Lecture 15Percussion Instruments (Plates)Keyboard Instruments (Piano)The Human Voice

Instructor: David Kirkby (dkirkby@uci.edu)

                                                                                 

Physics of Music, Lecture 15, D. Kirkby 2

MiscellaneousWe agreed that Problem Set #7 is worth 75 points, instead of the usual 50 points.

We agreed that the final exam will cover all the lectures (#1-18), and not just those since the midterm (#9-18).

I will be traveling on Tuesday next week. Prof. David Casper will give the first lecture on “Music and Technology”, covering topics such as:

•Loudspeakers, microphones•Amplifiers•Special effects (?)

The last two lectures will cover compression (eg, MP3) and techniques for synthesizing music electronically.

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Review of Lecture 14We covered those percussion instruments based on vibrating bars/rods and membranes.

We saw that the common feature of percussion instruments is their inharmonic timbre, and that is due to the more complicated nature of two-dimensional resonance.

Some percussion instruments (eg, xylophone) make adaptations so that they sound more harmonic and can be used melodically.

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Vibrations of PlatesA plate is a solid object whose thickness is small compared with its other dimensions.

A plate has the same relationship to a membrane as a rod/bar has to a string: tension force is replaced by stiffness and other dimensions (e.g. thickness) influence the sound.

The standing waves on a flat circular plate are similar to those of a circular membrane, but tend to be higher in frequency.

Plates are not necessarily flat in their resting position (unlike membranes).

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Cymbals, Gongs and TamtamsCymbals are circular plates, usually made of bronze, with an almost flat saucer-like shape.

Gongs and tamtams are similar to cymbals, but with morecurvature at their edges.

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Steel DrumsSteel drums are a recent invention, developed by trial and error using the 1000s of oil drums left on the beaches of Trinidad & Tobago by the British Navy after World War II.

The playing surface (pan) of asteel drum is hammered into aconcave shape with individualnote areas.

Listen to anexample…

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Bells and CarillonsBells are another form of vibrating plate: in this case the plate is curved into a bell shape (!)

A carillon is a set of tuned bells controlled from a keyboard. Listen to an example…

Handbells were developed to allow church bell ringers to practice without disturbing the whole neighborhood.

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Keyboard InstrumentsKeyboard instruments consist of tuned strings coupled to an air-filled cavity. Strings are struck or plucked by a mechanical action which is controlled from a keyboard.

Pianos, clavichords and harpsichords are all examples of keyboard instruments.

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Piano Construction

http://www.concertpitchpiano.com/GrandPianoConstruction.html

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Piano StringsPiano strings are made from high-strengthsteel and usually stretched to about half oftheir breaking strength on a metal frame.

The strings of a piano are almost idealone-dimensional strings, but have someinharmonicity that gets worse at higher harmonics.

Pianos cover the frequency range from 27.5 Hz (A0) to 4186 Hz (C8) with 88 keys (a ratio of 152:1).

Rather than have the longest strings 152x longer than the shortest ones, the tension and mass are varied in different ranges.

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Piano TuningA piano sounds best in tune when its octaves are stretched to match the inharmonicity of the string overtones.

Most notes on the piano have three corresponding strings. The piano sounds best when these strings are slightly out of tune with each other: this deliberate mistuning allows the vibrations of the string to last longer (otherwise, they transfer their energy too efficiently to the soundboard).

When the strings are too far out of tune, the result is a “honky-tonk” piano sound.

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Hammer-String InteractionsThe mechanical action that translates a key press into the hammer hitting the string is surprisingly complex:

http://www.concertpitchpiano.com/AnimatedGrandAction.html

This mechanism has 3 main purposes:

• to provide a lever action so that the hammer travels faster than the key,

• to provide an escapement action so that the hammer moves independently of the key,

• to raise and lower a felt damper that allows the string(s) to vibrate freely.

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Piano PedalsA piano usually has 2 or 3 foot-operated pedals.

The right-most pedal raises the dampers on all strings so that they continue to vibrate after a key is released, and are also free to vibrate sympathetically when other notes are played.

The left-most pedal makes the instrument quieter by either shifting the hammers to miss one string, or else by moving the hammers closer to the strings.

A center pedal, if present, usually sustainsonly those notes being played.

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Piano SoundboardThe sound board plays a similar role to the front and back plates of a string instrument, and is responsible for producing most of the sound that you hear.

Vibrations of the strings are transmitted to the sound board via a bridge.

Although the metal frame hold the strings does most of the work, some of the string tension is transmitted to the sound board via the bridge. This force totals ~300 lbs.

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The Human VoiceYour voice is primarily for communicating, but is also a very versatile musical instrument. Some of the questions we will address next are:

What is the instrument’s energy source?

What are the resonators in the ‘voice instrument’?

What is the difference between vowels and consonants?

What is the difference between spoken and sung words?

Is the voice more like a string, brass, or woodwind instrument?

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The Voice InstrumentThe source of energy is the air in your lungs that you force out, under pressure, through your vocal tract. The main chambers of your vocal tract are your larynx, oral cavity, and nasal cavity.

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Vocal ChordsThe word ‘chords’ suggests a string instrument, but in fact the vocal chords are more like a trumpet player’s lips.

http://www.entusa.com/normal_larynx_cable.htm

For a movie of the vocal chords in action, see:

Your vocal chords are located just behind your Adam’s apple.

The chords are normally open (so you can breathe!) but can be closed under muscle control.

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There are 3 main ways that you use your vocal chords to control the sounds you produce:

•Leave the chords open (“sss”) or partially open (“huh”)

•Suddenly opening the chords produces an explosive cough-like sound (say “Idiot!” vehemently)

•Rapidly open and close the chords to produce repetitive pulses of air (compare “zzz” and“sss” with your finger on your Adam’s apple).The last technique is the most versatile,

and is similar to how a brass instrument is played.

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An important difference between a brass player’s lips and the vocal chords is the absence of strong feedback from the rest of the instrument.

This means the frequency at which your chords vibrate is under your direct (muscle) control, and not determined by the resonances of your vocal tract.

The normal range of chord-vibration frequencies used by women is 140-400 Hz, and 70-200 Hz for men. The upper end of these ranges is extended about an octave for singing.

What sound do the vocal chords produce on their own?

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The sound produced by the vocal chords alone depends on how much force you use to try and close them against the pressure of air from your lungs:

time

Air

flow

th

rou

gh

voca

l ch

ord

s Whisper,breathy

Normal

Strained

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The Vocal TractThe total length of the vocal tract is 17-18cm. It is closed at the vocal folds and open at the mouth (and nose).

A half-open air column of the same length has resonant frequencies at about 500, 1500, 2500 Hz.

The vocal tract has resonances at similar frequencies, but unlike an ideal pipe, these resonances are of low quality and so spread over a wide range of frequencies (mostly because the walls of the vocal tract are soft).

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FormantsThe broad resonances of the vocal tract are called formants. They are driven sympathetically by the vibrations of the vocal chords. The result is that the vocal tract shapes the timbre produced by the vocal chords:

frequencyTimbre of normalchord vibrations

frequency

Formantresonancesof vocal tract

frequency

Resultingtimbre

Chords vibrate atthis frequency

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The Vocal Tract In Motion

“It’s 10 below outside.”

“Le boulangerbut onze bières.”

“Why did Ken set the soggynet on top of his deck?”

http://psyc.queensu.ca/faculty/munhall/x-ray/

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What does all this motion of the vocal tract do to the sound you produce?

You control the central frequencies of each formant by making adjustments to the shape of your vocal tract. The changes are mostly to the cross-sectional area and not to the length.

The main articulators that can vary the shape of the vocal tract are the:

•Lips,•Tongue,•Soft palate (gateway between oral and nasal cavities),

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Speech ArticulationAn articulator can partially (fricative) or completely (stop) block the passage of air through the vocal tract.

A partial blockage (fricative) causes a noisy hissing sound.

Observe how changing the shape of your vocal tract (articulation) determines the sound that you produce:http://www.chass.utoronto.ca/~danhall/phonetics/sammy.html

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The building blocks of speech are called phonemes.

A simple classification of phonemes groups them into vowels and consonants.

For acoustical study, a more useful classification is:•Plosives,•Fricatives,•Other consonants,•Pure vowels,•Dipthongs.

consonants

vowels

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Plosives and FricativesPlosive sounds (think explosive) result from a sudden release of air. Where the air is release determines the resulting consonant sound.

p,bt,d

k,g

Fricative sounds (think frying) result from turbulent airflow through a narrow constriction. The location of theconstriction determines the resulting consonant sound.

f,vth,th

s,zsh,zh

h

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Voiced SoundsPlosives are transients (try sustaining a single ‘p’ sound) but fricatives can be sustained. Both have the characteristic timbre of noise: a range of frequencies are produced with none standing out in particular.

Plosives and fricatives come in unvoiced and voiced forms (the first and second of each pair of examples). Unvoiced sounds are produced with the vocal chords open. The chords vibrate during voiced sounds. (Compare ‘sss’ and ‘zzz’).

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Other ConsonantsThe “other consonants” include the:

•Glides (or semivowels): w, y (look at the frequency analyzer to see why they are called glides),

•Liquids: l,r•Nasals: m,n,ng (voiced throughthe nose only)

mn

ng

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VowelsVowels are sustained, voiced sounds with a definite pitch.Their timbre is determined by the formants:

frequency

You produce different vowel sounds by adjusting the shape of your vocal tract to change the frequencies of these formants.

The pitch of a vowel is determined by how fast you vibrateyour vocal chords, while the timbre is determined by theformant frequencies.

This is the reason why the same vowel can be spoken orsung at different pitches.

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Vowels and FormantsHere are some examples of the vocal tract shape and corresponding timbre for some vowels:

http://hyperphysics.phy-astr.gsu.edu/hbase/music/vowel.html

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Vowel IdentificationLook at the spectrum of different vowels with the analyzer. Can you identify the formants? How do they change for different vowels?

To a good approximation,we can characterize eachvowel by the frequenciesof the lowest two (F1,F2)formants.

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There is a universal set of vowel sounds that can be produced (we all have the same vocal tract), although not all languages use all possible vowels.

Compare American and British english vowels:

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DipthongsFinally, the last category of sounds are dipthongs.

Dipthongs are sounds that morph from one vowel sound to another vowel sound, due to the motion of the tongue.

Some examples are:•“might” (ah-ee)•“mate” (eh-ee)•“moat” (aw-oo)•“mount” (a-ou)•“oil” (aw-ee)

Look at some dipthongs on the spectrum analyzer.

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The Singing VoiceThe main challenge for producing musical sound with the voice is that the formant frequencies are not harmonically related to the vibration frequency of the vocal chords.

When singing, you make several adaptations to adjust the frequencies of your formants to be more harmonic:

•Larynx is lowered,•Jaw is opened wider,•Tip of tongue and/or lips are pushed forward.

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Singer’s FormantThe lowering of the larynx helps to produce a new “singer’s formant” at high frequency (2500-3000 Hz), near the resonant frequency of the ear canal.

The origin of this formant is a narrowing of the larynx between the vocal chords and the epiglottis.

Watch this demo to see how the narrowing of this cavity alters the formants and the resulting sound:

Compare the frequency spectrum for spoken and sung vowels.

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ProjectionSinging instructors often use the metaphor of “projecting” your sound, as if you could beam it in a particular direction.

In fact, the sound you produce is too low in frequency to be directional, and nothing you can do alters how it spreads into a room.

Still, an opera singer can be heard clearly over an orchestra. This is largely because the singer’s formant is at a frequency where the orchestra is relatively quiet.

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Chest ResonanceAnother metaphor for playing wind instruments and singing is “chest resonance”.

This suggests that your lungs can act as resonators and therefore influence the timbre of a sound.

In fact, the vocal chords are an effective barrier between the vocal tract and the lungs, and the lining of the lungs is far too soft to support any resonant build up of acoustic energy.

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SummaryThis brings us to the end of our study of musical instruments.

We covered:•Strings•Woodwinds•Brasses•Percussion•Keyboard•Voice

The final unit of this course will cover some topics at the interface between physics, music, and technology.