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— | musicwiki:piano [2023/01/07 15:50] (current) – [All musical notation related images] ying | ||
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+ | ====== Math behind Piano keys ====== | ||
+ | =====Relationship between key groups===== | ||
+ | |||
+ | * piano keys are made of a set of octave key groups, each octave key group made from 7 white keys and 5 in-between black keys. (total 12 keys per octave key group) | ||
+ | * each octave key group is double the sound frequency of previous octave key groups | ||
+ | * example, | ||
+ | * octave key group 1, containing 7 white keys {" | ||
+ | * the C2 key from octave key group 2 is at sound frequency of 65.406 HZ, that is 32.703x2. | ||
+ | * the middle group (4th group), C4 is at 261.6Hz, = 65.406*2^2 | ||
+ | * as you can see, the number is exact "times power of 2", as you can guess, C7=C1x[2^(7-1)] =32.703x64=2092.9 (about 2093Hz) | ||
+ | |||
+ | * youtube: | ||
+ | - Music and math: The genius of Beethoven - Natalya St. Clair | ||
+ | * https:// | ||
+ | - beats and math | ||
+ | * https:// | ||
+ | =====Frequency Relationship within a key group and White vs Black keys===== | ||
+ | |||
+ | * study 1st octave key group, white keys {" | ||
+ | * C1=**32.703Hz** | ||
+ | * D1=36.708Hz = C1 + 4.0Hz | ||
+ | * E1=41.203Hz = D1 + 4.5Hz | ||
+ | * F1=43.654Hz = E1 + 2.4Hz (so F1 is "half step", aka "half incremental" | ||
+ | * G1=48.999HZ = F1 + 5.3Hz | ||
+ | * A1=55.000Hz = G1 + 6.0Hz | ||
+ | * B1=61.735Hz = A1 + 6.7Hz | ||
+ | * C2=**65.406Hz** = B1 + 3.7Hz (so C2 is mostly like "half step" from B1) | ||
+ | * so we can see, the incremental is based of a power function curve. | ||
+ | * based on that, "half step" incremental white keys has no in-between black keys, while those " | ||
+ | * in short, all keys in piano are layout in "half step" increment, either "black to white", | ||
+ | |||
+ | =====How Many key groups we need===== | ||
+ | * while average human can hear from 20Hz to 8000Hz, so from C1 32.7Hz to C8 4186Hz reaching C9's 8392Hz are enough; | ||
+ | * which means 8 sets * (7 white key+ 5 black key) = 96 keys | ||
+ | |||
+ | =====How much frequency difference to make a key identifiable and photographic-like-color-depth===== | ||
+ | |||
+ | * as in previous calculation, | ||
+ | * however, the real human hearing factor is that the effect of each key difference is about similar, like **" | ||
+ | * it is more a ratio difference than a count difference | ||
+ | * compare D1 to C1 (full step), 4Hz difference is roughly 1/8 of 32.703Hz (C1); D1=C1 * 1.12; | ||
+ | * compare B1 to A1 (full step), 6.7Hz difference is roughly 1/8 of 55Hz (A1); B1=A1 * 1.12; | ||
+ | * compare F1 to E1 (half step), 2.4Hz difference is roughly 1/16 of 41.203Hz (E1); F1=E1 * 1.06; | ||
+ | * compare C2 to B1 (half step), 3.7Hz difference is roughly 1/16 of 61.735Hz (B1); C2=B1 * 1.06; | ||
+ | |||
+ | * so, | ||
+ | * each key of piano is half step from nearby one, that is 1.06 times higher or lower than nearby one. | ||
+ | * each "full step" is 1.12 times higher or lower; since 1.12 = 1.06 * 1.06; | ||
+ | * each octave is 12 keys (half step) difference, power(1.06, 12) = 2 | ||
+ | * more accurately wrriten as **power(1.0595, | ||
+ | |||
+ | * so to pianist term, roughly 1/16 difference (or accurately 0.0595 difference) is about the minimum frequency difference to make identifiable | ||
+ | |||
+ | * related read: | ||
+ | * " | ||
+ | * Note names and frequencies calculator: http:// | ||
+ | |||
+ | =====Frequency and Loudness===== | ||
+ | |||
+ | * we often find, low frequency keys like in C1-C3 range, need to press harder than normal to make them sounds loud; while C4-C5 are easy to make it loud; while C6 and higher sound are easier to think it loud. that is because our hearing are sensitive to high frequency sound. | ||
+ | * here is a graph of "how loud" is same " | ||
+ | * Absolute threshold of hearing: http:// | ||
+ | * and our human ear use " | ||
+ | |||
+ | ===== All musical notation related images ===== | ||
+ | |||
+ | * guitar notation (E2 to E6) | ||
+ | {{musicwiki: | ||
+ | * octave sheet notation to piano mapping | ||
+ | {{musicwiki: | ||
+ | {{musicwiki: | ||
+ | * frequency ration based scale map | ||
+ | {{musicwiki: | ||
+ | {{musicwiki: | ||
+ | |||
+ | =====Property of Sound - soundwave and wave in general===== | ||
+ | |||
+ | * wave has these property (think of those waterwave) | ||
+ | * amplitude: height of wave | ||
+ | * wave length: distance between 2 high points | ||
+ | * period/ | ||
+ | * speed = wave length * frequency: how fast high point shift away | ||
+ | |||
+ | * soundwave | ||
+ | * amplitude: aka " | ||
+ | * wave length: | ||
+ | * frequency: aka " | ||
+ | * (Human range from 20Hz to 10kHz, piano 20Hz to 8kHz) | ||
+ | * speed: in air, about 300m/s; thus also means high frequency sound has short wavelength. | ||
+ | * lightwave | ||
+ | * frequency: around 10^14Hz, (100THz) | ||
+ | |||
+ | * sound to humans | ||
+ | * low frequency sound travels further, because of lower frequency are less absorbed when traveling through medium, and also less reflected by medium (better penetration into another medium) | ||
+ | * high frequency are more noticeable to humans, due to human ear nature. | ||
+ | * sound " | ||
+ | ====== Training Learning in keyboards ====== | ||
+ | |||
+ | * Jingle All the way: http:// | ||
+ | * We Wish You a Merry Christmas (Christmas Carol) [Easy Piano Tutorial] http:// | ||
+ | |||
+ | * Silent Night (Christmas Carol) [Easy Piano Tutorial] http:// | ||
+ | * Jingle Bells (Christmas Carol) [Easy Piano Tutorial] http:// | ||
+ | |||
+ | * Twinkle, Twinkle, Little Star [Easy Piano Tutorial] http:// | ||
+ | * Mozart version : http:// | ||
+ | * Guitar version : http:// | ||
+ | * Happy Birthday to You [Easy Piano Tutorial] http:// | ||
+ | |||
+ | ====== Songs ====== | ||
+ | |||
+ | * Japanese song | ||
+ | * Doraemon: http:// | ||
+ | |||
+ | |||
+ | Some tutorial collection | ||
+ | * http:// | ||
+ | * http:// | ||
+ | * | ||
+ | |||
+ | ====== Reference Site ====== | ||
+ | |||
+ | * https:// | ||
+ | |||
+ | ====== Reference Book ====== | ||
+ | |||
+ | * Piano Adventures series by Nancy and Randall Faber | ||
+ | * John Thompson' | ||
+ | * John Thompson' | ||
+ | * Hanon 60 exercises | ||
+ | * Czerny op. 599 | ||
+ | * Aural Training in Practise book 1 by Ronald Smith | ||
+ | |||
+ | ref: https:// | ||
+ | ====== 3D visualization ====== | ||
+ | |||
+ | * Maya code on generating piano keys | ||
+ | * white key on even X axis spacing, and Y axis represent half step and whole step relationship | ||
+ | * here is mel code <code javascript> | ||
+ | string $names[]={" | ||
+ | string $names2[]={" | ||
+ | |||
+ | // -- white keys only | ||
+ | $total=7*5; | ||
+ | for ($i=0; | ||
+ | int $n=$i%7; | ||
+ | int $oct=$i/7; | ||
+ | $tCube=`polyCube -ch on -o on -w 1 -h 1 -d 2 -cuv 4 -n ($names[$n]+" | ||
+ | float $s=$n; | ||
+ | if($n> | ||
+ | move -a $i ($oct*6+$s) $oct $tCube[0]; | ||
+ | } | ||
+ | for($i=1; | ||
+ | select -r (" | ||
+ | group -n (" | ||
+ | } | ||
+ | |||
+ | // -- white keys and black keys | ||
+ | $total=12*5; | ||
+ | for ($i=0; | ||
+ | int $n=$i%12; | ||
+ | int $oct=$i/12; | ||
+ | $tCube=`polyCube -ch on -o on -w 1 -h 1 -d 2 -cuv 4 -n (" | ||
+ | string $sn=$tCube[0]; | ||
+ | |||
+ | move -a ($oct*6+$n*0.5+$oct) ($oct*6+$n*0.5) ($oct+10) $tCube[0]; | ||
+ | if($n> | ||
+ | | ||
+ | if(`gmatch $sn " | ||
+ | } | ||
+ | </ |