An Experimental Study of the Wave-Composition of Nasal Voice Quality

Citation preview

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Acoustic spectra of non-nasal and nasal vowels til, iaj, and lo], phonatea b£ subject Relative intensity is plotted against frequency over a 40 decibelrange» the reference intensity tiein'g~gcT"dec it)els below" the total Intensity of tKe moat intense**wave plotted on each, 'graph*

56

energy, but It Is also absent In the posterior packed con­ dition when the spectra show the high frequencies to be greatly attenuated#

It would appear, therefore, that

neither the presence nor th© absence of high frequency energy can be considered necessary to perceptual nasality, except, perhaps, in the minor differentiation between closed and open nasality* Figure X gives the results for subject D*M*

With

respect to th© characteristic energy regions for the vowels it will be noted that the first region is very typical In location for all vowels and conditions, but that the loca­ tions of th© second regions for these vowels are not quite so typical*

For the non-nasal phonations of both [I] and

tss] the latter are found displaced downward from their typical frequencies, a condition which is understandable in [as] because of the singers* tendency to produce [a]. Ho explanation Is offered for this occurrence on [1]* On f th© non-nasal [o ] phonatlon the second contour is somewhat higher in peak frequency than the typical location of this region# Other consistent differences appear between these i spectra and those for subject H* 8* The most important Is the very great reduction in high frequency energy in the spectra for all vowels except [as]*

For [I] there Is no

high frequency energy of consequence above 3400 c*p*s* An interpretation of this difference may be ventured in

57

terms of the findings of Laaae

28*

0£ # olt*

29*

Qgm pit*

and Stout

09

.

These Inves-

tigators found that the amount of energy in the high par* tlals tended to decrease as pitch was raised*

Assuming

that it is the relative pitch level which is important in this relationship# the fact that the pitch used in this study is higher in the rang© of D*M*, a baritone, than in that of I!*S*, a tenor, may explain the differences in the relative magnitudes of the high frequency energy.

Whatever

the explanation, spectra for these two voices from previous research revealed the same difference* Comparison® of the nasal and the non-nasal phona— tions for each vowel are, in the main# corroborative of the differences already observed on the spectra for K*S*

The

main difference is that there is some indication of a low frequency contour with a peak frequency of approximately 300 c*p*s* on the non-nasal phonations of [&] and [o]»

In

both cases# however, t is becomes relatively more intense and well-defined on the nasal phonations as a result both of relative energy Increase in th© second and third partials and of decrease In the fourth.

As on the spectra for U.S.,

the lower characteristic vowel region for [se] Is attenuated on the nasal as compared to the non-nasal phonatlon, and

gives th© appearance of having a wider frequency band width. The changes In th© characteristic vowel region for [o] are also similar, on© principal contour®® being found on the

50*

The appearance of this region Is slightly ambiguous due to the relative prominence of the fifth partial. This may or may not be due to experimental error. In any case the data seem to suggest one contour more than two.

nasal phonatlon, with a peak frequency between 75Q and 800 e*p*s., whereas two are clearly defined by the data in the non—nasal [o ] spectrum*

The shifting upward in the second

region of £1] and [sb] Is also consistent with previous findings* An Interpretation of these differences between the non-nasal and nasal vowel lias been offered and will not be repeated here*

The data for this subject seem to fit the

interpretation as well as those from the first subject, with the possible exception of th© slightly ambiguous appearance of the nasal [o ] already noted* Th© only comparison in Figure X which shows the reduction in high frequency energy found In th© spectra for H.S* is with respect to the nasal and non-nasal [o], the nasal phonatlon containing no Important energy above 2900 c.p.s*# whereas in the non-nasal example some is shown as high as 3500 c#p.s.

Such a difference Is not observed, how­

ever, in comparing th© two [I] phonations, or the two pho­ nations of [te].

It will be recalled that this difference

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NASAL 131 SUBJECT G.D

NASAL PI SUBJECT V.S

Figure XX*

Acoustic spectra of the vowels [1 j» [a*] .» and U i , pinnated by three patlioYo^leally nasal voicesT- Relative intensity is plotted' against frequency over a 40 decibel range» the refer** enc'c In tenaity be . ,n t 20 decibels beTow the to tal intensity of the moat in tense wave plot** ted on eacii Vrapli*

m t m m >m mtfaM M M M ftM v

^ W N n ^ n m h m im M m m m iv w ^ w

rp»»w i

< N w *w

■>wi

uy t w n —

*w »a 4> m m *m h m h m *

GO

was also more apparent on Jo] for H*S* than It was on the other two vowels* As a whole, the findings on this baritone subject are in substantial agreement with those on the tenor, H»S»* especially In regard to the low frequency changes which seem to be the most evident feature of nasalisation*

Where

high frequency differences are observable, they are In the same direction* ^haal Vowel fhonatlons of Pathologic al Subjects*

Figure XI gives the data for the three patholog­

ical subjects*

Tlo detailed treatment of the phonemic aspects

of these spectra need be given*

Except for £1], the spectra

for the cleft palate subject, W*s*, are so chaotic in the regions important to vowel quality that It would be diffi­ cult to identify definite phonemic characteristics*

This is

u

not surprising In view of the narked severity of his path­ ological condition*

Th© spectra for both P*M* and 3*D*

indicate energy at the typical frequency location for the first region for [ee]*

Both also show energy In the fre­

quencies for th© second region of that vowel, but the spec­ trum for P*i!* shows no indication of a definite contour* The [q ] spectra, for both j?*H* and >*D*, show energy near the typical location for this vowel, the region for F*M* being somewhat low In comparison to typical values for the normal vowel* The two most important features of all of these spectra in Figure XI are the very marked prominence of one

bl

or more low frequency partlals* and the relative lack of high frequency energy ae compared to normal vowel spectra* In the spectra for W*S* the first partial is always the most intense partial of the wave*

In the spectra for

subjects P*M* and 3* D* the second and third partlals may also be strong*

The spectra for these subjects do not show

such definite indication of contours of low frequency re­ inforcement, although there is some indication of it in the spectra of [«>] and [o] for subject 3*D*

It is significant*

however* that each vowel of each subject shows energy in one or more of the first three partials* Moat of the spectra for these subjects which do show any amount of high frequency energy show It to be scattered* the values being sporadic and variable*

In only

three spectra* the [1] of subject F*M*# the [as] of W*S** and the [&] of S*D** la there any very definite Indication of contours of energy In the high frequencies*

In general*

CiJ tends to have the greatest amount of high frequency energy* [»] the next most* and to] least*

All values in

these frequencies* however* are markedly reduced as compared to the normal vowel spectrum* The data for these pathological subjects are* therefore* compatible with the findings from the rest of the study*

One prominent feature of their spectra Is

Increase in energy in the frequencies from 200 to 300 c*p*s** a condition which has been found to be consistently asso­ ciated with nasal voice quality.

A second characteristic is

marked reduction of the high, frequencies, giving fxirther support to the Interpretation that energy in the high frequencies is not necessary to perception of nasal quality, hut may he reduced by its failure to be normally transmit­ ted when the nasal cavities are male an Important part of the vocal resonating system*

III,

SUMMARY

Non-nasal and nasal comparisons were mad© be­ tween certain phonations, produced under conditions which varied nasality with respect to Its presence or absence, its character, and its relationship to phonetic structure* The procedure was to photograph oscillograms of the pho­ nations and to determine th© wav©-composition of certain selected waves by harmonic analysis* Three sustained vowel-nasal-vowel alternations, each consisting of a vowel alternated with a nasal conson­ ant, without Interruption of phonatlon, were produced by on© subject, the sam© vowel being used successively with each of th© three nasal consonants*

A wave-to-wav© analysis

of th© transltldhs revealed the following results; 1*

the vowel-to-nasal transition, th©

relative energy In a band of low frequencies centering around 250-270 c«p*s* was markedly increased*

At th© same

time, in a band of variable extent, just higher in fre­ quency, th© energy was considerably reduced*

2.,

A high, frequency band of considerable extent,

centering around 3200-3400 c.p.s*, showed progressive re­ duction of relative energy during the vowel-to-nasal transition* 3*

Changes in energy distributions, Indicative

of probable variations in vowel quality, were found in the frequencies from 600-1200 e.p.s. during the vowel-to-nasal transition* 4*

Acoustical changes occurring during the

nasal-to-vowel transitions were substantially the reverse of those for the vowel-to-nasal transitions,

f ~i

'The same subject produced sustained phonations of three vowels, both nasally and non-nasally without obstruc­ tion of the nasal passages, both nasally and non-nasally with the anterior nares occluded, and non-nasally with the naso-pharynx occluded.

Analysis of selected waves dis­

closed that: 1,

Occlusion of the anterior nares produced no

important effect upon the non-nasal vowel. 2*

Nasalization of the vowels v/as accompanied

in each case by the reinforcement of certain low frequencies, typically centering around 200 to 260 c.p.s., which were for the most part unreinforced on the non-nasal vowels. 3#

In both f®] and [o] nasalization of the vo%vels

was accompanied by a marked modification in the location or relative energy of the lower of the two regions generally regarded as important in determining vowel characteristics.

Ofk

4*

Th® only observable differ once between the

open nasal and anterior occluded nasal vowels was a slight increase in attenuation of high frequency energy on the latter* 5*

The occlusion of th© naso-pharynx had no

important effect on the frequencies below

2200

c*p*s*, but

produced marked attenuation in frequencies above that* 6*

The acoustical characteristics of vowel

quality, as found in the spectra of the non-nasal open vowels, substantiated previous research*

,

As a check on part of the results, a second subject sustained both nasal and non-nasal phonations of the vowels, under conditions of no cavity occlusion*

Analysis

of selected waves divulged the following results? 1*

Nasalization was accompanied by essentially

the same low frequency reinforcement as was found in the nasal consonants and the nasalized vowels of the first subject* 2*

Probably because of the generally less prom­

inent high frequency energy In all spectra for this sub­ ject, th© changes from non-nasal to nasal vowels in this region were less marked*

However, in the one vowel in

which a clear modification of this region was evident, it was in th© direction of attenuation of the relative energy in these frequencies*.

bt>

The results were checked further by securing phon&tiona of the same towels from three pathologically nasal voices*

Analysis of selected waves showed that: 1*

The outstanding characteristic of the spectra

of these subjects was great relative energy In the low frequencies* 2*

The high frequencies were markedly atten­

uated* Considering both the data obtained from this study and the present knowledge concerning the anatomical and physiological characteristics of the structures involved, certain tentative Interpretations are offered which sug­ gest relationships between these results and the probable resonance and transmission properties of the vocal mechanism*

APPKHDXX A Table X •

Relative Energy of the Partlals In Decibels Plus p F U m ? "thePlottlnF Base for the Sequence o f n Waves In JHe Frans'ltioFTtmTIT*--------------132,9

Par­ tial 1 2

3 4 5 6

7 8

9 10 11 12

13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

Fundamental Frequency 130.4 131.5 130.3 Wave Humber 37

28

36

3*9 5*9 1*4 5.7

6.5 9.1

7.9 9*9

6.1

6.0

7.9 13.8 13.8 10.4

9.1 13.9 14.0 8.5 -5.9 -7.9 -6.1 -8.3 -15.1

11.1

14.6 10.7 1.5 -9.0 -9.8 -13.5 -14.3

-10.1 —9.0 -8 .2

—9 .2 -12.0 -17.1

38

-12.5 -14.8 -11.3 —5 .6 -0.4 5.3 10.6

11.4 3.5 -4.4 -7.2 -9.8 —9.5 -7.9 -10.4

-16.3 -18.0 -17.1 -18.8 -18.2 -8.3 -6.1 -2.2 8.1 8.8

2.9 -3.2 -8.6 -13.1 -15 .9 -8.0 -11.0 -8.1

-18.2 -14.3 -6.7 -8.8 -2.7 7.2 8.2 —1.6 -8.1

-12.7 -15.1 -11.0 —6.9 -15.5 -11.7

39

9.5

10.3

10.8 6 .4 10.1

11*8

14 .4 13.6 6.9 -13.6 -13.1 -5.3 -9.0 -16.0

7.6 11.5 14.9 11.2

2.9 -13.6 -18.2 -7.8 -9.3 -20.0 -18.5 -18.2

-17.2 -20.0 —16 .9 -15.9 -15.9

131.8

-19.7 -18.5 -16.9 -20.0 -14.8 -8.3 -9.0 -3.8 6.1

5.9 -12.4 -20.0 -12.1 -12.4 - 12.1 -16.7 -15.2

-14.3 -14.9 -14.9 -11.7 -9.0 -2.0 5.4 4.7 —9 .1 -11.5 -14.7 -12.4 -7.0 -13.7 -15.9 -20.0 -19.2

* Omission of numbers indicate the absence of plottabl© energy values#

or

Table I.

(Cont.) 132,8

Par­ tial

Fundamental Frequency 133.4 133.8 134.3 Wave Pumber 42

40

41

1 2

11 #2

10.5 14.5

11.5 15.2

3 4 5

10.6

12.6

13.8 11.9 9.1 -2.5 -16.7 -18.0 -6.7 -15.5 - 12.6

13.9 7.3

10 .1 10.2 - 1.0 —0.8

6

7 8

9 10 11

12 13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

13*2

6.8

-10.1 —18 *0 —10 *9 -3.9 -12.4 -16.0 -18 .0

—11.9 -11.0 —B.l -5.4 -12.8 -17.2 -15.9 -20.0

-17.4 -13.4 -11.7 —20 .0

-19.2 —14.8 -18.0 —16 .0 -2.7 4.4 3.7 -6.7 -13.1 -11.8 - 11.0 -9.5 -13.7 -15.7 -16.7 -17.4

-10.1 -15.5 -19.7 -15.9 -7.1 -19.7 -3.1 4.5 3.3 -10.7 -14.7 -8.0 -14.1 -7.7 -13.6 -15.5

-18.0 —11.0 —18 .0 -19.7 —16 .9 -9,6 -9.7 —3 .2

43 13.2 18.0 8.3 2.9 -11.7 -6.0 -14.7 -8.8 -4.1 -2.7 - 11.0 -12.9 -11.3 -13.3 -14.8 -12.5 -5.3 -19.2 —13 .1 -17.4 —5 .9 -17,2 -5.6

2.0

1*6

1.4 -8.5

—0 *3 —8 *4 -11.1 -4 .6 -13.3 -7.5 -15.9 -6.2 -18.5 —14 .3

-10.0 -16.5 -12.1 -13.5 -14.8 -15.1 -15.7

134.0 44 12.0

18.9 4.8 -5 .5 -18 .2 -Q.5 -18.2 -10.9 -9.2 -5,8 -19.2 -17.8 -13.6 -16.9 -7.3 -16.9 -18.8 -3.9 -7.0 -10.9 -15.7 -5.4 -5.5 -10.5 -14.3 -12.6 -15 .2 -11.8 -19.2 -10.5 -15.2

Tat

(Cont#) 132*6

Fa 3 tii l 2 3 4 5 6

7

a 9 10

11 12

13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Fundamental Frequency 129.3 132 .2 134.5 Wave Humber 85

62

64

12.1

9.0 19.4 3.1 -6.5 -18.8 —4 .5 -6.9

18*7 6*9 •*3*8 -15.7 —3 *9 -9.1 -13.6 —6 *1 0.0

-13.3

-9.2 -8*2 -18.5

—9.6 -13.6 -17.8 -15 .1

—12 *2 -12.2 - 11.2

-11.5 -12.4 -18.0 -11.7 -5.1 -4.5 -11.3 -14.3 -2.8 -7.8 -14.4 -13.7 -11.4 -13.2 -14.3 —15 *2

—2 .8

-11.3 —5 *8 -20*0 -14.7 -9.0 -7.3 -18.8 —13.5 -14.3 —4 .0 -9.7 -17.8 —18 .0 - 11.8 —13.1 -15.4 -15.9

10.1

17.8 13.7 0.0

-5.2 -0.7 -7.9 -7.5 -9.6 -0 .8 —8 .4

-12.7 —12 *0

86

87

8.3 2 .9

7.6 9.5

14.3 14.4 11.2

10 .8 14 *6 10.8

9.1 -7.9 -13.6 —4 .0 -10.0 -15.1 -18.8

10*7 -11.9 -9.5 -2*4 -7.1 —9 .5 -16.9

■

—20 *0

- 11.1 -12.8

—11.4

—18.2

-18.5 -8.5 -4*5 -5.6

—6 .1

-13.6 —14*8 -7.9 - 1.6 -16*7 -9*9 -14.0 -13.4 - 10.1 -13.3 -16.0 -13.7

8 .8

2.8

-13.2 -14.8 -7.3 -12.6 -13.0 -14*8

132.9

-16.0 -10.8 -2.7 6.0

8.4 -9.3 -7.7 —12 .8 -11.0 —8.6

-10.9 -11.1 -19.7

2.6

5.4 7.3 -5.3 —6 .1

-17.2 -7*7 -12*2 -13.6 -14.2

017

Tat

{Cont*) 134.6

Fm tu I

2 3 4 5 6

7 9

89

8*4 10.0 1.0 11*2 13.9 11.7 10.9

4*6 7.2 0.8 9.5 12.6 13.1 12 .3 -6.2 -7.4 -4.1 -12.4 —16 .0

11 12 13 14 15 16 17 18 19

20 21

22 23 24 25 26 27 28 29 30 31 32 33 34 35

**8.4 -5.3 -8.0 -10.8 -16.5 -18.0 -15.5 -13.0 -7.8 -12.8 —5.4 -5.7 -3.8 5*8 6.0 6.5 1.6 —3 .5 —10 .0 -10.8 -7.8 -13.9 -14.1 -20.0

134.4

Wave Number 90

88

8 10

134.2

-19.7 —16.9 -13.2 -10.0 -14.1 —3 .2 0.4 -1.6 7.0 8.3 9.0 1.1 0.5 -7.6 -10.9 -11*4 —0 .4 -16.9 -14.1

4.2 6.9 2.3 8.5 12.6 13.1 12.7 -3.8 -7.5 -7.6 -11.3 —12 .6 -20.0 -17.8 -20 .0 —9 .5 -15.4 —18 .8 —14 *1 -5.4 0.3 —2 .1 7.2 8.5 9.2 1.6 0.7 -16.0 -7*6 -10.2 —9.4 -6.2 -14.3 -15.4

134.4

132.8

91

101

5.1 7.5 2.1 8.5 13.7 15.1 12.1 -4.0 -7.7 —6.9 -11.6 -13.9

6.7 7.6 2.0 8.7 14.0 13.2 11.6 0.4 -4.5 -7.6 -9.7 -13.3

-14.8 -17.4 -18.5 -11.3

-16.3 -19.2 -18.2 -18.8 -18.0

-14.3 -9.7 -4.2 -0.3 -1.4 7.0 8.7 9.7 0.5 0.7 —10.6 -11.3 —11.9 -9.0 -7.1 -14.1 -15 .5

-9.5 -5.0 -2.8 -4.0 3.7 8.9 6.7 0.4 -4.1 -9.1 -8.2 -9.7 -8.3 —18 .2 -17.8

YU

Table IX*

Relative Energy of the Paytlale In Decibels Pitas or Minus the Plotting Base fop the S equ eric© of™ Waves in the transition rond 1♦ 127 *0

Par­ tial 1 2

3 4 5 6

7 8

9 10 11 12

13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

Fundamental Frequency 126*5 127#3 *128*4 Wave dumber 32

27

31

5.3 5*0 3*1 12*3 12.7 11*9 14*3 3.3 -5.2 -•9*0 —6*4 -7*4 -12*1 -15*9

6*1

6.0

6 *0

7.1 4,0 13.4 13.8 9.1 12 *5 8 ,4 -7.4 -11.6 -8*9 -10,0

7.1 3*9 14.5 13.4 7.7 13,1 7.2 -12*7 -13*7 -11.7 -12.8

7.8 1.9 13.8 12.5 7.7 14.2 6*5 —14*1 -10.6 -10.5 -9.7 -18,5 -17.4

—16.5 -19.7

—20 *0

-17*4 -16.3 -15.4 -19.2 —10*0 -3*6 2*0 2*6

5*1 2*5 -9.7 -8*6 -7.4 -6.7 —9*9 -14*8

—18*8

—16,3

-15 .4 —11.9 -3,7 —4*4 -2.1

-14.8 -10.4 —4.6 -9.4 —3 .0 -1*6 3.3 2.7 —4 *5 -12.7 -17*4 -14.1 -12.2 -12.4 -16 *5 -19.2

0.0

3.7 4*1 -0*7 -8*5 -13.3 —9*4 -10*4 -14*1 -20*0 -15.2

33

-17*2 -17,8 -11.7 -7.3 -5*5 -8.3 -2.4 1.1

5,8 5.2 -8*2 —20 .0

-14.1 —14 *4 -13.2 -18.8

129*2 34 8,4 9.1 2.5 13*5 11,5 6,*2 13.4 7.3 1.5 —4.6 -10.8 —9 .0 -15*4 -13.6 —13*1 -18.0 -16.0 -13.3 -6*5 -4.3 -6*7 -1.3 2*7 7.5 5*4 -11.3 -19.7 -9.7 -16*0 -18.2 —16 *5 -19.7

YI

Table II*

{Oont*) 129*3

Par­ tial 1

a

5 4 $ 6

7 8

9 10 11 12

13 14 15 IS 17 18 19 20 21 22

25 24 25 26 27 28

29 SO 31 32 33 34 35

Fundamental Frequency 127*9 128.2 131.8 Wave Wumber 37

35

36

7*8 8.5 0.3 12.4 15 .6 4*0 9.6 4.8 6 .5 -1.3 -7.7 -11.5 -12 .4 -13.2 -10.9 -14*7 -20*0

10.1

11.5 2.2

14.1 11.7 5.1 8.5 3.7 10.7 -5*3 -9*7 -13*9 -9*9 -8.6 -12*7 -18*0

14.0 16.5 5.1 8.5 4.5 0.9 7*1 0.8 8.0

-5.9 —4 *4 —11.4 -7*5 -10*3 —10*3 -17*1 -18*8

38

45

12.3 18*6 4*2 -5*1 -1.6 -13*4

11*8

0*6 0.0

4*1 -10.4 -8*6 -15*2 -15*2 -7 *0 -20.0 -11*7 —12 *1

—16 *5 -6.7 -6 .1 —6 .0

—1.3 4.5 7.4 4.0

-a.o

-15*7 -17.2 —18 *0 -19.7

-16*3 —9*6 —6 *9 —14 *0 0.3 2*8

4.8 2.0

-3.3 - 12.6 —16*3 -17.4 -17.2 —12 .9 -14.1

127.3

-15*2 -1*2

-9*5 —5*4

—6 .8

—11 *8

-12*9 -6.2 -4.7 -2 *9 -5*1 -13.5

-17*4 -13.7 —13*2 -8*3 -10*0 -16*0

-18*2 -20.0

-18.2 -15*2 -20*0

18*8 6 *9 2.8

—11 *9 -13*6 -3*2 -6*1 -13*4 -9*9 -17*1 -12.1 -9*1 -11*5 —15 *1 -7*6 -3*7 —12 *4 -15*7 -12.8 —11 *5 -8.9 —11 *8

-12.1 -15*5 —18.8

-17*4

-19.7 -15*9

*abl#II.

(Cont«) 127.1

Par­ tial 1 2

3 4 5 6

7 8

9 ID IX

20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

Wav© dumber 69

67

68

10.7 19.1

10.6

11.0

17.9

6.0

10.8

—1.1 -18 .5 -16.9 -18.5 -17 .2 -4.9 -3.0 -12.8

7.1 -9.1 -20.0 —6.9 -2.2

11.3 7.9 13.9

6.2

3.2 —8 .6

—18 .5 -17.8 -19.2

12

13 14 15 16 17 18 19

Fundamental Frequency 128*9 125.6 124.8

-15.7 -19.2 -11*9 -11.1 -14.0 —4 .3 -4.0 -15.1 -15.9 —14 .0 -14.0 -12.8 -12.1 -14.2

—12 .2

10.6

- 0.6 1.6 1.8 10.2 8.1

1.4 -2.2 -8.7 -11.0 —20 .0

-12.8 -9.2 -10.7 -4.7 -0.9 -6*2 -17.8 -14.8 -16.9 -12.8 -12.1 -16.3 —8.2 -12.8

-19.7 -18.2

-19.7 -14.8 -11.8 -15 .4 -10.2 0.2 1.8

2.9 -2.2 0.3 1*4 -1.2 -7.8 -10.0 —19*2

124.0

70

71

7.0 9.6 4.0 12.3 13.5 6.7 2.9 5.3

7.2 9.2 0.3 10.3 14.4

10.2

-4.6 — 1*0 —6.6 -10.9 -9.1 -11.3 -13.6 -19.7 -20.0 -14.7 *■1.3 -6.4 -2.2 2.4 5.2 9.4 6.7 1.8

-14.1 -8.4 -14.8 -14.3 —16 *5 -18.5 -13.3

8 .8 2.6

7.9 9.3 -9.0 -4.5 —9.6 —11.1 -10.7 -14*9 -11.5 -16.5 -18.2 -13*6 -5.6 -7.3 -4.9 -3.2 4.5 7.4 9.9 3.3 -2.5 -17.1 -18.8 -17.2 -14.2 -17 .2

(Cont.) 123.6 72 1 2

5.3 7.7

3 4 5 6 7

1.2 11.2

a

9 10 n 12 13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

14.1 9.2 4.1 S *5 6.1

-3.7 -5.8 —10 .5 -13.4 -12.8 -15.5 -12.8 -10.0 -14.0 -15.2 -13.9 -5.8 -2.6 -2.7 -3.1 3.6 7.7 9.2 0.4 -0.8 —D .6 -14.2 -13.6 -14.1 -12.4 -14.8

Fundamental Frequent 123.3 123.3

127 #5

Wav© Numb 01? 73 74 4.7 6.9 2.9 11.7 15.0 9.7 7.7 9.9 -2.6 -8.6 —10 .4 -11.4 -13.9 -14.1 -18.2 -18.5 -15.5 -13.9 -20.0 -19.7 -15.9 -6.8 -1.4 -2.6 1.8

3.0 8.9 -0.6 -0.1 -11.6 -13.7 —13 .1 -12.3 -10.8 -14.8

3 .8 6.5 1.9 11.5 14 .9 9.7 9.2 9.9 -6.1 —8.6 -9.1 - 11.8 -14.2 -14.1 -17.8 -14.7 -18.5 -14.2 -15.2

82 3.4 5.1 1.6 12.4 14.7 8 .6

14.3 4.6 -3.3 -10.3 -9.4 -11.4 -17.8 -16.5 -

-17.4 -10.3 0.9 -2.7 4.1 7.3 8.3 -2.6 0.9 -8.9 -14.0 -17.2 -15.1 -19.7

10.0

-17.4 —4.2 -4.0 -3.2 2.2 1.2 -14.0 2.1 -7.7 -16.7 - 11.6 - 12.6 -12.3 -16 .5 -15.1

f *±

Table XII

Relative Energy of the Fartlals in Decibels Pins o#11Winn's the rlotting Base for the EemJence of mmmmgmrnmmmm' mm waves in the Transition Lono] . w p » *

136*8 Par­ tial

25

3 4 5

4* 9 6*3 -0*4 7.2 7.7

6

12.6

1 2

7

14.6

8

0.8

9

-10.7 -8.8 -8.8 -11.3

10 11 12

13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

-13.7

m

6.0

m

m

m

M

m

7.3 7.8 5.4

7.0 8.3

6.6

6.4 9.9 14.4 8.5 8.9 -5.2 -4.7 —14 .8 -7.7 -12*5

9.9 13.5 10.7 7.2 -6.9 -7.3 -12.4 -8.7 —18 .8 -15.9 -10.5 -7.6 -12.5 -19.7 -10.9 -8.8 3.7 2.7

8.9

8 .6

10.4 9.7 -3.4 -9.1 -15.9 —12 .4 -7.7

-10.9 -9.7 -8*4 -7.0 -9.1 -11.9 —14.1

m

Wave Kumber 28 29

11.2

0.5 -3.9

m

m

w m

»

«m w w w

nm

Fundamental Frequency 133.4 131.3 130.7

—8 .6

-7.8 -8.4 -15.5 -9.9 -5.7 5.3 -3.5

p m

-8 .1

-8.3 -13.4

8.2

-16.9 -14.1 -14.4 -16.0 -17.8 -18.8 -14.0 2.5 -2.7 3,0 8.7 10.3 0.9 -5.3 -12*0 —9 .1 -10.6 -11.7 —8 .0

-13.9 -19.7

i w m m Iv m m im m m m

130.7

30

31

5.9

8*4 9.1 9*9 6.4

8.0

9.3 5.3 10.1

11.0

14.5

13.8 8.5 8.4 -14.0 -9.7 -11.0 -10.0 - 11.2 -18.2 -18.5 -18.2 -10.9 - 12.0

8.0

9.3 - 10.0 -11.5 —12 .2

-7.9 -17.4 —15 .2 —13 *1 -14.2 -9.4 -10.4 -14.3 0.9 -2.1 4*4 8.5 9.4 3.0 -2.3 -16.7 —11.1 -7.1 -7.9 -10.5 -9.1 -17.1

-15.4 -0.3 -4.0 4.9 7,8 8.6

1**3 -8 ,5 —18 .0

-8.7 -7.7 -11.9 -8.9 —16 *5

m bm -

III*

(Cont.) 129*7

til

32

1

8.5 9*9 10.5 7.1 11*3 12.9 9.1 7*2 -10 .9 -8*4 -9*3 -5.8 -15.2 -19.7

2 3 4 5 6 7 8

9 10 11 IS 13 14 15 16 17 13 19 SO SI 22

23 24 25 26 27 28 29 30 31 32 33 34 35

-15.7 -8*1 —8 *6

-18*5 -20*0 -10*7 -1*5 -4.3 4*0 6*6

9.0 3.6 —4 *2 -15.4 - 10*8 -8.7 -10*7 -7.4 -13*4 -20.0

Fundamental Frequency 128.8 129.5 130.2 33

Wav© Kumber 34

9.7 11.0

11*3 6.3 10.8 11.8 8.1

35

36

9.7 11*9

10.8

12.7

10.7 13.1

12*1 6 *6 10*6 11.6

11.8

11*2

6.9 9.7 10*4 10.3 3.9 —8 .9 -G .6 -9.2 -7.3 -13.3 -17.4 -14.7 -18.0 -7.4 -8*7

6*4 9.0 8*9

8.9 -8*2

9.6 5*8 -7*7

-10*0 -11*3 -10.1 -16.5 -13*6 -19.7 -16.5 -11.3 -10.7

-9*1 —8.4 -14.0 -13*3 -19.2 —18.0 -10*7 -7.8

-17.4 -2.6 —4*1 2.0

4.5 9.4 5*6 -3.7 -11.6 -13.9 -10.7 -17*4 -17*8

131*0

—8 .2

-4.1 -10.9 1.4 5*3 8.1

3.1 —3*4 -13.0 -8.7 -16.3 -12.7 -10.3 -11.4

-19.7 -3.5 -12.5 1.4 6.4 7.9 2.4 -5*5 -14.1 -9.3 —15.9 -13.5 —16 *5

11.6

2*4 -10.4 -3*6 -7*1 -8*7 -7*7 -17.1 -15,4 -5.9 -11.0 -16.9 -14.1 —14 *1 -7.1 -6,5 2,0

9.3 6 .1

0*7 -3*8 -14.3 —5 *5 -12.7 -12.7 -10.7 —9,3 -13.4

76

Table III.

(Cont.) 131 *5

Par­ tial

Fundamental Frequency 132.2 134.5 135.7 Wave Number 39

37

38

1 2

12*4 13*6

12.7 14.7

3 4 5

10*8

10.8

6.3

5.6 7.4 6*7 11*3 —6 .4 -5.9 1*9 -7*6 -6 .9 —11* 4 -10*5 -16.7 -10*3 —6.1 -11.4 -9*0 —11 *5 -12.3 -15.9 -5.3

8*6

6

7.9

7

11.6 -1*6

8

9 10 11 12

13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

-6*7 -1.8 - 12*0 -11*1 —14*9 -12*4 -12.9 -14*9 -7*5 —10 .5 -13.2 -13*7 -9.5 -9 *1 1*8 8.6

4*8 -1*2 -7.5 -17*8 -6.4 -9*4 -15.1 —14 *1 -17.1

1*1

3.3 3*7 —6*4 -10*0 -10.0 -5.2 -13.3 -10*7 -18.0 -15.9 -16.7

13.3 15.2 10.9 5 .0 5.6 6.2 11.6

-5.6 -5,3 —7 .0 -6.2 —9*1 —9.4 -8.3 -16.9 -6.0 —6 .4 -9*5 -9.5 -13.0 —11.5 -7*5 1.4 0.8 1.6 -2.2

-12*3 -7.5 -11*9 -10.4 -9.5 —14 .1 -12*8 -16.9

40 13.8 15.7 10 .4 6.4 5.0 4.4 9.2 -17.2 -7.0 0.9 -12,4 -9.5 -9.1 -10*0 -17*8 -7.1 -7.0 —8*6 -7.8 -11.1 —8*5 -18.5 -8.7 2.0 2.1 1.6

-1.4 -16.7 -7*0 -8.8 -12.6 —10.9 -19.2 -20.0

137*2 41 14.4 16.4 10*4 4*8 2.3 1*3 5*2 —4*9 -0*1 -9.6 -11.0 -11*6 -12.1 -9.7 -3.6 -4.8 -14*1 -7.1 -4.6 -13*5 -15.4 -2*1 2.3 1.3 -1.7 -3.4 -11*8 -4.7 -9.0 -11.0 -18*8 -10.9 -16.9 -12.8

77

Table III*

(Cont.) 138,8

Par­ tial 1 2

3 4 5 6

7 8

9 10 11 12

13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35

136*8

135.5

Wave Humber 85

42

49

13*6 17*4 10*9 2*4 -5*0 —15*4 -7*9 -11*0 -0*2 0*3 -7*8 -10.4 -10.4 —14 *9 -5*9 -4*0 -1*4

12.4 17*6

12*9 17.2

11.1

11*6

3*4

-14*9 —9*4

3*9 —4*4 -10.9 5.5 —6 .3 -12.5

2.2

6.1

-5*6

—3*9 -4*5 -4*1 -3,3 -4*9 -1*7 -13*4 —4*8 -0*6 -6*6 -9*4 -14*2 -18*0

—11 *0

-4*1 -3.4 -1*9 -9*3 -7*2

-0*6 —S*4 1.8

-10*2 —13*1 -9*6 -7*4 -3.9 —1 *2

-8.5 -2*0 0.9 -8.5 -9*7 - 12*8

—8 *1

-15*4 -3.1 -5*7 -15*9 —6 *6

-14*2 -11*7 -18.2 -16*4

-6.2 0.0

-9*7 -4.1 —12*6 -12*8 -15.9 -10*4

-19.7 —3*1 —4 *8 -12.5 -16.9 -9*9 - 10*0 -13.7 —16*9 -14*2 -14*9

136.5

136*6

86

87

12.6

11*9 14.7

16.5 12.9 -5*1 2*3 -3.6 -0*3 -0.1 -12*3 6.2 -1.8

—3.8 -10.0 -5 *1 -3*6 3*5 —4*6 —4 *2 -2*2 —9 *6 -4.3 -7*8. —6*6 -7.0 —2 *4 -2.4 -5.6 —8.9 -8*0 -9*5 -12,1 —9*3 -15*5 -5.5 -17.8

11*2 1.1 6*2 2.0 6.6

6.3 -6.0 6.9 0*1

-2.5 -5*9 —3 *5 0*6

6*3 0.3 -5 *8 —2 *3 -8.7 —0 .4 2 *0

3 .5 4 *4 1,0

2.3 - 10.0 —1*2 -7*9 -9.2 -14.7 -8.7 -13.1

78

III.

(Cont.) 136 *2

t$i

88

1 2

10*1

5 4 5 6 7 B 9 10

11 IS 13 14 15 16 17 18 19 20 21 22

25 24 25 26 27 28 29 30 31 32 33 34 35

13 *5 10*9 5.5 8*6

7.0 10.0 8*2

-5*7 6*5 —2*0 -2*6 -3*8 -2.4 —1*9 5.5 -0.4 —5.1 -8.1 —7 *4 -12.3 3.1 4.5 4.0 0 .0

-1.8 -14.8 -7.3 —5.3 —5 *8 -11*4 -13.7 - 12.8 —16 *5

Fundamental Frequency 137.1 137.0 136.7 Wave Itaifeea* 89 90 9*5 12*5 8.1

5.9 9.5 9.9 11.9 9*3 -7.9 4.0 —4*0 —4 *5 -4.7 —6 .1

-2.9 5.1 0.2

-8.3 —8 .5 -14.4 -3*7 —15 *2 -0.8 6.2

4*8 -0.1 —1 *6 - 12.1

-4.5 -8.7 -7.6 —8 .0

-9.6 -15.5 -11.5

8.9 10.9 5.6

91

92

6.6 8.8

5.8 7.5 1.4 6*4 9.8 13.1 13.0

3.3 6.7

6.6 10.2 11.2

10.1 12.6

13.1

13.5

8 .8

10.1 -2 .8 1.8

-9.4 2.0 —2.8

—5 .0 -6.1 -3.7 -2*0 4*5 0.3 -10*9 -11.7 -12.8 -1*4 -3*2 —5 *1 4.7 7.3 -0.8 —3*5 -14.8 -10.7 —9 *2 —5 *8 —12.8 -7.4 —20 .0

-10.2

136.4

—4.8 —4.0 -7.4 —4 *7 —5 .8 2.3 2.4 —8.4 -15.1 -14.1 -7.9 —4 .3 5*8 5*6 4.1 -0.5 —4.9 -14.1 -9.5 -12.7 —9.2 -13.1 -13.4 -14.8

10.0

-1.5 -0.1 —6 .8

-6.3 -8.0 -9.1 -9.3 -2*7 2.0

-13.1 -14.8 -12*8 -7.6 -4.8 4.4 1.4 11*5 —0 .2

-6.7 -14.1 -14.7 -9*1 —9*5 -15*4 -10*9 —16*0 -14.7

Tal

III#

(Cont#) 136.1

Pa: tls 1

2 3 4 5 6

7 8 9 10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Fundamental Frequency 134.8 133.9 132 *8 Wave Humber 95

93

94

2.9 5.0 -2.2 5.7 9.1

4.5 4.6 -3.2

12.8 12.8 11.0

-5.9 -0.1 -8.7 —8*5 -7.4 -10.4 -11% 3 -9.9 -0.3 - 10*8 —8 .1

-8.7 -6.3 -4.8 4.5 8*9 11.4 3.2 -0.7 —7 .4 -11.7 —13 *8 -13.4 —12 .0

-6.7 -14.7 -15.9

13.1 12.4

3.5 5.1 -1.7 6.3 9*5 13.6 11.9

12.1

12.8

6.6 10.0

-13.3 -1.9 -11.0 —9.1 -9.1 -11.4 —14*1 -10*9 -5.3 -7*4 -7.7 -9*9 -4*3 —1.3 4.7 7.1 9*5 6.7 -5*2 -11.2 -19.7 -13*4 -9.6 -16.9 -13.9 -18.0

-5*8 -14*7 -9.1 -7.1 -12.5 -15.1 -17*8 —10.0 -11*4 -5.4 —5 .6 -3*6 -0.4 3*1 5*6 8 *4 8.5 -5.3 -9.1 ^17.4 -9*3 -15*7 -7.0 -11.9 -11.7

96 4*5 6.5 0*9 6.4 9.6 14*5 10*9 13*4 -17.4 -5*7 -11*9 —8*8 -14.0 -19.2 -18*8 -14.7 -11*4 -7*4 -9*4 -2.4 -6.1 -2.2 -0.9 2*2

6.7 7.9 —10 .2 —8 *6

-13.6 —8 *2

-9*5 -10.3 -14.1 -15.9

136.7 106 4.4 5.7 -1.7 8.7 11.0

12.4 14.1 1.6

-5.1 -8*.3 -9*9 -12.9 -18*5 -13*2 -S.7 -14*7 -7*8 1*1 0*8

-0*7 6.5 8.6 10.2 —2 .4 -6 .6

-17*4 -11*4 -10*2 -8.1 -7.9 -11.5

APPENDIX B

Figure I.

Diagram off *square-v/avexi circuit for callforating damping off the oscillograph element«