Major Chords Research Articles

The Gutman school; At what intellectual price

I remember reading Herbert Gutman's article on the early United Mine Workers union when it first came out (I happened to be an editor of New Politics then) and being happily surprised by its eye opening conclusions. But Herbert Hill's massive critique of it in this magazine's last number I now find overwhelmingly persuasive. Who could fail to be persuaded by Hill's erudition, logical acuity and eloquence? His critique strikes a major chord. There is nothing small-minded or picayune about it. It does not really contest the accuracy of the evidence Gutman gathered, nor does it call into question Gutman's integrity as an historian. What it does call into question is his judgment as an historian, the approach he brings to this particular subject. Every historian necessarily marks out the limits of his inquiry. He selects and appraises his data according to his hierarchy of values, implied or expressed. It is those values?along with his talent of course?that distinguishes him, that tells us where he stands in the community of historians and more generally in the life of his times. Thanks to Hill we realize to what extent Gutman discov? ered in the United Mine Workers of the 1890s a precious link with his own lifelong commitments to labor and peace and civil rights; com? mitments which the insurgent 1960s reawakened and revitalized. The result, however, was that he not only saw more than his discov? ery warranted, he failed to discover what was there, staring him in the face. This is what Hill demonstrates exhaustively and beyond the scintilla of a doubt. Though Hill rarely ventures far from the text, he provides a con? venient point of departure for a still broader discussion of what might be designated the Gutman school of scholarship, under whose vast rubric I include ethnic and feminist and economic as well as labor historians, historians of folk and popular culture, cliometri cians and anthropologists and documentary filmmakers. Whether aware of it or not, they tend to look at American workers from Gutman's angle of vision. Perhaps inspired as he was by E.P. Thompson's masterpiece, The Making of the English Working

Modeling the Perception of Tonal Structure with Neural Nets

ly summarized by the circle of fifths. Analogously, a net exposed to Indian ragas fills in expected tones when presented with subsets of the raga tones. An auto-associative net trained on the scales of one culture can be tested with the scales of another, making predictions about tonal implications 46 Computer Music Journal This content downloaded from 157.55.39.231 on Thu, 06 Oct 2016 04:43:25 UTC All use subject to http://about.jstor.org/terms generated in the minds of listeners hearing an unfamiliar form of music. A net trained on the Western major and minor scales seems to assimilate some Indian ragas to the Western scales, sometimes shifting the tonic (Bharucha and Olney 1989). Learning Hierarchical Representations Through Self-Organization Hierarchical relationships, such as between tones, chords, and keys, can be learned passively by algorithms for self-organization (Kohonen 1984; Linsker 1986; Rumelhart and McClelland 1986; Carpenter and Grossberg 1987). Most self-organization mechanisms assume the prior existence of abstract units into which the input units feed. These abstract units initially have no specialization, since the links from the input units are initially random. However, repeated exposure to commonly occurring patterns causes some of these abstract units to tune their responses to these patterns. One of the more straightforward, self-organization algorithms, called competitive learning (Rumelhart and McClelland 1986) accomplishes this as follows. For any given pattern some arbitrary abstract unit will respond more strongly than any other, simply because the weights are initially random. Of the links that feed into this unit, those that contributed to its activation are strengthened and the others are weakened. This unit's response will subsequently be even stronger in the presence of this pattern and weaker in the presence of other, dissimilar patterns. In similar fashion, other abstract units learn to specialize to other patterns. This process can be continued to even more abstract layers, at which units become tuned to patterns that commonly occur in the lower layer. The overwhelming preponderance of major and minor chords in the popular Western musical environment would drive such a net to form units that respond accordingly. Furthermore, the typical combinations in which these chords are used would drive units at a more abstract layer to register larger organizational units such as keys. The notion that individual neurons specialize to respond to complex auditory patterns has some preliminary empirical support from single-cell recording studies on animals (Weinberger and McKenna 1988). Once these chord and key units have organized themselves, the net models the implication of tones, chords, and keys given a set of tones. A hierarchical constraint satisfaction net built on this organization has been reported in earlier work (Bharucha 1987a; 1987b). In this net, called MUSACT, activation spreads from tone units to chord and key units and reverberates phasically through the net until a state of equilibrium is achieved. At equilibrium, all constraints inherent in the net have been satisfied. Given a key-instantiating context, the unit representing the tonic becomes the most highly activated. The other chord units are activated to lesser degrees the further they are from the tonic along the circle of fifths. Two behaviors of the net illustrate its emergent properties. First, the above activation pattern does not require the tonic chord to be played at all. An F major chord followed by a G major chord will cause the C major chord unit to be the most highly activated. Second, the circle of fifths implicit in the activation pattern cannot be accounted for on the basis of shared tones alone. If a C major context chord is played, the D major chord unit is more highly activated than the A major chord unit, even though the latter shares one tone with the sounded chord (C major) and the former shares none at all. A careful tracking of the net's behavior as activation reverberates and before it converges to an equilibrium state reveals a lower initial activiation of D major over A major, reflecting an initial bottom-up influence of shared tones. As activation has a chance to reverberate back from the key units (a top-down influence), this advantage is lost, and D major overtakes A major. So the circle of fifths is truly an emergent property of the simultaneous satisfaction of elementary associations between tones and clusters of tones. See Bharucha (1987a; 1987b) for details. Learning With Sequential Nets Some of the schematic expectancies that are essentially sequential, as in chord progressions, can be modeled with sequential nets. The architecture

An exploration of the Chinese pure‐tone system

After 300 years of effort in many countries aimed at resolving the inharmonicity of the 12‐interval equal‐tempered scale, a pure scale of 53 tones was proposed in 1816–1890, but it can not be applied usefully owing to its very great complexity. A survey of ancient Chinese musical literature and instruments and deductions from “Jing‐Fang's 60 Notes” of the Han Dynasty (209 BC‐220 AD) and Emperor Liang‐Wu's “Four Pass” scale (502–519 AD), led us to propose a 23‐tone scale. Its error curve corresponds precisely with that of the 53‐tone pure scale. The principle of Schisma is used for solving problems such as (a) that of the inharmonicity between Gong (do) and Jiao (mi), i.e., the major third; and (b) that the major and minor chords coexisted in an octave. We have derived a pure‐temperament scale of 23 tones that can be modulated for every tonic and that is consistent with the modern pure scale of 53 tones. We show that this 23 unequal‐interval pure scale is consistent with the intervals which were obtained by measurement from a stone flute made in the Qing Dynasty (1644–1908 AD).

Four new scales based on nonsuccessive‐integer‐ratio chords

Our previous work demonstrated that chords with frequency ratios 3:5:7: and 5:7:9: have many perceptual harmonic properties of major triads (4:5:6 ratios). The traditional diatonic scale can be constructed from three major chords, the tonic, the dominant, and the subdominant chords. Using analogous techniques with the new chords, we have constructed four new scales which we call the M579, M357a, M357b, and the P3579 scales. Pitches of the notes of these scales sound very different from the diatonic scale. All scales have clearly perceptable harmonic structure. All notes can be harmonized with consonant “major” chords. There are strong perceptual differences between consonant and dissonant chords. The M scales are based on an octave with a 2:1 frequency ratio. The P3579 scale has a 3:1 octave and was designed for timbres having only odd harmonics. In addition, P3579 is an equal tempered scale using a subset of 13 equal frequency divisions of the 3:1 octave. We believe these scales will be useful for nontra...

Intonation sensitivity for traditional and nontraditional chords.

We studied listeners' intonation sensitivity to traditional (major and minor) and nontraditional chords. The nontraditional chords have frequency ratios of 3:5:7 and 5:7:9 and, like the major chord, have coincident upper partials and unambiguous fundamental basses. The center tone only of each of these four triads was varied from its just (integer ratio) value by -30, -15, 0, +15, and +30 cents. Each tone had ten partials whose amplitudes decreased with frequency relative to the fundamental (9 dB per octave). Subjects judged which chord (or chordal sequence) of a pair was more in tune, smooth and/or pleasant. Listeners' intonation sensitivity curves exhibited regular patterns for both traditional and nontraditional chords. However, our subjects divided into two groups: One group preferred chords in just intonation and their preferences decreased monotonically as the intonation deviated from just intonation; the other group preferred intonations that deviated from just intonation by +/- 15 cents.

Duplex perception with musical stimuli.

Duplex perception, a phenomenon previously demonstrated for speech stimuli, is demonstrated here for musical stimuli. In the first experiment, major and minor chords are produced by dichotic fusion of two simultaneous piano notes presented to one ear (perfect fifth) with a “natural” or “flat” single note presented to the opposite ear. Musically trained subjects perceive simultaneously both the single tone and a fused (major or minor) chord. The chords are labeled more consistently than the single notes, even though the fused chords differ solely in terms of the contralateral notes. In a second experiment, using pure tones in place of piano notes, other musically trained subjects individually exhibited categorical perception for either the fused chord or the single tones, but never for both types of stimuli. The duplex phenomenon is discussed in terms of its implications for its specific component modes of perception.

Consonance and dissonance judgments of musical chords

The terms consonance and dissonance refer to subjective impressions of musical sounds. No studies have examined perception of consonance with stimuli other than two‐note chords. Naive and musically trained subjects rated the degree of consonance and dissonance (both smoothness and pleasantness judgments) of major, minor, diminished, and augmented three‐ and four‐note chords. These chords were presented in root position, first inversion, and second inversion and varied in their harmonic structures and intonations. Naive subjects were strongly influenced by harmonic structures of chords. Neither group of subjects made judgments contingent on the intonation system used. Both naive and musically trained subjects rated major chords as most consonant, followed by minor, diminished, and augmented chords. These patterns occurred in all conditions and were most pronounced for musically trained subjects. When all of the harmonics were present, root‐position chords were rated as most consonant and second inversions least consonant. These findings are discussed in terms of theories of consonance and dissonance.

Tonality and Atonality in the Prologue to Orlando di Lasso's Prophetiae Sibyllarum: Some Methodological Problems in Analysis of Sixteenth-Century Music

a triadic texture erode any sense of a stable tonal center. . . . In the first nine bars of the prologue to the prophecies Lasso uses all twelve tones; he builds triads on ten different degrees, six of which result in harmonies foreign to the mode if we take the mode as Mixolydian since the piece ends on G. Lasso strays as far as B-flat major and C minor in one direction, and B major in the other. This phrase, although beginning on a C major and ending on a G major chord, has no stable frame of tonal reference. Through the excessive modulation within so small a space we lose all orientation.2

Apparatus for forming chord signal

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Electronic organ with a three‐finger chord and one‐finger automatic chord playing mode selector

An electronic organ provided with a selector for selecting a three-finger chord playing mode or a one-finger chord playing mode. When the three-finger chord playing mode is selected, a chord is sounded by three or four fingers on a manual keyboard or lower keyboard as in the conventional electronic organ. On the other hand, when the one-finger chord playing mode is selected, there can be automatically sounded one of chord types, such as major, minor, seventh and minor seventh chords, which have, as the root note, the note of a key being actuated on the manual keyboard. The selection of a chord type is effected by a pedal keyboard.

The psychological representation of musical pitch in a tonal context

In this series of experiments, evidence was found for a complex psychological representation of musical pitch. The results of a scaling study, in which subjects judged the similarities between pairs of tones presented in an explicitly tonal context, suggest that musical listeners extract a pattern of relationships among tones that is determined not only by pitch height and chroma, but also by membership in the major triad chord and the diatonic scale associated with the tonal system of the context. Multidimensional scaling of the similarity ratings gave a three-dimensional conical structure around which the tones were ordered according to pitch height. The major triad components formed a closely related cluster near the vertex of the cone; the remaining diatonic scale tones formed a less closely related subset farther from the vertex; and, the nondiatonic tones, still farther from the vertex, were widely dispersed. The results also suggest that, in the psychological representation, tones less closely related to the tonality are less stable than tones closely related to the tonality, and that the representation incorporates the tendency for unstable tones to move toward the more stable tones in time, reflecting the dynamic character of musical tones. In the similarity ratings of the scaling study, tones less related to the tonality were judged more similar to tones more related to the tonality than the reverse temporal order. Furthermore, in a delayed recognition task memory performance for nondiatonic tones was less accurate than for diatonic tones, and nondiatonic tones were more often confused with diatonic tones than diatonic tones were confused with nondiatonic tones. These results indicate the tonality-specific nature of the psychological representation and argue that the perception of music depends not only on psychoacoustic properties of the tones, but also on processes that relate the tones to one another through contact with a well-defined and complex psychological representation of musical pitch.

Quantification of the hierarchy of tonal functions within a diatonic context.

Listeners rated test tones falling in the octave range from middle to high C according to how well each completed a diatonic C major scale played in an adjacent octave just before the final test tone. Ratings were well explained in terms of three factors. The factors were distance in pitch height from the context tones, octave equivalence, and the following hierarchy of tonal functions: tonic tone, other tones of the major triad chord, other tones of a diatonic scale, and the nondiatonic tones. In these ratings, pitch height was more prominent for less musical listeners or with less musical (sinusoidal) tones, whereas octave equivalence and the tonal hierarchy prevailed for musical listeners, especially with harmonically richer tones. Ratings for quarter tones interpolated halfway between the halftone steps of the standard chromatic scale were approximately the averages of ratings for adjacent chromatic tones, suggesting failure to discriminate tones at this fine level of division.

“Paradice's Only Map”: The Topos of the Locus Amoenus and the Structure of Marvell's Upon Appleton House

Upon Appleton House is a poem in which superficial sprightliness and subterranean portentousness, a variety of rhetorical stances, and a loose, episodic structure apparently conspire to create disunity. But a unifying principle is supplied by the formulaic topos of the locus amoenus. As this convention developed from Homer through the Elizabethans, it took on potentially ambiguous connotations of refection, generation, and eroticism. Marvell systematically exploits these connotations, making of the Fairfax estate a double microcosm which reflects a disorderly world and his own uncertain relation to it. The confusion is further mirrored in Marvell's deployment of the topos. As rhetorical device, its impact should normally be synchronous, so that its elements strike the reader as a unit, not as a sequence of terms successively qualifying one another. But Marvell breaks the unit down, anatomizes it, taking its topographical elements (garden, grass, shade, water) serially and discontinuously. Gradually, however, the locus reasserts its mythic totality. As it does, Marvell also traces a historical movement back through the development of civilization to the first locus amoenus, Eden, and a rhetorical movement from critical objectivity to devotional subjectivity. These movements come to a focus in the figure of Maria Fairfax, whom Marvell, as poet-priest, adores as summarizing the virtues of Appleton House, now become the emblem of a reordered cosmos, a refuge from the corrupting processes of time and change. The vision cannot last, as Marvell implies by sustaining the mocking extravagance of his language right through to the last, ambiguous lines. The unity is only poetic, conceptual, rhetorical. But a unity it is, sung out of confusions, with the locus amoenus as its major chord.

Quality of Organ Tones

The tones were produced by the pipe organ in the Smith Auditorium at Brigham Young University. They were picked up by a microphone placed at various positions in the auditorium and recorded on magnetic tape. The tape was taken into the laboratory where analyses of the tones were made. The structure of full organ tones becomes very complicated. For example, when the three keys for the major chord were depressed, there were 229 partials whose frequency and level were measured. After the analysis of the tone was made, a synthetic tone was constructed by our synthesizer. Judgment tests were made by juries to see if synthetic tones could be distinguished from real tones. These juries were unable to distinguish between them. The paper discusses musical warmth. It shows that it is definitely related to the level variation of the partials. These variations are due to the frequencies of several partials being close together, causing beats. Methods and apparatus were developed so that a tone could be warmed to any extent without using the large number partials produced in the pipe organ. A method of rating the warmth of organ tones is proposed and will be used in our future work on all musical tones.

A Note on the Four Chords in act II of A Midsummer Night's Dream

We know from the composer's own account that work on A Midsummer Night's Dream was by no means always easy going. Therefore when I accidentally stumbled (aurally, be it noted) upon the remarkable fact that the four chords used in Act II of the Dream were almost identical with those used in the setting of Keats's ‘Sonnet to Sleep’ in the Serenade I fully expected to learn that the composer had consciously borrowed from the earlier work, reversing the order of the first two chords (adding a B to the D major chord) and magically re-spacing and re-scoring them. As the poetic element in each piece is concerned with the properties of sleep (inducing a healing forgetfulness on the one hand, a fantastic change of identities on the other) the conscious re-working of those earlier chords of the Serenade would have seemed by no means inapt.

Massachusetts Medical Society

To be chosen to give the keynote address on the occasion of the founding of this Section is a mark of distinction that I appreciate as much as if I deserved it and that I accept with mingled feelings of pride and of humility.Let me sound the keynote of our meetings — rather let me sound the major chord on which the harmony will be founded. The first note of the chord is enthusiasm! Note the derivation of the word — ένθεος — a god within. As Pasteur exclaimed after thanking the Greeks for one of the most beautiful . . .

Sliding Tones in Oriental Music

Research Article| October 01 1945 Sliding Tones in Oriental Music Gerald Strang Gerald Strang Search for other works by this author on: This Site PubMed Google Scholar Bulletin of the American Musicological Society (1945) 8: 29–30. https://doi.org/10.2307/829396 Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter LinkedIn Tools Icon Tools Get Permissions Cite Icon Cite Search Site Citation Gerald Strang; Sliding Tones in Oriental Music. Bulletin of the American Musicological Society 1 October 1945; 8 29–30. doi: https://doi.org/10.2307/829396 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentJournal of the American Musicological Society Search This content is only available via PDF. Copyright 1946 The American Musicological Society, Inc. Article PDF first page preview Close Modal You do not currently have access to this content.

Incremental Coupled Musical Scales

The equation V/T = 2SN represents a family of preferred number series. S and N are of integer value, V is a rational number. One particular type series, which is both incremental and coupled, is defined by the following proportion for the terminal terms, i.e., extreme notes, of each scale, Nmax/Nmin = 2(S+C)/(S+C). C is an integer constant for each series of the type. Each of several incremental coupled series is an homologous train of scales whose notes are interpreted as frequencies, the ratios thereof being rational. Each scale possesses one more note than the preceding scale, and the highest frequency in each scale is an overlapping member of two arithmetic progressions. An octave is spanned within each scale. The lower scales of these series are separated in four groups. The several lowest scales compose two primitive and subsonic groups relating to tone quality. The next or sonic group consists of nine audible scales. Harmonic potentialities with respect to a new pure tone music are tabulated. One half of the sonic group notes are members of at least one major chord. Composition and rendition should be extraordinarily simple, since bass scales contain relatively few notes conforming to the recent findings that aural sensitivity to pitch progresses with sonic frequency.

The preference of twenty-five Negro college women for major and minor chords.

The preference of twenty-five Negro college women for major and minor chords.

長三和絃と短三和絃の感情的差異

長三和絃と短三和絃の感情的差異