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. o Metal Bars o Wooden Bars o Chimes o Bells o Strings

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

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

Frequencies of Longest Bar  P = 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.

Frequency Ratios Observed P/P = Q/P = 2.68 R/P = 3.73 S/P = 5.25 Computed P/P = Q/P = R/P = S/P = Simple model, but note that frequency R is not predicted

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.

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.

Small Clock Chimes

Characteristic Frequencies of One Rod NameFrequencyAmplitude P5 to 10Inaudible Q1801 RaRa RbRb S T

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)

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).

Terling Bells Bell Number Lowest (P) 2 nd (Q)3 rd (R)4 th (S)5 th (T)

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.

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.

Plucked Strings StringPitchLowest NumberName(P)2 nd (Q)3 rd (R)4 th (S)5 th (T) 1E4E B3B G3G D3D A2A E2E

Notes The frequency ratios are very nearly whole numbers Look at the A string P/P = Q/P = R/P = 2.99 S/P = T/P = 5.000

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

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

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

Harmonics 1st2nd Sum

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

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

Terling Bell #1 C 4 has a fundamental of Hz and D 5 #has a fundamental of 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 # Terling Bell #

Bell Harmonics

Find the Hidden Tune 1 st Tone2 nd Tone3 rd Tone 1 st Note nd Note rd Note th Note none 5 th Note th Note th Note th Note none

1 st Tone2 nd Tone3 rd ToneHarm. Fund.Note 1 st Note G4G4 2 nd Note G4G4 3 rd Note A4A4 4 th Note None34 494B4B4 5 th Note G4G4 6 th Note B4B4 7 th Note A4A4 8 th Note None45 293D4D4

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

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)

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