“Mathematics is involvedin some way in every fieldof study known tomankind. In fact, it couldbe argued thatmathematics is involvedin some way in everythingthat exists everywhere, oreven everything that isimagined to exist in anyconceivable reality. Anypossible or imaginedsituation that has anyrelationship whatsoever tospace, time, or thoughtwould also involvemathematics.”
Math is related to everything including music. Mathrelates to the rhythm, keys, and tuning. When you arelistening to music, you count the beats. When youplay the piano, you can count the keys as numbers.The piano needs to be constructed in a way so thatwhen the key is hit a specific frequency is given offfrequency is measured in hertz. The math of rhythmis about the time values (note lengths);whole, half, quarter, eighth, sixteenth, just keephalving that and you have the nearly the whole idea.The maths of meter, time signatures, is one of simplefractions.
Music is a field of study that has an obviousrelationship to mathematics. Music is, to manypeople, a nonverbal form of communication, thatreaches past the human intellect directly into the soul.However, music is not really created by mankind, butonly discovered, manipulated and reorganized bymankind. In reality, music is first and foremost aphenomena of nature, a result of the principles ofphysics and mathematics. Maths and music areusually organized into two separatecategories, without obvious overlap.
Maths is everywhere and it isa very important factor inplaying the piano. You needrhythm and you need to countthe beats. The right hand hasto play 4 evenly spaced notesin the same amount of timethe left plays 3, also spacedevenly. So each note in theright hand is played for onefourth of the totalinterval, while each note onthe left is played for one thirdof the interval.
The ‘Math of Intervals is the distance from one pitchto another. Intervals are measured by the number ofhalf steps between two pitches (the distancebetween any key on the keyboard on the immediateneighbour is a half step.) Knowing the number ofletter names and how many half-steps there arebetween one note and another are what allow youto determine the interval, and what quality, ithas, i.e. major, minor, diminished, augmented.Learning intervals is simply counting andmemorizing, not anywhere near a math function.‘For acoustics, the physics of sound, a much greaterdegree of maths is involved. For general musicreading, writing and performing, the maths requiredare basic counting, simple fractions and that is it.You may have heard the maths / music pointexaggerated as if the combination of the two were akey to understanding the universe.
One jumps out at you when you look at sheet music is the time signature. Another is the tempo, sometimes given as a metronome rate. Note values are fractions (quarter, sixteenth), so a dotted note means multiply the value by 1.5. These things arent very complicated, but they are right out there in front.
A little less visible but even more important is the matter of pitch. A pitch is created by a vibration. In the case of your piano, middle A vibrates a string 440 times a second. Physicists call this a frequency of 440 hertz, or 440 cycles per second.
If you go up an octave, you double the frequency. Other intervals are other ratios. Going up a fifth (from A to E) multiplies the frequency by 3/2, so E is (about) 660 hertz. The Greeks discovered that two strings played together sounded pleasant if the lengths of the strings were in ratios of small whole numbers: 2:1 (octave), 3:2 (fifth), 4:3 (fourth), 5:4 (third).
The interval from A to E (a fifth), in equal tempering, isnt exactly 3/2 = 1.5, but 2^(7/12) = 1.4983. (The "^" represents an exponent.) The interval of a fourth isnt 4/3 = 1.3333, but 2^(5/12) = 1.3348. The interval of a third isnt 5/4 = 1.25, but 2^(4/12) = 1.2599. I wont say exactly what equal tempering is, but you might be able to figure it out from what I said, depending on your math level. Equal tempering is related to a "logarithmic scale."
Black keys on the piano are shown as sharps, e.g. the # on the right of C represents C#, etc., and are shown only for the highest octave. Each successive frequency change in the chromatic scale is called a semitone and an octave has 12 semitones.
The word chord here means two notes whose frequency ratio is a small integer. Except for multiples of these basic chords, integers larger than about 10 produce chords not readily recognizable to the ear.
The interval between C and G is called a 5th, meanings; the second is a subset of the first. and the frequencies of C and G are in the ratio of 2 to 3. The major third has four semitones and the minor third has three. The number associated with each chord, e.g. four in the 4th, is the number of white keys, inclusive of the two end keys for the C-major scale, and has no further mathematical significance. Note that the word "scale" in "chromatic scale", "C-major scale", and "logarithmic or frequency scale" has different meanings; the second is a subset of the first.
|--Octave-- CDEFGAB 1 We can see from the " to an octave above that |--5th-- a 4th and a 5th "add up and a major 3rd and a CDEF 2 minor 3rd "add up" to a 5th. Note that this is an |--4th-- GAB addition in logarithmic space. The missing integer 3 7. |-Maj.3rd- C#D# 4 |-Min.3rd- EF# 5 | G#A#B 6 | C 8
The "equal tempered" (ET) chromatic scale consists of "equal" half-tone orsemitone rises for each successive note. They are equal in the sense thatthe ratio of the frequencies of any two adjacent notes is always the same.This property ensures that each note is the same as any other note(except for pitch). This uniformity of the notes allows the composer orperformer to use any key without hitting bad dissonances. There are 12equal semitones in an octave of an ET scale and each octave is an exactfactor of two in frequency. Therefore, the frequency change for eachsemitone is given bysemitone12 = 2 orsemitone = 21/12 = 1.05946. . . . . . . . . . . . . . . . . .This defines the ET chromatic scale and allows the calculation of thefrequency ratios of "chords" in this scale. How do the "chords" in ETcompare with the frequency ratios of the ideal chords? The comparisonsare shown in Table 2.2b and demonstrate that the chords from the ETscale are extremely close to the ideal chords.
You may not need to know the math behind music, but it is truly important to you. Music sounds good to us because of its mathematical patterns - rhythms and pitches - and math has been used over the years to make music sound better. Math and music belong together.
Made by-ZionTyreseGhazalAbdullahMuskan Sethi