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Music theory for nerds

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Re: Music theory for nerds

#261

Post by acjohnson55 »

ktRolster wrote: post #96
acjohnson55 wrote: post #91

Earlier quoted context omitted.

Or http://dmitri.tymoczko.com/geometry-of-music.html

That may be a very good book, but I'll be honest, it doesn't look like a very gentle introduction.

It's not :(. Although the average person could probably get a lot of good high-level info by browsing it.

I haven't yet come across anything that is a good gentle intro. Most resources that approach music and math make the mistake of treating music theory like the law, without any rationale for it provided. Music history textbooks typically give a lot more context of how our music theories emerged, but they don't talk about why that might be, based on acoustics, psychoacoustic, and math.

Maybe one day, I'll write the comprehensive intro I wish I'd had.

Re: Music theory for nerds

#262

Post by skrebbel »

perlgeek wrote: post #237
skrebbel wrote: post #174

I'd like to elaborate a bit, in the same "for nerds" manner, on where Eevee seems to get lost a bit with scales and notation. He (she? not sure) calls the A minor and C major scales the same, because they contain the same notes. That's not an odd thought, but it's like calling sine and cosine the same because both functions contain the same set of values, in the same order. The difference is phase. Basically, scales…

Thanks, that's an explanation I haven't heard that way before, but that makes sense to me. Follow-up question: how are phase of the scale and the piece of music synchronized? When I think in terms of a wave, I could Fourier-Transform it into sines or in cosines, or any other phase-shifted variant (a * sin(nx + const.))? Is it always the first note of the piece of music that "anchors" the piece in its scale? Does that…

Nice question, I think I can answer (although you'll soon notice that my understanding of this subject is limited as well)

First of all, this is a mathematically undecidable problem, as in that there exist tunes that could be in multiple scales. The extreme example is a melody that consists of only a single note. Ridiculous, but as a fellow nerd I'm sure you can see how I could call a single note a melody. So we have to lose the phase metaphor here a little bit.

Most songs "anchor" with the last note. If you really can't tell whether a song is in major or minor (songs in major are a bit happier, jollier; songs in minor a bit sadder and more melancholic), going for the very last note (or the last note of the chorus, if the song a chorus) is a very good bet. Find the core melody of the song, the thing everything is hung up on, the last note of that core melody is the ground note of the scale. This is a really safe bet.

There are, of course, exceptions, and then I think you'll need to do some mathematical analysis to find out which key the notes in the melody match the best to. I'm not 100% sure how this is defined but I'm sure people have researched it.

All that said, musicians don't really have this problem. After all, hardly any of this stuff was designed. The only genius piece of engineering in all this was the discovery that if you choose to 12 notes in an octave (and not 8 or 15 or whatever), you have a very versatile instrument that can play almost any melody at any pitch in a way that sounds pretty good to human ears (pretty good, not perfect, because of the all the ≈'s in the "Intervals" section of Eevee's article).

But the rest was discovered, not designed, just by fooling around. The analysis came after the music.

Musicians just start with a scale and then make the music they compose fit. This comes pretty natural to you with a bit of practice; most people have a pretty decent innate ability to hear which melodies "match" with a chord and which chords "match" with a previous chord. In all honesty, once you've understood things this far, I'd recommend fooling around with the easiest instrument or tool you know, rather than diving even deeper in to the mathematics of things :-)

Re: Music theory for nerds

#263

Post by Manishearth »

acjohnson55 wrote: post #255
Manishearth wrote: post #114

Earlier quoted context omitted.

> This is not the case for most other musical traditions. Do you have examples of musical traditions that don't do this? Both the Indian and Chinese musical systems do something similar. ---- I'm not really sure if this post is "wrong". It gets the chronology mixed up a bit -- talking of twelfth roots of two before talking about ratios, but I thought that was just done to help explain things by reverse-engineering th…

I'm not an expert, but Indian classical music isn't known for having harmony in the same sense [1]. Modern Indian music is influenced by Western music. I know even less about Chinese music, which isn't mentioned in that article. But in all the sources I've read, the concept of deeply developed chordal harmony is pretty unique to the Western music tradition. [1] https://en.wikipedia.org/wiki/Harmony

Right, it doesn't involve playing notes together the same way it's done in Western music.

I guess I misinterpreted what you were saying -- the Indian notes are still derived by looking at notes which sound harmonious when played together, roughly the same way Western notes are derived. They are not usually played together on the same instrument like you would with a piano or a guitar. Harmony between vocal parts is not uncommon as is harmony with background instruments like the tanpura. But yes, Indian music doesn't have harmony in the same sense as Western music. But the origins of the notes are very similar.

(I'm talking about classical Indian music, btw)

Re: Music theory for nerds

#264

Post by theOnliest »

tsm wrote: post #85

It seems like his questions were serious (not rhetorical), so I'll answer them for real. The answers pretend that the 20th century hasn't happened yet—there's no point explaining the interesting things people like Schoenberg did if you don't understand the mainstream tradition in place before them. 1) Why does notation allow for seven pitches, not 12? Because music is at most built out of 7-note scales, not 12. If so…

> Why does notation allow for seven pitches, not 12? Because music is at most built out of 7-note scales, not 12.

This answer is good, but I wanted to pick one tiny nit, which is that not all music is built out of 7-note scales. A lot of music is, but music that isn't doesn't often lie well on the staff. That's true, incidentally, whether there are more than 7 notes in the scale (12-tone music, lots of octatonic music from people like Stravinsky, Scriabin, etc.) or fewer (whole-tone music comes to mind, as does the slightly more esoteric hexatonic scale). Pentatonic music fits well on the staff because the pentatonic scale is a subset of the ordinary diatonic.

Re: Music theory for nerds

#265

Post by redial »

gugagore wrote: post #230
redial wrote: post #188

Earlier quoted context omitted.

Music is waves and frequency. Music appreciation is what you are describing. And appreciation is very dependant on culture . That is why Bach is not (as) appreciated in certain cultures . Just like photography. Why is one photograph more meaningful than another? it has nothing to do with photography, per se, it has everything to do with the culture of the person doing the appreciation. There is a link between the two…

"music is waves and frequency" in the same way that "spoken language is waves and frequency"---not very usefully. I think bringing in" appreciation" muddies the waters.

I was just responding to the parent who claimed that music was not "waves and frequency".

My point is music is (mostly) independent of its appreciation. Machines can, and do, make music based entirely on the theory of music.

Re: Music theory for nerds

#266

Post by redial »

pdkl95 wrote: post #232
redial wrote: post #188

Earlier quoted context omitted.

Music is waves and frequency. Music appreciation is what you are describing. And appreciation is very dependant on culture . That is why Bach is not (as) appreciated in certain cultures . Just like photography. Why is one photograph more meaningful than another? it has nothing to do with photography, per se, it has everything to do with the culture of the person doing the appreciation. There is a link between the two…

> Music is waves and frequency. Sound is waves and frequency. Music is a collection of sounds arranged in a specific sequence. > Music appreciation is what you are describing. And appreciation is very dependant on culture. Music relies on various "tropes" to construct a narrative. This includes the choice of key/scale (or none at all), ideas about timing and harmony, etc. These "standard parts" of music are usually f…

I was just responding to the parent who claimed that music was not "waves and frequency".

My point is music is (mostly) independent of its appreciation. Machines can, and do, make music based entirely on the theory of music.

Re: Music theory for nerds

#267

Post by msg »

abannin wrote: post #251
perlgeek wrote: post #237

Earlier quoted context omitted.

Thanks, that's an explanation I haven't heard that way before, but that makes sense to me. Follow-up question: how are phase of the scale and the piece of music synchronized? When I think in terms of a wave, I could Fourier-Transform it into sines or in cosines, or any other phase-shifted variant (a * sin(nx + const.))? Is it always the first note of the piece of music that "anchors" the piece in its scale? Does that…

This gets pretty complicated and subjective. Strictly speaking, a "note" cannot define a key. To determine a key, you really need at least 2 intervals, wherein interval a somehow resolves to interval b. Keys are just a mapping of relationships; how does each of the 12 notes relate to each other? If you just play a C major chord, you aren't really playing in the key of CMaj, you're just playing a CMaj chord. For examp…

That's funny because B+G, C+G to me says G major: a major third, then a fourth. Is the ear guided to keys by inversion, some inversions more natural or root-y than others?

I've been composing pop music for a long time without knowing stuff like this.

Re: Music theory for nerds

#268

Post by lexhaynes »

tehwalrus wrote: post #203

> 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? Much more interestingly, this touches on the reason why different pieces were given keys at all by their composers (think "foo in B flat minor by Chopin"). Musical instruments have to be tuned to a particular key. This is because of the frequency ratios: the circle of fifths…

I think the "dismissive" tone is entirely sarcastic, and really helps to de-emphasize the very intimidating complexity of music theory. I've always been curious about music theory, but have really failed to get anywhere close to learning it because of how formidable the field is. This article made that complexity feel a little less untouchable for someone who was not trained in music, and the sarcastically "dismissive" tone helped a lot.

Re: Music theory for nerds

#269

Post by acjohnson55 »

autarch wrote: post #95
acjohnson55 wrote: post #92

Earlier quoted context omitted.

Not to mention that A minor is generally considered to contain two additional notes compared to the A natural minor scale (AKA the A Aeolian mode).

Well, two _or_ one. The melodic (two) and harmonic (one) minor scales.

Sort of. They are separate scales, but if you compose (classical-style) music in a minor key, you don't typically pick one of those scales. The chords that appear might include any of those notes, even within individual phrases.

In my totally non-expert observation, contemporary music often is more modal, in the sense that it probably would just pick one of those scales (particularly natural minor) and stick to it.

Re: Music theory for nerds

#270

Post by dahart »

asmdb wrote: post #134
blake8086 wrote: post #130

Earlier quoted context omitted.

If a beginner can't immediately grasp musical notation, isn't that evidence that it is, in fact, absurd?

I'm curious, did you immediately grasp the syntax of every programming language you've ever learned?

Programming languages are a lot easier to grasp. ;)

The oldest programming languages are only 50 years old, whereas the oldest music notation is at least 4000 years old.

Most programming lanuguages haven't crossed any spoken languages, but modern music notation & terminology has been heavily developed by countries all over Asia and Europe.

This is a big reason why musical notation seems so weird at first, especially to engineers, because it is a legacy that comes from a different time, a different context, in a different language. The people who developed musical notation had different math, different logic and different musical motivations than we have now.

Think about this for a while and it starts to feel like a miracle that musical notation works at all, not to mention how well it works.

Programming languages were developed by people nearer to us in every way, and made to be logical and simple, so it makes sense that they're easier to grasp quickly.

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