Why are a piano’s black keys arranged in groups of three and two?
In: 44
I’ve scrolled through some of this and have yet to see the obvious answer. The piano’s black keys are arranged in groups of 2s and 3s so you can find your way around the keyboard. Simple as that. You can go into the hertz and the major scale and blah blah blah, it’s so that each key looks unique.
Test it. Hold a book up and cover all of the black keys so that all you can see is the white keys. You’ll instantly realize that unless you have a perfect ear, you’ll have no idea which key is which, because all the white keys will look exactly the same. Thus, the black keys also need to be in different groupings so that every single note looks unique from one another.
I’ve scrolled through some of this and have yet to see the obvious answer. The piano’s black keys are arranged in groups of 2s and 3s so you can find your way around the keyboard. Simple as that. You can go into the hertz and the major scale and blah blah blah, it’s so that each key looks unique.
Test it. Hold a book up and cover all of the black keys so that all you can see is the white keys. You’ll instantly realize that unless you have a perfect ear, you’ll have no idea which key is which, because all the white keys will look exactly the same. Thus, the black keys also need to be in different groupings so that every single note looks unique from one another.
I’ve scrolled through some of this and have yet to see the obvious answer. The piano’s black keys are arranged in groups of 2s and 3s so you can find your way around the keyboard. Simple as that. You can go into the hertz and the major scale and blah blah blah, it’s so that each key looks unique.
Test it. Hold a book up and cover all of the black keys so that all you can see is the white keys. You’ll instantly realize that unless you have a perfect ear, you’ll have no idea which key is which, because all the white keys will look exactly the same. Thus, the black keys also need to be in different groupings so that every single note looks unique from one another.
Amateur pianist here. A lot of people here are talking about the frequencies and stuff, which is important, but isn’t the whole story of why a piano keyboard looks like that. I will instead talk about the user interface portion of this.
To recap the frequency part in short, a long time ago, some people figured out that:
* There are 12 notes, if you go further they repeat themselves and sound nice while doing so
* Certain combinations of notes sound nice (chords) and these combinations also repeat every 12 notes
* If you mostly stuck to using only combinations of notes from a specific collection of notes, it is easier to make something that sounds nice
* In particular, one collection of notes is pretty easy to work with. This collection is called the major scale.
* The major scale is defined by a series of steps. You don’t use every note, only 7 out of the 12, and you can start anywhere and still be in a major scale as long as you follow that series of steps.
When making a keyboard instrument, you could just have a bunch of the white keys going 1-2-3-4-5-6-7-8-9-10-11-12 and repeating forever. There are several problems with this, though.
1. With wide white keys, your hands will not be big enough to play cool patterns. With narrower keys, your fingers will be so wide they tend to hit multiple notes at the same time, which does not sound great.
2. It is very hard to tell what note you are going to play before you play it because everything is a white key with no variation and no labeling.
3. There are no repeated structures in the keys that show musicians useful patterns that rely on repetition, you have to count up key by key and it is easy to lose your spot
To solve problem 1, we could convert some of the white keys to raised, out of the way black keys while keeping the white keys a reasonable width. Convert enough of the keys to black ones and you can strike a balance between being able to make chords with hands of finite width, and not accidentally hitting two notes at the same time with fingers of nonzero width.
Say we make every other second or third key black. This solves the space issue, but we still can’t tell which note is which at a glance or by touch.
Solving problems 2 and 3 at the same time, 12 is a very important number in music, so it would make sense to give the white and black keys a pattern that repeats every 12 notes (and doesn’t have any other factors) so musicians can rapidly identify what notes they are about to play, both by sight and by touch (a bit like the bump keys on a computer keyboard), and allow for easy location of “repeated” notes.
There are a number of ways we can accomplish this. 11 white then 1 black, 4 white-1 black-6 white-1 black, but remember the major scale from earlier? If we go white-black-white-black-white-white-black-white-black-white-black-white, and then repeat, all of the white keys now form a major scale, and we have a repeating pattern with no other factors. All of the other major scales (offset by a number of keys) now have a slightly understandable relationship between their relative pitch and the number of black keys they use. Thus it is now more easy to identify which collections of notes form a scale/key that sounds nice to play in.
That arrangement solves the wide hands problem and the note identifiability problem, while also presenting the musicians with a repeated pattern that makes it easier to identify what sounds nice.
There are other arrangements of white and black keys that solve these issues, but this is the one most of the world has standardized on, as anything else would make it very difficult to transfer between keyboard instruments. Drawing on a computer analogy, sure, DVORAK may be more efficient than QWERTY, but good luck getting the world to change.
Amateur pianist here. A lot of people here are talking about the frequencies and stuff, which is important, but isn’t the whole story of why a piano keyboard looks like that. I will instead talk about the user interface portion of this.
To recap the frequency part in short, a long time ago, some people figured out that:
* There are 12 notes, if you go further they repeat themselves and sound nice while doing so
* Certain combinations of notes sound nice (chords) and these combinations also repeat every 12 notes
* If you mostly stuck to using only combinations of notes from a specific collection of notes, it is easier to make something that sounds nice
* In particular, one collection of notes is pretty easy to work with. This collection is called the major scale.
* The major scale is defined by a series of steps. You don’t use every note, only 7 out of the 12, and you can start anywhere and still be in a major scale as long as you follow that series of steps.
When making a keyboard instrument, you could just have a bunch of the white keys going 1-2-3-4-5-6-7-8-9-10-11-12 and repeating forever. There are several problems with this, though.
1. With wide white keys, your hands will not be big enough to play cool patterns. With narrower keys, your fingers will be so wide they tend to hit multiple notes at the same time, which does not sound great.
2. It is very hard to tell what note you are going to play before you play it because everything is a white key with no variation and no labeling.
3. There are no repeated structures in the keys that show musicians useful patterns that rely on repetition, you have to count up key by key and it is easy to lose your spot
To solve problem 1, we could convert some of the white keys to raised, out of the way black keys while keeping the white keys a reasonable width. Convert enough of the keys to black ones and you can strike a balance between being able to make chords with hands of finite width, and not accidentally hitting two notes at the same time with fingers of nonzero width.
Say we make every other second or third key black. This solves the space issue, but we still can’t tell which note is which at a glance or by touch.
Solving problems 2 and 3 at the same time, 12 is a very important number in music, so it would make sense to give the white and black keys a pattern that repeats every 12 notes (and doesn’t have any other factors) so musicians can rapidly identify what notes they are about to play, both by sight and by touch (a bit like the bump keys on a computer keyboard), and allow for easy location of “repeated” notes.
There are a number of ways we can accomplish this. 11 white then 1 black, 4 white-1 black-6 white-1 black, but remember the major scale from earlier? If we go white-black-white-black-white-white-black-white-black-white-black-white, and then repeat, all of the white keys now form a major scale, and we have a repeating pattern with no other factors. All of the other major scales (offset by a number of keys) now have a slightly understandable relationship between their relative pitch and the number of black keys they use. Thus it is now more easy to identify which collections of notes form a scale/key that sounds nice to play in.
That arrangement solves the wide hands problem and the note identifiability problem, while also presenting the musicians with a repeated pattern that makes it easier to identify what sounds nice.
There are other arrangements of white and black keys that solve these issues, but this is the one most of the world has standardized on, as anything else would make it very difficult to transfer between keyboard instruments. Drawing on a computer analogy, sure, DVORAK may be more efficient than QWERTY, but good luck getting the world to change.
As yet, no-one has given the complete answer, despite giving the correct background about overtones and temperament etc, Namely, **the white notes in fact are equally spaced** in a particular rigorous sense (and it is this nearly mathematical symmetry which defined the role of the diatonic scale compared to other modes in the German/Austrian tradition, which the Russian Tchaikovsky was criticised for seeming to ignore in his early career, and was later consciously rejected as a necessary ingredient of composition by composers like Shonberg.)
so let’s start over at the beginning with a very uconfusing experiment. Start at
**F, a white note**
Now go up 7 semitones, you reach
**C, a white note**
Now go up 7 semtones, you reach
**G, a white note**
Now go up 7 semitones, you reach
**D, a white note**
Now go up 7 semitones, you reach
**A, a white note**
Now go up 7 semitones, you reach
**E, a white note**
Now go up 7 semitones, you reach
**B, a white note**
In that sense, the white notes *are* equally spaced. If you continue then you go through the 5 black notes, also equally spaced. What I am going to say next is *less* important than just that observation.
Not only are the white notes equally spaced in this sense, they are all a 3-adic ‘open ball neighbourhood’ of D in the sense that if you tuned your piano to perfect fifths going up and down 3 steps from D, the frequency component of 3 in the frequency ratios define a notion of “3-adic distance” https://en.wikipedia.org/wiki/P-adic_valuation and you are llooking at D and the three closest points to each side.
I have ignored a relation with octaves (that an unnecessary complication can be removed if you replace 7 with 19 in the exercise above) and the relation with the fact that 3^{12} is close to 2^{19} but it was frustrating to see people describing the backgroud for this notion and not actually mentioning the precise fact.
One could remove F and B and have a pentatonic scale equivalent to the set of black notes, or include Bb and F# and have an extended scale both centered around D.
Also, there is the combinatorial fact that if you replace F with F# it is the same as deleting the first term in the sequence and including one extra term, 7 semitones higher than the last term of B. Thus two transformations of the set which seem different — one changing one note by a semitone, the other shifting all notes by 7 semitones — are in fact the same transformation of the note classes mod 12. This is related to how 7 mod 12 is invertible.
Amateur pianist here. A lot of people here are talking about the frequencies and stuff, which is important, but isn’t the whole story of why a piano keyboard looks like that. I will instead talk about the user interface portion of this.
To recap the frequency part in short, a long time ago, some people figured out that:
* There are 12 notes, if you go further they repeat themselves and sound nice while doing so
* Certain combinations of notes sound nice (chords) and these combinations also repeat every 12 notes
* If you mostly stuck to using only combinations of notes from a specific collection of notes, it is easier to make something that sounds nice
* In particular, one collection of notes is pretty easy to work with. This collection is called the major scale.
* The major scale is defined by a series of steps. You don’t use every note, only 7 out of the 12, and you can start anywhere and still be in a major scale as long as you follow that series of steps.
When making a keyboard instrument, you could just have a bunch of the white keys going 1-2-3-4-5-6-7-8-9-10-11-12 and repeating forever. There are several problems with this, though.
1. With wide white keys, your hands will not be big enough to play cool patterns. With narrower keys, your fingers will be so wide they tend to hit multiple notes at the same time, which does not sound great.
2. It is very hard to tell what note you are going to play before you play it because everything is a white key with no variation and no labeling.
3. There are no repeated structures in the keys that show musicians useful patterns that rely on repetition, you have to count up key by key and it is easy to lose your spot
To solve problem 1, we could convert some of the white keys to raised, out of the way black keys while keeping the white keys a reasonable width. Convert enough of the keys to black ones and you can strike a balance between being able to make chords with hands of finite width, and not accidentally hitting two notes at the same time with fingers of nonzero width.
Say we make every other second or third key black. This solves the space issue, but we still can’t tell which note is which at a glance or by touch.
Solving problems 2 and 3 at the same time, 12 is a very important number in music, so it would make sense to give the white and black keys a pattern that repeats every 12 notes (and doesn’t have any other factors) so musicians can rapidly identify what notes they are about to play, both by sight and by touch (a bit like the bump keys on a computer keyboard), and allow for easy location of “repeated” notes.
There are a number of ways we can accomplish this. 11 white then 1 black, 4 white-1 black-6 white-1 black, but remember the major scale from earlier? If we go white-black-white-black-white-white-black-white-black-white-black-white, and then repeat, all of the white keys now form a major scale, and we have a repeating pattern with no other factors. All of the other major scales (offset by a number of keys) now have a slightly understandable relationship between their relative pitch and the number of black keys they use. Thus it is now more easy to identify which collections of notes form a scale/key that sounds nice to play in.
That arrangement solves the wide hands problem and the note identifiability problem, while also presenting the musicians with a repeated pattern that makes it easier to identify what sounds nice.
There are other arrangements of white and black keys that solve these issues, but this is the one most of the world has standardized on, as anything else would make it very difficult to transfer between keyboard instruments. Drawing on a computer analogy, sure, DVORAK may be more efficient than QWERTY, but good luck getting the world to change.
As yet, no-one has given the complete answer, despite giving the correct background about overtones and temperament etc, Namely, **the white notes in fact are equally spaced** in a particular rigorous sense (and it is this nearly mathematical symmetry which defined the role of the diatonic scale compared to other modes in the German/Austrian tradition, which the Russian Tchaikovsky was criticised for seeming to ignore in his early career, and was later consciously rejected as a necessary ingredient of composition by composers like Shonberg.)
so let’s start over at the beginning with a very uconfusing experiment. Start at
**F, a white note**
Now go up 7 semitones, you reach
**C, a white note**
Now go up 7 semtones, you reach
**G, a white note**
Now go up 7 semitones, you reach
**D, a white note**
Now go up 7 semitones, you reach
**A, a white note**
Now go up 7 semitones, you reach
**E, a white note**
Now go up 7 semitones, you reach
**B, a white note**
In that sense, the white notes *are* equally spaced. If you continue then you go through the 5 black notes, also equally spaced. What I am going to say next is *less* important than just that observation.
Not only are the white notes equally spaced in this sense, they are all a 3-adic ‘open ball neighbourhood’ of D in the sense that if you tuned your piano to perfect fifths going up and down 3 steps from D, the frequency component of 3 in the frequency ratios define a notion of “3-adic distance” https://en.wikipedia.org/wiki/P-adic_valuation and you are llooking at D and the three closest points to each side.
I have ignored a relation with octaves (that an unnecessary complication can be removed if you replace 7 with 19 in the exercise above) and the relation with the fact that 3^{12} is close to 2^{19} but it was frustrating to see people describing the backgroud for this notion and not actually mentioning the precise fact.
One could remove F and B and have a pentatonic scale equivalent to the set of black notes, or include Bb and F# and have an extended scale both centered around D.
Also, there is the combinatorial fact that if you replace F with F# it is the same as deleting the first term in the sequence and including one extra term, 7 semitones higher than the last term of B. Thus two transformations of the set which seem different — one changing one note by a semitone, the other shifting all notes by 7 semitones — are in fact the same transformation of the note classes mod 12. This is related to how 7 mod 12 is invertible.
As yet, no-one has given the complete answer, despite giving the correct background about overtones and temperament etc, Namely, **the white notes in fact are equally spaced** in a particular rigorous sense (and it is this nearly mathematical symmetry which defined the role of the diatonic scale compared to other modes in the German/Austrian tradition, which the Russian Tchaikovsky was criticised for seeming to ignore in his early career, and was later consciously rejected as a necessary ingredient of composition by composers like Shonberg.)
so let’s start over at the beginning with a very uconfusing experiment. Start at
**F, a white note**
Now go up 7 semitones, you reach
**C, a white note**
Now go up 7 semtones, you reach
**G, a white note**
Now go up 7 semitones, you reach
**D, a white note**
Now go up 7 semitones, you reach
**A, a white note**
Now go up 7 semitones, you reach
**E, a white note**
Now go up 7 semitones, you reach
**B, a white note**
In that sense, the white notes *are* equally spaced. If you continue then you go through the 5 black notes, also equally spaced. What I am going to say next is *less* important than just that observation.
Not only are the white notes equally spaced in this sense, they are all a 3-adic ‘open ball neighbourhood’ of D in the sense that if you tuned your piano to perfect fifths going up and down 3 steps from D, the frequency component of 3 in the frequency ratios define a notion of “3-adic distance” https://en.wikipedia.org/wiki/P-adic_valuation and you are llooking at D and the three closest points to each side.
I have ignored a relation with octaves (that an unnecessary complication can be removed if you replace 7 with 19 in the exercise above) and the relation with the fact that 3^{12} is close to 2^{19} but it was frustrating to see people describing the backgroud for this notion and not actually mentioning the precise fact.
One could remove F and B and have a pentatonic scale equivalent to the set of black notes, or include Bb and F# and have an extended scale both centered around D.
Also, there is the combinatorial fact that if you replace F with F# it is the same as deleting the first term in the sequence and including one extra term, 7 semitones higher than the last term of B. Thus two transformations of the set which seem different — one changing one note by a semitone, the other shifting all notes by 7 semitones — are in fact the same transformation of the note classes mod 12. This is related to how 7 mod 12 is invertible.
Imagine you have a big box of crayons. You want to draw a rainbow, but you only have seven colors: red, orange, yellow, green, blue, indigo and violet. You can use these colors to make a nice rainbow, but you can also mix them to make other colors. For example, if you mix red and yellow, you get orange. If you mix blue and yellow, you get green. If you mix red and blue, you get purple.
Now imagine you have a piano. A piano is like a big box of musical crayons. You can use the white keys to play seven different notes: C, D, E, F, G, A and B. These notes are like the colors of the rainbow. You can use them to make nice melodies, but you can also mix them to make other notes. For example, if you play C and E together, you get a note that sounds like C but higher. This note is called C sharp. If you play D and F together, you get a note that sounds like D but higher. This note is called D sharp.
The black keys on the piano are like the mixed notes. They are called sharps or flats depending on how you use them. For example, C sharp is also called D flat because it is between C and D. The black keys are arranged in groups of three and two because they follow a pattern. The pattern is: two white keys, one black key, three white keys, two black keys. This pattern repeats all over the piano. It helps you find the notes you want to play and make different sounds.
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