From Classicism to Romanticism
A more sophisticated use of clustering is found in a study by Katelyn Horn and David Huron (2012). The motivation for this study came from earlier studies that implied that the minor mode is used differently in the 19th century compared with other centuries. As you might expect, music in the minor mode is typically associated with a slower tempo and with a quieter dynamic level. However, in the 19th century that association reverses. On average, in the 19th century, music in the minor mode is faster and louder than music in the major mode (Post & Huron, 2009). In light of this work, Horn and Huron decided to investigate how music changes from the 18th century and the 19th century. Specifically, they focused on the period between 1750 and 1900. This period corresponds to the presumed shift from the so-called Classicism of the 18th century to the Romanticism of the 19th century.
Horn and Huron assembled a stratefied random sample containing 750 musical works. They sampled 250 works from each of three 50-year periods: 1750-1800, 1800-1850, and 1850 to 1900. In order to increase data independence, they sampled no more than two works written by any given composer.
In order to avoid sampling from just the beginnings of works, they devised a procedure that allowed a sample to be selected from throughout the work. Each work or movement was conceptually divided into “sections.” The beginning of a section was operationally defined as either (1) the beginning of the work, (2) immediately following a mid-work double barline, (3) immediately following a repeat sign, or (4) immediately following a new tempo marking or a change of meter. Having split a work or movement into a sequence of “sections,” they then randomly selected one section from each work. Using this sampling method, they avoided biasing the sample to how music begins.
Each randomly-selected section was coded according to five properties: mode, dynamic level, tempo, articulation, and date. With regard to mode, they categorized each sampled section as either “obviously major,” “obviously minor,” or “not obviously major or minor.” With regard to dynamic level, passages were coded according to the notated dynamic markings — such as pianissimo, mezzo piano, or triple forte. These markings were treated as an ordinal scale ranging from ppp, pp, p, mp, … to fff. The figure below shows that the most common dynamic marking for the 750 works is piano (p).
With regard to tempo, they made use of standard Italian tempo terms. Specifically, they made use of 19 common Italian terms that were independently ordered from slow to fast. The figure below shows the percentage of occurrence for the different tempo terms found in the sample of 750 works. The most common dynamic marking is allegro.
With regard to articulation, passages were coded according to the prevailing texture in the first 4-8 measures of the sampled section. This was a subjective evaluation on the part of the researchers. Passages were coded as one of five possibilities: very staccato, generally staccato, balanced or unclear, generally legato, or very legato. The figure below shows the percentage of occurrence for the different articulations. In general, legato is more common than staccato.
Having coded the sampled sections for their mode, dynamic, tempo, and articulation, several cluster analyses were carried out. First, all of the data from all 750 passages spanning 1750-1900 were analysed. The resulting dendrogram is shown below.
The short lines at the bottom of the dendrogram are the “leaves” — each line representing one of the 750 sampled passages. The numbers along the bottom identify specific passages (labelled by number).
Recall that cluster analysis does not tell you the “meaning” or origin of the groups. It simply tells you that there are statistically pertinent natural groupings that arise depending on the way you define similarity. All of the labels on the figure were added by the researchers. They represent efforts to interpret the meaning of each cluster and sub-cluster. For example, at the highest level, the tree exhibits two broad clusters. By examining the individual passages identified in each of the two clusters it is possible to interpret the meaning of this split. Roughly 98 percent of the musical passages in the right-most group were coded in the major mode (with 2 percent coded as ambiguous modality), whereas roughly 90 percent of the passages in the left-most group were coded in the minor mode (with 10 percent coded as ambiguous). In other words, the top-level clusters appear to represent the distinction between major- and minor-mode passages. Below this, both the major and minor clusters split into two broad categories. Once again, an examination of the individual passages suggests that the subdivisions represent the distinction between loud and quiet passages.
All of the clusters, of course, arise from combinations of the four musical features: major/minor mode, loud/quiet dynamic, fast/slow tempo, and staccato/legato articulation. By examining the individual musical passages, it is possible to identify the characteristics of each cluster. For example, the left-most cluster arises from the combination of loud, fast, staccato, and major-mode music. The cluster immediately to the right represents the combination of quiet, fast, staccato, and major-mode music. And so on.
As in the case of Johnson’s analysis of orchestral clusters into Standard, Power, and Color instruments, we are free to attempt to interpret the clusters here. For example, Horn and Huron applied the label “Joyful” to the major-loud-fast-staccato passages, and the label “Light/Effervescent” to the major-quiet-fast-staccato passages. It is important to recognize that these labels are post-hoc interpretive labels. The clusters have some objective basis in the data, but the labels are subjective impositions. Another researcher might disagree with these characterizations or offer alternative ways of interpreting the clusters. Nevertheless, the interpretive labels are useful ways of referring to the groups arising from the cluster analysis.
In interpreting the results, Horn and Huron made the following interpretations:
| “Joyful” | major | loud | fast | staccato |
| “Light/Effervescent” | major | quiet | fast | staccato |
| “Regal” | major | loud | slow | legato |
| “Tender Lyrical” | major | quiet | slow | legato |
| “Passionate” | minor | loud | fast | staccato |
| “Sneaky” | minor | quiet | fast | staccato |
| “Sad/Relaxed” | minor | quiet | slow | legato |
| “Serious” | minor | loud | slow | legato |
Having carried out a cluster analysis for all 750 works, Horn and Huron then carried out cluster analyses according to each of the 50-year periods. Below is the resulting dendrogram for the earliest period, 1750 to 1799.
A hundred years later (1850 to 1899), we can see that the musical samples produce a somewhat different clustering.
The table below summarizes the changes in clusters across the 150-year period of the study. The biggest change occurs with Light/Effervescent music. In the late 18th century, this represents the biggest cluster accounting for nearly 40% of musical passages. By the end of the 19th century, Light/Effervescent has virtually disappeared according to the sample. A second major change occurs with Sad/Relaxed music. Over the three 50-year periods, the amount of Sad/Relaxed music triples from 7% to 21%. Passionate music doubles (from 4% to 8%), but more importantly, Tender/Lyrical music doubles (from 22% to 44%).
In general, the results of the cluster analysis appear to be consistent with conventional musical interpretations regarding the historical change between the so-called Classical and Romantic periods. Light/Effervescent music which is so common in the Classical style nearly disappears. Joyful music declines slightly. Instead, there is a large increase in Tender/Lyrical music, accompanied by lesser increases in Sad/Relaxed, and Passionate musics.
References
Katelyn Horn and David Huron (2012). Major and minor: An empirical study of the transition between Classicism and Romanticism. In E. Cambouropoulos, C. Tsougras, P. Mavromatis & K. Pastiadis (editors), Proceedings of the 12th International Conference on Music Perception and Cognition. Thessaloniki, Greece: ESCOM, pp. 456-464.
Olaf Post and David Huron (2009). Music in minor modes is slower (except in the Romantic Period). Empirical Musicology Review, Vol. 4, No. 1, pp. 1-9.