t he university ot cbtcago ro m a n wyo ur: no c xxuu.“ COMBINATION TONES AND OTHER RELATED AUDITORY PHENOMENA A DI SSERTA TION SUBMITTED TO THE FA CULTY OF TH E GRADUA TE SCHOOL OF A RTS AND LITERATURE IN CANDIDA CY FO R THE DEG REE OF DOCTOR OF PHI LOSOPHY DEPARTMENT OF PSY CHOLOGY BY JOSEPH PETERSON u rr N o o r r un Psvc a o wc xcu. Rm " wa Sm u n . Pvumun AS “o uo c 39 , 1 908. PREFA CE . The first part of this mo no graph is devo ted primarily to a critical exposition of the important theories of combination to n and t t nt e n es a s a eme of th facts upo which they rest . This undertaking i nevitably leads to the mention of a considerable number of closely related phenomena whose significance for I e general theo ry is often crucial . n view of th conditions l n in the t t the t it n th t prevai i g li era ure of subjec , has bee ough expedient that this presentation should in the main follow h n n . n c nt nts c ro ological li es The full a alyt ical table of o e , t t t the n int n n oge her wi h divisio o sect io s , will readily e able he x readers who so desire to consult t te t o n special topics . The second part of the monograph report s cert ain experimcnta l t n t observa io s made by the au hor o n summation tones . In the pages which follow several physical terms are used which are commonly understood and need no defin i tion here . A few may be newto readers no t familiar with the literature l ” of acoustics . A pendular ( or pendu um ) vibration is a in - t n I t t n the simple , or s us form, vibra io . n several quo a io s ” ” n t and t n the n wor o e , some imes sou d , occurs where mea “ ” “ in t nt t n g is precisely that of he word tone . I errup io " ton e is used synonymously with i ntermittent tone . By transformation of the primaries is meant the process of superposi tion of vibra tions explained by Helmholtz in his m t t t n t n t he n n t n t n a hema ical de ermi a io of origi of combi a io o es . A c in t n t n o f r t r f n n omb a io o e may , cou se , be ei he a dif ere ce to e or a summation tone . and to n t the two t n Where p q are used desig a e primary o es , a p refe rs to the higher nd q to the lower tone . Frequently h and l are used for the higher a nd lower tones respectively : t e n no w h se are most commo ly used , especi ally by German ’ t the writers . N is some imes used for lower a nd n for the S t s it the e hiflier tone . ome wri ers have u ed for i nterrupt d and m for the interruptio n tone ; others have used these letters I l l i v PREFA CE . i th n e reverse order . Since quo tations are so frequently made from various writers no exclusive use of any of these letters can t well be adop ed here . In n t n the t an t n i desig a i g oc ave of y o e , usage also var es . ” ” S t c e. o t c and t o t s ome wri ers use , g , where hers use , s ill her c . In t s the no w n C C z hi paper more commo usage , g , l ” 3 C c 1 . c c C n o t c n 2 . vib , , , , has bee ad p ed , bei g 8 d I have taken the liberty to change all other markings into this t in the he ex nt l t t t n . In t erime a sys em quo a io s p par , however, the n x e where Koe ig forks were used e clusively, I hav simply th n t n . Ut Re etc . e en e. employed desig a io s used by Ko ig, g , a, s, , t h U n t e c 1 2 . z bei g same as ( 8 d . v ) In quo ting fro m the French and German where the trans t n o wn e n t t n la io is my , I hav used si gle quo a io marks t R t t E ter The heories of u herford , Waller , Hurs , mile E and t no t n n in t Kuile , wald, o hers , have bee co sidered his h . In th n on t e t t nt te paper e opi i of wri er, hey have co ribu d 5 e. n t n to the t t n n t n . o hi g subjec immedia ely u der co sidera io , , t in seco ndar t n n but as et co n cer a y audi ory phe ome a , are , y , cerned essentially with the prima ry phenomena of hearing . It in t nn t n to x t is a pleasure , his co ec io , e press gra itude and to c n a t n to t a k owledge oblig io my eachers , Professor J. R. l n r. n a d D . t on o o e A ge l J B Wa s , fr m wh m I have receiv d n t n and t t in co s a t advice pa ient cri icism . I am much debted to r . n n n M . W V . D. Bi gham for ki d suggestions a d assistance . I also wish to thank my fellow students of the psychological t t f x labora ory, who served as subjec s o r my e periments C T ON ENTS. A P RT . H STO C L N D I I RI A A Cac L. : 1 mmy BSE V T S A N D a e B T N m m . mal 8 E O R A ION T s , COM INA IO T To N Es, BEATS , RESONANCE PH BN OM BN A , IN BRRU PTION m TON Es A ND so FDa . PI E-HELM HOLTZ IAN DEV ELOPMENTS ’ a l i es e un r r scoveri N turall to . o h o ( ) Ea y D a y L ad T Y g s T e y, Becaum the First Difi erence Tone has a Frequency Equal to that o f the Bea ts o f the Primaries . ' 6 But h i l eo hm ( ) P ys ca Th ry is Opposed to such a View. O s ( c ) The O hm- Seebeck Con troversy ’ HELM H OLTz s PosxTrON A N D CON TamurrON s ’ ( a ) Being a Physiolo gist he Defends Ohms LawBetter than did Ohm imself who was h si i t H , a P y c s ’ b e he ( ) H elmholtz s R sonance Theo ry Illustrated . T Resonance o nce n as l el un . M r t io w u b . o ull C p Vag e y H d y T Y g , J e and o thers ‘ ’ ‘ ’ ( c ) The Princ iple o f Resonance ; Perfect and Imperfect o A li tio n to Anal i in Rwona t rs. pp ca ys s the Ear ’ 4 Wh elmho ltz o ul no t Ac ce t oun s heo r e ( ) y H C d p Y g T y. Th Pla ce of Stimula tio n in Co chlea is Impo rtant ’ ( e) Helmho ltz s Explanatio n o f Beats and o f Combinatio n ‘ ’ ‘ ’ ones b T , ( r) Subjective, ( 2 ) O jective I 3 , (I) From Theo retical Co nsideratio ns he Disco vers the Summa tio n f terw e one hich he A r s e rs. H thus T , w a d H a Ob ’ ta ins Ano ther Objection to Yo ung s Theo ry ' ( 1 ) An Inco nsistency in Helmho ltz s own Position ’ Bo sA N U ET s ATTE PTE P Q M D SU PLEM ENT . ’ ’ BosAN QU ET s STU DY OP B EATs ( FA voa AELE To HELM N OLTz s Tq av ) ’ mmAPP S As O PP NT To H eLM E LT Ko EAR AN ONE O z s VIEW . a Sho ws tha t Primaries o f Lar e Inte r ( ) g rval Beat. Lawfo the itch o f and lower be ts which ma p ”W a , y give rise co beat no ees o f similar orders V vi CON TEN TS . ’ ( 6) Koenig s Viewas to howthe Ear Experiences Beats and Beat To nes : Any Perio dic Fluctuatio n within Certain Limits o f Frequency may be Sensed as To ne i The nterrutio n ( c ) Experiments in Suppo rt o f th s View. I p ’ o ne enerate b nterru tio n o f a o ne b me ns T , G d y I p T y a o f a Perfo rated Disk K B WAs N OT TH E RST To P F R U CH ExPEruM ENTs O N IG FI ER O M S , HOWEV ER ’ ( a ) The Webers Experiment o n Rotating Tuning Fo rks ( 1 82 5 ) ’ ( b) Seebeck s Theo retical Investigation o f such Pheno mena ( 1 844 ) ’ ( c ) Helmho ltz s Experiment and M athematical Explanatio n d ee e eats the Weber x riment with li h l D f ( ) B tz R p E pe , S g t y i ( e) Stefan Co ntinues the Experiment ; Hears the Varia tio n o n d M athem tio T es an Develo ps atica l Explana n o f Them.