MUSICAL THEMES AND OCCURRENCES OF MELODIC CONFOUNDS Donald Byrd, Indiana University Bloomington Begun July-Dec. 2000; last revised June 2013 Thanks to Tim Crawford and Eric Nichols for some of the figures below. Some of these results appear in Byrd, Donald, & Crawford, Tim (2002). Problems of Music Information Retrieval in the Real World. Information Processing and Management 38, pp. 249-272. NOTE: this version of this document assumes a fixed-width font like Courier; with variable-width fonts, the tables won't be aligned properly. E. Selfridge-Field's "Conceptual and Representational Issues in Melodic Comparison" (in Hewlett, W., & Selfridge-Field, E., eds., Melodic Similarity: Concepts, Procedures, and Applications (Computing in Musicology 11), 1998) discusses three types of "confounds" in notated music: rests, repeated notes, and grace notes. A fourth type, trills and turns, are similar, though perhaps too easy to deal with in notation -- they can simply be ignored -- to matter for her purposes. A type of confound that's probably deeper than any of these is that of polyphony (in a broad sense): some themes are not monophonic, or at least not clearly so. Here are some statistics on occurrences in themes and incipits of all the above-mentioned confounds, plus a few additional interesting notational features: changes of clef, key signature, and time signature, plus fermatas, tuplets, and octave signs. Rests are counted herein only if internal to the theme/incipit, i.e., not at the very beginning or end. Repeated notes in the "musical" sense excludes cases where there are intervening rests, or (less clear-cut) cases like appogiaturas reiterated across the barline. (I've also some included information about the collections as a whole, especially the Barlow & Morgenstern work.) 1. In Barlow and Morgenstern's Dictionary of Musical Themes (Crown Publishers, 1948) This work contains "incipits" for about 10,000 themes of classical-tradition instrumental pieces. Only basic information is given: there are no dynamics, slurs, expression marks, or articulation marks, but -- in addition to clefs, key signatures, time signatures, notes, ties, and rests -- there are grace notes, trills, turns (all of which affect the performed pitches), plus fermatas. The most common first letter of the composer's last name is "B" (numbers go up to 1836); "S" seems to be next (numbers up to 1673). (A few themes have suffixes, so the actual counts are a bit higher, at least for "S".) The themes vary in length considerably, as follows: Extreme (that I've seen) Typical ------------------------ ----------- Measures 1(Beethoven, Honegger) to 18(Strauss) c. 2 to 5 Notes (attacks) 5(Holst) to 41(Thomas) c. 12 to 20 Regarding numbers of notes: 1. A runner-up for fewest notes is a Brahms theme (B1429), with 6. 2. Entries in the index generally describe fewer notes than the corresponding themes. Index entries range -- except for a 3-note entry, "GDC", which certainly looks like a mistake! -- from 6 to at least 11 when written out, and at least 14 with repetitions indicated, as in C(superscript)12 [in Stravinsky; NB it should be 15!]. To my knowledge, the longest notated duration is a breve (in Barber); of course wholes appear in many themes, and dotted wholes in several (e.g., Sibelius). The shortest notated duration is a 128th (in Francoeur); 64ths appear in quite a few themes. About 100 themes have only one rhythmic value and no rests; most are all quarters or all eighths, but some are in half notes or whole notes only. Quadruple-dotted notes appear (Franck) as well as several instances of triple-dotted notes (Bruckner, Liszt). The highest tuplet accessory numeral (i.e., numerator) is 13 (Paganini); nested tuplets occur at least once (Walton). The lowest pitch is G#1 (e.g., Prokofieff); the highest is B7 (Chavez). The most ledger lines below the staff are 4 (e.g., Chopin); the most above the staff, 5 (e.g., Liszt). Everything is in either treble or bass clef, even themes of viola concerti. There's at least one occurence of the beat-repeat sign (Enesco), and at least one of multibar rests (Strauss, S1375). We checked for a number of items in samples of 216 themes (all of pp. 20, 70, 120...520: 11 excerpts, including themes by Beethoven, Dvorak, Handel, Kodaly, Mozart, W. Schuman, Stravinsky, and others), and of 400 themes (all of pages with numbers ending with 00, 20, 50, and 70: 21 excerpts; this adds 184 themes to the previous sample, including Beethoven, Brahms, Debussy, Gluck, Hindemith, Sousa, etc.). Of the 216 themes, 127 (59%) are first or only themes; of the 400, 236 (59%) are. The shortest notated duration in the original 216 themes is a 32nd: it appears in a number of themes. The shortest notated duration in the additional 184 themes is also a 32nd, and it again appears in a number of themes. We also checked 967 themes (all of pp. 20, 30...520 except p.110) for rests and grace notes only. The numbers of themes that contain each type of item are: 216 400 967 ------- ------- ------- Repeated notes (in both literal and musical senses) 84 (39%) 170 (42.5%) Repeated notes (in the literal but not musical sense) 28 (13%) 43 (10.8%) Rests 82 (38%) 147 (36.8%) 313 (32%) Grace notes*1 30 (14%) 59 (14.8%) 155 (16%) Trills and turns 15 (7%) 30 (7.5%) Fermatas 2 (1%) 4 (1%) Clef changes 3 (1.4%) 5 (1.3%) Key signature changes 0 0 Meter changes 5 (2.3%) 7 (1.8%) Tuplets: triplets 13 (6%) 30 7.5%) Tuplets: other*2 3 (1.4%) 5 (1.3%) Octave signs 1 (<1%) 2 (<1%) Not strictly monophonic (involve 2-3 voices*3) 2 (1%) 3 (<1%) *1. Examples of themes in which grace notes make a particularly big difference, e.g., in how the theme is perceived, its location in an index, or both (NB turns can have similar effects): Haydn: Quartet in C, Op. 33 no. 3 (The Bird), I (1st and 2nd themes) Haydn: Symphony no. 88 in G, III Mozart: Divertimento in D, K. 136, I Schubert: Improptu in f minor, Op. 142 no. 1 *2. Other tuplets in the sample are with accessory numerals 2, 4, 5, and 6. *3. In the 400 themes in the samples, in all cases, two voices are for just 1 note. The following are examples of themes, selected from the entire book, that involve two or more voices: Bach: Adagio of the Sonata in g minor for solo violin (2 voices for just 1 note) Bach: Prelude in C major, Well-Tempered Clavier Book I (3 voices) Bach: Prelude in Bb major, Well-Tempered Clavier Book I (2 voices throughout) Bach: Prelude in b minor, Well-Tempered Clavier Book I (2 voices throughout) Beethoven: "Ghost" Trio, Op. 70 no. 1, II (2 voices for just 1 note) Beethoven: Symphony no. 2, IV (2 voices for almost half) Beethoven: Symphony no. 5, I (3 voices) Chopin: Scherzo no. 1 in b minor, Op. 20, 2nd theme Debussy: Golliwog's Cakewalk from Children's Corner Suite, 3rd theme (2 voices for just 1 note) Haydn: Quartet in A, Op. 55 no.1, I (2 voices throughout) Haydn: Symphony no. 104, I, introduction (2 voices for just 1 note) Rachmaninoff: Prelude in c-sharp minor, Op. 3 no. 2 Schubert: Symphony no. 5, I, introduction Wagner: Siegfried Idyll, 1st theme Wagner: Tristan und Isolde, Prelude, 1st "theme" ----------------------------------------------------------------------------- 2. In the anonymous Real Vocal Book (a "fake book", undoubtedly crammed with blatant copyright violations; undated but c. 1980) The Real Vocal Book contains melodies and chord symbols for about 225 complete pop songs. The longest notated duration is a whole, the shortest a 16th; both occur many times. There are many double-dotted notes, but none with more dots. The only tuplets are triplets. The vast majority of the songs are in 4/4, some in 3/4; one or two are in "cut" time (2/2), one (Take Five, of course) is in 5/4, and one (Send in the Clowns) is in a mix of 12/8 and 9/8. These songs cover a range of styles -- some are really jazz, not pop in the strict sense -- and finding a meaningful analog to incipits in them is not easy. 1ST TRY: for "incipits", I scanned to the end of the first ending, if any, but ignoring pickups ending the first ending; if no first ending, to the first double bar; but in no case going beyond the first page. (But this is not a very good analog to incipits: it certainly includes too much of many songs' main themes, and little if any bridges/choruses.) I checked every 4th song, 55 songs in all, so those starting on pages: 1, 7, 17, 25, 33, 41, 49, 57, 67, 77, 87, 97, 107, 115, 123, 133, 141, 151, 161, 169, 179, 189, 197, 207, 215, 225, 233, 241, 249, 257, 267, 275, 283, 291, 299, 307, 315, 325, 333, 343, 351, 359, 367, 377, 387, 395, 403, 411, 419, 427, 439, 447, 455, 463, 473. In this portion of these songs, there are no grace notes, trills, or turns; in fact, there appear to be none of these in the entire volume, but there are a few fermatas. The number that contain the other types of confound: Repeated notes (in both the literal and the musical senses) 29 (53%) Repeated notes (in the literal but not the musical sense) 8 (14.5%) Rests 37 (67%) 2ND TRY: for "incipits", I scanned the first two systems, but ignoring pickups ending the first ending; then the first two systems of the bridge/chorus, if any, so a maximum of two themes per song. (In some cases, especially jazz tunes, this is probably an oversimplification. For one thing, it sometimes goes well beyond incipits.) I checked every 5th song: in all 45 songs and 81 themes. Page numbers: 1, 13, 23, 33, 43, 53, 65, 77, 87, 101, 113, 123, 135, 147, 157, 167, 179, 189, 199, 211, 223, 233, 243, 253, 263, 275, 285, 295, 305, 315, 327, 339, 349, 359, 370, 379, 391, 399, 409, 421, 431, 445, 455, 465, 475. In this portion of these songs, there are no grace notes, trills, or turns (in fact, there appear to be none of these in the entire volume). The number that contain the other types of confound: Repeated notes (in both the literal and the musical senses) 37 (46%) Repeated notes (in the literal but not the musical sense) 6 (7.5%) Rests 39 (48%) ----------------------------------------------------------------------------- 3. In Worship in Song: A Friends Hymnal (Friends General Conference, 1996) Worship in Song contains 335 hymns. Starting with number 5, I considered every fifth hymn: 67 in all. As an analog of incipits, in each, I scanned the first two systems. In this portion of these songs, there are no grace notes, trills, or turns (in fact, there appear to be none of these in the entire volume). The number that contain the other types of confound: Repeated notes (in both the literal and the musical senses) 50 (75%) Repeated notes (in the literal but not the musical sense) 8 (12%) Rests 9 (13%)