| # | Date | Topics | References | Homework |
|---|---|---|---|---|
| 1 | F 9/5 | Introduction | - | - |
| 2 | M 9/8 | Vibrating strings | [H] ch. 2; [B] 1.4, 1.5, 1.6 | - |
| 3 | W 9/10 | Summary: From sound waves (loudness and pitch) to sine curves (amplitude and frequency) | [B] pp. 6, 21 | - |
| - | - | Review of trigonometry | Dave's short trig course | - |
| 4 | F 9/12 | Beats | [B] sec. 1.8 | HW 1: On the handout of trig problems, do p. 1: 42, 51; p. 2: 2; p. 3: 5, 9, 11, 17. (due 9/17) |
| 5 | M 9/15 | Change ringing: introduction | - | - |
| 6 | W 9/17 | Guest session run by bell ringers from Cambridge, England. Ringing on handbells. | - | - |
| 7 | F 9/19 | Permutations using cycles | handout (from Herstein) | - |
| 8 | M 9/22 | Describe plain hunt and bob minimus using permutations | handout (printed) | HW 2: Handout from Herstein: Problems 2 and 3 (due 9/24) |
| 9 | W 9/24 | [Mountain day!] | - | - |
| 10 | F 9/26 | Analysis of bob minimus using permutations | Handout | HW 3: Analyse bob doubles the same we did bob minimus in class. (Due 10/1) |
| 11 | M 9/29 | Even and odd permutations | Handout from Herstein | HW 4. (More problems from Herstein. Due 10/3) |
| 12 | W 10/1 | Comparison of Bell ringing (Stedman) with Steve Reich's minimalist music | - | - |
| 13 | F 10/3 | The nature of sound | [B] Ch. 1 | - |
| 14 | M 10/6 | The spectrum; Introduction to trigonometric series | [B] p. 22 | - |
| - | - | The bells at Utrecht Cathedral in the Netherlands | - | - |
| 15 | W 10/8 | Fourier series: finding spectrum for a periodic function (using calculus) | [B] 2.1, 2.2 | - |
| 16 | F 10/10 | Consonance and dissonance | [B] 4.1, 4.2 | - |
| - | M 10/13 | [Fall break] | - | - |
| 17 | W 10/15 | [no class] | - | - |
| 18 | F 10/17 | [no class] | - | - |
| 19 | M 10/20 | Consonance and dissonance (con't) | [B] 4.2 | HW 5 (due 10/24): Using the same analysis as in [B] 4.2 (checking how many overtones coincide): (1) Which sounds better, a perfect fifth or a perfect fourth? (2) Which sounds better, a perfect major third or a perfect minor third? (See [H] ch 2, [B] 5.5) |
| - | - | Artificial scales and overtones ([B] 4.6) | Demonstration using Bach chorale (handout) | - |
| 20 | W 10/22 | Just intonation--several choices here | Benson 5.5 | - |
| 21 | F 10/24 | Guest lecture by Sarah Bacon (from the Biology department) on the anatomy of the ear. | Handouts | - |
| 22 | M 10/27 | Pythagorean temperament scale and the spiral of fifths | Benson 5.2, 5.3 | - |
| 23 | W 10/29 | Eitz notation | Benson 5.9 | - |
| 24 | F 10/31 | Pythagorean and syntonic commas | Benson 5.8 | - |
| 25 | M 11/3 | Guest lecture by Bob Eisenstein (MHC Music Department), on music from Pythagoras through Machaut. | - | - |
| 26 | W 11/5 | Cents (5.4), | - | HW 6 (Do by 11/7 if possible) |
| - | - | Equal temperament | Benson 5.14 | - |
| - | - | - | CD: Christe playing Sweelink's "Ballo del granduca" on the mean-tone organ at Wellesley (handout) | - |
| 27 | F 11/7 | 1/4-comma and alpha-comma meantone | Benson 5.12 | HW 7: Fill in the table of values for intervals (Due 11/12) |
| - | - | Demonstration: "Capriccio cromatico" by T. Merula (d. 1665) | - | - |
| 28 | M 11/10 | Symmetry | Examples: Machaut "Ma fin est mon commencement"; J. S. Bach: Canons on the bass of the aria in the Goldberg variations (CD; scores) | - |
| 29 | W 11/12 | Discuss projects | - | - |
| - | - | - | Example of symmetry: Messain Chant d'oiseaux | - |
| 30 | F 11/14 | Mathematical symmetry | - | HW8: On both the handouts (canons on the bass of the Goldberg theme, and canons on the theme of the Musical Offering): Identify the type of the canon. Eg Canon at the fifth? By inversion? Retrograde? Augmentation/diminution? Write your answers directly on the handouts. (By the way, it looks like 10.I and 10.II are to be played together.) Due 11/19. |
| - | - | Examine some organ pipes | - | - |
| 31 | M 11/17 | Visit MHC Fisk organ. Meet in the chapel 8:45. | - | - |
| 32 | W 11/19 | Introduction to 1/f music | Harkleroad pp. 97--103; also Reference at Yale | - |
| 33 | F 11/21 | - | - | - |
| 34 | M 11/24 | African rhythms | Papers by Godfried Toussaint | - |
| 35 | M 12/1 | African rhythms (con't) | - | - |
| 36 | W 12/3 | Presentations | - | - |
| 37 | F 12/5 | (no class) | - | - |
| 38 | M 12/8 | Presentations | - | - |
| 39 | W 12/10 | Presentations | - | - |
| 40 | F 12/12 | Presentations | - | - |