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Music theory for nerds

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Re: Music theory for nerds

#331

Post by hiddenkrypt »

meggar wrote: post #308
hiddenkrypt wrote: post #287

Earlier quoted context omitted.

Db would be 01. Dbb would be 00. (or 11 and 10 for the octave) The point ajuc is making is that the flat-sharp accidentals aren't used or needed at all if you just assign numbers to each tone. There's no concept of flat or sharp, unless you want to deal with microtones.

The letters and flats/sharps give you key/value over frequencies, which is better than just a numeric index over a chromatic scale. Working with the keys allows for the same abstractions to be used with all 12 keys at the same time, on the same staff.

I'm not really arguing one way or the other, just pointing out that they're functionally equivalent. It's two different maps keying to the same set of frequencies. The BASE12 system described above would allow for keys as well, just with a different notation. Instead of flats/sharps marked next to the clef in traditional sheet music, the BASE12 system could start each line with a list of 'prohibited' notes. For example, when indicating that a piece is in the key of Gm, the staff in BASE12 could start with : [01,04,06,08,0b]. This indicates that the majority of the song will be made of the notes 7,9,b,0,2,3, and 5, and serves the same purpose as having two flats next to the treble clef, one on the middle line and one in the top space. Which of these systems would be easier for humans to grok is up for debate. I personally don't think either one is better.

Thinking about it, the traditional notation is just mapping to an octal system, with the key accidentals acting as modifiers to the map and the base-8 values being displayed graphically as vertical position on the staff.

Re: Music theory for nerds

#332

Post by SwellJoe »

zeta0134 wrote: post #319
SwellJoe wrote: post #118

Earlier quoted context omitted.

"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." I believe the Solfege named intervals (Do-Re-Mi-Fa-So-La-Ti-Do) are only taught as a historical oddity…

I was taught in the US, and Solfege was used prominently in my voice classes, but rarely in my theory and piano classes. I think it's a system that works well when you don't have to think about the actual note name that you're singing, as it describes intervals very well, but relates somewhat poorly to pitch. I grew up attending a Church of Christ, which used full congregational singing with four part harmony. Our so…

Shape note seems really clever! But, I can also see where it would break down in many cases. I learned music predominantly in a Jazz context. That'd be very tricky to use for jazz...especially the various modal types of jazz.

Re: Music theory for nerds

#333

Post by zhemao »

Ericson2314 wrote: post #49
nazgul17 wrote: post #9

Earlier quoted context omitted.

I would love something like that. Any pointer?

A large part of it hasn't been researched very mathematically, to my knowledge. If you google music+grammar you can get some stuff with a linguistic approach, which may be less empirically grounded but certainly a richer theory than the alternatives. And don't get me wrong, science is good but as musician mathematician a richer theory that overreaches reality is much more fun, and besides most of this stuff is cultur…

> Melody, Harmony, Rhythm, Form, Timbre

I think dynamics (or at least dynamic contrast) is also an important element.

> Timbre is the easiest to appreciate due to its lack of rich structure

It does have a rich structure, we just don't really understand it yet. Timbre is essentially the linear combination of harmonics of a single pitch. You could express it as a Fourier series. But we don't have a good model of how to play with specific timbres, since acoustic instruments don't really allow fine-grained control of timbre.

Re: Music theory for nerds

#334

Post by jacobolus »

lmm wrote: post #239
jacobolus wrote: post #199

Earlier quoted context omitted.

> (e.g. add a third to a fourth and you get a... sixth) Better: In equal temperament, log base two: add 4/12 to 5/12 and you get 9/12. In ratios (depending on tuning, these could be loose approximations): multiply 5/4 by 4/3 and you get 5/3.

Yes, I know. But having the log base 2^(1/7)-ish built in is useful. If we could just subtract 1 from all the numbers (i.e. what we call a fifth should be 4) then we would have a measure that actually made sense.

Eh. Calling it a “fifth” is making it clear that the label is an ordinal number: first second third fourth fifth ...

You need to think of it as “if the bottom note was the first note of a scale, where in the scale would the top note be?”

As with many questions of indexing, off by one errors are tricky.

It’s a system that confuses names for notes in a scale with names for intervals between notes. You’d rather they called them by cardinal numbers representing some kind of “distance”, instead of a count starting at one.

But that would be applying a later mathematical understanding on the earlier system. If that’s what you want, you should just use a log scale and count twelfth roots of two.

Ideally we’d switch all our indexing to start at zero, and use half-open intervals everywhere. Start at 0 AD, call the ground floor of a building “0”, start spreadsheets with row 0, switch Matlab to index from 0, et cetera. This is pretty unlikely to happen though.

Re: Music theory for nerds

#335

Post by lmm »

jacobolus wrote: post #334
lmm wrote: post #239

Earlier quoted context omitted.

Yes, I know. But having the log base 2^(1/7)-ish built in is useful. If we could just subtract 1 from all the numbers (i.e. what we call a fifth should be 4) then we would have a measure that actually made sense.

Eh. Calling it a “fifth” is making it clear that the label is an ordinal number: first second third fourth fifth ... You need to think of it as “if the bottom note was the first note of a scale, where in the scale would the top note be?” As with many questions of indexing, off by one errors are tricky. It’s a system that confuses names for notes in a scale with names for intervals between notes. You’d rather they cal…

> If that’s what you want, you should just use a log scale and count twelfth roots of two.

I don't want to count in twelfths, I want to count up the scale.

> call the ground floor of a building “0”

I'm a Brit, we do that here already.

Re: Music theory for nerds

#336

Post by gnaritas »

dietrichepp wrote: post #330
gnaritas wrote: post #304

Earlier quoted context omitted.

How does that make any sense at all? I don't see it making any more sense at all, not even a little bit. There's nothing arbitrary about C major/A minor being taught first as it's just the simplest scale with no sharps and flats. And calling a clearly minor scale major under a new system doesn't clear anything up for anyone.

The original question is frequently misinterpreted, so I can understand the confusion. I've seen the same question asked on forums a few times and someone always comes out of the woodwork saying that, "Well, ABCDEFG is a minor scale, not a major scale, what are you even going on about?" Let's ignore the part about why the scales we call C major / A minor being taught first, because we all agree that it makes sense to…

Ah, OK that's much clearer, I understand now. I'd say this, picking A for what is now C would be just as arbitrary as there is no "first" scale, they're all equally important and trying to match up a first scale to the first letter of the alphabet would be just as arbitrary. For those who feel the need to start with A, then start with minor scales, A minor first, artificial newbie weirdness solved.

Re: Music theory for nerds

#337

Post by _9nob »

brunorsini wrote: post #184
TheOtherHobbes wrote: post #179

Earlier quoted context omitted.

No, instruments really don't. The point of conventional instruments is that once you learn them - which takes years - you can instantly express almost any musical idea using all the possible degrees of freedom available on that instrument. With something like Ableton Push, you're one step removed from the sound generation, because you're triggering automata with a very limited expressive repertoire. (With Push, it's…

You seem to be pegged on what current controllers can do... And that's exactly what I am saying: they often suck! But they can improve and I am confident they will. When I am learning a brand new instrument I can literally feel my brain knowing exactly what I want to do way before my fingers/mouth/feet are able to perform the task at hand. How is this not an interface problem? With button controllers the best you'll…

Once you actually practice a physical instrument for a reasonable amount of time things like the concept of "memorizing where the minor 7th is" quickly become non issues - the only memorization involved is that of your muscles i.e. the cognitive load is essentially nonexistent. Involving more parts of your body than your cognition is one of the joys of playing a physical instrument, versus pressing a button and thinking a lot.

Re: Music theory for nerds

#338

Post by jacobolus »

lmm wrote: post #335
jacobolus wrote: post #334

Earlier quoted context omitted.

Eh. Calling it a “fifth” is making it clear that the label is an ordinal number: first second third fourth fifth ... You need to think of it as “if the bottom note was the first note of a scale, where in the scale would the top note be?” As with many questions of indexing, off by one errors are tricky. It’s a system that confuses names for notes in a scale with names for intervals between notes. You’d rather they cal…

> If that’s what you want, you should just use a log scale and count twelfth roots of two. I don't want to count in twelfths, I want to count up the scale. > call the ground floor of a building “0” I'm a Brit, we do that here already.

The intervals in a 7-note scale inherently don’t add up like that, because they’re not based on even divisions. So regardless we need to have 12 different named intervals for various numbers of semitones:

For instance, “minor second”, “major second”, “minor third”, “major third”, “perfect fourth”, “augmented fourth”, “perfect fifth”, “minor sixth”, “major sixth”, “minor seventh”, “major seventh”, “octave”.

Reducing all those ordinal numbers by one really doesn’t help all that much. You still have to remember how the “minor” and “major” labels interact for every interval in the scale, and remember that sometimes the interval between the same two notes is given multiple names depending on the key, etc., which is all horribly confusing mess.

Re: Music theory for nerds

#339

Post by lmm »

jacobolus wrote: post #338
lmm wrote: post #335

Earlier quoted context omitted.

> If that’s what you want, you should just use a log scale and count twelfth roots of two. I don't want to count in twelfths, I want to count up the scale. > call the ground floor of a building “0” I'm a Brit, we do that here already.

The intervals in a 7-note scale inherently don’t add up like that, because they’re not based on even divisions. So regardless we need to have 12 different named intervals for various numbers of semitones: For instance, “minor second”, “major second”, “minor third”, “major third”, “perfect fourth”, “augmented fourth”, “perfect fifth”, “minor sixth”, “major sixth”, “minor seventh”, “major seventh”, “octave”. Reducing a…

> Reducing all those ordinal numbers by one really doesn’t help all that much. You still have to remember how the “minor” and “major” labels interact for every interval in the scale, which is a horribly confusing mess.

Those interactions are pretty intuitive. Where defined, major + minor = perfect (considering an octave as perfect), perfect + major/minor = major/minor. As long as you remember which notes exist, you can't get it wrong, so you'll never get confused by a piece of arithmetic in an actual piece.

Re: Music theory for nerds

#340

Post by hamiltonkibbe »

acjohnson55 wrote: post #271
hamiltonkibbe wrote: post #220

Earlier quoted context omitted.

In jazz A minor generally implies A Dorian

Yeah, in my reading, it never seems that there was a compelling reason to chose Aeolian vs. Dorian as the definitive "minor". I think it's largely because common practice evolved to much more frequently approach the tonic from below instead of above. That would favor harmonic minor over Dorian. I suspect that this is because it allows for very similar cadences as major keys.

I think a lot of the time (in a jazz context) the chords are approached as almost individual elements or as part of a small "local" progression instead of in the context of the global key of the song, since the key could be changing as often as every couple bars. In the case of a common minor progression: B-E7alt-Am7 the major third of the dominant chord is the same note as the major 7 in the harmonic minor scale of the target minor chord, which would be one option for playing straight through that progression, but you'll often find that players will use either A harmonic minor, diminished, E altered, G# whole tone, etc. over the V7 and resolve to dorian or aeolian or something with a b7. It doesn't make much sense to analyze that progression in a classical context since those chords aren't entirely contained within any single key, and you end up something that looks like a key change, or has B as a secondary dominant implying a key change to the E7, where a jazz player would immediately recognize it as a minor 2-5-1
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