Primary-Cell and Contour Constituencies
and Concordances in the MelAnaly System
of Comparative Tune Analysis

2005  J. Marshall Bevil    All Rights Reserved
See also Centonization and Concordance in the American Southern Uplands Folksong Melody: a Study of the Musical Generative
and Transmittive Processes of an Oral Tradition. 
DissertationUniversity of North Texas, 1984.
(Ann Arbor: University Microfilms, International, 1984), passim.  

 

Introduction

            Early studies of oral-aural melodic transmission addressed both the issue of scale and that of melodic identity.  I have provided a select online bibliography as a starting point for those interested in examining earlier views in depth, and select earlier views and my conclusions regarding scale appear in one of my academic journal articles. I have explored, in detail, prominent earlier views concerning melodic identity in my dissertation (University of North Texas, 1984) and in several pre- and post-doctoral studies.
            In sum, earlier views of melodic kinship are divisible into two broad categories, each of which encompasses a range of concepts and views. The first, and earliest, category is that of connectionist hypothesis and theory, which held that the oral-aural melodic process involved the statement, perception, assimilation, and subsequent recall (either with or without modification) of a sequence of formulaic melodic patterns that had become established within a culture through frequent use. Beginning around the middle of the twentieth century, and coinciding with the rise to prominence of Gestalt psychological theories of cognition, were the various holistic theories that focused on such factors as tonal range and overall melodic morphology, with much less attention to short melodic patterns and little if any recognition of figural or motivic chaining.
            During the final quarter of the twentieth century, a number of investigators, myself included, began fashioning various syntheses of the two earlier, antithetical views, stating that holistic factors - overall melodic morphology, in particular - are very important, but that smaller structural units, especially the openings and closings of sections, can be and often are significant as well. My specific hypotheses and theories along that line are covered in detail both in my dissertation and in a number of pre- and post-doctoral investigations.
 

Primary Cells

Functions and Constituencies

        While MelAnaly assigns greater importance to overall melodic contour than it gives to motivic similarity or duplication, it recognizes the substantial importance of short patterns that open and close the two dual-phrase periods, or strains, of the standard binary, or bipartite, tonal melody. Those patterns, known in MelAnaly as primary cells, are designated incipit (tune opening), mediant cadence (formerly mediant close; cf. Centonization and Concordance ...), second strain opening (formerly fine strain opening), and final cadence (formerly final), and they function as mnemonic anchors of a melody. In addition, they comprise in combination a broad, general partial definition of the melody and, in so doing, provide a means of roughly classifying melodies and associating them with each other on the basis of cellular configurations. Rather than conflicting  with the cognitive psychological theory on which the emphasis on overall melodic morphology is based, the concept of primary cells is in line with that theory, specifically the Gestalt law of closure, which states that the memory trace of a perceived entity is, as a rule, especially sharp and clear, and hence readily assimilated and remembered, at its initial and terminal points.
        Each primary cell consists of either the first or the last three sounding events of a melodic period, or dual-phrase unit, and that cell has pitch factors, durational factors, and stress factors associated with each sounding event. The determination of three as the fixed number of sounding events in each primary cell was based on the consideration of strain openings and closings in a large number of different melodies. In most cases, three events were sufficient both to fit and to fill the role of formulaic opening and closing patterns. Furthermore, three-event motifs, when considered in combination with each other, appeared in most cases to be the ideal size for defining broad determinants of overall melodic rise and fall, for establishing the most pervasive rhythmic characteristics of a tune, and for providing broad bases for determining both general associations of melodies with each other and clear disparities between tunes. In individual cases wherein three-event patterns did not provide sufficient rough definition and delineation (for example, in melodies with more than one primary cell comprising a single pitch stated three times), the extension of the primary cell to include the first three different sounding events, in the broad-details contour reduction (see below), usually overcame the problem.
         Figure 1 shows two melodies with their primary cells bracketed.

Figure 1: Hymn tunes "Bethany" and "Propior Deo," with their primary cells bracketed.
See also complete online version, "And the Band Played On:
Hypotheses Concerning What Music Was Performed Near the Climax of the Titanic Disaster."


 

        Pitch. Each of the three tones in each of the four primary cells has three pitch factors: pitch class, chromatic suffix, and amplitude. Pitch class is indicated according the standard, A-G alphabetical system used in traditional music theory. The chromatic suffixes are either sharp or natural. Flats are expressed as either their enharmonically equivalent sharps (for example, B-flat = A-sharp) or, in the cases of C-flat and F-flat, their enharmonically equivalent naturals (B and E, respectively). Three overlapping spans of the anhemitonic gamut provide an adequate pitch amplitude range for all melodies considered (Figure 2). Melodies with predominantly major tonalities are transposed to the common gamut, shown in Figure 2, so that their minor thirds align as much as possible with that range; and their keynote, if one is determinable, is C. Prevailingly minor melodies are transposed so that their minor thirds align in the same fashion; and their keynote, if one is clear, is A. Congruency of minor thirds is the primary criterion in determining alignment with the common gamut, and keynote determination is of secondary significance unless the characteristic anhemitonic-pentatonic minor thirds are absent from the melody (see "Scale in Southern Appalachian Folksong: a Reexamination"). In so far as ranges are concerned, melodies are transposed to the central span of the common gamut as much as possible.

                                              Figure 2: The common anhemitonic gamut (without auxiliary B and F), full range.

 


        Numeric codes representing pitch factors are used to expedite the computer-assisted phase of comparative analysis (Figure 3).

Figure 3: Primary cells of "Bethany" and "Propior Deo" (transposed downward a fifth,
to the common gamut), with their pitch factors encoded.


 

 

        Duration.  The durations of individual primary cell members are expressed in sixteenth notes. For details, see the web page on codes.

Figure 4: Primary cells of "Bethany" and "Propior Deo," with their durational factors encoded.

 

        Stress.  Stress factors are encoded according to primary stress, secondary stress, neutral stress, and negative stress within a specified temporal framework.

 

Figure 5: Primary cells of "Bethany" and "Propior Deo," with their stress factors encoded.



 

The Complete Primary Cell Matrix (CPCM) / Array.

            During data preparation, the complete combination, or matrix (CPCM), of the notated primary cell factors of a melody, as shown in Figures 3-5 above, is stored electronically as a numeric array ( PC array, Figure 6) for later use in the computer-assisted phase of comparative analysis.

Figure 6: Complete primary cell matrices (CPCMs) and numeric arrays showing pitch, durational, and stress
factor codes of "Bethany" and "Propior Deo."

Illustration in Preparation
 

Concordances

        Pitch. 
There are three types of pitch concordance between primary cells. They are direct concordance, cross-concordance, and resequencing, and are illustrated in Figure 7, following the written explanations.
        Direct concordances are pitch duplications at corresponding positions within primary cells, as shown in the examples below. Each individual direct pitch concordance is given a value of 1 during the primary cell pitch scan. The highest level of primary cell pitch concordance between a control and test melody, 100%, exists whenever each of the three corresponding members of each of the four primary cells have matching pitches, i.e., whenever the primary cell pitch concordance tabulation is 12.
        Cross-concordances (XC) occur either when a non-repeating pitch at the first position in the control primary cell is duplicated at the second position in the test primary cell (12XC) or vice-versa (21XC), as shown below. Whenever the first two notes of the control primary cell exchange places in the corresponding primary cell of the test melody, a double cross-concordance (double XC) occurs, as shown. Each cross-concordance is given a value of   , and each double-cross concordance is given a value of   during the primary cell pitch scan.
        Resequencings (R) are similar to cross-concordances, but they involve an exchange of positions by either the first and third (13R) or the second and third (23R) members of the corresponding primary cells of the control and test melodies, as shown below. In order for there to be a resequencing, the corresponding uninvolved members of the primary cells must have identical pitches. Each resequencing is given a value of   during the primary cell pitch scan.

Figure 7: Primary cell pitch concordances.

                            
 

            At the conclusion of the primary cell pitch scan, the tabulated value of all the direct pitch concordances, cross-concordances, and resequencings is divided by 12 (the highest possible total, or the equivalent of direct pitch concordances of all tones in all four primary cells) and multiplied by 100. The percentage thereby obtained then is rounded to the nearest whole percentage point (Figure 8).

        Duration.  Text in Preparation

        Stress.  Text in Preparation

 

Figure 8: Primary cell concordance table and percentages, "Bethany" and "Propior Deo."

Illustration in Preparation
 

Secondary Cells

 

Constituencies

            Text in Preparation

      Figure 9: Secondary cells in "Bethany" and "Propior Deo," with encoded
secondary cells of downward-transposed melodies (G => C, etc.)
represented in a numeric array below.
 

 

Concordances

            Text in Preparation

 

Contour

Constituencies

        Overall melodic contour is divisible into three strata of graduated density and complexity. In MelAnaly, those strata are termed the elemental level, the broad details, and the specific details. While the threefold division of structural-perceptual layers hearkens back to Schenkerian and neo-Schenkerian procedures, MelAnaly differs from earlier methods of layer analysis in being totally melodic in its orientation and not including any harmonic support criteria. It also differs from Schenkerian models in that either all or very nearly all of the material comprising a given lower (i.e., less dense) level is included in higher, or denser, levels in every case. Finally, MelAnaly differs from more distinctly Schenkerian procedures in its use of stress factors as the almost exclusive determinants of contour constituencies apart from phrase opening and closings.

        Elemental Level.   Text in Preparation

 

Figure 10: Elemental levels of "Bethany" and "Propior Deo," with their pitches encoded.

Illustration in Preparation
 

        Broad Details.   Text in Preparation

 

Figure 11: Broad details of "Bethany" and "Propior Deo," with their pitches encoded.

Illustration in Preparation

 

        Specific Details.   Text in Preparation

 

Figure 12: Specific details of "Bethany" and "Propior Deo," with their pitches encoded.

                                                                                           Illustration in Preparation
 

 

Concordances

Text in Preparation

Elemental Level.

Text in Preparation

Figure 13: Elemental-level contour graph of "Bethany" (solid line) and "Propior Deo," (segmented line).

Illustration in Preparation
 

        Broad Details.  Text in Preparation

 

Figure 14: Broad-details contour graph of "Bethany" (solid line) and "Propior Deo," (segmented line).

                                                                                                   Illustration in Preparation
 

        Specific Details.  Text in Preparation

 

Figure 15: Specific-details contour graph of "Bethany" (solid line) and "Propior Deo," (segmented line).

Illustration in Preparation
 

 

Computer-Generated Conclusions

          Text in Preparation

Figure 16: Primary-cell and contour concordance percentages and conclusions, "Bethany" and "Propior Deo."

        Illustration in Preparation