A pitch is worth a thousand words, right?

The word pitch is nothing new for even the most cursory of music lovers.

We often casually describe sounds as high or low pitch, which is one of the easiest “shorthand” ways of describing music.

What the Pitch?

But when it comes to the technical bits, the pitch is a bit more complex than that.

What does it mean mathematically when we dub something “high pitched”?

What components of sound create pitch? 

Pitch is the position of a single sound in the complete range of possible sounds.

Musicians create melodies using two main elements, namely, duration, and pitch.

Pitch is a property of sounds more generally, and not just music.

Voices have a pitch, industrial machines have a pitch, animal calls have a pitch, and streams cascading over rocks have a pitch.

You get the picture.

So all notes have a pitch, but not all pitches can be ascribed to a musical note or be denoted on a musical staff. 

The Role of Frequency

Let’s get down to the nitty-gritty.

All of the music we hear is the product of sound waves, invisible vibrations that our ears interpret as either pleasant or unpleasant, inspiring or grating. 

Sound waves are made up of something called frequency.

Frequency describes how fast or slow the sound wave vibrates as it radiates outward from its source.

Pitch is an easy, one-syllable way to describe how our ears pick up on frequency.

The higher the frequency, the higher the pitch.

The lower the frequency, well, you get the gist!

So how do we describe pitch in a more detailed way?

How do we communicate frequency explicitly, rather than purely descriptively?

Enter the Hertz (Hz). No, not the ketchup.

Frequency can be measured as the number of times a sound wave repeats in one second.

This number is described in hertz. If a sound had a pitch of 200 Hz, that means the sound wave that creates the note that you hear repeats 200 times in one second.

We can’t even wrap our heads around how the first scientists discovered this.

Fun fact for you.

The human ear can only hear sounds, or “tones,” with pitches between 20 and 20,000 Hz – a pretty big range, but not inclusive of all the sounds that exist in our wild and wacky universe.

Nearly all of the music you will encounter is between 50 and 8,000 Hz.

The higher the hertz value, the higher the pitch: 880, for example, is considered high-pitched.

Fifty-five hertz is considered low frequency.

Pitch in Musical Notation

Musical staffs can be described as visual representations of the pitch.

As the notes ascend the scale, they rise in frequency, and thus, pitch.

Higher-pitched notes are the highest notes on the staff.

Higher pitches are represented on the treble clef of a standard musical scale.

Lower pitches are represented on the tenor or bass clef of a standard musical scale.

In most Western music, the scale is tuned to a standard where the A above the middle C note is 440 Hz.

This allows for standardization.

Musical notes (like C or B Minor) have a series of specific, unchanging frequencies across time and space.

In the Western musical tradition, there are 12 notes, listed in the chromatic scale, each of which has its own unique range of pitches and hertz values. 

Why do notes have more than one pitch?

Each note can be played in higher or lower octaves.

On the piano, the note C can be played in 8 different octaves and thus has 8 different pitches.

For note C, the pitch ranges from 32.70 Hz to 4186.01 Hz.

If you want to describe the pitch of a note at one octave higher, you simply double the hertz value.

To go up one more octave in pitch, you would double the hertz value again.

If a pitch is 440 Hz, for example, to describe the next octave up on the piano keyboard, you’d say it has a pitch of 880 Hz.

Perfect 4ths and 5th are also similar, pitch-wise.

Mathematically, the perfect 4th has a ratio of 4:3  to the main note, and the perfect 5th has a ratio of 3:2 above the main note.

An interesting point: when a note is out of tune, the frequency will not be correct, i.e. it will not conform to the normal and expected pitch for that note.

If you’ve ever heard an untuned guitar, you’ll know instinctively how “off” the notes sound.

That is your ear reacting to fluctuations in pitch.

Naming Pitches 

Musicians and composers name a pitch based on the name of the note and the octave the note appears in.

The note F in the third octave would be called an F3.

This offers a simple way for musicians to describe pitch without rattling off a list of long-winded hertz values.

Pitches that can be identified and named easily and consistently are called definite pitches.

Instruments like piano and guitar produce definite pitches.

Pitches that are harder to pin down and identify are called indefinite pitches.

Drums, tambourines, and cymbals produce indefinite pitches. 

The Role of Math

Notes in the same scale, and notes from the same chord, are mathematically related to each other by pitch.

When you think about it, it is miraculous how mathematical formulas create the harmonious and fluid sounds that come to us as music.

Harmonic, pleasant sounds are all intricately related in a logical way. 

Discordant, mathematically disproportionate notes from different scales sound jarring and unnatural.

Simply put, it is because the math doesn’t add up.

The math behind the scales does, however, add up, and that is why they sound so intuitive to the human ear.

The Power of the Pitch 

While you don’t need to drive yourself crazy memorizing all of the hertz values for all the notes on all the scales, it is vital to have a familiarity with the logic and structure behind the sound.

Music truly is a numbers game, and the math behind the melody is nothing short of magic, no?

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