The Power of Music
A. Metaphors of Music and Metrics
D. Blues: Text and Performance
E. Arbitrary Forms: Serial Music
Music affects verse most directly when verse is constructed with a particular musical form as the constitutive element:
One for the money,
two for the show,
three to make ready now go, cat, go.
Now don’t you step on my blue suede shoes.
You can do anything but lay off of my blue suede shoes.
Various metrical systems could be imagined to explain these verses: syllabic, accentual, even quantitative. But just because a literary analysis can be made to work does not mean it is correct or even legitimate. The above lines are, as we all know, lyrics based on music, and that is how their metrical form must be analyzed. To know this of any given poem or lyric often requires external evidence: we own a recorded version of this song; our grandparents sang it to us. With historical verses, whether a musical basis exists often requires speculation based on what we can consider as evidence (see chap. 6, D on John Donne).
Such cases are individual: we must speak of particular poems and particular music. They provide, perhaps, a limit to what a general study of versification can tell us about certain verse. Yet the influence of music on verse and discussions of verse is often indirect and does not consist solely of these limiting cases.
A. Metaphors of Music and Metrics
This first section addresses the use of musical language and terminology in the critical discussion and description of verse. Words such as rhythm, measure, tone, theme are common in discussions of verse. For some musical terminology, the strain in its application to verse is obvious: the word tone, for example, was popularized by I. A. Richards early in the twentieth century as the attitude of poets toward their work. In this case, there seems no relation between a musical tone and whatever the word might mean in poetry, and it is possible that Richards himself did not intend the musical reference. Other musical terminology is more problematic: motif and theme, and technical words such as measure, rhythm, and beat. When applied to verse, are these literal? or are they purely metaphorical?
A.1. Musical Notation
Musical notation has been invoked in the description of many verse types, and we have discussed a particular case in chapter 4, C above. To describe verse in musical notation is not the same as to claim that verse has a musical basis. When a verse is written for music, the musical notation applies not to the words but to the music that the words happen to fit. It is thus not quite correct even in these cases to imagine that the words are a direct function of the musical notation. When musical notation is applied to verse without accompanying music, that language becomes metaphorical.
A.1.1. Quantitative dactyls in verse are often usefully described through classical Western musical notation as measures consisting of a stressed half note followed by two quarter notes in 4/4 time, or a quarter note followed by two eighth notes in 4/8 time. The two quarter notes can be exchanged with a half note (or the two eighth notes with a quarter note). The musical analogy fails, however, in describing other common feet: an anapest cannot conveniently be described as a measure of two quarter notes and one half note in 4/4 time, since the conventional stress in a Western musical measure is on the first beat; in an anapest, that stress (the ictus) is on the last.
A.1.2. Musical notation has other basic limitations when applied to verse. As noted by many linguists, the perceived distinction between long and short syllables, even in languages where this distinction is fundamental, is not quantifiable and cannot be reduced to a simple musical notation that suggests a short is exactly or approximately half the duration of a long. Even in verses where such substitution is permitted (Latin dactylic hexameter), that substitution is a matter of convention and not necessarily a product of acoustic or linguistic reality (two shorts equal a long by convention, not because they occupy the same amount of actual time). In verse without feet or in verse with more complex rules of substitution, the musical analogy is of no help. In the opening syllables of Aeolic verse, long and short syllables are equivalent (chap. 2, E); and in none of this verse is there anything that can be usefully described as analogous to a musical measure. Somewhat paradoxically, it is precisely this verse that has the most claim to a real musical foundation.
A.1.3. Finally, the history of Western musical notation is not parallel to the history of Western versification and at times diverges as well from the history of Western music itself. The fact that Western musical notation works so convincingly in the description of certain verse forms is not a sign of the musical basis of such verse but rather an indication of the flexibility of the language itself.
A.2. Technical Musical Terminology
A.2.1. The terms measure, rhythm, and beat are often applied to verse, without explicit musical notation. A measure in musical notation is a specific and definable unit that controls the basic, repeated rhythm of the piece. In 3/4 time, a measure is a group of three quarter notes or their equivalent with an implied accent (ictus) on the first. In 4/4 time, a measure consists of four quarter notes or their equivalent. The closest analogue in verse is the metron in classical iambic verse (see chap. 2, B.1.4). In French metrics, the term measure has been used to describe the phrasal units that make up an Alexandrine. These units are not prescribed by rule but rather are the result of the particular phrase structure of particular lines; that is, a description of a French line in terms of such measures deals with the realized version of the verse pattern, not with the underlying structure. One line might have a structure 2 / 4 / 3 / 3; the following 1 / 5 / 4 / 2.
A.2.1.1. Such phrases are matters of stylistics and have nothing to do with the notion of a musical measure. A measure in music is a foundational unit (of description if not of composition); as used in the description of classical French Alexandrines (chap. 3, D.1), it is a unit that exists only in the analysis of particular verses. It is notable (perhaps the wrong word to use here!) that French music written during the period of the classical Alexandrine never treated its musical measures in this fashion.
A.2.2. The term rhythm can be particularly misleading in that it conflates levels of versification, composition, performance, stylistics, and even pure chance. The word is used in a number of senses but, to be intelligible, should refer to the deployment of variously marked elements in a line: in quantitative verse, it might be the relation of long and short syllables; in accentual verse, the relation of stressed and unstressed syllables. If these are basic elements of verse, rhythm is clearly part of versification, but if these are secondary elements, what we are dealing with is stylistics. In Greek or Latin hexameter, there is often a perceived rhythm of accents. But these accents can only be considered part of versification when there are specific rules or conventions for their use (for example, in Vergil’s hexameters, word accent and ictus must correspond in the last two feet; see chap. 2, D.1.2). Other rhythmic patterns can also be defined. One could speak of a rhythm of accents, of long or short, or even particular sounds. The rhythm of line 1 of Beowulf might be different from the rhythm of line 2 in any of these senses. But this is not necessarily a matter of versification. Other cases may be purely illusory, for example, the rhythms of, say, the liquid consonants r and l in “Mary had a little lamb”).
A.3. Motif and Theme
Musical terms on a higher level of organization include motif and theme. These are perfectly intelligible descriptive words for verse if used in direct analogy with their meanings in music: a motif is a short, recognizable pattern of notes; a theme is a larger unit of musical elements. In music, however, these are generally not descriptive of basic features of composition, nor would they be in most conventional poetry.1 Furthermore, the overuse of the word theme in literary criticism has rendered it almost useless for any purposes of literary analysis.
Poets frequently allude to the real or imagined musical bases of their verse. In classical and modern verse, sing is conventionally used as a metaphor for the writing of poetry; ode derives from the Greek word for song; many poems use the refrain; and even pure verbal repetitions in some modern verse seem based on music. Some forms are direct products of music; others that adopt these forms as a convention effectively turn the musical foundation into a metaphor for musical foundation.
B.1. Pseudo-musical forms are often in fixed stanzaic form, many of which originated with medieval musical or dance forms, as their names sometimes suggest: rondeau, sonnet, virelai. The French “fixed forms” as defined in the nineteenth century are the clearest example; all originated in musical forms but in their revived form had little or nothing to do with music (see chap. 3, G).
B.1.1. The most common pseudo-musical form in English is the sonnet—a fourteen-line stanza composed of three quatrains and a concluding couplet (Shakespearean) or two quatrains followed by two tercets or three-line units (Petrarchan). The sonnet is in English a pure imitation, since the musical basis of the form was lost before the verse form was adopted in English. English writers copied what was already a purely literary form from Petrarch, incorporating as they did some of the musical language that may or may not indicate the musical form.
B.2. Ode
One of the most interesting examples in English of a pseudo-musical form is the ode. Historically, the word has been used of two quite different genres, generally described as the Horatian ode and the English or romantic ode.
B.2.1. A Horatian ode is a variant of Horace’s poems in Aeolic form (see chap. 2, E). Although Horace’s meters could be imposed directly upon other languages, English versions usually only allude to that form. Classicists now disagree as to whether Horace’s stanzas should be analyzed as three- or four-line stanzas, but editions of his poems have always printed them as four-line stanzas, and all imitations have used this form. Most versions of Horation ode also attempt to reproduce common themes in Horace. One of the most famous in English is Andrew Marvell’s “An Horatian Ode: Upon Cromwell’s Return from Ireland.” The stanzaic form is shown in the following:
The forward youth that would appear
Must now forsake his Muses dear,
Nor in the shadows sing
His numbers languishing.
The relation to the Horatian ode is more visual than precisely metrical; Marvell’s stanza is an apparent imitation of or allusion to the fifth Asclepiad (see chap. 2, E.3). The musical foundations of this form are remote and are little more than metaphorical even in Horace.
B.2.2. The second form of ode is the romantic or English ode, modelled after the Greek odes of Pindar. Most histories associate this genre with the mid-seventeenth-century poet Abraham Cowley, but the form appears earlier in Ben Jonson. Among the basic forms is a repeating three-stanza unit: in Jonson, these stanzas are labelled turn, counter-turn, and stand (translating strophe, antistrophe, epode). The antistrophe repeats the metrical form of the strophe; the epode has a new form. The following is the opening “Turne” of Jonson’s “To the immortall memorie, and friendship of that noble paire, Sir Lucius Cary and Sir H. Morison”:
Brave Infant of Saguntum, cleare
Thy coming forth in that great yeare,
When the Prodigious Hannibal did crowne
His rage, with razing your immortall Towne.
Thou, looking then about,
Ere thou were halfe got out,
Wise child, didn’st hastily returne,
And mad’st thy Mothers wombe thine urne.
How summ’d a circle didst thou leave man-kind
Of deepest lore, could we the Centre find!
B.2.2.1. English poets exploited both the obscurity of Pindar’s language (as the above example shows) and the apparent freedom of Pindar’s verse, a freedom perhaps enhanced by the obscurity of the fundamental rules of that verse. Many English odes, including those of Jonson, do not follow the three-stanza form but simply repeat a unique stanza. Since there was no set form in a Pindaric stanza, poets could use or invent any line or stanza in English, as long as the form was repeatable. Metrically coherent stanzas could be constructed of any length, in any meter or rhyme scheme (for example, in Coleridge’s “Ode to Tranquillity”). In the fully developed romantic ode, even the requirement that successive stanzas repeat the same form is dropped (see as an example Coleridge’s “Dejection: An Ode”).
C.1. In 1602, Giulio Caccini published a book of madrigals, Le Nuove Musiche, with a polemical preface. In this preface, Caccini constructs a history of music casting himself and the members of his Florentine Camerata as reformers. The target of Caccini’s polemic is the obscuring of words in traditional music. That words when sung were often unintelligible had been a theme in discussions of music for some time. In Dante’s Divine Comedy, the obscurity of words is a given: “I seemed to hear a ‘Te Deum’ in voices mixed with melody. This image affected me just as when we hear people singing with an organ: now we understand the words, and now we do not” (Purgatory, canto 9). In its meetings of 1545–63, the Council of Trent had demanded that words in the Mass be intelligible: “For those masses celebrated with singing or with organ . . . the singing must be constituted so as not to give empty pleasure, but so that words can be clearly understood by all.” And still today, lyrics of popular music are often ill-heard and misunderstood, or simply invented by individual listeners and amateur singers.
C.1.1. Caccini’s polemic concerned secular music. To clarify the words, Caccini promotes monody over polyphony, that is, music with a single vocal line with harmonic accompaniment rather than the production of harmony through the combination of potentially independent melodic lines. The melody is itself subordinate to the words: notes are to be chosen, Caccini states, “according to the sentiments of the words.”2 In “The Role of the Guitar in the Rise of Monody” James Tyler notes that the popularity of the guitar is a direct function of this type of music.
C.1.2. The term Caccini used to describe the new style of music was stilo rappresentativo, generally translated as recitative, a declamatory verse set off from the more lyrical aria.3 Music in this style, whether found in opera or madrigal writing, was to be entirely dependent on words, and no musical element (e.g., a melodic interval or musical rhythm) was to be constructed unless it accorded with the sentiments expressed in the verse. Consequently, there was to be no purely virtuosic or ornamental musical element.
C.1.3. There are many paradoxes in this history. Caccini’s theory legitimized a new style of verse, the recitative, in which ordinary principles and restrictions of versification and musical considerations did not apply. But in practice, Caccini’s madrigals were innovative only in terms of music; many were written to support preexistent verse. Furthermore, the standard histories of opera beginning as early as the eighteenth century often complain that the style developed by Caccini and Monteverdi promoted the very kind of meaningless ornamented singing against which Caccini polemicized.
C.2. The History Revised
In the late nineteenth century, Nietzsche revisited the same polemic in Birth of Tragedy, with the operas of Richard Wagner as the central focus. In Nietzsche’s revisionist version of this history, the villains were the Florentines themselves and the genre of modern opera, which Nietzsche attributes to them. In recitative, music is subordinate to words; in Nietzschean terms, the musical, Dionysian element is thus subordinated to the rational, Socratic element characteristic of decadent modern culture. Nietzsche promoted instead the dominance of music which, as an enthusiastic Wagnerian in these early writings, he claimed to find in certain passages of Wagner’s Tristan.
C.2.1. Declamatory Verse
Wagner’s early opera Lohengrin is written in large part in conventional rhyme pairs (rhymes plates, or rhymes croisés); these lines alternate with decasyllables with distinct iambic rhythm, imitating, it seems, conventional late-nineteenth-century descriptions of English blank verse. In Wagner’s later work, an entirely different type of line develops. Some passages of what might be called musical highlights equivalent to the arias of the earlier operas are constructed on the basis of rhyme, accent, with a line length so short that these features appear to be ornamental rather than structural (e.g., the love-duet from Tristan, act 2, or the closing “Mild und leise” of act 3). Verses equivalent to earlier recitative seem roughly syllabic. In The Ring, declamatory verses often allude to verse systems and elements of verse systems (rhyme, meter, assonance, alliteration) but do not follow them. Even a visual inspection of the following lines from Götterdämmerung, act 3, reveals these allusions:
Starke Scheite schichtet mir dort
am Rande des Rheines zuhauf
Hoch und hell lodre die Glut,
die den edlen Leib
des hehrsten Helden verzehrt. . . .
Weiss ich nun, was dir frommt?
Alles, alles, alles weiss ich,
alles ward mir nun frei!
Auch deine Raben höre ich rauschen;
mit bang ersehnter Botschaft
send’ ich die beiden nun heim.
Ruhe, ruhe, du Gott!
———
[Stack stout logs for me in piles there / by the shore of the Rhine! High and bright let a fire blaze / which shall consume / the noble body of the mighty hero. . . . Everything, everything I know, / all is now clear to me! / I hear your ravens stirring too; / with dreaded desired tidings / I now send them both home. / Rest, rest now, o god!] (trans. Lionel Salter, Deutsche Grammaphone)
C.2.2. Such passages seem entirely freed of the constraints of versification, even while acknowledging and in some cases incorporating principles of those systems. In the language of the polemicists, the lines are constructed on the basis of the verbal meanings, not, as in classical verse, on abstract versification systems. Insofar as the music expresses both the specific and general content of these lines, the above example and others like it certainly seem in the spirit of Caccini’s polemic, although Nietzsche claims otherwise, and Wagner himself was silent about these early polemics. Verse defined this way is perhaps conveniently not subject to ordinary formalist debate: one cannot provide evidence for why a particular verse might correctly or incorrectly represent the abstract idea it conveys or is meant to convey, nor could one expect any serious agreement on what that idea might be.
D. Blues: Text and Performance
One of the most significant forms of popular music produced in the twentieth century is blues. I include it here because most readers are familiar with it and because it shows the instability of the levels of composition and performance discussed throughout this study, as well as the difficulty of providing strict definitions for these levels. What are the differences between the underlying form (the meter and versification), the realization of that form in the composer’s “text” or “song,” the associated stylistic features of that realization, and the performed variations of that form and stylistic features?
D.1. Basic Blues Progression
The basic blues progression consists of three chords, in classical music theory known as the tonic, subdominant, and dominant (labelled I, IV, and V). For the key of E, these are E, A, and B; for the key of C, they are C, F, and G. Most beginning guitarists can learn these in a day or so and play tolerable blues accompaniment by the end of the week. What has come to be the typical blues progression is in the following form; each numeral is a measure of four beats and the entire progression is in twelve measures:
I (IV) II
IV IV
I I
V IV I (V)
A familiar example is as follows:
There are thousands of blues songs written according to this formula.
D.2. Dropped Beat
A curious feature of these songs from a metrical standpoint can be seen by comparing some of the earliest recordings from the 1930s with recordings from the 1960s and later. Normally, one thinks of an evolving form as growing more complex and less rule-bound. In blues one hears the opposite. One of the most influential blues singers was Robert Johnson (d. 1938). Only twenty-nine songs in Johnson’s original recordings still exist, a few of them in multiple versions and some released only in the 1960s. Most of these are in the repertoire of modern blues musicians. In these and in those of his contemporary Son House, one of the most striking characteristics is the “dropped beat.” You can’t tap your foot to the recording of Johnson’s “I Believe I’ll Dust My Broom”; if you do, you will quickly get lost. For Johnson, and for many other blues players, when the vocal line ended (say, in the first line above), and there was nothing of any particular interest happening on the guitar, it was perfectly appropriate simply to begin the next line, cutting out part of the final measure of I. If too much was happening on the guitar, or the guitarist had difficulty negotiating a passage, the final bar could be extended.
The dropped beat (or less commonly an added beat) is so conventional in early blues that it is almost a rule.4 Even performances that are technically in perfect rhythm incorporate the illusion of such a missed beat (of many examples, the recording by Son House of “Lay Down Dirty Blues”). One could argue that the dropped beat is a conventional sign of spontaneity, in the same way as are the often bizarre and incongruous lyrics of a song such as Johnson’s “Red Hot.” This feature is often imitated in mid-century folk music, in much jazz, but oddly, rarely heard in standard blues of the late twentieth century. A performer such as B. B. King never in any of the recordings I’ve heard drops or adds a beat.
D.2.1. Implications
So let us suppose, hypothetically, that this dropped beat marks the difference between ’20s blues singers and those from the ’70s and ’80s. How do we describe it? One can define various levels here; for convenience, I will define four, but curious readers can of course multiply these: the abstract rigid form, the form realized in a particular song (by a composer), the song realized in a particular performance (by a performer), what is heard or experienced by a listener. The composer is certainly aware of each level, as is the listener listening to or imagining any particular song or performance.
It is tempting to try to arrange these levels in a hierarchy, but no hierarchy seems to work. I simply pose the alternatives below:
a) The dropped beat is simply a matter of performance; it is not imagined by the composer, and the listener experiences it simply as a quirk of a performer.
b) The dropped beat is part of the form itself, as much a requirement for early blues as the progression itself. Thus the written form of the song (in, say, classical Western musical notation) falsifies the actual song, however we define what that actual song might be.
c) The dropped beat is ignored by the listener.
d) The dropped beat is purely a function of musical competence: an amateur or professional musician working on or performing a song can add or drop beats at will. These are of absolutely no consequence unless an uninvited listener walks into the room.
e) The dropped beat is purely a matter of considerations of performance: soloists rarely get lost or tangled in strange rhythms and can always find or define their way out of such entanglements; a group, by contrast, needs a clearer rhythmic pattern in order to play together in a coherent fashion (jazz musicians of course might dispute this).
D.3. There is no need to confine this discussion to blues; the performed quirks of country music and folk music (deliberate vocal breaks, bad intonation, etc.) are analogous; and classical music poses the same problems from a somewhat different standpoint in the so-called original or period instrument revival and the surrounding polemics. The best a study of versification can do is pose a sketch of these levels, levels that may change in the history of a genre. In the above case, it is possible that stylistic quirks of Johnson become hardened into rules of performance, and finally into rules of genre. Or, alternatively, we could speak of a versification system as an abstract form realized most perfectly in a late, systematized form (perhaps the B. B. King version of the blues). Certain poetic cultures have a history congenial to this analysis (thus French verse evolves into a self-conscious classicism in the eighteenth century; quantitative verse evolves into the self-conscious and aristocratic Latin forms of the first century BCE). But for others, we must simply muck along as best we can.
E. Arbitrary Forms: Serial Music
Serial music or twelve-tone music is a particular form of what is called atonal music developed in the early twentieth-century by Arnold Schoenberg and Anton Webern. It is also the basis of the theories of music in Thomas Mann’s Doktor Faust. I include it as an example of how art is liberated from traditional strictures, not simply by ignoring those strictures but rather by imposing new and even more radical strictures on it.
E.1. In its simplest form, serial music avoids all traditional harmonies and melodic conventions by imposing an entirely new set of rules. Essentially, the tonal elements are the twelve notes in an octave of a tempered keyboard, where each step is a half-tone: C, C#/D♭, D, D#/E♭, E, F, F#/G♭, G . . . etc.
Each musical piece must be constructed of variants of a basic row of these twelve elements: the basic row consists of all twelve notes in whatever sequence the composer defines (say, 1, 9, 8, 6, 5, 3, 11, 10, 4, 2, 12, 7). I don’t know what this sounds like, but I could find out by playing it on a piano (C, A♭, G, F . . .). This basic row can be varied by playing it as an inversion, whereby upward intervals become downward intervals (1 [=13], 5, 6, 8 . . .).5 It can also be played backward (7, 12, 2, 4 . . .). It can also be played inverted and backward (7, 2, 12, 10 . . .). These four variant forms can then begin on any of the twelve notes themselves, giving forty-eight possible variations. Theoretically, there is no privileged note or apparent key in such music and no tonal center.
E.1.1. Modern listeners are familiar with much atonal music simply by being audiences of cinema. But most listeners not used to classical music will still find the sound of strict serial music as radical and jarring today as it was in the 1920s (listen, for example, to Webern’s Drei Geistliche Volkslieder of 1925). Paradoxically for the modern ear the most radical of musics is that which was produced by the most systematic and rigorous application of rules.
E.2. Modern Verse Analogues
Twelve-tone music is analogous to the experiments conducted by such poets as Verlaine in the late nineteenth century and by many poets in the twentieth century. Although French poets wrote free verse and prose poems, some of the most disruptive and revolutionary writing by Verlaine was the result of his application of arbitrary but fixed rules for composition (see chap. 3, C.4.2). Examples are also easily found in pictorial art where some of the most visually unsettling works, such as the paintings of Uccello or the modern drawings of Henri Flocon, have been produced not by rejecting but by strictly following the rules and implications of linear perspective.
E.2.1. Self-conscious artificial procedures are also used notably by at least some of the L=A=N=G=U=A=G=E poets of the mid- and late twentieth century and in certain compositions (poetic and musical) by John Cage, where arbitrary rules and chance combine to produce a work apparently free of strictures of traditional forms. It is often difficult to know whether the unsettling and often humorous effects produced by poets such as Susan Howe (e.g., from “The Midnight”: “For here we are here / BEDHANGINGS . . .”) or Ron Silliman (“I am Marion Delgado”) are due to the complete absence of formal and thematic rules or to the rigid application of unimaginable ones.
Texts: Early English texts from facsimiles of original editions in Early English Books Online, eebo.chadwyck.com. Among the many blues compilations, see Robert Johnson, Complete Recordings, 2 discs, Sony, 1990.
References: Charles Burney, A General History of Music: From the Earliest Ages to the Present Period, 4 vols. (London, 1789; rpt. New York: Dover, 1935); Friedrich Nietzsche, The Birth of Tragedy (1872; trans. Walter Kaufman 1967; New York: Modern Library, 2000); W. Oliver Strunk, Source Readings in Music History, rev. ed., ed. Leo Treitler (New York: W.W. Norton, 1998); James Tyler, “Italy: The Role of the Guitar in the Rise of Monody,” in James Tyler and Paul Sparks, The Guitar and Its Music: From the Renaissance to the Classical Era, pp. 37–50 (Oxford: Oxford Univ. Press, 2002). For the L=A=N=G=U=A=G=E poets, the evolving Wikipedia entry is perhaps the most appropriate starting point.
1. A set of versification rules that incorporates motif and theme certainly could be devised. For example: A poem is in four lines. Line 1 must contain the word lion; line 2 must contain a statement concerning transcendental philosophy; line 3 must be in eight syllables.
2. This history of early monody, and the centrality of the Florentine Camerata, was popularized by Giovanni Batista Doni in the mid-seventeenth century; Doni’s discussion was itself published in the eighteenth century and popularized in English through Charles Burney’s inclusion of it in his popular General History of Music in 1789. According to these histories, Italian opera as practiced in the eighteenth century originated in the theories of Caccini and his contemporaries and in the dominance of the word over music that they believed had precedent in the works of Plato. Caccini’s preface is available in Strunk’s Source Readings in Music History, pp. 607–17.
3. This became the basis for the distinction between recitative and aria in classical Italian opera; it is analogous to the difference between spoken and sung sections of eighteenth-century German Singspiel and even twentieth-century musical comedy.
4. This is also a characteristic feature of much of the early music collected in American Primitive: Vol. II: Pre-War Revenants (1897–1939), collected by John Fahey, Revenant Records, RVN 214, 2005.
5. In an inversion, the successive note is found by inverting the interval between notes: if in the initial row, the next note is 5 half-steps higher than the first, in the inversion, that note will be 5 half-steps lower: one can produce these mechanically simply by subtracting the numbers in the series from some other number.