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I 846 ) 2X P' t 8)9 I 8/1 e/, al J.1 'l t I Komal I 115 2t1 It ?4.J 18/ 11 Dhaivat" I 99 it /9 ) 6a.9 I ) t ) ) P\ P' 1tD S5 P/ 1)t 1)t 1)) t77' )i s5 c?.-1- 7g2' Panaham Panchar PanChatr, ) I 1.O j t I l .l t.7 211 nr P4 I I I ec.2 ( ,91 7/6 I (rc 1 Tivra Poi nt Madhyam ',I' P of t 41 R!st ) j l/ -. t Shu0dra ttn Madnyat: ) I I <1 212 ii5' 15 rPl j I 404 I I )8a 1) )g(,.) 5/t ,oo.r-.F Snudcha thuorla Gamhar Gardnar ?X I 1./ 1' I I I r2E P2 j;5.6 6/5 )tt.6 - P' 6/',' i )t9 s/1 )?6 I ). - PI ,1, rl 'r;.7 I . ,ta t 92.2 ( I zor .lr \ ril 5l SI c! noo l/ uo0 L/ 0m rrn NOA]H INDIAN RAGA TTT.JINGS CENTRAL JAVA PELOG & SLENDRO TIA{I^JGS - - Si Oarius (Slenoro) / tsLtJES Darbari Kanada St,uddtra Kalyan Hamsadhwani Kanjulm6em si N,taoeleine (Pelog) Lipur sih A CCMPARAT l2m JT 2.00 2N 2.00 200 2.AA I200.u 2.0o I 200 I2o0 2/l Ociav e ,rrili11 rrTlq 1.9551 l ti5l.l ,l 6L/)t 11 I i 46.6 j r crAl I I 16"3 I .9125 .122.6 I r9 40,2' I I r5.5 ?1/la t ll ?t/'/ 1.8878 um .l.8b6i r5l8 u l06E.l lr/8 noo t 1.s692 I tI ?9 1.8591 t0'|). r' 5lt,oe..r L t Major 7th tau9.a I i8 il/51 -lr- l ercq _l zolil fl 9/J I I0I7.5 9/' t017.5 e/5 ++ I0l?.5 i '1921 1.7889 J I D(x.9 -t 996.1 ICOO | t L6/el .7318 r ?7 t; i _JL i -J '7/t/ Minor 7th J 96).; I.7/.li 950 7/"1 968.8 968.E 728lr t 9Lti .h I I j t. t2/7 I 9t).t l?/; 9t).1 929.O 1a ) 945.9 2 L[,. I ti- 1.666 t i Bs!.;l :'.':L FR! ir I E 351.5 l6/ll l2l 1l- '1.62t)5 l[-;;,;. l'696E 8/' 8l 1.7 1.599) L sI2.9 H l,' I4 Minor 5tn I .587( ua,/ lJ,oo I l/1 t.5625 L r- ,-2.6 'tt!/9 7 51.9 15L"9 \ '5{!91 U ,-5 ,- "9 Ir 7 J5.tJ i- 129.2 lr 1 .515 t' ::I jUl.L- 1..9ts 7c0 ------J:rgtr Jll/2lP o96.6 i.49t6 I 6?t!.1 r 40/21 680.5 Perfeci ,tn I I L.t!52A 558. i f 6/ I'L 6ut1.7 il t il9.0 t.utlcz I 6)t.6 LA/1 6',I'7.' trl?.1) 7D/ q l 6C0 I.II4 590.2 ui r lql f i9.tr 1/5 r.1887 l 568.4 l.)6 r- 6 5t!1.9 I 2) /24 5t9.5 5I9 6 L.]le9) h96.L Jr-u/1* L.)t95 aE0 Perrecl 4rn 2l/66 4 70.E I L1078 46a.5 ?t/6 470.8 r rqnq tt L2. I ,l 9/1 tt)r.L 9/1 iL/ll at1.' ".?189 8l ,9'. ac0 .l[.i. ,JB6.J .?t!11 I 5/L ]- )E6.i ,l ,60 Ma.lor.lro lI/9 .l ,., . -t r.?2?t ls8.q -i j t-- I .?00 I ]t 5.8 6/i * ilt.6 6/5 6/rllJL5.6 l I lr0.l loo '195' )?/21 12l5/ I Yrn.or-iiC [ :::: l. I69 27t.0 i/6 266.9 251.6 I la8 Z/r0 21t.2 Ll4l 2)2.) E/ '' [*,-] 2m-.--_T6; I9l.l I'lli7 I i89 5 I L lo/9 u;" ta/9 ! E2,A Major 2no I L'i'.i l.I l;:.0 r iqlr lL/lL r:c,.e t 154.8 ff ),1,)l t26.1 ,l Q7I t?0 1.0694 I 16.l ) '/ t6/ l, III.7 qp t6/ t1 11,,,, t6/tI t, \ | 1.1 r 1( oo.r Minor 2nd lJ !.ct49 76'0 6),t 2b/21 t l.ol?? f{ ,,, 18.7 2 8 I/CC I.oUt( 000 t/1 ll*: I/'l l -ooco oon l.00gJ 000 Tonic l-coMMA TO-TON€ EGUqL 12 TOI.€ EQUAL VENITC.:ruE / I9.TON€ I6I.'AL 22 ER 5.LIMII JUST TEMPERAIV€NT ]I EQUAL TEMPEaAMENT iEv"ENAVENT PARTCH'S 4] tsEN JOHNSTCN'S - and, as I was saying, ... EzraSims (1979) ' pochissimo Slow-sustained-vocal ritenuto a tempo piirf< Viola (-l l--l (- -) o tenuto poco crescendo > quasi crescendo al m. 9 (-) poco tenuto poco pit energico t-l_-l t_.'3 <= E=7-) *3-) (-) poco a poco creseendo sempre ritenuto a piac-ere ((3+2+2)+(2+2) espressivo .- ii rr)* Introspective - a bit puzzled' verbal t2 Ja-. '- '-r- nonf> 7- 4:5-1 modo ordinario (- > come sopra -) -- and Psychoacoustics of Music 4l 800 700 Minor Third 600 rs 500 e Mojor Second esa Limit of Discriminotion 300 *--5- i of 200 t of, Minor Second t 100 \t ro t( 12345 Ito CENTER FREQUENCY IN KHZ )qul ancl limit of frcquency cliscrinrinatiorl as a functioll of nan :2.6 Critical bandwidth . (Based orr Introcluction to tlrc Physics ancl Psychophysics of Mtrsic Dy "/rrnrr Publisltcd with tlrc pertnission of Springer'Vcrlag, Hciclelberg.'1 the ity of the ear to cliscriminate adjacent tones. For exanlple. when the car io).: closely spaccd torles, there rvill be a certain amoullt of overlapping of I stimulatcd on thc basilar membrane. This causes the sensatioll of two e more complex than it would be for tones with greater scparations. The ltl ''difference betwccn the tones at wlticlt thc scnsatiott abruptly changcs is :o i the critical band.6 r-Cl of the critical band varies with frequency. It is a large pcrccntage of CS frequcncy of two toncs that arc at low frcquencies, ancl a small ie for two toncs of high frequcncies. Figure 2.6 shows thc changc of wiclth 9€[l-i band with frequency. Above about 440 Hz, the width of the band is he !l onstant at around onc-fourth of an octave,1.e., around the tnusical to a minor third (arouncl l9o/o). The fact that the critical bancl is a largcr t at low frcquencics hclps to explain thc comnton usagc of larger ntusical as lin the bass rcgister in rnost music. The width of thc critical bancl plays a r III€ te perception of loudncss and timbre, as well. Systems "music synthesis systcms offer thc musician complete freeclom of respect to tuning. This situation differs grcatly from tlte fixed intottation ic and some electronic instrurnents. In the following section, we will properties of four colnmon systems for tuning: equal tentperament, ion, meantonc tuning, and Pythagorcan tunit.tg. tempcrament with twelvc scmitonal divisions of the octavc is by far the l{non system of musical intonation used today in Western music for iinstruments. In the general casc of cclual tcmperantent, an intcrval / is a numbcr of intervals N all of cclual sizc (that is. all having cclual a W E t f f N F )- f fr f, rilo h2l nole1./^tL 'fi, o #( ffiil::;t::T':r-*---- 7 7 7 ,nal system is its b ion of tonalities, Ir 3\ on is not capable 3 e other cornmon 19 lt 7 intrieate musical 7 b 3 onality identity. I q B nheard rrrodula- 3 5 9 nd the arbitrary ! , from ldentities 4 rriety in that ex- I 18\ K9I nsible tonalities, 3 il 2 rrefore a greater ro il ns Equal Tem- 5 6 9 9 5 a mperament and il 0 I : two scts is ac- 1l f qlnnot coexist ind musical in- rhat-short of a and a paychic LMR 2l HtoilER le same musical t: % )t yet practical. Drecnau 9,-Txe ExpeNpn,p Toxerrry Dreuoxo age 110) is now irnit, each series ties, downward ,ality Diamond. olid lines from to left. t59 sSIg {- :f.- J- u Fl :LH NI'i E J=u - rycll o Sl*= trJ- l-s ilT* il- Jr" c-I s t F lr< s:r alSI'r Nl rF f I =.1or-l lH =l- cE :l a LJ s.tr'd a2 U' u, v) th U, v) o EF d € Cg fil t ca ca ca ca tE!r\ :q P E RC L: S S I O.\' 1.\'.'7R U M E.\-T S 261 Otonalities (ascending) are found in the six lines of blocks from lower left to upper right, Utonalities (descending) in the six Iines of blocks from upper left to lower right (see photograph and Diagram 17). It may be seen and heard immediately that each tone l'epresenrs ar least a dual identity;5/3, for example, may be considered either the 5 Odentity of the 4/3 Otonality or the 3 Udentity of the 5/4 Utonality. The total range is nearly thret2/ 1's, the identities of one tonality being spread over about a 2/ 1 and a half. The relationship of identities is always 4:5:6:7 :9:1 1 in Otonalities, and I / 4:1/ 5:1 /6:1 /7 :1 /9:1 /11 in Utonalities; consequently, the sequence of Odentities or Udentities is 1-5-3-7-9-11, rather than the 1-9-5-1 1-3-7 ol the Tonality Diamond. In specific range , the low 16/11 makes about 2E5 o'cles (ust above "middle C"), the middle l/1 makes 784 cycles, and the high 1 1/8 makes 2156 cycles. ,t,\ u-\i ) l/, I :+4 rr* 4 I L-_. t Lotitl I tt, t;\ Dracneu I7.-Br-ocr Fr,eN or tHr Davoxo Menrute 't built thc Diamond Marirnba in 1946 in Warrcn E. Cihon's shop in Madison, Wironsin, with Cilson's advice and assittance. The height from thc floor at the lowest block is 34 inchcs, at the highc* 41 I /2 inchcs. Tlrc center row of I / 1 's is 4E I /2 inchcs long, the tcrraccd top is 27 inchcs deep from thc front ldf,tof the l6/ll blocktothebackedgrof thel1/Eblock.Eachofthctensteps.i*s3/4 inch.Thcwhite- pine oosspicces of the base are 33 x 20 1/4 inches; width-S inches. Four 3/4-inch bronze posts suppon thc inslrument on the ba!e. 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