JAZZ COMPOSITIONS BASED ON THE CHORD PROGRESSION FROM THE "GOLDBERG" VARIATIONS
CLARK L. JOHNSTON
A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS
GRADUATE PROGRAM IN MUSIC YORK UNIVERSITY TORONTO, ONTARIO
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1*1 Canada Abstract
This thesis is an analysis of my compositions that are based on the same chord progression as J.S. Bach's "Goldberg" Variations. It also explains some of the fundamental concepts, as well as a bit of the history behind Bach's piece. Acknowledgements
I would like to give my gratitude first and foremost to my wife Silvia and daughter Naomi for their support and patience through this fascinating, but at times, trying endeavor.
Secondly, I'd like to thank my Mother and Lynn, without whom it would have been impossible to take this journey. Last, but definitely not least, I'd like to thank my advisor
Michael Coghlan for making this potentially daunting task as simple as possible.
-v- Table of Contents
Abstract iv
List of Figures vi
Introduction 1
The "Goldberg" Variations 3
"Variation #1" (Score) 11
"Variation #1" 18
Bach's Minor Variations 26
"Variation #2" (Score) 28
"Variation #2" 33
Bach's Fifth Canon 36
"Variation #3" (Score) 40
"Variation #3" 55
The "Interlude" 59
The "Head Out" 60
Conclusion 61
List of Works Cited 62
Discography 63
Appendix A: The Aria in Bach's own handwriting 64
Appendix B: Printed copy of the Aria 65
Appendix C: Variation #15 in Bach's Handwriting 66
-vi- Appendix D: Printed copy of Variation #15 67
List of Figures
The "Goldberg" Variations
Figure 1: The original published cover 6
Figure 2: List of Variations 8
Figure 3: The chord progression by analysis 9
Figure 4: Chord progression in figured bass 9
Figure 5: Progression in modern chord symbols 9
Figure 6: Chord progression divided into two sections 10
"Variation #1"
Figure 7: First three bars of melody in "Variation #1" 19
Figure 8: "Variation #1" with Bach's Chord progression 20
Figure 9: "Variation #1" (excerpt) - measures 3-4 of the melody 26
Bach's Minor Variations
Figure 10: Literal translation into the parallel minor. 26
Figure 11: Literal translation into the parallel minor in modern chord symbols. 26
Figure 12: Bach's chord progression in "Variation 15". 27
Figure 13: Bach's "Variation 15" in modem chord symbols. 27
-vii- "Variation #2"
Figure 14: Variation #2 with a literal translation of Bach's progression. 34
Figure 15: Early version of "Variation #2" 35
Bach's Fifth Canon
Figure 16: Bach's 2 voices of "Variation 15" lined up metrically 37
"Variation #3"
Figure 17: Bars 11-12 of "Variation #3" 56
Figure 18: The derivative lines for "Variation #3" 57
Figure 19: The "rhythmic" lines of "Variation #3" 58
Figure 20: The "condensed" version of the sax line. 59
-viii- Introduction
J. S. Bach's "Goldberg" Variations (originally entitled Clavier-tibung) has long been influencing jazz musicians. One of today's most renowned jazz pianists, Keith Jarrett, has recorded Bach's piece. (Bach, 1989) Such notables as Uri Caine (Bach, 2000) and
Jacques Loussier (Bach, 1999) have recorded their own renditions of the "Goldberg"
Variations in a jazz style. I have written my own set of compositions based on the same harmonic progression that Bach used throughout the piece, and this thesis is an analysis of my compositions and of the choices made in the compositional process.
The idea for this thesis came to me while I was working on an essay for an analysis course. I had taken on the challenge of analyzing the "Goldberg" Variations and was familiarizing myself with the chord progression that the variations are based on by improvising on them with my acoustic bass. I was alternating playing bass lines over the form with soloing over the form when I started to create different melodic lines over
Bach's progression. To familiarize myself more with Bach's progression, I started writing down some of these ideas and ended up composing a piece based on it. That was when I realized I could perhaps write my own set of variations and use them for my thesis.
I used Bach's progression without the repeats because I just found it redundant to repeat
-1- the first halves of my pieces and then go on to repeat the second halves as well. I used
Glenn Gould's early recording of the "Goldberg" Variations as my inspiration for this, as he leaves most of the repeats out during his performance. (Bach, 2002)
All of my variations have been written in latin jazz styles. The first one is a bossa nova, the second, a samba and the third uses a straight eighth note feel that starts in 5/4, then moves to 4/4, and ultimately 3/4. Bach wrote in the different styles of his day and I felt it appropriate for me to do the same. I did not want my compositions to sound like Bach's music. I feel that Bach wrote like Bach better than anybody ever has or ever will. As well, Brazilian jazz is a form of music for which I have an affinity due to my extensive experience as a performer.
My variations are meant to be performed in a conventional jazz context. That is, they are meant to be improvised on once the melody has been stated. After the initial statement of the melody there are solos by various instrumentalists and then there is a final statement of the melody. The only exception to this form is in "Variation #3" where the melody occurs between each solo as well as at the beginning and the end of the performance. Each time the melody enters, it is a little different because this variation changes time signatures. The melody is rephrased to fit into the new time signature.
It has been a real musical adventure and learning experience exploring one of the great
-2- masterpieces and using it as a framework for my own compositions. I have found that every time I embark on the journey of writing a new piece I never know where it will lead me and that I learn something new. My pieces were never written in order to be compared to or to challenge Bach's genius, but were written as a humble show of gratitude for what
Bach and his music has done for me.
The "Goldberg" Variations
Before I delve into my compositions and how they work, it is important to discuss the
origin and some of the fundamental features of Bach's "Goldberg" Variations. Published
in 1741/42, it has long been believed that the "Goldberg" Variations were written for
Count Keyserlingk of Dresden to be played by his house harpsichordist Johann Gottlieb
Goldberg when the Count was having trouble sleeping. This story has long been
perpetuated because it appears in the first published biography of Bach by J. N. Forkel
from 1802 where, on the subject of the "Goldberg" Variations, Forkel writes:
We owe them to Count Kaiserling, formerly Russian Ambassador at the Saxon Electoral Court, who frequently visited Leipzig with Goldberg, already mentioned among Bach's pupils. The Count was a great invalid and suffered from insomnia. Goldberg lived in the Ambassador's house and slept in the adjoining room, to be ready to play to him when he was wakeful. One day the Count asked Bach to write for Goldberg some Clavier music of a soothing and
-3- cheerful character that would relieve the tedium of sleepless nights. Bach thought a set of Variations most likely to fulfill the Count's needs, though, on account of the recurrence of the same basic harmony throughout, it was a form to which he had hitherto paid little attention. Like all his compositions at this period, however, the Variations are a masterpiece, and are the only example he has left us of this form. The Count always called them "my Variations" and was never weary of hearing them. For long afterwards when he could not sleep, he would say, "Play me one of my Variations, Goldberg." Perhaps Bach was never so well rewarded for any composition as for this. The Count gave him a golden goblet containing one hundred lois d'ors, though, as a work of art, Bach would not have been overpaid had the present been a thousand times as large. It may be observed, that in the engraved copy of the Variations there are serious mistakes, which the composer has corrected in his own copy. (Forkel p. 119-120)
In the book entitled Bach: Essays On His Life and Work, Christoph Wolff attacks the validity of this story:
Actually there is no documentary evidence to support Forkel's statement. On the contrary, a number of facts show Forkel's account to be rather untrustworthy. For one thing, for a commissioned work not to include an official dedication in its published version contradicts eighteenth-century custom. The original contains no trace of a dedicatory inscription. Also, the age of the doubtlessly gifted Johann Gottlieb Goldberg (1727-1756), who was brought to Bach in Keyserlingk in 1737 for instruction and was subsequently engaged as the latter's house harpsichordist, would seem to make it highly improbable that Bach had him, barely thirteen years old, in mind when he planned the work. On the other hand it is certainly conceivable—and there may lie the true seed of Forkel's anecdotal remark—that after the publication of the work Bach may have dedicated a freshly printed copy of the work to his patron, the count, from which Goldberg may frequently have played to while away the sleepless nights of his master. It can be proven that Bach stayed at Keyserlink's Dresdon house in November 1741, and it seems highly plausible that Bach gave him on that occasion a presentation copy of the last part of the Clavier-Ubung hot from the press.
All internal and external clues indicate that the so-called Goldberg Variations did not originate as an independently commissioned work, but were from the outset integrated into the overall concept of the Clavier-Ubung series, to which they constitute a grandiose finale. (Wolff p 212-213)
Clavier-Ubung is a German word meaning keyboard practice or exercise. The
-4- "Goldberg" Variations is the last set of keyboard exercises in a four part series. As can be seen in Figure 1, this piece was originally entitled Clavier-
Ubung, not Clavier-Ubung TV; it was nonetheless the fourth published Clavier-
Ubung. The first being Clavier-Ubung I or The Six Partitas. The second being Clavier-Ubung II, consisting of two parts known as The Italian
Concerto and The French Overture. And the third set being called Clavier-
Ubung III.
-5- Figure 1: The original published cover (Deadleafonafence, 2010)
L ' ' h "i 6 *•
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-6- The "Goldberg" Variations consists of an aria and 30 variations for solo harpsichord.
The variations have a similar chord progression to that of the aria, but the melodic material is varied throughout, like a chaconne. Every third variation is a canon except
#30 (which is a Quodlibet, a humorous medley combining several popular melodies), totaling nine canons altogether. Each of the nine canons is a canon at the interval of the
same number as its number in the series of canons; for example, the first canon, Variation
#3, is a canon at the unison. The next canon, Variation #6, has the following voice up a
major 2nd from the leading voice and so forth. It is interesting to note that the 3rd, 4th
and 8th canons have the following voice below the leading voice by the corresponding
intervals. Also, the 4th and 5th canons have the following voices in inversion. If we
leave aside the initial and final material of the work (specifically, the Aria, the first two
variations, the Quodlibet, and the aria da capo), the remaining material is areanged as
follows: the variations found just after each canon are varying Baroque forms which are
three dances (4, 7, 19), a fughetta (10), a French overture (16), and two ornate arias for
the right hand (13, 25). The second variation after each canon is an arabesque, "a fanciful
piano piece. Ornate passage varying or accompanying a theme" (Thinkquest, 2010). All
the variations are in G major except variations 15, 21, and 25, which are in g minor.
Figure 2 is a list of each variation and its corresponding key signature, time signature, bar
length, number of voices, character and the number of manuals or keyboards to be used
(Fujita 2010). This piece was written for a harpsichord that had two keyboards.
-7- Figure 2: List of Variations (Fujita 2010)
Name Key Rhythm Bars Voice Manual Character Aria G major 3/4 32 Variation 01 G major 3/4 32 2 One Vanation 02 G major 2/4 32 3 One Variation 03 G major 12/8 16 3 One canon all Unisono Variation 04 G major 3/8 32 4 One Vanation 05 G major 3/4 32 2 One or Two Variation 06 G major 3/8 32 3 One canon alia Secunda Variation 07 G major 6/8 32 2 One or Two Variation 08 G major 3/4 32 2 Two Variation 09 G major 4/4 16 3 One canon alia Terza Variation 10 G major 2/2 32 4 One Fuguetta Vanation 11 G major 12/16 32 2 Two Vanation 12 G major 3/4 32 3 One canon alia Quarta Variation 13 G major 3/4 32 3 Two Variation 14 G major 3/4 32 2 Two Variation 15 g minor 2/4 32 3 One canon alia Quinta trio sonata(Rahn, 2010) Variation 16 G major 2/2-3/8 48 One French Overture Variation 17 G major 3/4 32 2 Two G major 32 Variation 18 2/2 3 One canon alia marcia G major 32 Variation 19 3/8 3 One G major 32 Vanation 20 3/4 2 Two Vanation 21 g minor 16 4/4 3 One canon alia Settima Variation 22 G major 32 2/2 4 One Alia breve Variation 23 G major 32 3/4 24 Two Variation 24 G major 32 9/8 3 One canon alia Ottava Variation 25 g minor 32 3/4 3 Two Vanation 26 G major 32 18/16-3/4 3 Two Vanation 27 G major 32 6/8 2 Two Variation 28 G major 32 canon alia Nona 3/4 3 Two Variation 29 G major 32 3/4 3 One Variation 30 G major 32 Two Ana da Capo G major 4/4 32 4 Quodlibet 3/4 One
A simplified version the chord progression for the aria and, consequently, most of the
variations, is shown in Figures 3, 4 and 5, first by analysis, then in figured bass, and
finally, in modem chord symbols.
-8- Figure 3: The chord progression by analysis
1:1 V6 vii6/V (or vi) V | 1 16 ii6 V I 1 | I V6 vi V7/V | I V6 vi6 V7/V V :| ||: V7 16 ii6 V7/vi | 1 vi IV (or ii6) V7/vi vi 1 I ii6 16 ii V7 | | V7/TV rv V I :|
Figure 4: Chord progression in figured bass. (Goldberg, P. 3)
3,5.6# 3,5,6 iXjSS=£S= m 1£X_ ~&~ ~~o~-
6 ^m=^ JOE:
6 ft 6 3,5,6 # _Q_ JQL. .©— JQL ^ lEt.
3,5.6 *53 3 -o- -o- 33c;
Figure 5: Progression in modern chord symbols
:G D/F# C#o/E(orE-) | D G/B A-/C D | G G D/F# E- | A7 D/F# E-/G A7 | D :D7 G/B A-/C | B7 E- C (A-/C) B7 | E- A-/C G/B A- | D7 G7 C D | G
-9- The two sections of sixteen bars each, which could be thought of as A and B (see
Figure 6).
Figure 6: Chord progression divided into two sections
11:1 I V6 I vii6/V (or vi) V 1 16 I ii6 1 v I | I I V6 1 vi V7/V I V6 | vi6 | V7/V V B ||: V7 1 16 I ii6 V7/vi 1 vi | IV (or ii6) I V7/vi vi I ii6 1 16 1 ii V7 | V7/TV 1 rv 1 v I
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A V SJL^^O ((J/AQ //// 77777777//// 7777 ^777 ^^^777/ JIO V =ff f iuraig 6^3 A3 0/A«™a e^asiA™™^ tunuV a/A <™D jtH/iQ //// 77777T77////7/// 7/// 7777//// M2S I UIU, U1UJ fEU £uiuia 6^3 t3 D/i™iia6<|Aas //// 777777T7////7/// 7/// ^7^^7 7 7/ }di fp £ itmug 6^3 A3 O/tUitug ^as^inuiKj timiry a/A oiO tfj/z.CI 18 [IID] "Variation #1" This piece is performed as a bossa nova. Figure 8 shows "Variation #1" with Bach's chord progression above mine. The chord progression is very similar to the one in the "Goldberg" Variations except that I add sevenths and ninths to most of the chords, as opposed to leaving them as triads. The first chord (G6) is a G triad with the sixth degree of the G major scale added to the chord. This chord is often thought of as a more resolved sounding chord than the major seventh because it does not have the tension between the root and the major seventh. The major seventh of a maj7 chord can have a tendency to want to resolve up a semi-tone to the root. The second chord (F#dim7) can be thought of as D7b9/F# without the root (D). The original chord in Bach's progression is a D/F#, so by adding a minor seventh and a flat nine to Bach's chord we get D7b9/F#. One of the beautiful aspects of diminished seventh chords is that, because they are symmetrical chords made up entirely of minor thirds, they can be resolved in different ways. An F#dim7 has the same four pitches or enharmonic equivalents as Adim7, Cdim7, and Ebdim7 (or D#dim7), they just have different spellings. They can be thought of as the same chord in different inversions. So if we take these four diminished seventh chords and put major thirds below all of them, we come up with F7b9 (Adim7), Ab7b9 (Cdim7), B7b9 (D#dim7) and D7b9 (F#dim7). The common diminished -18- chord that all of these dominant seventh flat nine chords share allows them to substitute for each other. Therefore, the F#dim7 in the second bar of my composition not only implies a D7b9/F# chord but it also implies a B7b9/F#. With the Emin7 approaching in measure three, the B7b9 would resolve nicely to it as it is a secondary dominant leading to that chord. The reason I wanted the F#dim7 in the second measure was that I wanted the D# in the melody and I still wanted Bach's F# in the bass (see Figure 7). Figure 7: First three bars of the melody in "Variation #1" G6 Fttdim7 Emin7 A7 -19- ure 8: "Variation #1" with Bach's Chord progression written above mine. Bach's Chord Variation #1 Clark Johnston Progression: G D/F# C#dim/E D 6 7 -20- The three different notes in each bar of Figure 7 make up different triads: the first being a G triad in second inversion, and the second and third being D# and C# diminished triads. The brackets above the melody show that it is a falling sequence with the exception of the D# in the second measure. In keeping with Bach's progression I could have instead made that D# in the melody a D but I preferred the movement that the D# gave the melodic line, setting up the need for a resolution to the Emin7 chord. This type of chord progression occurs in countless jazz and tin pan ally compositions. It is very similar to the first six bars of the old standard There Will Never Be Another You by Harry Warren and Mack Gordon, which in the key of G major is: | Gmaj7 | Gmaj7 | F#min7b5 | B7b9 | Emin7 | A7 | The difference between my chord progression and the common one found in There Will Never Be Another You is that my chord progression does not have the secondary EImin7b5 chord of the relative minor. The F#dim7 in my composition gives the illusion of going to the II chord of e minor by having the F# in the bass, but it functions more as a dominant chord. I could have just gone with the old progression of the II-V to the relative minor (like the one just discussed) but I wanted Bach's bass movement and I wanted to write something a little different from what has been written for countless compositions. In fact, out of habit, the first few times I performed this piece I found myself unintentionally following through with the rest of the old standard progression that goes II-V of rv instead of resolving back to Imaj7 in measure five. So what I wanted to play was: | G6 | F#dim7 | Emin7 A7 | Dmin7 G7 | Cmaj71 -21- When I performed this composition with Toronto guitarist Geoff Young, about the harmonic structure, he stated that at first glance it appeared strange, but upon playing it, the harmony made sense. One of the reasons why he felt that the progression looked strange could have been because the F#dim7 progresses down a whole-step instead of the usual up or down a half-step. I could have called this chord a D#dim7/F# but to me, using the slash chord symbol means having to process more information. The third chord in Bach's progression is a C# diminished triad over E. Now, based on the aforementioned principle, we can add an A to the C# diminished triad to create an A7 chord. This A7 chord becomes a secondary dominant that leads to the D chord in measure four. What is often done with dominant seventh chords is that they are preceded by the II chord of the key from which that dominant seventh chord comes. In this case the temporary key center that we are leading to is D major, so in the key of D, the II chord is Emin7 and the V chord is A7. Figure 9: "Variation #1" (excerpt) - measures 3-4 of the melody C#dim/E D (Emin) 7 4 7 Emin7 A7 D sus D j) i F\ • :£ # W -22- Measure 20 of Figure 8 employs this concept in the key of E minor. As you can see in Figure 9, measure three is a II-V progression leading to D, but instead of going to just a D triad, this piece ultimately goes to a D7 on beat three of measure four. The D7sus4 chord at the beginning of bar three can be thought of as an Amin7/D. Therefore, that bar contains a II-V progression over V (D) in the bass. Once again it was the melody that dictated this progression. I wanted the G in the melody to be at the beginning of the bar. This would have clashed with the D7, so as a compromise between the melodic tendencies and the somewhat predetermined harmony, I preceded the D7 with a D7sus4 chord (which is a D7 chord with the fourth degree replacing the third of the chord) and then brought the melody down to the F# in the last half of the bar to make room for the D7. This concept occurs again in measure 12 (see Figure 8). I find it interesting that bar three is the only bar that employs 16th notes. They act as an appoggiatura leading to the F#. I tried conceiving of 16l notes elsewhere in this variation but they just seemed unnecessary to me. I thought about using them in measure 12, as that would be the same place of the second eight bar phrase, but the idea just seemed a little contrived to me. Rhythmically speaking, this composition uses a lot of syncopation in keeping with the Brazilian bossa nova style. The successive quarter notes occurring off the beats are very typical of bossa nova. In measure five, I put Bach's G/B chord into root position, so as to avoid octaves between -23- the bass and melody (see Figure 8). By avoiding octaves between the melody and the bass, the piece employs more interesting counterpoint between the two voices. In measure six, I used a C6 chord instead of the Amin/C. This is pretty much the same chord except that it has a G (the fifth of the C6 chord) added to it. It is like an Amin7 in first inversion or Amin7/G. This same concept also occurs in measures 14 and 25. I left the D7 that occurred in bar seven to be repeated in bar eight because resolving to the G chord, as Bach did (see Figure 8). Obviously Bach was successful with this progression but I felt that waiting for the D7 to resolve in measure nine seemed to fit better with the idiom that I was writing for. It also left room (during the soloing) for the guitarist to add tension onto the D7 by perhaps making it D7alt in the eighth measure. This increase in tension over the same fundamental chord (D7) can make the resolution to the next chord (G) a more desired destination. The melody in the second eight bar section (B9) is an answer to the first eight bar section. The first bar of each section are melodically identical; however, instead of following that with a steady melodic descent as in the first phrase, the melody climbs up to a D in measure ten (the second measure of the second section). Measures 12-14 are the same as measures 4-6 except that they are transposed up a fifth (see Figure 8). The next eight bar section (B17) is a sort of release from all the quarter note off beats. It -24- is rhythmically much slower than the first 16 bars, employing mostly half notes and dotted quarter notes but it acts as the climax. The G melody note in measure 22 is the highest note in the piece (see Figure 8). The melody in measures 17-18 and 21-22 is a sequence that moves up a whole-tone, adding to the climactic quality of this eight bar section. The last eight bars of this piece act as the conclusion by reversing the two four measure phrases in B9. The intervallic and rhythmic similarities between measures 13 and 25 are notable, but when the melody moves into measure 26, it strays from the pattern (see Figure 8). The melody in measures 29-30 is almost identical to that of 9-10 with the exception of one less quarter note D in measure 30. -25- Bach's Minor Variations As I mentioned earlier in the thesis, Bach's 15th, 21st, and 25th variations are in the parallel minor to G major: g minor. A literal translation of Bach's progression into the parallel minor might look like this: Figure 10: Literal translation into the parallel minor. II: i |V6 I viio6/V I v 1 i6 | iio6 1 v | i | i | V6 1 VI | V7/V I v6 | iio6/V | V7/V 1 v B II: V7 Ii6 | viio6/m | V7/VI 1 VI | TV (ii6) I V7/VI 1 VI | iio6 Ii6 | iio | V7 | V7/iv 1 iv 1 v | i Or: Figure 11: Literal translation into the parallel minor in modern chord symbols. II: G- | D/F# I C#o/E 1 D | G-/Bb | Ao/C 1 D 1 G- 1 G- | D/F# | Eb 1 A7 I D-/F | Eo/G 1 A7 1 D- B ||:D7 I G-/Bb | Ao/C | Bb7 I Eb | C- (Ao/C) I Bb7 I Eb | Ao/C | G-/Bb | Ao I D7 | G7 1 c- 1 D 1 G- -26- However, what Bach uses in variation fifteen is (see Figures 12 and 13): Figure 12: Bach's chord progression in Variation 15. H:i | V6 | VI viio6/V VI I V7 | i iv V 1 i iv6 1 16 V7 1 i | i6 V7 1 i V65 1 i I viio65/V i V65/V | v6 i V65 1 16 V7/V 1 v | V7 B ||: V7 1 16 | iio6 I V7/VI 1 | iv V42/VI 1 VI | V7/VI 1 VI 1 | V65/vi 1 iv V7/VII | V42 viio65 | V65 1 1 16 1 iv i | V7 1 i :H Or: Figure 13: Bach's chord progression in Variation 15 in modern chord symbols. II :G- | D/F# | Eb C#o/E Eb | D7 | G- C- D | G- C-/Eb | G-/Bb D7 1 G- | G-/Bb D7 | G- D7/F# 1 G- | C#07/E G- A7/C# | D-/F G- D7/F# | G-/Bb A7 1 D- | D7 B ll:D7 | G-/Bb | Ao/C | Bb7 1 | C- Bb7/Ab | Eb I Bb7 I Eb 1 I Bb7/D | C- C7 I D7/C F#o7/A | D7/F# 1 | G-/Bb I C- G- | D7 1 G- :H Bach still modulates to the v (d minor) and to the VI (Eb major) in the areas in which they would happen in the literal translation. It is interesting to note that Bach avoids the use of the ii dim6 or the ii dim that would happen in a literal translation from G major to g minor. Bach also has the same avoidances in variation twenty-one. -27- Variation #2 Clark Johnston Intro | Free Open Drum Solo Drums S ^77= ±: J = 95 ^ Traditional Samba Groove Dr II 7 7 77 7 77 7=7 7 77=7=7^=7 7 7 7=* 7777 7 7 7 7 =7 7 7 7 10 vb Voice j. -U jhju. -U- yrpJ IIJJJJ JLM- *^fe 6 G 1,7*1T^«i1i tS'l>9/A..Uvho/At* B/Dtt A Gtr 7 y y 7= y y y y y y y y =7 777 i GO B/D# F'ttu Simile F#*>/Att ; A Bass *>»r Pr pir^ 77 77=777 7 Dr \\ y y y y -7 y y y= yyyy~yyy=y 14 Voice \ A Gtr y y y y y y y y = y y y y =7 y y 7 7 6 7 Emin Aran B7b9 Cnwj A Bass ')'•$ y y y y \ y y y y \ y y y y \ y y y ^ Dr 11 y y y y =7 y y y y y y y y y y =7- 18 Voice 11 7 u 9 Fmaj*1a,* l # E^ Aim' J.tM>.jtvbo9 A Gtr / • y y =7= y y y — y y y y =7= 7 y y Fmaj*1 F7*11 E7^ Amin7 F#7b9 A Bass "jti yy y y \ y y y =^ yyy =7= / • / • Dr 11 • • y • • / • / ^=/ • y - y y y~^y Copynghl 2010 Clark Johnston -28- 22 ##E Voice FTpy ff r if Bmin7 rtmmW fF tftt7l>9l>9/A, # Bmin7 A Gtr yyyy =7= y y 7=^^y yyy =y= y y y Bmin7 C'lran* ptt7b9/Att Bmin' A Bass ')'•$ y y y y \ y y y y \ y y y y \ y y y=7 Dr j 11 • / • / \ y y y y \ y y y y \ y y y y \\ 26 |A17| l, ft Voice iipr i LTTT i y nt> p Tvr i IPT p"pr p Tpt iU i rjir * -"P IP p TPT *p iPr «p"p ^p T Sax * JJlJ i y J>IJyl nijJ J'I J'J J>iJ Jl 7 G6 G7 B l« D7l>9 A Gtr 7 7 7 7= 7777 7 y y y = y y y y 6 *> BD7l>7[.90 G D7b9 c A Bass 4>tf yyyy yyyy- y yyy =7= y y 7 Dr 11 yyyy =7= 7 7 y y y y y -y y y=7 30 J Voice $7 * y PIPP o pTpp ^'p f\y Tpt fl * ? PiPf fPr pTpp p-pp [TIT T Sax j jlJ j 7 * ?pipr - ^p ^r ^ Cmaj /E 6 Amin7 Dmin7 G7 C /E A Gtr yyy y= yyyy yyyy=yyyy Cmaj'/E Amin7 Dmin7 G7 C/E A Bass V-t 7 7 7 7 \ 7 7 7 7 \ 7 7 7 7 \ 7 7 7 =7=\ Dr ii 7 7 y y =7= y y y— / • / y = y y y =7= -29- 34 \M Voice s y J^p JiJ- n JMJJ ,yJ ;IJ i Tpt l y J> J> p ptp- JJ- JJI J> J g^ T Sax ^»* 7 j»j>r ftp- JJ. JJI^J jg>J i^j 7 Adim7 FSmin ^ B7aug A Gtr yyyy =7=7 7 y = y y y 7 7 7 7 =7 Adim7 G rttmm7^ B7aug : A Bass V <* / • / / \ y y y y \ y y y y \ y 7=7= Dr 11 y y y y 77 y 7= yyy y— / / 38 Fine Voice i3=*> M ^ J'li'J JJ-J JlJj ji Tpt |V p-r- Jj|J. p7- JM/J J^jJ Jpj jj T Sax &U- }\l -U- JLUJ J>J>J J1JJ ^^M E7[,9 7 Amin B7t9 Emm A Gtr yyy 7= yyy y -7 yyy =7= y y y 7 7 E7b9 Amin B b9 Emin A Bass *)'•$ 77 y y \ y y y y \ y y y y \ y y y=?= Dr n y y y y =7 y y /= y y y y -y y 7=7= -30- -xe- • ••• 7=7 7 7 =77=7=7= 7 7 7 7 7 7 7 7 =7777 =7=7=7=7= 7 77 7=HJQ 77/7 \77 77 \7 7 7 7 \7 7 7 7 \7 7 7 7 \7 77 7 \7 7 7 7 \7777 0. sseg y 11 rauia #V/6<]ijjJ s^™ ^ iUnua d fBUI i 6n iUiurv Mt3 njfiJ iift6 J 7777 =7=777 7=7=7=7= 7 7 7 7 7 7 7 7 7777 7=7=7=7= 7 7 7 7 •HO V lnnl iUiuig ftV/e 7 777 =7=7 7 7 =7=7=7=7= 7 7 7 7= 7 7 7 7 7 77 7 =7=7 7 7 +7=77 ^S 1 iimug #V/6 //// 77=7=7==77r77-=7=7=77=77 7 7 7=7=7=7= 7 7 7 7= 7 7 7 7I : t=W -id //// 7=77=7= 7 7 77=7777 7777 7777=7777 ^ sseg v (ma L D 61Z.3 gUTOJV t™iH #0/3 (tV/e<]z.#J n$Ld 9O • ••• |, \7 7 7 7 =7=7=7=7=yyyy 7777 7=7=7=7 JJO V °1°S Is! CBU| UIUJ u 1 m t o 6<|ia 9 v i™ a #a/a ttv/e^-i utta 9 ) 7 7 77 7=7=77=77-7=7 7=i 7777 7=7=77= 7777 7777 : *ES I U7 I r , , °r°sP : on -Z£- m7777=7777-7777=7777 yyyy\yyyy 7=77=7=7777===J\ ia :/••/ 7 7 7 7 777-y- 77 7 7 77 7 7 7 7 7 7 \7 7 7 7 \7 7 7 / 0 sseg v I UTnl un u™3 6 [|: //// \/777 \7777 \7777 \7777 \7yy7 //// 7=7=7=7 ™S I §np uraig 6<1ia twury 6 7 / y y-7=7=77=7=7=77= 7 7 7 7 7 7 7 7 7^7-77= 7=7=7=7= 7 7 7 7=9 lO yyyy yyyy yyyy yyyy yyyy yyyy yyyy y y y /===£ ssng y 3/93 z£> iulula i"iiuv 3/i^"JD LO 6 yyyy-7=7yy 7=7=7=7= yyyy yyyy 7777 7=77=7=77/7 •no v =$ u 3/9D i9 £™ a ^"V 3/if™iD z.O 6<\LC\ 9O 6 7777 yyyy yyyy yyyy yyyy yyyy yyyy yyyy *t)\ XBS I [Hi] "Variation #2" I decided to use a literal translation of Bach's progression into the minor key as my starting point for my own minor variation. Figure 14 shows a lead sheet of my second variation with a literal translation of Bach's progression (transposed to e minor) above my chord progression. At first glance Variation #2 appears to be in G major but it is actually in e minor. I transposed this variation to e minor so that the melody that I wrote would fit more comfortably on the trumpet. Figure 15 shows an early version of Variation #2. Much of the harmony is fundamentally the same as the final version. In order to avoid roots or bass notes in the melody, I changed the chord from a root position chord to an inversion or vice versa. The G6 chord that occurs in measures one and 18 have the same notes as the Emin7 that occurs in the earlier version, except that the bass has the third of the Emin7 chord instead of the root. The seventh, ninth, and sharp eleventh of the Fmaj9#l 1 in bar nine of the final version make up the Emin chord that exists in the earlier version. As well, the F7#l 1 in the second measure of the final version shares its third, seventh, and sharp eleven with the B7b9 in the earlier version. This is known as a tri-tone substitution, as the roots of these two chords are separated by a tri-tone. -33- Figure 14: Lead sheet of Variation #2 with a literal translation of Bach's progression transposed to e minor above my chord progression. Variation #2 Emin B/D# A#dim/C# B Clark Johnston ED G6 F7#" F#7l>9/A# B/D# I^U ff-^jj- ft' |[W^ J JLL/f * y^ Emin/G F#dim/A B Emin 7 7 5 Emin Amin6 B7b9 Cmaj l^'.J- CT JU Pir yr PIr v r * [A9|Emin B/D# c F#7 9 7 7b9 7 9 Fmaj #» F #» E Amin7 F# I>9 J J kj'r p p r *v i p r c r' t^ tr "r? i r" " -'- "r Brnin/D C#dim/E F#7 Bmin 73 Bmin7 Ctmin7!'5 F^^/At* Bmin7 ^P f\l*r rTr P^ [ATTI B7 Emin/G F#dim/A G7 7 9 7 7ph-^tpr-^p^ttvn^m7 B I> G« D7b9 G c Amin G7 C 27 Cmaj7/E Amin7 Dmin7 G7 C6/E •H-f-N* 25] Fffdim/A Emin/G Ffldim B7 25 Adim7 G F#min7l>5 B7aug J/ ft •, s ^—^ =- V n h 1 h 1 1- 1 —1 1 /L «> --f l_e_B—£—=m± J— . 11/J J J —m & -£ E7 Amin B Emin 29 E7^ Amin7 B7b9 Emin ^ifN^ =^mfc* i» 3—LL(m3 * <~zS Copyright 2010 Clark Johnston -34- Figure 15: Early version of Variation#2 Variation #2 Clark Johnston ED Emin B^9 B^dim7 B f r J u p r '? r Y T^OT 6 5 Emin Amin B7b9 Emin ffij- rt J i ^ M t II fA9] 7 7 Emin B7b9 Cmaj Ftt?b9 ^ $=F fr~'r E r dEtp=n 7 13 Bmin7 Cttmin ^ FU9/A% Bmin7 p-r r i r y r ^ Em 7 7 77 B7''9 Emin7 Adim G s^ ;*=* 27 Cmaj7 Amin7 Dmin7 G7 Cmaj7 fc •i- ? F ^^M^ |A25| 7 7 5 25 Adim Fttmin ^ B7b9 ?=* ^ # 7 29 E7^9 Amin B7b9 Emin J- O | J }=* =V=i $ tM f J * J ^ Copyright 2010 Clark Johnston -35- Bach's Fifth Canon As was mentioned earlier, the fifteenth variation is a canon at the fifth in contrary motion or inversion, a canone alia quinta in moto contrario. The leading voice starts and then the following voice enters a perfect fifth higher and moves by most of the same intervals but in the opposite direction as the leading voice. The following voice enters one full measure of 2/4 after the leading voice. Attached is a score (see Figure 16) with the two voices lined up so that there is no metric separation between them, making it easier to see the similarities as well as the differences between the two voices. Bach's following voice is not an exact inversion of the leading voice. He manipulates the line to match the harmony he wants to use. Included in the score is an exact inversion of the leading voice to provide a clear view of the notes he adjusts. A quick look at the second measure in Figure 16 shows us that Bach makes his first adjustment to the following line on the last half of beat two. An exact inversion has a B where Bach places a Bb. This keeps the following voice in g minor. Throughout this variation Bach keeps the following voice quite diatonic. For the most part, he is using the notes of g melodic minor with a few exceptions that allow the necessary modulations to d minor and Eb major. In fact, the places in which Bach strays from the exact inversion the most are during these temporary key centers. -36- Figure 16: Bach's 2 voices lined up metrically with an exact inversion '—' Exact Inversion Bach's Leadi ig Voice Gmi -37- Figure 16: Continued 17 U r I'L-rjr v^i n-y p rj ^ 7 7 Bl" E^ B^7 Cmi b7 D Bi> Et B b*~l7* r 1 *"lh P rj ^ ic—r I-I ir r_r •? LJ 7 7 Bb7 E^ B^ E*> obi . D $===*=-==! n n mo ^ 29 r ]<^fp g Gmi Cni i D7 0 ii 5 1. it_ » 9 — 1—W_ 0 -t Jr i 1? 1 a [J F * \\ ((\)^ ir ' • ' - tt Gmi Cmi D7 Gmi /i^ -38- Quite conveniently, the middle line of the treble clef staff acts as the mirror or the halfway point between the leading voice and the following voice. I cannot help but wonder how intentional this was for Bach. The only other canon that is in inversion is variation 12, a canon down a fourth which if transposed up an octave ends up being another canon at the fifth. That is to say that in variation twelve, Bach has the following voice start down a fourth from the leading voice, which is the equivalent of having it start up a fifth. Thus, as the first note of the leading voice is a G, the first note of the following voice is a D, just like "Variation 15". Having the middle line of the treble clef staff as the halfway point between the two voices surely makes it easier to imagine what the following voice is going to look like a bar later while composing the leading voice. This does not take anything away from Bach's genius; if anything, I feel that it shows how practical he was as a composer. -39- Variation #3 Clark Johnston i Straight Eighth Feel J = 130 * ^ » BD Trumpet 3=5 *B= Tenor Saxophone 3E G Sparse Comping D9/F* 3 D13 it _ Interacting with Bass Rhythm Ai /E Acoustic Guitar • • • • 7= / / / y y =77 yyy yyy// i D9/F» 13 D13 A /E j Acoustic Bass .'^J[ pr r pijr^rrpijr' 'rr VHIis^gp Simile 11 J j vH_hJ J)| J j xHjJ ^ Drums BSD y y y y y= yyy yy TLT L/ ^CT^ Tpt j I i $ T Sax » l> J- Gmaj'/B Ami7/C D7M> A Gtr y y y y y y y y y y =/ y y y y 7 Gmaj9/B Ami7/C D ^ A Bass mm ^¥ ^^ Dr ii yy/ / y yyyyyyyyy y A8 Tpt T Sax EfcEfc IT- 7 7 7 7 4 7 ? Gmaj D /ttt Emi A sus A A Gtr yyyy ~T^ /yyy y =/ y y y =7==~y^y~y / y Gmaj7 D7/F8 Emi7 A7sus4 A7 y'4 I r A Bass pr i p• jr p Dr II yyyy / =/=/ //y=//yyy =7=7 / / Copynght 2010 Clark Johnston -40- 12 Tpt T Sax U J O 4 ]J 4 i 6 7 D/Ftt Emi/G A9 Dmaj D A Gtr • • • y=y= y y y / y =y y y y -/— / y y y y 9 7 D/Ftt Emi/G A DmajG D A Bass » --% ^^4=E2 ^^ Dr ii y y y y y -y-y y y y = y y y y y =7=7 yyy 16 Tpt T Sax j J 'j i G7/B Cmaj7ttll B^9 Emi/G A Gtr • • • • =?= • • • • • yyy y =7= yyy y y 7 7 11 G /B Cmaj * B7b9 Emi/G ; A Bass :> »jrpr r Fu% Dr ^= • • • • • -^-x • y y= y y y y y =7=7 yyy -41- -Zfr- ////=7=///yy—///y-7-///// IF JQ sseg v $ \ \\ J J J J J J ^ iO z.a jury a/jBrao / / / / =7= / / y///yy/=7= / / yyy •no v iO z.a jury a/ifemo -> H*- iHS §fe X*S X ^s H J-- j** m 3^ -in r JpJ tdx ^ • • //^ 7/77/ =7 7 7/7= 7 / /// II iQ w w p p r iv rr*;<» sseg v 3/iiuy LIUIR Wtil / / / /7= 7 / 7 7 / - / y / /7= 7 / 7 / / •no V 3/iuiy tirag Wtii €34- p X*S 1 idl .a 28 Tpt Jcfr'^icjr^ 3& iw T Sax m m^E JJIJ jJJ^jljJJ^J j-irj 7 11 Cmaj * D7 A Gtr 7 y y yy=yyyyy=//yyy 7 Cmaj7*11 D A Bass S r r pr r P Dr w y y y y y~ yyyyy yyy// 31 Bl Tpt 9 9 7 D /Ft* 13 13 Gmaj /B Anu /C rj7l>9 O Solo A /E D T Sax ^^ yyy77 77777 yyyyy yyyyy=yyyyy~7^/yyy ¥ 9 9 7 D /F# 13 rj7(>9 A /E D13 Gmaj /B Ami /C 1= A Gtr yyyy/ =// y yy=7=77=7=7=777=77 yyyy/ yyyyy-yyyyy 9 13 9 7 D7b9 G Simile D /rtt A /E D13 Gmaj /B Ami /C A Bass '?•* yyyyy I yy y yy\ yyy yy\ yyyyy\ yyyyy\ yyyyy\ yy Dr 11 yyyy+ /yyy/ /yy//^yy//=7=77=77 ///y-7 ////7 B8 38 Gmaj7 D7/Ftt Emi7 A7 D/F« Eml/G A9 DmaJ6 D' % T Sax /yyyy=7=7/77 /yyy/ //yyy==77=77=7 ///// yy/ yy 7 6 7 Gmaj7 D7/Ft* Emi7 A D/Ftt Emi/G A9 Dmaj D A Gtr ± 7//yy=77777 //yy/ //yyy=77=777==77=7=77 yyyyyyyy yy 7 7 7 E 7 6 7 Gmaj D /Ftt ™ A D/F* Emi/G A9 Dmaj D : A Bass V * yyyyy\ yyyyA, yyyyy\ yyyyy\ yyyy/\ yyyyy\ yyyyy\ yyy yA Dr IE yyyyy=77777 yyy77 //yyy=7///y=777=/7 yyy yy -43- -tt- //// 77// yy// yyyy =7yyy F i •ta 9{iuns z/// 777=7=/yyy .km k Jdi.d Jdjrt^ SSEQ V , snunc &\LQ ua H/tiV jjj/ea y yyy 77=y=y=/yyy yy y y ==7yyy\ y y y y^y-yyy AO V ^ jfT/cO 61iO 3/jmV a/6fBlnO ElQ a/nv ///• \yyyy \yyyy \yy y y\ yyyy \/ / / s\ / / //% XBS X EXQ H/eiV jjHAa 6<]iCI OA'^V a/efetfD o «> ssnunuo3 ops JOUSX f/f °X %||yy/w yyyyy yyyyy yyyyy yyyyy yyyyy yyyyy yyyyy JQ \pyyyy yyyyy yyyyy yyyyy yyyyy y7=777 V"" %'.(* sseg v a fp,u ' njti 3 iO id tnny a/ifentfj 3/nny £1|///// yyyyy yyyyy yyyyy yyyyy yyyyy yyyyy y//// no V 9 LG itttferaD iO ACI jmy a/fe^o 3/™^ }\\///// yyyyy yyyyy yyyyy yyyyy yyyyy yyyyy yyyyy =*&i x*s x Bln D iO njjJ 3 i° id tnnv aZ/feraO 3/imy "ff I Era I yy yyy^7yyyy 77777= //yy7 yyyyy 7yyyy 11 ja //V \///// yyyyy yyyyy yyyyy yyyyy yyyyy ».£ sseg v O/nng fmn tnna 6<\LQ 6^9 njtt 3 ato yyyyy y///y 77yyy 7=7=7=77 yyyyy 7yyyy AO V ,11113 6 1U1 1feitQ £mi3 f^a D/ H fiijiH Itjti ato 9P Hjial SP- //yy 7=777=yyy/=/yyy 7yyy 7=7=7=7=yyyy yyy/ IF m yyyy 7-777-7=7=7=7-//yy 7yy y 7=7=7=7= "" *:<* sseg v fera LQ [ijtt D iO 6 •••• 7-7-77-yyyy=yyyy 7yyy 7777-//yy yyyy no V feu o La i* o 6 njjifeno 6<\L<3 \uiy iima O/iurv fS LQ iD L o[osrousxjopua yyyy 7=y y y =7=7=77- y y y 7- y y y y yyyy yyyy 11 -id ////\//yy\yyyy\y//y\yyyy\yyyy\yyyy $.(\ ssBg y i™3 «<)£a o/iraa 6^ta L(vn*0 ato yyyy 7^y y y =7=7=7=7= / y y-y- / / y y-^r yyy / / y7 no V lul tiui3 c^tii D/ 3 if™3 ato yyyy =77 y y =7=7=7-7-7 7 77= / / y y-=y yyy y y y7 X*S X $ timg 6<]t3 IU13 6<]ta JBUQ ato 9Z fiiol yyyy 77-77-7-7-77= //yy =7=77=7 yyy/ 77// 11 JQ -7-777 y yyy yyyy yyyy yyyy yyyy yyy/ ^ sseg y /BIUQ 6V O/TO13 jjj/a iV z,nna jj/id ttBino • •z/ 77=7=7= /yy/=yyyy 7yyy yyyy 7=7=77 •HO V It tfBina 6V OMH jjj/d tV iima fl-l/tO tfetno //// 7-777-/yyy=yyyy 7y// 7=7=7=7= /yyy 7 X«S X tfBtna 6V 0/™H jjj/Q tV iima jfil/id Jinno SJ> 91 m Tpt T Sax * ^w 13 D9/Ftt A /E iP D7f,us4 A Gtr yyy -y— y y y y y y y =7= y y y 7 % 9 13 G D /rtt A /E D7SUS4 A Bass y't yyyy \y yyy \y yyy \yyyy= Dr n y y y y =7 y y /= / y y y—/- / y y 95 Tpt # T Sax Gmaj9/B Ami7/C D7**11 A Gtr yyy y -/ y y y ~r y y =7= 9 1 Gmaj /B Ami7/C D* A Bass m yyy y y yyy / / y= =7E Dr ii y y y y — / y y y - y y y y 98 D8 Tpt "R T Sax 7 7 7 f w Gmaj 7 4 7 D /Ftt Emi A sus A A Gtr y / / =7= / y y y =/ y y 7= y y y 7 Cmiaj7 jjypfl Emi7 A7sus4 A7 A Bass ")•% yyyy \y yyy \y yyy \yyy Dr n y y y y =7 y y 7—• yyy =7==y y y -46- 102 Tpt ^ T Sax W^ 4 " 4 j^f Dmaj0 D' D/F& Emi/G A Gtr x xx -7^- y y y y =/ / y =/= / y=7 7 6 7 D/Ftt Emi/G A Dmaj D A Bass */# z y y y \ y y y /^=7 7= y y y y y =y= Dr IIZ yyy=7=yyyy y y y -7— y y y 106 [D16 Tpt # T Sax $ 4 '4 J^- 7 11 G7/B Cmaj * Emi/G A Gtr yyy -7— //yyy y /=/= yyyy 7 11 G7/B Cmaj * B7t>9 Enu/G A Bass ")$ y y y y \ y y y y \ y y y y \ y y y Dr \\yyyy-7//y=y y y y =7= / z z -47- -8fr- / / y =7= y yyy = yyy=7=y yyy 11 Jd y y y y \ y y y y \ y y y y \ y y y y ^ sseg Y LO iniy raia 0/iuTy yyy ~7- //yyyyy=7=//yy no V LQ imy ima 3/imV =M ffjrr-yf l^i g^ «S X J •rr/ rrrr r fTrJlf tdx iza\ £ii ~/ y y y y y y y == y / y y w Jd -y y / /yy 7==y= EZ£E '•' ' / m sseg Y Tm L 3. EI<|6<|A8 -7- 7 / / =7 / 7==7= 7 / 7= •HO V \<\b<\L& -Ht- ps »!S X idX Oil -617- yyyy /777- z zz/= yyyz 7y yy 7=77=7= / zyy zzz z 11 •"d yyyy \yyyy \y yyy \yyyy \yy yy \yyy y \y yyy \yyy y jjjp sseg Y Jurna 6V OA^S fld/d iV Aii"3 (tJ/td tfemr) //// Izzzz \y yyy \yyyy \yy yy \yyy y \y yyy \yyy y AO V Il ifeuiQ 6V D/ "3 j£/0 £V <.mi3 #ViCI £feuuj ^/ y y y y ^/y y y 7-7=7=7= 7 //^7=y y y y=7^77^7= y y y y g JO yyyy \yyyy \yyyy \yyyy \y yyy \yyy / \yyyy ^ ssBg Y nd 6<]ia otonv a/bfemo H/wv sa/6a y y y y-=7y y y 7==7=7=T= / y 7=7=/ y y y= y y y y / / y y no V £,a a/nV 6<]ia o/w a/efrmo jtjAa °PS X«S X tdX m w yyy/=//yy =7= / / z -7 yyy 11 Jd yyy y \ y y y y \ y Z y s \ s y y y $.£ ssBg Y L<3 ITjJAfelnO iO y y y 7= y y y y =7 y y y= z / ^=^ no V XBS X # d T^TCJ- JJ^^F 5^g^^ g 3 /. ,<# * ^ /// 09- yyy\yyy\yyy\yyy\yyy\yyy\yyy\y z s- •id y y y\y y y\y y y \y y y\y y y\y y y\y y y\l J t^~\ ssug Y ra 1 6V DA 3 fld/d £y Jing »l/id opiniS jBrao y y y =7=7=7= y y y= y y y 7=7=7= / / y y y y ^7 y y •HO V Iuj 6v o/nna jjij/a tv i a flato HI £ _i / / / ~7 7 7 ==7=7==7= 7 7=7= 7/y ffi Jd siiuus p^/ f f^* fm ^ w^m H Arlf J-ldrfDjJld J JJkl J JdE sseg Y n iCI 3/uV tt I/ 6a id 3/£nnv a/6lBtU9 tt " ' / / /\ / / /\ zz/| / / /\ /// \y y y\y / z % -HO V * id Dtonv a/efetno njid 3/eiV fli/ed r, jSI ssnuijuo^ ops JEjinQ p/£ ox ^ 1 =77=77=7=7=77 //// y yyy 7/7^7 yyyy /// / yyyy u Jd £11 zzzz |zzzz \yyyy \yyyy \yyyy \yyyy \yyyz \y yyy $.£ ssBg Y id njjifemo ^^ 6^£a tTlnv iIUTa D/miy 1 7-77-7 yyyy yyyy =7=7=7=7=7=77=7=// yy 7777-y yy7 ••10 V fera O id ntti 3 ifBrao 6<|id £nnv jing o/nnv M fral / / y7~==^y y y 7==7=7=7= 7 / 7=7= y y y y- y y y y yyyy qff Jd ////\///y\yyy/\/yyy\yyyy\yyyy\yyyy %.(, ssEg Y £iiug c<)ia o/nna £fBUQ ato Z Z ZZ ^=Z Z / 7=7=7-7- ///^////7/// 7 7/7 J10 V * iu y itraa 6<)z,a i)A 3 6 / / /= / y y =7 y y~ y y y w JQ ///\yyy\yyy\yyy ^(\ ssBg Y id 3/tiV ija/f,o y y y- y y y ==y y /= / z z JIO V id a/tiv jfi/ed X«S X ^ idX 7 Qo] /S yyy =7=7=7= //yyyy =7 / / =7-7=7= //yyyy 11 Jd / / /\/ / / \y y y\y y y \y y y \y y y \y y y\y y y ^ ssBg Y rpu O uflid t O ifemf) z.d „sns£Q 'tny img 3/^^ z / / =7=7=7= y y y= y y y yyy =7=7=7= / / y= y y y JJO V 9 njjid AfBmD ifcuir) td t,ST,std nnv i una 3/imV £11 spug ops JBtmQ y y y y y y =7=7=7= / / y- y y y / z z =7 z z 11 Jd yyy\yyy\yyy\yyy\yyy\yyy\yyy$.r= ssBg Y nug 6<|ia 9A™3 6<]ia uttifrtuo ato y y y y y y =7=7=7= / / y- / / y y y y =7 y y JJO V =* rBra ima 61i3 DA™3 6^a ntti 3 ato 09/ 185 Tpt T Sax $ 7 G7/B Ami7/C D ~7 / / ~z / —7= y / G7/B Ami7/C D7 A Bass *>:» 7 7 ====7= Z Z EZfE EZfE z • Dr II Z Z Z Z Z" =7= =7= Z • 188 [ox Tpt T Sax 7 Gmaj 7 7 7 D /Ftt Emi A f A Gtr -* / / / y y =7 y y— yyy 7 Gmaj7 D /Flt Emi7 A7 A Bass ')'•« yyy\yyy\yyy\yyy Dr w y y y -y y y= y y y ~y y y 192 Tpt = 3==£ T Sax 3 V ~i t D/Ftt Emi/G A9 A Gtr / / /= A / Z£ / y y= / / y= D/l I Emi/G A9 ; A Bass *>« z z EZ£E z z y^= yyy 7 y 7= Dr IIZ / / ^7- y y = y y z =^= • • -52- 196 [G16 Tpt m ^^ T Sax $ ¥ ^=^ w 7 11 7l>9 G/B Cmaj * B Emi/G A Gtr / y y y y y= y y y= z / =7=^7—/ / 7 1 G/B Cmaj * ' B7b9 Emi/G A Bass *)'•% yyy\yyy\yyy\y y y \ y / y= Dr H y y =7= y y y=-y— y y =7= y y =7 y y= 201 fG2i1 Tpt T Sax s 3^ 7 ^m 7l>9 ir B Emi6 Ami /C Bmi A Gtr z / /— / z y =7 y y~ y y y 7 B7l>9 Emi« Ami /C Bmi A Bass m•* / / / / / yyy y= yyy Dr iiz y y y y y = y z =7= yyy 205 Tpt 0 TJin\ j-nrm T Sax j j f=£=F ^ ^ 1 j j - ^mm 7 4 7 7 Ami D sus D G7 Cmaj A Gtr z z z yyy =7= y y y y =7= $ 7 Ami D7sus4 D7 G7 Cmaj A Bass >)••* y /- z -7 z z =7 y y= y z y Dr H/ z / -/ yyy z z ^= z / -53- 209 tr- Tpt n^cjJ gfrmr^ T Sax J ^ ^ J_J i ±^i. D7*11 G6 fc A Gtr I / y =7= EZ£ ^ EZEE Z • =^c D7*11 G6 : A Bass h>« z z EZEE EZ£E =7= EZE Dr HZ Z Z EZ£ EZEE EZE Z Z =7= ADLIB ON CUE 212 G6 ON OPEN VAMP Tpt m, EZE EZE EZE Z / EZZ£ ADLIB G6 ON CUE ON OPEN VAMP T Sax m ^7= =7= ^ 7 / EZZfE ON CUE G6 VAMP A Gtr ^7_ =7= =^ =7= y y ^77± ON CUE G6 VAMP A Bass ggg mm VAMP ON CUE Dr II |[: Z =^E =7= =^ / / // -54- Variation #3 Variation #3 was written for trumpet, tenor sax, guitar, bass, and drums. Seeing as every third variation of Bach's is a canon, I thought it only fitting that 1 make my third variation a canon. What I've done is taken the bass line from Figure 4 and assigned it to the trumpet and sax in inversion, retrograde, and at different rates. The piece starts with the harmony changing every five beats (which is one measure in 5/4), the trumpet changing notes every four beats, and the sax changing every three beats. Figure 18 shows the original bass line from Figure 4 plus the modified bass line that I used to derive the lines for the trumpet and sax. The trumpet has the inversion of the modified bass line starting up a perfect fifth and the saxophone has the trumpet line in retrograde, starting up a perfect fifth from the trumpet. The saxophone line ends up being a retrograde-inversion of the modified bass line, starting up a ninth from where the modified bass line starts. Most of Bach's piece was written with a 32 bar form, which makes the original bass line a 32 note "row". In an attempt to write something with a form that was a little different than the standard 32 bar form that occurs in countless jazz and tin pan ally compositions, I took out the repeated notes to create a 30 note row and subsequently a 30 bar form. Therefore, there is no G chord in measure nine and no D chord in measure 15. In canonic fashion, the trumpet enters first, followed by the sax, one full measure later. I -55- cut off some of the notes early by inserting rests into several of the places that seconds occurred between the two horns, so as to avoid awkward sounding voice leading. I also delayed some of the entries for the exact same reason. As well, I used accidentals to adjust the notes of the lines to make them fit with the chord changes. For instance, the C# in measure eleven appears as a C in the original line, but in order to fit the C into the A7 chord I raised it to a C# (see Figure 17). At first glance it may appear that I have not always been true to the derivative lines in my composition but the notes that are different can be thought of as enharmonic equivalents of the original notes that are found in the derivative lines. For instance, the F# in measure 12 can also be thought of as a Gb in order to coincide with the G that appears in the original line. There are several examples of this throughout the score. Figure 17: Bars 11-12 of "Variation #3" & j M4 JI A'sus* A7 D/Ftt //AS -7— A 7 / A / 7 A'sus* A D/Ftt jrprr FI^ ? / / / / rz= / / / / / -56- The acoustic bass line was manipulated to make the composition more interesting. I did contemplate the notion of having the bass hold one note for the duration of each bar but this seemed to quickly become monotonous. Nonetheless, the first note of each bar represents a note in the modified bass line, although not always in the same octave. Figure 18: The derivative lines for "Variation #3" The Saxophone line The trumpet line » 1 J J j jjJJr^jjJrJJi r rr^i-NrrJrJJri The modified bass line JJ '*' rrrr r'"rrJrrrrjJjjJjJJjjrjJrj• Bach Las an extra G here Bach has an extra D here The original line I I J h rrrrJ rrrrrrrrrTrrrrrrjjjrjj(j| As I mentioned earlier, the "melody" is restated in 4/4 and then finally in 3/4. The statement of the melody in 4/4 acts as an interlude between the sax solo and the guitar solo. As well, the time signature changes after one chorus of each solo into the next time signature. So each of the two soloists have one chorus in the old time signature and one chorus in the new time signature. After each soloist performs one chorus in the new time signature, the "melody" is restated in the new time signature. The idea here is to give -57- each voice a chance to work within the three different groupings of three, four, or five. When the harmony is in five, the trumpet is in four, and the saxophone is in three. When the composition goes into 4/4, the harmony is in four, the trumpet is in three and the sax is in three + two, equaling five. When the piece goes into 3/4, then the harmony is in three, the trumpet is in three + two (five), and the sax is in four (two + two). Because the sax starts in three, it finishes the 30 note line sooner than the trumpet, which is in four. The saxophone starts a melodic line in measure 20 that uses the same notes as before but is rhythmically more complicated, consisting of eighth notes and quarter notes. The trumpet begins a retrograde-inversion of the sax line starting up a fifth in measure 25. Figure 19 contains the melodies of the sax and trumpet without the accidentals. Figure 19: The "rhythmic" lines of "Variation #3" The Saxophone line -luj^-m V •UlJLnl The trumpel line W 1 5& m&fFJj^r JJJ m EfcS S crrLcrra '-ff^g The modified bass line J J r p r N ~J r JJ r J ii The way that I composed these lines was that after I had written all of the notes for the sax and the trumpet on the first cycle through, I noticed that I had 30 more beats (six bars of 5/4) for the trumpet and 50 more beats (ten bars of 5/4) for the sax. I decided to make -58- the line 30 beats long so that the trumpet would fit within the form. This meant that after the sax had stated the 30 beat line, it would have 20 beats left over (50 beats - 30 beats = 20 beats). I decided to condense the line to fit within the remaining 20 beats by shortening some of the values of the quarter notes. Figure 20 shows the rhythmically more complicated line, along with the "condensed" line, and the modified bass line, all without accidentals. As you can see, I didn't change anything until the half-note A that occurs about half-way through. I viewed that as a perfect opportunity to accelerate the progression of the 30 note line and I turned it into eighth notes. By having the two melodic lines become increasingly more active throughout, the desired effect of reaching a climax toward the end of the 30 bar form is achieved. Figure 20: The "condensed" version of the sax line. The saxophone line PJJJJJ r^JJJ^JjJjM JJJ JJnJJJJ JJjjjrJ I'he condensed saxophontone linline ^^ W ^t — w^-*-^: ^JJJ^JJJJ^JJJJJJJJ jjjt mm The modified bass line m p^ r JJr ^ The "Interlude" The Interlude is the statement of the melody in 4/4 which occurs after the sax solo (Dl). As was mentioned earlier, the harmony is moving in four while the sax is grouped in five -59- and the trumpet is grouped in three. If I had designated five beats to each note of the 30 note line, then it would have taken the sax more than one full time through the 30 bar form to complete the 30 note line. Instead, I decided to have the saxophone play two notes over each five beat period, grouped as 3 + 2. Once the sax plays all 30 notes of the line, it has 45 beats or 11 bars and one beat left over. There is now room for one pass through the rhythmic version of the line (because it is 30 beats long) with 15 beats left over (see p. 42). Because 30 + 2 = 15,1 decided to have the sax play the 30 note line as eighth notes so that it would get another complete pass through the line. However, once the trumpet has completed its 30 note line, it only has 26 beats left over. I condensed the rhythmic line again to fit within 26 beats by diminishing the values of some of the notes. The "Head Out" The "Head Out" is the final version of the melodic material, occurring after the guitar solo. This time the harmony moves in 3/4 while the sax changes notes every two beats and the trumpet alternates changing notes every three beats and then two beats as the sax did during the interlude (see p. 51). The sax changing notes every two beats represents four by adding 2 + 2. Once again, if the sax changed notes every four beats then it would overextend the form. This time, when the sax is finished its 30 note line, it has 30 beats left over (see p. 53). This is the perfect amount for a final statement of the rhythmic version of the line. However, once the trumpet has finished its 30 notes it only has 12 -60- beats left over. I decided to state the 30 note line with eighth notes until the final measure where the line is executed in 16l notes. This adds a necessary climax and conclusion to the piece, in that 16th notes have not occurred until this point but have been wanting and waiting to come out. Conclusion As with any great work of art, one could spend a lifetime investigating the "Goldberg" Variations. I feel that I have only scratched the surface when it comes to analyzing Bach's composition, but by writing my own set of variations on Bach's chord progression, I have gained a much deeper understanding of this piece than I had before I embarked on this musical adventure. Countless musicians have, for centuries now, been influenced by Bach's "Goldberg" Variations. I wrote these variations, not to be compared to such a work of art as the "Goldberg" Variations, but as a show of appreciation for what Bach and his music has done for me. -61- List of Works Cited Forkel, Johann Nikolaus, and Charles Sanford Terry. Johann Sebastian Bach; His Life, Art, and Work, Tr. from the German of Johann Nikolaus Forkel, with Notes and Appendices. London: Constable, 1920. Print. Fujita, Iori. "Music of Intellect the Goldberg Variations". March 27, 2010 Goldberg, Laurette, and Jonathan Rhodes. Lee. The Goldberg Variations Reader: a Performers' Guide and Anthology of Critical Appreciation. Berkeley, CA: MusicSources, 2002. Print. Photograph. Deadleafonafence.wordpress.com. Deadleafonafence, 24 Apr. 2010. Web. 29 Jan. 2011. Schmid, Balthasar. "Goldberg Variations." Wikipedia, the Free Encyclopedia. Irishmaestro, 14 July 2008. Web. 17 Apr. 2011. ThinkQuest, "Music Dictionary A-C". Oracle Education Foundation. March 27, 2010 "Goldberg Variations." Wikipedia, the Free Encyclopedia. Ed. Carl F. Becker. Kryalot, 17 Mar. 2006. Web. 17 Apr. 2011. Wolff, Christoph. Bach: Essays on His Life and Music. Cambridge, MA: Harvard UP, 1991. Print. -62- Discography Bach, J.S. (Composer). 1955 Goldberg Variations [Glenn Gould, Performer] On A State of Wonder the Complete Goldberg Variations 1955 & 1981. Sony Classical/Legacy, 2002. CD. Bach, J.S. (Composer). [Keith Jarrett, Performer] Goldberg Variations: Harpsichord. ECM Records, 1989. Call # DISC.910054 CD. Bach, J.S. (Composer). [Jacques Loussier Trio, Performer] Bach's Goldberg Variations. Telarc Distribution, 1999. CD. Bach, J.S. (Composer). [Uri Caine Ensemble, Performer] Goldberg Variations: Aria and 70 Variations Adapted, Arranged and Composed by Uri Caine. Mtinchen: Winter & Winter New Edition, 2000. Call # DISC.910054 CD. Gordon, M., & Warren, H. (Composers). There Will Never Be Another You [Chet Baker, Performer] On The Best of Chet Baker Sings. Capitol Records/Pacific Jazz, 1989. CD. -63- Appendix A: The Aria in Bach's own handwriting (Schmid, 2011) -64- Appendix B: Printed copy of the Aria (Becker, 2011) ASIA, iJ*. F—f1—:kir^—=f======^===^=====^ I OTfcdb J M-i-J [J i =*—^jSS L.nil^:ilJT p •*•; I i^ -65- Appendix C: Variation #15 in Bach's Handwriting (Schmid, 2011) m «-S"ra- ywi II m , L njgjtsj ~i , •_;,,•. UTTl "IK" •:-°"« *—•"••im , • » JM y>t&f"i;uij'.,t •*£ -66- Appendix D: Printed copy of Variation #15 (Becker, 2011) \»ritttlt» 15 CHUNK- &IU Oatas « HAA\, { m H&ui* SKSJ&Blff 4i»d«n(e. JJL± ** •lT===9=sr- zw4h± s^ll^^^^ ==•==§—=t r1 1 » ..^^..^ Wt J»~^T*g>w«gJ|Mn*i»W^ |P. I j*i«"i>i"'i"'»i""'Jfcn p»i^h, ft •" " •'"" • •''" "" ninin»p-n>i»"ni" 11» ' &.»»,I*WI^ M «"»• "* w — m»« ^aa^nplfli^w^t—w» ...„.~..,.....-~. ^ _ -67- -89- A *r*3T. T*—^»—S- IiZS5^ =^- 3H-T g*7 i —-J: ~w~*nicr _SB^—4t —g&— L. —~4-~Jg~.0&, ^=*£^=====:r2 r^r^&Jf-Fi