Poetic Waveforms, Discrete Fourier Transform Analysis of Phonemic Accumulations, and Love in the Garden of Tennyson’s Maud

Poetic Waveforms, Discrete Fourier Transform Analysis of Phonemic Accumulations, and Love in the Garden of Tennyson’s Maud

Marc R. Plamondon

Nipissing University

marc.r.plamondon@gmail.com


KEYWORDS / MOTS-CLÉS

phonostylistics, phonemic accumulation, Fourier Transform, Tennyson / phonostylistics, accumulation phonémique, Fourier Transforment, Tennyson


  • 1.0 Phonemic accumulations
  • 2.0 Phonemic accumulations: mathematical model
  • 3.0 Phonemic accumulations: graphical representation
  • 4.0 Discrete Fourier Transforms of phonemic accumulations
  • 5.0 Broad Shape Percentage and Ratios
  • 6.0 Interesting Phonemic Departures
  • 7.0 Love in Maud’s garden
  • Works Cited
  • Tables

Readers have often remarked upon the pleasant sounds of Tennyson’s poetry. In 1878, Henry Elsdale echoes popular sentiment when he writes: “Mr. Tennyson is a most careful student of the laws of euphony. By years of study and practice in versification his ear has been so trained to the harmonies of sound as to lead to a most remarkable phonetic agreement, by a process of more or less unconscious selection and euphonious grouping of his words. The admitted harmony and perfection of his versification generally is largely due to a close observance of these harmonies of sound” (180). And while some readers will admit that the success of Tennyson’s style is not all a result of necessarily beautiful sounds — in 1893 George Campbell Macaulay speaks of Tennyson’s poetic effects resulting from “the harmonious or discordant collocation of sounds” (xxvi) — many agree that Tennyson’s poetry demonstrates a heightened manipulation of sound combinations for its poetic effect and overall impression. Readers and scholars, however, have had trouble defining exactly what constitutes “remarkable phonetic agreement” and “harmonies of sound.” The present study proposes an approach to beginning to understand “phonetic agreement” and the collocation of harmonious and discordant sounds in poetry. It introduces the concept of phonemic accumulations to account for the effects the phonetic content might have upon a reader, and studies Tennyson’s lyrical “Come into the garden, Maud” to show how a phonemic approach to poetic stylistics can aid the reader in understanding how the sounds of words can combine in interesting ways.

Hugh Craig, in “Stylistic Analysis and Authorship Studies,” proposes a motivation for computer-assisted stylistics, namely “the uncovering of patterns of language use which because of their ‘background’ quality, or their emergence on a superhumanly wide scale, would otherwise not be noticed.” The present study explores some of these usually unnoticed patterns of language. Computer-assisted studies in stylistics have more often than not focused on the word; the current study, however, focuses on the phoneme, and thus constitutes a study in phonostylistics, the stylistic analysis of the phonetic or (in this case) phonemic content of texts.

Linguistic formalism has laid part of the theoretical groundwork for the present research. Roman Jakobson and Linda R. Waugh describe the importance of a linguistic approach to the study of literature:

Poetic language has forcefully entered into the field of linguistic research, and notwithstanding the objections, as multiple as they are vapid, of some literary critics shockingly unfamiliar with the new vistas and even with the primary principles of the science of language, linguists are assessing more and more systematically the manifold and intertwined problems of poetic sound shape and grammar, as well as of tropes, figures, and composition. [...]

Poetry, whether written or oral, whether the production of experienced professionals or of children, and whether oriented toward or against ordinary language, displays its own peculiar sound shape and grammatical structuration. (225)

While a basic understanding of linguistic elements has been brought to bear on poetic criticism, there remains a large field of unexplored territory. The “peculiar sound shape” of poetry in particular has not received much attention, due in no small part to the inherent complexities involved in its study. The advances in storage, memory, and processing speed of computers now allow for larger scopes and more detailed analysis of linguistic patterns in texts.

The present study focuses on the phonemic content of poetry. Roman Jakobson, in his seminal Six Lectures on Sound and Meaning, calls the phoneme the “cardinal element on which everything in the linguistic system hinges” (65). It is an element of language that is largely independent of individual speech patterns, it is more-or-less easily determined from the written word, and its occurrences can be tabulated. The phoneme thus lends itself well to a computer-based study of the sound content of language. One could study the detailed phonetic content of poetry, perhaps using a narrow phonetic transcription of a poem’s recitation; however, the recitation, and consequently the phonetic transcription, would vary from reciter to reciter – and even from one recitation to another by the same person. The phoneme and the broad phonetic transcription of poetry allow for the study of a more universal experience of a particular text without being hindered by specific minor variations in pronunciation.

Although Jakobson claims that on its own the phoneme “is not endowed with any specific meaning” (61), he acknowledges that it does contribute to the creation of meaning. And while other linguists have studied how the phoneme creates linguistic and semantic meaning, little work has been done to study how it creates poetic and aesthetic meaning. The occurrences of phonemes in a poem or any text, written or oral, in addition to creating words, create complex patterns whose full effects have not yet been characterized. Among scholars who have attempted to study these patterns is David Chisholm, who has studied German verse using a computer-assisted phonological approach: his calculations identify poetic loci where the phonological makeup of a poem parallels its semantic meaning. He finds that the patterns of repetition of phonemes on both the horizontal and vertical dimensions of poetry help to qualify German poetic techniques and trends. Carrol F. Coates, studying the occurrences of particular phonemes in French poetry, concludes that the phonemic frequency in poems is a key factor in the sound patterns particular to poetry:

Study of […] poems by Rimbaud, in addition to certain pieces of Beaudelaire, Verlaine, and Mallarmé, leads me to propose that the establishment of norms of phonemic frequency for the entire corpus of French poetry from Baudelaire to Verlaine (as a beginning) can serve as an empirical basis for further exploration of the functioning of sound patterns in poetic structuration. Perhaps eventually, these studies can at least contribute to more general theorizing on a poetic of metrical discourse. (94)

Reuven Tsur, taking his cue from Jakobson, attempts to reclaim the distinction between musical and unmusical sounds in poetry (and language in general) from the realm of expressionistic commentary. He does this in part by identifying phonemes and types of phonemes responsible for the distinction:

Certain speech sounds are considered more beautiful and more musical than others. Some other sounds, on the contrary, are deemed especially ugly or unmusical. The French language, for instance, is felt to be especially musical, thanks to the nasal vowels that abound in it and to the affricates /ts/ and /pf/ that are absent from it (and which are quite conspicuous in German, for instance). (64)

He concludes that the French Symbolist poets (of the nineteenth century) distinguish themselves from the earlier, seventeenth-century French poets by their particular use of nasal vowels. The implication of Tsur’s findings is that aesthetic meaning is created by the presence or absence of particular phonemes and phoneme groups: a heavy use of nasal vowels makes a poem beautiful. Poetic beauty becomes a quantifiable entity: the greater the frequency of nasal vowel phonemes in a poem, the greater the beauty of the poem.

Tsur attempts to distinguish the aesthetic of French Symbolists from that of the French Classicists by focusing on the use of one type of phoneme (nasal vowel sounds). While Tsur does not rely solely on the number of occurrences of the phonemes, these numbers are important to his proof, as they are for Coates. The present study, while taking into account such statistical tabulations, moves beyond this type of calculation towards a theory whose importance was revealed by a statistical study of the phonemic content of the poems of Alfred Tennyson and Robert Browning. For over a century, readers, reviewers, and commentators of poetry contrasted the style of the two poets, the large majority concluding that the poems of Tennyson are more lyrical, more melodious, more pleasant, and the poems of Browning are more harsh, more dissonant, more unmusical. The source of this difference is traditionally identified as the use Browning makes of “harsh” consonants and the use Tennyson makes of “pleasant” vowel sounds. A tabulation of the percentages of vowel and consonant use and the relative use made of different types of vowels (short, long, diphthong) and consonants (plosive, fricative, affricates, nasals) over a representative sample of poems for each poet reveals the remarkable result that there is little to no difference in usage between the two poets. One of two things must follow: either we reject the one hundred and fifty-year tradition of characterizing the difference between the two sets of poems, or we try to find a better way to characterize the difference in phoneme use.

I have developed a computer program, MetrePhone, to help assemble and process poetic data. [1] The first part of the program analyses the metre of a poem and looks for rhythmic and rhyming patterns. The second part of the program automatically transcribes a poem into its broad phonetic transcription and then allows the user to view the resulting phonemes using a few visualization tools. It also performs various extensive calculations on the phonemic content of the poem, including calculations of and relating to the phonemic accumulations.


1.0 Phonemic accumulations

The theory of phonemic accumulations originates with my current research into phonostylistics. I have based the theory on the following hypotheses:

1. A phoneme, whether read audibly or silently, produces an impression of itself on the reader’s (and listener’s) mind.
2. The impression produced by a phoneme diminishes quickly as successive phonemes are encountered.
3. When identical phonemes are encountered in close proximity, the overall impression of that phoneme is heightened considerably. This, on one level, results in alliteration, assonance, and any similar type of phonemic repetition: the repetition in close proximity of an individual language sound.
4. Phonemes can be grouped in order to assess the overall impression not simply of individual phonemes, but of types of phonemes.

The third hypothesis accounts for a more easily identifiable type of enjoyment of the sounds of poetry. Consider a short poem that contains twenty /s/ phonemes. If these phonemes are evenly distributed among the words and lines of the poem (say, one in each line but not occurring in a similar position in each line), then the effect of the /s/ phonemes would not be as great as in a poem of the same length with the same number of /s/ phonemes, but whose /s/ phonemes are mostly concentrated in one part of the poem (say, eighteen of the phonemes all occurring in the final three lines of the poem). This second poem will create a much stronger impression of /s/-ness on the reader as the final three lines are read. The typical reader is not likely to notice any significant /s/-ness in the first poem.

The fourth hypothesis represents the more practical approach to achieving meaningful results. If similar sounding phonemes can be grouped together, phonemes with similar effects upon the reader or the reading experience, then the overall effect of the qualities represented by the groups can be examined. For instance, the /s/ phoneme shares qualities with the /z/ phoneme and even the /f/ phoneme: they are all fricative consonants, and fricative consonants as a whole can be characterised as softer-sounding than other types of consonants. The harsher consonants are the plosives: the /b/, /k/, /p/, and /t/ phonemes potentially all contribute to an emphatic or possibly energetic sound impression. Phonemic accumulations represent a method of calculating the overall harsh-ness or emphatic-ness of the plosives and the overall soft-ness of the fricatives.

The calculation of phonemic accumulations is thus designed to provide a better evaluation of the use of phonemes in a text, one that goes beyond calculating the percentages of occurrences. The calculation is based on the theory of the persistence of phonemes, which is represented by the first two hypotheses above. This theory is based in turn on the theory of the persistence of vision, which claims that when light makes an impression upon the eye, the effect of that impression lasts for a very short period of time, but successive impressions upon the eye can accumulate in order to produce certain visual effects. The continuous motion one sees when viewing a motion picture is a visual effect resulting from the light impression of twenty-four image frames each second. Exactly why this occurs is not conclusively known. Whether it is an inherent property of the eye, the optic nerve, or the brain is unclear, but the effect is real and allows for the enjoyment of watching our favourite movies on the big screen. The persistence of phonemes is, analogously, what theoretically allows us to enjoy the sound effects when reading our favourite poems.


2.0 Phonemic accumulations: mathematical model

The theory of the persistence of phonemes states that the effect of a phoneme upon a reader is carried through to the following phonemes. This can be modelled mathematically: Figure 1 represents the function used by MetrePhone to calculate the effect of a phoneme when it is read. A phoneme exerts its strongest effect at point t = 0 on the graph, when it is encountered. At point t = 1, the next phoneme is being read, and the effect of the original phoneme is still strong. At point t = 2, the following phoneme is being read, but the effect of the original phoneme remains strong. At point t = 10, the effect of the original phoneme has diminished significantly. By point t = 20, the effect of the original phoneme has all but completely dissipated. The values represented by Figure 1 constitute the basis for all subsequent calculations of phonemic accumulations. The function in use for the calculations could have been any from a wide variety of functions. Two other interesting possibilities are linear decline (that is, a straight line graph) and exponential decay (such as describes the half-life of radiation). The function represented in Figure 1 was chosen because it bears a resemblance to a graph of the sound intensity after hitting a key on a piano, though in this case the diminution of intensity is less quick.


figure 1
Figure 1: Phoneme persistence function


The phoneme persistence function is a variation of the Gaussian (or normal) function, where t is raised to the power of 3 instead of 2; this produces a lengthier span during which the effect is strong and a quicker decline after that duration.

f(t) = Ae-t3/B

The actual values for the function, that is, the value for the initial intensity (A) and the rate at which that intensity fades (B), were chosen after repeated calculations and graphs involving various combinations. A value of 5 for A was found to allow for a significant phonemic effect, while still allowing for meaningful distinctions between successive phonemic clusterings. A value of 2000 for B was found to allow for a significant persistence of the effect of the phoneme among the immediately subsequent phonemes, while allowing for a quick diminishing of its effect after these. As such, a phoneme loses any of the effects of its persistence about twenty phonemes after it is encountered: this equates to approximately four or five syllables of English words, which seems a reasonable duration for the effect of a phoneme.

Thus, when a phoneme is encountered, the value of its persistence is set to 5. When the next phoneme is encountered, the value of the persistence of the original phoneme decreases to 4.9975, while the value for the second phoneme is set to 5; when the next phoneme is encountered, the value for the original phoneme becomes 4.9800; and when the next phoneme is encountered, its value becomes 4.9330 (while the values for all previous phonemes encountered decrease similarly). This continues until the persistence of the original phoneme reaches 0, indicating that it no longer has an effect on the reading experience. However, if another phoneme of the same type is encountered, then the function that determines its level of diminishing influence is reset at t = 0, and the value of the persistence of that phoneme is increased by 5. In this way, the cumulative effect of a phoneme can be calculated. This method of calculation reflects the theory that a quick succession of /b/ phonemes will create a more powerful /b/ effect than if the same number of /b/ phonemes were more evenly dispersed among the words of the poem.


3.0 Phonemic accumulations: graphical representation

The present study does not measure the effects of individual phonemes, but rather the effects of phonemes belonging to the same phoneme group. Table 1 shows the English consonant phonemes in the groups used by the computer application and the present study. Note that the affricate consonants are grouped with the fricatives for the purposes of reducing the number of groups. MetrePhone reads through the phonemic content of a poem. When it encounters a phoneme from a particular group, the accumulation value for that group is increased by a value of 5. When no phonemes for that group are encountered, the accumulation value for that group decreases according to the phoneme persistence function. Figure 2 is a representation of the resulting phonemic accumulations for the four consonantal groups in Robert Browning’s “My Last Duchess.” The data are calculated for each phoneme of the poem, but the graph shows the resulting values after each syllable of the poem, where the values of the phonemic accumulations for each phoneme group are calculated using the phoneme persistence function and the method described above. For the phonemic accumulations of most poems, including “My Last Duchess,” the graphs of the nasal and approximant accumulations do not display the same dramatic quality of peaks and troughs as do the first two graphs: the plosive and fricative accumulations tend to exhibit the most substantial and most pronounced variations within a poem.


figure 2
Figure 2: Phonemic accumulations for consonant groups for “My Last Duchess”


As Figure 2 shows for “My Last Duchess,” there is a general rise to a high point in the fricative accumulations about one third of the way through the poem, followed by a gradual decline, though there are significant localised peaks and troughs as the general shape declines. It is difficult to characterize these graphs beyond the simple calculations of the mean values and the peak values. But because these graphs resemble waveforms, they can be treated as such: the Discrete Fourier Transform (DFT) can be used both to characterize and transform the data represented by the accumulations graphs.


4.0 Discrete Fourier Transforms of phonemic accumulations

A Fourier Transform produces a decomposition of a function, signal, or waveform in general into its sinusoidal coefficients, which, while often infinite in number, necessarily characterize the shape of the waveform. The result has both mathematically real and mathematically imaginary components. As a general rule, while one is interested in retaining all the data, one is more interested in the magnitude of the values than the phase of the values, both of which are calculated from both the real and imaginary values of the Fourier Transform. The magnitude values are a calculation of the relative importance of sine waves of different frequencies to the overall constitution of the waveform. These produce a magnitude spectrum, which can be quantified and characterized. A Fourier Transform is thus used for wave spectrum analysis: it yields the relative strengths of the various frequencies that make up the waveform. For example, the Fourier Transform of a song recording can reveal at any given instant the relative strengths of the lower frequencies (the drums, the bass guitar), the mid-range frequencies (the lead guitar, the vocals), and the high frequencies (the higher vocals, the synthesizer, etc.). A graphic equalizer, such as that used in music production and playback, uses Fourier Transform techniques for its display. When the waveform is not continuous — that is, when it is sampled at discrete intervals — one cannot use the usual Fourier Transform proper, but an altered version, the Discrete Fourier Transform. Because the phonemic accumulation values in the present study are calculated for each phoneme and syllable in a poem, the results are not continuous but discrete, and therefore the Discrete Fourier Transform is used. Both the Fourier Transform and the Discrete Fourier Transform are invertible: the magnitude spectrum and the phase spectrum together contain all the information required to reconstruct the original waveform.

MetrePhone can calculate the Discrete Fourier Transform of the phonemic accumulations and then process the results. Before doing so, it quadruples the data. It assumes that the phonemic accumulation data, such as graphed in Figure 2, represent the first quarter of a full period of a wave. The second quarter is a reversed image of the first, the third quarter is a negative image of the first, and the last quarter is a reversed and negative image of the first. This technique allows the accumulation graphs to resemble more closely a periodic wave and consequently minimizes the effects of the boundaries of the data (at the beginning and ending of the poems).


figure 3
Figure 3: Discrete Fourier Transform of the plosive accumulations for “My Last Duchess”


Figure 3 is a graph of the magnitude spectrum of the Discrete Fourier Transform of the plosive accumulations of Robert Browning’s “My Last Duchess” (that is, it represents the magnitude spectrum of the DFT of the top graph of Figure 2). Figure 3 thus characterizes the shape of the plosive accumulation graph, in particular by characterizing the rapidity or gradualness of the rises and falls (the rapidity is an indication of a high frequency and the gradualness is an indication of a low frequency). The values are largest for the lowest frequency values, and tend to diminish as the frequency values increase. In the highest frequency region, the values are usually low and generally negligible because they represent miniscule variations in the shape of the wave. Figure 4 represents the magnitude spectrum of the Discrete Fourier Transform of the fricative accumulations of the same poem.


figure 4
Figure 4: Discrete Fourier Transform of the fricative accumulations for “My Last Duchess”


5.0 Broad Shape Percentage and Ratios

The Discrete Fourier Transform of the phonemic accumulations can be used to qualify the types of effects these consonantal phonemes have on the reading experience. One such calculation is the Broad Shape Percentage (BSP) of the accumulations: this is a calculation of the weight of the first three components (including the zero component) of the magnitude spectrum of the DFT relative to the weight of the full spectrum. The value is thus an indication of the relative importance of the “DC” magnitude (the zero component), the first quarter sine wave magnitude, and the first half sine wave magnitude to the overall shape of the phonemic accumulation waveform. The zero-order spectrum magnitude is high if the phonemic accumulations are at a high and steady value. The first-order spectrum magnitude is high if the phonemic accumulations grow from a low value to a high value (or, less probably, descend from a high value to a low value). The second-order spectrum magnitude is high if the phonemic accumulations grow from a low value to a high value and then descend back to a low value (or, less probably, start at a high value, descend to a low value, and return to a high value). These three values are a good indication of the broad shape of the phonemic accumulations graph and indicate the broad tendency for the accumulations to move to or from a climax.

A second calculation, the Fricative to Plosive Broad Shape Ratio (fpBSR), can then be obtained by dividing the Broad Shape Percentage value for the fricative accumulations by the Broad Shape Percentage value for the plosive accumulations of the same poem. The Fricative to Plosive Broad Shape Ratio is a measurement of the relative importance of the broad climactic shape of these two phonemic accumulation graphs. Poems with a fpBSR of 1 have equal Broad Shape Percentages for the fricative and plosive accumulations. This indicates that the fricatives and plosives have equally simple or equally complex waveforms for their fricative and plosive accumulations. Note that this says nothing of their relative weights: it is not a measure of the relative number of plosive and fricative phonemes in the poem, nor is it a measure of the relative intensities of the phonemic accumulations. It is instead an indication of whether or not the phoneme groups follow similarly simple or similarly complex variations in their accumulation intensities.

The results are highly intriguing. Table 2 lists the Fricative to Plosive Broad Shape Ratio values for fifty poems, drawn mostly from the nineteenth century.[2] Most values fall between 0.7 and 1.3, and the average value for the fifty poems is 1.03. The significance of the fpBSR value is elusive, but the value appears to be an indication of the poem’s characteristic use of sound. It seems that poems with lower fpBSR values are poems that rely more heavily on more naïve sound effects, with perhaps less complex or subtle sound/language effects. An obvious example is “Green Eggs and Ham,” which relies heavily on repetition and rhyme, but other poems such as “The splendour falls on castle walls” and even Blake’s “Introduction to the Songs of Innocence” are heavily dependent on more obvious sound effects, mostly resulting from repetition. The poems with a value less than one are poems that I would classify as generally read as “musical” poems — that is, poems with a simplistic or naïve relationship with music — or poems that are heavily onomatopoetic – that is, poems that seek to imitate external sounds, such as the sound of a bugle, with language effects. The poems with a value greater than one are poems that are more distanced from naïve sound effects: they are concerned perhaps with a more subtle interplay with the sounds of words.

The calculation of the fpBSR, resulting from the magnitude spectrum values of the DFT of the phonemic accumulation graphs, is a scalar value that characterizes the comparative shape of the two (fricative and plosive) phonemic accumulation graphs. For example, in terms of the phonemic content of the poems, the poems with a value less than one have more obvious climactic shapes in the plosive accumulations than in the fricative accumulations and have more localized variations in the fricative accumulations than the plosive accumulations. Contrarily, the poems with a value greater than one have more obvious climactic shapes in the fricative accumulations than in the plosive accumulations and have more localized variations in the plosive accumulations than the fricative accumulations. This measurement of the Fricative to Plosive Broad Shape Ratio bears out an analogy with music. Poems with a lower value are similar to musical compositions that present a singular, over-arching climactic structure. Many popular songs have this structure, as do such compositions as Ravel’s Bolero and the slow movement from Mahler’s Fourth Symphony: they have a quiet start and gradual rise in volume and tension to reach a large climax at the end. A musical composition that relies on more subtle or more frequent changes in dynamics and tension (as with perhaps a Beethoven symphonic movement) is analogous to a poem with a higher fpBSR value.

If the music analogy holds, then it is the broad climactic shape of the plosive accumulations counterpointed with the more localized rises and falls of the fricative accumulations that produce a poem with more naïve climactic effects. These poems have, as with the analogous musical compositions, a more immediate effect and a tendency to be more popular. The poems with lower values in Table 2 do tend to be more popularly enjoyed than the poems that have higher values. The poems with more sophisticated climactic effects — the Beethoven symphony poems — have more localized rises and falls of the plosive accumulations and a more broad climactic shape of the fricative accumulations. These poems tend to be more “literary” and less popular: for the most part, they are more difficult.

The interesting exception is Elizabeth Barrett Browning’s sonnet, “How do I love thee? Let me count the ways.” The seemingly anomalous result for this very famous sonnet can be partially explained by its position within Barrett Browning’s sonnet sequence. Figure 5 shows the Fricative to Plosive Broad Shape Ratio for every sonnet in the Sonnets from the Portuguese.

The sequence of sonnets displays a broad tendency to follow a pattern. Perhaps most notable is the way sonnets with a low ratio value are interspersed with sonnets with a high ratio value. The high values follow a broad shape, from a high point with sonnet VI to a low point with sonnet XXXII and to the highest point with sonnet XLIII, and the low values also follow a broad shape. The penultimate sonnet, “How do I love thee? Let me count the ways,” is remarkable here as the climax of the sequence, prepared for by some, if not all, of the sonnets that precede it. The sequence ends not with this high-ratio-value sonnet, but with one whose ratio value is less than one, suggesting a return to a more simple or naïve sound to end the sequence. While Figure 5 does not explain the penultimate sonnet’s popularity, it does help confirm its important position within the sonnet sequence and suggests that, as the climactic moment of the reading experience of the sequence, it is a natural choice to remove from the sequence for reading on its own.


figure 5
Figure 5: Sonnets from the Portuguese: Fricative to Plosive Broad Shape Ratio


6.0 Interesting Phonemic Departures

The Fricative to Plosive Broad Shape Ratio is potentially a powerful means with which to describe or categorize poems on a macro-stylistic level. Another interesting measurement is the Interesting Phonemic Departure, which gives insight to a poem’s use of language on a micro-stylistic level. This is obtained by observing the difference between the phonemic accumulations of a poem and a filtered version of the same data. The Fourier Transform is often used for filtering “noise” from such things as audio signals and digital images. Its application to digital image manipulation goes beyond filtering: it can be used for such transformations as image reconstruction, softening, and edge enhancement. For the purposes of noise filtering, especially as applied to audio signals, wavelengths that have only a very small presence in the magnitude spectrum can be removed in order to emphasize those wavelengths with a stronger presence. The reconstructed signal, using an Inverse Fourier Transform, will be identical to the original signal, except the selected wavelengths will have been filtered out, thereby usually reducing the background “noise” of the signal (such as the “hiss” in an audio signal).

To filter the phonemic accumulations, those frequencies that have a value in the magnitude spectrum below a value of 1 are removed (that is, they are set to 0) and the waveform is reconstructed using the inverse DFT with the remaining values. This filters out the phonemic “noise,” the smaller contributions to the waveform. What results is a less complex waveform, one that represents the broad tendencies of the phonemic accumulations to rise and fall during the reading experience. Theoretically, the filtered phonemic accumulations represent what the mind expects to experience based on the general word choices in the poem, the general distribution of plosives or fricatives throughout the poem. What the mind actually experiences is represented by the non-filtered phonemic accumulation graphs, which take into account the poem’s every phoneme. Figure 6 is a graph of the plosive accumulations (drawn with a solid line) of Tennyson’s “Come into the garden, Maud” with the filtered plosive accumulations (drawn with a dashed line). The filtered accumulations generally follow the same shape as the original accumulations, but many or all of the jagged areas are “smoothed” out. The Interesting Phonemic Departures occur where there is a significant difference between the actual and filtered accumulations. Figure 7 is a similar graph for the fricative accumulations. While there is no set paradigm for interpreting these graphs, including the Interesting Phonemic Departures, they do present the poetry commentator with locations within the poem upon which to concentrate attention, locations where the poem’s use of language may be particularly interesting or remarkable.


figure 6
Figure 6: Plosive and Filtered Plosive Accumulations for “Come into the garden, Maud”



figure 7
Figure 7: Fricative and Filtered Fricative Accumulations for “Come into the garden, Maud”


7.0 Love in Maud’s garden

Tennyson’s “Come into the garden, Maud” contains, as expected, a number of such interesting locations, and, in this poem, they tend to support the theory that the speaker’s madness is getting the better of him. The poem is the last lyric in the first part of the longer poem, Maud (1855). The speaker of the poem is in love with Maud, who is socially above him and thus always seems to be just out of his reach. At the end of Part I, Maud is hosting a dance in the Hall, to which the hero of the poem is not invited, but she has agreed to meet with him in the garden after the dance is over. The setting for “Come into the garden, Maud” is thus the garden where the speaker is longingly awaiting Maud’s arrival, with the last strains of the dance echoing about him. The lover has displayed in the whole poem up to this point a tendency towards madness. Tennyson says of Maud: “It shows the unfolding of a lonely, morbid soul, touched with inherited madness, under the influence of a pure and passionate love” (Van Dyke 97). The tensions in the “Come into the garden, Maud” lyric are thus between the pure love for Maud, the encroaching madness, and the underlying sense that Maud is entirely unattainable.

The moments in the poem where the fricative accumulations are high tend to correspond with moments of heightened emotional intensity when the speaker is expressing a pure or ecstatic love for the absent Maud. Conversely, the fricative accumulations are attenuated with the suggestion of impediments to his love. The Interesting Phonemic Departures when the fricative accumulations significantly exceed the expected accumulations, as revealed by the filtered accumulations, suggest more than anything those moments when the speaker seems to lose control over what he is expressing and perhaps reveals a bit more of his underlying, potential madness than he would otherwise wish to do.

One of the strongest fricative accumulation moments in the poem occurs shortly after its mid-point, with stanza seven and the beginning of the eighth stanza:


    
        From the meadow your walks have left so sweet					
        	That whenever a March-wind sighs
        He sets the jewel-print of your feet
        	In violets blue as your eyes,
        To the woody hollows in which we meet
        	And the valleys of Paradise.
        	

        The slender acacia would not shake
        	One long milk-bloom on the tree;
    

These lines celebrate the beauty and purity of Maud, especially within the natural setting. It is with the phrase “slender acacia” that the decline in the fricative accumulations occurs, just as the poem begins to use negative language to celebrate Maud (i.e., “would not”), thereby detracting from the intensity of the celebration. The other very strong climax in fricative accumulations occurs towards the end of the poem, with the tenth and the beginning of the eleventh (and last) stanzas:


    
        There has fallen a splendid tear
        	From the passion-flower at the gate.
        She is coming, my dove, my dear;
        	She is coming, my life, my fate;
        The red rose cries, “She is near, she is near;”
        	And the white rose weeps, “She is late;”
        The larkspur listens, “I hear, I hear;”
        	And the lily whispers, “I wait.”
        	

        She is coming, my own, my sweet;
	

It is right after the final occurrence of “She is coming” that the fricative accumulations decrease and do not reach the same heights again. The tenth stanza is of course an expression of anticipation: as the speaker expects Maud to join him in the garden at any moment, the flowers are described as in such a heightened emotional state that “splendid” tears are falling in anticipation. Again, the fricative accumulations closely follow the filtered accumulations, and these lines can certainly be read as the emotional climax of the poem. Note that the actual highest point here somewhat exceeds the expected (filtered) peak; it occurs with the tension-filled phrase, “I hear, I hear.”

While the fricative accumulations in the second half of the poem tend to correspond well with the filtered fricative accumulations, the first half shows some interesting departures. In the fourth stanza of the poem, the lover addresses one of the flowers directly, speaking of Maud and the others who are dancing inside:


	
        I said to the lily, “There is but one
        	With whom she has heart to be gay.
        When will the dancers leave her alone?
        	She is weary of dance and play.”
        Now half to the setting moon are gone,
        	And half to the rising day;
        Low on the sand and loud on the stone
        	The last wheel echoes away.
	

The filtered fricative accumulations suggest there should be a climax at the end of the second line of this stanza (at syllable 168), and this period of high fricative accumulations should decrease (which it does anyway) after the phrase, “Now half to the setting moon are gone.” This suggests that the reader should expect the first four lines of the stanza to be an expression of ecstasy or jubilation. The dance described is probably a happy one, but for the speaker of the poem the dance represents the other temptations and potential seductions of Maud and reminds him of his own exclusion. Interestingly, instead of following the climax in the filtered fricative accumulations, the actual accumulations show a reluctance to achieve the heightened state and climax that otherwise might be expected. The speaker’s use of consonants suggests a pull away from ecstatic joy to emotional caution.

The first major fricative accumulation climax in the poem occurs at the end of the second stanza:


    
        For a breeze of morning moves,
        	And the planet of Love is on high,
        Beginning to faint in the light that she loves
        	In a bed of daffodil sky,
        To faint in the light of the sun she loves,
        	To faint in his light, and to die.
	

There is a small climax at the phrase “is on high” in the second line of this stanza. The filtered fricative accumulations suggest there should be a climax at syllable 75 of the poem: “loves” from “light that she loves,” of the third line; they suggest that the stanza should have a climax half-way through it, followed by a general decrease in the fricative accumulations. While this approximately happens with the actual fricative accumulations, they do break from the expected waveform and reach a very high climax after the location of the expected climax with the phrase, “sun she loves, | To faint in his light” (at syllable 98). This is followed by the expected decrease, but the decrease is more dramatic, reaching its lowest point at “to die” and the following two words from the next stanza (“All night”). The filtered fricative accumulations suggest that as the brightness of the planet Venus (“the planet of Love”) fades in the morning sky, so too does the emotional intensity of the poem. The actual fricative accumulations, however, suggest that this fading of Venus is celebrated by the poem: it is indeed a signal to the lover in the garden that the dance is about to end and that Maud will be joining him. Thus, it is the fainting of Venus in the morning light that is celebrated (“To faint in the light of the sun she loves”), rather than the love of the dawning light. The planet Venus can be read as symbolic of Maud, while the rising sun is symbolic of the lover himself: he is in ascendancy as the dance ends. The filtered accumulations suggest that the love Maud has for the speaker is what should be celebrated, while the actual accumulations suggest that the lover is instead celebrating the overpowering of Maud’s light by his own: the male brightness eclipses the female brightness. The tension here between the filtered and actual fricative accumulations places a heavy emphasis on the final two lines of this stanza; this tension suggests the speaker’s desire is not just to love Maud, as his words generally imply, but to possess and overpower her.

The Interesting Phonemic Departure in the second stanza of the poem thus suggests that the poem is possibly working against itself in its expression of love for Maud. Aidan Day quotes the second stanza as an example of how “the protagonist shows himself constitutionally unable to avoid associating love with death” (175). This is entirely within the character of the speaker of the full poetic sequence, with its dips into and explorations of melancholia and madness. The final stanza includes another Interesting Phonemic Departure supporting the notion that the words of the speaker may sometimes work against himself:


    
         She is coming, my own, my sweet;
         	Were it ever so airy a tread,
         My heart would hear her and beat,
         	Were it earth in an earthy bed;
         My dust would hear her and beat,
         	Had I lain for a century dead,
         Would start and tremble under her feet,
         	And blossom in purple and red.
	

The final peak in the fricative accumulations occurs with the words “century dead” from the lines “My dust would hear her and beat, | Had I lain for a century dead.” The occurrence of the word “dead” in this final stanza is bracing: it is not what one would usually expect in a love poem. The effect the word has is supported by the way the fricative accumulations depart from the filtered fricative accumulations. The fricative accumulation climax here suggests that the speaker is aligning his own death with his love for Maud: that in expressing his love for death he is also expressing his love for Maud. As such, the love lyric becomes an expression of the speaker’s melancholia, morbidity, or madness.

The fricative accumulation climaxes in “Come into the garden, Maud” thus seem to occur when the poem is expressive of intense positive feelings: that is, of love and joy. The moments of Interesting Phonemic Departures support this and become an indication of those moments in the poem where what is otherwise expected is challenged or undermined, producing a more powerful poetic experience. It seems the graph of the filtered accumulations represents what our ear is expecting to hear, as set up by the poet, while the graph of the actual accumulations represents the poet’s craft in breaking away from the expectation. In the case of this poem, the Interesting Phonemic Departures suggest moments when the speaker is moving beyond an expression of love for Maud, into the realm of possessive madness. Tennyson himself said that the otherwise beautiful love lyric “had, & was intended to have, a taint of madness” (Mangles 69-70), and the Interesting Phonemic Departures help the reader locate this taint. It is perhaps no coincidence that as the poem ends with what Herbert Tucker calls “lines of prophetic rapture” (425), the fricative accumulations are very much declining while the plosive accumulations are increasing to their highest climax for the whole lyric. The “rapture” has shifted at the end from an ecstasy of love to an ecstasy of morbidity, and the plosive accumulations seem to suggest this.

The sequence of consonantal phonemes in Tennyson’s poem suggests there is a relationship between the abundance or concentration of fricative consonants and expressions of love, between the scarcity or dispersion of fricative consonants and expressions of anxiety. While the subjectivism inherent in literary interpretation impedes one’s ability to make a solid, definitive claim, the fricative and plosive phonemic accumulations reveal suggestive evidence allowing one to draw a relationship between the phonemic content of a poem and the semantic meaning of its words and the aesthetic impact the poem may have upon a reader. It is certainly probable that the measure of the cumulative effect of phoneme groups can lead to more profound insight into poetic stylistics than, say, calculating the percentage of occurrence of particular phonemes, such as affricate consonants or nasal vowels. Phonostylistics opens new doors leading to the interpretation and aesthetic analysis of texts by computational methods. Of course, this end goal may never be achieved: practising computational aesthetics may be equivalent to resorting to conversing with the flowers in the garden while one awaits the unlikely fulfilment of an unachievable love.



Works Cited

Chisholm, David. “Phonology and Style: A Computer-Assisted Approach to German Verse.” Computers and the Humanities 15 (1981): 199-210. Print.

Craig, Hugh. “Stylistic Analysis and Authorship Studies.” A Companion to Digital Humanities. Ed. Susan Schreibman, Ray Siemens, and John Unsworth. Oxford: Blackwell, 2004. Web. 18 February 2008 <http://www.digitalhumanities.org/companion/>.

Coates, Carrol F. “Phonemic Structuration and the Reading of the Poem: Rimbaud’s ‘Le Châtiment de Tartufe’ and ‘Cocher ivre.’” Understanding French Poetry: Essays for a New Millennium. Ed. Stamos Metzidakis. New York: Garland, 1994. Print.

Day, Aiden. Tennyson’s Scepticism. Houndmills, Bassignstoke, Hampshire: Palgrave Macmillan, 2005. Print.

Elsdale, Henry. Studies in the Idylls: An Essay on Mr. Tennyson’s “Idylls of the King.” London: Henry S. King, 1878. Print.

Jakobson, Roman. Six Lectures on Sound and Meaning. 1976. Trans. John Mepham. Hassocks, Sussex: Harvester, 1978. Print.

Jakobson, Roman, and Linda R. Waugh. The Sound Shape of Language. Assisted by Martha Taylor. Second edition. Berlin: Mouton de Gruyter, 1987. Print.

Macaulay, George Campbell. “Introduction.” The Holy Grail. By Alfred Tennyson. London: Macmillan, 1893. ix-xl. Print.

Mangles, James Henry. Tennyson at Aldworth: The Diary of James Henry Mangles. Ed. Earl A. Knies. Athens, Ohio: Ohio UP, 1984. Print.

Tennyson, Alfred. “Maud; A Monodrama (from Part I).” Representative Poetry Online. Ed. Ian Lancashire. U of Toronto Libraries. Web. 18 February 2008. <http://rpo.library.utoronto.ca/poem/2166.html>.

Tsur, Reuven. What Makes Sound Patterns Expressive?: The Poetic Mode of Speech Perception. Durham: Duke UP, 1992. Print.

Tucker, Herbert F. Tennyson and the Doom of Romanticism. Cambridge, MA: Harvard UP, 1988. Print.

Van Dyke, Henry. Studies in Tennyson. 1920. Port Washington, NY: Kennikat P, 1966. Print.



Tables

Table 1: British English consonant groups

Plosive

/p/ /b/ /t/ /d/ /k/ /g/

Nasal

/m/ /n/ /ŋ/

Fricative

/f/ /v/ /θ/ /ð/ /s/ /z/ /ʃ/ /ʒ/ /h/

Affricate

/ʧ/ /ʤ/

Approximant

/r/ /j/ /w/ /l/


Table 2: Fifty Poems and their Fricative to Plosive Broad Shape Ratio

Poem

fpBSR

Late, Late, so Late

0.52

Green Eggs and Ham

0.66

A Shropshire Lad II: Loveliest of Trees, the cherry now

0.67

Robin Redbreast

0.72

Introduction to the Songs of Innocence

0.74

The Princess: The Splendour Falls on Castle Walls

0.75

In Memorium A. H. H. OBIIT MDCCCXXXIII: 11

0.76

In Memorium A. H. H. OBIIT MDCCCXXXIII: 5

0.76

Youth and Calm

0.77

Requiescat

0.81

A Shropshire Lad XXI: In summertime on Bredon

0.83

The Princess: Tears, Idle Tears

0.84

Crossing the Bar

0.86

Nearer, my God, to Thee

0.87

Ulysses

0.88

Stopping by Woods

0.88

St. Agnes' Eve

0.91

Prospice

0.92

Two in the Campagna

0.93

My Star

0.95

Lady Geraldine's Courtship

0.96

A Ballad of Burdens

0.96

Mariana

0.96

In Memorium A. H. H. OBIIT MDCCCXXXIII: 7

0.97

Introduction to the Songs of Experience

0.98

Break, break, break

0.98

Porphyria's Lover

1.00

The Road not Taken

1.00

Dover Beach

1.02

Life in a Love

1.07

The Princess: Home they Brought her Warrior Dead

1.09

The Princess: Sweet and Low

1.13

A Ballad of Death

1.14

Love in a Life

1.14

The Princess: Now Sleeps the Crimson Petal

1.14

My Last Duchess

1.15

Maud

1.17

Forsaken Garden

1.17

Ave Atque Vale

1.18

Faustine

1.20

Song (Browning)

1.23

Memorabilia

1.24

Meeting at Night

1.27

Hymn to Proserpine

1.32

Garden of Proserpine

1.33

In the Valley of Cauteretz

1.40

In Memorium A. H. H. OBIIT MDCCCXXXIII:67

1.44

Serenade at the Villa

1.55

Among the Rocks

1.57

Sonnets from the Portuguese 43: How do I love thee?

1.97


Endnotes

[1] MetrePhone is a Windows-based program written in VisualBasic on the .NET platform. It is designed to be an aid to both the student and the scholar, offering a graphical user interface, colourization tools, and extensive calculation options. All processed data in MetrePhone can be saved as XML for use by other tools, but the preliminary raw data are drawn from an Access database. The phonemic data it uses are based on that in the sixteenth edition of the Cambridge English Pronouncing Dictionary (2003). At the moment of writing, MetrePhone is designed to work exclusively with poetic data, but future modifications will allow for prose and drama. A fuller account of the program and its treatment of metre can be found in “Virtual Verse Analysis: Analysing Patterns in Poetry” (Literary and Linguistic Computing 21 [Supplement, 2006]: 127-41). A fuller account of the study of the phonemic content of the poems of Browning and Tennyson (and other Victorian poets) can be found in “Computer-Assisted Phonetic Analysis of English Poetry: A Preliminary Case Study of Browning and Tennyson” (Text Technology 14 [2005]: 153-75).

[2] Most of the poems, including “Come into the garden, Maud” (quoted extensively below), are taken from Representative Poetry Online (rpo.library.utoronto.ca).



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