Delta Waves: Music and Sleep | Music Science | Part 1

If you have done any research into how music can help with sleep, you’ve probably come across the term “delta waves” or “delta wave music.” I have to admit that this topic was new to me, but I was intrigued. So I went ahead and did the research, and compiled the information for you.

Summary: delta waves are a type of brain wave that we experience in deep sleep. They are a very low frequency wave. By listening to binaural music (music played simultaneously in your left and right ear at different frequencies), they create a low frequency wave that mimics your brain’s delta waves. The goal is to influence your brain into emitting delta waves, thereby promoting sleep.

This is a huge topic, and in order to explain it fully this will be split into two parts. Part one will explain the music science, or how music can create new frequencies. Part two will explain brain waves and how they function during sleep. You can read part 2 here.

(If you’d like to see this content in video form, watch my YouTube video here.)

Music and Sound: The Basics

We first need to give definitions for music and sound. From there, we will expand these topics as we explore how music can create new frequencies.

Music actually has a very simple definition: it is the combination of sound and silence. But in order to fully understand that definition, we have to understand music’s two components. Silence is self-explanatory: it is the absence of sound. But what is sound?

Sound is a vibration which travels through the air, or other medium, and reaches your ear. These vibrations travel in the form of waves. We also need to understand the basic properties of sound waves, but I will keep this as simple as possible and only discuss the property most crucial to our discussion: frequency.

Frequency is the number of occurrences of a repeating event per unit of time. So if you bounce a ball once a second for one minute, the frequency of ball bounces is 60. In sound waves (and music), we measure frequency in hertz (Hz). Hertz is measured as one occurrence of a repeating event per second. So if we take our bouncing ball example, its hertz is 1 hertz because the repeating event (the ball bouncing) occurs once every second.

In music, the most common frequency we use is 440 Hz. This means that every second there are 440 vibrations, or sound waves, occurring.

Music and Frequency

There is a simple, direct relationship between music and frequency: the higher the frequency, the higher the pitch. In this case, I will define pitch as being the note that is sounded by an instrument. If you listen to a piccolo, the highest sounding instrument in the orchestra, the pitches it produces have a much higher frequency than the pitches of the double bass, the lowest sounding instrument in the orchestra.

Another relationship between music and frequency is that frequencies are proportional. As I mentioned above, the most common frequency we use in music is 440 Hz. This is our tuning A. So if you hear an orchestra tune before the concert, the oboe is playing the pitch A which has a frequency of 440 Hz. I won’t get into why certain frequencies have been given certain note names…that would become way too complicated…

But what is important is that frequencies can be doubled or halved, and they produce the same note name, but at a higher or lower pitch.

So let’s take our tuning A as an example. Tuning A’s frequency is 440 Hz. If we double its frequency, we arrive at 880 Hz. This new note is still an A, but it is higher in pitch. We say this 880 Hz A is one octave higher than our tuning A. If you listen to both frequencies, you will notice that they both sound the same, just one is higher than the other. The same is true if you take tuning A’s 440 Hz frequency and halve it to 220 Hz; we get a note that still sounds like an A, but this time it is an octave lower.

A – 220 Hz
A – 440 Hz (Tuning A)
A – 880 Hz

If you listen to all three tones above, you will notice that they all sound essentially the same, just higher or lower versions of the same tone.

The Harmonic Series

I won’t lie, this is starting to get much more technical. But stick with me, because this concept is fascinating!

When we play a note or tone, that pitch is known as the fundamental. Inside the fundamental, there are an infinite number of frequencies contained within the fundamental, and these resultant frequencies are known as overtones.

Overtones occur in a specific, mathematical sequence, and they are important to musicians in several ways. First, overtones are an important element of how musicians understand the tuning process and the science behind it. Second, and arguably more important, the harmonic series and its overtones are crucial to brass players (trumpet, trombone, etc.). Brass instruments are built around the harmonic series, and brass players know the harmonic series extremely well.

In Western music, we have twelve unique pitches (not including octaves). However, brass instruments only have seven different fingerings or positions they’re capable of producing. So how does a brass player with only seven positions play all twelve notes? The harmonic series. Each of the seven positions on a brass instrument is (technically) capable of producing an infinite number of pitches.

Let’s look at the chart below (ignore everything except the numbers 1-16). If you can’t read music, don’t worry. For the sake of this explanation, let’s pretend we are playing the tuba since this a good real-life example.

The harmonic series

Pitch number 1 in the above chart is our fundamental. This is also one of the lowest pitches the tuba can play. With the one fingering required to play that pitch, the tuba player can also play every other note in the harmonic series shown above. Simply by not changing their fingers, but by changing the shape of their mouth and increasing their air speed, the tuba player can produce pitches 2-16 (though it becomes harder the higher the pitches go).

This phenomenon occurs in every pitch, meaning you don’t have to play a low pitch for this sequence to work. However, it is easiest to explain and hear in lower pitches because they occur within our ears’ frequency range.

Difference Tones

The next way we can use the overtones of the harmonic series is by calculating difference tones. When two frequencies are played simultaneously, they create a resultant frequency known as a difference tone. The difference tone is calculated by subtracting one frequency from the other.

For example, let’s say we have two frequencies of 880 Hz and 440 Hz (two of our A’s from above). If we take 880 minus 440, we get a difference of 440. So if the frequencies 880 Hz and 440 Hz are played simultaneously, we get a resultant difference tone of 440 Hz. If you are not a musician, this may be difficult to hear, but this phenomenon is occurring.

We can use this same formula and apply it to the harmonic series. Looking at the chart above, let’s take pitch numbers 12 and 9. We subtract 9 from 12, and get a difference of 3. Pitch number 3 is the resultant difference tone that sounds when pitches 9 and 12 are played simultaneously.

As a quick fun fact, any two adjacent pitches in the harmonic series played simultaneously will result in a difference tone that is equal to the fundamental. For example, 7-6=1.

So after all of this technical analysis, why do difference tones matter? It is because difference tones are the basis behind why people listen to delta wave music.

Music and Delta Waves

When people listen to delta wave music, they are listening to two frequencies played binaurally. This means that two different frequencies are played simultaneously, with one frequency in your left ear, and one in your right. These are usually low frequencies, because we want a low, inaudible (to humans) difference tone that will mimic our brain’s delta waves (more on this in part two).

For example, in your right ear is a 300 Hz tone, and in your left ear is a 290 Hz tone. The difference tone is 10 Hz. This frequency falls below the human hearing range; however, our brain can supposedly process that frequency. This, in turn, is supposed to influence our brain waves to slow down and match the difference tone’s frequency. By slowing down our brain waves, we are promoting sleep because our brain waves have a lower frequency during sleep.

Part two will go into more detail about the science of brain waves, delta waves, and sleep.

Conclusion

If you are a professional musician or sound engineer, you may find these explanations unsatisfactory. But I think that’s okay. These topics are extremely dense and difficult to process by reading just one article.

My goal was to provide an introductory overview to music and sound waves, and how they can help influence our brain.

Don’t forget that there is a part two to this article. Let me know in the comments if you have any questions, if there is anything you want further explanation on, or anything else that can help make these articles as helpful as possible.

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