Musical instruments in 2D, 3D and 4D

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

Musical instruments in 2D, 3D and 4D

Postby Teragon » Mon Dec 28, 2015 9:20 pm

The number of dimensions determines the possible types of instruments and the ways to produce sound.

In 2D wind instruments and string instruments would be possible. Wind instruments would be similar to 3D in principle, but their acoustic colour might be a bit different as there is one lateral direction missing. String instruments are nothing that may be plucked in 2D, those intruments are beaten like a dulcimer or a paino via keys. Complex string instruments might be difficult to implement.

In 3D suddenly there is the possibility of a brane. In contrast to a string, a vibrating brane gives less consonant sounds because the standing waves are confined in 2D instead of 1D resulting in more eigenfrequencies. There are two ways to produce sound with those instruments: Drums and cymbals may be beat, cymbals may be played using a bow, resulting in a continuous, sharp sound. Also there are two other possibilities to play string instruments: Plucking and bowing. New sound colours and softer sounds are produced and it's possible to change the length of the strings with one's hand.

In 4D branes with 3 dimensions become possible, resulting in even more dissonant sounds than 3D percussion gives. The more complex geometry allows for a broader range of timbre. Both 2D and 3D branes could be used as percussion or be bowed. 2D cymbals and even drumheads could be plucked like a quitar. Modifiying the pitch with one's hands would be difficult though, as you would need ridiculously long fingers to do so. Still pressing against those strings would have an effect by damping the sound while increasing the frequency (as in 3D). The additional dimension would allow for more 1D strings on one instrument if the fingers of the player have the same length. Similary keys of pianos could be packed more tightly making it easier to play demanding music. Bowed instruments with 1D strings would have to be played using a 2D bow in order to stay on top of the strings. 2D strings could be either played with 1D or 2D bows. In the second case the vibrations moving along the lateral direction the bow is extented into might be damped more strongly, so if the string is not totally symmetrical the player could modify the sound depending on the orientation of the bow.

(Now comes the idea of using cross- or net-shaped strings for instruments in 3D - two coupled waves. I wonder what that would sound like...)
What is deep in our world is superficial in higher dimensions.
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Re: Musical instruments in 2D, 3D and 4D

Postby PatrickPowers » Tue Dec 29, 2015 6:06 pm

Teragon wrote:The number of dimensions determines the possible types of instruments and the ways to produce sound.

In 2D wind instruments and string instruments would be possible. Wind instruments would be similar to 3D in principle, but their acoustic colour might be a bit different as there is one lateral direction missing. String instruments are nothing that may be plucked in 2D, those intruments are beaten like a dulcimer or a paino via keys. Complex string instruments might be difficult to implement.

In 3D suddenly there is the possibility of a brane. In contrast to a string, a vibrating brane gives less consonant sounds because the standing waves are confined in 2D instead of 1D resulting in more eigenfrequencies. There are two ways to produce sound with those instruments: Drums and cymbals may be beat, cymbals may be played using a bow, resulting in a continuous, sharp sound. Also there are two other possibilities to play string instruments: Plucking and bowing. New sound colours and softer sounds are produced and it's possible to change the length of the strings with one's hand.

In 4D branes with 3 dimensions become possible, resulting in even more dissonant sounds than 3D percussion gives. The more complex geometry allows for a broader range of timbre. Both 2D and 3D branes could be used as percussion or be bowed. 2D cymbals and even drumheads could be plucked like a quitar. Modifiying the pitch with one's hands would be difficult though, as you would need ridiculously long fingers to do so. Still pressing against those strings would have an effect by damping the sound while increasing the frequency (as in 3D). The additional dimension would allow for more 1D strings on one instrument if the fingers of the player have the same length. Similary keys of pianos could be packed more tightly making it easier to play demanding music. Bowed instruments with 1D strings would have to be played using a 2D bow in order to stay on top of the strings. 2D strings could be either played with 1D or 2D bows. In the second case the vibrations moving along the lateral direction the bow is extented into might be damped more strongly, so if the string is not totally symmetrical the player could modify the sound depending on the orientation of the bow.

(Now comes the idea of using cross- or net-shaped strings for instruments in 3D - two coupled waves. I wonder what that would sound like...)



In 2D a string and a drumhead would be the same. In a sense it would be more accurate to call it a drumhead, because plucking would not be possible. Percussion only. But it would sound like a string.

It would be possible to change the length of a string with the "hand" in 2D. Oh, you mean with the hand only. You CAN change the pitch of a string in 2D with the hand only. One may touch the string on a node of the harmonic series, or pull on the end of the string to increase tension. There actually is a musical instrument like this in Viet Nam.

2D cymbals and even drumheads could be plucked like a quitar. Quite so! I never thought of that.


Similary keys of pianos could be packed more tightly making it easier to play demanding music.
This can be done in 3D, since the arrangement of piano keys is essentially 1D. 2D keyboards have been made but never caught on. Playing the piano is hard enough as it is.

I think it might be a good idea to get a higher octave or two by playing on distal regions of the keys. On current keyboards each hand can only play about an octave and a half, for a total of three octaves. It would be fairly easy to set up an electronic keyboard be able to get all 8 octaves at the same time with two hands. I thought it had potential but keyboard players hated the idea, so I gave up.

In 4D branes with 3 dimensions become possible. It is sort of possible to have a 3D as well. Just have a vibrating sphere. It has a bad sound though, a toneless thunk.

Sound itself is different in other dimensioned spaces, but I think you knew that.
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Re: Musical instruments in 2D, 3D and 4D

Postby Teragon » Fri Jan 01, 2016 10:34 pm

PatrickPowers wrote:In 2D a string and a drumhead would be the same. In a sense it would be more accurate to call it a drumhead, because plucking would not be possible. Percussion only. But it would sound like a string.


Depends on the classification you choose. You wouldn't call a piano percussion, right? Strings could be played like a piano in 2D.

PatrickPowers wrote:It would be possible to change the length of a string with the "hand" in 2D. Oh, you mean with the hand only. You CAN change the pitch of a string in 2D with the hand only. One may touch the string on a node of the harmonic series, or pull on the end of the string to increase tension. There actually is a musical instrument like this in Viet Nam.


Where did I say that? But yes, we could do that in 2D as well.

2D cymbals and even drumheads could be plucked like a quitar. Quite so! I never thought of that.

PatrickPowers wrote:
Similary keys of pianos could be packed more tightly making it easier to play demanding music.
This can be done in 3D, since the arrangement of piano keys is essentially 1D. 2D keyboards have been made but never caught on. Playing the piano is hard enough as it is.


Still it's easier in 4D. In 3D there's one lateral direction for your fingers and in the other direction you have to move your fingers back and forth over the length of a hole key. In 4D you just have two lateral directions and your fingers might be aligned in both directions naturally.

PatrickPowers wrote:I think it might be a good idea to get a higher octave or two by playing on distal regions of the keys. On current keyboards each hand can only play about an octave and a half, for a total of three octaves. It would be fairly easy to set up an electronic keyboard be able to get all 8 octaves at the same time with two hands. I thought it had potential but keyboard players hated the idea, so I gave up.


Keyboards that have two or three rows of keys already exist.

PatrickPowers wrote:In 4D branes with 3 dimensions become possible. It is sort of possible to have a 3D as well. Just have a vibrating sphere. It has a bad sound though, a toneless thunk.


You're right, kind of. The difference is, in 4D the 3D object is a membrane and the vibrations are perpendicular to it. In 3D it's only the borders that produce sound waves travelling to your ear. It will be more difficult to get the same amplitude with a nice excitation of all modes. (A cymbal sounds very different and not quite as nice if its vertical movement is inhibited and you hit it from the side).
What is deep in our world is superficial in higher dimensions.
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Re: Musical instruments in 2D, 3D and 4D

Postby PatrickPowers » Sat Jan 02, 2016 5:25 pm

Teragon wrote:
PatrickPowers wrote:In 2D a string and a drumhead would be the same. In a sense it would be more accurate to call it a drumhead, because plucking would not be possible. Percussion only. But it would sound like a string.


Depends on the classification you choose. You wouldn't call a piano percussion, right? Strings could be played like a piano in 2D.



The piano is a percussion instrument. I play the piano a bit. It's a challenge to get the basically harsh sound to sound good. It takes touch to not be a "pounder." Being able to get your hands on the strings definitely makes a difference. Blues guitarists get all sorts of subtlety out of that intimate contact.

Teragon wrote:
PatrickPowers wrote:Keyboards that have two or three rows of keys already exist.


True, but one is still limited to one-and-a-half octaves per hand, at least with the keyboards I've seen. I want to be able to get four octaves with one hand.

Rethinking this (to me) old idea, I might give it a try again. it would be cheap and easy to program a computer to decode signals from an alphanumeric keyboard as tones. You could span four octaves, eight with the shift keys. It would be great for playing angular lines. You could do things easily that would be quite difficult on a regular piano keyboard. The space bar could be a drum, etc.

The main reason piano keys are so long is to give mechanical advantage. Waste of space on an electronic instrument.

A friend of mine just invented a mandolin with frets a whole tone apart. To amazement, it sounds good. When he plays it, at least.
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Re: Musical instruments in 2D, 3D and 4D

Postby PatrickPowers » Sat Feb 06, 2016 3:28 am

By golly, someone beat me to it. A computer keyboard used to control a piano...

https://youtu.be/v9YHlK4P3IQ?t=9s

It sounds terrible, but that isn't the fault of the keyboard. Maybe someday I'll give it a try.
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Re: Musical instruments in 2D, 3D and 4D

Postby Teragon » Sat Feb 13, 2016 2:49 pm

The composition is interesting in my ears.
What is deep in our world is superficial in higher dimensions.
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Re: Musical instruments in 2D, 3D and 4D

Postby PatrickPowers » Fri Feb 26, 2016 2:03 pm

A realworld 2D keyboard! Or N D. Two spatial dimensions and maybe twenty dimensions in the more general sense. The round keys switch between dimensions, or modes if you prefer. The keyboard is a planar two-manifold embedded in a 20D or so space.

https://www.youtube.com/watch?v=E6gdXiCSR5o

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