Why is singing/playing an instrument off-key a thing? Why are some frequencies of the acoustic wave okay and some not okay?
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Sound is waves of air. Different ‘notes’ are the waves moving at different speeds. When those waves line up, it sounds nice because the waves are interfering with each other less. For example, if you take one sound then overlay another where the waves are moving twice as fast, the peaks of the waves will still overlap half the time.
Two notes that sound bad together likewise have waves that *don’t* line up. This means that you need to have at least two notes before you start producing “off-key” noises. No note is inherently good or bad. They just sound better or worse when played together (either right on top of each other or in quick succession). So long as your music is internally consistent in terms of how the waves relate to each other, it will sound nice, even if there’s no way to situate it within a larger musical theory or tradition. People just don’t tend to do that, however, because it’s hard and because music is a social activity. Having your own bespoke system of music theory makes you harder to play with.
Sound is waves of air. Different ‘notes’ are the waves moving at different speeds. When those waves line up, it sounds nice because the waves are interfering with each other less. For example, if you take one sound then overlay another where the waves are moving twice as fast, the peaks of the waves will still overlap half the time.
Two notes that sound bad together likewise have waves that *don’t* line up. This means that you need to have at least two notes before you start producing “off-key” noises. No note is inherently good or bad. They just sound better or worse when played together (either right on top of each other or in quick succession). So long as your music is internally consistent in terms of how the waves relate to each other, it will sound nice, even if there’s no way to situate it within a larger musical theory or tradition. People just don’t tend to do that, however, because it’s hard and because music is a social activity. Having your own bespoke system of music theory makes you harder to play with.
Sound is waves of air. Different ‘notes’ are the waves moving at different speeds. When those waves line up, it sounds nice because the waves are interfering with each other less. For example, if you take one sound then overlay another where the waves are moving twice as fast, the peaks of the waves will still overlap half the time.
Two notes that sound bad together likewise have waves that *don’t* line up. This means that you need to have at least two notes before you start producing “off-key” noises. No note is inherently good or bad. They just sound better or worse when played together (either right on top of each other or in quick succession). So long as your music is internally consistent in terms of how the waves relate to each other, it will sound nice, even if there’s no way to situate it within a larger musical theory or tradition. People just don’t tend to do that, however, because it’s hard and because music is a social activity. Having your own bespoke system of music theory makes you harder to play with.
This is really about temperament. Modern society favors a 12 tone temperament. That means that frequencies are divided into 12 steps before repeating at another octave. That is for every doubling of pitch/frequency, we divide into 12 even steps. There is some music that uses different temperaments, but I think it’s safe to assume we are talking about typical music.
That means anything outside of those 12 steps sounds unpleasing to us. The why for that would go well beyond ELI5 though. I consider music to be sort of an exploitation of the way humans communicate emotion. Pitch, Timbre, and tempo determine the emotion being conveyed. For example someone in a panic will speak at a very high pitch, high timbre, and with a fast tempo. Where as someone expressing sadness will speak in a more slow tempo with a lower pitch. Someone expressing sadness would do so in a minor key, while someone happy will use a major key. These are increments of those 12 steps. Different combinations produce different emotions. Changing a song from a major key to a minor key can change it from happy to sad.
So somewhere through time we developed these quantized frequencies to properly communicate emotions to each other. Going outside of these steps is kind of like speaking another language emotionally and we respond with displeasure. It goes against the way we evolved to communicate. It’s not really easy to give a simple answer because it could have easily been a different temperament. We would have evolved to use a 19 tone temperament and think that 12 tones sounds bad to us. It just happened that we have 12 tones. It had to be something. And another factor would be the symmetries of the notes. Each one having a wavelength. A note an octave up is going to double the frequency and you can fit two waves evenly into the lower octave. If you don’t stay within these steps that add up evenly, then the waveforms will beat against each other which tends to sound unpleasant to us. So the mathematics of it is probably how we evolved to where we are now. How waveforms sum also dictates the emotions communicated. A major scale may sound happy, a minor scale sad, a Phrygian scale may sound more mysterious. But once you go outside of this structure, meaning tuning that is between these 12 steps, you get dissonance and the emotional communication breaks.
This is really about temperament. Modern society favors a 12 tone temperament. That means that frequencies are divided into 12 steps before repeating at another octave. That is for every doubling of pitch/frequency, we divide into 12 even steps. There is some music that uses different temperaments, but I think it’s safe to assume we are talking about typical music.
That means anything outside of those 12 steps sounds unpleasing to us. The why for that would go well beyond ELI5 though. I consider music to be sort of an exploitation of the way humans communicate emotion. Pitch, Timbre, and tempo determine the emotion being conveyed. For example someone in a panic will speak at a very high pitch, high timbre, and with a fast tempo. Where as someone expressing sadness will speak in a more slow tempo with a lower pitch. Someone expressing sadness would do so in a minor key, while someone happy will use a major key. These are increments of those 12 steps. Different combinations produce different emotions. Changing a song from a major key to a minor key can change it from happy to sad.
So somewhere through time we developed these quantized frequencies to properly communicate emotions to each other. Going outside of these steps is kind of like speaking another language emotionally and we respond with displeasure. It goes against the way we evolved to communicate. It’s not really easy to give a simple answer because it could have easily been a different temperament. We would have evolved to use a 19 tone temperament and think that 12 tones sounds bad to us. It just happened that we have 12 tones. It had to be something. And another factor would be the symmetries of the notes. Each one having a wavelength. A note an octave up is going to double the frequency and you can fit two waves evenly into the lower octave. If you don’t stay within these steps that add up evenly, then the waveforms will beat against each other which tends to sound unpleasant to us. So the mathematics of it is probably how we evolved to where we are now. How waveforms sum also dictates the emotions communicated. A major scale may sound happy, a minor scale sad, a Phrygian scale may sound more mysterious. But once you go outside of this structure, meaning tuning that is between these 12 steps, you get dissonance and the emotional communication breaks.
This is really about temperament. Modern society favors a 12 tone temperament. That means that frequencies are divided into 12 steps before repeating at another octave. That is for every doubling of pitch/frequency, we divide into 12 even steps. There is some music that uses different temperaments, but I think it’s safe to assume we are talking about typical music.
That means anything outside of those 12 steps sounds unpleasing to us. The why for that would go well beyond ELI5 though. I consider music to be sort of an exploitation of the way humans communicate emotion. Pitch, Timbre, and tempo determine the emotion being conveyed. For example someone in a panic will speak at a very high pitch, high timbre, and with a fast tempo. Where as someone expressing sadness will speak in a more slow tempo with a lower pitch. Someone expressing sadness would do so in a minor key, while someone happy will use a major key. These are increments of those 12 steps. Different combinations produce different emotions. Changing a song from a major key to a minor key can change it from happy to sad.
So somewhere through time we developed these quantized frequencies to properly communicate emotions to each other. Going outside of these steps is kind of like speaking another language emotionally and we respond with displeasure. It goes against the way we evolved to communicate. It’s not really easy to give a simple answer because it could have easily been a different temperament. We would have evolved to use a 19 tone temperament and think that 12 tones sounds bad to us. It just happened that we have 12 tones. It had to be something. And another factor would be the symmetries of the notes. Each one having a wavelength. A note an octave up is going to double the frequency and you can fit two waves evenly into the lower octave. If you don’t stay within these steps that add up evenly, then the waveforms will beat against each other which tends to sound unpleasant to us. So the mathematics of it is probably how we evolved to where we are now. How waveforms sum also dictates the emotions communicated. A major scale may sound happy, a minor scale sad, a Phrygian scale may sound more mysterious. But once you go outside of this structure, meaning tuning that is between these 12 steps, you get dissonance and the emotional communication breaks.
First, musicality is about the pitch relationships between notes. When we say an instrument is *out-of-tune*, we mean that a named note is different from the expected pitch of that note, relative to either a standard (concert A at 440Hz), to another instrument, or to itself (a string on a guitar that is not tuned correctly relative to the other strings).
Acoustic instruments produce sound by harmonic motion – a plucked/bowed string, a column of air oscillating in a tube, a vibrating reed. The mathematical formula that describe the resulting frequency have references to a large number of physical quantities – mass, tension, length, elasticity. Some of those properties have other dependencies – temperature and humidity being the main ones. Things like the tension of a guitar string change over time as the string stretches, but the elasticity decreases.
What this means is that most instruments change their tune over time. For some instruments (like a piano) this may take months if it is in a stable environment and not moved. For others (like guitars and wind/brass instruments) they may need tuning every time they are played. In fact, wind and brass instruments need to be **warmed up** to playing temperature and humidity and then tuned again just prior to performing.
Instruments that need regular tuning also have accessible tuning pegs. This means that the pegs can be knocked, putting it out of tune. Wind instruments are tuned by moving the mouthpiece in or out. Brass instruments have a small slide with a locking nut.
First, musicality is about the pitch relationships between notes. When we say an instrument is *out-of-tune*, we mean that a named note is different from the expected pitch of that note, relative to either a standard (concert A at 440Hz), to another instrument, or to itself (a string on a guitar that is not tuned correctly relative to the other strings).
Acoustic instruments produce sound by harmonic motion – a plucked/bowed string, a column of air oscillating in a tube, a vibrating reed. The mathematical formula that describe the resulting frequency have references to a large number of physical quantities – mass, tension, length, elasticity. Some of those properties have other dependencies – temperature and humidity being the main ones. Things like the tension of a guitar string change over time as the string stretches, but the elasticity decreases.
What this means is that most instruments change their tune over time. For some instruments (like a piano) this may take months if it is in a stable environment and not moved. For others (like guitars and wind/brass instruments) they may need tuning every time they are played. In fact, wind and brass instruments need to be **warmed up** to playing temperature and humidity and then tuned again just prior to performing.
Instruments that need regular tuning also have accessible tuning pegs. This means that the pegs can be knocked, putting it out of tune. Wind instruments are tuned by moving the mouthpiece in or out. Brass instruments have a small slide with a locking nut.
First, musicality is about the pitch relationships between notes. When we say an instrument is *out-of-tune*, we mean that a named note is different from the expected pitch of that note, relative to either a standard (concert A at 440Hz), to another instrument, or to itself (a string on a guitar that is not tuned correctly relative to the other strings).
Acoustic instruments produce sound by harmonic motion – a plucked/bowed string, a column of air oscillating in a tube, a vibrating reed. The mathematical formula that describe the resulting frequency have references to a large number of physical quantities – mass, tension, length, elasticity. Some of those properties have other dependencies – temperature and humidity being the main ones. Things like the tension of a guitar string change over time as the string stretches, but the elasticity decreases.
What this means is that most instruments change their tune over time. For some instruments (like a piano) this may take months if it is in a stable environment and not moved. For others (like guitars and wind/brass instruments) they may need tuning every time they are played. In fact, wind and brass instruments need to be **warmed up** to playing temperature and humidity and then tuned again just prior to performing.
Instruments that need regular tuning also have accessible tuning pegs. This means that the pegs can be knocked, putting it out of tune. Wind instruments are tuned by moving the mouthpiece in or out. Brass instruments have a small slide with a locking nut.
Just playing a single note out of tune is not likely to be offensive to anyone, because there is no other reference sound to compare it to, to determine if it’s in tune or out of tune. However, if you play two (or more) notes that are out of tune with each other, it will often be immediately obvious to most observers. Here’s why:
A musical note is a vibration at a certain frequency. A 440Hz note means something that is vibrating back and forth 440 times per second, whether that’s a metal string, a column of air, a block of wood, etc.
When playing multiple musical notes together at the same time, they sound best when the frequencies of the notes are in simple ratios to one another. For instance, if you play an A at 440Hz and an E at 660Hz, they sound pleasing together. This is because their ratio is 3/2, which is a simple ratio. If instead you played an A at 440Hz and an off-key E at 668Hz, it would sound nasty, because their ratio is 57/110, which is not a simple ratio. This complex ratio creates strange chaotic non-periodic interactions between the 440Hz tone and 668Hz tone, which sound harsh to our ears.
Combinations of tones that are considered pleasing are called “consonant”, and non-pleasing combinations are called “dissonant”. Note that this isn’t a black and white distinction, consonance and dissonance exist on a spectrum, and this can be used as a tool by a skilled composer to achieve different effects.
Check out [https://en.wikipedia.org/wiki/Consonance_and_dissonance](https://en.wikipedia.org/wiki/Consonance_and_dissonance) for more info.
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