# Accurate understanding of the physics of sound?

I'm trying to learn theory. I'm starting with the physics of sound as the base. Here is what I (think I) know. Is this accurate?

Music is sound. Sound travels in waves. Sound waves have two properties: amplitude and frequency. Amplitude is the height of the sound wave and determines how loud something is. Amplitude has basically nothing to do with note differentials (i.e. A, B, etc.). Frequency measures sound wave cycles per second in hertz (Hz) and has everything to do with note differences. Each note has its own frequency. The general reference point with guitars is A = 440Hz. The audible spectrum for most humans is from 20Hz to 20000Hz. A 20 fret guitar with standard tuning ranges from 82.4Hz (E) to 1318.51Hz (E).

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– Dom
Apr 12 '19 at 20:17

I went down a similar road. There is an entire branch of physics related to sound that is called acoustics. Starting to look for books and more information on "acoustics" will help you find more and better materials as you move forward.

The subject of acoustics is pretty broad - there are many aspects of acoustics that are not directly applicable to understanding music. All music is sound, but not all sound is music. You might further narrow searches by looking for "musical acoustics".

Finally, there is a branch of science that isn't exactly psychology, physiology, or physics, but the branch deals with the intersection of all of those, and that is called psychoacoustics. Psychoacoustics is very relevant to the musical experience for the listener, and its findings can be very edifying to the musician, composer, and other musical creatives. It's basically the study of how humans generally interpret different sounds.

With that out of the way, let's address what you're trying to understand right now.

Music is sound. Sound travels in waves. Sound waves have two properties: amplitude and frequency. Amplitude is the height of the sound wave and determines how loud something is. Amplitude has basically nothing to do with chord differentials (i.e. A, B, etc.).

That's a pretty good grip on things up until the last few words. I think what you really mean by "chord differentials" is just "different notes". While it's 99% true that the amplitude or intensity of a sound wave does not affect the pitch (the scientific term for the perceived note) of a sound wave, it turns out that there is a very minor shift in pitch perception of the human ear between louder and softer sounds. Generally, we don't worry about this at all, because it's far too minor, but if you really want to know the science, then it has been observed that sound intensity affects pitch perception. As a musician, you can pretty much ignore that when composing or performing, at least for now.

Frequency measures sound wave cycles per second in hertz (Hz) and has everything to do with chord differences. Each chord has its own frequency.

Replace the word "chord" in that sentence with the word "pitch" and you'll be getting a lot close. From your question, I wonder if you might leave alone the idea of chords for right now, and focus on single notes or pitches. Remember, pitch is the scientific word for the perception of a note. The word "perception" is critical here, because a frequency or frequencies doesn't become a note until it is heard and decoded (perceived) by a human ear and brain. The thing is, the human ear and brain are not prefect scientific instruments - our perceptions can be funny sometimes.

Generally, yes, every pitch we perceive is based on a specific fundamental frequency. At the same time, actual musical sounds are almost always composed of many frequencies of sound all playing at the same time. Even a single note played on a instrument will produce many frequencies. The reason why we perceive several simultaneous frequencies as a single pitch or note is because those frequencies all have a mathematical relationship with each other. An example of a musical sound composed of many frequencies that are not related to a pitch is a crash cymbal. The frequencies of sound created by a crash cymbal do not have a mathematical relationship to each other, so instead of hearing a pitch or a note, we hear a kind of noise. That noise is still a musical sound (usually), but it's not a pitch or note. So the relationship between frequencies and notes is very important, but it's not very simple.

The general reference point with guitars is A = 440Hz. The audible spectrum for most humans is from 20Hz to 20000Hz. A 20 fret guitar with standard tuning ranges from 82.4Hz (E) to 1318.51Hz (E).

As others have noticed, the reference of 440 Hz for the A above middle C is a standard across all instruments, but it's not a universal standard. It is most popular in the USA (if I understand correctly). Some musicians and ensembles around the world that use what I will call "western" instruments (e.g., strings, brass, woodwinds, guitar, piano and the like) may tune to other standards like 435 Hz. Non-"western" instruments (e.g., sitar, gamelon, even bagpipes, etc.) may have entirely different and not at all standardized tunings.

The rest of the last quote above is correct, although there has been some dispute about how reliable the 20 - 20,000 Hz figure is.

• Yes, I said chord but meant note, thanks. My vocabulary is a bit limited still. It gets confusing because both notes and chords are measured in octaves from A to A. In theory (no pun) it would be easier if the components (notes) and product (chords) didn't have the same alphabetic and octave classifications. Apr 11 '19 at 18:45
• @GC123 That's a good point I had forgotten can be confusing: Notes and chords can sometimes share the same names. For what it's worth, when a chord has a name that looks like a note, such as "an A chord", that means that the chord has the note of the same name as one of its notes. So an A chord has an A as one of its notes, and a Bb chord has a Bb as one of its notes. Also, notes can never be major or minor or diminished or 7th all on their own, so as soon as you see anything after the letter, like Am7, you know it's a chord, and not a note. Apr 11 '19 at 18:49
• As a matter of interest, when you teach, what percentage of the time is spent on this side of lessons?
– Tim
Jun 5 '19 at 9:03
• @Tim I’m a little confused by the phrase “this side of lessons”, but I don’t think this stuff has come up before. I’ll teach a student anything they want to know, even if I don’t know it (yet) myself, and I generally let the student guide where we go. So every student learns different things. I don’t think a student has ever taken us too far down the road of acoustics before. Jun 5 '19 at 11:37
• I meant how much of a lesson would you normally spend on this facet of music with a student, given that it's done so well for you, as you say. I'm wondering whether you as a teacher deem it as an important part of the learning process, from what's in your answer. It's fairly obvious that I'm on the other side of the coin (from my answer!), but it's interesting to hear other teachers' takes on what gets included in lessons - and since this aspect appeared important, I wanted to know if it was in fact included in your lessons.
– Tim
Jun 5 '19 at 11:43

I'm tired of rote memorization.

You should not think your choice is between rote memorization (of something, I suppose you mean music theory) versus acoustics which is the science of sound - the hertz, waveforms, etc. you mention.

The acoustics info you put into your question is already more than you need to know to study music theory.

The vast bulk of music theory doesn't require acoustics knowledge. The overtone series is about the only thing comes up to (try) explaining the perception of consonance/dissonance.

The non-rote approach to music theory is all about pattern recognition and relative relationships. Even some things that seem like rote knowledge - key signatures, interval names, etc - can be broken down into categories and patterns.

I want to understand why say a pentatonic is constructed the way it is. TO understand that I need to understand the fundamental blocks.

These kinds of question come up a lot. Stuff like 'why are triads the basic kind of chord', 'why does major sound happy', 'where did the major scale come from', etc.

There are usually two kinds of answers:

1. because it sounds good
2. the intervals involved are acoustically resonant which is perceived as sounding good

Perfect fifths are very consonant and stable. They are super important in music theory. If you stake up four perfect fifths...

`C G D A E`

...you get a pentatonic scale.

That would be a typical music theory explanation of why a pentatonic scale is constructed as it is. But, as you can see, that explanation didn't really require any acoustical science.

EDIT

Also, theory is confusing. There are 12 notes in an octave from A to A. But octave is Latin for 8. Most skip the flatts/sharpes. Unless you start in a different key. These then are used to make chords. Chords also span octaves. So it is like level 2 of octaves. Chords are combined in different ways to make songs. Typically I IV V but not always. Then there are scales. Seemingly these can be chords and tones/notes. And these can be subdivided into pentatonics if you remove 4 and 7th or 2nd and 5th depending on major or minor. It is, to me, a confusing mess.

I want to elaborate on just one point to illustrate what seems to me an incomplete, lackadaisical attitude about theory which will not be remedied by applying acoustics.

There are 12 notes in an octave from A to A. But octave is Latin for 8.

You didn't really complete the thought. I think you meant to ask "why doesn't an octave contain 8 tones instead of 12?" The information you need to understand the answer is a combination of music history, etymology, and cardinal versus ordinal numbers.

Historically western musical scales used 7 diatonic tones which repeated "at the octave." Each tone was represented by a letter. In modern English the letters are `A B C D E F G`. to show the repeating at the octave let's use scientific pitch notation and write two octaves `A4 B4 C5 D5 E5 F5 G5 | A5 B5 C6 D6 E6 F6 G6 | A6`.

In music theory an octave is the distance between `A4` and `A5` or `A5` and `A6`. In muisc theory those distances are called intervals and the interval names are based on the ordinal number in the tone series. `A4` is first, there isn't no distance with only one tone, it is called a unison. `B4` is second, the distance from `A4` to `B4` is called a second. As we continue up the series `A5` is eighth and the Latin word for eighth is octavus from which the name of the interval is derived: octave. (The Latin cardinal for the quantity is octo, etymologically it is not the origin of the word octave.) Octave does not represent 8 as a quantity it represents the ordinal number eighth!

From a quantitative perspective an octave contains 7 tones, 7 pitch classes (heptatonic, Greek origin.) Historically, as music evolved chromatically, tones were added by half step between certain letters and indicated with sharps and flats. There are 12 chromatic tones in an octave. The common tonal system used today can be described as diatonic system modified with chromaticism. The 12 chromatic tones didn't replace the 7 diatonic tone system and music theory reflects that. Many theory concepts are in reference to the 7 tone diatonic system.

Notice that acoustics will provide absolutely nothing helpful to understanding these concepts. The reason is because music theory is it's own field of study! Like any other serious study it requires time to develop deep understanding.

• Using perfect fifths to explain the pentatonic scale leads me to immediately wonder, why are perfect fifths "very consonant and stable"? Certainly the fields of acoustics and psychoacoustics can speak to that subsequent question. Apr 11 '19 at 19:50
• Read my third sentence re. overtone series. Again, that's about the only acoustic science idea that seems necessary or the Pythagorean interval ratio explanation. Apr 11 '19 at 20:02
• But all of this is a kind of philosophical distraction to just studying music and learning theory terms. You only need to ask these "why does it sound good" questions if you somehow doubt what your ears tell you. But, I get the desire for an answer. I asked the same questions too. You just don't need a lot of acoustics knowledge to get the basic answer. Then when you ask other questions about harmony - why minor - the acoustic completely fails us and is revealed as not all that relevant to music as an art. Apr 11 '19 at 20:07
• I have used scientific understanding of all kinds of things to help me be a better artist, from acoustics for music to color theory for the graphic arts. While I'm not a dancer, understanding the sciences related to how our bodies work is certainly helpful. And we should not forget the many, many artists who took scientific approaches and produced compelling works of art. Georges Seurat springs to mind immediately. The arts do not stand alone in human thought. they are linked to science, philosophy, politics, psychology & medicine, etc. Apr 11 '19 at 20:12
• I would agree that one doesn't have to master any of the sciences to excel as an artist, but I strongly believe that no one should ever be dissuaded from taking a scientific approach to the arts. There's nothing wrong with doing so, and everyone has to take their own journey. Apr 11 '19 at 20:14

You are generally correct, but you have a few errors.

1. When you say "chord" is think you actually mean "pitch." A chord contains multiple pitches.
2. A = 440 Hz is standard for all Western instruments, not just guitar.
3. The highest note on a 20 fret guitar would be a C = 1046.5 Hz

Lastly, these facts have more to do with the field of acoustics, than with music theory. Music theory tends to deal more with the pitch names (A, B, C, etc.), than with pitch frequencies.

• Thank you. As I understand it, pitches span an octave. I personally cannot hear octave equivalence. I wonder if I might be tone deaf the same way people are color blind. As to this being irrelevant, I disagree. An octave spans from A to A which corresponds to a doubling of Hertz. So music theory in terms of pitch names (A, B, C) correspond almost exactly to hertz frequencies. Apr 11 '19 at 17:27
• Why does this matter? To me, tone deaf to octave equivalence, I at least understand why theory repeats A, B, C, etc over and over. It certainly isn't logical. But it equates to Hz. From there, I can understand the repetition. And that serves as a baseline for trying to understand 12 pitch octaves vs octave usually being 8 vs scales and ultimately pentatonics. Without an understanding of the parts, I'm not sure its possible to get beyond rote memorization. At least in my case. Apr 11 '19 at 17:28
• @GC123 -- pitch names do not "correspond almost exactly" to frequencies. Beyond the fact of octave equivalence there are different temperaments, and pitch names are an abstraction that allow temperament to be ignored in notation. An over-concern with the physics of sound production is in most ways the wrong path for a musician. Apr 11 '19 at 17:38
• David, could you explain why this is not correct then? liutaiomottola.com/formulae/freqtab.htm Apr 11 '19 at 17:41
• @GC123 -- I don't have any good web resources for you because I don't really use them. Even some of the websites that I have looked at that seem pretty good contain some mistakes, and these sorts of mistakes can be really confusing for learners. Good books have editors, and hopefully fewer mistakes. You can find some recommendations for books by searching the site. I really like the videos Jens Larsen has been posting at YouTube, and Rick Beato has a lot of good videos which might be worth checking out. Both of these, especially Jens, are mostly focused on guitar. Apr 11 '19 at 18:23

When one starts to learn about the theory of music, one never starts with the physics behind it. Physics is a science, and music is an art. One cannot use one to understand the other.

That apart, knowing the info. you point out - which is not all accurate - has no great relationship with music theory. Music theory is a set of ideas that have been found to work over centuries, and listed/explained in theory books for others to understand what can and does work. It is reflective rather than a set of laws which must be obeyed in order to make 'good music'.

Strongly suggest you ditch the idea, and read about some theory, whilst learning an instrument. Better still, find a (good) teacher, and put yourself in their hands.

• Tim, not trying to argue but I disagree. I have several teachers, each seems to have a slightly different understanding of theory. I've yet to find someone who can explain it in a way I understand or that seems to have a comprehensive grasp. Given probably 90% of guitar players I meet don't seem to have a clue either, I don't think I'm the exception to the rule.Below I added some comments on why I care about Hz and such if you care and where I'm trying to go with all of this. Thanks Apr 11 '19 at 17:33
• -1, not for the opinion on usefulness of physics as a starting point for music theory (mind, I sure enough do disagree with you there, but that's subjective), but for answering with a comment that doesn't answer the asked question. Apr 11 '19 at 17:55
• When I started learning about music, I started with the physics behind it (i.e., acoustics), and I'm doing just fine, thank you. "Physics is a science, and music is an art. One cannot use one to understand the other." I don't think I've seen anything on Music.SE I disagree with more strongly than that statement. Apr 11 '19 at 18:05
• @ToddWilcox -- I am going to have to get behind Tim on this a little bit. I don't at all think that an understanding of physics is useless for a musician (I was once a physicist, after all). But looking at the physics of music has almost nothing to do with the practice of playing music; i.e., it doesn't really help me to understand why a chord substitution works, or what scales I might play over a chord, or what turnarounds are idiomatic to the blues, or how passing notes are used in bebop, or why Art Farmer had such great phrasing. But there is no royal road to music.... Apr 11 '19 at 18:17
• @GC123, you seem to think that physics will eliminate the different oppinons regarding theory. As a physicist and musician I can say you are mistaken. Ambiguities in music theory are more likely due to (1) not having a good education, (2) forgetting the basics, (3) making stuff up. Helmholtz tried to use physics to understand why certain combinations of notes (harmony) are more pleasing than others. His work was somewhat successful but there are cultures that think dissonant intervals are pleasant while consonant intervals are unpleasant.
– user50691
Apr 12 '19 at 17:23

To add to the other answers, sound waves don't really have a "height". They are actually waves of high and low air pressure that radiate outwards from whatever is making the sound. Or, equivalently, the air molecules that are subjected to the sound wave vibrate backwards and forwards, rather than up and down.

People tend to draw sound as if it were "up and down" waves, just because that's a lot easier to draw.

• They certainly do have a height: plot pressure vs. time. For that matter, if you were to propagate a pressure wave down an elastic tube, you would see the tube expanding where the pressure wave is greater than 1 atm and collapsing where it's less than 1 atm. Apr 12 '19 at 13:04
• That expansion, if it is really there, is due to the strain on the material of the tube. It does not imply "height" or that there is a transverse component to the acoustic wave in the air. Waves in fluids (air, water) are purely longitudinal.
– user50691
Apr 12 '19 at 17:19

Ok, first there is no music, or sound for that matter without air, and water. the sound vibrates the water molecules in the air, this carries the sound along. thicker the air is with water vapor, the farther the sound is carried. that's why speakers will produce sound that carries great distances underwater. Dolphins, Whales can be heard singing for miles underwater. acoustic dynamics is fluid dynamics. withoutout them you hear nothing.

• Sound propogates just fine in dry air (which is a compressible medium: exactly what is needed to propogate sound waves). Apr 16 '19 at 23:27