DOCSLIB.ORG

Tonal Fusion of Consonant Musical Intervals: the Oomph in Stumpf

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Tonal Fusion of Consonant Musical Intervals: the Oomph in Stumpf Perception & Psychophysics 1987. 41 (1). 73-84 Tonal fusion of consonant musical intervals: The oomph in Stumpf LUCINDA A. DEWITI' and ROBERT G. CROWDER Yale University, New Haven, Connecticut Three experiments investigated Stumpf's fusion principle of tonal consonance. In Experiment 1, subjects listened to single tones or to tone pairs that represented 12 musical intervals and indi­ cated whether they thought one or two tones had sounded. The fusion principle would be sup­ ported by an increase in reaction times or errors in response to conventionally consonant inter­ vals as opposed to dissonant ones. A significant main effect of interval size was found in the error data of Experiment 1, with the most errors produced by intervals of an octave (12 semitones). Experiment 2 compared a smaller set of intervals in distinguishing two- from three-tone combi­ nations. A significant main effect of interval size was found in both the response time and error data in a direction consistent with the fusion principle. Experiment 3 investigated an explana­ tion of the fusion principle based on the harmonic series. In three-tone combinations, more fu­ sion of the higher pair of tones was observed when the lower pair formed an octave or perfect fifth than when the lower pair formed a tritone. Fusion may represent a tendency for people to interpret pitch combinations that could represent harmonics resulting from a single fundamen­ tal as timbres rather than as chords. The perceived consonance and dissonance of pairs of consonance and dissonance depend on the existence ofa tones has been of musical interest for over 2,500 years. "framework for the normative expectations" (Cazden, Since Pythagoras's time, many theories have been pro­ 1980, p. 158) such as that defined within a certain stylis­ posed to explain why some combinations of tones sound tic period. more pleasant (consonant) and others more unpleasant Of the two types ofconsonance, tonal consonance has (dissonant). These explanations of consonance and dis­ been the more thoroughly investigated experimentally and sonance fall into two general categories: (1) "rational" is the subject of this report. In general, investigations of theories with an acoustic basis in "natural law," or sim­ tonal consonance require listeners to judge or rate pairs ple integer ratios, and (2) "empirical" theories based on of tones as to their consonance-dissonance, smoothness­ context and learning (or brainwashing) (Cazden, 1980; roughness, or pleasantness-unpleasantness. Although the see also Terhardt, 1984). use ofverbal labels is a perfectly valid way ofmeasuring Today the accepted view ofconsonance and dissonance consonance and dissonance, converging evidence from a includes aspects of both approaches. Two types of con­ nonverbal, more objective measure would certainly add sonance are distinguished, tonal consonance and musical to our understanding of this phenomenon. The idea for consonance. Tonal consonance refers to "the particular our choice of a nonverbal measure came from Stumpf's sensory experience associated to isolated tone pairs with principle of tonal fusion (as described in Apel, 1972, simple frequency ratios" (plomp & Levelt, 1965, p. 548). p. 201, Boring, 1942, and Roberts, 1983). Musical consonance, on the other hand, refers to the func­ Stumpf's doctrine oftonal fusion holds that "tones tend tional relationships brought about by a "sonorous event to fuse, to interpenetrate each other, with the result that ... expected to resolve" (dissonance) and "the moment the total perception becomes something different from the to which it ultimately resolves" (consonance) (Cazden, mere concurrence ofits components (as the Gestalt psy­ 1980, p. 157). These functional definitions of musical chologists also said later), and that different combinations vary in their degree of fusion" (Boring, 1942, p. 360). Preparation of this article was supported under a National Science Stumpf conducted an experiment that provided evidence Foundation graduate fellowship to Lucinda DeWitt and by National in support of his fusion principle. Untrained subjects Science Foundation Grant BNS 82-19661 to Robert Crowder. The listened to simultaneously presented musical intervals and authors appreciate the use of facilities at Haskins Laboratories (NICHD reported their introspections (single tone or two different Contract NOI HD5291O) and the assistance of Bruno Repp in stimulus analysis. A preliminary version of Experiment I was conducted by the tones) of the pairs. The measure of degree of perceived second author with Richard E. Pollinger in December 1957. This was consonance was the percentage of subjects falsely judg­ a project for an introductory psychology course at the University of ing a pair of tones as "single tone." Figure 1 illustrates Michigan. The late Professor Carl Brown suggested the idea behind the the results (data from Apel, 1972). study and the methodology for testing it. The authors are indebted to Even setting aside our skepticism about experimental him most of all. Requests for reprints should be sent to either author at the Department ofPsychology, Yale University, Box llA, Yale Sta­ procedures and demand characteristics that could com­ tion, New Haven, CT 06520. promise these data, we might wonder whether reaction 73 Copyright 1987 Psychonomic Society, Inc. 74 DEWITT AND CROWDER Stumpf 80 70 60 Percent of 50 listeners judging "one 40 tone" 30 20 10 0 Octave Fifth Fourth Third Tritone Second Interval Figure 1. Percentage of listeners judging "one tone" to a tone pair as a function of the musical interval of the pair (experiment by Stumpf, data from Apel, 1972). time would not be a better measure. A longer response instances ofthe intervals presented were chosen randomly from all time to indicate "two tones" when the pair oftones forms possibilities within this range. The tones were played using the a consonant interval and a shorter response time to dis­ "square" waveform setting on the Commodore 64, a complex wave sonant (less fused) intervals would be consistent with sounding similar to an organ tone and described by the manufac­ turer as "a bright, hollow square wave" (Commodore 64 Program­ Stumpf's concept. We investigated consonance and dis­ mer's Reference Guide, 1984, p. 464). The tones and tone pairs sonance using a timed discrimination task in three ex­ were arranged randomly within each block. periments. Procedure. The tones were played through the speaker built into the computer and heard in the open air by the subjects. During a EXPERIMENT 1 set of practice trials, the subjects were instructed to adjust the in­ tensity of the tones to a comfortable level, and this level was re­ tained throughout the experiment. On each trial, the subject heard In Experiment 1, we presented all possible musical in­ a tone or tone pair and then responded by pressing one key (z) on tervals to determine which intervals, if any, would the computer keyboard for a single tone and another key (I) for produce fusion (a slow response time or a judgment of two simultaneous tones. The tone(s) continued to sound until the "one tone" to a presentation of two tones). Since Stumpf's subject responded, but the subjects were encouraged to respond as fusion principle has not been tested using methods other quickly and accurately as they could. The subject then pressed the than introspection, the purpose of this experiment was space bar to hear the next trial. After completing all the trials, the subjects filled out a musical background questionnaire ofour own simply to try to find nonintrospective evidence that fu­ design. sion may operate in the perception of musical intervals. Results and Discussion Method Subjects. Seven students from an introductory psychology class Latency. Single tones as well as unison pairs were ex­ participated in the experiment for course credit. cluded from the analyses because the correct responses Apparatus. A Commodore 64 computer generated and produced to them were different from those given to the other in­ the stimuli and collected subjects' responses and response times. tervals, but the unison pairs were very successful as con­ Design. Four blocks of 195 trialswere presented. Each contained trol pairs in that no subject could distinguish between the 65 single tones and to each of the following pair types: unison, single tone trials and the unison trials. An initial glance minor second, major second, minor third, major third, perfect fourth, tritone, perfect fifth, minor sixth, major sixth, minor seventh, at the response time data revealed no obvious effects of major seventh, and octave. These intervals span from 0 to 12 semi­ interval type (mean response times in milliseconds were: tones. The unison intervals (zero semitones) were included as a con­ minor seconds, 521; major seconds, 528; minor thirds, trol for the single tones. Although overall intensity on the Com­ 514; major thirds, 511; perfect fourths, 518; tritones, 512; modore 64 is supposed to beequated for composite sounds (whether perfect fifths, 524; minor sixths, 513; major sixths, 515; one, two, or three tones are playing simultaneously), we were con­ minor sevenths, 514; major sevenths, 518; octaves, 528). cerned that a subtle difference between the one- and two-tone con­ A 4 blocks X 12 intervals x 7 subjects analysis of vari­ ditions might exist; therefore, we included a two-tone condition with both notes ofthe same frequency. The frequencies of the tones in­ ance (ANOVA) performed on the mean correct response cluded the equal-tempered semitone steps between 261.6 Hz (mid­ times revealed no main effect of interval type. There was dle q and 987.8 Hz (85, two octaves above middle C). The specific a significant effect of block [F(3,18) = 28.839, CONSONANT MUSICAL INTERVALS 75 Experiment 1 25 20 15 Percent Errors 10 5 o Oct M7 m7 M6 me P5 TT P4 M3 m3 M2 m2 lntarval Figure 2. Mean pen:entage ofincorrect ("one tone" to a tonepair) judgments per block as a fundion of the musical interval of the tone pair (Experiment 1).
Load more

Recommended publications
  • Naming a Chord Once You Know the Common Names of the Intervals, the Naming of Chords Is a Little Less Daunting
    Naming a Chord Once you know the common names of the intervals, the naming of chords is a little less daunting. Still, there are a few conventions and short-hand terms that many musicians use, that may be confusing at times. A few terms are used throughout the maze of chord names, and it is good to know what they refer to: Major / Minor – a “minor” note is one half step below the “major.” When naming intervals, all but the “perfect” intervals (1,4, 5, 8) are either major or minor. Generally if neither word is used, major is assumed, unless the situation is obvious. However, when used in naming extended chords, the word “minor” usually is reserved to indicate that the third of the triad is flatted. The word “major” is reserved to designate the major seventh interval as opposed to the minor or dominant seventh. It is assumed that the third is major, unless the word “minor” is said, right after the letter name of the chord. Similarly, in a seventh chord, the seventh interval is assumed to be a minor seventh (aka “dominant seventh), unless the word “major” comes right before the word “seventh.” Thus a common “C7” would mean a C major triad with a dominant seventh (CEGBb) While a “Cmaj7” (or CM7) would mean a C major triad with the major seventh interval added (CEGB), And a “Cmin7” (or Cm7) would mean a C minor triad with a dominant seventh interval added (CEbGBb) The dissonant “Cm(M7)” – “C minor major seventh” is fairly uncommon outside of modern jazz: it would mean a C minor triad with the major seventh interval added (CEbGB) Suspended – To suspend a note would mean to raise it up a half step.
    [Show full text]
  • The 17-Tone Puzzle — and the Neo-Medieval Key That Unlocks It
    The 17-tone Puzzle — And the Neo-medieval Key That Unlocks It by George Secor A Grave Misunderstanding The 17 division of the octave has to be one of the most misunderstood alternative tuning systems available to the microtonal experimenter. In comparison with divisions such as 19, 22, and 31, it has two major advantages: not only are its fifths better in tune, but it is also more manageable, considering its very reasonable number of tones per octave. A third advantage becomes apparent immediately upon hearing diatonic melodies played in it, one note at a time: 17 is wonderful for melody, outshining both the twelve-tone equal temperament (12-ET) and the Pythagorean tuning in this respect. The most serious problem becomes apparent when we discover that diatonic harmony in this system sounds highly dissonant, considerably more so than is the case with either 12-ET or the Pythagorean tuning, on which we were hoping to improve. Without any further thought, most experimenters thus consign the 17-tone system to the discard pile, confident in the knowledge that there are, after all, much better alternatives available. My own thinking about 17 started in exactly this way. In 1976, having been a microtonal experimenter for thirteen years, I went on record, dismissing 17-ET in only a couple of sentences: The 17-tone equal temperament is of questionable harmonic utility. If you try it, I doubt you’ll stay with it for long.1 Since that time I have become aware of some things which have caused me to change my opinion completely.
    [Show full text]
  • A. Types of Chords in Tonal Music
    1 Kristen Masada and Razvan Bunescu: A Segmental CRF Model for Chord Recognition in Symbolic Music A. Types of Chords in Tonal Music minished triads most frequently contain a diminished A chord is a group of notes that form a cohesive har- seventh interval (9 half steps), producing a fully di- monic unit to the listener when sounding simulta- minished seventh chord, or a minor seventh interval, neously (Aldwell et al., 2011). We design our sys- creating a half-diminished seventh chord. tem to handle the following types of chords: triads, augmented 6th chords, suspended chords, and power A.2 Augmented 6th Chords chords. An augmented 6th chord is a type of chromatic chord defined by an augmented sixth interval between the A.1 Triads lowest and highest notes of the chord (Aldwell et al., A triad is the prototypical instance of a chord. It is 2011). The three most common types of augmented based on a root note, which forms the lowest note of a 6th chords are Italian, German, and French sixth chord in standard position. A third and a fifth are then chords, as shown in Figure 8 in the key of A minor. built on top of this root to create a three-note chord. In- In a minor scale, Italian sixth chords can be seen as verted triads also exist, where the third or fifth instead iv chords with a sharpened root, in the first inversion. appears as the lowest note. The chord labels used in Thus, they can be created by stacking the sixth, first, our system do not distinguish among inversions of the and sharpened fourth scale degrees.
    [Show full text]
  • Shifting Exercises with Double Stops to Test Intonation
    VERY ROUGH AND PRELIMINARY DRAFT!!! Shifting Exercises with Double Stops to Test Intonation These exercises were inspired by lessons I had from 1968 to 1970 with David Smiley of the San Francisco Symphony. I don’t have the book he used, but I believe it was one those written by Dounis on the scientific or artist's technique of violin playing. The exercises were difficult and frustrating, and involved shifting and double stops. Smiley also emphasized routine testing notes against other strings, and I also found some of his tasks frustrating because I couldn’t hear intervals that apparently seemed so familiar to a professional musician. When I found myself giving violin lessons in 2011, I had a mathematical understanding of why it was so difficult to hear certain musical intervals, and decided not to focus on them in my teaching. By then I had also developed some exercises to develop my own intonation. These exercises focus entirely on what is called the just scale. Pianos use the equal tempered scale, which is the predominate choice of intonation in orchestras and symphonies (I NEED VERIFICATION THAT THIS IS TRUE). It takes many years and many types of exercises and activities to become a good violinist. But I contend that everyone should start by mastering the following double stops in “just” intonation: 1. Practice the intervals shown above for all possible pairs of strings on your violin or viola. Learn the first two first, then add one interval at a time. They get harder to hear as you go down the list for reasons having to do with the fractions: 1/2, 2/3, 3/4, 3/5, 4/5, 5/6.
    [Show full text]
  • The Devil's Interval by Jerry Tachoir
    Sound Enhanced Hear the music example in the Members Only section of the PAS Web site at www.pas.org The Devil’s Interval BY JERRY TACHOIR he natural progression from consonance to dissonance and ii7 chords. In other words, Dm7 to G7 can now be A-flat m7 to resolution helps make music interesting and satisfying. G7, and both can resolve to either a C or a G-flat. Using the TMusic would be extremely bland without the use of disso- other dominant chord, D-flat (with the basic ii7 to V7 of A-flat nance. Imagine a world of parallel thirds and sixths and no dis- m7 to D-flat 7), we can substitute the other relative ii7 chord, sonance/resolution. creating the progression Dm7 to D-flat 7 which, again, can re- The prime interval requiring resolution is the tritone—an solve to either a C or a G-flat. augmented 4th or diminished 5th. Known in the early church Here are all the possibilities (Note: enharmonic spellings as the “Devil’s interval,” tritones were actually prohibited in of- were used to simplify the spelling of some chords—e.g., B in- ficial church music. Imagine Bach’s struggle to take music stead of C-flat): through its normal progression of tonic, subdominant, domi- nant, and back to tonic without the use of this interval. Dm7 G7 C Dm7 G7 Gb The tritone is the characteristic interval of all dominant bw chords, created by the “guide tones,” or the 3rd and 7th. The 4 ˙ ˙ w ˙ ˙ tritone interval can be resolved in two types of contrary motion: &4˙ ˙ w ˙ ˙ bbw one in which both notes move in by half steps, and one in which ˙ ˙ w ˙ ˙ b w both notes move out by half steps.
    [Show full text]
  • Ninth, Eleventh and Thirteenth Chords Ninth, Eleventh and Thirteen Chords Sometimes Referred to As Chords with 'Extensions', I.E
    Ninth, Eleventh and Thirteenth chords Ninth, Eleventh and Thirteen chords sometimes referred to as chords with 'extensions', i.e. extending the seventh chord to include tones that are stacking the interval of a third above the basic chord tones. These chords with upper extensions occur mostly on the V chord. The ninth chord is sometimes viewed as superimposing the vii7 chord on top of the V7 chord. The combination of the two chord creates a ninth chord. In major keys the ninth of the dominant ninth chord is a whole step above the root (plus octaves) w w w w w & c w w w C major: V7 vii7 V9 G7 Bm7b5 G9 ? c ∑ ∑ ∑ In the minor keys the ninth of the dominant ninth chord is a half step above the root (plus octaves). In chord symbols it is referred to as a b9, i.e. E7b9. The 'flat' terminology is use to indicate that the ninth is lowered compared to the major key version of the dominant ninth chord. Note that in many keys, the ninth is not literally a flatted note but might be a natural. 4 w w w & #w #w #w A minor: V7 vii7 V9 E7 G#dim7 E7b9 ? ∑ ∑ ∑ The dominant ninth usually resolves to I and the ninth often resolves down in parallel motion with the seventh of the chord. 7 ˙ ˙ ˙ ˙ & ˙ ˙ #˙ ˙ C major: V9 I A minor: V9 i G9 C E7b9 Am ˙ ˙ ˙ ˙ ˙ ? ˙ ˙ The dominant ninth chord is often used in a II-V-I chord progression where the II chord˙ and the I chord are both seventh chords and the V chord is a incomplete ninth with the fifth omitted.
    [Show full text]
  • Boris's Bells, by Way of Schubert and Others
    Boris's Bells, By Way of Schubert and Others Mark DeVoto We define "bell chords" as different dominant-seventh chords whose roots are separated by multiples of interval 3, the minor third. The sobriquet derives from the most famous such pair of harmonies, the alternating D7 and AI? that constitute the entire harmonic substance of the first thirty-eight measures of scene 2 of the Prologue in Musorgsky's opera Boris Godunov (1874) (example O. Example 1: Paradigm of the Boris Godunov bell succession: AJ,7-D7. A~7 D7 '~~&gl n'IO D>: y 7 G: y7 The Boris bell chords are an early milestone in the history of nonfunctional harmony; yet the two harmonies, considered individually, are ofcourse abso­ lutely functional in classical contexts. This essay traces some ofthe historical antecedents of the bell chords as well as their developing descendants. Dominant Harmony The dominant-seventh chord is rightly recognized as the most unambiguous of the essential tonal resources in classical harmonic progression, and the V7-1 progression is the strongest means of moving harmony forward in immediate musical time. To put it another way, the expectation of tonic harmony to follow a dominant-seventh sonority is a principal component of forehearing; we assume, in our ordinary and long-tested experience oftonal music, that the tonic function will follow the dominant-seventh function and be fortified by it. So familiar is this everyday phenomenon that it hardly needs to be stated; we need mention it here only to assert the contrary case, namely, that the dominant-seventh function followed by something else introduces the element of the unexpected.
    [Show full text]
  • The Development of Duke Ellington's Compositional Style: a Comparative Analysis of Three Selected Works
    University of Kentucky UKnowledge University of Kentucky Master's Theses Graduate School 2001 THE DEVELOPMENT OF DUKE ELLINGTON'S COMPOSITIONAL STYLE: A COMPARATIVE ANALYSIS OF THREE SELECTED WORKS Eric S. Strother University of Kentucky, [email protected] Right click to open a feedback form in a new tab to let us know how this document benefits ou.y Recommended Citation Strother, Eric S., "THE DEVELOPMENT OF DUKE ELLINGTON'S COMPOSITIONAL STYLE: A COMPARATIVE ANALYSIS OF THREE SELECTED WORKS" (2001). University of Kentucky Master's Theses. 381. https://uknowledge.uky.edu/gradschool_theses/381 This Thesis is brought to you for free and open access by the Graduate School at UKnowledge. It has been accepted for inclusion in University of Kentucky Master's Theses by an authorized administrator of UKnowledge. For more information, please contact [email protected]. ABSTRACT OF THESIS THE DEVELOPMENT OF DUKE ELLINGTON’S COMPOSITIONAL STYLE: A COMPARATIVE ANALYSIS OF THREE SELECTED WORKS Edward Kennedy “Duke” Ellington’s compositions are significant to the study of jazz and American music in general. This study examines his compositional style through a comparative analysis of three works from each of his main stylistic periods. The analyses focus on form, instrumentation, texture and harmony, melody, tonality, and rhythm. Each piece is examined on its own and their significant features are compared. Eric S. Strother May 1, 2001 THE DEVELOPMENT OF DUKE ELLINGTON’S COMPOSITIONAL STYLE: A COMPARATIVE ANALYSIS OF THREE SELECTED WORKS By Eric Scott Strother Richard Domek Director of Thesis Kate Covington Director of Graduate Studies May 1, 2001 RULES FOR THE USE OF THESES Unpublished theses submitted for the Master’s degree and deposited in the University of Kentucky Library are as a rule open for inspection, but are to be used only with due regard to the rights of the authors.
    [Show full text]
  • 85 Modern Interval Reference Songs Contents
    ! EasyEarTraining.com 85 Modern Interval Reference Songs This is a list of modern interval reference songs, provided by EasyEarTraining.com to accompany the article: Interval Reference Songs - That You've Actually Heard Of! Do you know a great modern reference song not included here? Let us know! http://www.easyeartraining.com/forums/ Oh - and don't miss the special offer at the back of this booklet... Contents Minor Second 2 Major Second 5 Minor Third 8 Major Third 11 Perfect Fourth 15 Tri-Tone 18 Perfect Fifth 21 Minor Sixth 24 Major Sixth 26 Minor Seventh 29 Major Seventh 30 Perfect Octave 32 !1 Copyright 2014 Easy Ear Training Ltd ! EasyEarTraining.com Minor Second Ascending K'naan - Wavin' Flag Section: Chorus Interval: “your - flag” http://www.youtube.com/watch?v=amXeJrA-wDc Enrique Iglesias - Somebody's Me Section: “You.. Do you remember me” Interval: ”do - you” https://www.youtube.com/watch?v=gv9hrQzU0cA Backstreet Boys - Show Me the Meaning Section: “Show me the meaning of being lonely” Interval: “of - BE” !2 Copyright 2014 Easy Ear Training Ltd ! EasyEarTraining.com https://www.youtube.com/watch? v=aBt8fN7mJNg Descending Avenged Sevenfold - Dear God Section: “Some search never findin’ a way” (bridge) Interval: “Some search” https://www.youtube.com/watch?v=mzX0rhF8buo Bryan Adams - Summer of ‘69 Section: “Those were the best days of my life” Interval: “the - best” https://www.youtube.com/watch? v=9f06QZCVUHg MYMP - Especially for You Section: “Especially” Interval: “Espe-cially” http://www.youtube.com/watch?v=IimqpTcrakU !3 Copyright 2014 Easy Ear Training Ltd ! EasyEarTraining.com The Pixies - Where Is My Mind Section: Introduction/Bridge (wee-ooh) Interval: “Wee-Ooh” https://www.youtube.com/watch?v=GrHl0wpagFc !4 Copyright 2014 Easy Ear Training Ltd ! EasyEarTraining.com Major Second Ascending Katy Perry - Wide Awake Section: “I’m wide awake” Interval: “wi-de a-wake” https://www.youtube.com/watch?v=k0BWlvnBmIE Breaking Benjamin - Diary of Jane Section: “If I have to.
    [Show full text]
  • Frequency Ratios and the Perception of Tone Patterns
    Psychonomic Bulletin & Review 1994, 1 (2), 191-201 Frequency ratios and the perception of tone patterns E. GLENN SCHELLENBERG University of Windsor, Windsor, Ontario, Canada and SANDRA E. TREHUB University of Toronto, Mississauga, Ontario, Canada We quantified the relative simplicity of frequency ratios and reanalyzed data from several studies on the perception of simultaneous and sequential tones. Simplicity offrequency ratios accounted for judgments of consonance and dissonance and for judgments of similarity across a wide range of tasks and listeners. It also accounted for the relative ease of discriminating tone patterns by musically experienced and inexperienced listeners. These findings confirm the generality ofpre­ vious suggestions of perceptual processing advantages for pairs of tones related by simple fre­ quency ratios. Since the time of Pythagoras, the relative simplicity of monics of a single complex tone. Currently, the degree the frequency relations between tones has been consid­ of perceived consonance is believed to result from both ered fundamental to consonance (pleasantness) and dis­ sensory and experiential factors. Whereas sensory con­ sonance (unpleasantness) in music. Most naturally OCCUf­ sonance is constant across musical styles and cultures, mu­ ring tones (e.g., the sounds of speech or music) are sical consonance presumably results from learning what complex, consisting of multiple pure-tone (sine wave) sounds pleasant in a particular musical style. components. Terhardt (1974, 1978, 1984) has suggested Helmholtz (1885/1954) proposed that the consonance that relations between different tones may be influenced of two simultaneous complex tones is a function of the by relations between components of a single complex tone. ratio between their fundamental frequencies-the simpler For single complex tones, ineluding those of speech and the ratio, the more harmonics the tones have in common.
    [Show full text]
  • Vocal Similarity Predicts the Relative Attraction of Musical Chords
    Vocal similarity predicts the relative attraction of musical chords Daniel L. Bowlinga,1, Dale Purvesb,1, and Kamraan Z. Gillc aDepartment of Cognitive Biology, University of Vienna, Vienna 1090, Austria; bDuke Institute for Brain Sciences, Duke University, Durham, NC 27708; and cDepartment of Pathology, CBLPath, Rye Brook, NY 10573 Contributed by D. Purves, November 21, 2017 (sent for review July 27, 2017; reviewed by Aniruddh D. Patel and Laurel J. Trainor) Musical chords are combinations of two or more tones played to conspecific vocalization. Accordingly, we here ask whether the together. While many different chords are used in music, some are consonance of tone combinations in music can be rationalized on heard as more attractive (consonant) than others. We have pre- this basis: that is, whether our attraction to specific chords is pre- viously suggested that, for reasons of biological advantage, human dicted by their relative similarity to human vocalization. tonal preferences can be understood in terms of the spectral Answering this question requires perceptual data that docu- similarity of tone combinations to harmonic human vocalizations. ment the relative consonance of chords. Previous evaluations have Using the chromatic scale, we tested this theory further by focused on the two-tone combinations (“dyads”) that define the assessing the perceived consonance of all possible dyads, triads, chromatic scale, a set of 12 tones over an octave used in much and tetrads within a single octave. Our results show that the music worldwide (Table S1). Studies of dyadic consonance have consonance of chords is predicted by their relative similarity to been repeated many times over the last century and, despite some voiced speech sounds.
    [Show full text]
  • Information to Users
    INFORMATION TO USERS This manuscript has been reproduced from the microfihn master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely afreet reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI University Microfilms International A Bell & Howell Information Company 3 0 0 North Z eeb Road. Ann Arbor. Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9401386 Enharmonicism in theory and practice in 18 th-century music Telesco, Paula Jean, Ph.D. The Ohio State University, 1993 Copyright ©1993 by Telesco, Paula Jean.
    [Show full text]