November 15, 2012
Presentation Handout (pdf)
1. Contextual Analysis of Chorale Phrase Harmonizations by J.S. Bach for iPad
This iPad Web app was created for MUSC 116 Music Theory II to allow the student to interactively explore 7 chorale phrase harmonizations by J.S. Bach. It was designed to serve as an interactive online answer key for MUSC 116 Worksheet 7-3 (pdf). Students are challenged to apply what they learned in lecture about the phrase model (Laitz 2011) and contextual analysis (Clendinning and Marvin 2011) to these 7 phrases. The app presents the student with five views of each phrase: 1. SATB score; 2. Roman numeral analysis; 3. Contextual analysis (Roman numerals; phrase-model symbols T, PD & D and expansion lines; and cadence ID); 4. S-B counterpoint (Kostka and Payne 2013); and 5. S-B counterpoint analysis. Two recordings are provided for each phrase: SATB and S-B. Students are also asked to sing each line along with the app's playback. The analytical commentary accompanying each example reviews important concepts presented in the reading and lecture.2. Ratio to Cents for iPhone
This simple iPhone Web app allows the student to convert a frequency ratio to cents on an iPhone. The app also works on other phones, iPads, other tablets, and desktop computers, but is optimized for an iPhone display. The app uses the following conversion formula:
c = 1200 * log2(f2/f1)
where c is cents, and f2/f1 is a pitch interval expressed as a frequency ratio (Campbell and Greated 2001, p. 79). The student enters a frequency ratio (e.g., 2/1, 3/2, 2/3, 5/4, 5/3, 6/5, etc.) and the app calculates the interval's equivalent size in cents. (By convention, there are 1200 cents in an 2/1 octave. Thus, there are 100 cents in an twelve-tone equal-tempered (12tet) semitone, and a cent = 1/100 12tet semitone.) Cents allow the sizes of intervals in various tunings and temperaments to be easily compared.The app also calculates the interval's decimal equivalent. All values are rounded to 3 decimal places.
An upward just perfect fifth (P5), whose frequency ratio is 3/2, is equivalent to 702 cents (i.e. 701.955 rounded to the nearest cent). A downward just perfect fourth (3/4) is approximately -498 cents. In twelve-tone equal temperament (12tet), a P5 spans 7 semitones, thus an 12tet P5 is equivalent to 700 cents. A just P5 is approximately 2 cents larger than a 12tet P5. A P4 spans 5 semitones (500 cents), so a just P4 is approximately 2 cents smaller than an 12tet P4.
J.S. Bach Chorale Harmonizations
- JSBChorales.net, Chorales by Riemenschneider Number
jQuery & jQuery Mobile
TouchSwipe jQuery Plugin
- Little Web Hut
Web-App Development Reference
Tools used in Project
Apple iOS Developer Center
Ambrose, Z. Philip. Texts for the Complete Vocal Works [of J.S. Bach] with English Translation and Commentary. Available online at: http://www.uvm.edu/~classics/faculty/bach/
Bach, Johann Sebastian, and Albert Riemenschneider. 1941. 371 Harmonized Chorales and 69 Chorale Melodies with Figured Bass. New York: G. Schirmer.
Benjamin, Thomas. 2003. The Craft of Tonal Counterpoint, 2nd ed. New York: Routledge.
Campbell, Murray, and Clive A. Greated. 2001. The Musicians' Guide to Acoustics. Oxford: Oxford University Press.
Clendinning, Jane Piper and Elizabeth West Marvin. 2011. The Musician's Guide to Theory and Analysis, 2nd ed. New York: Norton.
Cone, Edward T. 1960. "Analysis Today." The Musical Quarterly 46/2 (Apr., 1960): 172-88.
Hadlock, Kris. 2012. jQuery Mobile: Develop and Design. Berkeley, CA: Peachpit Press.
Kostka, Stefan, Dorothy Payne and Byron Almén. 2013. Tonal Harmony: With An Introduction to Twentieth-Century Music, 7th ed. New York: McGraw-Hill.
Laitz, Steven. 2011. The Complete Musician: An Integrated Approach to Tonal Theory, Analysis, and Listening, 3rd ed. New York: Oxford.
MacDonald, Matthew. 2011. HTML5: The Missing Manual. Sebastopol, CA: O'Reilly Media.
McFarland, David Sawyer. 2009. CSS: The Missing Manual, 2nd Edition. Sebastopol, CA: O'Reilly Media.