2. MATH 5: COMPOSITION Michael Blum

3. MATH 5: COMPOSITION Michael Blum

4. Organ Pedal

6. Ratio to f 0 HzdBn from A440n/12Roundedn from nearest ANoteDegreeNote Frequency 1 51.35 26-37.19-3.099067342-31.19G#1A5 1.3 70.2 12-31.78-2.647960588-27.78C#2A#1 1.6 84.87 9.2-28.49-2.374176941-24.49F2B5 2.1 110.53 28.7-23.92-1.99306552511.92A2C1 2.8 149.81 17.3-18.65-1.5543695956.65D2C#4 3.4 186.47 14.2-14.86-1.2385599812.86F#3D4 4 218.42 16.7-12.12-1.0103985590.12A3D#2 4.6 248.27 14.4-9.91-0.82559358109.91B3E4 5.1 277.6 18.3-7.97-0.66449595607.97C#4F1 5.5 298.83 16-6.70-0.55817853406.70D4F#4 6 328.92 20-5.04-0.4197667905.04E4G3 6.8 369.25 18.3-3.03-0.25290560303.03F#4G#3 7.2 393.34 18-1.94-0.16172661801.94G4 7.6 414.84 15-1.02-0.08494851401.02G#4 8 439.42 25-0.02-0.00190298900.02A4 8.5 465.61 13.60.980.0816185200.98A#4 9 492.84 27.91.960.16361582901.96B4 10.1 555.16 14.84.020.335400104.02C#5 10.7 587.08 7.94.990.41605358604.99D5 12 659.88 51.17.020.58470016907.02E5 13.5 740.53 38.29.010.75105465909.01F#5 14.3 786.09 22.210.050.837190973010.05G5 15.2 831.63 15.311.020.918438279011.02G#5 16.1 880.33 4612.011.00054090910.01A5 18 988.15 30.314.011.16722653412.01B5 20.2 1108.9 53.816.001.33355384114.00C#6 21.4 1173.61 23.116.981.4153776414.98D6 22.7 1244.31 25.118.001.49977052616.00D#6 24 1319.2 36.819.011.58408787517.01E6 25.5 1397.23 25.520.001.66699409518.00F6 27 1481 30.721.011.75099621219.01F#6 28.6 1569.51 15.222.021.834738792110.02G6 30.3 1664.63 19.223.041.919626114111.04G#6 32.1 1763.22 51.124.032.00263706520.03A6 35.9 1974.09 21.125.992.16561233621.99B6 38.1 2091.53 26.226.992.24898326322.99C7 40.4 2218.4 3328.012.33394409324.01C#7 42.8 2350.42 29.529.012.41734314825.01D7 45.3 2489.45 21.230.002.50025161126.00D#7 48 2637.75 22.931.002.58373240727.00E7 53.9 2960.07 2333.002.75005586429.00F#7 72 3959.58 18.538.043.1697719832.04B7

7. Motif A Variation on Motif A Relationship to Organ Pedal f 0 = 55 Hz (A 1 ) A – 1f, 2f, 4f, 8f, 16f, 32f B – 4.6f, 9f, 18f, 36f, 72f C# - 1.3f, 5f, 10f, 20f, 40f D# - 22.7f, 40.4f E – 6f, 12f, 24f, 48f F# - 3.4f, 6.8f, 13.6f, 27f G# - 1f, 7.6f, 15.2f, 30.3f

8. Relationship to Organ Pedal f 0 = 55 Hz (A 1 ) A – 1f, 2f, 4f, 8f, 16f, 32f B – 4.6f, 9f, 18f, 36f, 72f C – 38f C# - 1.3f, 5f, 10f, 20f, 40f D# - 22.7f, 40.4f E – 6f, 12f, 24f, 48f F# - 3.4f, 6.8f, 13.6f, 27f G – 7.2f, 14.3f, 28.6f G# - 1f, 7.6f, 15.2f, 30.3f Motif B

9. Dissonance in Motif B

10. Strongest Partials (above 25dB) Frequency (Hz)Intensity (dB)% Relative to Previous Partial 41.8634.3n/a 60.7631.731.1% 82.0855.526.0% 111.8740.826.6% 125.0242.110.5% 166.7837.125.0% 192.4825.913.4% 207.9629.27.4% 261.4156.320.4% 277.1839.85.7% 290.91254.7% 329.753611.8% 783.1647.457.9% 796.5931.61.7% 880.4131.89.5% 982.4525.610.4% 1109.793211.5% 1568.2139.629.2% Dissonance: ≤15%

11. Melodic Transformation (Reflection in the X axis)

12. Instrumentation Vibraphone Percussive; bell-like; the long sustain of the 1 st, 2 nd and 3 rd partials create beats Has partials at f 0, 3.26f 0, 7f 0, 12f 0, 18.5f 0, 26.23f 0

13. Instrumentation Harp Evenly spaced partials, mellow timbre Has partials at f 0, 2f 0, 3f 0, 4f 0, 5f 0, 6f 0, … (decrease in intensity as they increase in frequency)

14. Instrumentation Pizzicato (Plucked) Strings Percussive, evenly spaced partials Strong partials at f 0, 2f 0, 3f 0, 4f 0, 8f 0

15. Conclusion What is the tone created by the organ pedal and the dissonances in the melody? What impact does the timbre of the instruments have on the piece? What does this piece communicate to you? What is the contour of the piece?