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Stage 3: Basilar membrane filtering The simulationof the bandpassfilteringeffectof the basilarmembranewas achievedusinga set of digital u fi72 critical-band gammatone filters suppliedto us by Roy PattersonandJohnHoldsworth Pattersonet al.

The theorybehindtheserounded- exponential roex filter shapesis givenin Pattersonand Moore The gammatonefunctionprovidesa close approximationto the impulseresponseof the roex filters. How- ever,this divergenceonly occursat 30 dB belowthe central tip of the filter.

The filtersare alsolinearandhavethe same Despitethesereservations, we believethat - Autocorrelograms -- thefiltersworkwellasa firstapproximation. Modeloutputat threestages of processingin response to a stimulus composed of the first ten harmonicsof Hz at 50 dB1 per component. Pressuregainsat the outerand middleear seetext. Howitt:Phasemodel wnloaded 02 Jun to The verticalline graphto the rightof instantaneous amplitudeof the signalafter filtering,and g, thefilteroutputsin Fig.

Becauseof the The amount of transmitter released into the cleft at time wide rangeof stimulusintensitiesused,the cochleogram t is k t q t dt, whereq t is the amountof transmitterin a scaleischangedfromdisplayto displayandtheverticalline free storelying closeto the membrane. Transmitteris recoveredfromthecleftby reuptakeinto The stimulusin Fig.

Someof it is, however,lost from parison with the calculatedexcitation pattern given in the cleftandfrom the systemaltogetherat a ratel c t. This Moore andGlasberg ,Fig. Recoveredtransmitteris held brieflyin a repro- cessing store[contents,to t ], whenceit is returnedto the D. Stage 4: Mechanical to neural transduction freetransmitterstoreat a ratex w t , whereit is againavail- The outputof eachfilterwaspassedto a hair-cellsimu- ablefor releasefrom thecell;r, l, andx areparametersof the model.

The modeland its properties transmitter,cleftandreprocessing stores,but deficiencies in aregivenmorefully in Meddis , anda computer theamountof freetransmitter causedby thelosses fromthe programis givenin Meddiset al. Amounts of reneeis linearly related to the amount of transmittersub- transmitterheld in the free transmitterpool are expressed stancein thesynapticcleftbetweenthe innerhair cellandits here as fractionsof an arbitrary maximum valuem, which corresponding auditorynerve hasbeensetto unity in this implementation.

This fiberhasa normally, 0. This permeabilityis modulatedby the of auditory-nervefiring Fig. The modelalsoshowsphaselockingto stimulusfinestructureup to 5 kHz. This latter propertyis crucialto the phenomena discussed later in this article.

Further details of the model's performancecanalsobe foundin Meddis , and Meddis et al. The verticalline graphto the right of Fig. Meddis andM. Hewitt:Phasemodel wnloaded 02 Jun to More elaborate functionsfor Wit are available Gaumond et al. Note that Fig.

For the stimuli used in this study medium intensity,continuous stimuli , refractoryeffectsmakevery little differenceto the probabilityof firing. Someproperties of thehaircellmodel: a rate-intensity functionat ence on what follows and it will be omitted.

We assume that onset i ms andduringsteadystate; b rateresponse to a l-kHz, ms tonepulse; c timeconstants of rapidandshort-termadaptation; and d n is largeenoughto justifya smoothapproximation to the phaselockingto stimuliin therange kHz.

This is an assumption be limited by a time constant11,of approximately2. However,real The histogramentryfor theinterval6t at timet for channelk fibersdo showa variety of differentproperties,particularly can be found as follows: in spontaneousrateanddynamicrange.

That varietyhasnot beenmodeledin thisimplementation. The computation of theinterspikeintervalhistogramis E. Stage 5: Refractory effects in the form of a runningautocorrelationcalculation. Lick- The probabilityof spikegenerationin a fiberdepends on lider formally demonstratedthe autocorrelationna- the recenthistoryof firing of that fiber. This effectwas ap- ture of his system. We shall, therefore,call the histograms proximatedby the followingformula autocorrelationfunctions ACFs to emphasizethe point.

Licklider doesnot explainwhy the afteradjustmentfor refractoryeffects,pit is the unadjusted time constant should be 2. Note functionsuggestsa similarvalue 3 ms.

Accordingly,the histogramwas,in practice,computed We set only overa 7. Howitt: Phasemodel wnloaded 02 Jun to Figure 3 c showsthe summaryACF at the bottomof -- Autocorrelograms - the figure. For manypurposes, thisgivesa satisfactory result. For example, in Fig. ACF Period ms. Missing fundamental FIG.

Modeloutputin response to resolved harmonics. Thestimuluscon- Figure3 c illustratesthe pitchextractionabilityof the sistsof the 3rd, 4th, and 51hharmonics of a Hz fundamental. The stimulusiscomposed of a funda- mentalanda setof successive andequal-amplitudeharmon- ics in cosinephase. However, listenersperceivethe satme pitchevenwhenthefundamental component ismissing.

Fig- ure 6 illustratesthe response of the modelto a stimuluscom- posedof only the 3rd, 4th, and 5th harmonicsof a Hz fundamentalat 50 dB1 per component. The summaryACF showsa clearpeakat a periodof 5 mswhichcorresponds to a frequencyof Hz even thoughthere is no component presentat that frequencyin the stimulus. When the ACFs are summedvertically,the presenceof a peakat 5 ms in all activechannelscreatesa major peak in the summary ACF.

However,the model producesappropriatepitchestimatesevenwhenthe compo- nentsare not resolved. Figure 7 showsthe model'sresponse to a three-component stimulusharmoniccomplexwherethe - componenttonesare the 14th, 15th,and 16thharmonicsof 81 Hz. Here, the individualcomponents arenot resolvedby the filters. The modelproducesan ACF peakat Hz. Period ms. We shall return to this issue FIG. Model outputin responseto unresolvedharmonics. The stimulus below in connectionwith the "existenceregion" of virtual consistsof the 14th, 15th, and 16lb harmonics of a Hz fundamental.

The importantpointhereisthatthemodelidentifies a ent from those predictedby the model. The two lowest pitch in both circumstances and it doessowithin the same matches and Hz are substantially lowerthanpre- explanatoryframework.

Bothkindsof pitchperceptarise dicted by the model This effectis be- from the samemechanism--theaggregate of a setof inter- lievedto be causedby nonlineareffectsin the cochleawhich spikeintervalhistograms. Theseadditional B. Ambiguous pitch components appearto blendwith the originalstimulusand Many stimuliwith a pitch quality yield a numberof alterthe frequency of theambiguous virtualpitchesoneither discretepitchmatchesin matchingexperiments.

Schouten et sideof the predominant fundamental pitch. Their otherharmonics andat thesameamplitude , a component subjectswereaskedto matchthepitchof thisstimulus witha likelyto bepresentash nonlineardistortionproduct.

It cor- secondharmonicstimulusof variablepitch. Betweenthesevalues,therewereregions where the 10thand 11th harmonics. The resulting summary ACF pitchmatcheswereabsent. Thevalleys Hz. The biggestdiscrepancy betweenthedataandthemod- betweenthesepeaksrepresentregionsin which pitch el'sresponse isnowlessthan3 Hz. Wehavenotpursued this matcheswouldnot beexpected. We shalldiscuss the discre- lineof investigation further,in thisarticle,because theap- pancies in pitchestimates below.

Thefirstpointtonoteisthe propriatemethodformodelingthenonlinearities introduced model'spropertyof generatinga numberof discretecandi- by the cochlearemain controversial. The pitchmatchesof Schouten et al. Pitchshift of equallyspacedcomponents Inharmonic equallyspacedtonecomplexes canalsogive riseto virtualpitchpercepts Walliser,;deBoer,; Schouten et al.

We canthinkof these complexes asharmoniccomplexes whosecomponents have all beenshiftedin frequencyby the sameamount.

Inhar- monicstimulisuchastheseareimportanttheoretically be- causetheenvelope of thestimulusisnotaffectedby thefre- quencyshift. Discretepitchmatches Schoutenel al, The stimulusis the FIG. Pitchof stimuliwith inharmonic equallyspaced components. Themarked peaks The stimuliconsistof a six equal-amplitude harmonicsof Hz with a in the summaryACF suggest that pitchmatchescouldbe madeat The majorpeaksof thesummary , ,, and Hz.

ACFs in the regionof Hz indicatepossiblepitch matches. Meddis and M. Hewitt: Phase model nloaded 02 Jun to The Hz shiftconditionyieldsa dominantpeak slightlylower than Hz but a Hz shift againbrings 34o thecomponents backintoa harmonicrelationship 2nd-7th harmonicsof Hz andthe dominantpeakisagainat harmonic number of lowest Hz.

Thestimuliareequallyspaced, equal-amplitude from a morecompleteexplorationof theeffectof shifts. The components witha izspacing. Thepointsplottedindicate themajor stimulusisagaincomposed of sixtonesseparated by I00 Hz.

Both6 and! The sequence beginswith a stimuluswhoselowest componentis Hz harmonicnumberis 1. Given that we love him dearly as a friend and found that we have excellent chemistry both on stage and in the studio, and he is a master of all of his instruments, hiring him as our full-time bassist was the logical solution. His irreplaceable ability and insight brought so much to the production and bass on Periphery II: TTIP - we don't feel that anyone else would be able to take on the roles he has filled.

He has already been writing with us for new material, and we are proud to have him on board! Having felt like part of the "family" for quite some time this feels like an incredibly natural step. I've had the pleasure of watching them grow to their current stage and can't wait to see where we can take the band together! There is already a trailer for the album which you can check out below, and you can also make your way to the Sumerian Records store to pre-order some of their merch and CDs.

Muramasa 2. Have a Blast featuring Guthrie Govan 3. Facepalm Mute 4. The fact that they managed to do this while keeping their heads above water in the sea of copycats in commendable. This is the first time that Sotelo was actively involved in the writing process, as he was a hurried addition to a debut album that had long been written before his joining. With Periphery II , Sotelo wrote his own lyrics and vocal melodies, and it shows with his confident and charismatic delivery.

His growth as a vocalist is remarkable in all forms, which should win a handful of critics over. He is without a doubt a driving force on the record, and anyone still clamoring for an instrumental release is irrationally begging for a fraction of the big picture. Sotelo was also adamant about recording vocals without the use of pitch correction, save for backing harmonies. As such, his performance feels much more organic.

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