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). This is in than the highly overused melodies, phrases, periods, rebettika, and traditional distinction to twelve-tone eclectic. It is computer and movements have clear and contemporary Irish equal temperament, the music, in the sense that tonal centers. It is world music. tuning system in general it was produced with music, in the sense that it Some of the shorter use in the West for the digital instruments under is inspired and influenced pieces use fixed scales, last 200 years, in which MIDI control, but it does by many musical cultures. traditional or otherwise, all intervals other than the not involve algorithmic It is unapologetically whereas the longer, more octave are intentionally composition, artificial derivative. I have drawn on complex pieces use some mistuned to varying intelligence, or the more the resources of most of form of “extended” Just degrees, for the sake of arcane techniques used by the musics I have played, Intonation; these more convenience. As a result, academic computer-music studied, or merely listened extensive pitch sets were consonance is compro- composers. All pieces are to and enjoyed. Gamelan, not predetermined, but mised and the intervallic through-composed in the the predominant influence evolved in the process of palette is impoverished. laborious, old-fashioned in much of my earlier work, composition, as demanded This music is the result way; the composer is solely has retreated into the by the growth of melody, of a long and slow learning responsible for all aesthetic background, but may still be harmony, and counterpoint. Uncommon Practice Contents Title Time Tuning Dithyramb 6:37 Al Farabi’s chromatic (seven-limit) Fake Irish Music 8:28 five-limit modal/triadic, with occasional sevens in cadential seventh chords Fake Greek Music 3:58 harmonic series (8, 9, 10, 11, 12, 14, 15, 16, 17) Paradigms Lost 4:39 five-limit modal/triadic, with frequent sevens as blue notes and in dominant-seventh chords Contrapunctus 1.01 14:57 extended seven-limit Bodhisattvas in Berkeley? — Mu! 6:14 extended eleven-limit Rituals and Ceremonies 11:46 extended seven-limit David Doty … is a deeply serious composer Doty’s CD is an eclectic tour of musical styles of considerable talent, with unusual harmonic brought into the realm of extended JI, taking us and melodic gifts…. This is music to be listened on a harmonic progression toboggan ride over the to carefully, savouring the quality of a sudden supposed bumps of comma shifts and “anomalous” harmonic twist, the feeling of being subtly and pairs of tones.… Far from subverting a tonal sense gently launched into an unsuspected harmonic or confusing modal perception, these context- territory. dependent tweakings provide for a succession of clear harmonies that convincingly support the ——Warren Burt, Chroma melody and structure in these musical contexts. Doty is one of our major tuning theorists, and for ——Bill Alves, 1/1 tuning-sensitive ears, the pure and subtly shifting intonations [show] in a simple, engaging, crystalline context what’s possible with enough well-tuned … no big reverb, no compression, no aural exciters; pitches per octave. just music ——Kyle Gann, Village Voice ——Jim Aiken, Keyboard Uncommon Practice is available from — Physical CDs CDBaby— http://cdbaby.com/cd/davidbdoty Frog Peak Music—http://www.frogpeak.org/fpartists/fpdoty.html • PO Box 1052, Lebanon NH 03766 • 603-448-8837 Digital Downloads iTunes Store • http://phobos.apple.com/WebObjects/MZStore.woa/wa/ viewAlbum?playListId=268661156 Many Other Sources (Google “David B Doty” + “Uncommon Practice” + download) Samples at http://www.dbdoty.com/UCP/ucp_sound.html THE JUST INTONATION PPRIRIMMEERR An Introduction to the Theory and Practice of Just Intonation by David B. Doty Third Edition, November 2002 Third Edtion, December 2002 Fifth Printing, December 2016 ISBN 0-9726810-0-0 ©1993, 1994, 2002: David B. Doty www.dbdoty.com/Words/Primer1.html [email protected] invisible type iii Contents The Harmonic Series and the Subharmonic Series Preface to the Third Edition (2002) .................... iv ........................................................................... 28 Preface to the Second Edition (1994) ................. iv Converting Ratios to a Harmonic or Introduction ..................................... 1 Subharmonic Series Segment ..................... 28 Identities ...................................................... 30 What is Just Intonation? ...................................... 1 Prime Numbers, Primary Intervals, A Little History .................................................... 2 and Prime Limits ............................................... 30 Antiquity ....................................................... 2 What is a Chord? ............................................... 30 The Middle Ages and the Renaissance ......... 2 Interval Names .................................................. 32 The Common-Practice Period Notation ............................................................. 32 and the Rise of Temperament ....................... 3 Anomalies .......................................................... 33 The End of Common Practice ....................... 5 Tetrachords and Tetrachordal Scales ................ 33 The Twentieth-Century Just Intonation Revival The Ladder of Primes, Part One:Two, ............................................................................. 6 Three, and Five ................................ 35 The Purpose of this Publication ........................... 7 Acoustic and Psychoacoustic One, the Foundation .......................................... 36 Background ........................................ 9 Two, the Empty Matrix ..................................... 36 The Three Limit (Pythagorean Tuning) ............. 36 Introduction ......................................................... 9 The Pythagorean (Ditone) Diatonic Scale .. 36 Periodic Vibrations .............................................. 9 Pythagorean Chromatic Scales What is an Interval? ........................................... 10 and the Pythagorean Comma ...................... 37 Superposition of Pure Tones ...............................11 Chords ......................................................... 38 Phase Relationships ................................... 12 The Five Limit ................................................... 38 Interference Beats ....................................... 12 Constructing a Five-Limit Major Scale ...... 39 The Harmonic Series ......................................... 14 The Supertonic Problem ............................. 40 Difference Tones ................................................ 16 The Five-Limit Lattice ................................ 42 Periodicity Pitch ................................................ 17 The Great Diesis ......................................... 44 Complex Tones with Harmonic Partials ............ 19 The Harmonic Duodene .............................. 45 Coincident or Beating Harmonics ............... 20 Five Limit Chords ....................................... 46 Arthur H. Benade’s “Special Relationships” Condissonant Chords in the Five Limit ...... 47 .................................................................... 22 Deficiencies of the Five Limit .................... 48 Special Relationships Beyond the Octave .. 23 The Ladder of Primes, Part Two: On the Consonance of Relationships Seven and Beyond ............................. 51 Involving Higher Harmonics ...................... 24 Basic Definitions, Conventions, Seven-Limit Intervals ........................................ 51 and Procedures ............................... 25 New Consonances ....................................... 51 Whole Tones ............................................... 54 Introduction ......................................................