Why are a piano’s black keys arranged in groups of three and two?
In: 44
Sound waves can have different frequencies, and this pretty much correlates to pitch. Higher pitch has higher frequency. But you can have a sound is between the standard notes. So sound frequencies can be anything, the ones that are notes can be thought of a ladder. You can’t stand between two rungs, only on one.
How they’re spaced involves some math into music theory, so let’s jump ahead to the chromatic scale. This is a twelve-note scale https://en.wikipedia.org/wiki/Chromatic_scale https://en.wikipedia.org/wiki/Diatonic_and_chromatic goes into more depth of scales that are a subset, for example a C major scale.
An instrument like the violin or trombone can make pitches between the notes. For a violin, you can put your finger at any point, not just the frets like on a guitar. With a piano you’re not changing the length of the string, you’re sounding a separate set of strings.
You could arrange a piano keyboard with one row of the same color key, one per tone on the chromatic scale, but then you’d need to keep track of what size steps to make for your major and minor scales: Do you skip a key or not to go up or down one full note? For chords, what shape do you need to make with your fingers?
Among other things, having a repeating pattern means you can locate a given note by its place in the pattern.
Sound waves can have different frequencies, and this pretty much correlates to pitch. Higher pitch has higher frequency. But you can have a sound is between the standard notes. So sound frequencies can be anything, the ones that are notes can be thought of a ladder. You can’t stand between two rungs, only on one.
How they’re spaced involves some math into music theory, so let’s jump ahead to the chromatic scale. This is a twelve-note scale https://en.wikipedia.org/wiki/Chromatic_scale https://en.wikipedia.org/wiki/Diatonic_and_chromatic goes into more depth of scales that are a subset, for example a C major scale.
An instrument like the violin or trombone can make pitches between the notes. For a violin, you can put your finger at any point, not just the frets like on a guitar. With a piano you’re not changing the length of the string, you’re sounding a separate set of strings.
You could arrange a piano keyboard with one row of the same color key, one per tone on the chromatic scale, but then you’d need to keep track of what size steps to make for your major and minor scales: Do you skip a key or not to go up or down one full note? For chords, what shape do you need to make with your fingers?
Among other things, having a repeating pattern means you can locate a given note by its place in the pattern.
I’m going to add a simpler reply, just to put a finer point on the great explanation already given. A Cliff notes version, since this is ELI5.
1. The smallest distance between notes in Western music is the half step. And two half steps put together make a whole step.
2. We like to arrange the notes that we will use in writing music into a linear array, called a scale. It’s like you’re going to draw with crayons, but instead of using all 64 in the box, you choose 7 colors for your picture.
3. Now, here’s the weird part. You know how you expect a staircase to be all even sizes? It would be weird if every now and then the staircase had a short step here and there. Well, Western music is weird in that way. We have been trained by hundreds of years of music history to like a scale that is uneven. A major scale is mostly whole steps, but there is a half step between notes 3 and 4, and also between 7 and 8 (And 8 is just a repetition of the first note, just to make it feel complete and like we came home, or finished the story. A staircase like that would look weird, right? But that’s what sounds good to us.
4. The C major scale is the easiest to see this with. It’s just the white keys, CDEFGAB[C]. I bracketed the last one, because it’s not a new unique note, it just makes the scale feel finished. C to D has a black key between them, so that’s a whole step. Same for D to E. But E to F, there’s that half step. Then all whole steps until B to C, which has no black key between, so it’s a half step. Minor scales put the half steps in different places, but it still is an uneven array of notes.
So scales are uneven, which is weird and not symmetrical, but that’s what sounds good to us. Playing other scales uses different notes, but that arrangement of distances stays the same. Why do we like it? Some say it is because that’s the kind of music you hear your whole life, some have even said it’s hardwired in the brain.
Interestingly, a lot of musical items are uneven, or don’t make sense to a non-musician (“Hey, why are all the doorways in your house different heights?”) And if you try to change something that’s uneven (like a major chord) into something that is…. more logical? Symmetrical? It often sounds weird or unsettling [such as an Augmented triad].
And of course, this is Western music. If you live in India or Asia, there might be other systems that I’m just not qualified to talk about. In Western music, the study of non-Western music is called ethnomusicology.
I’m going to add a simpler reply, just to put a finer point on the great explanation already given. A Cliff notes version, since this is ELI5.
1. The smallest distance between notes in Western music is the half step. And two half steps put together make a whole step.
2. We like to arrange the notes that we will use in writing music into a linear array, called a scale. It’s like you’re going to draw with crayons, but instead of using all 64 in the box, you choose 7 colors for your picture.
3. Now, here’s the weird part. You know how you expect a staircase to be all even sizes? It would be weird if every now and then the staircase had a short step here and there. Well, Western music is weird in that way. We have been trained by hundreds of years of music history to like a scale that is uneven. A major scale is mostly whole steps, but there is a half step between notes 3 and 4, and also between 7 and 8 (And 8 is just a repetition of the first note, just to make it feel complete and like we came home, or finished the story. A staircase like that would look weird, right? But that’s what sounds good to us.
4. The C major scale is the easiest to see this with. It’s just the white keys, CDEFGAB[C]. I bracketed the last one, because it’s not a new unique note, it just makes the scale feel finished. C to D has a black key between them, so that’s a whole step. Same for D to E. But E to F, there’s that half step. Then all whole steps until B to C, which has no black key between, so it’s a half step. Minor scales put the half steps in different places, but it still is an uneven array of notes.
So scales are uneven, which is weird and not symmetrical, but that’s what sounds good to us. Playing other scales uses different notes, but that arrangement of distances stays the same. Why do we like it? Some say it is because that’s the kind of music you hear your whole life, some have even said it’s hardwired in the brain.
Interestingly, a lot of musical items are uneven, or don’t make sense to a non-musician (“Hey, why are all the doorways in your house different heights?”) And if you try to change something that’s uneven (like a major chord) into something that is…. more logical? Symmetrical? It often sounds weird or unsettling [such as an Augmented triad].
And of course, this is Western music. If you live in India or Asia, there might be other systems that I’m just not qualified to talk about. In Western music, the study of non-Western music is called ethnomusicology.
I’m going to add a simpler reply, just to put a finer point on the great explanation already given. A Cliff notes version, since this is ELI5.
1. The smallest distance between notes in Western music is the half step. And two half steps put together make a whole step.
2. We like to arrange the notes that we will use in writing music into a linear array, called a scale. It’s like you’re going to draw with crayons, but instead of using all 64 in the box, you choose 7 colors for your picture.
3. Now, here’s the weird part. You know how you expect a staircase to be all even sizes? It would be weird if every now and then the staircase had a short step here and there. Well, Western music is weird in that way. We have been trained by hundreds of years of music history to like a scale that is uneven. A major scale is mostly whole steps, but there is a half step between notes 3 and 4, and also between 7 and 8 (And 8 is just a repetition of the first note, just to make it feel complete and like we came home, or finished the story. A staircase like that would look weird, right? But that’s what sounds good to us.
4. The C major scale is the easiest to see this with. It’s just the white keys, CDEFGAB[C]. I bracketed the last one, because it’s not a new unique note, it just makes the scale feel finished. C to D has a black key between them, so that’s a whole step. Same for D to E. But E to F, there’s that half step. Then all whole steps until B to C, which has no black key between, so it’s a half step. Minor scales put the half steps in different places, but it still is an uneven array of notes.
So scales are uneven, which is weird and not symmetrical, but that’s what sounds good to us. Playing other scales uses different notes, but that arrangement of distances stays the same. Why do we like it? Some say it is because that’s the kind of music you hear your whole life, some have even said it’s hardwired in the brain.
Interestingly, a lot of musical items are uneven, or don’t make sense to a non-musician (“Hey, why are all the doorways in your house different heights?”) And if you try to change something that’s uneven (like a major chord) into something that is…. more logical? Symmetrical? It often sounds weird or unsettling [such as an Augmented triad].
And of course, this is Western music. If you live in India or Asia, there might be other systems that I’m just not qualified to talk about. In Western music, the study of non-Western music is called ethnomusicology.
There are 12 notes in total.
However only 7 are used in a major scale.
Pianos are in C major, so the notes used in the scale are white and the remaining 5 are black.
As for why they are in that specific grouping, that’s just due to the definition of a major scale.
Major scales are defined as:
1) starting note
2) note after next
3) note after next
4) next note
5) note after next
6) note after next
7) note after next
8) next note and we are back to the starting note but an octave higher.
The notes that are skipped are the black keys and this is why they are in the 2, 3 pattern.
ELI5: That’s how music is shaped.
…
ELI10: So you might know that sound is made of vibrations in the air. Western cultures (America, Europe) ended up liking sounds with certain math ratios of each other (like 2x, 1.5x etc.) After hundreds of years this settled into known patterns in music theory, forming things like “octaves” (2x frequency) and “scales” (series of notes in order). There are 8 notes in a scale including 1 repeating note before a pattern repeats, with the 8th one being one “octave” up from where the scale started. It just so happens that, again because of how culture and math worked out, there are actually 12 “half steps” between octaves because some notes sound better going the next half step and some sound better going the next whole step (2 half steps). The white keys are then organized so they sound best in a “default” setting, but the other half steps are still there for funky things. Try it yourself! Start on a low (left) white key and play only white keys in sequence up (move to right). It sounds kind of happy, right? That’s C Major scale. Or, start on any key and go the nearest note in sequence up (right), including black keys when they’re there. It sounds kind of mystical, right? That’s the chromatic scale.
…
ELI18: So, although the pitch of a note is often represented by a single frequency, there are these things called overtones and harmonics that underlie practically every sound. The waveform of a given sound often looks far wigglier than a sine wave, and those wiggles within wiggles can be expressed as additions of multiple waves of certain mathematical ratios, with the most prominent overall frequency called the fundamental. The wavelengths are related by the harmonic series: 1, 1/2, 1/3, 1/4… The harmonics contained in a sound define its “timbre,” the texture of a note, and the reason a flute and a violin playing the same note sound noticeably different than each other, and why different people’s voices sound different. (If this waveform analysis interests you, you might Google “fast Fourier transform,” a common way of breaking down a sound into its fundamental and harmonics).
Despite differing timbre, the prominence of the first few overtones tend to be quite common, and thus causes notes with fundamentals that hit overtones of other fundamentals to resonate (being at the same frequency) with those overtones, which ends up defining quite a few of the notes found in music. In both Western traditions and the stereotypical Asian pentatonic scale, for example, you find what western music theory calls the “fifth”, which is the relation of the 1st and 2nd harmonics above the fundamental, or 1/3 vs 1/2 = 3/2. It forms something like the halfway point between octaves – if X hz is the fundamental, and 2*X is the next octave up, then 3/2*X is the fifth.
Western music ended up taking advantage of a few more partials than that, which by the Baroque period (1600 to 1750), in large part thanks to the prolific composer Johann Sebastian Bach, settled more or less into 2 archetypes, the major scale and minor scale. Within major and minor scales, 7 repeating notes can be defined, with an 8th corresponding to the 1st note (called the tonic), hence “octave.” These notes could roughly be defined as being a “whole step” or “half step” away from each other, with a whole step being roughly the distance between 7th and 8th partials. So despite 7 mixed whole- and half-steps (+ 8th to restart cycle) for scales, if measured only in half-steps, it would be 11 half-steps (+12th to restart cycle). The half-steps only scale is called the chromatic scale.
Note that I mentioned “roughly.” The ratios between notes end up “drifting” a little when key changes come into play; that is, if one splits an octave into 12 multiplicatively equal parts to form the half-steps of the chromatic scale, notes don’t quite match up with the harmonics noted above. For example, tonic X hz * 2^(7/12) represents the “fifth” on the scale so it sounds very close to X hz * 3/2, but it doesn’t line up exactly. If you’re interested in this difference, you can Google “equal temperament” (the system of 2^(n/12)) and/or “just temperament” (the system following harmonics like 3/2). In fact because of the challenge of tuning (temperament), JS Bach wrote the “well tempered clavier,” a set of pieces meant to be played based on each note of the chromatic scale (and thus hitting all the white and black keys as the tonics of their respective scales).
Further reading:.
* https://en.m.wikipedia.org/wiki/Harmonic_series_(music)
* https://dsp.stackexchange.com/questions/61908/i-dont-understand-harmonics-why-do-they-happen (waveform analysis)
* https://en.m.wikipedia.org/wiki/Equal_temperament
There are 12 notes in total.
However only 7 are used in a major scale.
Pianos are in C major, so the notes used in the scale are white and the remaining 5 are black.
As for why they are in that specific grouping, that’s just due to the definition of a major scale.
Major scales are defined as:
1) starting note
2) note after next
3) note after next
4) next note
5) note after next
6) note after next
7) note after next
8) next note and we are back to the starting note but an octave higher.
The notes that are skipped are the black keys and this is why they are in the 2, 3 pattern.
ELI5: That’s how music is shaped.
…
ELI10: So you might know that sound is made of vibrations in the air. Western cultures (America, Europe) ended up liking sounds with certain math ratios of each other (like 2x, 1.5x etc.) After hundreds of years this settled into known patterns in music theory, forming things like “octaves” (2x frequency) and “scales” (series of notes in order). There are 8 notes in a scale including 1 repeating note before a pattern repeats, with the 8th one being one “octave” up from where the scale started. It just so happens that, again because of how culture and math worked out, there are actually 12 “half steps” between octaves because some notes sound better going the next half step and some sound better going the next whole step (2 half steps). The white keys are then organized so they sound best in a “default” setting, but the other half steps are still there for funky things. Try it yourself! Start on a low (left) white key and play only white keys in sequence up (move to right). It sounds kind of happy, right? That’s C Major scale. Or, start on any key and go the nearest note in sequence up (right), including black keys when they’re there. It sounds kind of mystical, right? That’s the chromatic scale.
…
ELI18: So, although the pitch of a note is often represented by a single frequency, there are these things called overtones and harmonics that underlie practically every sound. The waveform of a given sound often looks far wigglier than a sine wave, and those wiggles within wiggles can be expressed as additions of multiple waves of certain mathematical ratios, with the most prominent overall frequency called the fundamental. The wavelengths are related by the harmonic series: 1, 1/2, 1/3, 1/4… The harmonics contained in a sound define its “timbre,” the texture of a note, and the reason a flute and a violin playing the same note sound noticeably different than each other, and why different people’s voices sound different. (If this waveform analysis interests you, you might Google “fast Fourier transform,” a common way of breaking down a sound into its fundamental and harmonics).
Despite differing timbre, the prominence of the first few overtones tend to be quite common, and thus causes notes with fundamentals that hit overtones of other fundamentals to resonate (being at the same frequency) with those overtones, which ends up defining quite a few of the notes found in music. In both Western traditions and the stereotypical Asian pentatonic scale, for example, you find what western music theory calls the “fifth”, which is the relation of the 1st and 2nd harmonics above the fundamental, or 1/3 vs 1/2 = 3/2. It forms something like the halfway point between octaves – if X hz is the fundamental, and 2*X is the next octave up, then 3/2*X is the fifth.
Western music ended up taking advantage of a few more partials than that, which by the Baroque period (1600 to 1750), in large part thanks to the prolific composer Johann Sebastian Bach, settled more or less into 2 archetypes, the major scale and minor scale. Within major and minor scales, 7 repeating notes can be defined, with an 8th corresponding to the 1st note (called the tonic), hence “octave.” These notes could roughly be defined as being a “whole step” or “half step” away from each other, with a whole step being roughly the distance between 7th and 8th partials. So despite 7 mixed whole- and half-steps (+ 8th to restart cycle) for scales, if measured only in half-steps, it would be 11 half-steps (+12th to restart cycle). The half-steps only scale is called the chromatic scale.
Note that I mentioned “roughly.” The ratios between notes end up “drifting” a little when key changes come into play; that is, if one splits an octave into 12 multiplicatively equal parts to form the half-steps of the chromatic scale, notes don’t quite match up with the harmonics noted above. For example, tonic X hz * 2^(7/12) represents the “fifth” on the scale so it sounds very close to X hz * 3/2, but it doesn’t line up exactly. If you’re interested in this difference, you can Google “equal temperament” (the system of 2^(n/12)) and/or “just temperament” (the system following harmonics like 3/2). In fact because of the challenge of tuning (temperament), JS Bach wrote the “well tempered clavier,” a set of pieces meant to be played based on each note of the chromatic scale (and thus hitting all the white and black keys as the tonics of their respective scales).
Further reading:.
* https://en.m.wikipedia.org/wiki/Harmonic_series_(music)
* https://dsp.stackexchange.com/questions/61908/i-dont-understand-harmonics-why-do-they-happen (waveform analysis)
* https://en.m.wikipedia.org/wiki/Equal_temperament
ELI5: That’s how music is shaped.
…
ELI10: So you might know that sound is made of vibrations in the air. Western cultures (America, Europe) ended up liking sounds with certain math ratios of each other (like 2x, 1.5x etc.) After hundreds of years this settled into known patterns in music theory, forming things like “octaves” (2x frequency) and “scales” (series of notes in order). There are 8 notes in a scale including 1 repeating note before a pattern repeats, with the 8th one being one “octave” up from where the scale started. It just so happens that, again because of how culture and math worked out, there are actually 12 “half steps” between octaves because some notes sound better going the next half step and some sound better going the next whole step (2 half steps). The white keys are then organized so they sound best in a “default” setting, but the other half steps are still there for funky things. Try it yourself! Start on a low (left) white key and play only white keys in sequence up (move to right). It sounds kind of happy, right? That’s C Major scale. Or, start on any key and go the nearest note in sequence up (right), including black keys when they’re there. It sounds kind of mystical, right? That’s the chromatic scale.
…
ELI18: So, although the pitch of a note is often represented by a single frequency, there are these things called overtones and harmonics that underlie practically every sound. The waveform of a given sound often looks far wigglier than a sine wave, and those wiggles within wiggles can be expressed as additions of multiple waves of certain mathematical ratios, with the most prominent overall frequency called the fundamental. The wavelengths are related by the harmonic series: 1, 1/2, 1/3, 1/4… The harmonics contained in a sound define its “timbre,” the texture of a note, and the reason a flute and a violin playing the same note sound noticeably different than each other, and why different people’s voices sound different. (If this waveform analysis interests you, you might Google “fast Fourier transform,” a common way of breaking down a sound into its fundamental and harmonics).
Despite differing timbre, the prominence of the first few overtones tend to be quite common, and thus causes notes with fundamentals that hit overtones of other fundamentals to resonate (being at the same frequency) with those overtones, which ends up defining quite a few of the notes found in music. In both Western traditions and the stereotypical Asian pentatonic scale, for example, you find what western music theory calls the “fifth”, which is the relation of the 1st and 2nd harmonics above the fundamental, or 1/3 vs 1/2 = 3/2. It forms something like the halfway point between octaves – if X hz is the fundamental, and 2*X is the next octave up, then 3/2*X is the fifth.
Western music ended up taking advantage of a few more partials than that, which by the Baroque period (1600 to 1750), in large part thanks to the prolific composer Johann Sebastian Bach, settled more or less into 2 archetypes, the major scale and minor scale. Within major and minor scales, 7 repeating notes can be defined, with an 8th corresponding to the 1st note (called the tonic), hence “octave.” These notes could roughly be defined as being a “whole step” or “half step” away from each other, with a whole step being roughly the distance between 7th and 8th partials. So despite 7 mixed whole- and half-steps (+ 8th to restart cycle) for scales, if measured only in half-steps, it would be 11 half-steps (+12th to restart cycle). The half-steps only scale is called the chromatic scale.
Note that I mentioned “roughly.” The ratios between notes end up “drifting” a little when key changes come into play; that is, if one splits an octave into 12 multiplicatively equal parts to form the half-steps of the chromatic scale, notes don’t quite match up with the harmonics noted above. For example, tonic X hz * 2^(7/12) represents the “fifth” on the scale so it sounds very close to X hz * 3/2, but it doesn’t line up exactly. If you’re interested in this difference, you can Google “equal temperament” (the system of 2^(n/12)) and/or “just temperament” (the system following harmonics like 3/2). In fact because of the challenge of tuning (temperament), JS Bach wrote the “well tempered clavier,” a set of pieces meant to be played based on each note of the chromatic scale (and thus hitting all the white and black keys as the tonics of their respective scales).
Further reading:.
* https://en.m.wikipedia.org/wiki/Harmonic_series_(music)
* https://dsp.stackexchange.com/questions/61908/i-dont-understand-harmonics-why-do-they-happen (waveform analysis)
* https://en.m.wikipedia.org/wiki/Equal_temperament
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