Chapter 3 Sounds in harmony（第2页）

Table3。Harmoniousintervals

&obuildaharpwithstrihsdeffable3，butallofthesamethiess，tension，andmaterial，wewouldveryeasilybeabletomakesimple，reaso-soundingchordswithit—infaypairroupofsugsplayedtogetherwouldn’tsoundtoobad。

Thissystemiscalledthepentatoowasdisdepelybynumerousamusimanypartsoftheworldandisstillverypopulartoday（‘AmazingGrace’，‘MyGirl’，and‘IShottheSherifl’arewritteninit）。Theblathepianoareaseriesofpentatonicscales，soifyoupressthemrandomlyitwon’tsoundashorribleasifyoudothesamewiththewhiteones。

Evees

Althoughpeoplelikemusiy，theyalsolikeabitofdisdthepentatotootunefulandsafeforposerswhowaogetheiraudiendpushtheboundaries。Also，ffveaveisstillnotthatmany:buthowtoaddmore?Ahisquestiouriesofcarefulexperimentae，leadingffnallytoasystemcalledequaltemperament。Inthissystem，anoctaveisdividedupies，eachasemitone，oros，apart。

&htheideathatwhatmattersinmusicareratiosofhemselves，semitosaredeffermsofratios。Eachsuccessivesemito6perthigherthantheohismeansthatthehigherthezdihehigherthenoteis。

Afewposershaveexperimehmorethaesperodextranotesmayappearbriefiy，inmovinggraduallyfromohertoahisiscalledaglissando，orslide）。However，inallcultures，thenumberof‘proper’aveisalmostalwaystwelve。

Haviwelvenotes，peopleproceededtousejusteightofthemperoame）。Thereareonlyseveesinaheeighthisthesameastheffrst，justoavehigher（evenprofessionalmusiediatelyidentifyaruggletosaywhichoctaveitis）。

Thereasonwhyweuseohetwelvenotesinanoctavewasresolvedin1956byGeeMiller，apsychologist，whofouallythatourshort-termmemoryorethaems—hendiflereime。

Thereisasemitoweeesinthefullgroupoftwelve，soanygroupofseveweakeourscalewillinewhiitoo。So，wemighthavethisscale:AgapBCgapDgapEFgapG。（Asysequeesinwhicheachishigherthanthepree。）

&hatwehaveasetofseveestodeffneourseauseothernotesinapieusic。Ifwewahose‘gap’hemwithsymbolswhi‘asemitoheeinthesitohee’。

&ioethatffllstheffrstgapinourscaleaboveiscfuarlltehdereistuhbedriAvidsheadripf　（rweqruititreend;fi）sourchB　sfimata（lwlerriftrteanctffi）o。nNsoatrees　rmefaeyrrbeedtoasmies。

Inieusicthereisusuallyatersmorethahekeyonic。Usually，thisheoneonwhigbeginsandends。IheRaieistheonesungon‘Some’and‘I’。ThewayJvuerdsyioGnairslasnaidd　stioninthtehkeeffylmof，　Ethfiisatis。Efiat（Eff）。Hence，her

Howisascale?Themaiionisthemoodofthepiece:ifthepat，celebratory，up-beatpiece，（s）heislikelytoajorscale。Toiecewhichislessemotionallyclearaminorkeyisusually。Theprimaryobjectivediflereweenmajorandmia（natural）majorssistsofatonic（whibeahesixnoteswhich‘fftbest’withit，itheirwavelehemaximumhesimplestpossiblewhole-ioswitheachother。Thesoundwaveshenbiregularevenpatternspossible。Iakesthepentatonidaddstwomorehesetwoheleadingnote，hasafrequendsevehatofthelowestnote。

Inanaturalmiwoofthehepentatonic，plustheleadingnote，havebeenlost（theyaredown-shiftedbyasemitoisthatthereisnsetofsimplewhole-ios，aisvaguer，moreplex，andlessplete-sounding。

Additionally，whenwehearanysungorplayedisinvariably（extheeelestruments）apasfullsetofharmonies。Majorstainallsuiestoo，butmi。Hehereisageuralness’or‘pleteness’inmajorscaleswhichislaminorones。‘AmazingGrad‘MyGirl’arebothinmajorscales，‘IShottheSherifl’　isminor。

Itusedtobe（andoallystillis）claimedthatindividualkeyshavetheirowionalqualities（inadditioioweenmajorandminor）。shavedemohisisnotso。Itislikelythatthisideaarhthereputationsoffamousoriialpieusic—imitatioobeinthesamekey，whicebecameassociatedwiththeemotionalqualityiisnottosaythatthechoiceofkeyisarbitrary:someisaredesigthenotesofaparticularkeyarephysicallyeasiertoplay。

Soundsequences

&herawmaterialsofmusipositionaresimilartheworldover，therehasbeedifleresdevelopmeernmusic，relativelyfewnotesareused，buttheyareofteher（chords）orioeachother（harmonies）。Ifwehadtojugglemorethainusipositionwouldbemoredifflparticular，polyphoaneousplayingofdiflerentmelodies—wouldbeewell-nighimpossible。Iernmusiymoreobeused，butbinatiohisdiflerenapproachfedthroughtoidesigrumearandaurallypolyphoerhesitar，onlyproduoteatatime，buteasilyvarythatnoterapidlyandsubtly。

Thediflereernandothermusicmayhavetheirihtury，whenpolyphonybegahoughtherearesomeolyphonyhasfarearlierroots）。Frompolyphboththecharacteristicallymulti-tuneapproachoftheWestaudiesofharmoodevelopit。Ithasbeehereasoexperimentswithpolyphonywasadesiretohavemen，women，andsiher。

Melodies

Playsomenotesinsequendyouhaveatueicallyamelody。Ifwefetaboutthediflerehenwhatislooselycalledtherhythmisallthatremaiivelengthsofthenotesahespeed（tempo）withwhichthewholethingisplayed，aerre，orsometimesmeasure）。Thisiseigofthewordrhythm，whichrefersohpattern。IheRaihm（teicalversion）is:‘long，long，medium，short，short，medium，medium’。

&reisihetimesigimesigheetre（‘e’）iswritten44。Thelivestheuospecifythebeat:14chets）。Theupperspeciffesthehesebeatspergroup。Iheendshowiecalledabar（soeis‘fourcrotchetbeatstothebar’）。

&theonlykimatterinmusic—theotherkindotwotonesthplaytogether。Everysoofteroughsofthetillcide，addiiora-highor-lowpressure。Theeflectisheardasalow-frequehefrequencyofwhichisthediflerehefrequemakeitup（Figure13）。

WatybladwhitethrillerfeaturingLondonpolidyou’llhearaswhehemblowshiswhistle:suchwhistlesusedtwopipesofslightlydiflereoproducetheirarrestingsousaren’talleasant:saopcalledthevoixcéleste，whitrolsasetofslightlyout-of-tunepipes。Whenplayedalonges，thebeatsproducedmakeapleasantlywaveringsound。

13。Beats。

Ialbreak

&ionalwaytoclassifymusistrumentsispartlybywhattheywereinallymadeof，herings，brass，woodwind，andmiseous（per）。Anotherwayisbywhetherached（likeapiano）orunpitched（likemaraypieusieedsrhythm，andusinganon-pitchedsourceavoidsdissohe‘melody’iishattherhythmsourcebeamusistrumeisteLully（1632–87）usedtothumpabigstitheground。Thisisnolongerfashionable，perhapspartlybecauseLullydiedfromit，havinghithimselforactedterminalgangre。Drumssoonbecameamorepopularshtheyarealsousedasasourceofthe‘actual’music。Forthisreason，whiledrumssuchasbassdrumsandsnaredrumsareuledrumsarepitched。

Mostpitstrumeheirherbystriking，plug，astrie，orothersolidanofairvibratebyprovidingitwithenergyfromlungsorbellows。Ineverycase，itisresonanceplusovertones（and，inthecaseofbells，uones，alsocalledsubharmonics）thatprovidetherequiredsound。

Thismakesitseemsimpletostructamusistrument，buttherearethreepligfactors。Theffrstisthatasuchasametalplatewillnotoawaveleslength，butalsoatwavelengthstwiceitswidthawillproduceothersoundsasittwists，too。

Theset—averyusefulplayers—isthatwhesuchasa12isstruck（orpluckedorbowed）itwillmoveiermionlybyitslengthbutalsobythepositiorikingpoipointhasnooptionbuttobeaheeringhaveobenodes，soifthestringisstrufromawillmakeafuhaian，andhehof160cm。Therewillbeanothersoundwithaian。Theseposidlyasthestring’svibrationshiftstowardsitsnaturalmodeofvibration，whichistohaveahedhencemakea240gthtoiveeflectisthatrepluellowersound，near-endplugaharsherone。

&ubesbehaveisimilaripe，thesimplestmotionisoneinwhichthereisfreemovementattheopenendaheree）atthed:soa12cmpipewillhaveafuha0dtheffrsta12cm（plusabitduetotheeion），hehofabout48cm。But，justasinastring，thisishesththefualisdeffhepipe’slength，otherresonanceswillbeproducedagtoitswidth。Themixihefualaonesproducediflerenttimbres:iubes，thereismyinlowerharmonidthetimbreismorerounded，whilethinnerpipesarebrighter（orshriller，dependingonyourtaste）。Theffnalsiderationforimakersisthatastriwopointsmakesaveryquietsoundisverythiionoinysurroundingvolumeofair。Iurringintoamusistrument，amuchgreatervolumeofairmustbeputinmotioricguitar，thisisaplishedbyusiioringtoinduceasmallelectritinpickups（magswoundwithffnewire）。Inacousticguitarsariruments，thewoodensoundboard（top）isvibratedbythestringanditslargeareamovesmuchmoreairtharingalone。Also，atlowfrequehehollowbodiesofsustrumentsactasHelmholtzresonators。

&ristrumentsdonotaddeher，theyverttheenergyprovidedbybow，plectrum，orairblasttoana。Ihebodyoftheisthefrequencytowardsthe4kHzregion，thiswillsouethefactthatthesouuallyreducedalittlebyfriallosses。Thisloudemsfromthestrusystems，asweshallseeinChapter4。