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I read the following on the internet:

Oboe

According to some experts, above-average intelligence is important in playing the very intricate oboe. Others say the oboe is ideal for determined, tight-lipped, stubborn introverts.

https://www.creativesoulmusic.com/blog/what-instrument-should-your-child-play-based-on-their-personality#:~:text=Oboe,tight%2Dlipped%2C%20stubborn%20introverts.

Can I ask the following question?

Is there a musical instrument that would be preferred by those who are good at mathematics / abstract thinking (and enjoy toying with abstract ideas)?

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    I have a degree in pure mathematics and when I read your question the first thing that popped into my head was piano. Aside from that, this question seems a bit subjective to me. – Todd Wilcox Sep 24 at 13:56
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    BTW, I read this as a joke: "Others say the oboe is ideal for determined, tight-lipped, stubborn introverts" – Todd Wilcox Sep 24 at 14:23
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    @ToddWilcox - why would you think the piano is more maths orientated than any other? – Tim Sep 24 at 16:20
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    @Tim Most pianists I know have 10 independent fingers – AlexanderJ93 Sep 24 at 17:45
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    @AlexanderJ93 - being a pedant, I know plenty with eight fingers, what planet are yours from? And usually not all being used simultaneously. But, jesting aside, fair point, so piano wins - so far! – Tim Sep 24 at 18:24

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No.

I respectfully differ from all the other answers (so far) and answer your question with a strong no, I don't think that any instrument, or any class of instruments, would be consistently preferred by people with a bias for math or abstract thinking. (With a single caveat that I'll explain at the bottom).

The reasoning that some instruments, like the piano, or even the computer, may have some more "math" in them compared to, say, the violin, may be correct on a superficial level, but music is infinitely more rich and complex than that. And to further generalize that being math-oriented makes you more interested in certain instruments, doesn't make sense to me in principle, and is also not observed in practice.

And why not? Because any instrument, from the simplest to the most complex, is amenable to an infinite number of different approaches, and whether it is melodic or harmonic, even the greatest human genius will never exhaust all its possibilities. A mathematically inclined person who falls in love with any instrument, will never run out of expressive options, no matter how simple the instrument.

For example, yes, musical time is divided mathematically, beats are divided in 2 or 3 or 4... but that's just the start, that's just day one. From day two and for the rest of your life, what matters is expressiveness, groove, a good touch, blending with the other musicians, and so on.

The caveat I mentioned earlier is this. Some instruments are easier to play initially than others. You can press the key of a piano, or blow into a harmonica, and you'll get almost the same sound as a pro. On the other hand, getting a trumpet or a violin, or an oboe, to play just a single note well, takes a lot of work. And in the latter case, unless you are forced by your parents, it takes a lot of personal motivation, patience, and commitment just to get started and persist for quite some time through all the initial difficulties, until you reach the point where you start to get your first rewards. And from that point of view, I think it's reasonable to imagine that certain types of people rather than others are more likely to do it.

But once again, I don't think that math-oriented brains would tend to select certain instruments. On the contrary, I think that a math-oriented brain can easily find reasons to enjoy and love pretty much any instrument at all!

Bonus example: we'll probably agree that someone like Einstein was math- and abstract thinking-oriented, and he played the violin.

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    I might say it depends on the math. A pure algebraist I would expect to gravitate more towards complex discrete structures such as one deals with as a pianist or drummer, while a fan of complex analysis might find the trombone endlessly fascinating. But I don’t think it’s all equivalent from a math perspective. Producing excellent clarinet timbre is not at all mathematically interesting to me, but playing 8th notes on the hats and simultaneous quarter note triplets on the kick is mathematical joy made physical to my mind. This answer seems like a musician point of view. – Todd Wilcox Sep 24 at 13:58
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    One very slight nit pick. Anyone pressing one key of a piano will get exactly the same sound as a pro, given the same volume, because (if we don't include fancy damping techiques) that's all you can do with one key on a piano. The hammer is ballistic and the only information it carries is velocity. – Scott Wallace Sep 24 at 14:25
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    @ScottWallace A widely held misconception, even among musicians, although not among better pianists. It has recently come to my attention, to my surprise, that upper key noise is quite noticeable and is a huge component in why a child banging on the piano sounds less pleasant than a great pianist playing fortissimo. That is just one area where playing the piano is not just about hitting the right key at the right time. – Todd Wilcox Sep 24 at 14:28
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    @ScottWallace - pressing one key on a piano is hardly a start. It's pressing several, together and separately and consecutively, that shows the difference between someone who's a muso and someone who's not. Maybe an organ..? – Tim Sep 24 at 16:24
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    There's an old story about a pianist and a clarinetist. The clarinetist steps up to the piano and presses a key saying "Wow, this is easy, they're all just laid out in order, no effort or skill required!" then looks at the sheet music and says "Wait, I have to play all these notes at once?!" Meanwhile the pianist looks at some clarinet sheet music and says "There's only one line of notes! This is easy!" Then picks up the instrument and spends hours just trying to get any sound at all out of the thing, days before they get one that doesn't sound like a duck being tortured... – Darrel Hoffman Sep 24 at 17:39
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The most abstract "instrument" would be a synthesizer or sound-generating software.

However, in terms of a traditional instrument, I would say organ is the most abstract in the way you're asking, as it allows for the fundamental aspect of musics -- melody, harmony, and rhythm -- to be addressed simultaneously, plus orchestration and timbre. Piano would be next for similar reasons, followed by other keyboard instruments.

Guitar also allows for similarly integrated use of melody, harmony, and rhythm.

On the other hand, percussion, with its focus on mathematical rhythmic relationships might be very appealing.

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  • Unfortunately organ does not allow for separate dynamics on individual notes in the way that a piano does. – Todd Wilcox Sep 24 at 17:32
  • I’ve written my answer before I’ve seen that you’re mentioning the organ too. I agree with you but I think the existing repertory for the instrument is also an important factor. – Albrecht Hügli Sep 25 at 3:53
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Literally abstract - Theremin or voice. Possibly, but only possibly, instruments with continuous pitch, such as violin, trombone, fretless bass.

I take that website with a large pinch of salt, in fact, it's pretty abstract in its thinking!

With a mathematical mind, any instrument - as music and maths are closely related in several ways, and those with mathematical minds often play well. If one is good at counting, percussion might suit - there's often hundreds of bars' rests to count when playing (or not..!) in an orchestra.

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    Theramin! Nice thought. Continuous pitched instruments do present lots of possibiities. So, "slide piano"? (Which led me to this craziness) – Aaron Sep 24 at 8:39
  • Theramin was my initial gut reaction to the question, lots of good answers here. – Dale Sep 25 at 7:24
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Background: I hold a B.S. in pure mathematics and my favorite branch of math is Algebra.

If you love the large structures of math; the linear transformations between two Euclidean spaces, topology, generating functions, manifolds, attempting to visualize 4 or more dimensions, Cartesian cross-products, Godel's incompleteness theorem, Cauchy, Cantor, etc., then my suggestion is you start with piano and set your sights on the symphony orchestra as your "instrument".

That really means you're not learning one instrument, you're learning music. The piano is a good, convenient map of "western" (tonal, equal-tempered music) that would help you get a grip on "all the notes". Once you have a couple years of piano under your belt, I'd pick up a used/student-level violin, viola, or cello and start down that road. Then a flute or clarinet and trumpet or trombone. Really almost any member of the woodwind and brass family would do, I'm recommending the most portable and less challenging ones. Pick up some kind of percussion - could be glockenspiel, but learning to play rock drums is actually quite helpful in understanding orchestral percussion. And learn to sing.

The goal is learning to make an entire orchestra your instrument. It becomes that when you have learned to compose and conduct, but understanding all the parts of the orchestra are critical for both of those.

At some point, start exploring jazz theory, non-western music, atonality, 20th century music, rock & pop, blues, EDM and synthesis, etc. All of these are part of mastering music as a whole, and contemporary "symphonic" composition often includes many of those elements.

The possibilities of the 21st century "orchestra" (in quotes because now synthesizers, electric guitars, conch shells, balalaikas, you name it, are used in "orchestral" compositions) are manifold, no pun intended. Merely comparing Penderecki to Hans Zimmer to Andrew Lloyd Weber can easily lead one to conclude that ensembles are the ultimate musical "instruments".

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  • I considered 'the orchestra', which encompasses just about everything (where's the didgeridoo..?) but was discouraged as the question asks about a musical instrument in the singular. But it could be argued that a composer, or indeed a conductor, has his 'instrument' - the orchestra. – Tim Sep 25 at 7:55
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Any kind of sound design and production

The BBC Radiophonic Workshop pioneered much of what we'd describe today as syntheser, "found sound", and sound design generally. Musician-engineers such as Daphne Oram and Delia Derbyshire are iconic figures today. Their work was highly technical, often requiring them to design their own electronics or other equipment. Sound designers today perhaps need less equipment, but the challenge of how to do it remains, and especially how to make music with it.

The mixing desk

Mix engineers such as Chris Lord-Alge amongst others have a vital role in turning the raw instrument tracks into an actual recorded song. Mix engineering requires not only an intimate knowledge of music, musical styles, and the flexibility to adapt your own style to the recording artist, but also an extensive understanding of all the effects and techniques available to make it happen.

Turntables

Anyone who grew up in the 80s will remember the rise of turntablism. It's still going strong, and the technical requirements of doing that are substantial.

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I'd also say no, because it's not obvious to me that a taste for abstraction in mathematics, which comes in different forms (algebraic isn't the same as logical for example), has a parallel in music.

The haziness of the latter is why the answers here differ so. A theremin can be considered abstract because of how sound is produced and controlled. People also make the argument that a piano is more abstract than a violin because it's more mechanical. But both are about sound production, they aren't conceptual, which is where mathematical abstraction lives.

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No. The math is in the music. The instrument is a tool to produce the math.

Do mathematicians prefer ink pens, pencils, chalk, or markers? Paper, blackboard or dry erase board? The answer will all boil down to either preference, or what’s available to them at the time, or whatever fits the context.

Take Brian May...legendary musician, physicist and mathematician. The guitar is his instrument of preference, however he also uses the piano from time to time because there are certain ideas that are expressed better with a different tool. He also uses his vocal chords.

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If you want something that's on the abstract side and provides good opportunities for a mathematically-oriented mind, I'll recommend the Theremin. It's what you get when you cross a musical instrument with a broken AM radio transmitter. What makes the instrument particularly abstract is that you don't manipulate it directly, you move your hand through the air to interact with the electromagnetic field generated by the instrument.

There are a number of things that make this instrument particularly interesting (IMO) from a mathematical standpoint.

  • Being an analog electronic instrument, you can construct transfer functions for the underlying circuits and model the instrument's output mathematically. It was invented by a physicist, who has already done this for the earliest designs.
  • Electrical schematics for different varieties of Theremin are available online.
  • This is one of the only instruments that I know of that you can build yourself without any special skills or expensive equipment and still end up with something that's good enough quality to play (not simply a novelty).
  • The design of the instrument lends itself to easy modification. Modifying or adding to the Theremin circuit can change the sound of the output in many interesting ways (analogous to how an effects pedal changes the sound of an electric guitar). The output is closer to a pure tone and lacks the complex harmonics of traditional instruments, so it's much easier to model and predict how a circuit modification would impact the sound.
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Yes: the church organ - including even the legs and ten fingers - and all the 100reds of pipes and the different registrations, the fascination of it’s mechanism, the history of its invention and development, the existing works written for it.

Mind the art of the fugue or e.g. the toccata in d-minor by Bach. I don’t know any other compositions like these (and the w.t.c.) that would be a greater challenge for mathematicians - analyzing, listening, performing on a church organ.

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Well, does typing

Play[Sin[440*2 Pi t], {t, 0, 4}]

into Mathematica count? I would say this is perhaps the purest, math-oriented way to play "music" - type down the function for the sound you want.

Related research article: Using math to generate annoying, scratching sounds.

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My background is in physics and classical piano, and my answer would be guitar:

  • Except for the different step between 2nd and 3rd strings in standard tuning, the same scale is played the same way everywhere.
  • Similarly, the same chord shapes work in all keys. Because of these two features, you don't get lost in the details of fingerings and memorizing scales
  • It is easy to change tuning and get a different system for the points above
  • The single instrument can cover a lot of ground between single note melodies, chord textures, percussive playing and any combination of those.
  • The harmonics and resonances that the are basis for Western music theory are really easy to find and experiment with
  • It is easy to adventure into microtonality, but unlike fretless instruments playing fixed pitches is even easier.
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