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Music theory for nerds

eev.ee

11–20 of 390 posts

Re: Music theory for nerds

#11
This source is a bit wordy. Let’s summarize:

The core idea of music made with harmonic sounds is that “notes” with frequencies at small-integer ratios will “harmonize”. Harmonic sounds means something like a vibrating string where the vibrations are integer multiples of some fundamental frequency, because other non-integer-multiple vibrations are damped out by the fixture of the string at two points. Different (non-harmonic) types of sounds often sound better with a different sort of scale, for details see this book http://sethares.engr.wisc.edu/ttss.html

* * *

The “octave”, 2:1, is the simplest whole-number ratio, and makes many of the vibrations in two notes in such frequency ratio align with each-other, to the point that two harmonic sounds exactly an octave apart almost sound like the same sound.

Other simple ratios like 3:1, 4:3, 5:4, etc. also “harmonize”, with (not quite as) many aligned overtones.

The core idea of the 12-note musical scale (pretty much regardless of specific tuning) is the approximation:

3^12 = 531441 ≈ 524288 = 2^19

3/2 ≈ 2^(7/12) [this is accurate to about 0.1%]

Or another way to say this: 7/12 of “doubling” on a log scale is very nearly “three-to-two”. Musicians call this ratio a “perfect fifth”.

In the case of equal temperament, an octave is split into 12 precisely equal steps (on a log scale), each one the 12th root of 2.

There’s one other nice approximation to take advantage of:

5^3 = 125 ≈ 128 = 2^7

5/4 ≈ 2^(4/12) [this approximation is only accurate to about 1%]

Musicians call this ratio a “major third”.

* * *

Even outside music, these approximations can be useful for doing approximate computations.

If only our society switched from decimal to “duodecimal” numerals, it would be very natural to use logarithms base two, notated with “duodecimal” fractions.

If you have a number expressed in log base two, and you use duodecimal notation, approximately multiplying or dividing by 2, 3, 4, 5, 6, 8, 9, 10, 12, ... is very easy using addition/subtraction of easy-to-remember multiples of 2^(1/12).

Unfortunately our society instead has slide rules and measurement scales (decibels, etc.) which are all built around logarithms base ten, and decimal notation.

Re: Music theory for nerds

#12
This is great, but I would recommend Robert Greenberg's "How to Listen to and Understand Great Music". He goes through the history of western music in a way that makes it clear why Amin != Cmaj, and other questions that the OP has. Yes, sheet music is crap, and he explains how it evolved to be the way it is, after which you'll be much more forgiving. He's a great speaker who obviously knows the material inside and out.

Re: Music theory for nerds

#13
post #10
post #4

This has got to be some of the worst jargon and notation for anything, ever. Indeed. I'm a musician, and something non-musicians often ask (especially techies, it seems) is why we use such an archaic notation system. The reason is simply that a certain number of musicians have developed the skill of sight reading which is the ability to perform a composition directly from a written sheet, with little or no rehearsal.…

>why we use such an archaic notation system. The answer is, because it works, and nobody has managed to propose a better one.

One attempt was Hummingbird. http://www.hummingbirdnotation.com

Re: Music theory for nerds

#14
post #4

This has got to be some of the worst jargon and notation for anything, ever. Indeed. I'm a musician, and something non-musicians often ask (especially techies, it seems) is why we use such an archaic notation system. The reason is simply that a certain number of musicians have developed the skill of sight reading which is the ability to perform a composition directly from a written sheet, with little or no rehearsal.…

I can sight read for winds and voice, but not for Piano, despite being able to play Piano relatively well. Thus, this explanation will probably apply mostly to single-voice musicians.

1. Find Do. This is the first note of the Major scale in the key which you are playing. Find it on the page, and burn it into your mind; everything you're about to do centers on the location of Do. In the key of C (white keys on a piano) Do is right in the middle of the grand staves, keeping things simple. If you know where Do is, you don't have to care about the key signature for like 97% of the notes you're going to read, and you can make educated guesses about what the sharps and flats do by using your musical intuition. Once you've found Do on the page, figure out where Do is musically, and keep it in your head. Make sure that when you're singing or playing any other note, you know where you are relative to Do, and can jump back there without losing your place.

2. Learn your intervals, and learn Solfege. If you're a musician, you already know these things in principal, even if you don't know the words or the terminology. In particular, you should be able to "hear" the distance between Do-Mi-Sol without too much difficulty, because you hear those distances in music a lot.

3. When you're sight reading the first note in a passage, find the note, then step it off visually to the nearest Do. If you're good, you can also step it off to the nearest Sol. I usually root myself on Do and Sol both in a given passage, as it gives me less visual separation between any note I need to find in a hurry.

4. For every note after that first note, pay mind to the spacing on the page:

4a. Moving up and down the scale should be easy; you're a musician, you already know what a scale sounds like, just sing along.

4b. Moving up or down from one line to the next line is a third. Most often you'll hear these relative to Do-Mi-So-Ti in major keys, and La-Do-Mi in minor keys. You'll hear these a lot, so get used to reading them quickly.

4c. Get a good feel for common jumps while you're at it. As a Bass singer, I got really good at reading jumps between Do-Fa and Do-So, because those chord progressions exist in everything, and their sole purpose in life is to make bass singers bored out of their mind. You're a human, in addition to a musician, so you'll pick up on the patterns in any given composition and have the common tricks down before you even realize what your brain is doing. Don't question that, let your brain be awesome all on its own.

That sounds like a lot of steps, until you realize that you're performing most of them already to make sense of any piece of music that you play. Don't worry about the names or the terminology, you can use numbers (1-3-5) if that's easier, or just "hear" it if you don't feel like you need an aide. Remember, the goal is to drop the aide and be able to just perform these steps on your own eventually.

I'm analytical in nature, so I'm always thinking about these things. I suspect the reason most musicians can't describe this process very well is because the process of analyzing our craft detracts from the quality of its output. The more you can commit to "muscle memory" as a musician, the more you can pull your analytical mind out of the process of a performance, the easier it becomes. Your body's built in reflexes are faster than your analytical brain will ever be, and good musicians tap into that biological strength through loads of practice.

Re: Music theory for nerds

#15
One thing that is particularly arbitrary is that C is named "C" rather than "A", which would make far more sense (given that it is the root note of the only major scale that has no sharps or flats).

Re: Music theory for nerds

#16
post #8

TLDR: a person who knows nothing about music or music theory gripes about music and music theory. Admittedly knows nothing, right off the bat and several times throughout the text. How can you declare something to be "terrible", "the worst notation for anything ever", and so forth if you admittedly know nothing of the subject? I know nothing about databases, would reading the Wikipedia page on NoSQL entitle me to dec…

It can be clear to a newcomer that a system has problems without needing to understand everything, or even very much. Sometimes the newcomer is wrong, but a quick scan of the comments here indicate that a number of musicians agree.

Re: Music theory for nerds

#17
post #8

TLDR: a person who knows nothing about music or music theory gripes about music and music theory. Admittedly knows nothing, right off the bat and several times throughout the text. How can you declare something to be "terrible", "the worst notation for anything ever", and so forth if you admittedly know nothing of the subject? I know nothing about databases, would reading the Wikipedia page on NoSQL entitle me to dec…

If reading the Wikipedia page on NoSQL offered you a completely opaque and unhelpful window into how NoSQL worked, and if every tutorial and typical description of the subject seemed to assume you already understood NoSQL, then yes. It would.

Re: Music theory for nerds

#18
post #5

>I suppose it’s possible to change the sound of an entire piece of music just by changing the key signature, but does anyone actually do that? >How would that work for music that also uses notes outside the scale? These seem more like questions of composition, which I definitely don’t know anything about. From wikipedia: Although transpositions are usually written out, musicians are occasionally asked to transpose mu…

I don't think the author was referring to transposition there. I think that was about leaving the notes on the staff the same but just changing the key signature. This is done sometimes as a novelty, and the best example is changing something from a major key to a minor key or vice versa.

The article has a link to a recording of Für Elise in a major key [1], and there are many similar renditions of other pieces around. You could in principle do this with any of the seven modes, not just major and minor.

As for notes outside the scale, it seems like these key-signature-changing compositions typically keep them the same (like the D# in Für Elise).

[1] https://www.youtube.com/watch?v=Y-rZD2AsHbI

Re: Music theory for nerds

#19
post #4

This has got to be some of the worst jargon and notation for anything, ever. Indeed. I'm a musician, and something non-musicians often ask (especially techies, it seems) is why we use such an archaic notation system. The reason is simply that a certain number of musicians have developed the skill of sight reading which is the ability to perform a composition directly from a written sheet, with little or no rehearsal.…

It's a lot like why the QWERTY keyboard remains dominant.

Re: Music theory for nerds

#20
> Also, this notation has a slight problem. That problem is that sheet music is terrible.

> This has got to be some of the worst jargon and notation for anything, ever.

I hear it bandied around in these articles that music notation is awful. Can someone explain to me why? I'm not much of a musician, but I can work my way through sheet music if necessary, or write it when I want to. I don't remember what it was like to learn to read and write music so I'm not going to understand why it's so bad just by thinking about it.

First of all, the lines and spaces make a ton of sense to me. When you're playing, reading, or writing a piece, you spend most of your time in a key with a diatonic scale. Maybe you're thinking about the chords: I, vi, ii, V7. The lines and spaces are great for giving you that kind of information. I guess this "completely obscures the relationship between the pitches". I guess that's the case if you forget what key you're playing in. The alternative would be to make the staff fully chromatic, but that sounds like it has a bunch of disadvantages for most music.

The chromatic staff (http://musicnotation.org/) looks terrible to me, since it spreads out the notes farther. I've already memorized all of the diatonic scales, and now the diatonic scales are jumping around, and the staff covers a shorter interval so you get more of those 8va or 15ma.

Hummingbird (http://www.hummingbirdnotation.com/) seems like classical notation, just with more redundancy and the symbols changed around a little bit. Maybe it's better but it's a minor improvement at best.

Clairnote (http://clairnote.org/) looks the worst of them all, with half-steps being half-way between lines and spaces. It looks like a recipe for making mistakes and misreading music.

I'm not about to say that it's easy to read music notation, just that the notation seems to have a reasonable amount of logic to it. The idea that somehow it's the notation that's terrible and music itself would be easier to understand or play if we just had better notation--I don't buy it. Maybe someone could convince me.

(Addendum: If you think the chromatic scale is the "right" scale for notating most music, as in "Chromatic staff" or "Clairnote", as an exercise... why do you think that the chromatic scale is correct? Is it because it represents both sets of keys on the piano or the frets on a guitar? Is it because of the mathematical relationship between the notes? My counterargument, against the chromatic scale, is presented by Bobby McFerrin: https://www.youtube.com/watch?v=ne6tB2KiZuk)

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