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Middle C is 261.63 Hz. The next half-step up (C#) is 277.183 Hz.

Why are these notes, while a tone at, say, 265 Hz, is not? Or what about 269.1488 Hz -- nearly absolute middle of the two?

Why do we recognize certain frequencies as notes?

Middle C is 261.63 Hz. The next half-step up (C#) is 277.183 Hz. Why are these notes, while a tone at, say, 265 Hz, is not? Or what about 269.1488 Hz -- nearly absolute middle of the two? Why do we recognize certain frequencies as notes?

(post is archived)

[–] • 9 pts

The music scale you're referring to is only the Chromatic scale. There are tones between the half steps (quarter steps) between the quarters (1/8ths) and possibly between the eighths as well.

There are several musical scales that can reach these tones and & frequencies - Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Locrian, Major Pentatonic, Minor Pentatonic, Arabian, Egyptian, Hawaii, and Japanese scales like Ryukyu and Miyakobushi are all I know off the top of my head.

Look em up.

[–] • 4 pts
  • Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Locrian,

Those are modes, not scale. Formed by changing which note you start with in a musical scale.

[–] • 0 pt

Modes are still scales.

[–] • 0 pt

Maybe colloquially, but 'scale' is being used meaning several things at once here. They are built on the diatonic scale, which is a subset of the chromatic scale. To offer dorian or ionian as an alternative to the chromatic scale is nonsense.

Worse, none of this has to do with pitch. You can say A=420 and build a chromatic scale using it.

[–] • 3 pts

This isn't what op was asking.

Get a fretless instrument and there's infinite tones.

You can pick whatever freq you want for any note you want. Every octave is double that.

The notes we use are just a standard we've set.

If anything, he's hinting at the difference between equal temperament vs just temperaments.

[–] [deleted] • 1 pt

There are several musical scales that can reach these tones and & frequencies - Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Locrian, Major Pentatonic, Minor Pentatonic

Incorrect, yet strangely the most popular answer here.

These are MODES - just different ways of arranging the tones.

There are [possibly] ... tones between the eighths as well

Of course there are. Harmonics aren't discrete; you can pick any frequency to arbitrary precision and it has an associated tone.

OP, ignore this guy

[–] • 0 pt

You have no idea what you're talking about. The chromatic scale IS NOT THE UNIVERSAL SALE USED AROUND THE WORLD - it was decided that it would be THE PRIMARY SCALE FOR WESTERN CULTURES AND MUSIC.

Listen to traditional Japanese music compared to European and American classical - the tones are completely because they use different instruments to achieve their sounds.

OP IGNORE THIS GUY

[–] [deleted] • 1 pt

LOL

You are refuting things that I never said or implied. Of course 12 TET isn't the only way to divide the octave, but you act like there isn't a tone corresponding to every frequency out there. The problem isn't so much that what you think you know is wrong, you are just explaining it in a way that is completely off base.

You know something, but you don't know the difference between scales and modes, or between scales and tones.

To say that the (e.g.) Dorian mode (say, of F) can "reach" frequencies that the regular Eb major scale can't "reach" is ludicrous. They're the same [set of] notes.

At this point I would adjust my original warning:

OP, don't ignore this guy, but rather use him as an example of how a little knowledge in the wrong hands can be destructive.

[–] • 0 pt
[–] [deleted] • 4 pts (edited )

Why do we recognize certain frequencies as notes?

We don't. Frequencies can change based on how a musical instrument is tuned.

However since quite some time it became common to tune them according to equal temperament.

Our ears enjoy notes played together that conform to simple ratios, like 2/3. The more complicated a ratio is, the more dissonant it sounds to us. There are different ways to tune instruments because it's basically impossible to have all 12 notes in an octave conform to a perfect ratio, some notes will always be slightly off. Equal temperament distributes the dissonance on all 12 notes equally, which makes it much easier for composers and players.

And if a ratio is doubled or halved, our ears perceive it as the same "note". That's why notes keep repeating on the Piano.

It has to do with the way our brain analyses sound. Every human has a slightly different pitch. Women are higher pitched than men. Instead of analyzing every frequency on it's own, our brain sort of doubles and halves everything such that in the end it only has to analyze a limited amount of input. (It "normalizes" the input). That's why middle C and high C somehow sound different yet totally the same.

Additionally, have you wondered why the very some note, say middle C, sounds different on a Piano and on a Guitar? How can they sound different to us if they are the same frequency?

That's because only a sine wave would produce a pure frequency. Notes played on instruments have "Overtones". The frequency repeats a certain pattern in higher frequencies that varies slightly by instruments. Our brain is really good at analyzing those frequencies, such that if a speaker only plays the overtones, you start to imagine the corresponding lower frequency. Earbuds use this to make you imagine bass sounds, as the speakers are in fact to small to actually play low frequencies. That's also why lower quality speakers sounds "Metallic". They can only play part of the overtones and the illusion starts to fade.

Our brain is incredibly good at analyzing those overtones and it appears that there is a relationship between music rules and those overtunes. Basically, when you hear music certain parts of your brain that analyze sound according to some math are overstimulated in a way they'd never be stimulated by nature. Humans and animals have different musical taste however (birds have their own "music theory" that is different from ours), because there is also a big relationship between the human voice and how we emotionally perceive music.

If you want to learn this stuff, I recommend specifically searching for 'scientific' music theory. It will not teach you how to compose. But regular music theory is to a large extend outdated and has many myths. If you wish to compose rock, edm or any modern genre anticipate to break a lot of music theory rules.

[–] • 3 pts

Because people got together and standardized middle A as 440hz before then people around the world used differnt notes and couldnt play together.

[–] • 1 pt

The absolute frequency doesn't matter. You can adjust tuning any amount and it won't matter; what matters are the ratios between notes, as that allows form pleasing chords when notes combine. This is a really good video about .

[–] [deleted] • 1 pt

I believe that it is completely arbitrary. There's no reason you can't play a tone at 269.1488 and call that C... but you won't be in tune with anyone else following the standard.

A "popular" alternative tuning for instance would be A=432 hz instead of A=440 hz.

[–] • 1 pt (edited )

Octaves are double the frequency of the previous octave.

High notes actually contain a slight version of all the following octaves’ notes when they are played.

So that’s how the notes work when they jump octaves. The rest of the notes I’m guessing are evenly spaced between the two octaves of A at 440 hz and 880 hz?

[–] [deleted] • 1 pt

evenly spaced

Well, not linearly, but by a factor of the twelfth root of 2 (i.e. 21/12)

[–] • 0 pt (edited )

The oldest tunings are octave divisions. So for example an octave might perhaps be tuned to 400 and 800 hz. The 5th then is the mean average: 600 hz. The major third then is the mean of 400 and 600 = 500 hz. These divisions are ratios of small integers. If you play 400, 500, 600 hz together you'll have the pleasant sound of a major triad.

But such simple tunings have problems with dissonance. There is a "wolf fifth" between the 4th and the 7th tone. Also, the circle of 5ths doesn't actually close to a circle since (3/2)n != 2m for all integer n and m != 0. In other words repeated movement by a 5th will never be equal to any other number of repeated movements by an octave. This breaks modulation, modes, and borrowed chords.

So the modern tuning is simply a 12 tone even division of the octave. We take the octave ratio = 2/1 and say each of 12 halfsteps is the ratio r=21/12, therefore r12 = 2. So if A is 220 hz then C is 220 * r3 = 261.62557 since C is 3 halfsteps above A. C# is 220 * r4 and so on.

[–] • 0 pt

The real question is "what do they want"

[–] • 0 pt

It's just a standard that people made up for convenience. It's arguably as arbitrary as the length of an inch, or the weight of a pound.

[–] • 0 pt

Because European-based assholes decided 440Hz was "center A". I prefer a 432Hz tuning, myself. It feels richer and fuller and deeper.

The numerical ratios between the notes stay fixed: 1:2 is an octave, 1:1.5 is harmonic. When you iterate harmonics within an octave you get approximately twelve notes.

So that's why. It's not limited to 440Hz or 432Hz, you can choose any frequency, call that your center note, and build the frequency ratios out from there. I promise they'll sound good. Harmonics sound nice in any tuning. The aesthetic difference produced by different tunings is hard to explain, you just have to experience it.

You can just skip the rest of this comment.

The ancient Greeks took two strings, one at twice the length of the other. This defines the octave. Take the smaller string, multiply it by 1.5, is it longer then the longer string? No. Multiply that string by 1.5, yielding 2.25. is it longer than the longer string? Yes, so cut it in half (1.125). Multiply that string by 1.5, you get 1.6875. On the 12th iteration, it's 1:1.0136, just over 1% different... but when actually tuning say, a piano, you can't ignore it. You have to favor the ivories or distribute the sonic irregularity evenly. The next time the harmonics iterate to such a nice octave, it's at 41, with a 1:0.9886. Some instruments have been built for that scale, but few.

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