1. See, for example, Louis Vierne, "Carillon de Westminster," from Pieces de Fantaisie for organ. 

2. For more information about the instrument, consult its web site: http://www.cc.rochester.edu/College/MUR/carillon.html. 

3. Quoted in W. W. Starmer, "Chimes," Proceedings of the Musical Association 34th session, (1907-8): 8. 

4. The melodic sequence from Parsifal upon which the chime is based is found at the end of the "Good Friday" scene in the third act. According to Percival Price (Bells and Man [Oxford: Oxford University Press, 1983], 182), this sequence ". . . is associated with the Benedictine Abbey of Beuron, Germany, which in 1869 installed a swinging peal of four bells sounding, in descending order, the notes B-flat, G, F, and D above middle C. Wagner wanted the bells sounding a minor seventh lower in order to suggest the solemnity of the Monastery of the Holy Grail. . . . The only place where the Parsifal Quarters may be heard complete and on bells of the deep pitches that Wagner envisioned is at the Riverside Church." For more information about the carillon at Riverside, consult its web site: http://theriversidechurchny.org/about_carillon.html

5. For a useful web site (with bibliography) concerning clock jacks although not dealing with those in tower clocks, consult: http://www.database.com/~lemur/dm-clock-jacks.html

6. See Starmer, "Chimes," p. 9. Starmer quotes a "Dr. Raven," to whom was written a letter by a "Mr. Amps," who apparently knew the origination story of the chime. Dr. Raven notes that Crotch's permutations show evidence of a systematic order ". . . not unworthy of Fabian Stedman." Stedman was the author of Campanologia (Cambridige, 1677), the first thorough examination of change ringing and its permutational nature. Campanologia can fairly be said to be the first work of in which group theory was applied to a musical situation.

7. See David Lewin, Generalized Musical Intervals and Transformations (New Haven: Yale University Press, 1987), 134-5, 209 ff. For a more concise treatment, see David Lewin, "On Partial Ordering," Perspectives of New Music 14-15 (1976): 252-59. 

8. For more information about "Tilted Arc," including bibliography, consult: http://www.arts.arizona.edu/are476/files/tilted_arc.htm 

9. The hour strike on G is correct, despite the obvious clash with the remainder of the chime. This G is the lowest bell in the Hopeman Carillon, and it also struck the hours when the Westminster Quarters (also set in F major) chimed from that instrument. Many chimes lack a bell large enough to act as a suboctave tonic for hour strikes, so hour strikes often occur on whatever the largest bell is regardless of key.

10. University of Rochester Campus Times, Februrary 3, 2000.

End of Footnotes