AIL also publishes ads like the ones that appear regularly on these pages inPULSE-the publication of the Long Island Section of the IEEE. Normally, we havea firm rule not to put the same ad in both the PULSE and SPECTRUM. But so manypeople have liked this month's ad, which was previously printed in PULSE, thatwe are violating our rule and reprinting it here. This ad is in two parts; the nextone will be published next month.

Dr. Paul Kintner runs AlL's digital lab. He is also an accomplished musician.Obviously, under the circumstances, the work in Paul's basement on a digitalpiano tuner was just bound to happen, if only for his own amusement. (For ourLong Island audience, please forgive ust-unless you would like to read it again.)

An Electronic Piano-Tuner Based On Digital TechniquesPart I

Many an electronic engineer has "in- new scale, starting with, say, D and using is very sensitive to detecting small fre-vented" the electronic piano-tuner. It seems the same frequencies. Most find the result quency differences between tones, especiallyalmost trivial: establish a set of reference displeasing and suitable only for such if fraught with harmonics. Duplicating thefrequencies (it should be easy to be more music as extra sad folk tunes. process electronically does not appear fea-precise than the ear), combine with some But let us form a D-scale based on the sible, and we have no choice but to carryfrequency comparison device, and, lo, an- same integer ratios as for the C-scale. We out two independent tunings. If similarother industry is automated! In fact, some find that we can use some of the C-scale results are then to be obtained, quite highelectronic tuners have been marketed; how- frequencies but some new values will have precision and stability is required-enoughever, acceptance has been something less to be introduced. In fact, nineteen fre- that inexpensive frequency generators suchthan enthusiastic. The blind tuners are un- quencies are necessary to get five additional as R-C oscillators are ruled out.derstandably not interested; the rest must integer scales. But a look at the piano 3. Octaves. The human tuner tunes hisfeel that their ears not only require no shows that only twelve frequencies and octaves by comparing the second-harmoniccapital investment, but are easy to trans- their octaves give twelve decent sounding of the lower with the higher frequency.port and require no power outlet. The scales. How is it done? Since 2/1 frequency generation is easily ob-adequacy of ears cannot be questioned; Actually, the development of the twelve tained electronically, we should have noafter all, the task of piano tuning is merely frequency, or tempered scale, took a good problem. However, it turns out that thethat of satisfying other ears. deal of effort. But around the time of second harmonic of a piano string is not in

But in spite of a sustained lack of appre- Bach it was discovered that twelve fre- an exact 2/1 ratio; it is slightly greaterciation, both from tuners and loved ones, quencies with the same adjacent ratio of based on the ratio of string stiffness tothe author has devoted untold hours in the / 12 __ string tension. The human tuner, therefore,basement to the development of a succession 1.0595 = + 2 ) give twelve iden- produces what is known as "stretchedof electronic tuners. By tuning his own tical sounding scales which are close octaves"; the upper end of the piano tunedpiano every two weeks, the expenditures snoundtintegsers,ahc ar closeall this way is technically sharp and the bot-involved have been justified. But the real th tae th tom is flat. We have a choice; shall wereward lies in the Challenge, as with moun- b rt themot tsener istantheomes duplicate this effect, which musicians aretains and high-fidelity systems. To date, /t2 athio for thaeteg seredl oeswosut used to but which will be clumsy elec-

asthe earihas notabeenerealied,ibutthe for the 5/4 ratio, which is 1.26 with tronically, or shall we merely tune to aasotrghe cotianou. Teen reanthf, hes ten- the tempered instead of 1.25. 2/1 ratio? The author has taken the lattercentio ntegratued circ ise edgietl taewited. Our first task then with the electronic course to date. Most find the result satis-clent gintegraten. circuit iseagerlyawaited. tuner is to generate the frequencies repre- factory, especially if they are not told whatThe task of tuning can be divided into ting the tempeantune.fis represents hasbeen utone.

threhe prs:t (1) etablisintheqene btwemere setig th reduescale. This represntosl ha beniqe done.be sdt bansal

thsae p(2) unisoandl(3)octav e stehred no problem for a single set of frequencies In general, the nature of the piano tone-caler tnebasiself dtirves otwo:.The (tuning fork oscillators might be used). non-integer harmonics, rapidly decaying,electronic tuner itself divides into two: () But this would mean that eveiry piano must and frequency shifts with time-will com-the reference frequency generation, and (2) be tuned to the same absolute standard. plicate the frequency comparison task.the frequency comparison portion. We will While adbe hsi o rcia;mnandfirstmdiscussiea ionale fromquenciesnd-it piano is best tuned as found, and evenpoint of the piano. Next month, a descrip- the best vary slightly with the seasons. Wetion of a tuner which uses digital techniques thus have the problem of accomplishing Next month we will describe some at-

1i.l bemipedSabthitempredl saeb what the human tuner finds easy-gener- tempts at a solution together with how digitalgisiThemsete twelv efrequen edsbete ating the frequencies on a continuously techniques have been used to obtain stabletighepin octave. m beefinestb t variable absolute standard. We shall find reference frequencies which can be variedcosdrthe basisforveIthivalusTheofitrsim-o that a =1:-3 percent variation from the continuously on an absolute basis.posiesthsae whsich plesethei Wales.Ther ear- international value of A = 440 cps willplest scale whichplearingshes ter sthernw suffice.can be formed by starting at some frequency 2 Unisons. Most of the piano tones areand forming six additional frequencies withthe ratios to the initial frequency of 9/8, geeaewihtotthestig,wih AcmlebunstofuritheisNow,A A /I I 1- - 1- - - 1- nre tuned to be in uin.ody Nf articls isi avahia on r t W

ghinnsinglo te scale,rpataedn done octhAve

kesoc-nd-oItheopiano, mstariga middliedC (ithen- ___

ers desire greater variety. We might try a lCUTLRHAMMER 0/VISION ______________________

IEEE spectrum MAY 1965 For more information on advertisements use the reader service pagwe 5