Mathematics and Society - OS X Lion Server

-~r:Jb Wb ON TWb, !:~Mb ~Ql:OUbN[l,J ?Cyclesper secanThe chart below gives the frequencies of the tones of a piano. The frequency ofthe A above middle C is 440 cycles per second. This means any string, reed or vocalchord would have to vibrate 440 times in one second to produce a tone which wouldmatch the pitch of this A on a (tuned) piano. Use the chart to answer the questionsbelow.cOr-! 0'\~6 ",c!, '" M .,. 0'" co co M "'0'" r--", "'.-1M r!..", o~'" "'0 0.,. M'" M .,. '".,.r-!r--'" co 0'"r-!'" co '"'" co "1"'''1 "I r-- .,. . . '". '". . . ° . . . . . . . . . . co .,. Or-!'" r-- '"ON. . . . . . . . • M '" M '" '" .... r-- r-! .,. "I "'0N 0.,. co"'", r-! co'" "I'" '" '"'".,.CO "'r-!co'"'" .... NOr-! M'" COO M r-- r-!MMM r-! "I "I'" r-! '" "I.,."'CO "I .,."I MM .,. '" '" '" M r--'" r-- '" r-! r-! r-! r-! r-! "I "I "I M M.,..,.r-- co '" r-! r-! r-!r-!r-! "IN "1M M'" '"oco M COM .,. '" 0'"'" '" r-- .... '" 0 .... r-! M r-! r-!O O.,.M M MO OCO '" M'" 0 .... '" .... '"0'"° "'0 0'" ° 00 '" '" OM Or-! 00'" 0.,. co coco '" 0 0"'''' '" '" NO oco "I .,.'" ."IN or--r-! r-! '" M r-! MN '" '" M. . . . . . . . . .MO COO Or-!O"'co .... .... "1 .,..,.'" '" or-- ...::t M 0'\ . . . . . . . . . . .'" M '" r-- M'" Or-!'". . . . . . .OM° "'.,. .,.'" O"'r-! OM M M '" '" "I r-- '"co M Or-- .,. r-- r-!'" '" '" .... '" .,. M '" M "I '" co'" .,.M '" co or-! r-!r-! r-!r-! r-!r-! "I "IN "I M M M.,..... 0 "I "'r-! M co "'r-! MN .... r-- r-!N M .,. '" r-- '" "I .,. '" '" "I .,. '" '" "I co '" co co '" 0 r-!M M '" r-- '" 0 M'" .... r-! "''''r-!"1M M M .,. .,. .,. '" '" '" .....,. .,.co co '" r-!r-! r-! r-!r-! r-!r-! "INN "1M MM '" '" '"'" r-- co '"ccc~ ~ ~ ~ ~-+CMIDDLECcCC-1. List the frequencies from smallest to largest of all the C's on the piano. Whatpattern do you find in these numbers?2.3.List theChoose apattern?frequencies ofI:>black key (B ,the G's. Does the same pattern occur?b bA , E , etc.). Do the frequency numbers make the same4. A C major triad consists of a C, an E (4 half-steps above C) and a G (7 half-stepsabove C). An F major triad consists of an F, an A (4 half-steps above F) and a C(7 half-steps above F). Fill out the charts below for the C and F triads. Do yousee a pattern in the charts?I I tC E I G E+-C G+-CI'" I A c A';'!'" C';'I'"yoU MIGHT USEA CALCULAiOR TOl-lELP FII.lD PAITERNSAND DOTI-IECOMPUTATIO!..l..~G5.40G I 82.A0'7 I 97. 9991'30.812(;1.G3523.25,104G . 5 I I I k~----.J43.GS41 55.0008'7.30'71'74.(;1349.2.'31>5.400IG98.~ I I I I~,