A Whole Different Serving of Tapioca: Exploring Just Intonation Dissonance
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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. -
3 Manual Microtonal Organ Ruben Sverre Gjertsen 2013
3 Manual Microtonal Organ http://www.bek.no/~ruben/Research/Downloads/software.html Ruben Sverre Gjertsen 2013 An interface to existing software A motivation for creating this instrument has been an interest for gaining experience with a large range of intonation systems. This software instrument is built with Max 61, as an interface to the Fluidsynth object2. Fluidsynth offers possibilities for retuning soundfont banks (Sf2 format) to 12-tone or full-register tunings. Max 6 introduced the dictionary format, which has been useful for creating a tuning database in text format, as well as storing presets. This tuning database can naturally be expanded by users, if tunings are written in the syntax read by this instrument. The freely available Jeux organ soundfont3 has been used as a default soundfont, while any instrument in the sf2 format can be loaded. The organ interface The organ window 3 MIDI Keyboards This instrument contains 3 separate fluidsynth modules, named Manual 1-3. 3 keysliders can be played staccato by the mouse for testing, while the most musically sufficient option is performing from connected MIDI keyboards. Available inputs will be automatically recognized and can be selected from the menus. To keep some of the manuals silent, select the bottom alternative "to 2ManualMicroORGANircamSpat 1", which will not receive MIDI signal, unless another program (for instance Sibelius) is sending them. A separate menu can be used to select a foot trigger. The red toggle must be pressed for this to be active. This has been tested with Behringer FCB1010 triggers. Other devices could possibly require adjustments to the patch. -
Download the Just Intonation Primer
THE JUST INTONATION PPRIRIMMEERR An introduction to the theory and practice of Just Intonation by David B. Doty Uncommon Practice — a CD of original music in Just Intonation by David B. Doty This CD contains seven compositions in Just Intonation in diverse styles — ranging from short “fractured pop tunes” to extended orchestral movements — realized by means of MIDI technology. My principal objectives in creating this music were twofold: to explore some of the novel possibilities offered by Just Intonation and to make emotionally and intellectually satisfying music. I believe I have achieved both of these goals to a significant degree. ——David B. Doty The selections on this CD process—about synthesis, decisions. This is definitely detected in certain struc- were composed between sampling, and MIDI, about not experimental music, in tures and styles of elabora- approximately 1984 and Just Intonation, and about the Cageian sense—I am tion. More prominent are 1995 and recorded in 1998. what compositional styles more interested in result styles of polyphony from the All of them use some form and techniques are suited (aesthetic response) than Western European Middle of Just Intonation. This to various just tunings. process. Ages and Renaissance, method of tuning is com- Taken collectively, there It is tonal music (with a garage rock from the 1960s, mendable for its inherent is no conventional name lowercase t), music in which Balkan instrumental dance beauty, its variety, and its for the music that resulted hierarchic relations of tones music, the ancient Japanese long history (it is as old from this process, other are important and in which court music gagaku, Greek as civilization). -
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. -
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. -
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. -
Guitar Best Practices Years 1, 2, 3 and 4 Nafme Council for Guitar
Guitar Best Practices Years 1, 2, 3 and 4 Many schools today offer guitar classes and guitar ensembles as a form of music instruction. While guitar is a popular music choice for students to take, there are many teachers offering instruction where guitar is their secondary instrument. The NAfME Guitar Council collaborated and compiled lists of Guitar Best Practices for each year of study. They comprise a set of technical skills, music experiences, and music theory knowledge that guitar students should know through their scholastic career. As a Guitar Council, we have taken careful consideration to ensure that the lists are applicable to middle school and high school guitar class instruction, and may be covered through a wide variety of method books and music styles (classical, country, folk, jazz, pop). All items on the list can be performed on acoustic, classical, and/or electric guitars. NAfME Council for Guitar Education Best Practices Outline for a Year One Guitar Class YEAR ONE - At the completion of year one, students will be able to: 1. Perform using correct sitting posture and appropriate hand positions 2. Play a sixteen measure melody composed with eighth notes at a moderate tempo using alternate picking 3. Read standard music notation and play on all six strings in first position up to the fourth fret 4. Play melodies in the keys C major, a minor, G major, e minor, D major, b minor, F major and d minor 5. Play one octave scales including C major, G major, A major, D major and E major in first position 6. -
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. -
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. -
Playing Music in Just Intonation: a Dynamically Adaptive Tuning Scheme
Karolin Stange,∗ Christoph Wick,† Playing Music in Just and Haye Hinrichsen∗∗ ∗Hochschule fur¨ Musik, Intonation: A Dynamically Hofstallstraße 6-8, 97070 Wurzburg,¨ Germany Adaptive Tuning Scheme †Fakultat¨ fur¨ Mathematik und Informatik ∗∗Fakultat¨ fur¨ Physik und Astronomie †∗∗Universitat¨ Wurzburg¨ Am Hubland, Campus Sud,¨ 97074 Wurzburg,¨ Germany Web: www.just-intonation.org [email protected] [email protected] [email protected] Abstract: We investigate a dynamically adaptive tuning scheme for microtonal tuning of musical instruments, allowing the performer to play music in just intonation in any key. Unlike other methods, which are based on a procedural analysis of the chordal structure, our tuning scheme continually solves a system of linear equations, rather than relying on sequences of conditional if-then clauses. In complex situations, where not all intervals of a chord can be tuned according to the frequency ratios of just intonation, the method automatically yields a tempered compromise. We outline the implementation of the algorithm in an open-source software project that we have provided to demonstrate the feasibility of the tuning method. The first attempts to mathematically characterize is particularly pronounced if m and n are small. musical intervals date back to Pythagoras, who Examples include the perfect octave (m:n = 2:1), noted that the consonance of two tones played on the perfect fifth (3:2), and the perfect fourth (4:3). a monochord can be related to simple fractions Larger values of mand n tend to correspond to more of the corresponding string lengths (for a general dissonant intervals. If a normally consonant interval introduction see, e.g., Geller 1997; White and White is sufficiently detuned from just intonation (i.e., the 2014). -
A Study of Microtones in Pop Music
University of Huddersfield Repository Chadwin, Daniel James Applying microtonality to pop songwriting: A study of microtones in pop music Original Citation Chadwin, Daniel James (2019) Applying microtonality to pop songwriting: A study of microtones in pop music. Masters thesis, University of Huddersfield. This version is available at http://eprints.hud.ac.uk/id/eprint/34977/ The University Repository is a digital collection of the research output of the University, available on Open Access. Copyright and Moral Rights for the items on this site are retained by the individual author and/or other copyright owners. Users may access full items free of charge; copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational or not-for-profit purposes without prior permission or charge, provided: • The authors, title and full bibliographic details is credited in any copy; • A hyperlink and/or URL is included for the original metadata page; and • The content is not changed in any way. For more information, including our policy and submission procedure, please contact the Repository Team at: [email protected]. http://eprints.hud.ac.uk/ Applying microtonality to pop songwriting A study of microtones in pop music Daniel James Chadwin Student number: 1568815 A thesis submitted to the University of Huddersfield in partial fulfilment of the requirements for the degree of Master of Arts University of Huddersfield May 2019 1 Abstract While temperament and expanded tunings have not been widely adopted by pop and rock musicians historically speaking, there has recently been an increased interest in microtones from modern artists and in online discussion. -
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