WendyGarloo ?O. Box1024 Tuning:At the New YorkCit, New York 10276USA Grcssroads lntrodrciion planned the construction of instruments that per- formed within the new "tunitrg of choice," and all The arena o{ musical scales and tuning has cer_ publishedpapers or books demonstretingthe supe- tainly not been a quiet place to be for the past thlee dority of their new scales in at least some way over hundred yeals. But it might iust as well have beenif €qual temperament.The tradition has continued we iudge by the results: the same 12V2 equally with Yunik and Swi{t {1980),Blackwood (1982),and temperedscale established then as the best avail- the presentauthor (Milano 1986),and shows no able tuning compromise, by J. S. Bach and many sign of slowing down despite the apparent apathy otheis lHelrnholtz 1954j Apel 1972),remains to with which the musical mainstream has regularly this day essentially the only scale heard in Westem grceted eech new proposal. music. That monopoly crossesall musical styles, of course therc's a perf€ctly reasonable explana- {rom the most contemporary of jazz and av^rf,t' tion lor the mainstream's evident preferetrce to rc- "rut-bound" gardeclassical, and musical masteeieces from the main when by now there are at least past, to the latest technopop rock with fancy s)'n- a dozen clearly better-sounding ways to tune our thesizers,and everwvherein between.Instruments scales,i{ only for at least part of the time: it re' ol the symphonyorchestra a((empr with varyirrg quires a lot of effort ol several kinds. I'm typing this deSreesof successto live up ro lhe 100-centsemi manuscript using a Dvorak keyboard (lor the ffrst tone, even though many would find it inherently far time!), and I assureyou it's not easyto unlearn the easierto do otherwise: the stdngs to "lapse" into QWERTY habits of a lifetime, even though I can Pythagoieen tuning, the brass into several keys of akeady feel the actual superiodty of this unloved lust irtonation lBarbour 1953).And th€se easily but demonstrablv better kevboard. It's been around might do so w€re it not for the constant viligance since 1934,and only now with computers and speed "directory on the part oI performe$, add the rcadily available and accuratedata-entry tasks such as yerdsticks for equal temperament prcvided by the assistance"is tlere th€ slightest chanceit may be woodwinds to some extent, but more so by the harp, resurrected as a long overdue replacement for the organ, or omnipresent piano {in€xact standards that deliberately slow (no kidding! ) layout developed by they may in truth be). Sholes over a century ago. part Yet this appeient lack of adventuiousness is not Musical keyboards are a {undamental of the due to any lack oI good altematives (olson 1967' west's music-makinSculture, so keyboerdsneed to Backus 1977j Lloyd atrdBoyle 1979i Batemen I980j be addrcssed with regard to compatibility with any Balzano1980) or their champions.Indeed an experi' existent or {orthcoming tuning scheme. cleerly the enced musician would have to be prepostercusly fretless strinS falnily is almost utuesticted as to naive, sheltered,and deaf (!lnot to have encoun_ the paticular scalesand tuning that can be used (the different tered at least a name or two like Yasser{19751 or musiciatr's ears and training are rather a Pertch (1979),or in an eerlier er4 Bosanquet,white, matterl. This is sufffcieot reasonlor the histodcal Brcwn, or Ceneral Thompson (Helmholtz 1954; concern given to new and modiffed keyboard designs Partch 1979).These pioneercwere certainly not by past proponents of tuni[g reform {Bosanquet, white, Yasser, etc.), although in ptactic€ Partch and known Ior the shy reticence on behalf oI their "made various turriDg re{orm proposals. Nearly all built or others havefrequently do" with the standard seven'white, ff ve-black. But as with Dvorak replacing QWERTY, it's diIff- Coplright@ 1986 by WendyCados- cult to challenge any sort of standaid, once thet 29 r standardhas persisted for more than one genera- This unlortunate quality of,,sentenceffrst, verdict tion.We all tend ro torgetrhe precrriousn(ss wrrn afterwards"places Barbour,s otherwise laudable which all standardsare birrled, and grant rhoserhat achievemenrinro the samezealot,s DulDit with come beiore us a sadosanct status which is likely Partch, Yacser,Bosanquet, poole, Brown, perret, unjustifiable, and which the origin:l desisners Captain Herschel, ceneml Thompson, and others. mighr, if alive today, quite 6Jrd liughable Rerbo.jl's Tuning and Temperdm ena also suffels hom several snall ellors: "Furthermore, Turingand the Zealot Cx 3 and Eg 3 differed by only six c€nts . ." {p. ll2). The secondnote ought be No doubt lrustrations do spawn a missiotrary zeal, and thereis ampleerrdence thar all of rhepioneeis ". ingenious mechenism by which DL and we've been talking about had th€ir Iair shareot At couldbe subsnruredtor Cdand DI . frustration and zeal. It,s both instructive and amus- (p. 108).But cl is the ffJth aboveC{, not Dl. ing to read, back-to'back,the books on tuning by ". and(the Io8 ofl 2r3.1r,t7579t6lOO,... Partch {1979)and Barbour (19531.partch was argu- {p.119). But rhecorrect log is .1747916100. ably the greatestchampion of Iust intonauon ot thrscentury, and hr: writrnglrequenlly lapses into and, in lighr o{ many more as above, from olten iumorous sarcasm: hypocracy: "There Name-Your-Octave-Pay,your-pounds-and,Take, were, as usual with Kircher, maly It-Away lenninSs(Partch 1979, p.3941 eIIoIs. ." {p.lI0). and emphatic impatience with those who seem and from sarcasm: most unwilling to acceptthe clear supeionry or "Only Just tuning: in the desiSn of the keyboards did the in- vento$ show their ingenuitt an . and the ear doesnot budgelor an instanr ingenuity rhst might better have beendevoted lrom its demand for e modicum o{ consonanc€ to something more piactical" (p. 113). in hamonic music nor enjoy being bilked by near-consonanceswhich it is told to rear as which quite ignores the ingenuity spent developinS- consonances.The eat Acceptssubstitutes th€ traditional seven-white,five,black kevboard ,given,,, againstits will lPartch 1979,p. 4t7). Barbouraccepts as a ro sav norhing of (he While understandable,rhe penasive undertone is menrsot many possiblegood new scalesrhat really eventually wearyinS(even if most often justiffed) oo requre ettonand inSenuiry ro find.Talk aboul and doeslittle to attract complete sympathy Irom a a closedmindset! And Barbourreprese[ts amorg neutral partch musiral theonsrsthe bestoI the knowledgeable reader.Barbour,s classic study (which "champions" generouslyprarseslis no Iesssubtlely dogrna(lc, al- on beba.lfof equal temperament. I his (his certajnlvseems (o be, lhoughin case(he a priori idealrs nor rus(in- subieclrhat al(racrspas- tonation, but equal temperament.He calculates sionatewords ls€eLloyd and Boyle 1979,Chapter g every alternative tuning's ,deviation,, from l2\az lor evenmorel from all sides! and argues most on behalf of those which exhibit the least mean and standard deviations from equal The Grossroads temperament.There's somethinsuncorfortably circular in the reasoning throughout the book, sort It mav seem unJairro \rngle our Barbouras abore, of like: although somebowI wince more from his and other theo sts' polemic on behalf oI ,,the haves,.or status Civen, equal temperament 'the quo versus ha\,eno(s,'ol anyone who mighrnot Therefore, equal temperament iorallv a&ee wllh rhe finalsenrenceof Barbour,s Q. E, D. book: 30 Computer Music lounal Perhapsthe philosophical Neidhardt should be equel temperament is not altogetheres benign as allowed to have the Iast word on the subject: all of us born into it commonly assumei "Thus equal temperament carrieswith itself Th€ ffrst oI these pieces contained a number its comJort atrd discomlot, like the holy estate o{ sustainedmajor thirds, which work perfectly ofnatrimony." well on an orSantuned to one of the unequal temperamentscommon in the seventeenth That's a cute quote, but its use here is not a little century but which frght unmercifully on to- smu& suggestingwhat was "good enoughfor day'sequally temperedinstruments. Dudng Grandpa"ought be good enough in peryetuity for the playing of it the audience stirred uneasily, the rest of us. There'sno thought I've read by even and, when I have played the tape, numeious the most me.*ianic of rurung reformisrs that rai'es musicians . have askedme what terrible my hackles as much. thing went wrong with the olgan. Most are in- The truth of the matter is that up until now credulouswh€n the explanation is given, cvcn there's simply b€en no way to investigate beyond when they listen to the piece by Bach played the standardscale within the limits of the precision the sameev€nin8 on the identical organ,sound- o{ the availabletechnology. Acoustic instruments rng. .lrkerhe admjrable rnsuumenr rt rs, arealmost compatible with a i5 lo-cent pitch Bach . arrangedlor his thilds to come and toleranceat best. A ffne grandpiano cannot be ex- go, well disguisedby their musical context." pectedto perfom much better (Helmloltz 1954, (BenadeI976, pp. 312-313). pp.485-493), its particularly pro- not to overlook Computer-controlledsynthesis, on the other 1977,p. 292, nouncedoctave stretching {Backus hand, has no inherent need to respectthese here- pp.3I3 a phenomenonwe will Benede1976, 322), tofore inescapablelimitations. There's certainly lven rhebest anaJog synthesizers examinelater. little n€ed here to provide any further motivation much better, and up until recently did a cannotdo for breaking out of the three-century "rut" that this (l shudderto rememberthe constant pitch lot worse long introductory material has documented-The drifts while reelizirg swttchetl on Bach on tn eaiy exponential growth in computers has ffnally ex- Moog!). pandedto include systemsdesigned expressly for More frustreting than that is the usual limit on music production, editin& and p€rformanceat low really the number of notes in an octave,which was elough cost to b€ as affordableas, say,a goodgrand "economic" musicians of Bach's wholly reasonfor piano.