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'- '-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).
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