Augmented Sixth Chords Are Predominant Chords, Meaning They Are Used to Approach Dominant Chords
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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. -
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. -
Augmented Sixth Chords Are Predominant Chords, Meaning They Are Used to Approach Dominant Chords
Augmentedmusic Sixth theory for musicians Chords and normal people by toby w. rush like that moment of incredible tension just before the hero finally kisses the leading lady, the half-step is the go-to interval for creating tension in music of the common ˙ practice period. it drives the entire style! ˙ if one half-step can create such strong tension, how about two half-steps sounding simultaneously? Let’s get creative here for a minute to find a cool new way to approach a diatonic chord. in this case, we’ll use them to approach the dominant triad. ...and approach that first, we’ll start with octave with a half step the doubled root of a below the top note, V chord... #˙ ˙ #˙ ˙ ˙ ˙ & b ˙ ˙ & b ˙ ˙ V & ˙ V ...and, finally, add the V ...and a half step above tonic as the third note. the bottom note... the result is a new chord, one we call the augmented sixth chord, after the interval created by the top and bottom notes. augmented sixth chords are predominant chords, meaning they are used to approach dominant chords. if we just use they are usually used to approach dominant triads, three notes not dominant sevenths, because of the doubled and double the roots present in dominant triads. tonic, we get the #w italian ww however, they also often augmented sixth. b w & approach tonic chords & #˙ ˙ It.6 in second inversion, ˙ ˙ which also contain a doubled fifth scale degree. ? b˙ n˙ b ˙ ˙ if we add the 6 Ger.6 I4 second scale degree instead ˙ ˙ rarely, augmented sixth chords of doubling the # w & ˙ ˙ are found transposed down tonic, we get the ww a perfect fifth, analyzed as french b w ˙ ˙ “on flat two,” and used to augmented sixth. -
The Augmented Sixth Chord
CHAPTER24 The Augmented Sixth Chord Characteristics, Derivation, and Behavior The two excerpts in Example 24.1 are from different style periods, yet they share several features. In terms of form and harmony, both divide into two subphrases and close with strong half cadences. Further, the pre-dominant harmony in both examples is the same: an altered iv6 chord. Indeed, we hear not a Phrygian cadence (iv6-V), but rather some chromatic version, where the diatonic major sixth above the bass is raised a half step to create the strongly directed interval of the augmented sixth (+6). The new half-step ascent (#4-5) mirrors the bass's half-step descent (6-5). We refer to such chromatic pre-dominants as augmented sixth chords because of the characteristic interval between the bass 6 and the upper-voice #4. Listen to both excerpts in Example 24.1, noting the striking sound of the augmented sixth chords. EXAMPLE 24.1 A. Schubert, WaltzinG minor, Die letzte Walzer, op. 127, no. 12, D. 146 472 CHAPTER 24 THE AUGMENTED SIXTH CHORD 473 B. Handel, "Since by Man Came Death," Messiah, HWV 56 Example 24.2 demonstrates the derivation of the augmented sixth chord from the Phrygian cadence. Example 24.2A represents a traditional Phrygian half cadence. In Example 24.2B, the chromatic F# fills the space between F and G, and the passing motion creates an interval of an augmented sixth. Finally, Example 24.2C shows the augmented sixth chord as a harmonic entity, with no consonant preparation. EXAMPLE 24.2 Phrygian Cadence Generates the Augmented Sixth Chord Given that the augmented sixth chord also occurs in major, one might ask if it is an example of an applied chord or a mixture chord? To answer this question, consider the diatonic progression in Example 24.3A. -
Augmented 6Ths
TutorTube: Augmented 6ths Summer 2020 Introduction Hello and welcome to TutorTube, where The Learning Center’s Lead Tutors help you understand challenging course concepts with easy to understand videos. My name is Darren Churn, Lead Tutor for Music Theory. In today’s video, we will explore Augmented 6ths. Let’s get started. Augmented 6ths Augmented 6th chords are appropriately named due to the fact that they contain an Augmented 6th interval. They are used most commonly as predominant chords that resolve to the dominant. Augmented 6ths are not written as roman numerals like most chords you would analyze. Instead, the chord is identified as one of three types of augmented chords: Italian, French, and German. These chords can be found in major or minor keys and each of these types uses the same solfege base of Le Do Fi. The solfege refers to a lowered 6th scale degree (Le), the tonic (Do), and a raised 4th (Fi) scale degree. Our augmented 6th interval is between the Le and the Fi. Let’s look at the specific types. Italian The first type of augmented 6th chord is Italian. Italian augmented 6ths are the only chords in this category that are not 7th chords. In an Italian chord, we still have our base of Le, Do, Fi. The last note that we add simply doubles Do. This example that we have is based in the key of C. Our Le will be Ab, our Do will be C, and our Fi will be F#. Since this is an Italian chord, we will simply add another C to double the Do. -
The Death and Resurrection of Function
THE DEATH AND RESURRECTION OF FUNCTION A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By John Gabriel Miller, B.A., M.C.M., M.A. ***** The Ohio State University 2008 Doctoral Examination Committee: Approved by Dr. Gregory Proctor, Advisor Dr. Graeme Boone ________________________ Dr. Lora Gingerich Dobos Advisor Graduate Program in Music Copyright by John Gabriel Miller 2008 ABSTRACT Function is one of those words that everyone understands, yet everyone understands a little differently. Although the impact and pervasiveness of function in tonal theory today is undeniable, a single, unambiguous definition of the term has yet to be agreed upon. So many theorists—Daniel Harrison, Joel Lester, Eytan Agmon, Charles Smith, William Caplin, and Gregory Proctor, to name a few—have so many different nuanced understandings of function that it is nearly impossible for conversations on the subject to be completely understood by all parties. This is because function comprises at least four distinct aspects, which, when all called by the same name, function , create ambiguity, confusion, and contradiction. Part I of the dissertation first illuminates this ambiguity in the term function by giving a historical basis for four different aspects of function, three of which are traced to Riemann, and one of which is traced all the way back to Rameau. A solution to the problem of ambiguity is then proposed: the elimination of the term function . In place of function , four new terms—behavior , kinship , province , and quality —are invoked, each uniquely corresponding to one of the four aspects of function identified. -
Regular Mappings and Marvel Temperaments
Regular Mappings and Marvel Temperaments Graham Breed This is the annotated version of the slides for the presentation I gave at Beyond the Semitone in Aberdeen, October 2013. The annotations cover things I said, or should have said, or might have said if I’d had more time. 0.1 Motivation Goals of Regular Temperament Regular temperaments are systems that approximate just intonation using fewer notes. This assumes there’s something special about just intonation that you want to preserve, and if you don’t feel this, temperament won’t be useful to you. The ”regular” part means each just ratio is tuned in a consistent way, and more than one just ratio will typically approximate to the same tempered interval. The list below is roughly prioritized, and the tuning is the least important thing. There’s a trap in microtonal literature that you focus on the tuning, and people think it’s all about tuning, although the tuning is only a tool in the service of exploring new harmonies, or making just intonation scales more manageable. • New harmonic systems • Frugal scales • Notation • Generalized keyboards • Tuning Beyond Temperament These ideas come from the study of temperaments, but can still be useful if you don’t use temperament. This is why I talk about a ”regular mapping paradigm” rather than ”regular temperament theory”. 1 I added some citations for the academic audience, and also to avoid giving the impression that everything I was talking about was original to me. Christian Kaernbach, who gave the talk after mine, discussed the idea that musicians might not play the (simplistic) theoretically correct pitches, and that doesn’t mean they’re wrong. -
Advanced Music Theory Handbell Musicians of America Certification Course C3 Course Outline Instructor: Michael J
Advanced Music Theory Handbell Musicians of America Certification Course C3 Course Outline Instructor: Michael J. Glasgow I. Pitch names and how handbells use them a. C1 through C8 (handbell designation C2 through C9) b. Transposing reminder II. Rhythmic values of notes and rests a. British/international nomenclature (from Renaissance period, if not before) i. Thirty-second (demisemiquaver) b. Tuplets: beyond basic triplets i. Ties in tuplets (implied and overt) 1. “swung” eighth notes ii. Sometimes they expand (“stretch”) the note value 1. Example: eighth-note duplets in compound meter iii. Often – especially in simple meters – they “compress” the notes into a tighter ratio. The number on the beam/bracket indicates that that number of notes should be played in the time traditionally occupied by the next lower “standard grouping” of them that space. 1. Example: in 4/4 time, a quintuplet over one beat would be shown as five sixteenth-notes, since the next lower “standard grouping of notes in one beat” from five is four, and four sixteenth notes usually take up one beat. 2. Example: a nonuplet of nine sixteenth-notes in 4/4 time would be like saying that those nine sixteenth-notes should be played in the space normally occupied by eight sixteenth-notes (two beats). iv. Nested tuplets v. Ambiguity: many systems, many guides, no panacea for all situations 1. Use basic math and intuition. Interpret the printed page with context clues; create the printed page with common sense. 2. Example: if we wanted to indicate seven notes played evenly over an entire measure of 4/4 time, we could use a “compressed” ratio of 7:4, and bracket together seven quarter-notes; however, it would also be acceptable to use a “stretched” ratio of 7:8, and show seven eighth-notes. -
An Exploration of Cultural Transmission Through the Application of Jazz Theory to the Music of Frederic Chopin
BearWorks MSU Graduate Theses Fall 2020 An Exploration of Cultural Transmission through the Application of Jazz Theory to the Music of Frederic Chopin Aaron Michael King Missouri State University, [email protected] As with any intellectual project, the content and views expressed in this thesis may be considered objectionable by some readers. However, this student-scholar’s work has been judged to have academic value by the student’s thesis committee members trained in the discipline. The content and views expressed in this thesis are those of the student-scholar and are not endorsed by Missouri State University, its Graduate College, or its employees. Follow this and additional works at: https://bearworks.missouristate.edu/theses Part of the Music Theory Commons Recommended Citation King, Aaron Michael, "An Exploration of Cultural Transmission through the Application of Jazz Theory to the Music of Frederic Chopin" (2020). MSU Graduate Theses. 3565. https://bearworks.missouristate.edu/theses/3565 This article or document was made available through BearWorks, the institutional repository of Missouri State University. The work contained in it may be protected by copyright and require permission of the copyright holder for reuse or redistribution. For more information, please contact [email protected]. AN EXPLORATION OF CULTURAL TRANSMISSION THROUGH THE APPLICATION OF JAZZ THEORY TO THE MUSIC OF FREDERIC CHOPIN A Master’s Thesis Presented to The Graduate College of Missouri State University TEMPLATE In Partial Fulfillment Of the Requirements for the Degree Master of Music By Aaron Michael King December 2020 Copyright 2020 by Aaron Michael King ii AN EXPLORATION OF CULTURAL TRANSMISSION THROUGH THE APPLICATION OF JAZZ THEORY TO THE MUSIC OF FREDERIC CHOPIN Music Missouri State University, December 2020 Master of Music Aaron Michael King ABSTRACT Connections between classical music and jazz were observed and detailed, providing an expanded understanding of the cultural underpinnings of Western music. -
Less Common Augmented Sixth Chord Spellings
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. -
The Augmented Sixth Chord
Theory Dr. Crist The Augmented Sixth Chord The augmented sixth chord was born in the Baroque period but occurs with greater frequency in the Romantic period. The aug. sixth chord may be understood as being derived from chromatic alterations of the iiº7 or iv7 chords. They do not function as subdominants, however, but function as predominants. All augmented sixth chords contain the interval of an augmented sixth, specifically scale degrees b6 and #4 which frame the dominant. The interval of the augmented sixth resolves outwards to an octave. The tonic also appears in every augmented sixth chord. There are three different "flavors" of augmented sixth chords: Italian, French, and German. They each include the augmented sixth, the tonic, and one other note as follows: Italian : double the tonic French - add the supertonic German : add the mediant. c minor: It+6 Fr+6 Gr+6 Progression: To avoid parallel fifths, the Gr+6 should resolve to iP before progressing to V. It+6 ---------- V or iP Fr+6 ---------- V or iP Gr+6 ---------- iP then to V c minor: It+6 Fr+6 Gr+6 Resolution: The interval of the augmented sixth resolves outwards. Common tones and stepwise motion should be used in the remaining voices. When the following chord is a V7, #4 should progress to natural 4 (the 7th of the V7): c minor: It+6 V7 The Individual Augmented Sixth Chords Italian - Derived from the progression i --- iv6 --- V. In order to intensify or embellish the melodic/harmonic progression to V, the root is altered and raised up a half-step creating a leading-tone relation to the dominant. -
Introduction to Augmented Sixth Chords
MUS 357– Aaron Grant INTRODUCTION TO AUGMENTED SIXTH CHORDS EXPLORE Label the key and Roman numerals of the harmonies in the following example. Do any harmonies stand out as odd? Discuss with a partner which chord is difficult to label, and describe how that harmony’s voice leading works as well as where it falls within the phrase. Schubert, Waltz in G minor, Die letzte Walzer, op. 127, no. 12, D. 146 KEY POINTS: The harmony above is an example of an augmented sixth chord: a group of harmonies that each share the same tendency tones of raised 4^ and lowered 6^ . The half-step resolution of both scale degrees to 5^ create a powerful drive towards V. As such, this chord always preceeds a dominant, and typically appears before strong cadences. 1. When voicing this chord, lowered 6^ typically occurs in the bass with raised 4^ relegated to an upper voice; the two tendency tones, thus, create an interval of an augmented sixth that gives the chord its name. 2. Both tendency tones always resolve by half step to 5.^ 3. Raise 4^ requires an accidental in both major and minor keys, but lowered 6^ only needs an accidental in major. 4. Because augmented sixth chords always preceed the dominant of a cadence, they are a type of predominant chord. 5. All augmented sixth chords contain scale degrees ß^6 (le), ƒ^4 (fi), and 1^ (do). MUS 357– Aaron Grant THREE COMMON TYPES OF AUGMENTED SIXTH CHORDS: The three most common types of augmented sixth chords are defined by the fourth note of the augmented sixth chord.