Where Music Meet Science Part 1: Pitch and Frequency

Summary

In this educational video, Scott Laird from the North Carolina School of Science and Math introduces the concept of frequency in music. He explains how pitch relates to frequency, with high pitches corresponding to high frequencies and low pitches to low frequencies. Laird uses diagrams and examples to illustrate how sound waves are created and measured, emphasizing that frequency is measured in cycles per second, or Hertz. The video also covers how octave relationships are calculated through frequency doubling, providing a foundation for understanding music's mathematical connections.

Takeaways

• 🎵 The term 'frequency' is introduced as a key concept in understanding music and its relationship to pitch.
• 🔍 Different musical instruments are chosen for their range of pitches, which is a result of varying sound frequencies.
• 🌊 Sound is created by the movement of air molecules, which form wave-like patterns that can be visualized as they move out from the source.
• 📊 The pitch 'A' above middle C, also known as A440, is used as a standard tuning reference in orchestras worldwide.
• 👂 The frequency of A440 is 440 cycles per second, which is also referred to as 440 Hertz (Hz).
• 📉 The size of the sound wave corresponds to the pitch: smaller waves represent higher frequencies (higher pitch), and larger waves represent lower frequencies (lower pitch).
• 🔄 The frequency of a sound wave is measured in cycles per second, or Hertz, which is a measure of how many times a wave vibrates in one second.
• 🎶 Octave relationships in music are mathematically represented by a doubling of frequency; for example, one octave above A440 is A880.
• 🎻 Different instruments tune to different 'A' frequencies based on their pitch range, such as the cello at A220 and the tuba at A110.
• 📚 Understanding the mathematical relationships between pitches and frequencies can deepen one's appreciation and knowledge of music theory.

Q & A

What is the main topic of the video?

The main topic of the video is the relationship between frequency and musical pitches, explaining how different frequencies correspond to different pitches in music.

What is the role of Scott Laird in the video?

Scott Laird is a music instructor at the North Carolina School of Science and Math, and he introduces the concept of frequency and its relation to music.

What is the significance of the number 440 in the context of the video?

The number 440 refers to the frequency of the tuning note A above middle C on the piano, which is commonly used by orchestras worldwide to tune their instruments.

How is the pitch of a sound related to its frequency?

The pitch of a sound is directly related to its frequency; higher frequencies correspond to higher pitches, while lower frequencies correspond to lower pitches.

What causes sound waves and how are they related to music?

Sound waves are caused by changes in air pressure, which occur when air molecules are forced together and then expand apart. These waves are the basis of music, as different instruments produce sound waves with varying frequencies, resulting in different pitches.

What is the term for one complete vibration of a wave?

One complete vibration of a wave is known as a cycle.

What is the relationship between the frequency of an A 440 and an A 220?

The frequency of an A 220 is one octave lower than an A 440. This means that the A 220 has half the frequency of the A 440, which is 220 cycles per second compared to 440 cycles per second.

How does the size of a sound wave relate to its frequency?

The size of a sound wave is inversely related to its frequency. Smaller waves are created for higher frequencies (higher pitches), and larger waves are created for lower frequencies (lower pitches).

What is the term used to measure frequency, and what does it represent?

The term used to measure frequency is Hertz (Hz), which represents the number of cycles per second.

What is the octave relationship between pitches in terms of frequency?

The octave relationship between pitches is represented by a doubling relationship in frequency. For example, if one pitch is at 440 Hz, the next octave higher would be at 880 Hz.

What does the video suggest about the importance of understanding frequency in music?

Understanding frequency in music is important because it allows musicians and listeners to appreciate the mathematical relationships between pitches and to better understand the unique sound characteristics of different instruments.

Outlines

00:00

🎵 Introduction to Frequency and Music

In this introductory segment, Scott Laird, a music instructor, sets the stage for the lesson on frequency in music. He explains that frequency is the scientific term for pitch, which is crucial for understanding music. The lesson aims to provide a working understanding of frequency, teach the parts of a sound wave, and enable students to calculate octave relationships using frequency. Scott uses the analogy of a pebble dropped in water to explain how sound waves are created, comparing the ripples in water to the wave-like motion of air molecules when sound is produced. He introduces the concept that the size and speed of the waves are related to frequency, with smaller and faster waves corresponding to higher pitches and larger, slower waves to lower pitches. The segment concludes with a focus on the pitch A, which is often used to tune musical instruments and is referred to as A440, indicating 440 cycles per second.

05:03

🔍 Exploring Cycles, Hertz, and Octaves

This paragraph delves deeper into the concept of cycles per second, also known as Hertz (Hz), which defines the frequency of a sound wave. Scott explains that the pitch A440 has 440 complete vibrations or cycles in one second, which is its frequency. The lesson progresses to demonstrate how different instruments tune to various frequencies, such as the cello tuning to A220, which is one octave lower than A440. The segment also introduces the concept of octaves, explaining that moving up one octave in pitch results in the frequency doubling. Scott challenges the audience to identify the frequency of the next octave above the violin's A440, which would be 880 Hz. The summary concludes with a brief mention of other interesting frequencies, such as the lowest open string on a bass or guitar, and a review of the key points learned about frequency and its relationship to music.

10:14

🌟 Sound Creation and Octave Relationships

In the final paragraph, Scott summarizes the key takeaways from the lesson. He emphasizes that sound is created by changes in air pressure that occur in wave-like motions. He reiterates that faster waves represent high pitches, while slower waves represent low pitches. The concept of a cycle, or one complete vibration of a wave, is highlighted as the basis for measuring frequency in Hertz. The lesson concludes with the important revelation that octave relationships in music are mathematically represented by a doubling of frequency. Scott expresses his hope that the insights into frequency have enriched the understanding of music and looks forward to further exploration in future lessons. The segment ends with a farewell from the North Carolina School of Science and Math.

Keywords

💡Frequency

Frequency refers to the number of occurrences of a repeating event per unit of time. In the context of the video, it is the number of wave vibrations or cycles that occur in one second, which is directly related to pitch. A higher frequency corresponds to a higher pitch, while a lower frequency corresponds to a lower pitch. The video explains that frequency is measured in Hertz (Hz), and the term is central to understanding how different pitches are produced by various musical instruments.

💡Pitch

Pitch is the perceptual property of a sound that allows its frequency to be identified as 'high' or 'low'. It is determined by the frequency of the sound wave; higher frequencies produce higher pitches, and lower frequencies produce lower pitches. In the video, pitch is used to describe the different musical notes produced by instruments and is directly related to the frequency of the sound waves they emit.

💡Sound Wave

A sound wave is a disturbance that propagates through an elastic medium, such as air, as a result of a vibrating object. In the video, the concept of sound waves is used to explain how sound is created and travels. The script describes how sound waves move from the source in all directions, getting quieter as they travel further, and how the size and speed of these waves relate to their frequency.

💡Hertz

Hertz is the unit of frequency in the International System of Units (SI) and is defined as one cycle per second. The term is used in the video to describe the frequency of sound waves. For example, the tuning note A 440 is named as such because it has a frequency of 440 Hertz, meaning the sound wave completes 440 cycles in one second.

💡Octave

An octave is the interval between one musical pitch and another with half or double its frequency. In the video, the concept of octaves is used to explain the relationship between pitches and frequencies. When moving up one octave in pitch, the frequency doubles. This is demonstrated by comparing the frequencies of different instruments tuning to various 'A' notes, such as the violin at 440 Hz, the cello at 220 Hz, and the tuba at 110 Hz.

💡Cycle

A cycle is one complete vibration or oscillation of a wave. In the context of sound waves, a cycle represents the time it takes for air molecules to be compressed and then expanded once. The video uses the term to explain how frequency is measured as the number of cycles per second, which is also the definition of Hertz.

💡Air Pressure

Air pressure is the force exerted by air molecules on a surface. In the video, it is mentioned that changes in air pressure create sound waves. The rise and fall of a sound wave represent the air molecules being forced together and then pushing apart, which is a direct result of changes in air pressure.

💡Wave-like Motion

Wave-like motion is a repetitive pattern of movement that travels through a medium, similar to how waves travel through water. The video uses the analogy of water waves created by a pebble to explain how sound waves are created and propagate through the air, with the speed and size of the waves relating to the frequency of the sound.

💡Tuning

Tuning is the process of adjusting the pitch of a musical instrument to play in harmony with others. The video discusses how different instruments tune to specific frequencies, such as the A 440, to ensure they are playing the correct pitch. Tuning is crucial for orchestras and helps to maintain a consistent pitch reference for all musicians.

💡Orchestra

An orchestra is a large instrumental ensemble that typically includes sections such as strings, woodwinds, brass, and percussion. The video mentions that orchestras traditionally tune their instruments to the pitch A 440, which is known as the concert pitch. This standardization allows for harmonious musical performances across different ensembles and instruments.

💡Doubling Relationship

A doubling relationship refers to the mathematical pattern where each successive value is double the previous one. In the context of the video, this concept is used to describe the relationship between octaves in music. When moving up an octave, the frequency of the sound wave doubles, which is a fundamental principle in understanding musical scales and harmony.

Highlights

Introduction to the term frequency and its relation to music

Understanding frequency as a numerical representation of pitch

The role of pitch in music composition and instrument selection

Explanation of sound creation through air molecule vibrations

Illustration of sound wave motion similar to water ripples

The significance of the tuning note A 440 in orchestras

Listening to orchestra tuning to unlock the secret of 440 cycles per second

Microscopic view of a sound wave to understand cycles

Definition of a cycle as one complete vibration of a wave

Frequency measured in cycles per second or Hertz

The relationship between frequency and octaves in music

Calculating octave relationships using frequency

Comparing frequencies of different instruments tuning to A

Understanding the pattern of frequency doubling per octave

Practical examples of frequency in various musical instruments

Review of the mathematical relationships between pitches and frequencies

Anticipation of the next lesson on complex waves and instrument sounds

Closing remarks and invitation to future lessons

Transcripts

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 math today we will

be introducing the term frequency and

begin to relate the numerical

information of frequency to the musical

knowledge that you already have

following today's lesson you will have a

working understanding of the term

frequency you will know the various

parts of a sound wave and you will be

able to calculate octave relationships

using your knowledge of frequency so

without any further delay let's begin

any time you listen to music and sounds

I'm sure that you are aware that there

are high pitched sounds and low pitched

sounds and many sounds in-between great

composers write music that has many

pitches ranging from high to low and

that keeps the music interesting many

musicians choose their instrument based

on the musical range of that instrument

that is how high or low that instrument

will play one person may like the sound

of a tuba

or string bass while another may be

drawn to the higher sounds of a flute or

a viola

all of these various pitches are a

result of sounds that are different

frequencies so another way to think of

pitch is to think of frequency if an

instrument has a high pitch then it has

a high frequency if an instrument has a

low pitch then it has a low frequency

but the question remains frequency of

what and how can it be measured well

here is where the science comes in sound

occurs when air molecules are forced

together after being forced together

they then expand farther apart creating

a wave-like motion of air look at the

cone of a stereo speaker as it is

playing music with a loud beat notice

how the speaker pushes out with each

beat this compresses air molecules and

begins the wave-like motion here is

another illustration of how it works

air reacts in a manner that is very

similar to water when a pebble is

dropped into it creating a series of

waves that move out in a circular motion

think of the water as the air and the

pebble as the sound the sound waves move

out from the sound source in all

directions getting quieter as it gets

further and further away a small pebble

can represent a high frequency or high

pitch it creates small waves that are

very close together a large rock can

represent low frequencies or low pitches

it creates much larger waves that

require much more space to develop so we

can tell that the speed and the size of

a wave relate to that waves frequency

also we have learned that frequency is

another term for pitch but let's dig a

little deeper let's look at the diagram

of a sound wave this is a diagram of the

pitch a it is the a above middle C on

the piano

it is also the pitch that in Orchestra

traditionally uses to tune the

instruments orchestras around the world

tune their instruments to the pitch a

this is also often referred to as a 440

440 is the number that we're interested

in today let's listen to the orchestra

as it tunes

to unlock the secret of the number 440

let's go back to a diagram of a

Soundwave this diagram represents the

pitch created by a violin playing the

tuning note a 440 in order to unlock the

secrets of the diagram we must zoom in

on the wave just as if we were looking

at it under a microscope now we are

looking at a very small portion of that

sound wave we said earlier that sounds

are created when molecules of air are

forced together the rise in the wave

represents the time that the molecules

are forced together the fall of the wave

represents the molecules pushing apart

so the y axis is air pressure you will

notice that it happens over and over

this takes time so the x axis represents

time one complete vibration of a wave is

known as a cycle and this is how we

begin to relate these pitches to numbers

can you guess how many complete

vibrations or cycles and a 440 goes

through in one second

the answer is in the name of the pitch

if you guessed 440 cycles per second you

were absolutely correct

this single vibration actually occurs

440 times in one second this is the

waves frequency the number of cycles or

waves that occur in one second let's

look at how fast that really is

anytime we hear that pitch the a above

middle C on the piano it is the

frequency 440 cycles per second let's

listen to a few different instruments

playing that same pitch or frequency

who

another name for cycles per second is

Hertz so we might say that you have just

heard several instruments playing a

pitch that is 440 Hertz or Hz so to more

completely define frequency it is cycles

per second or Hertz now let's take a

look at some instruments that tune two

pitches that are closely related to a

440 first let's listen to a cello tuning

is the pitch that the cello is playing

higher or lower than a 440

if you answered lower you were correct

in fact it is one octave lower than the

violin a let's take a look at the

diagram of the pitch that the cello

played after seeing both pitches as

diagrammed can anyone guess the

frequency of the cello

if you guessed 220 you are correct when

the cellist tunes their instrument they

hear an a 440 and play an a 220 this is

because the cello is a lower pitched

instrument the cellos tuning note is a

220 or 220

here are some other instruments that

tune to a 220

now let's listen to an instrument that

Tunes to yet another a

is this a higher or lower than the cello

eh

if you said lower you are correct

if the cello a is 220 Hertz then what is

the tuba a if you answered 110 you are

correct

let's look at the comparison of the

graphs of each of these pitches let's

listen to one more instrument playing

yet another a

using the formula that we have

established can you name the frequency

of the basis tuning note the basis

tuning note is 55 Hertz or 55 cycles per

second let's look at each of these

numbers and try to find a pattern

notice that as we move up one octave in

pitch the frequency doubles can you

determine the frequency of the next

octave above the violin if you said 880

then you are correct

might there be other frequencies that

you could be interested in here are a

few that you may find interesting this

is the lowest open string on an upright

or electric bass

this is the lowest open string on a

guitar

let's review all that we have learned

today first the sound is created by

changes in air pressure second these

changes occur in a wave-like motion

third faster waves or frequencies

represent high pitches slower waves or

frequencies represent low pitches fourth

one complete vibration of a wave is a

cycle and frequency or pitch is measured

in cycles per second or Hertz finally

octave relationships between pitches are

represented by a doubling relationship

these mathematical relationships between

pitches of frequencies can open a whole

new world of understanding of music as

you begin to use them more and more in

the next lesson we will discuss the

notion of complex waves and the unique

sound of each instrument in the

orchestra I hope that you have enjoyed

learning about frequency today and how

it relates to our lives I look forward

to working with you again in the future

for now so long from the North Carolina

school of science and math