A Bit About Intervals

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A Bit About Intervals In order to study intervals, let's consider (as ever!) C Major scale. 1 2 3 4 5 6 7 Octave A couple of important points before we start: An interval is essentially the 'distance' between two notes. Intervals are always viewed from the point of view of their lowest note. Early music used exclusively what we call 'Perfect Intervals' as they were considered sacred. Perfect fourth Perfect fifth Perfect octave Perfect unison The remaining intervals in the major scale we call unsurprisingly 'Major Intervals' thus: Major second Major third Major sixth Major seventh If we flatten a major interval, the resulting interval we call a 'Minor Interval' thus: Minor second Minor third Minor sixth Minor seventh Copyright © Pete Cook October 2007 A Bit About Intervals Page 2 There are two more types of interval: Diminished intervals and Augmented intervals. You'll find that some of these intervals sound the same as some we've met already, but it is important to understand the sounds and 'spellings' of these intervals for reasons of 'correct musical grammar'. Of course, in reality you're only going to meet some of these in everyday musical life, the others reside pretty much in 'Theoryland'. If we flatten a perfect interval, the resultant interval we call a 'diminished interval' Diminished unison Diminished fourth Diminished fifth Diminished octave (sounds like maj 3rd) (sounds like maj 7th) Similarly, flattening minor intervals gives diminished intervals Diminished second Diminished third Diminished sixth Diminished seventh (sounds like perf unis) (sounds like maj 2nd) (sounds like perf 5th) (sounds like maj 6th) If we sharpen a perfect interval, the resultant interval we call an 'augmented interval'. Augmented unison Augmented fourth Augmented fifth Augmented octave (sounds like min 2nd) a.k.a. 'Tritone' (sounds like min 6th) (sounds like min 9th) (sounds like dim 5th) Similarly, sharpening major intervals gives augmented intervals. Augmented second Augmented third Augmented sixth Augmented seventh (sounds like min 3rd) (sounds like perf 4th) (sounds like min 7th) (sounds like perf octave) Don't worry if all this seems a little daunting, I've covered intervals in much greater detail than you'll probably need here, but I think it's important to get 'the big picture'. Copyright © Pete Cook October 2007.

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Tonalandextratonal Functions of Theaugmented
TONAL AND EXTRATONAL FUNCTIONS OF THE AUGMENTED TRIAD IN THE HARMONIC STRUCTURE OF WEBERN'S 'DEHMEL SONGS' By ROBERT GARTH PRESTON B. Mus., Brandon University, 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES (School of Music, Music Theory) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1989 © Garth Preston, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) ii ABSTRACT: TONAL AND EXTRATONAL FUNCTIONS OF THE AUGMENTED TRIAD IN THE HARMONIC STRUCTURE OF WEBERN'S 'DEHMEL SONGS' The composing of the 'Dehmel Songs' marks a pivotal juncture both in Webern's oeuvre and in the history of music in general. The years that saw the birth of this cycle of five songs, 1906-8, comprise what is generally regarded as a period of transition, in the work of Schoenberg, Webern and Berg, from a 'late tonal' style of composition to an early 'atonal' style. In this study I approach the 'Dehmel Songs' from the perspective that its harmonic structure as a whole can be rendered intelligible in a theoretical way by combining a simple pitch-class-set analysis, which essentially involves graphing the pattern of recurrence of the 'augmented triad' as a motivic harmonic entity—a pattern which is in fact serial in nature-through the course of the unfolding harmonic progression, with a tonal interpretation that uses that pattern as a referential pitch-class skeleton.
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