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Part2[Chapter1:]69OnMensuralMusic

[c7r]Ihavecompletedthefirstpartofthisskill(ars)andnowwillapproachthesecond,inwhichifIwillbealittlefreerandmoreprolix,letthereadernotwonder,70sincethepresentsubjectprevailsbyfarovertheformerbothintheextentandimportanceofthesubjectandatthesametimeinsweetness.Indeed,itprevailsinthemultitudeofitsnotes,thediversityofitssigns,theinequality71ofitsTactus72andProportions,sothatyouwillfindnofacetthatdoesnotdifferfromtheotherinsomedistinction.ForthisreasonattheoutsetofthislittlebooksoalsohereIadmonishtheboys73thattheyshoulddiligentlyinquireintothesong(cantilena)presentedandthoroughlystudyitsnature,observethesignsofitsDegrees74(gradus)andofProportions,AugmentationandDiminution,aswellastheindividualattributesofthenotes,lestcarelessnessandignoranceoftheseimposeuponthem,athingweseehappensinthepracticeofmany.Butnowtothesubjectathand.Notatedmusicistheknowledge(scientia)75ofsingingmusicalDegressandProportionsaccordingtocertainnotatedmeasure.Thisconsistsinvariousandplainlydissimilarshapesofnotes,restsandsigns.Ashape(figura)istheveryconditionordispositionbywhichanynoteorrestcanberecognizedwithcertainty.Indeed,someofthenotesarecalledsimple,someligatures,somemajorandsomeminor.

69ListeniusprovidesnochapterheadingfortheopeningofPart2.70Schooltextsforteachingmusic,especiallyinthetraditionoftheLutheranLatinSchools,weretypicallydividedintotwosections,thefirstdevotedmainlytomusicfundamentalsinsupportof“choral”music(monophonicplainchant),andtheseconddevotedtomensuralmusicinsupportofpolyphonyandthecomplexitiesofmensuralnotation.71Ihavechosenconsistentlytocapitalizewordsthatareimportanttermsinthetechniqueofmensuralnotationandrelatedsubjects.Ihavefoundthatthismakesthemsomehowmoreemphaticandseemstogivethereadersomethingto“hangonto”inthecomplexandoftenconfusingdescriptionstofollow.72Hepreviouslymadeclearthattheequalityofrhythmicvaluesisadistinctivecharacterofplainchant.73TheaddresstotheboysinthethirdpersonisasubtleindicationthatListeniusistalkingtotheteacherinateacher’stext,nottothestudents.74“Degree”isthecommonEnglishtermatthisperiodforthedifferentmensurallevelsofMood,TempusandProlation.75Listenius’syntaxhereisnotquitecorrect,butthemeaningisclear.

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OntheNumberoftheSimpleNotes(Figura)

TheThreelasttypestoghetherwiththeirrestsaremoresuitableforinstrumentalmusicthanforthehumanvoicebecauseoftheirexcessivespeed.Theyareaddedasakindofsupplementtotheupper

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ones,withwhichtheancients76arereportedtohavebeencontent,notbecausenomoreandnomorerefinedcanbeconceived,butforthesakeofamoreelegantandsweetmelody.

[c8r]Chapter2:OnRests Arestisalinedrawnthroughlinesandspacesdenotingsilence.Oritisashape(figura)indicatinganartisticcessationfrommusic(cantus),whichindicatestothesingers77thattheymustbrieflyabstainfromsinging(cantus).Musicians,78then,positionrestsbothforrestingthevoiceandforthesweetnessofthesong,which[rest]existsbothinFugasandmusicaltypesinperfectprolations79thatenterreciprocally,andalsoin[voicesin]harmonies,80bothforcadencesandforreintegrating[them]bymeansofsilencesorproceedingotherwise.81Likewiseforavoidingprohibitedintervals,suchasconsecutiveperfectintervals,82concerningwhichIspeakinthethirdpart.83Thereare,then,sevenrestscorrespondingtotheaforesaidnotes,exceptingtheMaxima,whichhasnosimilarone,unlesssomeonewouldliketoattributetoitageneralrest.84

76“Ancient”couldrefertothoseasrecentlyasonlytwoorafewgenerationsprevious,thoughsomeauthorswoulddistinguishtheseas“veteres.”77ListeniususesthisexactquotefromGaffurius,PracticaMusice,Bk.1,Ch.6,“estfiguraartificiosamacantudesistentiammonstrans,quaecantoribusinnuit.”GaffuriushimselfseemsindebtedtoTinctoris,Tractatusdenotisetpausis,Pt.2,Ch.1(CSIV,p.45)78Seay’stranslationofthispassagefrom“Musicians”to“otherwise”isquitedifferentfrommyown.Thecriticalpointisthatitisacoordinateconstructionconnectedwiththeparticles“tum...tum,”whichmeansthattheirrespectiveelementsmustbekeptdistinct.Thus,itisnotpossibletotake“perfectisspeciebus,etc.”fromthefirstmemberandtransferitto“concordantiis,”inthesecondmemberasSeayhasdone.Listeniushasalsoalreadygivenustheterm“modus”oralternatively“intervallum”forinterval,soSeay’sunderstandingofspeciebuswiththatsensedoesnotseemjustified.Listenius’Latinhereis,frankly,oneoftheworstspotsintheentirebookandSeay’sfrustrationismorethanjustified.79Listenius’referencetofugaasaperfectspeciesisilluminatedbyTinctorisonthegeneraofcompositionsinTractatusderegularivalorenotarum,Ch.1,“Porrocantusaliiexomnibusquantitatibusperfectiscomponuntur.”“Furthersome[compositions]arecomposedfromallperfectquantities.”ThisiselaboratedinCh.16:Maxima=3Longs,9Breves,27Semibreves,81Minims,etc.Suchasongusingallperfectsubdivisionswouldmakeforverylongphrasesandhavegreatneedofrestsfortherefreshmentofthesingers’voices,asListeniussaysinChapter4whenconsideringMajorMoodPerfect.Ibelieve,however,thatListeniusprobablymeanssomethingmoregeneral,as“compositionutilizingperfectsubdivisionsatmultiplelevels.”80ItseemsthatListeniusismakingacomparisonofhowrestsareusedintwodiferentpolyphonictextures:strictconunterpointasintheFugaascomparedtothefreerharmonicallyconceivedpolyphony,thelatterofwhichheexpressesbyconcordantiis,here“[voicesin]harmonies.”81ThisphrasemaybeanattempttoconvertintomusicaltermsRhau’scommentsonrestsunderhisfirstheadingwhenhespeaksoftheorator’suseofsilence,Enchiridionmusicaemensuralis,Chapter1,G5v.82ThisalsodealswithpurposesfoundinRhau’ssamediscussion.83Thereisnothirdpartnordoeshediscussissuesofcounterpointandvoiceleadinginthisbook.Listeniuswroteonlytwobooks,thisandanearlierRudimenta.Thereferencemustbetooneofthelessfamous“ghosts”thatmusicauthorsseemoftentobepredictingtowritebutnevergetaroundtoorneverlivetocomplete,Praetoriusbeingoneofthemorefamousexamples.84Heexplainsthegeneralrestbelowasabarlinethroughthestaffthatseparatespartsofthework.

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Nevertheless,observethatthisdoesnothappeneverywhere,forinAlterationcertainnotesarealtered,namely,becauseofthecompositionoftheternarynumber.85Indeed,restsofthesearenotaltered,onthecontrary.86InImperfection are[c8v]imperfected,therestcorrespondingtoitisnotimperfected.Intheremainingtypes,namelyAugmentation,DiminutionandProprotions,theyareequaltotheirnotesinwhateverwaywetryinitsplace.Therenowremain,asIwillbrieflytell,thesubjectofmodalandgeneralrests. Modalisalinefillingthreespacesorfourlines,equaltoaperfectLong,indicatingeitherMajorMoodPerfectorMinorMoodPerfect,whosenameithas.Majorisdouble,Minorisotherwise.Tobesure,notwithoutcausedidFranchinus[Gaffurius]saytwoareplacedforMajorwhenweascribeonetoMinor.87Nowthegeneralrestis[1]astrokedrawnacrossthroughallthelinesinthemiddleofthemusic(cantus)andcorespondswithcardinalnotesor[2]repeatsigns.88Asong(cantilena)repeatsthepartthussetapartandseparatedfromtheremaining,evenwhentheotherscontinue,89asisseeninthemassofJosquin“Quaeestista”andinthesong(carmen)ofJohannWalther“Nonmorier.”Itconcludesthemusic(cantus)attheend.

85Listeniusdiscussesimperfectionandalterationbelow.86ThisisasummaryofGaffurius’owntreatmentinPracticaMusice,Bk.2,Ch.6.87Asusedforthispurpose,thesearenotactualrestsbutsignsofMajororMinorMood,GaffuriusinPracticaMusice,Bk2.,Ch.7.88Listeniusgivesnoclueastowhichnotesare“cardinal.”Probablyhemeansthefiveprincipalonesthathealludestoasmostappropriatetovocalmusic:Maxima,Long,Breve,SemibreveandMinim.89Itwasacommonpracticetousearepeatsigninonlyonevoicewhenitspartrepeatedasectionofmusicandtheothersdidnot.Thepracticewasstillinuseaslateasthenineteenthcentury.

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HereFollowsanExerciseontheSixMusicalSyllables(Vox)

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AnotherExerciseontheSyllables(Vox)AnExerciseontheEightIndividualNotes.

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[d2v]Chapter3:OnLigatures Aligatureistheproperconnectionofindividualnotesbymeansofastrokeontherightorleftside.Ithastwoforms,squareoroblique.Square[istheone]whosenoteisdrawnwithasquarebody.Oblique[istheone]whosenoteiswritenwithanobliqueandtransversebody.Therearefournotes

onlythatcanbecombinedinligatures,namely [Maxima,90Long,Breve,Semibreve],whichchangebyvariousconnections,formsandquantities,exceptingone,theMaxima,whicheverywhereissimilartoitself.They[thenotes]areboundinthelikemanneratthebeginning,middleandend,exceptingtheLong,whichisneverjoinedinthemiddle[ofaligature]ontheexampleandauthorityofantiquity,althoughinourowntimebycertainonesitisdoneonthecontrary,aswillbemoreclearfromtheversesbelow.Further,everynotethatcanbeboundinligatureiseitheraninitial,amedialoranultima.Everymedialisbetweenthefirstandlast.NowIwillreciteinsong91therulesofindividualones,bywhichboysmaymoreeasilycommitthemtomemory,itpleasesmetodescribe.Nowbeginningwiththeinitials.

RulesforInitials[1]Thefirst92whenitlacksatailisaLongwhentheseconddescends.93[2]ThesameoneisaBrevewhenthesecondascends.[3]ItisaBreveiftheleftsidesendsforthatail.[4]ItiscalledaSemibreveifthat[tail]leadsupward.

[d3r]Thereisonlyoneruleformedials[5]AnythinginthemiddleisaBreve,withoneexception.94

90TheMaximainoriginisnothingotherthanthetriplexorduplexLong,thefirstmentionofwhichWolfattributestoFrancoofCologne,HandbuchderNotationskunde,1,336.ThishelpsexplainwhyauthorsalwaysremarkthatMajorMoodPerfectissorareandalsohelpsexplaintheelaborationofthecumbersometwo-moodsystemofMajorandMinorMood.WolfalsoattributestotheItaliantheoristProsdocimusdeBeldemandis(d.1428)thefirstmentionofthesecondlevelofMood,theModusMaximarum,idem,1,338.91PoetryasamnemonicdeviceisanotherpedagogicaltechniquethatListeniusinheritsfromtheMiddleAges.92Ihaveaddedthenumbersinbrackets,whichdonotrefertothelineofthepoembuttothenumberoftheexamplebelow.93TheserulesconformwithothersfoundIncontemporarysourcesandalsowiththosefoundinApel,NotationofPolyphonicMusic900-1600,thoughthereisoneinconsistency,forwhichIprovideanexplanatorynoteinitsproperplace.94Theexceptionistheligaturewithanascendingtail,cf.thefourthlineabove.

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OntheUltimas[6]ThelastascendingisaBreveinanyligature,[7]Exceptwhenitbearsatailontheleft.[8,9]ThelastisaLongwhensquareanddepndingfromahigherone.95

OnthePositionsofIndividualNotesAMaximacanbeatthebeginningorinmiddleorend.ALongcanneverbeinthemiddlebutisboundattheend.ABreveproperlyoccupiesthebeginningandallpositionsASemibreveislikewiseattheendmiddleandbeginning.

95IfthisismeanttoincludetheSemibreveligature(cumoppositaproprietate)in#9,thenfurtherexplanationisrequired.Contemporaryunderstandingisthatthisc.o.p.ligaturealwaysindicatesthatthefirsttwoareSemibreves.Morley’srulecreatesthesameambiguity.Listeniusseemstohaveoverlookedthesameproblem,thattherulesrequiregreaterprecision,i.e.,“AligatureoftwonotesthatbeginswithanascendingtailisalwaysSemibreve+Semibreve.Foraligatureoftwonotesthatdoesnotbeginwithanascendingtailandallligatureswithascendingtailofmorethantwonotes,thelastnoteisLongifdescending.”

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AnExerciseontheRules

[d4v]Chapter4:OntheThreeMusicalDegrees TherearethreemusicalDegrees,namelyMood,TempusandProlation.96MoodistheobligatorymensurationofLongsandMaximas.Indeed,thereisamongnotes(insomewayasinotherthings)a96Asearliernoted,aDegreeisalevelofmensuration.Theterminologyissomewhatbefuddledbythefactthatthesystemhasbeenexpandedtoincludefouractuallevelsforthesakeofanunhistoricaltheoreticalcompleteness,yettheterminologyhasnotbeensimilarlyexpanded.Becauseofthis,Moodhasbeenmadetoservedoubledutyforboththeuppertwolevels.ThesearetheMajorMood(ModusMaximarum,MaximasubdividedintoLongs)andtheMinorMood(ModusLongarum,LongsubdividedintoBreves),respectivelycalledintheEnglishauthorstheGreatMoodandLess(er)Mood.WolfreportsthatFrancoofColognewasthefirsttorecognizeduplexandtriplexformsoftheLong,whichhethensaysProsdocimusdeBeldemandis(d.1428)wasfirsttorecognizeasModusMaximarum,Wolf,Notationskunde,1,336-338.Themensurationsignsweresimilarlyforcedintoalienservice,whichhasalreadyappearedaboveinconnectionwiththerests,where¡3indicatedtheMajorMoodand

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manneralwaystobeobserved,inregardtothemeasureoftime,whichtheyconsiderexpressedbyregularrhythm.HereintheorderofDegreesproperlyfirstplaceisallotted[toMood],becauseitexercisesitspoweronthefirstandspecialnotes,namelyMaximaandLong.97Tempusisnextbecauseitactsonthenextones,theBreves.Prolation,then,isthelastbecauseitconcernsthelastones,SemibrevesandMinims.98Forantiquitypossessed[only]somanynotes,towhichtheyattributedtheseDegreesindividually,99aspropertothemselves,sothattheymightnotbecomeactivelymixedupinall.[d5r]

MoodIs

OfTwoTypes

MajorMoodistherequisitemeasureofLongsintheMaximaandisitselfdouble.

PerfectiswhenintheMaximathereare3LongsandinaLong3Breves.¡3ImperfectiswhentherearetwoLongsinaMaximaand2BrevesinaLong.C3100

MinoristhenumberofBrevesinaLongaccordingtotherequisiteconsideration.Itisalsodouble

PerfectiswhenaLongisworth3Breves.¡2ImperfectiswhenaLongisworthonly2Breves.C2

¡2theMinorMood.Mostimportanttonote,thenumbers3and2emphaticallydonotrefertothesubdivisionbuttoMajorMood(3)andMinorMood(2).ThissituationisevenfurtherconfusedbythefactthatthesubdivisionoftheSemibreveintoMinimsissometimesalsoreferredtoasMajorandMinor.GaffuriusdiscussesthisissueinPracticaMusice,Bk.2,Ch.7,statingthatMoodisthedivisionoftheLong.Thenhesays“Nonnulliautemdicuntmodumessemensurambreviuminlongis&longaruminmaximis.”“Some,however,saythatMoodisthemeasureofBrevesinaLongandofLongsinaMaxima.”But,thenbelowhefurtherqualifiesthatstatement.“Hancautemlongaeconsyderationem:modumminoremvocantrecentiores:respectumodiinmaximaconsistentis.Veteresautemilliunicum.s.&maximae&longaeposueremodumacsiunussinealteroperfectioncomputataconstituinonposset.”“Morerecent[musicians]callthiscalculationoflongstheMinorMood,incomparisonwiththeMoodconsistingintheMaxima.Earlier[musicians]howeverpositedasingleMoodoftheMaximaandLong,asifonewithouttheother,whenperfectioniscomputed,werenotpossibleforconstituting[it].”BythetimeofTinctoristhesystemoftwolevelsofMoodisrecognized.MostearlierauthorsreferonlytotheMoodasthedivisionofLongsintoBreves.ConsideringthattheMaximawasnotoriginallyadistinctnotebutwasaduplexortriplexLong,andfurtherthatallauthorsIamawareofsaythattheMajorMoodPerfect(3Longs=1Maxima)isseldomorneverfound,evenGaffurius’reservationseemsabitofahistoricaldistortion,probablyinfluencedbyhisfamousfriendTinctoris,whosereputationforover-theorizationisfamous.Thus,theevidencewouldseemtoindicatethatthefullyelaboratedTwo-Moodsystemisaconstructbytheoristsforthesakeofatidy,butlargelynon-historicalsystem.97ListeniusnodsandomitstheDegree’sname,Mood.98By“lastones”Listeniusmeansthelastofthenotesthatheisconcernedwith,theMaxima,Long,Breve,SemibreveandMinim.HeisnotconcernedwiththelesservaluesoftheSemiminim,FusaandSemifusa,whichlatterthreearealwaysduple(orimperfect)subdivision.99Thereiswhatcanonlybeamisprinthereofsigillatimforsingillatim.Theformerwouldhavetobeanadverbcoinedfromsigillatus,“decoratedwithfigures,”whichmightleadthereadertoassumeListeniuswasawkwardlyintroducingtheissueofmensurationsigns.100NotethatListenius,asotherauthors,doesnotherediscussthepossibilityof2LongsinaMaximaand3BrevesinaLong,andtheequivalentconditionatthelevelofMinorMood.Hisfollowingchartdoesincludefurtherpossibilities.

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Verymanysongs(carmen)andexamplesarefoundofMinorMoodPerfect,asthatofJosquinbeyondcounting,andespeciallytheMissaProdefunctisofthesameman;likewise“Puernatus”OfJohannesMouton. Indeed,oftheMajorMoodPerfect,therearealmostnoextantexamples,evenbecauseoftheannonyingandirritatingretardationofthenotesinthissign.

OnTempus

TempusisDouble101PerfectiswhentheBreveisworth3Semibreves.Itssignsare:¡3,C3¡

ImperfectiswhentheBreveisworth2Semibreves.Itssignsare:¡1,C2,C

ProlationistheproperdispositionofSemibevesandisdouble.

101NotethatfourofthesignsdodoubledutyInbothMoodandTempuslevelswithoutdistinguishingthedifferentsignificances.

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[d5v]OnProlation

ProlationMajorProlationiswhentheSemibrevemakes3

Minims.¯= Itssignsare:

MinoriswhentheSemibreveisworth2Minims.

¯= Itssignsare:¡,C

Fromthethingssaid,ProlationwithoutTempusandMajorMoodwithoutMinorandMinorMoodMinorwithoutTempus,Ihaveestablishedisnotpossibleinsong(cantilena).102 OntheextrinsicsignsoftheaforesaidDegreesIhaveinterspersedinpassingwiththeprecedingones,forinvainareMood,TempusandProlationrecognizedapartfromtheirsigns.TheexpressionsofDegreealsoareknownbymeansofcertainintrinsicsigns,namelybythecompletionofnotes,orthedispositionofrests.103IndeedtwoorthreeLongsincolorationareanindicationofMood,Brevesortwosemibreverestscombined[isanindication]ofTempus.ThreeormoreSemibrevesortwosuccessive[d6r]sighs(astheyarecalled)ofprolationareanindicationofProlation,aswrittenhere.

102Gaffuriussayssoingreaterdetail,PracticaMusicaBk.2,Ch.7.103Inotherwords,hemeansbycharacteristicsimplicitinthemusic,whichhehasjustsaidisnearlyimpossible.

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AnotherExampleoftheThreeDegrees

[d8v]TableinwhichtheQuantityofanyNotemaybeExplainedbytheVarietyofSigns

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Chapter5:OnAugmentation104[Thereaderiscautionedthatitisvitaltoreadthisnote.]

[e1r]NotinappropriatelyisProlationconnectedwithAugmentation,sincetheymakeuseofthesamesignsandnotesincommon,andyet105itisdonemorefreelyintheformer[illa,Prolation]thanthelatter[hacAugmentation].Inthiscase106[ofAugmentation][PerfectProlationis]inonlyonepartofthesong(cantilena),[whereas]in[Prolation]itisinall[parts],andthisexactperfectSemibreve,orthreeMinims,isworthaProportionateTactus.107Inthisway,indeed,theperfectSemibreveismeasuredwith

104ThistextismuchtroubledbytheconfusioncausedwithListenius’analogyofperfectprolationinAugmentationascomparedwithregularPerfectProlation.AccordingtoApel,atthistimethesignsofPerfectProlationindicatethattheMinimreceivestheTactusinsongswithallvoicesinPerfectprolation(pp.163-164).ThisisalsotrueinthecaseofPerfectProlationinonevoicewhenusedforAugmentation.WhatListeniusnevermakesexplicitisthatwhenPerfectProlationisusedinonlyonevoiceforAugmentation,theothervoicesmustbeinImperfectProlation.Tohim,nodoubt,thisseemedimplicit—thoughschoolboyslikelywouldhavebeendependentontheteacher’sexplanation—buthisanalogyhasconfusedthedistinction.Beyondthis,onceagainListeniusexhibitsthetendencyforhisLatintodeterioratewhenthesubjectbecomesmorecomplicated.HissourceisprobablyOrnithoparchus,Bk.2,Ch.7[F4r],(Dowlandtranslation,p.47)asdemonstratedbythesimilarityofListenius’definitiontothethirdidentificationofOrnithoparchus.Ornithoparchussays,“Tertiumestpunctusinsignotemporali,circaunamdumtaxatcantilenapartemrepertus.Unamdico,namsiapudomnesoffenditur,nonaugmentationissedmaiorisprolationiseritindicium.”“Thethirdisapointinthesignoftempusfoundinonlyonepartofthesong.OneIsay,forifitisfoundinall,thenitisnotaugmentationbutanindicationofmajorprolation.”(Dowlandp.47).Listenius’subsequentlyattemptedexplanationfairlyclearlyalsoderivesfromOrnithoparchus’secondandthirdrules,ofwhichheprettywellmakesahashaswell.ThistypeofAugmentationwasrelativelynew,unfamiliarandoftenconfusedinListenius’time.Apel(p.166)saysTinctorisreferstothepracticeinProportionaleMusicesBk.3,Ch.2(CSIV,171),yetwithoutcompleteclarity.IhavefoundnomentionofitinGaffurius,atleastwhereitmightbeexpectedinPracticaMusice,Bk.4,Ch.4undersubtripla,butGaffuriusisreallymoreinterestedinthemathematicalrelationshipsthanintheirpracticalrealization.SebaldHeyden’slaterwork,Deartecandendi(1540)—Book2,Chapter2,Millertranslationp.70ff.—discussesthisspeciesofAugmentation,describingthreedifferentpossibleinterpretationsofit.Ofallthepossibleinterpretationsapparentlyinuseatthetime,Listenius’ownisonlyoneandthesimplest.105Seayreads“sothatitmaybedone....”Theoriginalis“tametsiidliberiussit.”ThereisnojustificationinclassicalLatin,ashumanistLatinimitates,totaketheconcessiveparticle“tametsi”asequivalenttothesubordinatingconjunctionofresult“ut,”“sothat.”IamconsiderablylessfamiliarwithmedievalLatinbutknowofnosuchusage.InanycaseListenius’Latinishumanist,classical.106Theuseofhacconnectedspecificallywith“inonepartonly”makesclearthatListenius’useofthecorrelativeshicandilleistraditionalas,respectively,“thelatter,”“theformer.”107ListeniuslaterdefinestheProportionateTactusaswhensomevalueotherthantheSemibrevereceivestheTactus;inthiscasetheMinim.IbelieveSeaygoesamissherebynotunderstandingthereferencetobetotheProportionateTactusofChapter10.Thepedagogicaltechniqueofthetimewasnot“progressive,”butwhatIcallsynchronic,inwhichanypartofthetextmightberelevantforunderstandinganyotherpartofthetextdespiteitsactualsequenceofpresentationinthebook.OneofthethingsthatmakesthispassagesoconfusingisthatbothProlationandAugmentation,asListeniussayshere,utilizetheProprotionateTactus,becauseinbothofthemtheMinimreceivestheTactus.ThedifferenceisthatininProlationallthevoicesareinPerfectProlation,whileinAugmentationonlyonevoiceisinPerfectProlation,whileintheothervoicestheSemibrevereceivestheTactus.

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awholeTactus108foreachofthreeMinims.Whenceitisclear109thatAugmentationisnothingother

thananenlargementofnotes.110Itisindicatedextrinsicallybythesesigns and insomeonepart[only]ofthesong(Cantilena),or[itis]inscribedinacanon111[suchas]“BrevebecomesMaxima,”“Semibreve[becomes]Long,”etc.,or“itincreasesbydouble,triple,”etc.112

108Listenius’useofthephrase“integrotactu”doesnotapparentlyhavethesignificanceofhislaterdefinitionofTactusIntegralisbutmeanssimplytheentireTactusequaltoaSemibreveintheotherpartsforeachMinim.InthisIagreewithSeay’sreading.Listeniustherebyfurtherconfuseswhatisprobablythemostobscurepassageinthebook.109Nocommentontheironyofthisstatement.110Thephraseis“Undeliquet,nihilaliudesseaugmentationemquamnotularummultiplicationem.”IcannotagreewithSeay’sreadingof“itisnothingbutaugmentationratherthanamultiplactionofnotes.”Nihilaliud...quamisaverycommon,evenstereotypedphrasethathasappearedmanytimespreviouslyinListenius’textwiththenormalmeaningof“nothingother/else...than”or“itisonly.”“Ratherthan”isequallycommonandis“potiusquam.”Myreadingalsotakes“multiplicatio”withastandardmeaningofboththeverbanditssubstantivederivativeof“increase,”whichIhaverenderedas“enlargement”forgreaterclarityinthecontext.111Acanonisadescriptiveorexplanatorywordorphrase.112ThesearereferencestoothermeansofindicatingAugmentationofdifferenttypes.

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[e1v]Chapter6:OnDiminution Diminution,thecontraryspeciestoAugmentation,isacertaindecreaseofnotesandmeasure,differingnotatallfromsemiditie,113exceptthatthelatter[haec=semiditie]concernsperfectsignsandtheformer[illa=diminution][concerns]imperfectsigns.Imaketheunderstandingofitthreefold.114Canonicisfirst,whenthequantityofnotesormeasureisvaried,accordingtotheinscriptionofacanon,soastodescribeitindupla,etc.,or“lettheMaximabeaLong,”“theLongaBreve,”etc.,whichIleavetotheintelligenceandjudgmentofmusicians.Numberissecond,whentheproportionduplaortripla,thatisadoubleortriplediminutionofthenotes,isrepresentedbysomenumberasinthisway:¡2,C2C3,inorderthatitmaybecomeclearbymeansoftheproportions.Strokeisthird,whenastrokeintersectsthesignofTempus

orProlation,inthisway:

113Seayhastakenthiswiththesimplemeaningof“halving,”butitwasalsoatermforaspecificconceptofdiminutionintheseventeenthcenturyatleastasearlyasOrnithoparchus(1517)andknownaswidelyasMorleyinEnglandattheendofthecentury,thelatterprobablyundertheinfluenceoftheformer.ListeniusappearstoshowtheinfluenceofRhauand/orOrnithoparcushere.114Thisotherwisequitelucidpassageeitherinvolvesamostunfortunateandconfusingerror,or—evenworse—possiblyindicatesthatListeniusdoesnotunderstandhissubject.Ihaveexpandedthepassageinordertorevealtheproblem.Theoppositionoftheformsofhicandille,standardsinceclassicaltimescorrelatesinEnglishashic=latter,ille=former.Indeed,ListeniususedthiscorrelationcorrectlyinanotherwiseveryconfusingpassagejustinthepreviouschapteronAugmentation.Thus,Listeniusclearlysaysthatsemiditieappliestoperfectmensuration.Unfortunately,hiscorrelationreversesthecorrectone.Semiditie,theEnglishformoftheword,relatesonlytoimperfectsigns,whereasdiminution(proper)alludestoperfectmensuration.ThisisgenerallyacceptedandisasstatedbyOrnithoparchusinhisMicrololgusof1517Bk.2,Ch.8:“semiditasestprimarienotarummensure

medietas,inimperfecttemporetantumlocabilis,cuiushecsuntsigna .“SemiditieisthehalvingoftheprimarymeasureofnotesappearingonlyinImperfectTempus,whosesignsare,etc.”(MicrologusH8r).ThelikelysourceforListenius’discussionisRhau’searlierEnchiridion,whichgivesashorterformofthatfoundlaterinOrnithoparchus,“Nihilasemiditatediscrepant,nisiquodilla[diminution]insignisperfectis...reperitur,haec[semiditas]inimperfectis,”Rhau,Enchiridionmusicaemensuralis,Part2ofEnchiridionutriusquemusicaepracticae(H8r).Further,IdonotfindthetermusedbyGaffuriusinhischapterondiminutioninPracticaMusiceof1496,whichotherwiseappearstobeListenius’mainsource.Alasthope,thoughIfearaforlornone,isthatthepronouncorrelationisnotabsolutelyrigid,thoughIhavenevermetwithituseddifferently.Anauthormayusethehic/illeformsastheyrelatetoemphasisinhisownmind,asifhic=mostprominent,ille=lessprominent,orthelike.FollowingcloselyuponthedifficultyheseemstohavefeltwithAugmentation,Iassumethathehasconfusedthetwotypesofdiminution.Ironicallytheissueisvirtuallyadistinctionwithoutadifferencebecausebotharesimplydupladiminutionsapartfromthedistinctionofapplicationtoeitherperfectionorimperfection.Seay,perhapswisely,avoidstheissuebymeansofavaguetranslationwithwhichIcannotquiteagree,“innowaydifferentthanhalving,exceptthatitmayhappenontheonehandinperfectsigns,ontheotherinimperfect.”