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Where Music Meet Science Part 3: Frequency and Harmonics



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hello and welcome to where music meets

science my name is Scott Laird and I'm a

music instructor at the North Carolina

School of Science and Mathematics in our

last lesson we learned about frequency

and Tambor the unique sound that each

instrument makes in this lesson we will

be learning about harmonics and the

relationship between harmonics and the

music that we listen to every day in

order to do this let's begin by looking

at the notes that make up a major scale

a major scale has eight tones

much of the music that we listen to

every day is based on a major scale all

styles of music from pop to folk to

classical and even rock and roll use the

major scale as the foundation for their

melodies and harmonies for today's

lesson we will be using the a major

scale this is because in the past two

lessons we focused on the note a however

all of the concepts that we cover in

today's lesson relate to all of the

major scales an a major scale has eight

tones they are

these can be represented with a number

as we consider each step of the scale

now let's consider some of the important

parts of a scale certainly the two A's

number one and eight are the most

important notes of the scale they are

known as the tonic and they bear the

name of the scale in this case a major

the next note of importance is the fifth

note of the scale it is known as the

dominant of the scale and is generally

considered to be the second most

important note in the major scale

next we have the third note of the major

scale this note is known as the mediant

and it is the tone that makes a scale

major

lastly the tonic mediant and dominant or

the first third and fifth notes of the

scale all work together to form a major

triad or a chord

again we hear major chords every day in

music

now let's take a look at frequencies and

harmonics and how they relate to major

chords think back to our last lesson on

frequencies and Tambor when the cello

sounded and a 220 other frequencies

showed up in the wave that we studied

those frequencies are four hundred forty

six hundred sixty and 880 Hertz note

that the numbers representing the

frequencies are all related they are all

multiples of two hundred twenty Hertz

the fundamental frequency multiples of

two hundred twenty include the following

numbers two hundred twenty times two

equals 440 two hundred twenty times

three equals six hundred sixty two

hundred twenty times four equals eight

hundred eighty two hundred twenty times

five equals one thousand one hundred two

hundred twenty times six equals one

thousand three hundred twenty two

hundred twenty times seven equals one

thousand five hundred forty two hundred

twenty times eight equals one thousand

seven hundred sixty look again at the 3d

representation of the cellos a two

twenty

can you see the wave at each of these

frequencies we know that a the tonic

note is 220 Hertz

what other frequencies that are shown

are the note a

as you can see there are four A's

represented in these numbers to 24 48 80

and 1760 but what about the other

numbers first there's the frequency 660

it is the pitch e220 446 68 80 note that

E is the fifth or dominant note into a

major scale so clearly the first three

harmonics are closely related to the a

major scale they are the tonic dominant

and tonic notes now let's look at the

fourth fifth and sixth harmonics

using what we know about octaves and

doubling we can name another one of the

harmonics

what is 660 times two the answer of

course is 1320 what is the name of that

pitch

if you answered II you are correct now

let's use some reasoning to figure out

the fourth harmonic 1100 Hertz if you

guessed c-sharp you are correct

remember that c-sharp is the median of

the a major scale or the third note of

the scale the fourth harmonic or fourth

multiple of a fundamental is always the

third note of the major scale finally

the seventh harmonic is AG natural now

this may not seem to fit into the

pattern of the a major scale a major has

a G sharp G sharp is the seventh note of

the scale and well it would take more

time than we have today to fully explain

the presence of a G natural in this

series I would like you to hear what it

sounds like within the chord a C sharp E

G natural

the G natural makes the cord dominant a

dominant chord feels like it should be

moving on to another chord now let's

listen to the fundamental and each of

the harmonics in order

let's review some of the material that

we've covered in today's lesson first we

discussed the major scale and the

important notes in the major scale we

said that the 1st and 8th step of the

scale are the most important tones and

that the 5th and 3rd tone of the scale

also serve very important roles when

these tones are played together they

form a major chord or triad

next our goal is for you to understand

that there are many frequencies

represented in each note that we here

this group of frequencies which are

multiples of the fundamental frequency

are called harmonics

next we considered the numbers that

would follow if we listed the

fundamental and the first six multiples

of a 220 we then looked at the pitch

names that are associated with those

frequencies finally we found a pattern

in those pitches the first six multiples

of a fundamental are the first third

fifth and eighth notes in the major

scale beginning on the fundamental

we can draw a close comparison between

the harmonics of a note and the major

scale and chord associated with that

note thank you for joining me today for

where music meets science frequencies

and harmonics if today's topic was a

particular interest to you don't stop

here I encourage you to go to your

school library or your community library

and continue to learn about frequencies

there are a variety of careers that one

might pursue if they're interested in

this topic from physicist to sound

engineer to hearing specialist to

acoustic architect a sound engineer uses

his knowledge of frequencies and sound

to create good sounding recordings and

pleasing live sound support in a variety

of venues here at the school of science

and math we had a guest lecturer who

uses her knowledge of frequencies to

study and predict underwater earthquakes

architects use their knowledge of

frequency to choose materials for

buildings architects want some rooms to

be quite loud and reverberant while

others need to be very quiet finally

hearing specialists use their knowledge

of frequencies to diagnose hearing

problems and to accurately provide

recommendations for solving those

problems it has been a pleasure working

with you today and I look forward to the

next time we get together