Harmony of barrie netles, Ejercicios de Matemáticas

¡Descarga Harmony of barrie netles y más Ejercicios en PDF de Matemáticas solo en Docsity! Harmony 2 by Barrie Nettles Berklee college of music  Blank Page Mio This ís the first substantial revision of the Harmony 2 workbook in several years. The revision clarifies important passages, supplies better musical examples for a number of topics, and improves the readability and consistency in many areas. It is the result of a careful examination of the previous edition and the overall Harmony department curriculum. A number of colleagues in the Harmony department and the Profes- sional Writing Division made valuable contributions to the content and language. Coming as it does at the beginning of the first complete curriculum review in the college's history, this edition represents a first step in what will be an exciting and challenging process, one that will result in a set of materials that will reflect the changing music of the time and the needs and learning styles of today's students.  Blank Page HARMONY 2 Spring 2007 Edition TABLE OF CONTENTS IET — Diatonic Functioning Dominant Chords Secondary DominantS.......ooooooocoooomomo.. Harmonic Rhythm. c.ooooccccccccao Extended DominaniS......ooooccocoiconcccncco Deceptive Resoluti0N........o.oooooooomommo... Related I-7 ChordS....ooooooccccccocnoocnco ms JETA — Guide Tone Line Development Harmonic Continuity .......ooooooooommmmomo.. Guide Tone LineS......ocooccoccccccocccoocoo — Minor Key Harmony Minor Key HarMoOny.....ooococococccccononc Available Tensions — Minor KeyS ...........:... Subdominant MiNOr.....oocoocccccccccccccc Modal Interchange........oooocococcccco coo Line ClihÉéS.....oooocoocccccocccccc ro Melody and RhythM......oooococccccoc Melody/Harmony Relationship............ a Secondary Dominants The secondary dominant chords in the key resolve to the diatonic chords other than land VIL7(5): Secondary Imaz M7 IVmaz “AL 1-7 lominant s 4 , +4 PS Resolutions Amaj7 C*7 Dmaj7: Fi7 B7 Imaz vz uz “%n 17 Amajz — Flz7 pz ad e ex. 2 Imaz m7 vez “v IVmaj7 Amajz. Chz Ez A7TTTA Dmajz ex. 3 Imaj7 IVmaj? 'ME7 A v7 Amaj7 Dmajz. Ch7 B7 E7 ex. 4 Imaz V7 Ima” '/M VEZ Amaj7 E7 Dmajz- Ch Tapiz ex.5 Poor o? Compare the sound of the preceding resolutions to their diatonic counterparts: ex. 1 ex. 2 ex. 3 El B-7 elzbs) oh7 Amajz Dmajz e ex. 4 ex. 5 B-7 E7 oz Pz 2 — HARMONY 2 - Part 1  ES Y VA Y An VA, Secondary Dominants Secondary dominants are our first encounter with chromaticism, the use of non-diatonic tones in a key. Secondary dominants are considered diatonically related chords because their function is to intensify the move- ment to a diatonic chord, Notice that secondary dominants have diatonic roots. The chord of resolution (sometimes called the target chord) of a second- ary dominant can be any chord in the key other than the Tor the VI ?5, The chord built on the seventh scale degree is omitted because move- ment to the unstable VIL-7'5 is not a resolution. In addition, it's second- ary dominant would require a non-diatonic root. When any dominant chord resolves as expected (with root motion down a perfect fifth), an arrow is used to show the resolution: VA wz “Ay _ 1vmaj7 G7 TA 7 G7 *Cmaj? YA m7 VA vi7 e7 a C-7 G7TAC7 The diagonal slash means “of.” For example, V7/Il means “V7 of IL.” It is not necessary to indicate the quality of the target chord in the analysis: V?7/1-7 is not necessary. To summarize, all secondary dominants share certain characteristics: » Atleast one of the chord tones is not diatonic. * The expected resolution is down a perfect fifth to a diatonic target chord. + The rootis diatonic. HARMONY 2 — Part 1 — 3 Secondary Dominants Available Tensions: Secondary Dominants VA An MU VA VAn Available Tension Criteria 4 — HARMONY 2 - Part 1 The tensions for secondary dominant chords reflect the chord's func- tion, which is to provide strong resolution to a diatonic chord. Diatonic tensions, whether in a melody or added to a chord voicing, reinforce the relationship of the chord to the key. h » p 9 bt £ na TAS. , AS es fo L Diatonic Tensions —1 12 Chord Tones ————] 87 » to ba LH ram a 125 E AY EZ u y 2.0 ' L Diatonic Tensions — LL Chord Tones ———— 9 13 £ e7 id XX e e Chord Tones LL Diatonic Tensions —1 o too 1 D7 b da 2 HE y a) 12S uy XL u LO OT emoritones —— L Diatonic Tensions —) E7 lo ds ls (ho = A 12 Chord Tones ————1 eN E Diatonic Tensions —| The available tensions for secondary dominants are those notes which are diatonic to the key, other than 11. + Thel9 labelis based on ertharmonic spelling of a diatonic note. + 11 is never “available” as a tension or sustained melody note on a dominant chord, (There are rare stylistic or arranging-driven exceptions to this rule, but for the purposes of functional tonal harmony this is a crucial principle.) + $9 may coexist with b9 if either is diatonic. + É9 is not used together with 9 or b9.  ES Stress Patterns Harmonic Rhythm Chords in a progression will receive strong or weak stress, depending upon their placement. This relative strength of stress strongly influences the composer's choice of function, especially regarding dominant chords. ln any grouping of four pulsations S W os w Ss Wo os w eto, + S- the first pulse is the strongest; + W- the second pulse is not as weak as the last; + S- the third pulse is not as strong as the first; + W - the last pulse is the weakest; This pattern of stress holds true for harmonic thythms of: 2 beats per chord: Cc A7 F G7(sus4) € A F G7(sus4) nA4l! | | | ) WANT 1 1 I “l s wW s w Ss wW Ss w 4 beats per chord: C6 A7 D7 67 n4p- Le py 4 !J UA | PMA ZAR Y h Ss W s w 8 beats per chord: D-7 G7 E-7 A7 n4pl- ] ig | | | lil ly UA a! 171] IN! 1 s w Ss w HARMONY 2 — Part 1 — 7 Harmonic Rhythm Due to the generally consistent use of four-beat stress patterns (strongest-weaker-strong-weakest), the harmonic rhythm in Í time is usually one or two measures per chord: Cmaj? Fmaj7 E-7. A7 D-7 G7- Cmaj7 G7(sus4) AL | | rre LrrLeccH At” 12721 172 [27717 12 il Ss W os w Ss wW s w D-7 G7 AT D7 n31 ¡A Lslreglgl Ll Al LAN EN | | PRA PA“ s w s w Stress at Cadences wili most often occur from a weak beat to a strong beat: Cadences F pe F Bo O7ísuss) F n 4) | AS, y Ly Y Cal 271 ? Í 17 fl s M— s w Ss MU—s w Tn examining many pieces of music, it is clear that V7, the primary domú- nant in a key, typically occurs on a weak stress point, and the tonic chord typically occurs on a strong stress point. In other words, cadences most often occur from a weak beat to a strong beat, for example: 1 VIZ IVmaj7 v7 F Dz7 B”maj7 c7 n4H- Le A Ar e | LJ e Ar AR ! 1 11 M7 (V7) M-7 VI7 17 V7 16 AT O D7 B-7. E-7 A7. DIT*G6 8 — HARMONY 2 - Part 1 Harmonic Rhythm s Secondary This characteristic of dominant resolution from weak stress to stronger Dominant is also found wh dary domi luti . Stress stress is also found when secondary dominant resolution occurs: Patterns Y v a VA An ar VA 3 ! Cmajz 877 ez ET dz o7 Ag TA Measure stress: S wW Ss o W : . i : h ; Beat stress: S u—— Ss Q— Ss Y—> Ss =>: 1 Viv ima AL 17 v7 16 c c7 Fmaj7 A7 D-7 G7 C6 Although the G7 in measure 4 above appears to be on a strong stress and resolves to a strong stress, the strength of the measure on which it appears is weaker than the measure on which the C chord appears, The end of a phrase (meas. 4) is “weaker” than the beginning of a phrase (meas. 5). In music with irregular harmonic rhythm, larger stress patterns that span a phrase often override detailed chord-to-chord activity. Secondary dominants are usually found on a weak beat. If they are on a strong beat, they will usually start a pattern of extended dominants. To summarize, secondary dominants typically occur on a weak harmonic stress, and usually resolve to their expected diatonic targets. There are exceptions to this pattern, but it is still a useful guide in constructing smooth, natural-sounding chord progressions. HARMON!Y 2 - Part 1 — 9  NANA a Deceptive Resolution Analysis () a e a 12 — HARMONY 2 -— Part 1 Another common characteristic of dominants can be demonstrated by continuing the previous example with a secondary dominant occurring on a very weak stress point. 6) V7 — Imaj7 VA A AAA o7 “er or maz A7 Tn this context, the A7 meets all the criteria for a secondary dominant chord: + Tts placement is weakly stressed, and + Itcan potentially resolve down a perfect fifth to a diatonic chord on a strong beat. However, when the progression repeats, the A7 resolves deceptively back to the series of extended dominant chords following the cycle of fifths: A7 — D7 — G7 — C7 — F7. This is a commonly found example of deceptive resolution and requires an appropriate analysis to show it's sound versus actual resolution. Chords are first analyzed for their sound within the progression: a V7 Imaj7 An AAA TA D7 “er *c7 “E7 Bmajz A7 The deceptive resolution is parenthesized: 6) v7 — Imaj? (A) CATA A A D7 G7 Cc7 F7 B*maj7 A7 The analysis above shows that the function of A7 in the key of Bb will sound like V7/111 (V7 of D-7), even though it does not actually resolve to TII-7. Although the parentheses (_) indicating deceptive resolution ate directly above the A7, the listenet's perception of its deceptive resolution will always be after the fact.  Deceptive Resolution Chords" Available Tensions Deceptive Resolution Although the A7 does not resolve to the expected D-—7, it does resolve down a perfect fifih. Therefore, an arrow is used to indicate its resolution. 6) V7 — Imaj7 (4) o7 “er “cr 7 Braz A7 This dual analysis (the use of parentheses and an arrow) explains that: 1. the A7 initially has one function—to create the expectation of resolu- tion to a diatonic chord. However, 2. when it resolves, it has a different, though entirely acceptable, function as a deceptive resolution to an extended dominant. Deceptive resolution requires the expectation that a dominant chord will resolve diatonically. For example, the A7 above sounds like V7/I11; the use of£b9, $9 and b13 as available tensions in a melody or chord voicing will reinforce that sound and make the deceptive resolution even clearer. A composer or arranger will sometimes choose to use tensions in the melody or the chord voicing that soften the effect of the deceptive resolu- tion, Use of optional tensions in this way is a matter of taste, style and judgment. Optional (non-diatonic) tensions will be explored in much more detail in Harmony 3. The generalities set forth here are only that — generalities. As has been stated before, any observation is ín the ear of the listener. The placement of a chord on a strong or weak harmonie siress affects the lístener's perception of its func- tion. The composer's melody, the player's note-choices, and the arranger's voicings also play a part in creating tonality and rich, compelling progres- sions, The fundamental functional relationships are the foundation on which music is built; creative extension and alteration of these concepts allows us to create almost infinite variety. HARMONY 2 — Part 1 — 13 14 — HARMONY 2 - Part 1 SUMMARY OF DOMINANT CHORD FUNCTION + PRIMARY DOMINANYT: + V7 —The primary cadence chord with expected resolution to L + Usually found on a weak stress point. + Usually cadences to tonic at a strong stress point. + May resolve deceptively. (V7) + Available tensions are most often diatonic. Note: Different veteran teachers at Berldee have historically used slightly different analysis symbols. In the interest of consistency, we will indicate deceptive resolution of a dominant 7th chord by enclosing the Roman numeral of the dominant chord in parentheses, The symbol V7/1 will no longer be used to express the primary dominant, When V7 resolves to l, we use an arrow. When V7 resolves deceptively, we will use (V7) and no arrow. + SECONDARY DOMINANTS: A + V7/-V7/1- V7/TV - V7/V - V7/ VI — The dominants of the ( secondary chords in the key. (Those chords other than 1) + Found on a weak stress point. + Expected resolution is down a perfect fifth to a diatonic chord, other than L + May resolve deceptively. Use parentheses. (V7/1D, etc. + Available tensions are usually diatonic. + EXTENDED DOMINANTES: + Dominants which are extensions outside the key but function into the key. a e o a a + Found on a strong stress point or: + Continuation of a pattern of dominant resolution following the cycle of fifths. + Available tensions are the same as V7/V. + The first extended dominant of a pattern will have a numerical indicator to show its root's scale degree.  1765) vzbs) Related 1-7 Chords The relation may appear as 1-7(5) v7é 9): 11-765) vzba) Imaj7 16 a:7és) certo)” *Fmajz F6 Indeed, any of the following combinations may occur without changing the function of the progresión: ez co* G-765) cis E AS == ES E » y ná e-7 fe)" F a-7és) Ca E 0 vo PO o — a e + = + y == = Harmonic rhythm directly affects the 1_____1 relationship. With the inclusion of a dominant chord's related 11-7, harmonic activity is in- creased without deterring from the dominant resolution. The harmonic rhythm of the y may be even: B-7 ETT a (| 4 E HE E + + H Ss W s w ez Ea — wW so w or one of the two chords may appear for longer duration: HARMONY 2 — Part 1 — 17 Related [1-7 Chords Repeated AAA A ____, may be repeated. With any of these configurations, the 11-7 will be on a stronger stress point than the V7 and the resolution of the V7 will be to a strong stress. D-7 67 D-7 67 E-7 A7 E7 A7 E AAA e + a == Ss wW s w Ss W 5 w (The G7 to D-7 and the A7 to E-7 in the above example are retrogressions, not deceptive resolutions.) “Line clichés” may occur within a H-7 V7. (Line clichés will be discussed later in this book.) D- er T*omajz ar Er ar” LA — —— A] d HA a + AA A 3 o P + F P Es = Related 11-7 chords of extended dominants may be the chord of resolution: A7 07 ar a Extended === rea Dominant EXE , + E ] Loa o = A NS = A7 AAA ca Interpolated ll-7 18 — HARMONY 2- Part 1 ox, they may appear interpolated (placed in between) prior to the chord of resolution (their related V7): Az DIT D7*er TT a7*crT ar 7 Ed tj Lu LJ Ear j E jE z > y 3 j ql Guide Tone Line Development Part 2 A short review of the 4 part Voice Leading Principles from Harmony 1 will include: + Consideration of scale tone tendencies: + Stable tones are 1, 3, and 5 of the key. + Unstable tones (2, 4, 6, 7) tend to move to the nearest stable tone. * Non-diatonic pitches tend to move to the nearest diatonic pitch, in the direction of the accidental. Sharps ascend, flats descend. + Linkage between chord tones is preferred in the following order of movement: + Common tone. + Chromatic steps, + Whole steps. + Major or minor 3rds. + Roots are in the bass voice unless a new bass note is specifically called for. + Spacing between adjacent voices is less than an octave except any interval may appear between the tenor and bass voices, . + The 5h of the chord may be omitted and any other chord tone doubled or available tension added. Q- 4 or o B7 EZ A7 D7 Fe C(sus4) % Leading Review F r F B7 Email D7É5) G7ísus4) AP? Cíaddo) HARMONY 2 -- Part 2 — 19 Harmonic Continuity Range Consideration 22 — HARMONY 2 - Part 2 It can be seen that as the harmonic continuity ís developed, the two top voices will progressively get lower and possibly infringe upon the bass. A practical range for the top two voices is from E below middle C to C above middle C. If the voices begin to appear too low for the given range, an adjustment may be made within the duration of any chord: Cmaj? A7 D7 e7 0-7 F7 E7 A7 Pr Adjusted by Inversion It also possible to adjust the position of the voices by octave transposition. Since the tonic chord represents a poínt of harmonic arrival and departute, any position is available after the I chord: Cmaj7 A7 D7 67 Cmaj7 .F7 E7 AT F P (a leading suspended Anvadditional location where voice leading may be suspended is at the end of a phrase. Harmonic Continuity SUMMARY OF HARMONIC CONTINUITY METHODS + For bass motion in fifths: + 3 to 7 --- In one voice the 3rd moves to the 7th. + 7 to 3 — The other voice moves from the 7th to the 3rd. » For bass motion in steps: + Both voices move with the bass in similar motion. + For bass motion in 3rds: + 3to7 and? to 3 (as above) may be used or: + Similar motion in all voices may be used. +* For common tone bass notes: + Adjust the chord tones, + Range considerations: + Use roots in the bass (unless a new bass note is indicated). +* Keep top two voices between E below and C above middle C. + Keep the top voices within an octave of each other. HARMONY 2 — Part 2 — 23  [RANAS Single Lines Voice Led 24 — HARMONY 2 -— Part 2 The result of the harmonic continuity method of voice leading of the essential chord tones is root motion and the two guide tones lines. Guide tone lines are single lines which are developed by the voice leading of the necessary chord tones and guide the listener through the harmonies. Individual guide tone lines may be one of three configurations: « One of the lines created by the previous process or — + The other line created by the previous process or — + A combination of the two lines: Omaj? D? Gífus)Q7 P7t5E7 D7 B7 06 1 1 Y Y ; ' : 1 a 1 : : ' E E RN, , . : : : a : PANG E == + a Note that for purposes of guide tone lines, scale tone tendencies are not the most important consideration for individual pitch movement. Of primary importance is as complete a harmonic sound as possible given the limitation of only one moving line. However, the basic guide tone line is often improved and made more interesting by the inclusion of added pitches which meet the require- ments of scale tone tendencies. Cmaj?. D? Gsus) G7 Flrés)F-7 D7 B7 Ce 7 ==: 3 A E A + + A ++ Pa + y + ' í A : A 1 , . , 1 + 4 8 Y ¡e ba 3 , = A 1 1 o! 1 HEEE ASEO 204022 + S A E == + Some of the common adjustments which can be made to improve the basic guide tone lines while observing scale tone tendencies include: + Preceding the 7th of the chord with the root. (Measures 2 ér 4) + Using the root or 5th as the guide tone line if itis logical to voice lead into them. (Measures 2, 3, 4, 85) Common Diatonic Minor Key Chords Other Minor Key Chords Minor Keys Melodies and harmonies in minor keys may be diatonic to any of the above scale sources or diatonic to a mixture of them. This is an essential quality of minor key harmony and results in its richness and variety. Despite the distinct scales we describe as harmonic sources, itis most useful to think of minor key music as a combination of all scales that have a minor 3rd: composite minor. Natural minor diatonic chords: 17 1-7(5) Pimaj7 1Y-7 V-7 Vima? PvIz Harmonic minor diatonic chords: Iomaj? 11705) imaj? 1-7 V7 PVimajz VIC7 Harmonic minor is a natural minor scale with its 7th degree raised to create a dominant-functioning V7 or VII*7 chord. Ascending melodic minor diatonic chords: Imaz 117 PHlemaj? IV7 V7 VI(5)VIL7(5) Ascending melodic minor is a harmonic minor scale with a raised 6th degree to eliminate the awkward augmented 2nd between scale degrees 6and7. Dorian minor diatonic chords: >lmaj7 1V7 VvZ7 vizzb5)'VIlmaj7 17 17 HARMONY 2 - Part 3 — 27 Minor Keys Dorian yields only a single commonly used chord that is not already in the other scales. Dorian and Phrygian are important as minor modali- ties and as modal interchange sources in major key harmonies. Modal interchange will be covered in detail in the next chapter; modal progres- sions, although very common in contemporary music, will be covered in Harmony 4. Here are all forms of the chords derived from all the minor scale sources: E Ls Emaj7 17 Thel chords (tonic) me I- 1705) 17 The II chords (subdominant) , > me Pm Pillmaj? — "Il+maj7 The "III chords (tonic) TV chords (subdominant) y- V v7 vz(9) v7(0) V chords (only V7's are dominant) The VI chords VI ve »vT6 > Vimaj7 VI-7(5) evi chords are subdominant, VIP is tonic) VI vie Pym6 PvIZ PViimaj? VIP7. VIL7(5) The VI chords 28 — HARMONY 2 - Part 3 Analysis Symbols Minor Keys The analysis symbols reflect the interval distance of the root of the chord from the tonic. In the example below, the root of the bVImaj7 chord is a minor sixth from the first degree of the scale. Even though an accidental is not necessary to notate the chord on the staff, bVI” refers to its posi- tion in the chromatic scale, and reminds us that when solfeging a bass line, it will sound as “le,” not “la.” This practice also allows us to clearly distinguish between chords built on different qualities of the same scale degree. E 27 vil) Dimaj7 — V7susd V7 ez emo. cts Cmaj7 B7sus4 B7 Some further observations about minor key harmonies: + The +maj7, -maj7 and VII? chords from harmonic or melodic minor are chord qualities that are not diatonic to major. + Although there are dominant chords built on IV, V and bVI V7is the only one with dominant function. The 1V7 and bVII7 are usually considered subdominant chords because they contain neither the leading tone to the tonic nor root motion by perfect 5th to the E chord. I£)VII7 progresses back to I, the motion can be under- stood as a subdominant minor cadence: p PI L6 1v7 G- F7 66 07 + The V—7 chord is not a dominant chord, though it is built on dominant scale degree 5, and can sound like a cadence chord. In context, if it cadences to tonic L, an arrow is not used. - TV7 17 V—”7 ec- F7 e-7 G7 e G—7 e—7 0-7 HARMONY 2 - Part 3 — 29 AVAILABLE TENSIONS — MINOR KEYS 32 — HARMONY 2 - Part 3 The available tensions in minor key are based upon the same criteria as the available tensions in major except there are many more choices of what is diatonic in minor than in major. In other words, there are more correct available tensións in minor. In addition, while in major key harmonies the 13 is normally not available on a -7 chord, it is available in minor context if it is diatonic and care is used. Available tensions for secondary dominants will be diatonic and meet the previous available tension criteria and exceptions for dominant chords. (Here again there are alternative diatonic choices). For example: % % o 3 4, 87 trom trom E from E7 from harmonic or natural harmonic or natural melodis minor minor melodie minor minor Extended dominants will have available tensions of 9 and 13 as in major key.  SUBDOMINANT MINOR Tonic Minor Non-tonic Non-dominant Functioning Dominant The natural minor chords can be categorized as either tonic sounds or as non-tonic sounds by examining which chords contain the characteristic pitch of natural minor — scale degree b6. The 11-705), IV-7, "Vimaj7 and PY117 chords contain this scale degree. 17 1765) "Mlmajl7 17 V7 Vimajz PVI7 C-7 D-7b5) Emajz F-7 G-7 Alma -B%7 Tonic minor chords: 1-7 llmaj7 e-7 Emaj7 Non-tonic chords in natural minor: 11705) 14-7 vz PVimaz uz D7é5) F7 67 Abmaj? 7 o Since the dominant structure (pVI17) in this parallel key is not built on the dominant degree (V, a perfect fifth above the tonic D), it is nota dominant functioning chord, only a dominant chord in sound. This is a subtle distinction, but when used a major key, the bVII7 chord commonly progresses back to l instead of resolving down a fifth. HARMONY 2 - Part 3 — 33 Subdominant Minor Subdominant minor is the name applied to the non-tonic natural minor chords containing scale degree b6, which has traditionally been seen as Subdominant the lowered third of the IV chord in major. These subdominant minor Minor Chords chords are sometimes found as cadence chords, as in measures 4 and 8 of this example: 1V7 1V-7 PVI7 Cmaj7 F-7 Cmaj7 C7 Fmaj7 F-7 87 Ll E E PVimaj7 11-765) v7b9) Cmaj7 A'maj? Cmaj? E-7P5) A7PO) A D7(5) G7é9y A LJ LJ p rt tr The 1-7 and bIIImaj7 chords are categorized as tonic minor chords. The strongest tonic minor sound is the tonic chord (1-7); the bIlimaj7 is a weaker tonic minor sound; the V-7 is not heard as tonic since scale degree b3 (needed for the minor key) is neither a chord tone nor an available tension: Tonic Weaker Tonic 17 PlImaj7 les 2 > IZ p AZ p e ES e Non-Tonic vV-7 he A = XK AS 34 — HARMONY 2 - Part 3 Paraliel Primary Major Parallel Natural Minor Parallel Harmonic Minor Modal Interchange Although there are many possibilities, the most common modal inter- change chords are found in parallel harmonic minor and parallel natural minor. D major Imaz? 17 IE7 IVmaj7? V7 VI7 VIL7C5) Imaj7 D natural minor 17 1275) 'imaj7 147 V-7 PVimaj? pun 17 D harmonic minor Emaj7 m7C5) >JL+maj7 1IV7 V7 » Vimaj7 Ye q The effectiveness of modal interchange relies on a clearly established major or minor key — too much mixture results ín an ambiguous tonality: G e c E pr A-7(5) D7susá D7bo) 29 Further, replacing the 1 chord with a parallel tonic, especially at the be- ginning or end of a section, is especially powerful and tends to tonicize the parallel key rather than simply color the primary key: 6- a7 Cmaj7 E7 HARMONY 2 - Part 3 — 37 Modal Interchange Mixolydian Modal Interchange Modal Interchange Available Tensions Dorian Modal Interchange Natural Minor Modal Interchange 38 — HARMONY 2 — Part 3 In addition to the modal interchange chords from harmonic and natural minor, the bVlímaj7 chord is an example of a modal interchange chord from Mixolydian. V—7 is also derived from Mixolydian. 6-7 Bmaj? 07 e Modal interchange chords, especially the group of IV chords, are some- times preceded by a secondary dominant. However, most other modal interchange chords have non-diatonic roots, so their dominants do not sound like typical secondary dominants. The available tensions for modal interchange chords are determined by either the major key in which they are functioning or by the parallel scale from which they ate derived. The choice is up to the composer or arrang- er and is subject to the familiar avajlable tension rules. Tonic Minor Modal Interchange Chords 17 9 tt 13 is available ¡f used with care 9 4113 Subdominant Minor Chords o 11b13 ba 175 “his is the rare case of 11-745) tunctioning as a subdominant minor chord (natural 9) 13 is available if used with care bVImaj7 o Hi ta bvu7 o 4 ta Modal Interchange Other Altered Subdominant Minor Chords 94113 » blImaj7 From paralle! Phrygian TV-maj7 Since maj7 and maj6 chords are interchangeable, the maj 7h degree and the maj 6th degree are interchangeable DVIZ o +13 ss +. Harmonic Minor Modal Interchange Chords » 11/13 » 1-7(5) Note that a is not available b and to may both be present in a voicing or melody. Note that 11 is not an available tension v7b9) Mixolydian Moda! Interchange Chords 9 11 vz7 13 is available if used with care >YlImaj7 ob SUMMARY OF THE BASIC MODAL INTERCHANGE CHORDS * Tonic minor: * 17 + bIlimaj7 + Subdominant minor: »- blImaj? (from parallel Phrygian) * 11-7(5) (not commonly found as a stand-alone modal interchange chord) + IV,TV-6,1V-7, IV-maj7 + bVImaj7, bVI6, LVI7 * PvIz + 11-705) V7('9) — from harmonic minor A, » bVIImaj?, V-7 — from Mixolydian HARMONY 2 — Part 3 — 39 Minor Keys 515 —6—»7 1—majz —7—6 as part of 3 6—*7 —maj7 —1 as part of Line clichés Within Major Chords 42 — HARMONY 2 — Part 3 Though line clichés are associated with minor keys, they will be found in Tajor key harmonies. Most often on the I-, IV-, and VI- chords: Iv- F- ? Teis not unusual for the line cliché to be present on the II- chord and to be completed on the V7 chord: Y- v7 D- G7 AA2 AA SS P P P AT Or the line cliché may appear as part of a dual function secondary dominant progression: vi Y, A-6 A7 Ax(maj7) D7 CI In major, line clichés may appear on the 1 major and IV major triads. Blues Blues and Melodies ¡ANY ERy3 Paga! Blues harmonies have their basis in early American church music. The acencs primary cadence used in hymns of the Protestant church has been subdominant (with dominant cadences being less important). Subdominant cadence is traditionally called “plagal cadence”: Iv 1 e F g Typical of plagal cadence is the sound of “A-men”, used following most hymns: Iv I 8 F g Primary Blues Triads Thus, the primary chords found in blues are the l and IV chords. The basic scale used for blues melodies is a pentatonic (5 note) scale, but NOT the major pentatonic scale. The blues scale is NOT diatonic to the harmonies: Blues Melodic 1 3 4 5 1 5 4 3 1 Scale The above scale (scale degrees 1, , 4,5, ”, 1) can be seen as a minor pentatonic scale. The important characteristic of the blues scale is its exclusion of any half steps and the relationships it creates with the major key harmonies; the scale degrees »3 and?7 create an unusual sound with the major key harmonies. This melodic relationship with the harmonies results in the “blue notes”: HARMONY 2 — Part 4— 43 Blues Primary Blues Seventh Chords Primary Tensions for Seventh Chords 44 — HARMONY 2 — Part 4 When the blues melodic pitches are superimposed over the harmonic structures, the extensions for the seventh degrees of the fundamental chords can be added: The I and IV triads therefore become 17 and 1V7 respectively: The basic available tensions for the primary chords are those which appear melodicaliy: Y : V7 F7d0) 7(9) 175 dh s 719 An exception to the previous observations regarding available tensions should be noted in the case of the 17('9) chord in blues. Though *9 and la normally may coexist, »9 should NOT be used with 9 on the 17 chord in blues since it is not part of the blues scale. The 9 tends to suggest dominant function; 17 in blues is tonic. Ade Added lelodic 5 (a) Available Tensions Blues The basic blues melodic scale has become more complex also; it now contains chromatic motion between the 4th and 5th scale degrees - »5 orlá, The contemporary blue notes are », 5, ds, YA 1katos to1ostsostror The available tensions for the three basic blues chords are those which meet the previous criteria: + Diatonic to the blues scale or borrowed from diatonic major; + Either a major 9th or a 49th above a chord tone; + For the dominant functioning V7 chord, » may be added since 19 ¡s diatonic (as is 23). Diatonic to blues: Added pitches diatonic to major: 7 T7 I7 E7ho) F749,13) — F7(9113) 1Y7 v7 v7 v7 do) crtota»13) c7(9413) Any additional diatonic chords or secondary dominants or extended dominanis from major key harmonies will have available tensions from their major key context. HARMONY 2 — Part 4 — 47 Blues BLUES VARIATION: Primary Chords' Placement 48 — HARMONY 2 - Part 4 There is one important characteristic which can be seen in all blues: the placement of the primary chords within the 12 measure form: o _Fonic - . eS + + j p Subdominant Tonic E : = e 2» Cadenee Tonic E 3 ol Variations to blues demonstrate this pattern in two different ways: + Harmonic motion from and back to the primary chord in each area of the form, and /or » Harmonic movement to the next primary chord (the tonic chord in measures 1, 7, and 11; the subdominant chord in measure 5; the first cadence chord in measure 9). Thus, a tonic chord will appear in the first measure; any subsequent harmonic activity in the first 4 measure phrase will be back to the tonic chord and /or motion to the subdominant chord which appears in the 5th measure: a F7 87 F7 A-7(8) 1114) Subdominant B7 «> qn Ll «8 u-745) tve Blues In the previous example, there is a subdominant cadence back to the primary chord (tonic) from measure 2 to 3; measure 4 contains a com- monly used blues chord which approaches the IV chord. The 15-765) can be identified as an upper structure of the 17(9) chord (which may also be seen as the secondary dominant of TV (V7/IV): AT7Ú5 F7 Measures 5 and 6 will start with the subdominant and contain motion back to subdominant and /or have movement to tonic in measure 7: Tonic . F7 B7 F7 A-765) És y y , ] á Tonic Subdominant a er e ea Y ES + + ] Sy - , Le , $ Í 3 e The B”7 occurring in measure 6 is another commonly found blues chord. ThetIV*7 chord is an approach chord to 1 from IV; most often the resolution of its root is chromatic and therefore the 1 chord appears inverted. This is an example of a blue note as a root function: 17 hvz7 7 »> 87 B%7 FZ % HARMONY 2 - Part 4 — 49 Melodic Construction MELODIC SCALES AND INTERVALS 52 — HARMONY 2 - Part 4 This section of Part 4 is an overview of melodic construction and methods of melodic analysis. lt should neither be viewed as a complete course ín song writing nor composition in general. However, the materials discussed will assist the student in understanding how melodies are created and how to observe what makes the good songs persist, Scales have long been the source for melodies. By examining a universally known melody, some observations about melodic scales and intervals can be made. JOY TO THE WORLD : 2 3 . 93 ; 4 4 = + + E 2 , . 7 . ¿ . E e E > EA Í A+ — =- S E E pa on s 1 EéÉ a == EE Z ] ol E + p ny w 1 ae + + E : z 4 es z S $ A This traditional carol demonstrates typical scale /melody Characteristics: The melody begins with a complete descending major scale. Note the locations of the half steps: Melodic Construction The melody turns around and ascends through the upper tetrachord (leaping over the lower tetrachord): The original descending scale occurs twice again but is incomplete; from scale degree 1 down to scale degree 3 only: 7 9 so pr . A EE EE HAS = > EE O 00 There is then a series of three notes in opposite directions which finish using the missing 2 notes from measures 8 into 11 (scale degrees 2 and 1): "a a 1 15 18 et — + = — as sE E e y The last four measures begin with the incomplete scale from measures 8 into 11 but here the top portion of the scale has the 7th degree omitted: pe EEE ses Ye 1 01 Why omit the 7th degree? (The following is pure conjecture, since the composer could have used the 7th degree.) However, it appears unnecessary since this portion of the original scale was used twice already in measures 8 — 11 at the top of the page. The forward motion of the entire melody is preserved in the 4th measure by the leap over the lower tetrachord which finally appears as the last four notes of the tune. Tf the composer had chosen to use the entire scale in measures 4 through 7, there would be no reason to continue! 1 2 3 “ 6+ + e Pas E == EH += == 3 + E + $ —i > — HARMONY 2- Part 4 — 53 Melodic Construction 54 — HARMONY 2-— Part 4 Here is the melody with the stable pitches shown. Note that each scale sequence begins and ends on a stable pitch with the exception of the three note scale in measures 14 and 15, and with the same exception, the stable pitches occupy most of the dovn beats as opposed to off the beats. (Many simple songs, such as the example used here, contain portions which are mainly constructed of stable pitches. The more unstable pitches used, the more sophisticated sounding the song becomes.) : 2 s a 9, + 7 La E EA 2 E => e = ¡a s . 7 a Ae E E e 2H | e T Y y A — o so “ cd = ÉS A == ya “ s s , E AA A ! . 2 5 E + w sw » F bt F a y] Y A RES G E + ] e » Va There are only four leaps in the entire tune and all are from a stable pitch. When a pitch is leaped from, it tends to be exposed to the listener and retained. The key of D major is very strong since the stable tones (the diatonic tonic chord) are stressed both rhythmically and intervalically. Intervals can be used to describe melodic pitch relationships. The range of the melody is a perfect octave from D to D. The opening melodic statement is a major scale which descends that octave: 1 2 a 4  oO, Climax Melodic Construction Here the melodic curve is exagerated: 1 2 a 4 5 8 7 a The melodic curve of this tune helps to show: + The directional movement down or up. + Repeated pitches or long notes where the melody “siows down.” + The repetition which occurs in measures 8 - 9, and 10 - 11 is observable. * The sequence in measures 12 - 13, and 14 - 15 is observable. * The melodic leaps appear as “spikes” while the conjunct motion appears smooth. + The largest leap (an octave) occurs in measure 16, four measures before the end. This may be described as the melody's climax, the point where the strongest stress is placed. Most good melodies contain a climax around % or more towards the end. This ensures the attention of the listener for the duration of the melody. HARMONY 2 — Part 4 — 57 Melodic Construction MELODIC MANIPU! je] Repetítion * Sequence Inversion Retrograde Retrograde inversion 58 — HARMONY 2 — Part 4 The repeating of melodic motifs has been seen in previous chapters; repetition and sequence are examples of the simplest forms of motif manipulation. Melodic ideas are repeated in order to instill in the listener predictability and coherence and at the same time creating interest through diversity. Without this continual use of singular fragments, the melody would tend to ramble from one idea to the next, never fortifying the composer's initial motif. Many melodies axe written intuitively, but when examined they will be found to contain simple ideas which are subtly repeated in disguised form. The following examples represent the melodic alteration devises used for development of motivic ideas: el The motif may be moved to another pitch level: Sequence , E E = ] S 5 E + ja The motif may be presented upside down: Inversion 4 + Y a dz AS j (This inversion is also moved lo a different pitch level and the interval The motif may appear backwards: relationships remain diatonic,) Retrograde 2 + + Ha E + sy + $ ES == + = + j The motif may appear both backwards and upside down: Retrograde Inversion $ E E + E E =p. E === E  Interval Expansion Interval Contraction Chromatic Alterations Melodic Construction The intervals within the motif may be made larger: Expansion — ===>, HE y > - f (The motif ls also sequenced) The intervals within the motif may be made smaller: Contraction 4 , E ae E o e $ a E A (The mati is also sequenced) The motifs may be connected with a common pitch: (Common pitch) (Here the motif also appears in retrograde) All the above examples have been consciously held to the diatanic. However, all the manipulation techniques are possible with chromatic alterations: EÉ + + EX E + ES j e ma a NOOO, o y == ? y o When rhythm is added to the equation, the potential transformations are almost unlimited. Here portions of the original motif is reduced in rhythmic values: HARMONY 2 — Part 4— 59 Melodic Construction Song Form 62 — HARMONY 2 — Part 4 Phrase lZ—m==_— == Phrase 2 “A sentence is incomplete, “The period signifies until a period appears.” the conclusion of the thought.” In the example, the “story” about the sentence is complete enough to give the reader the information necessary to know “why” the sentence is incompleto; the first section is complete. However, it would be more informative for us to get more information about the importance of the above statements. Therefore, the composer could go on to explain further using additional sections until the song is finished: Section A ._ Section B_ -— — Added sections as needed, Phrases 1-2 Phrases 3-4 Additional phrases Though the lyrics of this imáginary song continually change, the music they are sung to will often repeat as shown before. In fact, in real music, the lyrics may, and often do, repeat also. The sections within a song make up the song forin of the music and are universally designated alphabetical: A = First section and any susequent repeats of that section. (Lyrical changes and very minor music changes are disregarded.) B = Second section and the repeats of it. C = Third section and the repeats of it. D- and so forth. Some of the common song forms are: Á AB ABA AAB AABA ABAC ABCA ABABC — ABACD There are not many songs with more then four differing sections. Another very common method of repetition of melodic ideas occurs within a song. Most songs (and in fact compositions of all kinds) contain sections which are literal repeats of previous sections. The repetition of complete musical statements aids the listener with recall of the basic content and adds cohesion to the overall composition. Melodic Construction The following is the example song analyzed for structure: form; phrases; motifs; motif manipulations. JOY TO THE WORLD Phrase 1 F 7 measures fl + , 3 í z TS 2 E E = A La. “Ti Mot Perfect 5th Leap (Phrase 1) Phrase 2 —1 4 measures q . - ] E E PE 43 $ + p = == ] Motif. restatement Retrograde (1st half) (incomplete) (Phrase 2) Phrase 3 " 4 measures ay ma | > z ==> o z E = > AAA o Repetition Retrograde Minor Sth Sequence Leap (Phrase 3) Phrase 4 1N 4 measures 'quence Repetition (expanded) Octave leap (Phrase 4) 7 se 19 ! pb == - 4 AAA Repetition Song form -— A (one complete section) N.B.: There is a lot of analysis on this page! Good musicians will differ as to its validity. However, though it may not be correct to some, itis not wrong. There will be many analysis possibilities. HARMONY 2 - Part 4 — 63 Melodic Construction An equally acceptable and appropriate analysis might be as follows: Phrase 1 pt e A Á f= E AE j = => A, 7 L— Motif Sequence Perfect 5th Leap Phrase 2 Phrase 3 a. measures — 1 r 2 MEASUTES pa E E + AER e Y Y 7 Y == f Retrograde Repetition Elision (Phase 3) Phrase 4 Phrase 5 o 2 measures Pr 2 measures He >= 53 HEEE 25 E + dae n= y Ñ Sequence Repetition Sequence Retrograde Minor 6th Sequence Leap Phrase 6 Phrase 7 ans ! [ 2 measures r 4 measures A E == == j s E a] $ : > Y 'equence Retrograde Sequence| Repettiom Sequence (expanded) Octave Leap (Phrase 7) 1 04 == E === = y XT) Sequence Though the phrase lengths for this analysis are shorter, even by combining them and applying the criteria for sections, the song form will remain A. 1f the lyrics were taken into consideration, although they would change for each repeat to the entiré melody, the form would remain: A repeated. Additional analysis possibilities may include combination of both of the above, and the analysis on the previous page. Within limitations, the correct analysis is in the eyes and ears of the beholder! 64 — HARMONY 2 —Part 4 Anticipation Delayed Attack Melodic Construction Style also effects our perception of rhythm. Jazz and styles of music which contain jazz influences (many contemporary styles of popular music) will be seen to contain syncopations. Instead of the melodic pitches occurring on the beats, as was seen above, the pitches will often appear prior to the stressed beats or occasionally after the stressed beat: Anticipations are those pitches which: » appear a half beat prior to the stress (or rarely a full beat) and + are tied into the stressed beat O or + followed by a rest on the stressed beat O . y O o e e) Delayed attacks are those pitches which: * appear a half beat after the stress (or rarely a full beat) and + are preceded by a rest on the stressed beat. HH HARMONY 2 — Part 4 — 67 Melodic Construction Cadence Augmentation Diminution - 68 — HARMONY 2 — Part 4 Of special importance to melodies is the melodic cadence. Most often the cadence will occur to a strong stressed beat. Melodic cadence pitches are typically the stable pitches of the scale. + + y Cadence , Es EEE pi q + = y 4 — 1 > Ss w s w s W s w E = Y y u E E + + 3 y => s wW s s w Rhythmic alteration is a subtle means of disguising repeated motifs. Melodies may contain augmentation or diminution of rhythms. Augmented thythms are stretched out in time while diminished rhythms are reduced in time: Augmentation + E y + ] + HÍ y >> 555552) + al 1 + tl Diminution >= 20H = + a - + 1 MEL: 4 Approach Note ( Passing Tone Chromatic Passing Tone Y/HARMONY RELATIONSHIP Melodic Construction In the previous chapters dealing with melody, the emphasis has been on observing the overall shape and content of melodic fragments and viewing the melody as a whole. The focus will now be on the individual note relationships to each other and to the harmonies. Every melody note can be: » An available pitch to the harmony as either a; Chord tone or An available tension. + An approach note. + A choice of the above. An approach note is a melody pitch which is a beat or less in duration and which moves by steg to a target note. The target note is either a chord tone or tension. Approach notes are found in many configurations. A passing tone is an approach note which moves by scale step between two available pitches a third apart: D-7 D-7 D-7 D-7 Ef E + A yr E y NH) a + 7 E 4 y == GS * 9 9 ' The approach notes are circled and the target pitch is identified. Traditionally a passing tone is defined as a non-chord tone which moves by step to a chord tone and is usually found on a weak beat, Note that in the above example, the more contemporary situation where the passing tone may pass between either a chord tone or tension to another chord' tone or tension. Passing tones may also be chromatic. Unlike-scale passing tones, they will most often be non-diatonic to the key at that moment: D-7 e7 Cmaj? Lp + A + Ea Py y — RAS $ j HARMONY 2 - Part4— 69 Melodic Construction Double Time Feel Melodic Suspension Repeated Motifs 72 — HARMONY 2 - Part 4 Some styles of music incorporate double time feel in the notation. Although the time signature may indicate a pulse of quarter notes, the feel of the beat is at the eighth note level. Therefore the primary beat value for the notes is doubled: F C7(susá) 67 07. B7 F7 Delayed attacks will not affect the harmonies as do anticipations. Ar7 D7 G D, a de A $222 j e 2 3 A melodic suspension is a melody pitch which is tied from one chord into another for a beat or less. When melodic suspensions occur, the harmonies will change when the melody resumes movement. (However, the harmonic rhythm is still perceived by the listener as changing on the stronger stress points. fa chordal instrument and/or a rhythm section is involved, the chords in the underlying harmonies may actually change.): D E7 A7 7 E7 O AT in O a + 3 oa PA q 3 N_—_———— B 3 (11) Of importance to the analysis of any given melody is the concept of repetition. Most often, when a section, phrase, motif is repeated, either exactly or ina disguised form, the analysis of the individual notes will follow the same repeated pattern: Cmaj7_G7(susá) C6 Fmejz B-7(8) E7 A-7 D7(9) A E o al + RASO AAA e 1 1 “Y T + 94 4113 5  Melodic Construction Choices are available when observing melodic approach notes. Both the previous analysis and the following, though different, are equally plausible. Again, the choice is in the ear of the beholder: Cmaj? G7(sus4) C6_ Fmaj7 B-765) E7 AZ: -D7b9) q - E E. E 5 F Po e + A + + + Y 5 4 1 13 5 Approach notes usually appear on weak stresses, though, as in the case of the A in measure 3 (since it must be an approach note), they occasionally will be on the beat. SUMMARY OF APPROACH NOTE PATTERNS + Approach notes must resolve to a target note by step (half or whole). + The target note must be available to the harmony. + Notes not available to the harmony must be approach notes; available tensions and chord tones may be approach notes. » If the motif repeats, the approach patterns will most often repeat. » Approach notes are most often on weak stresses, Stressed approach notes are uncommon. + The approach note patterns are: + Passing tones + Unprepared approach notes » Upper and lower neighbor tones + Double chromatic approach notes + Indirect resolutions HARMONY 2 — Part 4— 73 HARMONY 2 VOCABULARY 12 bar blues antecedent anticipation approach note augmentation auxiliary blues blue notes climax conjunct consequent contraction deceptive resolution delayed attack diminution double chromatic approach double time feel disjunct dual function expansion extended dominant form guide tone line(s) harmonic continuity harmonic rhythm indirect resolution interpolated inversion leap line cliché melodic curve melodic suspension meter modal interchange motif (motive) neighbor tone non-dominant function parenthetical analysis passing tone phrase plagal cadence primary dominant repetition retrograde tetrograde inversion secondary dominant í section sequence similar motion stress pattern strum, the subdominant minor unprepared approach