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Chapter 5

Chapter 5. Pitch: The Simplest Musical Implication of Characteristic Oscillations. Characteristic Frequencies. Here we will look at some classes of instruments and some of the frequencies they emit. Metal Bars Wooden Bars Chimes Bells Strings. Scientific Process.

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Chapter 5

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  1. Chapter 5 Pitch: The Simplest Musical Implication of Characteristic Oscillations

  2. Characteristic Frequencies • Here we will look at some classes of instruments and some of the frequencies they emit. • Metal Bars • Wooden Bars • Chimes • Bells • Strings

  3. Scientific Process • This chapter presents experiments with various instrument groups. • Many times conclusions are not reached. • Note the differences between the frequencies recorded and the perception of pitch. • A future chapter will explain

  4. Rectangular Bars • Consider a glockenspiel (orchestra bells ) • Freely floating bars • 2.5 – 3 octave range starting at C6 • Played by striking bars with a hammer

  5. Frequencies of Longest Bar • P = 1046.5 Hz • Q = 2810 Hz • R = 3906 Hz • S = 5494 Hz Benade often will label different frequencies with a letter if he has need of the label again.

  6. Frequency Ratios Computed P/P = 1.000 Q/P = 2.756 R/P = S/P = 5.404 Simple model, but note that frequency R is not predicted Observed • P/P = 1.000 • Q/P = 2.68 • R/P = 3.73 • S/P = 5.25

  7. Differences • The discrepancy between the model and P/P, Q/P, and S/P is due mostly to the mounting technique and tuning. • The missing R/P ratio in the model is an oversight of the model.

  8. Wooden Bars - Xylophones • The damping times are different than metal bars. • There will be other frequencies in the hardwood bars due to the graininess of the wood.

  9. Small Clock Chimes

  10. Characteristic Frequencies of One Rod

  11. Observations • Rod generally sounds either just above F3 (near Q) or just above C5 (near the R’s) - depending on who is listening. • Each group hears the other tone as well as the high-pitched T, but they differ in their assignment of it. But nobody picks a pitch at S or T. • Look at the amplitude column • Decay times about the same • We’ll come back to these questions Q (180) R (525, 530) S (1063) T (1772)

  12. Bells • Classic study is Lord Rayleigh on the Terling Bells • System of eight bells of different tones. • In order to compare we normalize the frequencies so that the lowest frequency on each bell is what the listener calls middle C (261.6 Hz).

  13. Terling Bells

  14. Notes • All of the P tones are above middle C, even though the listener called them C. • The range of the Q tone is very large • Could some of the Q’s be actually misidentified C5? But C5 is 523 Hz – not close • R’s only roughly agree and S and T vary widely • Changing the amplitude has little effect on the pitch assignment.

  15. Plucked Strings • String stretched tightly between supports is struck or plucked and allowed to freely oscillate. • piano, guitar, harpsichord, harp • Again we normalize so that the lowest frequency is 300 Hz.

  16. Plucked Strings

  17. Notes • The frequency ratios are very nearly whole numbers • Look at the A string P/P = 1.000 Q/P = 1.985 R/P = 2.99 S/P = 3.994 T/P = 5.000

  18. Differences from Whole Number Ratios • Influenced by guitar, strings, and weather • Same for piano – differences small in the middle of the keyboard – greater at the ends

  19. Instruments with Integer Harmonics • Upper frequencies are integer multiples of the fundamental • Voice, strings, woodwinds, brass • All are capable of sustained sound fn = nf1

  20. Integer Multiples fo 2fo 3fo 4fo Sum

  21. 1st 2nd Sum Harmonics

  22. Assigned Pitches • Our ears assign pitches based on any whole number sequences they can find. • Assigned pitch is the lowest frequency that gives harmonics • Some harmonics may be missing, but the pattern is recognized • Tone knob on a stereo • Perfect tone suppression • Cheap radio

  23. Chime Pitches • Earlier we saw that experienced people disagree on the pitch of clock chimes. Some got F3 and others C5

  24. Terling Bell #1 • C4 has a fundamental of 261.5 Hz and D5#has a fundamental of 622.25. Look at the first several harmonics of C4

  25. Bell Harmonics

  26. 1st Tone 2nd Tone 3rd Tone 1st Note 392 1176 1568 2nd Note 1176 1568 1960 3rd Note 880 1320 2200 4th Note 1482 1976 none 5th Note 392 784 1960 6th Note 494 1482 2470 7th Note 440 1760 2200 8th Note 1172 1465 none Find the Hidden Tune

  27. Review Characteristics of Impulsively produced sounds: • Made up of damped sinusoids • Frequencies characteristic of the object

  28. Classes of Instruments • Sustained Tones • Voice • Bowed Instruments • Orchestral Wind instruments • Ringing Tones that die away • Bells • Strings that are plucked or struck • String pulled to one side and released (harpsichord, guitar, harp) • String struck by a hammer (piano, cimbalom, clavichord)

  29. Sequence of events for stringed striking or plucking String vibrates  drives bridge  drives soundboard  drives air in the room  drives ear

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