ETAATONS SYNOPSS "Making the simple complicated is commonplace; making the complicated simple, aesomely simple, thats' creativity!" harles Mingus The eltadiatonics Method emraces the evolution of chord symology. t is an outcome of the Baroque figured ass (lassical) as utilized y Bach, Handel and Scarlatti, Standardized hord Symol Notation (Jazz), as formalized y arl Brandt and linton Roemer and the Nashville Numer System (ountry). t utilizes symols from all of the these systems and primarily includes: Araic numers:,2,,4,,,,8,,0,,2 and Roman numerals:,,,v,v,v, and V Seven letters of our alphaet: A,B,,,E,F and G The flat, ( ) sharp, ( ) and natural ( n )symols eltadiatonics Symols, and T ø Ñ Ron i Salvio 204 Meado Run Music ASAP All Rights Reserved The results creates a succinct universal method readily accessile to all musicians, composers, theorists, song riters and improvisors. yads PU 2 4 T P8 Perfect Unison Minor Second eltadiatonics Harmonic ntervals * * Major Second Minor Third Major Third Perfect Fourth Tritone Augmented 4th iminished th Perfect Fifth Augmented Fifth 0 2 2 4 4 8 Minor Sixth ommon practice interval names and chromatic figures from the fundamental tone "". Ñ Major Sixth ominant ( Minor ) Major Perfect Octave * Nicolas Slonimsky in his ook ictionary of Music states; "Property of notes that sound the same ut are notated differently; F sharp and G flat are enharmonically equivalent, as are G sharp and A flat." n eltadiatonics e minimize the use of doule flats and sharps and simplify notation henever possile. See the diminished seventh chord on page.
2 The Four Foundational hords All diatonic harmony, from simple three note chords (triads) to complex harmonies of the th, are derived from these four qualities. Examine the chords outer fifth interval: oth major and minor qualities contain perfect fifths (P). The augmented fifth (+) is raised or sharpened ( ), the diminished fifth ( or T for Tritone) is loered or flatted ( ). Examine each chords comination of major ( ) and minor ( ) thirds. Each chord contains to thirds, one on top of the other, in four unique orientations. The major interval figuration,,,is the default from hich the other triads are altered. When e loer, or flat the rd, e produce a minor triad. When e raise, or sharpen the th, e produce an augmented triad. When e loer, or flat the rd and th, e produce a diminished triad. eltadiatonics Symols for Triads Quality Symol nterval Figures Third Quality Outer Fifths Major Augmented Minor iminished Ñ P + T P ( )
The Seven Foundational hords The triad ith the addition of another major or minor third layered on top reveals three ne harmonic qualities. We ill examine these essential harmonic colors in the folloing ays: eltadiatonic symols, staff notation, interval figures, fifth analysis, compound triads and thirds.one fundamental precept in eltadiatonics is the use of the numeral "" hich y default equals a. This symol is used exclusively for a dominant funtion, never for major or minor sevenths. n addition, since all dominant functions contain the tritone, as either a diminished fifth or an augmented fourth, these intervals are simply replaced ith the symol T, for tritone, to lessen confusion. This is a significant departure eteen common practice jazz notation, Nashville Numering System and most traditional theory texts. Harmonic Quality Symols Staff Notation nterval Figures ayered Thirds hord Names Major eltadiatonics Symols for hords of the Ñ Augmented Major Minor Major ominant Minor ø Half iminished iminished * () * The doctrine of enharmonic equivalence lost its practical significance in notation ith the advent of organized atonality..." B is a B is B is a B, And never flat ill it e. is a is a is a, And never B sharp ill it e. B doule flat is nonsensical When e kno it's just a plain old A. And hy e unduly forensical, nsisting the G doule sharp is not A Nicolas Slonminsky
4 ntervalic Fifth Analysis ith Template All chords of the seventh contain to cominations of the folloing three intervals: perfect fifths, (P) diminished fifths, (T) and augmented fifths (+). hoose the chord quality you are looking for and the chord root note, or letter name, that you ant to construct a seventh chord on. On the root () play the fifth indicated and then figure up a major third () or a minor third ( ) and form the other fifth indicated. The template elo can e used starting on any of the telve chromatic tones. Here is a helpful visual aid in finding perfect fifths (P) and tritone (T) intervals on a keyoard. AllP contain to lack keys or to hite keys ith the exception of B and F, lack and hite and B and F, hite and lack. All T are hite and lack, or lack and hite ith the exception of F and B and B and F hich are oth hite and hite. eltadiatonics Fifth Analysis Ñ ø ( ) P P P + + P T P P P P T T T Major Augmented Major Minor Major ominant Minor Half iminished iminished
Overlapping Triad Analysis ith Template We can also vie chords of the seventh as a comination of to overlapping triad qualites derived from the Four Foundational Triads. Examination of these templates ill shed light on the asic principles of chord sustitution (interchangeaility of major and minor, diminished and dominant). Using the template elo choose the chord quality you ish to hear in any key. hoose the root note, or letter name that you ant to construct a seventh chord on. On that root () play the triad indicated and then figure up a major third () or a minor third ( ) and form the other triads quality. ross check using Fifth analysis. eltadiatonic ual Triad Analysis E E + Ñ E + E E E ø E Template Ñ Ñ Major Augmented Major Minor Major ominant Minor Half iminished iminished
nversion of Triads and hords of the The idea of a musical shorthand notation system is not ne. The Baroque classical period eteen 00 and 0 gave us a system hich used Araic numerical figures, ritten elo a single ass note, alloing the accompianist to realize the harmonies aove it. n the 00's jazz composers egan using the first seven letters of the alphaet along ith Araic numerals, placed aove the melody, for harmonies to e realized elo it. This chart compares Baroque notation, current practice slash chord notation, British and eltadiatonic symols. n the eltadiatonic shorthand system e use a specific configuration of diagonal and horizontal slash lines for compound and polytonal chord construction. For compound chord structures the letter to the left of the diagonal slash line indicates a chord; the letter to the right of the slash designates a single note in the ass. For polytonal chords e use a horizontal line designating that there are to chord qualities, one placed aove the other. Both configurations are designed to simplify inversion of triads and sevenths as ell as highly altered chords and upper structures. G F ine onfiguration for hords G dominant seventh ith an F in the ass F F sharp major triad over a triad urrent common practice symols ell accepted in most genres. Used in eltadiatonics for simple chords. Figured ass, full figuration E Figures elo, harmony aove G 4 G G B hord Symols aove hamony elo G 4 G F 4 2 Figured ass, usual areviation 4 4 2 British symols eltadiatonic symols used for complex structures a c 2 Ga G G G Gc G 2 Gd G
Quartal Trichords ith nversions Vincent Persichetti in his ook Tentieth-entury Harmony states; "Three kinds of intervallic arrangements of three-note chords y fourths are possile; perfect-perfect, perfect augmented and augmented perfect." n eltadiatonics e provide a symol and classification for each of them as ell as their inversions. Arnold Schoenerg in his ook Theory of Harmony states; " elieve an exploration of quartal harmony, filling out the tertian system...ought to open up certain ne prospects for the theorist. eltadiatonics trichord interval figuration is calculated from the root of the chord upard to the next tone, then from that tone to the upper tone. The tritones symol T, replaces the augmented fourth ( Ñ4) and the diminsihed fifth ( ). Quartal Trichords in the Major Scale Perfect- Augmented Perfect-Perfect Perfect-Perfect Augmented- Perfect Perfect-Perfect 4T 4 E 4 FT4 G4 A4 B4 V V V V 4T 4 4 T4 4 4 4 nversions of Quartal Trichord Qualities Perfect-Perfect Perfect-Augmented Augmented-Perfect 4 G42 24 4T FT B4 FT4 B4 ET 4 42 24 4T T 4 T4 4 T
8 Evolutionary Triads and hords of the The eltadiatonic Method emraces change. Belo are additional triads found in todays music that have developed over time ut lack proper classification and symols. The outer intervals of all of the triads contain a P (perfect fifth). The 42 and 24 triads are knon as the Suspension Triads, an outcome of the inversion of the perfect-perfect quartal trichord. Note: The Araic numeral "" has several applications in eltadiatonics. t can e part of traditional chord figuration ith "" eing the root note or it can indicate a minor second, if applied to Quartal Trichords nversions. f found under an upright or inverted triangle it ould indicate a first inversion of the chord. Tenty- First entury Triads 42 Suspension Triads 24 T T 2 4 4 2 T R T R T Major Tenty-First entury hords of the 4 Tritone Major iminished Minor-Major Minor T Tritone ominant Ñ Augmented ominant
The closly stacked thirds of triads and chords of the seventh serve us ell for the study of harmony, hoever they have a limited use in the creating of part riting and composition. They must e freed from this closeness of stacked thirds and spread out into a ne order, one hich uses the same notes in different arrangements. The process of spacing chords is a technique called hord Voicing and egins simply ith inversions of the triad. n order to truly understand chord voicing e have to ask ourselves this question; Why does a particular chord arrangement sound etter than another The anser lies in the science of sound, for the orderliness of a common triad relates to one of the asic las of acoustics, ~~~~~~~~~~ virations. When a note is played on the piano its string, hich has een tightend to produce a certain frequency, virates for the hole of its length. Simultaneously, it virates in sections of a half, a third, a quarter, a fifth and so on. Each of these sections produce a faint note of its on according to its frequency. These faint notes are called Harmonic Overtones or Partials. The example elo shos all the tones that are actually virating, hoever the higher harmonics are inaudile. The time line of Western music can e seen in parallel to the ovetone series. The Harmonic Series 00-80 20-0 0-00 00-40 40-00 00-0 0-800 800-00 00-Present Monophonic hant Fundamental Tone Organum Early Polyphony Early Gothic :0 0: :8 8: : : :4 4: ate Renaissance Baroque lassical Romantic Modern Gothic ominant Harmonic Jazz Modulation Extensions Electronic 2: :2 4: :4 : : 8: :8 0: :0 2: :2 2: : 4: : : : 8: : 0: : 2: : As the fundamental tone "" is struck on the piano; the string egins to virate. This creates proportional virations ~~~~~ in hole numer ratios that reside in the same space. This phenomenon produces hat is kno as the Harmonic Series. :2 2: :2 2: ~~ ~~ ~~~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~~ ~~~ ~~ ~~~ ~~ ~~ ~~~ ~~~ ~~ ~~~ ~~~ ~~ ~~~ ~~~ ~~ ~~~ ~~~ ~~ ~~~ ~~~ ~~ ~~~ ~~ ~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~~ ~~~~~~~ ~~~~~~~ ~~~~~~~ ~~~~~~~~~ ~~~~~~~~~~ ~~~~~~~~~ ~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ : 2: : 0: : 8: : : : 4: : 2: n
0 The intervals of the harmonic series egin ith an octave and end ith a minor second. The first four tones virate the pefect octave, fifth and fourth. The remaining telve tones employ major and minor thirds and seconds. The first triad to appear is the second inversion of a major triad ( 4 ) to hich have assigned the name The Alpha hord. (The first voicing in Bach's Prelude of the "Well- Tempered lavier") This essential inversion ill resonate in many of the Upper Structure Vocings used y todays composers and improvisors. Triads A B 2 4 8 0 2 4 P8 P P4 2 2 2 2 H E F G n hords of the J K The Four Foundational Triad Qualities as they appear in the Hamonic Series Upper Structure Alpha hord E G B + A 2 B E F G Super Tonic
hords of the as they appear in the Harmonic Series The first chord of the seventh to appear is the dominant V chord () from the su-dominant key of F (found a perfect fifth elo the fundamental tone ) (tones 4 -) The next chord is the V chord (E ø ) also found in the key of F the half-diminished seventh. (tones -). Next is the chord, (found a perfect fifth aove the fundamental tone ) found oth in the G harmonic and melodic minor, (G ) the minor-major seventh. (tones -) and lastly the chord from those keys (B ) the augmented-major seventh. (tones -). + H M N E J G K B ø + + + The Roman numeral analysis of the chords of the seventh uses overlapping triads ith eing the ottom triad and or, eing the top triad. A chords of the ninth consists of to triads, the top triad uilt upon the uppermost note of the loer triad (the th). Elevenths use triads uilt on and V (or V) and thirteenths use a chord of the seventh on the ottom ith a traid uilt on the Supertonic, ninth or. hords of the th, th th The Altered ominant as found in the Hamonic Series G B + () () M N V V+
2 ntroduction to oer and Upper Structures The last example elo demonstrates the sequence of triads as found in the harmonic series. The end results produces a dominant quality () commonly knon as a (). f e vie it as a compound structure e find a simple dominant seventh () as the oer Structure () and a major triad () (the supertonic,) as the Upper Structure (U). When e alter tones in the series e find ne sequences of triads ith end results producing a major thirteenth ith a sharp eleventh (altered dominant) and a minor thirteenth (natural th, unaltered dominant). ompare the complexity of the common practice jazz symols (found in the ovals) to the U/ symology of eltadiatonics. E G B V V U ma() Thirteenth Eleventh Ninth Triad E G B V V E G B V V Ñ Ñ U U mi ()
Triads and Quartal Trichord Voicings No e ill egin to comine triads and quartal trichords in a manner that mirrors the harmonic series. The (loer structure) ill e made of the perfect-perfect or a 4 quality chord. The U (upper structure) ill contain triads as Alpha hords or root and first inversions. These voicings can e used for major or minor settings depending upon the underlying fundamental tone chosen. For example if e sustain a lo "" () (use the sostenuto pedal, the middle pedal, on the piano) and play the vocings over it e create major quality vocings. f e choose an "A" (V) or "" () e create minor voicings. This phenomenon is due to the make up of all major and minor chords of the seventh eing comprised of P (perfect fifths) containing no tritones. An additional phenomenon is that e can create a dominant affect (ithout a tritone present) y sustaining a "G" (V) in the ass and playing the voicings over it. U Open Six-Part Voicings * * * * Alpha hords * F F G F G 4 2 2 2 2 4 4 V4 V4 V4 V4 4 4 lose Six-Part Voicings U V42 V42 42 42 42 42 V42 V42
4 Understanding and Applying Upper Structures Much analysis has een done in the jazz community in exploring upperstructures and polytonal chords. Pioneers include arl Brandt, linton Roemer, John Novello, Randy Halerstadt, Jason Martineau and Mark evine. n the classical orld e oe much to Vincent Persichetti, Arnold Schoenerg and ominic Alldis, to name a fe. Of course analysis comes after the fact and e have heard and these voicings come to us from classical composers and pianists, including ut not limited to, hopin, eussy, Ravel, Milhaud and jazz pianists; Bill Evans, hick orea, Herie Hancock ave Brueck and Keith Jarrett. Many texts are no coming out of the Berklee Press ith various methods to descrie and apply upper and loer structures. Hoever to date there is no system that communicates the symology needed to truly understand and simplifiy these complex harmonies for the average student and composer. elieve, and think you ill agree, given the examples elo that eltadiatonics offers a consolidated system incorporating many of the past efforts into a useale theory hich could enefit a majority of students. Major Triads-Roman Numeral Function Over a Pedal Tone V V V V V V V V / / E / E/ F/ F/ G / G/ A / A/ B / B/ ommon Practice Slash hord Symols
ommon practice upper-structure voicings generally avoid triads that contain the 4th or the major seventh. Hoever our ears are constantly changing and todays tension or disonance may ecome tomorros release or consonance. For example common practice does not recognize the UV as an upper-structure, hoever it is already eing assimilated into our repertoire as the example elo ill verify. The example at A reveals all the major and minor upper-structures ith the addition of the UV aove the fundamental tone "". Upper-structure funtion numers along ith eltadiatonic chord symology and altered figures are listed elo the staves. Of importance is to notice the asence of the root of the dominant in the loer-structure and the inversions of the triads in the upper-structures. The example at B demonstrates the movment (resolution) of the altered dominants to the tonic. The example at demonstrates the Alpha hord in parallel motion (constant structures) in a diminished sequence. U A U U U U V U V UV UV U U U U V All Major Minor Upper-Structures aove the Fundamental Tone "" R 8 0 Notice the enharmonic notation (ex. = E) U B Altered ominants Resolution to Tonic A A G A G 2 2 2 U UV U V U V U V U V ET F Alpha hords in a iminished Sequence 2 B 2 A 2 U V UV U ( ) ( ) ( ) Note ho the loer-structure dominant voicing may contain the root of the chord () or may not (ET) ith the th generally omitted. isten to the difference of the voicings hen e invert the loer-structure tritone ET to B T. ET B T F
Tritone Sustitutions Effect on Upper-Structures The Tritone (T) occurs naturally in our major scale as an interval containing three major seconds or hole tones. t is the comination of the leading tone (V) and the sudominant tone (V) that creates hat is traditionally knon as an interval of an augmented fourth or hen inverted an interval of a diminished fifth. n eltadiatonics e simply use the letter T for either inversion eliminating much confusion. t is essential to understand that this interval is part of the dominant or V chord containing the leading tone, as a third () and the su-dominant tone, as minor seven or flat seven ( ). The phenomenon of the and is truly aesome. t dictates all qualities of major and minor seventh chords. As and it is shared y to keys found a tritone aay from a keys dominant. When e susitute the root of the dominant, a tritone aay from the original keys V chord the Araic numers ecome inverted and its Roman numeral function changes. Major Scale T (+4) 2 2 2 The leading tone, the third of the dominant, resolves upard to the tonic. The su-dominant tone, the flat seven of the dominant, resolves donard to the tonics third. (Outard Resloution of the Tritone) G Mixolydian mode T ( ) 2 2 2 2 G G Notice the leading tone () still resloves up to the tonic hile the su-dominant tone () moves don to the third of the tonic. (nard Resolution of the Tritone) V - -
The examples elo demonstrates hat happens hen e change the root of the upperstructure ith a root a tritone aay. Also notice that the triads are all Alpha hords. n eltadiatonics hen e understand the principle of the voicing e eventually eliminate the inversion symology (ecomes understood) hich further simplifies the symol. When composing or creating a lead sheet this ill makes the process very concise. Write in the remaing chord symols and upper-structure function Roman numerals. E T E 2 A U V E U Eliminate nversion Symol (precise voicing symol) (ecomes understood) F V B V E A V G V V E V V V B G F A
8 The Effect of the oer-structure on an Alpha hord The loer-structure of a voicing can change an Alpha hords quality significantly. When e use a perfect fourth as the loer-structure e hear diatonic modal voiced harmony. When e apply the tritone interval as the loer-structure e hear altered dominant qualities. When e apply the major third e also hear altered dominant qualities due to the tritones presence eteen the third of the loer-structure and the fifth of the upper-structure. Ex. A demonstrates the use eltadiatonics 4 vocing. (Mark evine has symolozied it nicely as SW the "So What" chord vocing as used y Bill Evans in the "Kind of Blue Recording". Hoever this voicing can e traced ack to the early 20th century French composers Ravel, eussy, Satie and Faure. n eltadiatonics the 4 voicing is constructed using three or four stacked perfect fourths ith a major third on top. A A4 (A4) U 4 U B T G T (E) A T (B ) ( ) U V (R) ( ) U (R) A U T U R ()
Voicing -V- hords using oer and Upper-Structures These -V- voicings employ simple loer and upper-structures. Note the enharmonic difference of the Araic numerals and the rtten notation. * Symols in ( ) indicate the precise voicings of the loer-structure. UV 2 4 U F 2 4 8 0 U V 2 4 8 * 0 E G V A G (BT) G4 U 4 4 2 G(BT) B G(BT) 0 G24
20 Notice that the and chords have no alterations to the Araic numerals. This is ecause they are found ithin the key (diatonic). The myriad mutations of the dominant are full of variety and color (chromatic). U V 2 8 2 42 4 U V 2 4 8 0 U 8 F G2 E G(BT) G(BT) A24 0 8 G42 A G(F2) 2 E4 U 2 4 42 2 B G (B ) 8 0