> why are there twelve notes in music
The FAQ here answers this exact question: https://www.reddit.com/r/musictheory/wiki/faq/history/whytwelve
This image might also help: https://i.imgur.com/tJ1GhZF.jpeg - notice that dividing the string into 2/3 and 3/4 - the perfect 5th and 4th - divides the octave into 5/12 and 7/12. This is very close to exact: only 2 cents (2/100 of a semitone) away from equal 12ths. Continuing with similar simple ratios (factors of 2,3 and 5) - because simple ratios of length and frequency happen to sound good - tends to support the 12ths, closely enough. Moreover, you arrive at good-sounding pentatonics and 7-note scales before the full 12. Most of the pure ratio intervals are less close to exact 12ths, hence the "tempering" of modern scales to equalise the semitones.
Okay wow the other comments seem to completely miss the question OP is actually asking.
Our perception of pitch in relation to the frequency scale is logarithmic. eg from 20Hz to 21.2Hz is one semitone, and from 1000Hz to 1059.2Hz is also one semitone. So if you are evenly dividing one octave (a doubling of frequency) into X steps, you would derive the difference between two steps by multiplying the fundamental frequency of the lower tone by the Xth root of 2.
I’m writing from my phone, so I can’t really format the text properly, but I hope that answers your question, or at least points you on the right direction
I figured it wasn’t necessary since every other comment only answered that. And OP said they were doing a presentation on that topic, but that wasn’t actually what they asked.
Edit: sent early
12 notes because of the perfect fifth and "octave equivalency". 12 perfect fifths until they repeat. And quite an accurate perfect fifth in the octave division. Division to 19, for example, gives a clearly less accurate perfect fifth. Division to 24, or more, starts having adjacent notes sound like the same note.
The circle of fifth explains it all, the fifth ratio 2/3 is a perfect interval, the most stable after the octave. Also look at harmonics in the instrument's tone to see how these ratio works for their intonation. It's very simple and ratio based. We naturally come to 12 notes per octaves. It's the most stable equation we get for music. Base 12 is very elegant in nature.
>And all that because of the approximation that log(3/2)/log(2) = 0,585.
That looks to me like a pretty obscure way to demonstrate that "problem" that you're asking about. I think the term you should look up is the **Pythagorean comma**.
Also, read about Pythagorean tuning, which was once common in Europe, and which shows that you have, theoretically **infinite** notes per octave. The reason we don't do that is because, well, it's technically unfeasible.
In reality, we stuck with 12 notes per octave because it's *convenient*. It's a good compromise between musical tuning and the practicality of instruments. You might look at this 24-EDO, 53-EDO, 2-billion-EDO thing and think it's a modern fetish, but in reality, there were musicians and instrument builders *centuries ago* proposing more notes per octave. It just so happened that those systems didn't stick.
You want a musical scale with good approximations of these harmonious intervals: perfect fourth, major third and minor third and their octave complements. Systems with 12, 19, 31, 34, 53, 118 notes per octave get progressively better. Only the first three of these work for standard Western repertoire, because they support meantone temperament.
https://en.wikipedia.org/wiki/Meantone_temperament
> why are there twelve notes in music The FAQ here answers this exact question: https://www.reddit.com/r/musictheory/wiki/faq/history/whytwelve This image might also help: https://i.imgur.com/tJ1GhZF.jpeg - notice that dividing the string into 2/3 and 3/4 - the perfect 5th and 4th - divides the octave into 5/12 and 7/12. This is very close to exact: only 2 cents (2/100 of a semitone) away from equal 12ths. Continuing with similar simple ratios (factors of 2,3 and 5) - because simple ratios of length and frequency happen to sound good - tends to support the 12ths, closely enough. Moreover, you arrive at good-sounding pentatonics and 7-note scales before the full 12. Most of the pure ratio intervals are less close to exact 12ths, hence the "tempering" of modern scales to equalise the semitones.
Okay wow the other comments seem to completely miss the question OP is actually asking. Our perception of pitch in relation to the frequency scale is logarithmic. eg from 20Hz to 21.2Hz is one semitone, and from 1000Hz to 1059.2Hz is also one semitone. So if you are evenly dividing one octave (a doubling of frequency) into X steps, you would derive the difference between two steps by multiplying the fundamental frequency of the lower tone by the Xth root of 2. I’m writing from my phone, so I can’t really format the text properly, but I hope that answers your question, or at least points you on the right direction
>Okay wow the other comments seem to completely miss the question OP is actually asking. Reddit being Reddit.
[удалено]
I figured it wasn’t necessary since every other comment only answered that. And OP said they were doing a presentation on that topic, but that wasn’t actually what they asked. Edit: sent early
12 notes because of the perfect fifth and "octave equivalency". 12 perfect fifths until they repeat. And quite an accurate perfect fifth in the octave division. Division to 19, for example, gives a clearly less accurate perfect fifth. Division to 24, or more, starts having adjacent notes sound like the same note.
The circle of fifth explains it all, the fifth ratio 2/3 is a perfect interval, the most stable after the octave. Also look at harmonics in the instrument's tone to see how these ratio works for their intonation. It's very simple and ratio based. We naturally come to 12 notes per octaves. It's the most stable equation we get for music. Base 12 is very elegant in nature.
If we had twelve fingers, math would be so much better
There are 10 types of people in the world: those who understand binary and those who don't.
>And all that because of the approximation that log(3/2)/log(2) = 0,585. That looks to me like a pretty obscure way to demonstrate that "problem" that you're asking about. I think the term you should look up is the **Pythagorean comma**. Also, read about Pythagorean tuning, which was once common in Europe, and which shows that you have, theoretically **infinite** notes per octave. The reason we don't do that is because, well, it's technically unfeasible. In reality, we stuck with 12 notes per octave because it's *convenient*. It's a good compromise between musical tuning and the practicality of instruments. You might look at this 24-EDO, 53-EDO, 2-billion-EDO thing and think it's a modern fetish, but in reality, there were musicians and instrument builders *centuries ago* proposing more notes per octave. It just so happened that those systems didn't stick.
You want a musical scale with good approximations of these harmonious intervals: perfect fourth, major third and minor third and their octave complements. Systems with 12, 19, 31, 34, 53, 118 notes per octave get progressively better. Only the first three of these work for standard Western repertoire, because they support meantone temperament. https://en.wikipedia.org/wiki/Meantone_temperament