Less Common Augmented Sixth Chord Spellings

Total Page：16

File Type：pdf, Size：1020Kb

MUS 357– Aaron Grant LESS COMMON AUGMENTED SIXTH CHORD SPELLINGS EXPLORE Although most of the augmented sixth chords you will find in the literature can be described as one of the three "national" types we have been working with, there are some less common variants of these chords that are important to discuss. Two of these types are displayed below. Analyze these passages with a partner, and discuss the two new forms of augmented sixth chords marked with arrows. How do they differ from typical augmented sixth chord spellings or voicings? Does the voice leading still work the same? Tchaikovsky, Sleeping Beauty, scene 1, mm. 62–78 MUS 357– Aaron Grant Schubert, "Der Doppelgänger," mm. 36–43 36 40 KEY POINTS In the Tchaikovsky excerpt, we see an example of a German diminished-third chord (Ger°3). This chord games its name because it places raised scale degree 4 in the bass, thus inverted the characteristic augmented sixth interval into a diminshed third. Note that: • This chord is typically approached through chromatic voice exchange. • The voice leading of a German diminished 7th chord still maintains the same voice leading as a typically German augmented sixth. In the Schubert song, we see an example of a secondary augmented-sixth chord—a type of chord that uses the same principals of the augmented sixth to lead to a tonic rather than a dominant chord. Note that: • The typical augmented sixth is maintained given ß^2 in the bass and 7^ in an upper voice. • This is an example of a German augmented sixth (albeit one that becomes a French), but any of our three main augmented sixth chords can appear as a secondary augmented sixth. MUS 357– Aaron Grant OTHER VARIANTS Aside from the above two variants of augmented-sixth chords, it is also worth noting that there are two alternate spellings that composers sometimes take advantage of: • A Ger+6 chord can be spelled with raised 2^ taking the place of 3.^ • A Fr+6 chord can be spelled with 7^ taking the place of 1^ In both cases, continue to label the chords as German and French augmented-sixth chords as normal. Moreover, the chord still resolves as expected, with all voices moving by step or common tone to members of the next chord. .

Copy Link

Recommended publications

Third Report to the Thirteenth Session of the General Assembly
UNITED COpy ADVISORY COMMITTEE ON ADMINISTRATIVE AND BUDGETARY QUESTIONS ·THIRD REPORT TO THE THIRTEENTH SESSION OF THE GENERAL ASSEMBLY GENERAL ASSEMBLY OFFICIAL RECORDS : THIRTEPNfH· SESSION i SUPPLEMENT No. f {A/ 3860) \ / -,-------~/ NEW YORK, 1958 .I , (49 p.) UNITED NATIONS ADVISORY COMMITTEE ON ADMINISTRATIVE AND BUDGETARY QUESTIONS THffiD REPORT TO THE THIRTEENTH SESSION OF THE GENERAL ASSEMBLY GENERAL ASS'EMBLY OFFICIAL RECORDS : THIRTEENTH SESSION SUPPLEMENT No. 7 (Aj3860) Ner..o York, 1958 NOr.fE Symbols of United Nations documents are composed of capital letters combined with figures. Mention of such a symbol indicates a reference to a United Nations document. TABLE OF CONTENTS Page FOREWORD . v REPORT TO THE GENERAL ASSEMBLY ON THE BUDGET ESTIMATES FOR 1959 Chapter Paragraphs Page 1. ApPRAISAL OF THE BUDGET ESTIMATES FOR 1959 OF PERSONNEL Estimates for 1959 . 1-7 1 Comparison with 1958 appropriations . 8-10 2 Major items of increase in the 1959 initial estimates . 11-14 3 Assessments for 1958 and 1959 . 15-17 3 Form of presentation of the 1959 estimates . 18-28 4 Procedures for the Advisory Committee's budget examination . 29-32 5 Conferences and meetings . 33-40 6 Work and organization of the Secretariat . 41-45 7 Economic Commission for Africa . 46 7 Established posts. .............................................. 47-52 7 General expenses . 53-54 9 Public information expenses . 55 9 Administrative costs of technical assistance . 56-63 9 Appropriation resolution . 64-66 10 Working Capital Fund . 67-68 10 Comparative table of appropriations as proposed by the Secretary- General and recommended by the Advisory Committee . 11 Appendix I. Draft appropriation resolution for the financial year 1959 12 Appendix II.
[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]
Andrián Pertout
Andrián Pertout Three Microtonal Compositions: The Utilization of Tuning Systems in Modern Composition Volume 1 Submitted in partial fulfilment of the requirements of the degree of Doctor of Philosophy Produced on acid-free paper Faculty of Music The University of Melbourne March, 2007 Abstract Three Microtonal Compositions: The Utilization of Tuning Systems in Modern Composition encompasses the work undertaken by Lou Harrison (widely regarded as one of America’s most influential and original composers) with regards to just intonation, and tuning and scale systems from around the globe – also taking into account the influential work of Alain Daniélou (Introduction to the Study of Musical Scales), Harry Partch (Genesis of a Music), and Ben Johnston (Scalar Order as a Compositional Resource). The essence of the project being to reveal the compositional applications of a selection of Persian, Indonesian, and Japanese musical scales utilized in three very distinct systems: theory versus performance practice and the ‘Scale of Fifths’, or cyclic division of the octave; the equally-tempered division of the octave; and the ‘Scale of Proportions’, or harmonic division of the octave championed by Harrison, among others – outlining their theoretical and aesthetic rationale, as well as their historical foundations. The project begins with the creation of three new microtonal works tailored to address some of the compositional issues of each system, and ending with an articulated exposition; obtained via the investigation of written sources, disclosure
[Show full text]
Brain Tumors : Practical Guide to Diagnosis and Treatment
Brain Tumors DK616x_C000a.indd 1 09/01/2006 8:49:40 AM NEUROLOGICAL DISEASE AND THERAPY Advisory Board Gordon H. Baltuch, M.D., Ph.D. Department of Neurosurgery University of Pennsylvania Philadelphia, Pennsylvania, U.S.A. Cheryl Bushnell, M.D., M.H.S. Duke Center for Cerebrovascular Disease Department of Medicine, Division of Neurology Duke University Medical Center Durham, North Carolina, U.S.A. Louis R. Caplan, M.D. Professor of Neurology Harvard University School of Medicine Beth Israel Deaconess Medical Center Boston, Massachusetts, U.S.A. Mark A. Stacy, M.D. Movement Disorders Center Duke University Medical Center Durham, North Carolina, U.S.A. Mark H. Tuszynski, M.D., Ph.D. Professor of Neurosciences Director, Center for Neural Repair University of California—San Diego La Jolla, California, U.S.A. DK616x_C000a.indd 2 09/01/2006 8:49:43 AM 1. Handbook of Parkinson’s Disease, edited by William C. Koller 2. Medical Therapy of Acute Stroke, edited by Mark Fisher 3. Familial Alzheimer’s Disease: Molecular Genetics and Clinical Perspectives, edited by Gary D. Miner, Ralph W. Richter, John P. Blass, Jimmie L. Valentine, and Linda A. Winters-Miner 4. Alzheimer’s Disease: Treatment and Long-Term Management, edited by Jeffrey L. Cummings and Bruce L. Miller 5. Therapy of Parkinson’s Disease, edited by William C. Koller and George Paulson 6. Handbook of Sleep Disorders, edited by Michael J. Thorpy 7. Epilepsy and Sudden Death, edited by Claire M. Lathers and Paul L. Schraeder 8. Handbook of Multiple Sclerosis, edited by Stuart D. Cook 9. Memory Disorders: Research and Clinical Practice, edited by Takehiko Yanagihara and Ronald C.
[Show full text]
Generalized Interval System and Its Applications
Generalized Interval System and Its Applications Minseon Song May 17, 2014 Abstract Transformational theory is a modern branch of music theory developed by David Lewin. This theory focuses on the transformation of musical objects rather than the objects them- selves to find meaningful patterns in both tonal and atonal music. A generalized interval system is an integral part of transformational theory. It takes the concept of an interval, most commonly used with pitches, and through the application of group theory, generalizes beyond pitches. In this paper we examine generalized interval systems, beginning with the definition, then exploring the ways they can be transformed, and finally explaining com- monly used musical transformation techniques with ideas from group theory. We then apply the the tools given to both tonal and atonal music. A basic understanding of group theory and post tonal music theory will be useful in fully understanding this paper. Contents 1 Introduction 2 2 A Crash Course in Music Theory 2 3 Introduction to the Generalized Interval System 8 4 Transforming GISs 11 5 Developmental Techniques in GIS 13 5.1 Transpositions . 14 5.2 Interval Preserving Functions . 16 5.3 Inversion Functions . 18 5.4 Interval Reversing Functions . 23 6 Rhythmic GIS 24 7 Application of GIS 28 7.1 Analysis of Atonal Music . 28 7.1.1 Luigi Dallapiccola: Quaderno Musicale di Annalibera, No. 3 . 29 7.1.2 Karlheinz Stockhausen: Kreuzspiel, Part 1 . 34 7.2 Analysis of Tonal Music: Der Spiegel Duet . 38 8 Conclusion 41 A Just Intonation 44 1 1 Introduction David Lewin(1933 - 2003) is an American music theorist.
[Show full text]
The Perceptual Attraction of Pre-Dominant Chords 1
Running Head: THE PERCEPTUAL ATTRACTION OF PRE-DOMINANT CHORDS 1 The Perceptual Attraction of Pre-Dominant Chords Jenine Brown1, Daphne Tan2, David John Baker3 1Peabody Institute of The Johns Hopkins University 2University of Toronto 3Goldsmiths, University of London [ACCEPTED AT MUSIC PERCEPTION IN APRIL 2021] Author Note Jenine Brown, Department of Music Theory, Peabody Institute of the Johns Hopkins University, Baltimore, MD, USA; Daphne Tan, Faculty of Music, University of Toronto, Toronto, ON, Canada; David John Baker, Department of Computing, Goldsmiths, University of London, London, United Kingdom. Corresponding Author: Jenine Brown, Peabody Institute of The John Hopkins University, 1 E. Mt. Vernon Pl., Baltimore, MD, 21202, [email protected] 1 THE PERCEPTUAL ATTRACTION OF PRE-DOMINANT CHORDS 2 Abstract Among the three primary tonal functions described in modern theory textbooks, the pre-dominant has the highest number of representative chords. We posit that one unifying feature of the pre-dominant function is its attraction to V, and the experiment reported here investigates factors that may contribute to this perception. Participants were junior/senior music majors, freshman music majors, and people from the general population recruited on Prolific.co. In each trial four Shepard-tone sounds in the key of C were presented: 1) the tonic note, 2) one of 31 different chords, 3) the dominant triad, and 4) the tonic note. Participants rated the strength of attraction between the second and third chords. Across all individuals, diatonic and chromatic pre-dominant chords were rated significantly higher than non-pre-dominant chords and bridge chords. Further, music theory training moderated this relationship, with individuals with more theory training rating pre-dominant chords as being more attracted to the dominant.
[Show full text]
Standard for Data Processing of Measured Data (Draft) WP 3 Deliverable/Task: 3.3
Joint Monitoring Programme for Ambient Noise North Sea 2018 – 2020 Standard for Data Processing of Measured Data (Draft) WP 3 Deliverable/Task: 3.3 Authors: L. Wang, J Ward, S Robinson Affiliations: NPL Date: February 2019 INTERREG North Sea Region JOMOPANS Project Full Title Joint Monitoring Programme for Ambient Noise North Sea Project Acronym Jomopans Programme Interreg North Region Programme Programme Priority Priority 3 Sustainable North Sea Region Colophon Name Niels Kinneging (Project Manager) Organization Name Rijkswaterstaat Email [email protected] Phone +31 6 5321 5242 This report should be cited: XXXXXXXXXXX Cover picture: NPL 2 INTERREG North Sea Region JOMOPANS Table of contents 1 Data quality assurance and pre-processing .......................................................................... 5 1.1 Introduction ........................................................................................................................... 5 1.2 Check for missing data and data consistency ....................................................................... 5 1.3 Removal of contaminated data ............................................................................................. 5 1.4 Checks for clipping and distortion ......................................................................................... 5 1.5 Checking for spurious signals ............................................................................................... 6 1.6 Software control ...................................................................................................................
[Show full text]
Hexatonic Cycles
CHAPTER Two H e x a t o n i c C y c l e s Chapter 1 proposed that triads could be related by voice leading, independently of roots, diatonic collections, and other central premises of classical theory. Th is chapter pursues that proposal, considering two triads to be closely related if they share two common tones and their remaining tones are separated by semitone. Motion between them thus involves a single unit of work. Positioning each triad beside its closest relations produces a preliminary map of the triadic universe. Th e map serves some analytical purposes, which are explored in this chapter. Because it is not fully connected, it will be supplemented with other relations developed in chapters 4 and 5. Th e simplicity of the model is a pedagogical advantage, as it presents a circum- scribed environment in which to develop some central concepts, terms, and modes of representation that are used throughout the book. Th e model highlights the central role of what is traditionally called the chromatic major-third relation, although that relation is theorized here without reference to harmonic roots. It draws attention to the contrary-motion property that is inherent in and exclusive to triadic pairs in that relation. Th at property, I argue, underlies the association of chromatic major-third relations with supernatural phenomena and altered states of consciousness in the early nineteenth century. Finally, the model is suffi cient to provide preliminary support for the central theoretical claim of this study: that the capacity for minimal voice leading between chords of a single type is a special property of consonant triads, resulting from their status as minimal perturbations of perfectly even augmented triads.
[Show full text]
Evaluating Prolongation in Extended Tonality
Evaluating Prolongation in Extended Tonality <http://mod7.shorturl.com/prolongation.htm> Robert T. Kelley Florida State University In this paper I shall offer strategies for deciding what is structural in extended-tonal music and provide new theoretical qualifications that allow for a conservative evaluation of prolongational analyses. Straus (1987) provides several criteria for finding post-tonal prolongation, but these can simply be reduced down to one important consideration: Non-tertian music clouds the distinction between harmonic and melodic intervals. Because linear analysis depends upon this distinction, any expansion of the prolongational approach for non-tertian music must find alternative means for defining the ways in which transient tones elaborate upon structural chord tones to foster a sense of prolongation. The theoretical work that Straus criticizes (Salzer 1952, Travis 1959, 1966, 1970, Morgan 1976, et al.) fails to provide a method for discriminating structural tones from transient tones. More recently, Santa (1999) has provided associational models for hierarchical analysis of some post-tonal music. Further, Santa has devised systems for determining salience as a basis for the assertion of structural chords and melodic pitches in a hierarchical analysis. While a true prolongational perspective cannot be extended to address most post-tonal music, it may be possible to salvage a prolongational approach in a restricted body of post-tonal music that retains some features of tonality, such as harmonic function, parsimonious voice leading, or an underlying diatonic collection. Taking into consideration Straus’s theoretical proviso, we can build a model for prolongational analysis of non-tertian music by establishing how non-tertian chords may attain the status of structural harmonies.
[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]
Design, Harmony, and Voice Leading
From: AAAI Technical Report WS-96-03. Compilation copyright © 1996, AAAI (www.aaai.org). All rights reserved. Design, Harmony, and Voice Leading GarryS. Sittler University of Illinois at Urbana-Champaign Department of Computer Science Urbana, Illinois 61801 [email protected] Abstract General voice leading rules have evolved with Western This paper describes an automated design system music over time. These rules comein several categories. which harmonizes music. The goal is to take a given Some,such as the available major, minor, diminished, and melody line and produce four part harmonyaccording augmentedtriads, are dictated by the structure and the to procedures set forth by harmonization and voice pitches of the twelve notes within an octave. Others are leading techniques. Voice leading techniques provide based on preferences of what sounds pleasant to the human some guidance about how to produce a musical ear. Manyof these types of rules designate musical arrangement. Manyof these techniques, however, are situations which are prohibited. Another category could be represented by rules which specify certain situations called heuristic knowledge.Several of these rules are based which must be avoided. Thus, the principle challenge is how to determine what design choices should be on what a composer might do, and they are also good made based on what cannot be done. methods for avoiding the prohibited situations. Each category is further explained and exemplified below. Eachof the seven notes in a scale has associated with it a Introduction triad which is formed with the two notes forming intervals of a third and a fifth above it. The possible triads for a The process of automated design involves choosing major scale are as follows: appropriate values for a given set of design parameters.
[Show full text]
In Search of the Perfect Musical Scale
In Search of the Perfect Musical Scale J. N. Hooker Carnegie Mellon University, Pittsburgh, USA [email protected] May 2017 Abstract We analyze results of a search for alternative musical scales that share the main advantages of classical scales: pitch frequencies that bear simple ratios to each other, and multiple keys based on an un- derlying chromatic scale with tempered tuning. The search is based on combinatorics and a constraint programming model that assigns frequency ratios to intervals. We ﬁnd that certain 11-note scales on a 19-note chromatic stand out as superior to all others. These scales enjoy harmonic and structural possibilities that go signiﬁcantly beyond what is available in classical scales and therefore provide a possible medium for innovative musical composition. 1 Introduction The classical major and minor scales of Western music have two attractive characteristics: pitch frequencies that bear simple ratios to each other, and multiple keys based on an underlying chromatic scale with tempered tuning. Simple ratios allow for rich and intelligible harmonies, while multiple keys greatly expand possibilities for complex musical structure. While these tra- ditional scales have provided the basis for a fabulous outpouring of musical creativity over several centuries, one might ask whether they provide the natural or inevitable framework for music. Perhaps there are alternative scales with the same favorable characteristics|simple ratios and multiple keys|that could unleash even greater creativity. This paper summarizes the results of a recent study [8] that undertook a systematic search for musically appealing alternative scales. The search 1 restricts itself to diatonic scales, whose adjacent notes are separated by a whole tone or semitone.
[Show full text]