lover, Jaquino. Now engaged to her, she has persuaded her future father-in-law that she should be a fuller partner to him in his job, his assistant in the most arduous tasks. The job before them is to dig the grave of a long and unjustly held political prisoner whom the commandant of the prison, Pizarro, is about to murder. This prisoner may be her husband Florestan, as Leonore suspects, and as we, but not she, know it is. This is why she has disguised herself-to find him, to save him. At this melodramatic moment of disguise and blocked knowledge-at this moment when Beethoven writes a Melodramdiscoveries of identity-his, hers-are incipient. Will all be revealed or will she be there only to witness his death, to prepare his grave?Beethoven's Melodram (figure 1) begins with a brief descent partway down a scale, ending with a tremolo punctuation on a diminished seventh chord. After this moment of musical descent and suspension, Leonore speaks in a voice that, the stage direction indicates, is halb laut (164), mezza voce: she remarks how cold it is this deep underground. Rocco responds by commenting that it is quite natural since they are down deep (Das ist naturlich, es ist ja tief [164]). Rocco's common sense is belied by the unresolved musical descent down the scale and by a tremolo chord that changes from a seventh to a diminished seventh. …

Exploring Tetrachordal Voice-Leading Spaces Within and Around the MORRIS Constellation

[1] Building on Robert Morris's (1990) research on hexachordal ZC-relations, Stephen Soderberg (1998) identifies a constellation of ten hexachords that embed either one diminished seventh chord or two diminished triads. Soderberg divides the constellation, called MORRIS (or T-HEX), into four overlapping eight-hexachord sub-constellations based on tetrachordal subset content. The first of these sub-constellations, TRISTAN, includes the hexachords that embed two instances of set class 4-27[0258], the set class of the major-minor and half-diminished seventh chords. Similarly, constellations ZAUBER, AGITATION, and BROODING include the hexachords that embed two instances of set classes 4-18[0147], 4-13[0136], and 4-12[0236], respectively. Soderberg characterizes each of these tetrachordal set types as a of the diminished seventh chord. When the w, is 1, the result is set class 4-27-that is, moving any pc of a diminished seventh chord by interval class (ic) 1 creates a member of set class 4-27. Similarly, setting w = 2, 4, and 5 creates set classes 4-18, 4-13, and 4-12, respectively. The article goes on to point out a general property of voice leading: in each hexachord the pair of tetrachords can be connected by holding two pitch classes in common and by moving two others by ±w. The cases involving 4-27 and ic 1 voice leading (TRISTAN) are familiar-ii-V7,the Tristan chord with resolution, A7-B7at the beginning of Debussy's Faune, and others-and have been addressed in the theoretic literature by several authors.(1) Example 1 presents the MORRIS constellation and its four overlapping sub-constellations, henceforth called MORRIS1,MORRIS2,MORRIS4,and MORRIS5,with each subscript indicating the warp index, w.Example 1. The MORRIS Constellation (after Soderberg 1998)[2] Taking Soderberg's MORRIS constellation as a starting point, this study explores a wide variety of voice-leading transformations involving set types 4-27, 4-18, 4-13, and 4-12. It starts with the tetrachordal voice-leading transformations that produce the MORRISwhexachords-the nine ways that a tetrachord may be connected to another in the same set class by holding two pitch classes in common and by moving two others by ±w. (For each value of w there are nine transformations but only eight hexachord types because two of the transformations yield the same hexachord type.) The article then greatly expands the scope of inquiry, not only by allowing a given tetrachord to connect to any member of the same set class, but also by considering all twenty-four ways to voice-lead each of these twenty-four tetrachordal connections. As a result, each of these much larger voice-leading spaces-MORRIS+1,MORRIS+2,MORRIS+4,and MORRIS+5-contains 576 (= 24 × 24) voice-leading transformations. Each MORRISwis a subset of its corresponding MORRIS+w.[3] The paper provides an organized view of the entire MORRISw/MORRIS+wsystem, but it also develops other voice-leading spaces within MORRISw/MORRIS+w,each of which involves only a few of the MORRISw/MORRIS+wvoice-leading transformations. The additional voice-leading spaces usually also include rules for requiring, preferring, allowing, or forbidding one transformation to follow another. Although the number of potential voice-leading spaces is infinite,(2) my reasons for creating the ones I do are simple-to exercise melodic control over intervallic characteristics of the voices and to exercise harmonic control, not only of the individual tetrachords, but over the total pc content of sets of adjacent tetrachords. For example, in one space defined below a set of six MORRIS5voice-leading transformations can be concatenated in any order but remain within a single octatonic collection, in another space four MORRIS+4transformations are strung together so that one voice descends chromatically while the other voices also move stepwise, and in a third example ten MORRIS+2transformations are arranged so that each voice is saturated with a different interval class. …

E-quadruple flat: Tovey’s Whimsy

This paper examines the development section of Beethoven’s Appassionata Sonata in light of Donald Francis Tovey’s whimsical remark about the appearance of an E-quadruple flat. In addition to considering Tovey’s idea, this paper examines the analysis by Heinrich Schenker, and compares the two different analysts’ interpretations. This paper concludes with a renewed examination of the passage leading into the climactic diminished-seventh chord that ends the development section, offering a detailed voice-leading analysis, as well as an idea about its programmatic meaning.

‘Tout, dans ses charmes, est dangereux’: music, gesture and the dangers of French pantomime, 1748–1775

AbstractIn 1779 Chabanon noted the potential danger inherent in gesture because it might produce instantaneous and harmful effects. This article examines how Rameau, Rousseau and Grétry incorporated putatively dangerous gestures into the pantomimes they wrote for their operas, and explains why these pantomimes matter at all. In Rameau's Pygmalion (1748), Rousseau's Le Devin du village (1752–3) and Grétry's Céphale et Procris (1773, 1775), pantomime was presented as a type of dance opposite to the conventional social dance. But the significance of this binary opposition changed drastically around 1750, in response to Rousseau's own moral philosophy developed most notably in the First Discourse (1750). Whereas the pantomimes in Rameau's Pygmalion dismiss peasants as uncultured, it is high culture that becomes the source of corruption in the pantomime of Rousseau's Le Devin du village, where uncultured peasants are praised for their morality. Grétry extended Rousseau's moral claim in the pantomime of Céphale et Procris by commending an uneducated girl who turns down sexual advances from a courtier. Central to these pantomimes are the ways in which musical syntax correlates with drama. Contrary to the predictable syntax in most social dances, these pantomimes bring to the surface syntactical anomalies that may be taken to represent moral licence: an unexpected pause, a jarring diminished-seventh chord, and a phrase in a minuet with odd-number bars communicate danger. Although social dances were still the backbone of most French operas, pantomime provided an experimental interface by which composers contested the meanings of expressive topoi; it thus emerged as a vehicle for progressive social thinking.

The Third-Act Prelude of WagnerÕs Parsifal: Genesis, Form, and Dramatic Meaning

The Prelude to the third act of Parsifal is one of Wagner's most advanced essays in expanded tonality. One author has described it as "set[ting] foot in atonal territory as it re-explores the melancholy, disjointed polytonal idiom of the introduction to the third act of Tristan," and a noted analyst has suggested that it is motion around the diminished-seventh chord including Bb rather than the tonic triad of Bb minor that defines the background structure of the Prelude. This music also raises issues of form and expressive meaning that have yet to be thoroughly addressed. A valuable means of approaching the Prelude is through Wagner's surviving compositional documents, particularly the individual sketches for the Prelude that preceded the writing-out of his first continuous draft for the third act (the Kompositionsskizze [Composition Draft]). These manuscripts are held in the Wagner-Archiv at Bayreuth. When these sketches are transcribed and compared with the detailed record contained in Cosima Wagner's diary entries, insight can be gained into the way that Wagner composed the Prelude, during late October 1878. This article shows in detail how the Prelude was composed on the basis of sketch sources that are virtually complete. It is supported by several facsimiles of Wagner's sketches, transcriptions, analytical graphs, and music examples. The study indicates that the "melancholy, disjointed polytonal" idiom of the Prelude is coordinated with a framework of associated tonalities reaching across vast stretches of musical time. These include not only the Bb-minor idiom of Titurel's burial, but also the associated tonality of Parsifal's Prophecy motive. The structural background of the Prelude to act III of Parsifal is not simply a diminished-seventh prolongation, but a tensional framework of motivic combinations and rotational cycles that effectively convey the bleak wandering and promise of deliverance that lie at the core of the drama.

Non-Tonic Settings of the Primary Tone in Beethoven Piano Sonatas

Beginnings of movements by Beethoven often convey a feeling of instability, tension, and expectation. Frequently, opening themes sound introductory and points of harmonic arrival or resolution are delayed. Among the musical techniques described by Heinrich Schenker that heighten the inner tension of such openings, is the setting of the primary tone of the fundamental line-the first Urlinie tone-by a harmony other than the tonic.' This non-tonic setting heightens the dramatic effect of the primary tone. The primary tone is approached either by a rising arpeggiation or an initial linear ascent, two voice-leading procedures which Schenker described as representing a retardation or delaying at the very outset of the piece.2 A dramatic example of upper-voice arpeggiation to the primary tone is the opening section of the Marcia Funebre from Beethoven's Piano Sonata in Ab major, Op. 26, analyzed by Schenker in Free Composition (Example i). The primary tone cb2 (3) arrives only in m. 17, where it is included within the applied diminished seventh of V. The diagonal line connecting the primary tone with the initial Ab in the bass indicates that the Cb2 of m. 17 is part of a prolongation of the opening tonic chord. In m. 18, the striking diminished-seventh chord is emphasized by syncopation and sf a procedure typical of Beethoven (Example 2). An illustration of initial linear ascent to a primary tone is the opening theme (mm. 1-9) of the Largo e mesto from Beethoven's Piano Sonata in D Major, Op. 1o, No. 3, another passage analyzed by Schenker

Identifying musical instruments from multiple versus single notes

These experiments investigated to what degree the identification of a musical instrument depends on change of timbre across total pitch range. Subjects were trained to recognize 12 orchestral musical instruments (natural recordings) by name. Each instrument was represented by a variety of pitches sampled regularly from the standard pitch range of that instrument. The sampling was four notes per octave, effectively forming (in musical terms) a diminished seventh chord arpeggio. First listeners identified the instruments from single note presentations taken from the arpeggios. Results showed that an instrument’s identity is not equally salient across its range of notes, in ways that differ for each instrument. Next listeners were tested on a variable number of notes (N=1,2,...,7) sampled from the arpeggio presented during training in such a way that with increasing N, a greater amount of the arpeggio’s total range was included. Results showed that on average, recognition improved as increasingly recognizable notes (experiment 1) were included in the arpeggio. The relationship between the rate of improvement with N and the recognizability of the single notes is explored. An auditory gestalt called ‘‘macrotimbre’’ is proposed to consider the role across-range timbre changes play in the identification of an instrument. [Work supported by NIH.]

The Role of the Piano Introduction in Schubert's 'Lieder'

Discussions of the piano introductions in Schubert's Lieder often centre on how the music sets the mood for the subsequent text. My interest in whether or not more could be said about the introductions, in analytical terms, was aroused especially by those Schubert songs opening with a dramatic musical statement which is not mimicked by the vocal entry. 'Erlk6nig', 'Die Stadt', and 'Der Lindenbaum' are good examples. I wish to demonstrate that these seemingly separate musical ideas the distinctive piano introduction and the subsequent vocal line are in fact structurally similar, and similar on more than one level. This paper examines the introductory passages from seven Schubert songs and identifies various melodic motives in the piano introduction which take on greater significance when they recur in the subsequent music, both in the piano and the voice and at both the foreground and middleground levels. After studying several songs, I will raise the following questions: At what point is the primary note established in a Schubert song, after the voice enters, or perhaps in the piano introduction? How can the relationships between the introduction and the vocal line be graphed convincingly? In Free Composition, Figure 103, Number 4, Heinrich Schenker shows a firstorder arpeggiation and a pair of unfolding thirds in bs 7-14 of 'Die Stadt'.1 I would like to take Schenker's idea of the third as a structural interval in this song and relate it to the music which occurs before and after bs 7-14. As illustrated in Ex. 1, the piano introduction of 'Die Stadt' presents a dramatic arpeggiated diminished-seventh chord, reducible to a succession of minor thirds. What was just a whisper of thirds in the introduction, at the foreground level, expands to the middleground for the voice in bs 17-25, as shown in Ex. 2. These nine bars correspond to the introduction not only because of the diminished-seventh chord, but also because the vocal line spans an octave at the middleground, from c' to c2, echoing the octave in the left-hand part of the piano introduction, from C to c. A direct relationship can therefore be drawn between the surface of the piano introduction, the distinctive melodic figures of arpeggiated thirds and octave doublings, and the middleground of the vocal