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An ELI5 (summarized from the video linked below because I am not this clever or smart) is that each key represents a set of notes that are harmonious with each other. By changing keys, the set of harmonious notes changes. Keys that are close to each other share more harmonious notes than keys that are far apart, so the key of C and the key of G have very similar sets of harmonious notes except for one. The further away you get from our example of the key of C, the bigger the differences — there are still common notes, but fewer of them.
These common notes allow a musician to bridge from one key to another via these shared harmonious noted without the listener noticing, and then produce a dramatic and unexpected change. You were expecting something in the key of C, but the musician had switched keys via the common set of harmonious notes and you never noticed. They then introduced something that is harmonious to the key they were playing in, but unexpected because you were “listening in the key of C” and that’s drama!
The science is that the different harmonious notes are specific ratios of the base note that is being played. Others have explained those ratios better than I can. Look up what a chord is to get a sense of why those specific three notes played together sound harmonious and any other three notes doesn’t.
I can’t explain without writing a book. Instead, [I offer a video that explains it](https://youtu.be/62tIvfP9A2w), uses a few analogies, a visual model, and discusses John Coltrane’s Giant Steps to make sense of it. It doesn’t even get to keys until more than halfway through, with the first half being prelude explaining a bit of the structure of fifths. It’s a good explainer, but I had to watch it twice to help put it together myself.
There aren’t any correct notes. Our usual key signatures are just the collection of notes that sounded good at the time the key signatures were standardized, to the people that standardized the.
You can use math to try to reverse justify their decisions but it’s really a wag the dog type situation.
Other cultures have different scale patterns based on the instruments they had and what sounded good to the.
Second part of the question is worded badly. I guess the question is “why only notes in a scale sound good when playing over progression in that scale”. The answer is that the premise is wrong. All notes can sound good in a given progression when used well. Lets simplify and not use progressions, just a single chord, for example A. A is composed of A, C# and E notes. If you play on a guitar A chord and on another guitar notes A, C# and E in whatever way they should sound “in place”, “consonant” etc. If you play for example D# (tritone) and linger on that note it will feel very out of place. Its not in the A major scale. But, if you play your A, C# and E and add just a smidge of D# there it will make your playing a lot more interesting and pleasing overall.
Just like a visible colors, a single note in a scale is made of many colors called overtones that vary in strength(amplitude). Two of these colors, the octave (second overtone) and the fifth(third) are very present that when we move up a scale note, we are getting a preview of those overtones c(c-g)d(d-a)e(e-b)f(f-c)g(g-d)a(a-e)b(b-f#)c
It’s about the circle of fifths, really. …Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A#… Notice that all the notes without accidentals (the white keys) are contiguous (in a row). We defined them that way, of course. Also A#=Bb, it repeats, it’s a circle after all.
The circle of fifths itself exists because of mathematics, and arguably it’s not just fifths (a 3:2 ratio) but also thirds (5:4) that are relevant, and the reasons why are complicated. We don’t like dissonance which is highest when note frequencies are near unison but not at unison (think of a graph like x*exp(-x)), including when that happens between overtones/harmonics, and that naturally leads to preference for simple ratios, the simpler the better. 12 equally spaced notes is an optimum that’s much better than 11 or 13, and that’s not a simple fact to derive, but it is “natural” and requires no assumptions about culture. It’s not a coincidence that 2^(19)≈3^(12) or 2^(7)≈5^(3) – those are, effectively, reasons why 12 is an optimum. But that’s all overcomplicating the issue, I think.
Yes, the science is vibration which is just objects dancing back and forth.
The notes that sounds good together are the dancers that move together in time while also dancing at different speeds. A slow dancer spinning and a fast dancer spinning can match up so that they both start and stop facing the same direction. The only difference is how many times they have turned.
With sound, the dancer that moves faster sounds higher to our ears. As long as the dancers come together every once in a while, it’s satisfying and sounds good.
I think there is multiple questions here. I can try and explain why we don’t use arbitrary frequencies in music.
Notes can be expressed as fractions of other notes. The key takes the name of the root note of the key and the other notes are fractions of that note. The perfect fifth is exactly 3/2 the frequency of the root note. The perfect fourth is 4/3. The major third is 5/4. The smaller these numbers in the fractions, the more consonant it sounds. The larger the numbers in the fractions, the more dissonant in sounds.
Why do fractions with smaller numbers sound more consonant? I don’t know but I think it might have something to do with the wave pulses lining up and our brains liking that rhythm.
The notes used in a piece cannot be too dissonant otherwise the music sounds like garbage/noise. Too consonant and it can be boring. Typically scales or musical pieces contain the mostly consonant notes (smallest fractions) with some dissonant notes to add flavour.
In western music, an octave is divided into 12 equal intervals called semitones. Key signatures sound good because of the way that tones resonate and interact with each other; it works because ratios of the sound frequencies between the pitches on the scale are equal, so it’s easy to find those notes that harmonise.
Visually if you were to show each semitone as a soundwave, the higher the frequency/ pitch, the tighter the sound wave becomes. The peaks and troughs of these sound waves are related, and can either clash or harmonise.
Sound Waves are made up of two parts: Amplitude (Loudness) and Frequency (Pitch). When frequencies interact, you get interference. If the frequencies are whole number multiples of each other, you get harmonics which sound good. The octave is the distance between a note (the tonic) and the next harmonic of it, and this froms the basis of scales and key signatures. If the frequencies don’t have whole number ratios, fractions with small number tend to sound better than those with larger numbers.
Unfortunately, dividing up space in an octave is a fairly complex problem as you want to maximize the number of low number ratio between the tonic and the frequencies you choose to assign to notes in your scale. In Europe when the musical notation was being developed and standardized, various composers actually argued about how to do this. Bach even wrote several pieces of music design to sound “right” which the pitches he prefered and bad in those he did not.
There are actually several different ways to do this, leading to numerous different musical scale in different culture, all of which are valid. However, as a child, you get exposed to the versions used most commonly in your culture and you learn to hear those as normal and you learn the cultural signifiers assigned to them. This is why the European Major scale “sounds” happier and the Minor “sounds” sad, and why it sounds “wrong” when those pitches are used in different ways by other musical systems.
A heptatonic scale can be thought of as 7 notes, or 7 5ths from each of those notes. The more P5s there are in that sequence, the more “consonant” it will sound.
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