Statistical characteristics of tonal harmony: A corpus study of Beethoven's string quartets — PLOS ONE

Claims

1. corpus-findings
   Analysing the Annotated Beethoven Corpus, about 28,000 expert chord labels for Beethoven's string quartets, Moss and colleagues found that chord frequencies follow a power-law-like distribution in which a few chords make up much of the data. Tonic and dominant chords account for more than 60% of all chords in major-key passages and more than 50% in minor. They also found that chord transitions are directed in time, and that tonal harmony works differently at the levels of chords and keys.

   "Using resampling methods, this study shows that 1) the rank-frequency distribution of chords resembles a power law, i.e. few chords govern a large proportion of the data; 2) chord transitions are referential and chord predictability is significantly affected by distinguished chord features; 3) tonal harmony conveys directedness in time; and 4) tonal harmony operates differently at the hierarchical levels of chords and keys. ... In particular, I , i , and V chords account for more than 60% of all chords in major, and more than 50% of all chords in minor, clearly demonstrating their primacy in tonal music which reflects the principle of centricity."

   Locator: section: Abstract; Results · Quote language: en
2. directedness-fifth
   A chord transition is asymmetrical if one chord proceeds to another more often than the reverse, and such asymmetries are thought to shape listeners' expectations through implicit learning. The descending-fifth root motion, especially V to I, is generally identified as central to tonal harmony, and dissonant chords such as seventh chords and suspensions create specific expectations about the chords that follow.

   "A chord transition A → B is asymmetrical if chord A proceeds more often to chord B than vice versa [ 18 ]. This has cognitive implications, as the statistical regularities of chord transitions in tonal music arguably impact on the formation of listening expectations through implicit learning [ 17 , 34 , 35 ]. ... The descending fifth is a prototypical example of an authentic transition; it is generally identified as central for tonal harmony [ 7 , 8 , 36 , 37 ] as opposed to other Western musical styles [ 38 ], especially when its goal is the tonic ( V → I , or V → i ). Further, the presence of chord types with certain features contributes to both referentiality and directedness. This applies, for instance, to dissonant chords such as seventh chords and suspensions, as they create specific expectations of the following chords"

   Locator: section: The notion of tonal harmony · Quote language: en
3. period-and-dimensions
   Tonal harmony is commonly associated with the common-practice period, between the middle of the 17th century and the second half of the 19th, and its organizing principles remain prevalent in contemporary pop and film music. Moss and colleagues characterize it along four dimensions: centricity (a few central chords govern the harmonic lexicon), referentiality (chords are oriented toward reference points such as the tonic), directedness (a preference for asymmetric progressions) and hierarchy (chords nested within local keys, which are nested within a global key).

   "Tonal harmony is commonly associated with the historical period between the middle of the 17th and the second half of the 19th century, the so-called common-practice period [ 14 , 25 ]. The organization principles of tonal harmony are still prevalent in contemporary Pop and film music [ 26 – 30 ]. Despite notable differences in the conception of tonal harmony, many theoretical treatises share the focus on a small number of central features [ 10 , 11 ], which are here subsumed under the dimensions of centricity , referentiality , directedness , and hierarchy ."

   Locator: section: The notion of tonal harmony · Quote language: en