Is there some inherent quality in the frequencies that make them notes, or is it just an arbitrary human construct?
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It is sort of arbitrary but there is a quality of the frequencies that make them sound good together. In general notes that share a lot of the same harmonics sound good together. We have after lots of negotiations over hundreds of years agreed that 440Hz is a note. And any notes that is double or half frequencies of a note is also considered a note. This is because they share half the harmonics, we even say they are the same notes just in different octaves. So for example 880Hz is a note. Then we have decided that a frequency that have a ratio of 3:2 to a note is also a note. Again they share a lot of harmonics. Lastly we also consider frequencies of ratios 5:4 and 6:5 to other notes to be notes. This covers the four most basic harmonic ratios used in western music.
It turns out that a lot of these ratios land pretty close to each other, even if they are not exactly right. This is because multiplying ratios can give different numbers depending on which ratios you multiply but the actual numbers get close. So we group these close ratios together. We therefore end up with 12 different frequencies in each octave that we consider to be notes. The frequencies that lie between these do not share many harmonics with any of the other notes and is therefore not considered notes.
We could use different ratios and get different notes. This is sometimes the case in non-western music. And even some western music use ratios not established in certain songs. So it is kind of arbitrary which note we started with and exactly which ratios we use. You can make good music with frequencies that is not considered notes in the western music scale.
Musical notes all have mathematical relationships with one another. However, the particular set of frequencies that that are typically used for music is more arbitrary. You could tune an entire ensemble of instruments slightly off the normal frequencies used and most people wouldn’t be able to tell the difference as long as they use the same set of frequencies relative to each other.
There is a close to universal music scale that everyone uses, but there are cultures that use notes (frequencies) that don’t fall in line the same way and whose frequencies fall in between. Some even have more or less notes than what’s considered universal.
One example is the [Pelog scale](https://www..wikipedia.org/wiki/Pelog)
It is a completely arbitrary human construct. In the western world, we have agreed that a note resonating at 440 hertz is a “middle A” (A4), and that the chords and scales we use are built on a logarithmic scale based on that note, 12 notes to an octave scale in “equal temperament.”
There are also 12-note scales built on unequal temperament, whose frequency values deviate from a pure logarithmic standpoint – but they are not widely used today. They *were* widely used in the past, especially in the pre-baroque period.
Non-western music – especially in south Asia – often bases music on completely different frequencies and scales, e.g. an octave with 20 or 22 notes in the scale. Again, completely arbitrary.
It’s ultimately arbitrary (kind of). Looking at a music note frequency chart will help understand.
Each octave is divided into 12 notes. The notes are (sort of) evenly distributed in that octave. The difference in frequency between each successive note is not equal, but the ratios between the frequencies of successive notes are equal.
When you go up an octave you double the frequency of whatever note you’re playing.
This is all done because notes whose frequencies have simple ratios sound good together, and this system allows for a lot of different notes that have nice ratios. Playing A1 and A0 (2:1) sounds good. Playing C2 and A2 (3:2) sounds good. For reasons.
That said you could tune your guitar to a slightly higher frequency, and as long as the ratios between each string were the same it would still sound good. But we standardize the exact frequency so multiple instruments can be played in unison.
There are mathematical relationships between different notes (e.g. an octave is two frequencies whose relationship is 2:1) but for the precise frequencies themselves, its arbitrary.
In western music, “concert pitch” is defined such that the note A4 is 440 Hz but in the past other tunings were common, and in other musical traditions you’ll have different tunings and different ways of dividing up the notes.
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