* An earlier version of this paper was presented at the 14th Nordic Musicological Conference in Helsinky in August 2004.

1. Laure Schnapper. "Ostinato," in The New Grove Dictionary of Music and Musicians, 2nd ed. (New York: Grove's Dictionaries, 2001), vol. 18, 782.

2. A single peak between two statements is sufficient for the presentation of the gesture, but a double peak between three statements is more typical and expresses the gesture more completely. For examples with a single peak, see example 3 (Dona Elvira) as well as Schubert's song "Frühlingstraum" (No. 11 in Die Winterreise, D. 911), mm. 12-15.

3. See "Là ci darem la mano" (No. 7 in Mozart's Don Giovanni, K. 527). The first phrase (mm. 1-8) is repeated with expansion (mm. 9-18). The expansion includes one obstinate peak (m. 16). As in Example 5 [Verdi], the text setting of the repeat is modified, in this case since the peak takes the first syllable of the repeat rather than interpolating a filling word.

4. As William Rothstein notes, the expansion usually relates to a middleground prototype and only now and then to an explicit, foreground prototype. See Rothstein, "Rhythm and the Theory of Structural Levels" (Ph.D. diss., Yale Univ., 1981), 152 and 162.

5. In Chopin's prelude Op. 28, No. 7 (m. 4 vs. m. 12) the full rhyme prevents any obstinate feeling. In Chopin's mazurka Op. 50, No. 1, mm. 77-80, a similar gesture is closer to the obstinacy gesture due to the location on the weak beats.

6. See William Rothstein, Phrase Rhythm in Tonal Music (New York: Schirmer, 1989); Janet Schmalfeldt, "Cadential Processes: The Evaded Cadence and the 'One More Time' Technique," Journal of Musicological Research, 12/1-2 (1992): 1-52. For a phrase expansion that lacks the feeling of obstinacy, see the main theme of Beethoven, piano sonata Op. 2, No. 3/i. Some expansions might be borderline cases that contain a mild sense of obstinacy. For instance, see Schubert's song "Wohin" (No. 2 in Die Sch�ne M�llerin, D. 795), mm. 27-34.

7. Rothstein (Phrase Rhythm, 68) distinguishes external expansions (prefixes or suffixes) from internal ones. Earlier, Rothstein referred to suffixes as "extensions." See William Rothstein, "Rhythm and the Theory of Structural Levels," 152.

8. For the concept of "shadow meter" see Frank Samarotto, "Strange Dimensions: Regularity and Irregularity in Deep Levels of Rhythmic Reduction," in Schenker Studies 2, ed. Carl Schachter and Hedi Siegel (Cambridge: Cambridge Univ. Press, 1999), 222-238, esp. 235.

9. Another example: Chopin, mazurka Op. 59, No. 2, mm. 16-20. The main theme ends three times with perfect authentic cadences. The two first endings leap upward from ^1 after a single eighth note.

10. Deceptive cadences also occur in the coda of Mozart's horn quintet/iii, mm. 176-84. In that case, the peaks themselves appear after the cadences, harmonized as I⁶.

11. For a distinction of dominant arrival from a genuine half-cadence, see William E. Caplin, Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart and Beethoven (Oxford: Oxford Univ. Press, 1998), 79. Another example without phrase expansion: Schumann, "Ende vom Lied," Fantasiest�ck Op. 12, No. 8, mm. 9-16.

12. The hypermeter of this theme is ambiguous from the start. The bass begins only after the strong beat of the harmonically stable m. 1, whereas the harmonically unstable m. 2 is emphasized by means of a high long note. Recomposition that leaves two-measure interval between the obstinate peaks would support hearing them as occurring on strong measures (as if m. 2 is strong), but another recomposition that omits the obstinacy gesture altogether would support the reading of m. 1 as a strong measure.

For a repeat that includes the obstinacy gesture and preceding material, see also Schubert, symphony No. 5/i, mm. 80-91.

13. The device of surface rhythmic subdivision is common in various contexts, even when a basic idea of a theme recurs immediately (e.g., in Mozart's piano sonata K. 330/i). In Papageno's aria in example 4, the rhythmic surface of the three cadential statements varies, and the last statement ends in most conventional equal sixteenth-notes. However, in this case the rhythmic subdivision does not affect the peaks themselves. Sometimes, a metrical shift alone can create an impression similar to rhythmic subdivision. See for example, in Beethoven's piano sonata Op. 27, No. 2/ii, mm. 28-36: the intensification of syncopation compensates here for the lack of any melodic or harmonic differences between the theme and its recapitulation.

14. For other slow examples, see Beethoven, piano concerto No. 3/ii, mm. 20-24; Mozart, string quartet K. 458/iii, mm. 21-23. In the latter example, the weak-beat sforzando occurs on a passing tone, while the peaks appear on II⁶ on strong beats, after surface figuration syncopations.

15. The concept of auxiliary cadence derives from Heinrich Schenker, Free Composition (New York: Longman, [1935/1956] 1979), 88, �244. Regarding the function of auxiliary cadences as anticipations, see Rothstein, "Rhythm and the Theory of Structural Levels," 123; another view: Poundie Burstein, "Unraveling Schenker's Concept of the Auxiliary Cadence," Music Theory Spectrum 27/2 (2005): 159-85, esp. 164-67.

16. In Beethoven's Tempest sonata/iii (Ex. 22 ahead), the exposition has ^8 after ^5 and the coda adds the higher ^3. See also ahead example 25 (Smetana). For ^5 after ^3, see Mendelssohn, trio for piano and strings No. 1/i, mm. 17-36 (clear obstinacy despite the lack of syncopations), and Beethoven, piano sonata Op. 2, No. 2/iv, mm. 26-32. The latter example is exceptional in that it does not end with a cadence. Occasionally, however, the same pitch recurs at the peak, e.g., twice ^5 in Beethoven, piano concerto No. 3/ii, mm. 50 and 52. In this case, the bass changes: the first peak is harmonized as I6 whereas the second peak is supported by a root position tonic. For a single tonic peak, see Schubert, piano sonata Op. 164 (D. 537)/iv, m. 14 (^5 over I⁶).

17. The principle of ascending peaks sometimes appears in a concise form. See for example Franck's symphony/i, second theme, mm. 129-30; Brahms, piano concerto No. 1/i, mm. 158 vs. 162. A larger phrase building arises in Verdi's Aida act 1 scene 1, from F forwards (the entire melody appears in the first violins part, Amneris joins portions of the melody): the first phrase reaches ^8 (=the upper ^1) toward its end, the second phrase reaches the upper b^2 in a parallel location, whereas a third phrase rises immediately to the upper ^3.

18. In Mozart's horn quintet (see footnote 10 above), the peaks are on tones of the tonic (^5 and ^8), after deceptive cadences.

19. Rosen, The Romantic Generation (Cambridge: Harvard Univ. Press, 1995), 67-68. For plagal arpeggiations (^6 after ^4) see also Mozart, piano trio K. 496/ii , suffix to main theme, mm. 8-10, and-with symmetrical and less obstinate phrasing - "Là ci darem la mano" (No. 7 in Mozart's Don Giovanni), m. 35 vs. m. 38, and the theme of Mendelssohn's song without words Op. 30, No. 3. Recorded on Deutsche Grammophon 445 881-2.

20. Recorded on Deutsche Grammophon 445 881-2.

21. More complicated secundal relations appear in Chopin's prelude Op. 28, No. 15, mm. 9-18. The basic phrase involves an ascending sequence, and the expansion that creates a mild sense of obstinacy contracts the higher repeat in a shorter unit.

22. For secondary dominants of IV in situations that are at least mildly related to the obstinacy gesture, see V7/IV in Mozart, piano sonata K. 279/i, mm. 12-13, and the syncopated VII�⁷/IV in the coda of Mendelssohn's song without words Op. 30, No. 4, mm. 119-31. In the latter piece, melodic peaks appear as part of the repeated phrase rather than between the phrases. The last repeat indicates closure by eliminating a final syncopation (not that of the VII�⁷/IV).

23. Earlier in the same ensemble, a more conventional gesture of growing obstinacy takes place (mm. 38-43). A special device that occurs in that case is a slowing down of the final cadence. The dramatic effect of the written-out ritenuto is somewhat contrary to the forceful drive of obstinacy.

24. ^6 harmonized as V⁹ also serves in the middle section Chopin's mazurka Op. 17, No. 1, as the lower of two peaks. The higher peak is ^2 (the fifth of V). The entire phrase is symmetrical (and thus lacks essential features of the obstinacy gesture), and is then repeated with the last ^2 an octave higher.

25. See a milder case of a reinforced half cadence by means of repeated syncopated stressed peaks in Beethoven, symphony No. 1/ii, mm. 23-25. That case differs from the ordinary obstinacy gesture since the repeated idea is encapsulated (in a compressed form) in the peaks themselves.

26. Strictly speaking, the elimination of syncopation is also a temporal element as discussed in the previous paragraph.

27. Another example of strong-beat emphasized ascending peaks: Schubert, piano sonata Op. 78 (D. 894)/ii, mm. 25-31 (mentioned as an evaded cadence in Schmalfeldt, "One-More-Time Technique," 42).

The specific emotional impacts of instrumental passages is an intricate matter. Attempts to prove precise meanings have limited success. For that approach, see the Levinson's claims that certain passages in Mendelssohn's Hebrides overture express hope (as distinct from other positive emotions). See Jerrold Levinson, "Hope in the Hebrides," in Music, Art and Metaphysics, 336-75. (Ithaca: Cornell Univ. Press, 1990). Some passages do not sound obstinate even though they seem to fulfill all theoretical requirements for that. For example, in Beethoven's piano sonata Op. 26/iv, mm. 42-48, ascending peaks on weak beats after deceptive cadences with dynamic emphasis nevertheless do not possess the expected obstinate character. Perhaps this derives from the lack of true syncopation, as the peaks are short and begin descending scales.

28. See the following cadences (some of which are discussed above): deceptive cadence in Example 3 (Dona Elvira); imperfect authentic cadences in Example 1 (Figaro); weakened perfect authentic cadence in Example 5 (Verdi) and also in Mozart, violin concerto K. 218/i, mm. 34-38 (even without a melodic peak) and piano concerto K. 595/iii, mm. 21-26; evaded cadence (an implied authentic cadence which fails to reach its goal harmony) in Example 20 (Chopin); abandoned cadence (an implied authentic cadence which is not realized due to the elimination of V5/3) in Mozart, piano sonata K. 333/i, mm. 5-10. For the definitions of cadences see Caplin, Classical Form, 253-56.

29. See Mozart, string quartet K. 458/iii; Mendelssohn, song without words Op. 30, No. 4; (footnotes 14 and 22 above, respectively).

30. See a similar case in Mozart's piano sonata K. 310/iii, mm. 13-20. The passage includes a single repeat, but the lead-in recurs again (leading to the subsequent phrase) and in real time it sounds as if an additional repeat is going to take place.

31. Janet Schmalfeldt, too, points to opera buffa as the source of the "one-more-time" technique, which is reminiscent of (but rarely overlaps) the gesture of growing obstinacy. "One-More-Time Technique," 21-22.

32. An exceptional clear obstinacy gesture in Haydn's works takes place in the finale of piano trio Hob. xvi: 27. The repeat of the main theme (mm. 36-47) modifies the consequent of the parallel period to introduce a single syncopated peak (harmonized II⁶); in the coda (mm. 238-49), that peak recurs three times and thus a clear obstinacy gesture emerges. In Haydn's symphony No. 102/i, mm. 49-51, a sense of obstinacy occurs in the middle of a bridge rather than towards the end, as is more typical.

33. See Scarlatti's keyboard sonatas K. 96, mm. 94-102; K. 132, mm. 29-33; K. 209, mm. 89-94; K. 540, mm. 38-46. I thank Reuven Naveh for the three first examples.

34. The model for such a work in the field of musicology may be found in the study of the particular musical figure ^1-^7-^4-^3 in Robert O. Gjerdingen, A Classic Turn of Phrase: Music and the Psychology of Convention (Philadelphia: Univ. of Pennsylvania Press: 1988).

35. Leonard G. Ratner, Classic Music: Expression, Form, and Style (New York: Schirmer, 1980), 9-29.

36. For a case indicated in a book on forms, see Mozart, piano sonata K. 310/iii, mm. 13-20, in Caplin, Classical Form, Example 4.14. Caplin shows the repeated contrasting idea in the consequent of a parallel period. Cf. footnote 30 above.

37. Among five recordings of this sonata in the anthology Great Pianists of the 20th Century, that played by Svyatoslav Richter brings the gesture out with special emphasis. Richter dramatizes the obstinacy gesture, by making a huge fermata at the highest peak in the coda, among other things, to the extent that it becomes almost the climactic apex of the entire movement.

38. A less extreme example of recurring gesture of obstinacy related to the main theme: Schumann, symphony No. 3/v, mm. 27-47. The peaks in mm. 30 and 34 are integrated in their environment, rather than being salient exceptions as most obstinate peaks (cf. the ascending leaps to weak beats in the theme, m. 29).