LOUDNESS OF HARMONIC AND INHARMONIC TWO-TONE COMPLEXES by HOWARD LAWRENCE GOLUB S.B., University of Virginia 1973 SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY February ,1975 Signature of Author. ./.&V-"YSM ./:-.-..6 - Departmentof Aerospace Engr. Certified by........tr'-.r;@'--jrcf'--' :-0nw---. Thesis Suprryisor . A Accepted by...t.v. e.-- eve.r. . r. . . . . .......... Chairman, Departmental Committee MAR 191975) -2- ABSTRACT LOUDNESS OF HARMONIC AND INHARMONIC TWO-TONE COMPLEXES by Howard Lawrence Golub "Submitted to the Departihent of Aeronautics and Astronautics on February,1975 in partial fulfillment of the requirements for the degree of Master of Science." Subjects were required to adjust eight comjarison two-tone complexes to a two-tone standard. For the comparison sound containing two frequencies in a 2:3 ratio, the loudness was much softer than expected. It was also discovered that the loudness confusion (or standard deviation) resembled very closely the averaged equiloudness curves attained with the above paradigm. Loudness is a function of pitch for monotones and this also seems to be true for two-tone complexes. Therefore, iitch con- fusion should be directly pronortional to the loudness confusion which is directly proportional to the averaged equiloudness curves. Or, more simily, it was hypothesized here from the supporting evidence (without rigorous proof), that the loudness of two-tone complexes is a function of pitch ambiguity as well as intensity and pitch, Thesis Supervisor: Dr.K.U.Ingard Title: Professor of Physics -3- ACKNOWLEDGEMENTS I would like to thank Dr. J.K. Haviland of the University of Virginia for his immeasurable influence in pointing me in the right direction, and Dr. A. Houtsma of the Massachusetts Institute of Technology for keeping me there. -4- TABLE OF CONTENTS Chapter No. 1 2 3 4 5 Introduction Theory Experimental Set-Up Discussion of Data Conclusion and Direction for Future Work Page No. 5 10 16 24 43 Appendix A Discussion of Combination Tones and Difference Tones Figures 1 2 3 4, 5, 6, 7, 8 9, 10 11, 12, 13 14, 15 16 A B-e References, Focal Computer Program Output Format Curve of Zwicker, Flottorp, and Stevens DIOT-DISS Case DIOT-CONS Case DICH-DISS Case DICH-CONS Case Standard Deviation of Previously Reported Results Amplitude and Phase of 2f1 -f 2 CT Amplitude and Phase of f2 -fl CT 17 19 22 25, 27-30 31, 32 34-36 38, 39 41 47 48 49-51 46 -5- Chapter 1 INTRODUCTION An accer ted definition of noise is: "a sound which lacks agreeable musical quality" or is noticeably unileasant. An excess of noise has been blamed for increased blood pressure, leading to heart attacks (first major killer in the United States), hyper-nervous tension, chronic anxiety, a decrease in sexual drive (which is serious in ;itself), and all ar6und un- easiness. Although two-tone complexes (the stimuli in these experiments) are not the type of noise usually found in nature, it is a first step in quantitatively understanding exactly what noise really is. The need to quantify the degree of noisiness or "musical- ity" of a sound becomes increasingly clearer, as the need to quantify annoyance becomes important. In order for one to leg- islate on the noise limits of any noise maker, we must first specify what is meant 1 recisely by a noise level and how to meas- ure it. Because we are now living:in this new era, A.E. ("After Einstein"), in order for us to define Irecisely what noise is, the obvious question that should first be answered is noise rel- ative to who or what. This question can simply be answered psychoacoustically, as noise relative to one standard deviation (or approximately 70%) of the population. In other words, people decide what noise is quantitatively, and the answer to this question can only be achieved by focusing on rerception. Although -6- this might seem to be an obvious point, it is not difficult to fall into the trap of thinking that a sound-level meter sets noise criteria instead of people. Why is the noise from a jet aircraft so very disturbing and uncomfortable, while the music from a symphony by Beethoven is so beautiful and easy to listen to? The sound intensities (measured on A-scale sound level meters) at most parts of the symphony are very close to that of the aircraft, at an average height for landing maneuvers, yet one is considered as noise and the other as music. It was not an accident that the afore- mentioned definition of noise contained 'musical quality' to describe it. There are really three reasons that can aptly explain this question. The first difference between music and noise is the time structure, there one sound has a more or less random time variation, and the other sound has a carefully de- fined time structure of which only a genius can construct. The second te asonxis -the intensity variation, or dynamics. Again, the jet engine has a doppler type intensity variation at landing maneuvers, and of course, the music is carefully controlled. The last and most interesting difference will be called "spectral shape", or "frequency placements" within the sound. Although the jet noise has a large bandwidth, it should be noted that a symphony orchestra does also; it ranges from a piccolo to a bass fiddle, almost the entire audible range. It is readily seen that -7- the two spectra are obviously very different; while the music is comprised of the intricate summatidn of consonant (musically defined) sounds, the noise is the random summation of dissonant (again musically defined) sounds. It is this difference that this paper will attempt to focus on. It is the writer's contention that there is a continuum between music and noise and that a point on this continuum can be defined by the three parameters of time, intensity, and frequency variations. Therefore, in order for us to define or quantify noise, music must inherently be defined or quanti- fied also. Just exactly what do we mean by 'quantifying' music? Plomp2 tried to do a comparison dealing with the per- centage of chords where the rates were separated by a quarter critical bandwidth and a full critical bandwidth between a Mozart composition and a Schoenberg work. This was done to corroborate his ideas on consonance versus dissonance. Determinations were investigated as a function of critical bandwidth, but these methods still didn't really help to define music! Others have attempted to use methods or paradigms dealing with music to specify pitch, but these experiments just tend to imply things instead 3 of defining them. There has been surprisingly little accomplished about the idea of music versus annoyance or loudness in any quantitative way. The only method feasible seems to be the same as that for noise,---the use of perception for quantification with respect to loudness or annoyance. The prevailing attitude of "You can't quantify an art form" seems to hinder progress. But again we must pose the question, how can we understand what -8- noise is withour understanding its relation to music? If "Led Zepplin" had been heard twenty years ago, it would have been considered as distasteful and noisy to everyone; or if Mozart's music had been played by one of the ancient Romans, it would have certainly been considered as noise. People's tastes change with the changing times. You can even say that music is noise that has evolved over 5000 years! How then can music (an art form) be generally described and quantified? A closer look revedIS that although the time and intensity varia- tional structures have changed with each of these different modes of music, the spectral compostion, or frequency placements per notes or unit sound (and for the most part the instruments) did not. The Western form of music (Oriental music has a differ- ent spectral structure which presents an interesting question as to physiological and psychological differences) always contained a special order of frequencies per note which is called tonality. Up until about sixty years ago, this was the only form really utilized by musicians and composers. With the advent of people like Schoenberg and Stravinsky, seriology was introduced which presents a different frequency structure. However, it should be noted that Stravinsky's most famous works (The Rites of Spring) were tonal, and his works containing seriology have yet to gain significant recognition, fifty years later. It has been known since Pythagoras of ancient Greece that sounds containing harmonic frequency progressions are treated differently within the additory system than are those -9- sounds of arbitrary frequency placements. People like J.L. Goldstein,4 Plomp,5 Houtsma,6 Schouten,7 and many others all have dealt with it in relation to pitch phenomena. It is now time to link the musicality of a sound to the subjective loudness or annoyance of that sound. The difference between loudness and annoyance is indeed a subtle one, and in literature -_ annoyance is usually associated with more complex sounds (found in nature). However, in these experiments they will be assumed the same. Through preliminary testing, where subjects were instructed to match loudness and/or annoyance, there were no statistically significant dif- ferences in the subject's response. This is not to say, however, that with other stimuli (more complex in nature) this difference would not be greater. Loudness will be used as the experimental parameter along with th .aforementioned assumption. Although the stimuli used in the following experiments are not natural in either presentation or frequency spectrum, the basic psychoacoustic assumptions sholld hold.. These are in fact that subjects will respond to these stimuli as if they were natural and that the results may be generalized to apply to more complex stimuli with a little more proof. The following pages contain the theory, experimental setup, data, discussion of data and direction for future work, which will serve to further clarify the effects of rela- tive frequency placements within a discrete sound spectrum on subjective loudness. -10- Chapter 2 THEORY The "Noisiness" (PNdB, Noys) of a monotone has been found by Kryter,8 to vary with frequency (Hz) at a constant selected intensity (measured in dB). The unit of loudness for single tones is called phons. For a more complex discrete sound, the methods of Loudness Summation (in sones) presented by S.S. Stevens9 or Zwicker's procedure for calculating loudness are as of now the major ways to assign a complex sound a particular loudness. Even these procedures are not regularly used; the A-scale, a poor representation of an inverted threshold curve used for its simplicity, is the law makers scale for most en- vironmental noise such as traffic,street noise, etc. These methods handle the problem of the loudness of complex sounds from a standpoint of monotone, or narrow bandwidth loudness summations. Although spectral positioning is taken into account somewhat when making this summation, the relative positioning of the frequencies within the sound has been ignored. It should be quite evident that loudness summation shouldn't necessarily be a linear process. Phenomena such as combination tones, dif- ference tones, and central nervous system effects all ediitribute to the probability that loudness summing is indeed a nonlinear process, of which simply adding the loudness of monotones does not yield a very accurate measure of subjective loudness. -11- For a sound containing more than one frequency, or narrow band of frequencies, the loudness might also be dependent on the structure or the ratios of these frequencies within the sound spectrum. Thus, a harmonic or consonant spectrum containing frequencies related by integer ratios could appear to be softer than a random or dissonant spectrum, even though the intensity of both sounds (A-scale, dBA) are the same. A major reason for this idea could be explained by the combination tone and difference tone phenomenon. The combination tone, thanks to the work of J.L. Goldstein (1967)10 with his paper on "Auditory Nonlinearity", can be used to explain one possible reason for the difference in loudness between a dis- sonant and consonant sound. The combination tone appears at 2F1-F2 , where F1 and F2 are the first and second frequencies of any ordered pair of frequencies in a discrete complex sound. For any harmonic sound spectrum of f1,f 2.'.'n' where: 1f0 = f1 2f0 = f f= fundamental n4= fn. The combination tones as well as the difference tones (F2-F1)0 lie directly on a frequency lower than that pair in succession. -12- For example, if the sound were comprised of: Sound......................f 1-f2 -- f Combination tones..........2fi-f2-2f2~f3 Difference tones...........f 2 -f1 -- f 3 -f2 since f2= 2f1 , f3=3fl Overall sound..............f 1-f 2 3 In the special case of a sound containing two frequencies, as used in this experiment, of which they are in a 2:3 ratio, or the second and third partial of a harmonic series, the difference tone and the combination tone will have the frequency value of the 'fundamental of this series. Although this seems to indicate that another frequency should be added somehow into the loudness summation, it was shown (again by Goldstein and J.L- Hall ) that at the intensities used here (68 dB S.P.L.) and at the frequency separation (2:3), the combination tone as well as the difference tone would not be at all appreciable. There are also some complex interference phenomena occuring between these two (depending on the relative phase of the primaries), since they are at the same frequency, which also tends to substantiate the above assumption. In contrast however, for a dissonant sound of f1 , f2''' n where: Aft0 = f Bf =, =f2. A, B...Zn are, in general) Znf &If not integers. f,= a common frequency An example of this can be: Sound....................-fl--f 2 -f 3 Combination tones........ 2fi-f2--2f2 -f3 Difference tones.........f2~ l f3 2 since F2 = f1B/A, f3 = fIC/A. Overall sound: f -f 1 (2-B/A)--f (B/A-1)--fB---f (2B/A-C/A)-f1 (C/A-B/A)--f1 C. It can be readily seen that the dissonant sound has more independent frequencies than the consonant, thereby creating more frequencies to sum into the overall loudness summation. It seems that the amplitude of the combination tones are proportional to the distance in Hz of F1 and F2 , as well as to the intensities, and the two primary frequencies would have to be faily close to- gether and with moderately high intensities for these combination tones to be heard.12 The fact that a minor third (5:6) is just at the limits of producing audible combination tones seems to in- dicate that for most musical intervals, combination tones are usually not even audible, as is probably the case for the major fifth (2:3) used in these experiments. In summing up, for a harmonic sound, the combination tones and difference tones if audible, always lie directly on one of the lower partials, while for a dissonant sound, they usually do not. The combination tones have amplitudes of 20-30 dB(depending -14- on primary frequency separation) below the mait frequencies which indicate that when they lie directly on the main frequen- cies, they are masked and do not contribute significantly to the overall loudness. However, for a dissonant sound it would be very possible for the combination and difference tones to lie in areas (these areas can be identified by the single tone masking curves) where they would not be effectively mafked and in which case they would have some effect on the overall loudness. Although the calculation of loudness for complex sounds would probably be more correct when we include nonlinear aural harmonics, as we shall see from the following experiments, effects that arise in the central nervous system (or somewhere past the superior olivary complex) seem to be much more important. This finding sho&,ld not seem too surprising due to the fact that pitch was found to be interpreted primarily in the central nervous system as shown in the work by A. Houtsma and J.L. Goldstein (" The Central Origin of the Pitch Complex Tones; Evidence from Musical Interval Recognition"). Although the above hypothe- sis utilizing combination and difference tones is very palatable and sounds as though it offers the answer, as we shall see, it is only a negligable part of the total effect. We are now treading on that infinitely thin line between physiology and psychology when trying to explain an effect like this. It seems the more we learn (microscopically) about the central nervous system, the more we attribute specific perceptual -15- effects to "just" physiology, and that which we do not know very much about, such as the area past the neural joining of the two auditory systems (left and right ears), we attribute to psychology. Since this effect (consonant sounds appear softer than dissonant sounds) must occur in an area of the brain of which little is known microscopically, as we shall show later, we shall henceforth consider it a psychological effect, at least macroscopically speaking. The fact that harmonically-oriented sounds do sound softer than dissonant sounds should not, of course, be assumed. The following experiments are devoted to the testing of this hypothe- sis. Although the following is not definite proof of this hypothe- sis, for nothing in perception is definite, the following experi- ments,rwebelieve, offer a positive and convincing trend. -16- Chapter 3 EXPERIEMENTAL SET-UP The objective of these experiments is to find the re- lation between the loudness of a two tone complex and the relative position (in iz) of their frequencies. For each test sound, the first frequency (fl) was always set to a value of 1060 Hz, while the second (f2), the parameter of the experiment, was variable. The intensities of both pri- mary frequencies of the standard sound (1060-1108 Hz or 1060- 1590 Hz) were always set to a constant 65 dB throughout the test. With the aid of the PDP-12 computer and sound-proof room set-up (found at the Communications Bioengineering Group, R.L.E., at M.I.T.), the testing procedure was initiated as com- pletely automated, where the computer controlled and tabulated the experiment (see Figure #1 for the actual focal computer program used). The experimental paradigm was designed to give the subject as much time as he or she needed to compare the loudness of a standard two frequency sound to a comparison two frequency sound. The subject was allowed to switch freely between the standard and the comparison sounds, heard diotical- ly (condition in which the sound stimulus presented to each ear is identical through TDH-39 Audiology-type earphones), at will. There were eight trials per test in which the standard was the -17- FIGURE #1 FOCAL COMPUTER PROGRAM C-PSYCBL 1974 V-36 01.01 C AS( FOR NEC. INF3 01.0 T "SUBJECT NO.". ! 01.10 A "wrIAT KEYBOAN) IS SUU-",414 ANS(N.1) 01.I S LM=0sS UI=OsS P=4sS Ll=0S Z=O0S T=0iS W1=8 01.12 S U=90 01.15 A "WHICH OSCILLATES?"mA.11 $1.16 A "WHICH ATTENUAINS?"DAmtsDI 01.17 A "WHIIH SWIT~r4?".Tl, 01.18 X ATT(604.,A)IK ATT(i6dadsd) 01.20 A "WHICH SOLEU IS STAND. I FOR DISS.2 FR CONS.?'Sl.1 01.21 A gels IT AREGULAR TEST I-YE5 9 2-N3?"DN5,1 01.22 I 5R-2)2.kI5 01.23 A "HOW MANY TEST FnEw. WdAT ARE THE",WIDI 01.24 S P=WI 01.25 F Jr=1l*WlI A 8(J) 02.K1 X ZEN(O)iK CL(K(l00kv0,d)IX WATCO)IS Z=Fe4(CN-1)*4+1)-1 02.02 'T 211 L.1 02.10 1 (L-8)2.01,2.3.2.1 02.30 T 3,Uo! 02.40 K LMPCO0E8Kj LMP(0511) 02.t0 1 (51-2)3.l,4.153 03.10 C SET ISS AS SIAND. 03.11 K ESW(0,0Tl)sK ESW(JI1Tl) 03.14 ATT(60,3,A)l4 ATT(60.0.8) 03.20 K o)SCC1060,OK);X OSCC1II ,0Y) 03.22 A ZE$CO)SX CL.((515dl1) 03.25 K WATUO) 03.33 K LMP(0#0,),) LMP(1,0,1J FO:)t 5.01 04.05 C SET CONS. S STAND. 04.07 K ESAt0,T1lX ESWC1.1,T1) 04.09 K ATTC60,0*A)IX ATT(60,kB) 04.10 XOSCC1060,0,X)JX OSC(1590,0Y) 04.12 X ZER(0)JK CLK(50i 1) 04.15 K WATCO) 04.20 X LMPCO.0,8)JX LMPC1.0.1)JGOTO 5.01 05.01 1 (rO-2)5.15,9.015 05.15 S a(I)=11$6s S B(2)=1225S 8(3) = 12655 S $(4)z1333 05.20 S 5(5)=154035 8(6)=1590S 8(7)2165015 8(8)=1800 05.30 K ZEcCO)JK CLK(100,0,0)KX WATC0)iS Z=FANS(CN-1)*4+)-1 05.40 I (Z-3)5.5p5.6.5.5 05.50 Z(Z-8)5.3,10.015 05.60! 1(L8-1)6.0h16.1,6.1 06.01 K LMP(COI$I)JA LMP(1,03) 06.02 1 (T)6.05.6.05.6.1 06. 15 S QE=FRAN(P)JS W7=ud 06.36 K ESW(0,0,Tl);K ESW(1,1,Tl) 06.10 K OSC(B(7),0,Y);K ATT(U+P+LI,0.A)IX ATTCU+P+Lt.0,B) 06.11 X ZER(C)Oi CLK(5030l) 06.12 K WAT(0) 06.15 K LM$(kJ.Os8)JA LMPCI(103) 06.18 S T=T+1 06.20 X ZEN(0)iK CLK(0id0m,0)SK WAT(0)sS Z=FANS((N-l)*4+1)-1 06.25 1 (Z-14)6.3.7.02,7.02 06.30 1 (Z-9)6.4#10.011 06.40 1 CZ-1)6.2,2.4,6.2 07.02 K ATT(r+Ll+U.0,A)jX ATT(P+L1+Upd.kh) 07.03 S L8=LS+1 107.10 1 (L8-1)7.2,7.3,7.2- 07.20 X ZER(0);X CLK(100,0,d)IX WAT(O)SS Z=FANS((N-1)*4*1)-1 07.30 1 (Z-l4)7.6,7.57.4 07. 40 1-2r0OTO 7.02 05.30 05. 40 05.0 53 05.60 06.131 06.02 06. 15 06. 06 06.10 06. 1 06. 12 06. 15 06. 18 06.20 06.25 06.30 06.40 07.12 13.03 07. 10 07.20 07.,30 07.40 07.50 07.60 07.70 09.01 GOTO 5.3 S 0.J1+1IS LdrLS+15 =WfJS 1=0 A ESw(00.TI) A LMP(v%..8)JA LMPC Isd.2) S L=LI++U-60 S L1=0 I (J1-2) 10.14.,10.1, 1.* 16 S U=90jGOlO1 0.2 S U= 50JG010 1062 I (Ut-4) 10. 17,10. 18 10.20 S U=4IG'JO 10.2 S U= 351IGo)1J 1k3. r .%3.02, "FOR TEST",Q1."W1i A SEC T %3.02, "F(2)-F( I) ="sn(w7)-1060, . T 23.02. "Al1ENUATIJAN WAS".25*L "I I (Ol-4) 10.38. 10.381 I (LWl-6)I10.33a10.34.1(d.35 S U=30JGOFO 10. 38 S uq, G0rO 10.38 S Ul-9! I (Wi-WI)10.39.12.013 S C(wl)=W7 I (w7-P)110.5.10.i31 S N=0 S US=FRAN(PL S 8=8+1. I (t(X)-U8)10.55,10.41.10.55 I (8-U1)10.51,10.63 C THIS IS FON NEW SOUND ASSIGNMENI GOTO 10.9 S P=P-l S m=0 S WB=FMAN(P) S R=R+1 I (CCR)-8)I0.88.10.82.10.88 I CR-Q1)10.86.10.93 S Q7=98 T 23.U.! I (CI-WI)2.4.12.0l3 10.01{ 0.02 I0.c5 10. 16) 10.17 S10.12 S10.14 10.19 S10. 16 110.17 10.13 10.20 10.I25 10.30 10.31 10.32 10.33 10.34 113.35 113.38 10.39 10.40 10.41 10.5( 13.56 10.53 10.55 10.60 10. 80 10.82 lid.85 10.86 10.87 10.38 10, 90 It.IN 10.92 12401 12.10 JND FREw. sF" 4,d(U7),I L)t", I LMP(0.5)A LMP(l,0.4) UIT *1 ZER(0)JA CLK(100,0,O)fA WAT(O)JS Z=FANS((J-I)*4+1)-l (Z-3)5.515.6,5.5 (Z-8)5.3.10.01; (LB-1 ).0Ie.#1,6.1 LMP($.e7O.8)I A LMP(L,0.3) (T)6.056.056.1 QS=F RAN ( P)S W7=ud ESW(0,01 TI) ;AESW(I1,p1,1 TI) OSCC8(7),0,Y)JA ATT(U+P+LIDO.A)JX ATT(U+P+LI,0.B) LER((3 CLK(501011) WAT(0) LMe( Om o8 ) JA LMP( I Ov3) T= T+I ZEN(0)1X CLK(100O0.OfA WAT(1)JS Z=FANS(CN-1)*4+1)-1 (-14)6.3#7.02P7.02 (t-t3)6.4,I10.013 (Z-1)6.2,2.4,6.2 ATTC +LI+L,10A)3 AATTCP+LI+U.0,d) Ld=LB+I (L8-1)7.2.7.3.7.2 ZEk(0);X CLK(I00.0,0)JA WAT(0)S ZcFANSCCN-I)*4+1)-1 (Z-14)7.6,7.5,7.4 Ll=LI-21G01O 7.32 LI=L1+21GOTO 7.02 (Z-8)7.7, 10.013 (4-1)7.2.2.47.2 A 9' -18- same sound throughout. When the subject felt that he or she had adequately equalized the 'loudness' of the comparison sound to that of the standard, he or she would then depress a trial-ending button, which automatically selected a new com- parison sound with a new initial intensity. The subject was instructed to continue the same orocedure with the new compari- son sound as he did with the previous one until all eight com- parison sounds were heard and analyzed. For each trial the initial intensity of the comparison sound was randomized along with the order of presentation of each of the eight stimuli per test. The attenuaters were ad- justed to step .5dB per press, or .5dB/second if the attenuater button was held down. There were basically two intensity con- trols or attenuater buttons,---one for positive and one for negative attenuation. When the trial ending button was pressed, the computer automatically took the total adjusted attenuation of the comparison and subtracted from it the constant attenu- ation of the standard and then generated this number (Intensity comp. sound Intensity ). The standard has a constant S.P.L. of stand. sound 68 dB S.P.L. An example of the output format for one test can be seen in Figure #2. The test computer program has the ability of presenting any of the two standards per test. The first, which shall be named as the "dissonant stand.", had a second frequency of 1108 Hz,---exactly one fourth of a critical bandwidth (the size of te ctitical bandwidths measured by Zwicker, Flottorp, and ., . .. . ... , .. , - -W - .. ' . . . L. 'o - ,-' L 4 1 , , fk $ ;, N ., "to,,. , . , , ft I k.L jig fl, .. - . ., . x;L, - A .. ", ; .'i , :z , . 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I I L " "; , , .- r.. L. , , , - : , : : " , T , I',- . . e .1 '. .. ; L.. , - I . I . - I1 1 r 'I T E S ? , , . . . i . , , , . " 1. I . L . .1 - j ,-: ., ,. I~ I . '' ,'. ,'Jr,, , , r ..H - 0 ; , -, , ;, . q I .11.. .. ., "A , . .11 1. I -o s . . j,-,Ir . - , , . .. . . I ., .1 j , ," r . L ,, - 11 - I " _ : , , , -L . , . . I 'c ' I , ":e..."" _ 1 I i,. - 1 _. I . . : ; , -. , , , 14 1, :. , ,I , . H j C . I ;l 7 - , I , , 7 L ,. 11 . I I ., I ;, - , I . . , - . , 1. . , . . , . i 'I - , , - ,.; , , , I " - , , , , - , ,; I , ., - r . .1 I I , , , - r, .1, , . . . .1 I . - - 1, . I I 11 1;F . , . , . - ", 2; I -, .L , : _, I . , .iw , i I I : ", , i , ' - ' " :? j I -L "' 2 . .I 7 L ' -. . , ' ,r:, , _ f i I , _ ., I , ., ! I. , ,P '. . , ,, . . I . - " , - - I I , I. , . lp , L r - I I . . - I I I I . . I . . :I . L 1 '.. _ [" ,,'. ', , I.' . . I -_ -. 1,( r I I . . . . I I ,i. , "L L. ll I . 11 ,. , . -I. I ., ,'r . ,?>- . ,,, ; '.. I 1. . . . , " A i.- I r . I . . . 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I . , . d:.1 , " . , , .. '. : '! 4 , I-, .. , ;. " , ', '' ; I . - , . I . . . I . . . . ,. . - . . I . . ., - . . I . . .: . . . , . - . I I i .: ,. . ! . I .1 . - L . . . , , I . . I I I - . . " - , V , . . . , , . . I . . , ,; '% i-l 1_L_ . , f , I , I , ! , . I . : i ; : . , . I i . . , . I I I . , i! , , , , " , , , 1. ; I I , , I j , , ! , 1, - ; -, ; , - I I I . . . I . : . . ,:, . . , , . %t5i 04 1 I . ,. ., , .- , '. . . , . p . I . L do I 'L , . I , . I I . , ; , . . - . I L I I I . I I i r I .; , , , . . I . I . . I . , . . I . . . : , , . . . .. . . , - , " ., I " ; . . - , : : r I . I - I , I . . , . . 1. , i . I . I I I , I . . I . . . i I - . . k"'. ;. " ,; -,;: , , . . 1 . , I .. : I I .L" , : I i . . . . : I I r r . . - . i . .. .1 N ' : I - ,,, , " , : , . r I ' , I , - , I . , , , : , ' . r , I . . I I " - . . I , . , . L ! - . I , ! , . : ! I - .1 I 1. . I . - I I .1 I .1 . I . . I ., . I I . , . I q . . ''' ., l. -, :.. . , 'i, " _ . I I . I I , l . I , , Ii.' ; ! I i . , . . j . I ; ": 11 j, L_, " . _ , ,_ . . . . , i . ; 1 : ;,- . . ,. , L _, ' ' ' 1 ' . 1 - I I . 7 1 . I - . . . r I . I , . ; . I I . i , I I . , ,r . ., , 'j.I 1. ,r , - ., , . . I . I I I . L , . , :1 . ", I - ,,, . . . : . ' - - :, ,; I!.' i, I ! I , . r 1 . , L . . I I %!, :.' ,-!' lil, i ; . . . . I - I 11, , ,, I 11,j . I I - .I ! . -1,.' r. ,.Ie ', , , . ., '. ,., , ": , . . I j I,, ' - , ! - , - L ' ' - , - .: - . I , I . . I , .t , ii-'I" . , - . , " , ' I ' ' ' - 14' , .. I . " ' : 4 I I . I I . . I I -, ; I . I -, - -, , . L , 1 ., ! r,4 I . L , . I , -I -I I ' ." -14. _'- I ,- . .I I .: .-1, , : , I i . .. .. 1 '., ,f! I .fiF 11L" . -1 ... , - , i I ,;j ' ' , ' I .0 ;: , . , , . . . - , , ; , I, -. . , , , I , , , 7 1r IL -, "..6 I .I 11 ',: , ."; : , . , r I . I , . , , I , ' - _ , L " I . I . . I , . . . . '- , - , - , I . N , . I . : -,' , , , . 1 . . . . ! ,. ' , r, _ , ,'.!i, , . : i- r, 1 L I , 1, I " , : ' ;,I,, , , , , i, , , h .I'. ;.,. - , , ,,.r " ! .. . , li , , - , , . , I :, , : I . . I . . . I . .i , :. , , ... " . i ; : , . I. . ., . I : , , . , .I I " :. .L ., i 11 . ' ., I:;. , .1 1 " , . '. ,4 , , I . : , , I I . . I . - I . , :, I !- , 1 , . . I I . . - i , . . I .,: 1. I , ."i's :6 .- " i r ? - ', . , f : , i . I I ., . , . , , : r , - I 1,; -, -, , . , I I I I _1 1 I ii : 1 , . I "', !. :'N . L , I . I- '" ,' , ' _' 'I . , , :,L r . . . , f : r I , r , k . , : 3.1 ,. ,.. .. I., I - I r I L I - . - ! : I " I . . - , , . . I r . 'i , . i"I" I , : " I . -, I . I '. .i. i ,,: , III I I - . , , , V ; . ... . . . C a , ,! . - , I .1 , I , , .W Lj - - ' . .' .. ' ' ' .. - , _ ' .. i ' . . - ' : : . I , , : I , . .. . :1. ,, ,; - ,,, ', 1 ; 'I ,i - . , , -.. ; . , L i - . . 1. . . I . I I I . - . . . i I . . ' % , . I r I - ; , . . . I , 1 " 4' , . _ -- "jI- , : . , . . , . , . . . I - ': . , . . , ; , , . - . ; I L: , . , . I I . L. J , , I . ;. I I . . , . . . - _i, .,.., l'. ; .1 ; j . . , : , , , I . 1'k'. ,' . . ,ij ' - I - ' ' I ; ' , . . ' , .' ' r.' i I - L" . :,. : . - , I , i . . . . :, . , , '41 ) ! , ,- -I , "; 1 : , , " . I - ; . . , I . I . . " . . - . .1 I '. ,_ . , ,, . , . -- , :,., . I . . . I-, -; , _ ., I , . I , . . I . . , i . I . r IL .. . .1 I . . I . . ., - , - ' , P '. '! ', , - ", I I I I j . . .. . , . , = I j , - . I I : ... " .; llL,.j17 - , m; . . . ;, ' I i " , , I., . . " " , .. ... ; - , 'A, .. , : 1 1 " , - I : , , , . . . . . - 'L , ' 'L, .: ' .. ' L . : - . . ... I , , w .1 i I , .I-- - . _.. - . . . . , L - . " . ., . .. , . ". , . , 1. r .., . . . - , ; . . . - . pl, F. - :,:,!, " : , - '; " ,, i , . I , " , - 1 . -41 I ' ,_ - . - , , , , , , ., :1.. , , - .; , % I , , . I ; I , , - , - , . ,, mj , r,, , , , , , , . . . . , I I .4 . . . . I 11 .- - . . t 4 L l - . I , I ,L . , : , -Z . ' . , I " ,I : . _ , " . 0- ,:, ,." ? I I ': 'r % , 7 I I I I I - , " . : ! -, 'I., .il I , '. .'s. i," , - - _ , -. :,'. ' , . .. ' ? ' _. r ' . 'i'L , ! i . - , , - - 51 4 ' ,: "P i , .it P. ...... , . I. , , " I ' I , ' I -r ( .1 II 1 - : , , " . , IP -20- Stevens in 1957)13 away from 1060 Hz, the first frequency. The reason for this selection of a second frequency was taken from the work by Plomp and G.F. Smoorenberg14 in their definition of maximum dissonance as a function of crtical bands. The second, or "consonant standard", had a second frequency of 1590 Hz or exactly the third partial of a fundamental of 530 liz with 1060 Hz (or fI) being the second partial. Or, the two frequencies were in a ratio of 2:3 and a frequency distance larg- er than a critical bandwidth of approximately 180-190 Hz at this frequency range, also in agreement with Plomp's specifica- tions. The second frequency of the comparison sounds were chosen strategically to approximate the same trends achieved by Zwicker and Stevens (1957)16 in their work on loudness summation and its relation to critical bands. In effect, their results showed that if a complex sound (in their experiments, four fre- quency complexes were used with the frequency difference of the first and last frequency defined as the bandwidth)had a bandwidth less than that of a critical band, it would be equal in loudness to that of another sound with a bandwidth or AF within that same critical band. As the tF of the complex sound increased, the subjective loudness also increased monotonically, at least up until the largest AF tested or about 1500 Hz. It should be noted that in this paper Stevens did make some reference to the fact that some spectra he tested, when they contained equal intervals, seemed to be perceived as louder. Although at first -21- glance this seems to be in contradiction with the ideas pre- sented here, however, ftom a closer inspection of the frequency values, it can be seen that these spectra were not harmonic progressions; they just had equal intervals, and were not in integer ratios. The curve of loudness versus A F (refer to Figure #3) that they had attained was somewhat dependent on intensity of their standard. However, at 65-70dB, the curve was most well behaved and pronounced. There are essentially three differences between this experiment and ours. First, the standard they had used was a pure tone (1000 Hz), so the subject had to compare a complex sound to a pure tone. This can be considered a mild form of cross-modality testing which can only add confusion. We are not affected by pure tones as we. are complex sounds; if we were, the whole problem would indeed be quite simple. The second major difference is our concentration on 4'F's corresponding to harmonic or consonant progressions.17 If the ideas presentedbefore are correct, then a very narrow (frequency-wise) dip about 5-10 Hz wide, should be seen in the curve at a AF of a harmonic. Indeed, if one is not looking specifically for it, it could very easily be over- looked, and if seen once or twice could be dismissed as exper- imental error. The reasons for the dip bein!'gso narrow at the consonances can possibly be explained by the concept of mistuned .;onsonances, where two frequencies very close to a harmonic 0Curve of Zwi.cker, Flotterp, and Stevens (1957)Figure #3. aT-tone adjusted C-complex adjusted +++~4*~N -~--H#~-+V--'4 d, ig~ Intensity of Standard 58 dB S.P.L. i - 4--4- - -ji 4-4 L 4-- ._z. AF (F4 F1) Hz 0oo --4--- ~471E I~~2I~ Iz~ I4~i1 I ~ -tLLUI: H4 -- r- -1 ~rnIIzzi1iK4z iH++iH'A +i*+.+4 -4--+1 4 no data point corresponding to harmonic. i rs *-4 4- ..- 4, :3 I c I I I . I . - . I - -5 77-7-- . . - i . . 1 i i - 1 - -, 1 1 iF -4 i , 1 . q m ! i - 1 6 - 1 i - i I I . ! i 1 - -P4 , ! 0 ! I ! m m ! , 1 , IF 1 1 -. i : i 1 . I . 1 ! I . 1 , q-JL -1. ...P 77 O . 4.4-4 4 I jL 10 -23- ratio could produce beating and therefore sound dissonant .18 For example, if a first frequency was set to 1060 Hz and the second was mistuned to 1598 Hz (mistuned by 8 Hz), this would not necessarily sound as pleasing or musically consonant. The third and final difference between Steven's experi- ment and ours, is that he used four frequencies in his compari- son sound to our two. This factor does not seem to be very im- portant due to some preliminary tests in which we presented to the subjects through the same experimental paradigm, two four tone stimuli,---the first being a consonant progression (500-1000-1500-2000 Hz) with a A F of 1500 Hz, and the second a dissonant stimulus (500-633-1745-2000 Hz) also with a A F of 1500 Hz. The subjects consistently adjusted the dissonant stimuli softer (or heard them as louder) by 4-5dB. This result seems to indicate that the effect- gets progressively larger with the increasing number of comonent frequencies up until at least four (we did not test for more than this), and that if we had used four frequencies in these experiments, the dip would probably have been even more pronounced. It should also be noted that the loudness of two, three tone complexes were compared (in the Senior Thesis, "A Look at Noise and its Effect on Man", by H.L. Golub), and the loudness differential was ap- proximately 2-3 dB. The following data does show-the.monbtonic upward trend as that achieved by Stevens and Co., however, with one inter- esting difference,---the area around the A F corresponding to the harmonic. -24- Chapter 4 DISSCUSSION OF DATA The eight comparison sounds have second frequencies (F2) of 1108, 1225, 1265, 1333, 1540, 1590, 1650, 1800 Hz, and a first frequency (F1) of a constant 1060 Hz. Hence, for the dissonant standard, a comparison sound with a F2 equal to 1108 Hz was the control of the experiment, and for the con- sonant standard, an F2 equal to 1590 Hz was the control. The first group of tests involved the case where all the stimuli were introduced diotically, with half consisting of the dis- sonant standard and the other half, the consonant standard. Figure #4 contains the results obtained from eight subjects, where the (Intensity - Intensity dB is the ordinate and comp. stand. the log 1 0 (&F) Hz, or the log 10 of the frequency difference of F2 - 1060 Hz as the abscissa. All of these curves are the re- sult of diotically introduced stimuli with a dissonant standard. It is readily seen that there is indeed a 'dip' at a A F cor- responding to a.F2:F1 of 3:2 for each of the subjects tested. There is also the upward trend noted in Steven's work after the critical band, corresponding to approximately 160-200 Hz. Al- though the slope of these upward trends vary, this is to be expected due to the fact that these curves were obtained after only one test for each subject. These representative curves are presented to show the repetition and consistency of this 'dip', and that from subject to subject, it appears quite visably. 0 0 Figure #4. DIOT-DISS Subjects 1,3,4,5,7,8,12,15 (1 Test Each) LI. 4 AF (F2-F,) Hz _U 4J1 -~ - CW u ~~ ..... 3 I in~ I :- 4+ I 54 - ! lw m i , I w 1 OF. K 0 l 1 f h m i 1 lb i 0 . 0 ! -. 1 1 - qw I t A p I O #1 T izy -ii -T-- --w- -26- Altogether twenty-two subjects were tested with varied nuber of tests per subject. There were eighteen subjects who were just tested once (Refer to Figure #4 for eight of these), and out of the curves of those eighteen, sixteen showed definite 'dip' type patterns at the consonant, while the other two were ambiguous. Out of the remaining four, each was tested twenty, eighteen, eighteen and ten times respective- ly. Out of these, a total of sixty-six, only three were with- out these 'dips' at the harmonic for the diotic case. In summing up, for twenty-two subjects of which there were a total eighty-four of these curves, only five did not effective- ly show the 'dip', or 94.1% of all those tested effectively e did.1 Curves showing the average of those four tested more than once for the diotic dissonance (diot-diss) case can be seen on Figures #5-#8. It can be readily seen that the 'dip' is most apparent here. The other half of Athis first group of tests consisted of the diotic case with a consonant standard (diot-cons). The curves for two of the four subjects for this case can be seen on Figures #9 and #10. The curves are representative of all those tested and there doesn't seem to be any contradiction between this case and that of the dissonant standard. The overall levels of the 'dip' are lower for the consonant standard case, but the trend is still very apparent. As of now, there have been"no gross deviations between mpg ~ -- 'I~ I 11 - I I- 1 GRAPH PAPER D PRINTED INI U I-A- Figure #5. I DIOT-DISS 1'4-H!' !T i I 11 71* 11 WIN Empirical Predicted--------- F- ~ 'I- 'SW 4-144 -T -r E T L. 4- --- F 4tbt4 4 T-7T 7ttttvti4l I -4 ---- %1Z7P.TI ,t-4-ll'hl i14 1-1-i-rrrlrTlit7 i- -9-i- H----H*/-+ +HIH4-HH ltt- I bY(F 2-F1)Hz CD -rd 43V2 03 1m~S~47: 1W 0 Subject GM (Average of 10 Tests) I 3 a jjjjj49:. iYEZ2ft~ 4-'4 4 -r--r-~ 1- Ls C ' 1 i , 1 - 1-1-4-r-14 i'AR , 111 a r I .L I - . - #1147 R - -.w- I' F-17 - ~-tI I v a 6 I .oo,. I I , a . , . 1 .5.. 1 1 .511 I P- IET U- -I-a-..-- ", Is L Figure #6. DIOT-DISS SubjectJS (Average of 9 Tests) -1 - e = 4.J -- g: - J tno 41' - d ,-H tL-- ' FI r Empirical E Predicted---------- ~-~r rrn -rrr _i17 it ~11:ttStIiPcpZclnriuiv-Talfta IIF5iti 77y~7Ij vV11 -4- -4 - -- - - -- - J - - -- - T .71 -itt-tilt itttltt:lm 1+T 1-7--- -:-Th -3 trw-i - = 7 -7- -- L AF (F2-F1 ) Hz t } .H44 'PD910v A4W~tu :lrlc -tt + wAils tt72r7T 4Z4T-41 171. -. ~ ~ ~H -+47H--.. - -A T-T-h--tr --- - 4 2 --- -- a 4, 3 1. fJ O) I tfl T-- - r---l Aw. - - -- r ---- - - 17 I .T ; , %61 l, lm , , , '! ; , ; i ; Il i i i m , " H ii Lif~t-rit i -T----7-, -- - T - IT~ 1 . I: GRAPH PAPER PRINeTED 114 U S. A. -1 -- .i--- + i 1 - i, I -, - I , .... . , -.- I. -.- I - -;- -I 1000 GRAPH PAPER PRINTLD IN U S.A. DIOT-DISS ubject FP (Average of 9 Tests)4 At4 H fH Empirical- Predicted--- 1 - _1 1 irTrThhT tt-i ~1~ -r 3-7-1 -1-- t T -A4---4 1#- --4 4-T- ifi i Uri 1 LL+4 4 -j- f-. L; 4. .. l- ) 1J.1.4. I I .I I I. 2 1 AF (F2 -F ) Hz 2 "- 1 6.m. a 0 5 Figure #7. Ili 4 3 2. 0 tf4J 'n 4-)0 u 4 ) T-1 --L f .LL t .' 7T i 4'I LA - - T I - - . - 10 1T ~i lJ F1 11 TT II 1 Ii 11 .1 1- 1. 1J iI I LI 1 11 1 1. 11 1. 11 T1 1 11 - - I 1- 1 1i I ' l- II l t r r 11 u- 11 11 11 1I nr Iu Tm n m l1 Fi ir iI II I ill I - L1# HI+ 41- 11: Idrl l#Ii #t +N 14 - t m uI IIL VL IJL LL IT LL IIL IL LL LY L[L LL Th LL LL L I: i i - I4 tii tit fIi tH H ti ll Il it tl iN ili r:i V - - $ o m m m 4# 4t ltl t -r tl m - I l - [ -- f EEU ~hH ~hT ~hT - - t t - rr k - - 4 4 kW i - W- itttf - a- 1 tt 1 H tit FB i~ - - - - - 'fill r :z - (D TI T - j ( - - - H~ mT ITI I1I ~i~ riFI TV ~rn TI [[FF 117 M lI II II J Il lL L L L L L iL 2 I. - - HH tiI -H -iI Q. . C (D I- 0I tsM IT Th T~ fir flh ~h P~ h~ iT I rF ITT illI? 72 - I dIH itt L- LL i L L L' 41 H +- .L - L- S- 44 --- i LL - A 'K I iI iiiL A, ~ - L - t L - - - - - T~ ~ L - - - 7 - I- - n - - - 4 - L I I I I4 L. L~ ~4 #I 'M -F Tf . 71 -A - A- 1 A, - 4. A - L + _ j- l. - 4. 1 IS . 4 L. i - 1 1- 4' . i 14 1 - 1. ., 1 Li j - i- 1 4 L - A -L - j A L I,- _ 1 L J. L : - - _ l _ 1 LL L - 1 fl- H IP L I L L L.L T P - _ t- - U H I _ L L 1 6 L ;: A f# A_ - - L tt T' 1- - 4 _ Tt l - 4 L it;q -T- l - # # T I I + L + 4 - 4 f4 -- , FH +W J+ H+ U W H I+ H I 0 4 'TI fl-0 H ' He i rtf 11 1 11 11 1 T T T F1 I li II II I'l I I I I I i a i i i i i i i i i ! i F E I I H il l - 19 -4 4w t -- "u 1 - Hi :K - Il- 4- - t- - - f-- - I - M-H T- - - M T TM 64l -H A4 fl4 l+H - - L- JL - I L - T I fli i tIt IP PI T" . I - I- - - - Itil 1 1 - . 4 .A L . 4.. 1 . 14 ow rCOXPh i d t A . INEA I% U . It t.7 GRAPH PAPER PRINTED ip U SA. 0 00 Figure #9. DIOT-CONS Subject GM (Average of 10 Tests) 4-- ... ' I IA(F2F FF) Hz I "1 '"11 ' T1T ' r, -I- Empirical Predicted----- -4' L4 7TT~T~i~p-422 ----1 -- -- 4 -t 1' --- - - --7 1 441I~4 C2ZA14A41 IT, _--- -- -- r- z '4i z 2 -e-~ -~4-{ -~ '-,4 it I- H t ~ H-i-H- -~ Ht--H- t4 ~ j4-, -i -~-~ L~4~ ~-1'--' 3 1 20I L 41 3 C 51 I I -- -------- ---------- A 7- +1-LL .. ! I E 41 H4t- -, -r l-H3j-A4R TIA ii-T- (js i 1 1 1 1 1 11 11 1 11 1 |||1 11 1| ||| 1. 1 11 11 11 11 l ill lil t I n t e n s it y I n t e n s it y dB c o m p. s t a n d . - MM " IIIJ Utf lhLII IWI I+1IH i4- ri i- n s- u n -s JI1 -- -44 - i- L.A . L f IJ ltI I Iit IwI I tI 1 4 4 4-14 +1t - Irn tiv I Li HT h-d i 1 -I 4 F H+ fl I-i tt l it - 1I ~ l tt It i EEE rJQ CD 0 c+%- . CD . L CD CD - 0 - I - - - f- - - 1 L L A L LL L- L I- * I I t hE EL t 1- t 0 H n 0 z 4ItH tiIIf t i I -1''1 1!'1 F1 ] TI , 44 -1 L 1] T L L[ L iL t t i { - - J-- L- 4- L. 11 11 If 1 1 A ' KP j~Fv L WW I- - l- - - - - L I1 . IL - It I. A 4 - I... L Pl o M CD P - .u- . - 1 - I - - - - - - - - - , I A - Iu i- - A 11 7' - L- 6 1 - + - - - - - - - - t - I-+ tI I A tu - ti . A. a - I+ I- 14 H - ~ T1 I~ 1 tr j I II I- I N - - - M I - - 1 ri ! i I i i i ti! I'l I'l lri ! I I 11 ll 1 111 11 -H -M 111 11 11 11 1 H IM H I Tf f - 4+ H- 4 L- " L I I T I IL L L-4 -A 1-1 1 44 4- 14 -1 m I I I q I I H F+ H - - - 4 4 44 4 t+ - H + -- i- If - - 4 - . T -A-- - L- -t IM -- - - t - t 4 1-4 - 1 1 1 1 1 1 H I -H HN 1d I I I - - - . . t- tl 9 is I I TIT TM - i- -FF R-J ]:Fr -F-f w T w f - 11-1 4 -4- '+ 1-- 1 T 4- 1 -- T fl - - il- 1- 3. 71 " I- IF HI F-I i - 1 I- R r Ii11 1- t, h $- - lll fl-' R-F 14 44 : . F-f f:ff -33- the empirical and predicted results. It was concluded that the combination tone hypothesis for the explanation of the 'dip' would be tested by introducing the stimuli dichotically (each frequency to a different ear). Since it is known that combination and difference tones are a monaural effect,---or more specifically, originating at the basilar membrane of the inner ear, if there is only one frequency introduced to each ear at a time, there would be no combination tones 20 present. The pitch of the sound would be the same; however, the confusion would vary in some complicated manner. This shall be discussed further later on in this paper. For all the following tests,the standard sounds as well as the comparison sounds were all introduced dichotically. There were three subjects tested ten,nine,and nine times each for the dissonant standard and two subjects tested five times each for the consonant standard. Figures#11-13 show the curves for the dichotically introduced stimuli with a dissonant standard (dich-diss). The curves are most striking with respect to the 'dip' in that they are not affected to any significant degree by the fact that there are no nonlinear tones present. If anything, the 'dip' is even more pronounced. This fact seems to imply quite strongly that this harmonic effect seems to be the result of some central nervous system phenomena, or at least somewhere past the neural joining of the two ears (superior olivary complex). It probably occurs more centrally than this due to some psychoacoustical and neurophysiological re..sons which are beyond the scope of this paper. At any rate, G PAPI GRAPH PAPIER NWe74wu;S.A. Figure #11. I- - 'G -4 - I - -4 DICH-DISS Subject GM (Average of 10 Tests) r P ~ ~ ~ ~ ~ ~ ~ ~ ~ I AL'%.-n..eda- * a *-- "" AM T-f J.M.M1 . Emp irical 1441~ t Predicted -------- .... ~~4 A. -4 ---- 4 -1 -- h4 --- L A4,m - : -1-- - ----JJT 7 T4 IIl -4 1 -- I* 17 1JI!J17 ;H k- 4 - 7593 i+it --i-l -5+4 -- t . A' ;;zliW -----1 -~-' - ii-- (F (z2 -- Ls7 - --- - -1 -EIE 4 I - -- 4 - -- J. J '-14-A J 1-4 -4-. .- V 4- ..--. 4 - I- 4-P---t- -tl.., l .... l.,b . 1000 0 0 -5 I 0 BW- .-i --, , 1 , " ' ' 1- -. -- - -- --- i --- ' . . --i i- -1- - -++- - -7--' . . ! 1 1 . . i 9 , ! m i i 1 1 - I i i m i i i I I i ! ; I i - i k - 14 T T 14 tf i T. T N I A t r- -r v v v S--4.4-1 4 NO. 31.193. 20 DIVISIONS PER INCH (120 DIVISIONS) BY TWO 4 2!2-INCH CYCLES RATIO RULING. IN STOCK DIRECT PROM CODExJl CO. NC NORWOOD. MASS. 02 GRAPH PAPER ie\ PUIN1~ INU SA a 0 DICH-DISS Subject JS (Average of 9, Tests) . EmpiricalPredicted-------- -4--. ~I _ -1 ~~Thz'i U -Frd - - rd: t 1 O - 0 -4-4-- -4-4-4- -4--- W E I1 ' - A 1 11 -+ 4 1.- -- ~ -4---4 JAI- -J- - t iIi . J 4---L T -44- TI I-, T'- 4* - - .-- -1 i. -. -- -- -- - - -. - .-- I-I - -- P4t Htil I2~ -4-4 L7~ 4-4- -tt -41--- I -i b AF (F2 )FF) Hz 2W AO& A 1 Figure #12. :1~zIz L1j A .2 0 LAi U' H---."' ft- I : , .U% , - -.TOKI -4-4-1- - ! ! , i i I i i 0 a 1 , m ! I m i i I ! . , i , IF f . i ! I i , . 7 ! I -r i-irF-T-7-1 I A - - -- - - - T- 4 I I 4 I TI,+4- H4-- -4- -4 4 7---,, T71-=9Z;i F777 TF T "- 4-1 -- L4 X11-1, .l -37- as stated earlier, these dichotic tests indicate that most of the effect must be attributed to an area of the brain about which little is known and as a matter of definition, it is therefore a psychological effect. The curves shown on Figure's #14 and #15 are those for the dichotic presentation of the stimuli with a consonant stand- ard. They are the most ambiguous of all four cases and in- deed are not easily explained. It is these curves howeve;, that prove to be the most interesting. These curves seem to in- dicate that although the value of the intensity - intensity comp. stand. was lower at the harmonic than that at the dissonant, there was no apparent 'dip' at the consonant. Instead there is a very large depression centered on the AF corresponding to the consonant. The possible explanation of this fact and the fact that for the diot-cons casethe dissonant end of the curves was- not elevated above the value of the consonant, as is here, lead us to conclude that we are not using the correct parameters. If instead of using the AF for the abscissa, we.. used the psychoacoustic value of pitch and the relative confusion (or more simply, the difference between the standard deviation of each pith determination of the standard subtracted from the comparison) as the parameters, these equiloudness curves should be more consistent under any case. The idea that the loudness of a discrete complex sound is a function only of the intensity, pitch, and pitch confusion is of course, a new one and has not been directly proven here. However, the standard deviations of GRAPH PAPER V.4 Ri ire #14- T I ! .I I I I I 'I i'*i ' Subject GM (Average of 5 Tests) - Empirical- -Predidted ----------- ~~LH H-A+1 4-+ iici4: TT~F 2 4~TF1 z1~ .,+---r -i -I-H 4- -T 1Tdi 1 .z~J 1~-Tr1 1y~TI j~?i~t~4 ~ i jill-fl I -L I _. _ _ _ 41~ - AZ1Z~4IJ~-i~44tz AF (F2-F1 ) Hz b ' I I 1 I U 2 -1 1 1- 1 i a 0 0 I I 1 fl 4- a4J P 4i- 0 - ue * 3 :2. 0 I I ~~1 'T 000O .Awp I . . . . . "-rr-1-444 ': . " I I -4t D -F--"r T - 4# GRAPH PAPER "- 0 5 DICH-CONS ject JS (Average of 5 Tests) -. -T-I I , I F1 1 -' - I AF (F2 -F 1 ) Hz ,.x -m orrTM T'N'. I _ i A __ Empirical Prd ted- - - - -- 4~1~7~1 - Figure #15. Sub m) f4J u to - J I w iTooo t -T,- 4 T-- -V'4-'; 1 1 L7 J1 - --- , -ul - ti - +4, -1-t -- -- A-1 4 - . - - - -1 - -n +H4-4 - 4ml ! I I I I I I . in r- 1 -I - I 'A 1 -L4 14 ] .- T d4-1 :T! .7 -Ir- ~ t I- ---- 1 --it'.'i -40- the loudness determinations for each A F tested are shown on Figure #16 and they certainly seem to agree with the above hypothesis. The similarity between these curves and their respective equiloudness curves presented (Figures #4-#16) is almost uncanny. The fact that the shape of the dich-cons case for both types of curves has almost exactly the same trends, with the curve being high at the smaller AF's and showing a somewhat large depression centered at the jF of a 2:3 ratio, indicates that the 'ambiguity' of the sound is directly proportional to the loudness estimation. Other interesting similarities exist for the other three cases and their respective curves; since a very definite 'dip' occurs at the consonant and for small AF's, the values 6f the intensity - intensity are low. comp. stand. Therefore, with the above explanation, there isn't neces- sarily any inconsistency with this last case (dich-cons) con- cerning the disappearance of the 'dip' at the consonant. Har- monically-oriented sounds have been known21 to have much smal- ler pitch ambiguities (or pitch confusions) than comparable sounds and this of course, is in accordance with this hypoth- esis. On the other hand, generally speaking, dissonant sounds have much greater pitch ambiguities (as can be seen analytically from Goldstein's pitch model22 and experimentally from the 23 24work of Smoorenberg and Plomp ) and this also is very much in agreement with this hypothesis as well as the observations. Almost everything seems to fall into place. Since the loudness ambiguity resembles the average loudness estimate quite closely, and if we assume that the loudness ambiguity is directly related -t UJ-,I . I. I.U..U GRAPH PAPER 0 - . ,.. t .-..- . u. MASSG. u2 PRINTED IN U S.A. is STANDARD DEVIATION OF PREVIOUSLY REPORTED RESULTS I F- -1 - If -I --it, h -t-- i re #.1 . DIOT-DISSI DIOT-CONSI DICH-DISS DICH-CONSI ---- (Avg. of 33) ,(Avg. of 19) *------(Avg. of 24) U.e.'-- (Avg. of 10) mm -:-- ::p -P- -4- -fI till] t il lr j j - -[f -4 -- - 1J 1- - 4- -- $414 14 Ilt~ihtI il 4- fI I I Efl 1-i~~i ~ 1 FVIiI 1 T T C I 1 0tll tlltll11 LtI IIIIII t i.I I T11lT I S 4 S 2. I -I!1r 1E 1t11]'FT-4 Cd-14-144+1+1 -1 4IW -IiH A 4-"t tt14 ttl+Sj] Ul till Ltd -44~~I 1l~lI4 illdHA 14-hltt '': i~~4k II~1 A F. (F2 -Fl) Hz 5001000 0 TT17YIJITPJ ${P1TT11t1i~ limit ilti 41444144411 , -A - 14 4--"-4-W- I1 if i 1 1 1 1 P 4 i I I i - i4,v- +1 I ! T I I -4 -" -4-4 -T-WT717-1 1 1 q q I i "4444 44T F-J, -TA's 11 fl-0-1 14--1 tijili ---,LT- i -il-i, r4 14 +44J-L .1 I 1-9 5,00 to the pitch ambiguity, the loudness estimate is therefore some function of the pitch confusion also. This assumption does not seem too far fetched since it was determined here that the loudness of two-tone complexes is some function of pitch. The diotically presented stimuli produce