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Google “[harmonics](https://www.beyondmusictheory.org/the-harmonic-series/)” or “overtones.”
Overtones are, in essence, the note oscillating at its own frequency, then that frequency doubled, then trebled (“tones whose frequency is an integer multiple of a fundamental frequency”), etc.
Certain notes work together because of their harmonics. Other notes when played together clash for the same reason, and that dissonance leads to a feeling of satisfaction when the chord resolves to one with no such dissonance.
Because of math. The frequencies of certain notes relative to certain other notes make ratios that fit nicely together and overlap cleanly, whereas other combinations of notes have frequencies that don’t have mathematically compatible ratios that causes them to sound dissonant and gross when played together. Keys are bundles of notes that sound good together, as a sort of “cheat sheet” to know which good sounding notes are available for combination, given that you start with the root note of the key.
While there are some answers to your question using overtones or mathematical structures, there’s a different answer you should consider:
What are the “correct notes”? For example, let’s say you play a C major scale, but accidentally play an F# (F sharp) instead of an F natural (C major has no sharps, only naturals.)
Depending upon what you’re doing with the scale, the F# could sound wrong. But it could also sound right depending upon the context!
If you as a composer like the F#, there’s nothing wrong about using it. If you play the scale with an F# instead of F natural, you’ve just played a different scale. Instead of C major, you just played C Lydian. Or if you start on the note G, you just played G major.
There is no mathematical theory which says C major is better than C Lydian or G major. All those scales can sound good in a song.
In fact, there are many scales will all sorts of different notes, sometimes mixing sharps and flats and naturals, which sound good. What makes things sound good or not is much more complex than math, as you need to take into account culture, tradition, history, and the desires of both the composer and the audience.
Since you’re five and haven’t done fractions yet, lets start with the basics. The notes we usually use aren’t just made up by people out of thin air. They are based on math. Without jumping into fractions too deep, think of them as like pieces of a pie. Or here, like lengths of string.
For example, if you take a string, play it, and fold it and cut it in exactly half, the half string note will move air twice as fast. We call that an octave. The full string and the half string sound nice together because they vibrate in a simple pattern, one twice as fast as the other.
When you learn fractions in 2nd or 3rd grade, we can come back to how all the other notes we usually use are other simple mathematic divisions of a string. But again, they make more recognizable patterns our ears seem to like because they are vibrating 3 times, 4 times, 5 times, stuff like that of the full string base.
And this goes back interestingly way way back in human understanding. Your parent can read this too you, it explains how a flute made 40,000 years ago used similar math that we still use for those notes in music. https://www.theguardian.com/music/2013/feb/15/ice-age-flute
It’s worth mentioning that scales work the same way regardless of the key signature.
If you could assign numbers to the notes instead of letters, the distance between each note is the same for any key signature. The only difference is where you start.
Once youve learned the major scale in one key signature, you’ve got the theory down for every key signature.
As mentioned by others, the harmonic series or overtones have inspired key signatures in some cultures.
Regarding the second statement, what sounds “good” is subjective, and any note can sound “correct” if the chords complement it. It is better to describe sounds by their characteristics such as bright, dark, tension, etc. You don’t listen to music because it sounds good and correct, but because it is expressive of something.
Yes.
Ideally, wavelengths that are an exact fraction or multiple of another wavelength, sound good together. Such as double wavelength, 1/3, 4/5, etc. Wavelength is the inverse of frequency, and music notes are usually specified by frequency.
Doubling or halving a frequency gives the next octave up or down, respectively. For example, the note A above middle C is defined to be 440 Hz (a Hertz is one cycle per second, so 440 Hz means the vibrating object [a string, etc] is vibrating 440x per second). So the next A above, is double frequency (880) with the next A below, being half frequency (220).
Since using exact fractions doesn’t give us evenly-spaced notes on the scale, it was decided to use “equal temperament” which means the ratio between any two consecutive notes would be the same. It turns out that using the 12th root of 2 as that ratio will give us 12 equally spaced notes.
So with A being 440, A♯ (not #) or B♭ (not b) is approximately 466.2 Hz, B is approximately 493.9 Hz, C is approximately 523.3 Hz, C♯/D♭ is approximately 554.4 Hz, etc.
Key signatures essentially just indicate (or dictate) what the tonal center is, what notes are in the scale that you can pick from, and it all affects the overall flavor.
It sounds like what you are talking about is the difference between consonant (pleasant) and dissonant (harsh) intervals of simultaneous notes. Dissonance is not prohibited by any means, and can add color and flavor.
“Sounding good” is as much an art as a science, and while there are general rules, most can be bent or broken. Often, the dissonance that can come about with mistakes can improve the overall experience. There is a very old concept about it (I’m paraphrasing): “If you screw up once, it’s a mistake. To fix it, just repeat the mistake. They’ll think you meant to do it, and you’ll be considered a trail blazer.”. The short form of this is: “Screw up once, it’s a *mistake*. Do it twice, and it’s *Jazz*…”
For more information, your Google search terms should include “Learning Music Theory”. There are free tutorials that will help explain the mechanics of all of this.
Some people will justify this with frequencies and their ratios, but that preference isn’t actually universal so that doesn’t really make sense. There are cultures that don’t use the western classical system of keys, and even western pop music doesn’t treat keys the same as Mozart did (a lot more ambiguity over what the key is nowadays)
So the “why” is just culture, but there is music theory that describes what’s going on and can be somewhat scientific
I’m alsowilling to bet that you like the sound of “wrong” notes if they’re used well, and they can really bring beauty to a piece of music
The scale doesn’t sound right with certain notes, the scale IS the notes.
Scales are a sequence of note distances and can be started at any point. However, in order to maintain the note distances when playing starting from some notes, you will need to add sharps (or flats)
Here is a bit of a crash course on scales, please feel free to ask if anything is unclear. Trust me this is much simpler than it looks, just take your time reading.
Scales are a series of note distances, the smallest distance in most modern music is a half step. So from C to C#.
The distance between C and D is a step.
A scale is a combination of distances, for example, C major is C D E F G A B C.
Now, here is an interesting thing, there is a half step between E and F, and a half step between B and C. So it isn’t just full steps here; if you write down only the note distances of this scale you get this:
(For reference, T is a step, and S is a half step; because they are Tonos and Semi-tonos)
T T S T T T S
This is the distance between notes in a C major scale. Now let’s imagine you want to do G major. You take this note distance, but this time the first note will be G, and we will end on G an octave higher. So let’s see what happens. Remember the order for a major scale.
TTSTTTS
G to A is a step, all good.
A to B is a step, all good. We need a half step next
B to C is a half step, we are still in good track.
C to D is a step, nice.
D to E is a step, we need one more.
E to F is a half step. We have a problem here. In order to get the sound of a major scale, we need a step here. So what can we do? We play F#
E to F# is a step, we need a half to end the scale. Luckily, we already are playing F#, which is just F a half step higher, and F# to G is a half step.
This is why you have to mix and match black keys to get scales that aren’t natural, because a scale is a sequence that can be transposed to any key!
G major is easy enough becausd it has just one black note on a piano, which is F# (F sharp).
However, other scales need different combinations to achieve the same sequence of note distances.
Like D major, which requires both F# as well as C#, or F major, which only uses Bb (B flat)
The rest is sound science and harmony, some frequencies fit in well with others, their peaks and valleys fitting in nicely together. For example, let’s say you play A, in standard tuning that is 440hz. An octave higher, A is 880hz.
If you imagine both sound waves together, you should notice that they will fit in very nicely and that they they sync up. Both waves will be at the same step in their cycle every time the longer one resets. This is perfect harmony. There are different degrees of harmony, the next important one is fifths (think C + G) and then 3rds and 6ths.
This is why C major is C-E-G
1st, 3rd, and 5th. Really nice harmony there.
Within a scale, if established by a chord or melody, any notes that exist within the scale should sound nice (though not necessarily at the same time) as they are part of the same harmony. So if you are playing on the key of C major, your base chord will be C major, and any notes in the scale should sound good in the melody as long as you don’t try to play them all at once and respect some basic guidelines.
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