Speech Science VI

Resonances

WS 2007-8

Resonances

Reading:

Borden, Harris & Raphael, p. 95-112

Kent p. 329-343

Pompino-Marschall p. 102-116

Reetz p. 33-39

Recapitulation … and something new

• The glottal waveform is a harmonically rich signal with energy in the whole frequency range important for speech.

• So, the glottal waveform supplies the acoustic energy needed for all the different (voiced) speech sounds.

We call it the “source“ for the speech signal

• To form different sounds, the energy has to be modified into different patterns;The basic shape of theglottal excitation is(more or less) constant.

Source-Filter Model

• The “source“ is filtered (modified) to produce different speech sounds:

The resonatorproperties changeaccording to theshape of the vocaltract.

The glottal signalpasses through ahollow space (the vocal tract) withspecific resonatorproperties

Understanding resonance

• The easiest way to understand resonances is to consider the vocal tract for the vowel :

The vowel is produced with a neutral tongue shape (no extreme constrictions)

Calculating resonances ofa „uniform tube with oneend closed and the otheropen“ shows that they are very similar to those found for

The principles of resonance 1

Resonance means favouring certain frequencies: WHY are some selected and others not?

The pressure changes of some wavelengths (1, 3, 5 etc.) fit bettertogether than others(2, 4, 6 etc.)

The principles of resonance 2

Wavelengths with minimum pressurevariation at the open end of the tube (lips)have some energy reflected and therefore die out less quickly.

Minimum pressure change exists at the point of maximum deviation; i.e. for1/4, 3/4, 5/4 , 7/4 etc of a cycle.

Calculating resonances

The speed of sound is, say 340 metres per second …

The length of our standard vocal tract (larynx to lips) is 17 cm.

So, the frequency ofthe resonances are:R1 = 0.25 x 340 0.17 = 500 Hz

R2 = 0.75 x 340 0.17 = 1500 Hz

R3 = 1.25 x 340 0.17 = 2500 Hz

Complexity of the vocal tract resonator

Variation in the vertical cross-section

Variation in the horizontal cross-section

For calculation purposesthe continually changingcross-sectional area isdiscretized

Resonances are NOT harmonics

The vocal tract is heavily damped ….. …. which means the filters are broad

So several harmonicsfall into the area ofresonance.

This is fortunate,because F0 (and allthe harmonics) changeas the sentence tunechanges.

Independence of filter from source

Since resonances are a product of the vocal-tract shape, while the (periodic) excitation arises at the glottis, the two are independent of each other:

Cf. same excitation,different resonance

Independence of filter from source 2

The relationship between source and filter is reversed in this case:

We have a different excitation but the same resonance

Independence of filter from source 3

It is not necessary for the source to be periodic (which is important when you whisper)!

Here we have noise excitation (continuous spectrum), the same resonance ….. but different damping.

Voice pitch vs. vowel quality

Here we have three different glottal frequencies all supporting the same shape spectrum (in this case the vowel [i]

Vowel demo

Cavities and vowel quality

Vocal tract shape for the vowels in the words: (1) heed, (2) hid, (3) head, (4) had, (5) father, (6) good, (7) food. (from A Course in Phonetics, 1975, by Peter Ladefoged)

Cavities and vowel quality 2

Here the first and second formant frequency values (F1 & F2) are shown in relation to the pharynx cavity and the front oral cavity size, as well as to tongue height and position.

German vowels

Formant values for German vowels

1 2 3 4 Panels 1, 2 and 4 have the same F1 values: higher values for more open vowels. Panel 3 shows very high F1 for /a/ and /a:/.F2 reflects size of front cavity:Back and lip-rounded vowels have lower F2

How to remember formant values

freq.

F2

F1