First watch this video (you can go to 4:30):

Info:

Spoiler

In an effort to clarify the testing reform and to defend the importance of times tables, Nick Gibb, the Schools Minister, appeared on Good Morning Britain. During the interview, host Jeremy Kyle, asked Gibb to provide the answer to a simple maths question. When asked what 8 x 9 was, Gibb laughed and refused to answer the question. He stated that he wasn’t going to get into this because he has learnt from bitter experience never to answer these kind of questions on live television. His response frustrated the presenters on the program and prompted the question of why is it so important for an 8 year old to prove their times table skills when the Schools Minister wasn’t prepared to do so himself.

Of course, you can laugh at the video and mock the poor minister, but I didn't post it here for that purpose.

The main elements and structure of music are connected by numbers. One can ignore this undeniable fact and deny it or look at it as a pervasive phenomenon that is present at all stages of making music.

One of the main reasons that the works of great composers have endured in history is that math and precise calculations are seen in most of their works. Without accurate calculations, it is not possible to manage different parts of music.

 

It's a nice topic but would have been better as a tentative question rather than those extravagant claims.
So, I will now play devil's advocate and strongly claim the opposite.
It's going to emphasise the (regularly confused) difference between
knowledge and theories that describe knowledge (they are not the same thing)

When you catch a ball (if you catch it) your brain performs a set of very clever tricks.
But no-one is thinking about numbers when they catch a ball.
You have knowledge (you know how to catch a ball)
If you want to teach a robot to catch a ball you will need to analyse what is going on and describe the physics
using a huge amount of maths in your descriptions.

So, the philosophical question...
[1] is the maths an essential (physical) part of what's going on when you catch a ball
OR
[2] is the maths just the best way humans know of modelling and describing what's going on?

When you've (never) finished the endless philosophical debate... I think you should probably lean more towards [2]

BUT whatever you decide you still have to recognise that the human child can catch a ball better than the robot
without ever explicitly thinking about maths! even when the maths required to describe that act is quite advanced.

Now apply the same argument to making music.
You can compose brilliant music without ever understanding maths (or even music theory - with or without maths).
Just because people can't describe it without using theory doesn't mean theory was explicitly required when composing it.

Knowledge of how to catch a ball is not the same as theory describing the act of catching a ball.
Knowledge of how to compose music is not the same as theory describing the structure of a piece of music.
We can inspect and discuss our theories.
We can't discuss our knowledge without resorting to using just more descriptive theories.
(that's why we regularly confuse knowledge and theories that describe knowledge)

Musicians can demonstrate their extensive musical knowledge (just by making music)
and they might be completely ignorant of any and all music theory that merely describes that knowledge.

p.s.
Even if some concepts do need to be focussed on, explicitly and consciously,
mathematics is not always the best way of visualising the concepts.
Maths is occasionally the best way, occasionally the only way.
But in art we do explore other wonderful options.

p.p.s
This post reminds me of the kind of question that a regular repeat member to this forum would have written.
What are the mathematical odds I wonder?

 

Last edited: Nov 2, 2020

You provided a good explanation, but you know making music isn't like catching a ball.

Children learn something introductory before going to school, after repeating a lot and harassing their parents and putting them in states. Language is one of those things.

The whole words they learn in 6 years may not reach 2,000 words. And they don't know the meaning of many words. The sentences they are capable of making are mostly short and devoid of any linguistic elegance. After entering school, and learning systematically, the process of principled thinking begins.

Can anyone become a great poet without going to school? Is anyone able to think and express profound concepts without studying a huge mountain of books? I don't think there is such a thing in practice, except in very limited circumstances.

Like learning the language, music begins at first with practice and repetition, but without learning music knowledge, no one will be able to make amazing pieces. Of course, my goal in this section isn't to express the bare necessities of learning music knowledge (because many of the discussions in music knowledge aren't based on mathematics), but the main focus of the discussion is on math. Mathematics lays the firm cornerstone of many human thoughts and also various sciences, and by escaping from it, one cannot find a safe and peaceful haven and stay put for a long time.

 

I don't see any relation to music in this video, but there's a "Great Course" (that's really great) on How Music and Mathematics Relate by Dr. David Kung. The accompanying book is free: http://www.chrysalis-foundation.org/wp-content/uploads/2019/06/1373_MusicandMath_8-28.pdf

 

Something to consider to avoid hyped-up pseudo-academic ideas.
Finding arbitrary and spurious connections is NOT science. It's just a recipe for new-age woo-woo mysticism.

A few examples to illustrate...

Example [1]...
If I like eating chocolate and you also like eating chocolate, then ok we do have something in common,
but it's a wild stretch to then say that we are now related, that I influence you or you influence me.

Example [2]...
Consciousness is mysterious. Quantum fields are also mysterious.
Therefore consciousness and quantum fields must be related. (wwwoooooohhh)

Example [3]... (maths and music)
Recursion is an interesting idea. You can find recursion in maths, and in music, and in visual art, and in language,
and in computer programming, and in lots of other places. Just because we can find recursion in maths and also find it in music does not mean we have found a magical connection between maths and music.

I don't want to criticise the course mentioned above "How Music and Mathematics Relate" because I think those TTC courses serve a really nice role in the 'serious edutainment' sphere. But while watching that course it's worth spotting the occasions when the alleged links between maths and music are just spurious.
There's an entire chapter on 'Self-Reference from Bach to Godel' which is guilty of what I describe above.
I think the Lecture/Chapter is still a lovely topic to explore (great edutainment) but it is only exploring an idea that both music and maths (and art, and language, and programming) can all work with.
It is NOT describing some intrinsic magical connection between music and maths. (but as thought provoking - good stuff )

Finding ideas that maths and music both share is a nice area to explore. (I like it)
Finding ways of describing musical phenomena using mathematics is also a nice exploration. (I like it)
But neither of the above imply any fundamental connections between music and maths. (I'm not gullible)

Anyone that enjoys seeing music concepts described mathematically should check out a book called
A Geometry of Music- Harmony and Counterpoint in the Extended Common Practice (and no surprise - Sister Site can help)

Lastly, some wonky logic can lead you well over a cliff...

Analyse that and all you find is a crazy bait-and-switch non-sequitur.
The sentence in red is reasonable (the bait that you sign up to),
but the sentence in blue has no logical connection to the previous sentence,
and is just a totally wacky claim, (the switch that got smuggled in after you bought the bait).

You find the same weird bait-and-switch in the original claims...

Sorry @Epcot, but I just can't take any of those claims seriously.They are hijacking and devaluing your own nice topic.
The logic is just too wonky and I couldn't be bothered to speculate on what psychologically motivates those strange claims.

 

Absolutely on point!

The universe has no faculties.

 

I normally have nothing to say about threads such as this, but consider this: if music is math then why don't we still use Pythagorean tuning?

 

OP can save money.
No need for a MIDI controller keyboard.
Just buy a 7.99 Casio or Texas Instruments calculator.

 

I think we should all keep calm and listen to "Foster" The People...

 

Sorry to share a video that only a fraction of people in here can understand but I will try to resume a bit and I'm sure you can find the equivalence in english if that's interesting you :

Why music sounds right, why there are 12 notes of music? This guy recreates the 12 notes from scratch using one mathematic formula, he also speaks of traditional music and why the pentas (the first ones you find using this formula, which is the same as dividing your string by 2 and 2 and 2 (etc) to find new notes with the harmonics for those who heard about that, first is octavia, then 5th, third, etc).
Very interesting thing is about how notes are barely detuning naturally when you scale up if we follow natural harmonics (that explains why the quarter-tone cultures) and how that leaded occidentals to the tempered tuning (and he speaks about others ways composers were using to manage this barely not equal space between octaves from middle-age), etc..
I found it really passionating to learn that effectively music is 100% physical law, and therefore 100% mathematical...

That said obviously what you do with those notes is 100% emotional and cultural in my opinion, even if you could analyse it in a mathematical way, that's not the point, but the origin is clearly scientific!

 

Last edited: Dec 22, 2020

The fact that it's possible to explain a phenomenon with maths doesn't mean that you need maths to create that phenomenon.

 

Thanks for sharing the video. I'll admit I haven't watched it - I don't need to. I will just assume that it's good and has provided many beautiful insights about relationships that can be found between maths, physics, sound, music.
And many of those mathematical modelling insights will undoubtedly be the stuff that dates from Pythagoras or even older.
A well trodden path for a few thousand years. All good stuff - well worth understanding.
So I like and agree with your enthusiasm for all of that.
BUT to leap from those insights to this next conclusion is metaphysical nonsense

Not even vaguely true!
Maths is one of humanity's modelling devices; just one of many and one of our best.
But, importantly, it is ONLY a modelling device.
Unfortunate how some people (even some scientists) fall into the naive mistake of assuming that maths is anything other than that.

From comparing 'music' and 'mathematical models of music' all your know is that 'music' and the 'models of that music' share some concepts. It does not mean that either one is dependent upon the other.
Compare these statements...
[1] "Music is 'made of' maths"
[2] "Maths is 'made of' music"
Both statements are metaphysically ridiculous.
People find it easy to see how ridiculous [2] is, but some are naively seduced into believing that [1] makes sense - it does not!

I think that's right, and I'd push a bit further...
"doesn't mean that the phenomenon has to be dependent upon maths in any way at all"

 

Because for the most part there is no difference between 12 equal and Pythagorean, which was probably the defining system of Babylonians, Chinese etc (popular in Europe up until some point in Medieval times). Western music is actually based on Meantone tuning, which is more complex thing, basically the opposite of Pythagorean - you have bad fifth, but good major and minor thirds. Both Pythagorean and Meantone meet only in 12 equal. If you want to sound like Mozart etc, you have to use 12 notes out of bigger system like 55 or 43 etc, preferably also have a keyboard with split sharps to your taste or organ with mechanism that controls which enhamonics will play, manipulating the pipes.

 

Just as physics is a conglomerate of models to describe interrelated events in our environment.

 

maths for sequencing:


1
2
4
8
16
32
64
128

everything else is just showing off

 

There are 11 groups of people in this world
- Those that understand binary
- Those that don't
- and those that have heard this joke too many times already and stopped reading it 5 seconds ago

 

Music as an organism?

 

Last edited: Dec 22, 2020

1)

They learn by copying and repeating mostly. No "math" is involved in this. Grammar, rhetoric are useful for people who want to develop themseves. And they aren't needed for being a poet. Poems are really needed for this. You could become a great poet just by reading poems. All other things are important and useful, but they aren't essential.

2) Theory describes all the possibilities. You (as a musician) choose one of them. All the time. Why? How? Does "math" explain it too?

3) There is a system of all possibilities but there is something else. Something new. Something inpredictable. May be, accidental. If all the things would be predictable, we could say that there is nothing new. All is known.

Do all the music pieces preexist somewhere? I don't think so. This isn't interesting. This is boring. We are able to invent.

 

There is another perspective to this being the existential one.

What people term as comfort zones is very often due to the facility for humankind to be able to label something or categorise it or take it apart to work out how something works, so they can feel comfort rather than uncertainty or discomfort. You can go as deep or shallow as desired on that from arithmetic to binary to hexadecimal, so on and so forth.
Sure there is mathematics in music. 4/4 in its simplest form says that most obviously. Certain pulses e.g. 3/4 or 5/4 or 7/8. 13/8 etcetera... have their own groove. These can be simply played or analysed, or both.

I am not convinced there is any winning argument on this topic for the simple reason that hemiolas, polyrhythms, counterpoint and way too many labelled techniques and mechanisms to list, are all a part of music, all which can sound pleasing or horrible, but definitely an integral part of the musical spectrum in one way or another, whether simply or in complexity.

The existential aspect would potentially cry out why label anything? It just exists. While there is truth in that, living a true existential life is not completely possible. What I've read here where there is no ridicule and acknowledgement given, there are solid points on all sides. True, music just is and should be played, and also true, it has a formula to it. Academia has its place. It again boils down to the documentation aspects and the understanding of being able to put into practice as something useful. People speak of history, without documentation from ancient times through to these days being a database, there is no history being remembered so there are uses, in one way or another.

 

Last edited by a moderator: Dec 22, 2020

I am working on a guitar riff based song called E-mc squared. The faster I go the more mass it has-this song is so heavy, man....Harmonics have some very interesting math, but I don't think about that much when searching for the right chord.