Accurate understanding of the physics of sound?

Question

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).

Answer 1

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.

Answer 2

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.

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EDIT

I want to make an addition after reading this comment on another answer from the OP:

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.

Answer 6

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.