ANALYZING CHORD SUCCESSIONS IN J.S. BACH'S MODAL ...

FROM MUSIC THEORY TO GRAPH THEORY: ANALYZING CHORD

SUCCESSIONS IN J.S. BACH’S MODAL CHORALES

by

Veronica Lizárraga

HONORS THESIS

Submitted to Texas State University in partial fulfillment

of the requirements for graduation in the Honors College

December 2021

Thesis Supervisor: Cynthia I. Gonzales Second Reader: Daniela Ferrero

COPYRIGHT

by

Veronica Lizárraga

2021

FAIR USE AND AUTHOR’S PERMISSION STATEMENT

Fair Use

This work is protected by the Copyright Laws of the United States (Public Law 94-553, section 107). Consistent with fair use as defined in the Copyright Laws, brief quotations from this material are allowed with proper acknowledgement. Use of this material for financial gain without the author’s express written permission is not allowed.

Duplication Permission As the copyright holder of this work I, Veronica Lizarraga, refuse permission to copy in excess of the “Fair Use” exemption without my written permission.

v

TABLE OF CONTENTS

Page ACKNOWLEDGEMENTS .............................................................................................. vi LIST OF TABLES ........................................................................................................... vii LIST OF FIGURES ......................................................................................................... viii ABSTRACT ...................................................................................................................... ix CHAPTER

I. INTRODUCTION ................................................................................................ 1 II. METHODOLOGY ............................................................................................. 1 III. MODES ............................................................................................................ 3

Dorian ...................................................................................................... 3

Phrygian .................................................................................................. 5

Mixolydian .............................................................................................. 7

Aeolian .................................................................................................... 9 IV. FINDINGS ...................................................................................................... 11 V. CONCLUSION ................................................................................................ 12

APPENDIX SECTION ..................................................................................................... 13

REFERENCES CITED ..................................................................................................... 26

vi

ACKNOWLEDGEMENTS

First and foremost, I would like to acknowledge and thank all my past music educators for instilling a sense of passion and curiosity for music in me. Specifically, I would not have been able to take on this thesis without the mentorship received from Dr. Cynthia I. Gonzales. As my first university-level music theory educator, her passion inspired and encouraged my pursuit of more complex theoretical concepts. Secondly, I would like to acknowledge my honors graph theory professor and second reader for this thesis, Dr. Daniela Ferrero. The freedom she gave us to choose our final project and make it relevant to each student’s interests enabled me to explore and develop different ways of organizing and displaying data. I would also like to acknowledge my dear friend Carson Holland who worked with me in finding the different functions in Excel that helped to more efficiently gather data. Lastly, I would like to thank my cousin Gabriel Adauto for encouraging me to pursue this thesis in the first place despite the workload and time I knew this project would require.

vii

LIST OF TABLES Table Page 1. Dorian Chorales ............................................................................................................. 3 2. Phrygian Chorales ......................................................................................................... 5 3. Mixolydian Chorales ..................................................................................................... 7 4. Aeolian Chorales ........................................................................................................... 9

5. Succession Frequencies ............................................................................................... 11

6. Dorian Successions ...................................................................................................... 13 7. Dorian Label Counts .................................................................................................... 14 8. Dorian Succession Counts ........................................................................................... 14 9. Phrygian Successions ................................................................................................. 15 10. Phrygian Label Counts ................................................................................................ 17 11. Phrygian Succession Counts ........................................................................................ 18 12. Mixolydian Successions .............................................................................................. 19 13. Mixolydian Label Counts ............................................................................................ 20 14. Mixolydian Succession Counts ................................................................................... 21 15. Aeolian Successions .................................................................................................... 22 16. Aeolian Label Counts .................................................................................................. 24 17. Aeolian Succession Counts ......................................................................................... 25

viii

LIST OF FIGURES Figure Page 1. Dorian ............................................................................................................................ 4 2. Phrygian ......................................................................................................................... 6 3. Mixolydian ..................................................................................................................... 8 4. Aeolian ......................................................................................................................... 10

ix

ABSTRACT

Johann Sebastian Bach’s 413 chorale settings are a common source of analytical

examples in music theory classrooms. While most of this repertoire is tonal--that is, an

ordering of seven adjacent pitches that creates a major or minor scale--38 chorales are

modal. These 38 chorales, as identified in Lori Burns’ Bach’s Modal Chorales (1995),

are the focus of my research. In this thesis, I will map out the frequency of adjacent chord

successions in Bach’s modal chorales, focusing on the last phrase that confirms the modal

identity of each chorale. My research will provide insight into the harmonic structure of

Bach’s modal chorales.

1

I. INTRODUCTION

Music theory, universally required for all collegiate undergraduate music majors,

explores the norms of tonal music based on a collection of pitches referred to as a tonal

scale. These scales generate harmonies that are explored within music theory classes, as

well as the most common order in which the harmonies progress. Less studied in the

undergraduate curriculum are harmonies produced by modal scales, which predate the

establishment of tonal music. In this thesis, I will explore four modes, the harmonies they

yield, and their most common harmonic successions.

II. METHODOLOGY

My methodology was a three-part process. First, I researched which Bach

chorales are modal and analyzed their harmonic successions. Second, I gathered data

about the modal successions and finally, I displayed the data in graphic form.

Lori Burns’ book Bach’s Modal Chorales provides the list of repertoire I analyzed

for this thesis. I consulted Christopher Carnecki’s book J.S. Bach 413 Chorales:

Analyzed as a point of departure for my own harmonic analysis, which often differed

from his. In this thesis, I analyzed harmonic successions in the last phrase of each modal

chorale. For the sake of avoiding outliers, inversions of all triads and seventh chords are

categorized as if in root position, except for cadential !" chords.

To tally the occurrences of each harmony, I created the Succession Tables for

each of the four modes to record every chord and the subsequent chord as an individual

succession. Once all of the chorales’ chordal successions were input, I recorded all of the

chord labels found in each mode and used COUNTIF functions in Microsoft Excel to

calculate the amount of times each chord occurred within the first column of the

2

Succession Table so that the label for each individual succession would only count once

(e.g. COUNTIF(A1:A239,"V7/bVII"). In creating the Succession Count Tables, I

recorded each kind of two chord succession for each mode and then used a two value

COUNTIF function to count how many times each succession occurred (e.g.

COUNTIFS(A3:A165,"iv",B3:B165,"V7/iv")). The only time the COUTIF function did

not work was when there were different capitalizations of the same letter. For example, I

had to manually count and input the amount of times v-I versus V-I occurred so that it

would not count them as the same succession and double the number of occurrences in

the table.

In planning how to display the data from the tables, I chose to create the figures

on Prezi because of how easy it was to manipulate shapes, text, and arrows compared to

any other software I tried. I had to find a way to display the harmonies, successions, and

their frequencies. I created one figure for each of the four modes, four figures in total.

Each roman numeral label/chord is represented by a circle. The size of a circle was

dependent on how frequent the chord occurred. If the frequency of a chord was higher,

the circle for that chord was bigger and if the frequency of a chord was lower, the circle

was smaller. Each succession is represented by an arrow. The thickness of an arrow was

dependent on how frequent the succession occurred. The higher the frequency of a

succession, the thicker the line of the arrow. The colors for each chord and succession are

different in order to distinguish them from each other, but the same color corresponds to

the same chord and succession for each mode in order to visually compare data between

the different modes.

3

III. MODES

Most typically, the intervals above tonic include a perfect fourth and fifth as well

as a major second. The third, sixth, and seventh tones above the tonic are “modal scale

degrees” because they most often vary from mode to mode. In a major mode such as

Mixolydian, the third is always major while in a minor mode such as Dorian, Phrygian,

and Aeolian, the intervals include a minor third and minor seventh.

Dorian

Burns lists seven chorales as being in the Dorian mode, as shown in Table 1.

Chorale Title Catalog Number

Als Jesus Christus in der Nacht BWV 265

Christ lag in Todesbanden BWV 277

Erschienen ist der herrlich Tag BWV 145/5

Hilf, Gott, laß mir’s gelingen BWV 343

Jesu, meine Freude BWV 227/7

Mit Fried und Freud ich fahr dahin BWV 83/5

Wir glauben all an einen Gott BWV 437

The first figure was created from Bach’s chorales in the Dorian mode. The Dorian mode

features a minor third and minor seventh above the tonic. The Dorian mode generates the

following harmonies: i ii III IV v viº ♭VII. Within the last phrases of the Dorian mode

chorales, the most frequent chord successions were V7-i and V-i.

4

Figure 1

5

Phrygian

Burns lists twelve chorales as being in the Phrygian mode, as shown in Table 2.

Chorale Title Catalog Number

Aus tiefer Not schrei ich zu dir BWV 38/6

Befiehl du deine Wege BWV 272

Christum wir sollen loben schon BWV 121/6

Christus, der uns selig macht BWV 283

Erbarm dich mein, O Herre Gott BWV 305

Es woll’ uns Gott genӓdig sein BWV 311

Herr Gott, dich loben wir BWV 328

Herr, nun laß in Friede BWV 337

Herzlich tut mich verlangen BWV 153/5

Kyrie, Gott Vater in Ewigkeit BWV 371

O Haupt voll Blut und Wunden BWV 244/72, 248/5

Mitten wir im Leben sind BWV 383

The second figure was created from Bach’s chorales in the Phrygian mode. The Phrygian

mode features a minor second, minor third, minor sixth, and minor seventh scale degrees

above the tonic. The Phrygian mode generates the following harmonies: I ♭II ♭III iv vº

♭VI ♭vii. Within the last phrases of the Phrygian chorales, the most frequent chord

successions were bII-bVI, iv-I, and V7/iv-iv.

6

Figure 2

7

Mixolydian

Burns lists nine chorales as being in the Mixolydian mode, as shown in Table 3.

Chorale Name Catalog Number

Der du bist drei in Einigkeit BWV 293

Die Nacht ist kommen BWV 296

Dies sind die heiligen zehn Gebot BWV 298

Es ist das Heil uns kommen her BWV 155/5

Gelobet seist du, Jesu Christ BWV 64/2 BWV 91/6

BWV 248/28

Komm, Gott Schöpfer, heiliger Geist BWV 370

Warum sollt ich mich den grämen BWV 422

The third figure was created from Bach’s chorales in the Mixolydian mode. The

Mixolydian mode is characterized by a lowered minor seventh scale degree above the

tonic. The Mixolydian mode generates the following harmonies: I ii iiiº IV v vi ♭VII.

Within the last phrases of the Mixolydian chorales, the most frequent chord successions

were IV-I, V-V7, and V7-I.

8

Figure 3

9

Aeolian

Burns lists eleven chorales as being in the Dorian mode, as shown in Table 4.

Chorale Name Catalog Number

Ach lieben Christen seid getröst BWV 256

Ach was soll ich Sünder machen BWV 259

Allein zu dir, Herr Jesu Christ BWV 261

Das walt mein Gott BWV 291

Helft mir Gotts Güte preisen BWV 183

Ich ruf zu dir, Herr Jesu Christ BWV 177/5

Meine Seel erhebt den Herren BWV 10/7

Von Gott will ich nicht lassen BWV 419

Wär Gott nicht mit uns diese Zeit BWV 14.5

Was mein Gott will, das gescheh allzeit BWV 111.6

Wer nur den lieben Gott läßt walten BWV 197.10

The fourth figure was created from Bach’s chorales in the Aeolian mode, also known as

natural minor. The Aeolian mode is characterized by a minor third, minor sixth, and

minor seventh scale degree above the tonic. The Aeolian mode generates the following

harmonies: I iiº ♭III iv v ♭VI ♭VII. Within the last phrases of the Aeolian chorales, the

most frequent chord successions were V-V7, V7-I, and V7-i.

10

Figure 4

11

IV. FINDINGS

Each mode and its most frequent and second most frequent successions are listed in Table

5 below:

Mode Most Frequent Succession

Second Most Frequent Succession

Dorian V7-i V-i Phrygian bII-bVI iv-I and V7/iv-iv

Mixolydian IV-I V-V7 and V7-I Aeolian V-V7 V7-I and V7-i

.......... In the Dorian and Aeolian modes, the tonic and dominant harmonies were the most

frequent. In the Mixolydian mode, the tonic and subdominant harmonies were most

common and in the Phrygian mode, the tonic, submediant and leading tone harmonies

were most common.

Some successions included harmonies that were not among the typical harmonies

generated in the given mode. Although Phrygian is considered a minor mode, every

Phrygian chorale ended in a major tonic harmony due to a picardy third, a raised major

third of the expected minor harmony. The most frequent succession in the Dorian mode

was V7-I when typically, the dominant harmony in the Dorian mode is minor given the

lowered seventh scale degree. Thus, is interesting to note Bach’s use of musica ficta in

this mode as well as the other minor modes. Though these chromatic alterations make

modes less distinct, they “create a more urgent sense of motion by forming less-stable

intervals that move satisfyingly (by half-step motion) to more-stable ones” (Karp) such as

those seen in Bach’s cadences.

12

V. CONCLUSION

In this thesis, I explored four modes, the harmonies they yielded, and their most

common harmonic successions. Using graph theory to organize and display data for each

mode revealed more in-depth, global data about Bach’s chorales and the way that he

composed them.

13

APPENDIX SECTION

Dorian Successions

I bVIIbVII bIIIbIII viio7viio7 ii VV V7V7 ii

V7/iv iviv cad64cad64 V7V7 II

iio cad64cad64 V7V7 II

V ii bVIbVI bIIIbIII IV7IV7 iiii viioviio ii iiØ7iiØ7 iiØiiØ V7V7 II

BWV 265

BWV 277

BWV 145/5

BWV 343

i iv7iv7 viioviio i i iiØ7iiØ7 vv v7v7 V7/iv V7/iv iv64iv64 II

V7 ii iioiio V7V7 ii VV ii VV V7V7 i i

V ii V7V7 ii iiØ7iiØ7 VV ii viio7/Vviio7/V VV V7V7 ii

BWV 83/5

BWV 437

BWV 227/7

14

Dorian Label Counts

Dorian Succession Counts

Labels Counti 14I 5

cad64 2ii 1

iiØ7 3iio 2bIII 2iv 1

iv64 1iv7 1IV7 1v 1v7 1V 7V7 9

V7/iv 2bVI 1bVII 1viio 2viio7 1viio7/V 1iiØ 1

Successions CountI-bVII 1

i-V 3i-bVI 1i-iiØ7 3i -iv7 1i-iio 1i-V7 1

i-viio7/V 1cad64-V7 2

ii-viio 1iiØ7-V 1

iiØ7-iiØ 1iiØ-V7 1iiØ7-v 1iio-V7 1

iio -cad64 1bIII-viio7 1bIII-IV7 1

iv-cad64 1iv64-I 1

iv7-viio 1IV7-ii 1v-v7 1

v7-V7/iv 1V-V7 3V-i 4

V7-i 6V7-I 3

V7/iv-iv 1V7/iv-iv64 1

bVI-bIII 1bVII-bIII 1

viio-i 2viio7-i 1

viio7/V-V 1

15

Phrygian Successions

bVI iviv II bIIbII bVIbVI biiibiii bviibvii V7/ivV7/iv iviv

bIII viio7/bIIIviio7/bIII viio7/Vviio7/V VV V7V7 ii

bvii iviv bIIbII bVIbVI IV7IV7 vovo V/ivV/iv iviv V7/ivV7/iv iviv II

BWV 38/6

BWV 272

BWV 121/6

bvii viio7/bviiviio7/bvii bvii

bvii V/bIIV/bII bIIbII bVIbVI bviibvii I

I

bVI bIIIbIII bVIbVI iviv bIII

bIII bVIbVI bIIbII bVIbVI bviibvii vovo bvii7

bvii7 II

bVI bIIIbIII bIIbII bVIbVI biiibiii bviibvii V7/iv

V7/iv iviv iv64

iv64 II

BMV 283

BWV 305

BMV 311

16

bIII bVIbVI bviibvii II V7/ivV7/iv iviv cad64cad64 II

bII bVIbVI bVI7bVI7 viivii II

bVI bviibvii bVIbVI V7/bIIIV7/bIII bIIIbIII V/ivV/iv iviv II

bIII bviibvii bIIIbIII V7/bviiV7/bvii bviibvii V/ivV/iv iviv II

BWV 328

BWV 337

BWV 153/5

BWV 371

O Haupt voll Blunt und WundenbVI V7/bVIV7/bVI bVIbVI iiiiii iii7iii7 V7/ivV7/iv iviv II

vii bIIbII bVIbVI V7/bviiV7/bvii bviibvii II

BWV 383

17

Phrygian Label Counts

Labels CountI 12bII 7bIII 8i 1biii 2iii 1iii7 1iv 11iv64 1IV7 1vo 2V 1V7 1

cad64 1V/iv 3V/bII 1V7/bIII 1V7/iv 5V7/bvii 2V7/bVI 1bVI 17bVI7 1vii 2bvii 12bvii7 1

viio7/bvii 1viio7/bIII 1viio7/V 1

18

Phrygian Succession Counts

Successions CountI-V7/iv 1I-bII 1bII-bVI 7bIII-bvii 1bIII-bVI 1bIII-bII 1

bIII-viio7/bIII 1bIII-V/iv 1bIII-V7/bvii 1biii-bvii 2iii-iii7 1

iii7-V7/iv 1iv-bII 1iv-V7/iv 1iv-I 5iv-bIII 1iv-iv64 1iv-cad64 1iv64-I 1IV7-vo 1vo-V/iv 1vo-bvii7 1V-V7 1V7-i 1V/iv-iv 3V/bII-bII 1V7/bIII-bIII 1V7/bvii-bvii 2

V7/bVI-bVI 1V7/iv-iv 5bVI-IV7 1bVI-bvii 4bVI-bIII 2bVI-iv 2bVI-bII 1bVI-biii 2bVI-bVI7 1bVI-V7/bIII 1bVI-V7/bVI 1bVI-iii 1

bVI-V7/bvii 1bVI7-vii 1cad64-I 1vii-bII 1vii-I 1bvii-iv 1

bvii-viio7/bvii 1bvii-V/bII 1bvii-V7/iv 2bvii-bVI 1bvii-bIII 1bvii-V/iv 1bvii7-I 1

viio7/bvii-bvii 1bvii-I 3

viio7/bIII-viio7/V 1viio7/V-V 1

19

Mixolydian Successions

v v7v7 iiii II vv v7v7 vivi ii7ii7 VV V7V7 II

I IVIV IV7IV7 VV V7V7 II

v V7/IV

V7/IV IVIV II

I IVIV VV II VV V7V7 II

BWV 293

BWV 296

BWV 298

BWV 155/5

V V7V7 viio/iiviio/ii iiii bVIIbVII IVIV II vv v7v7 vi vi IVIV II

I V7/IVV7/IV IVIV II

I VV V7/VV7/V VV V7/IVV7/IV IVIV V7/VV7/V viio/viviio/vi vivi V7V7 II V7/VV7/V v7v7 II IVIV II

BWV 248/26

BWV 64/2

BWV 91/6

20

Mixolydian Label Count

Labels CountI 19ii 4ii7 1iii 1IV 9v 6v7 5V 8V7 7

V7/IV 3V7/V 3vi 3vi7 1bVII 2viio 1viio/ii 1viio/vi 1IV7 1

vi iiii vv bVIIbVII V7V7 IVIV II

iii vi7vi7 iiii viioviio II VV V7V7 II

BWV 370

BWV 422

21

Mixolydian Succession Count

Successions CountI-v 2I-IV 3I-V 3

I-V7/IV 1I-V7/V 1ii-I 1

ii-bVII 1ii-v 1ii-viio 1ii7-V 1iii-vi7 1IV-IV7 1IV-I 6IV-V 1

IV-V7/V 1v-v7 3v-bVII 2v-V7/IV 1v7-ii 1v7-vi 2

v7-I 2V-V7 5V-I 1

V-V7/V 1V-V7/IV 1

V7-I 5V7-IV 1

V7-viio/ii 1V7/IV-IV 3V7/V-V 1

V7/V-viio/vi 1V7/V-v7 1

vi-ii7 1vi-IV 1vi-V7 1vi7-ii 1

bVII-V7 1bVII-IV 1

viio-I 1viio/ii-ii 1

viio/vi-vi 1IV7-V 1

22

Aeolian Successions

BWV 256 bIII bVII bVII iv iv viio7 viio7 i i iv iv iio iio V V I I

BWV 259

V7/bVII bVII bVII V V i i bVI bVI iiØ65 iiØ65 V V V7 V7 I I

BWV 197/10 bIII viio viio i i iiØ65 iiØ65 V V bVI bVI iiØ7 iiØ7 cad64 cad64 V V V7 V7 I I

BWV 261 bIII IV7 IV7 viio viio i i bVI7 bVI7 iiØ7 iiØ7 V7 V7 bVI bVI iiØ65 iiØ65 V V V7 V7 I I

BWV 291

i viio7 viio7 i i iiØ65 iiØ65 V V V7 V7 I I

BWV 183/5

i iv iv viiØ7 viiØ7 cad64 cad64 V7 V7 I I

23

BWV 177/5 iv V V V7 V7 i i V V i i iiØ65 iiØ65 cad64 cad64 V V V7 V7 I I

BWV 10/7

bIII v v bVII bVII iv7 iv7 iio iio IV IV viio viio i i v v iio iio V7/iv V7/iv iv iv V7/iv V7/iv iv iv I I

BWV 419 iio6 bIII bIII bVI bVI cad64 cad64 V V V7 V7 i i

BWV 14/5

bIII i i iv iv V7 V7 i i V V V7 V7 I I

BWV 111/6

bIII bVII bVII iv iv IV IV V7 V7 i i IV7 IV7 V V V7 V7 i i V V V7 V7 i i

24

Aeolian Label Count

Labels Counti 16I 9

cad64 4iio 3iiØ7 2iiØ65 5bIII 7iv 8iv7 1IV 2IV7 2V 13v 2V7 13

V7/bVII 1V7/iv 2bVI 3bVII 4viio7 2viiØ7 1viio 3bVI7 1

25

Aeolian Succession Count

Successions Count i-viio7 1

cad64-V 3 iio-IV 1 iio-V 1

iio-V7/iv 1 iiØ7-V7 1

iiØ7-cad64 1 iiØ65-V 4

iiØ65-cad64 1 bIII-bVII 2 bIII-IV7 1

bIII-v 1 bIII-bVI 1

bIII-i 1 iv-I 1

iv-iio 1 iv-IV 1 iv-V 1 iv-V7 2

iv-viio7 1 iv-viiØ7 1 iv-V7/iv 1 IV-V7 2 IV-viio 1 iv7-iio 1

IV7-viio 1 IV7-V 1

V-I 1 V-i 2

V-V7 10 V-bVI 1 v-bVII 1 v-iio 1 V7-i 6 V7-I 6

V7/bVII-bVII 1 V7/iv-iv 2

bVI-cad64 1 bVI-iiØ7 1 bVI-iiØ65 1

bVII-iv 2 bVII-iv7 1 bVII-V 1 viio7-i 2

viiØ7-cad64 1 i-iiØ65 3

i-iv 3 i-IV7 1 i-V 3 i-v 1

i-bVI 1 i-bVI7 1

cad64-V7 1 viio-i 2

bVI7-iiØ7 1

26

REFERENCES CITED

Burns, Lori. Bach’s Modal Chorals. Stuyvesant, NY: Pendragon Press, 1995. Czarnecki, Christopher. J.S. Bach 413 Chorales: Analyzed. United State of America:

SeeZar Publications, 2013. Karp, Theodore. "musica ficta." Encyclopedia Britannica, December 5, 2007. Accessed

November 24, 2021, https://www.britannica.com/art/musica-ficta.