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

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Presentation on theme: "Chapter 5 Pitch: The Simplest Musical Implication of Characteristic Oscillations."— Presentation transcript:

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2 Chapter 5 Pitch: The Simplest Musical Implication of Characteristic Oscillations

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

4 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. o A future chapter will explain

5 Rectangular Bars Consider a glockenspiel (orchestra bells ) o Freely floating bars o 2.5 – 3 octave range starting at C 6 o Played by striking bars with a hammer

6 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.

7 Frequency Ratios Observed P/P = 1.000 Q/P = 2.68 R/P = 3.73 S/P = 5.25 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

8 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.

9 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.

10 Small Clock Chimes

11 Characteristic Frequencies of One Rod NameFrequencyAmplitude P5 to 10Inaudible Q1801 RaRa 52510 RbRb 5306.3 S106322 T177244.7

12 Observations Rod generally sounds either just above F 3 (near Q) or just above C 5 (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. o Look at the amplitude column o Decay times about the same We’ll come back to these questions Q (180) R (525, 530) S (1063) T (1772)

13 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).

14 Terling Bells Bell Number Lowest (P) 2 nd (Q)3 rd (R)4 th (S)5 th (T) 12784676207861046 2286458590832982 32675326417641071 42755126207961026 52725446228191033

15 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 o Could some of the Q’s be actually misidentified C 5 ? But C 5 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.

16 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.

17 Plucked Strings StringPitchLowest NumberName(P)2 nd (Q)3 rd (R)4 th (S)5 th (T) 1E4E4 300.0600.9900.21200.01500.9 2B3B3 300.0599.2900.01200.11500.0 3G3G3 300.0602.0902.81204.61504.1 4D3D3 300.0600.6900.01204.51508.2 5A2A2 300.0595.4897.01198.11500.0 6E2E2 300.0603.7900.01201.91500.0

18 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

19 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

20 Instruments with Integer Harmonics Upper frequencies are integer multiples of the fundamental Voice, strings, woodwinds, brass All are capable of sustained sound f n = nf 1

21 Integer Multiples fofo 2f o 3f o 4f o Sum

22 Harmonics 1st2nd Sum

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

24 Chime Pitches Earlier we saw that experienced people disagree on the pitch of clock chimes. Some got F 3 and others C 5

25 Terling Bell #1 C 4 has a fundamental of 261.5 Hz and D 5 #has a fundamental of 622.25. Look at the first several harmonics of C 4 C4C4 2*C 4 D 5 #3*C 4 4*C 4 2*D 5 # C 4 - D 5 #261.5523622.25784.510461244.5 Terling Bell #12784676207861046

26 Bell Harmonics

27 Find the Hidden Tune 1 st Tone2 nd Tone3 rd Tone 1 st Note39211761568 2 nd Note117615681960 3 rd Note88013202200 4 th Note14821976none 5 th Note3927841960 6 th Note49414822470 7 th Note44017602200 8 th Note11721465none

28 1 st Tone2 nd Tone3 rd ToneHarm. Fund.Note 1 st Note39211761568134392G4G4 2 nd Note117615681960345392G4G4 3 rd Note88013202200235440A4A4 4 th Note14821976None34 494B4B4 5 th Note3927841960125392G4G4 6 th Note49414822470135494B4B4 7 th Note44017602200145440A4A4 8 th Note11721465None45 293D4D4

29 Review Characteristics of Impulsively produced sounds: Made up of damped sinusoids Frequencies characteristic of the object

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

31 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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