Talk:Music theory

This article is or was the subject of a Wiki Education Foundation-supported course assignment. Further details are available on the course page. Student editor(s): Ciolkokm9975, RonniL (article contribs). The archives to this page contain the following threads:

• Archive 1: no table of contents. Archived 15 August 2009.
• Archive 2: 49 different threads, Archived 7 January 2015.
• Archive 3: Geographical Imbalance (2007-2012); Musical parameters in infobox (2013); Intro (2008-2013); To do (2009-2014); Adding Confusing Language (2014); Music Theory – Main Article - Suggested major revision (2014); Major theorists (2014); Tone, pitch, and note (2014). Archived 7 January 2015.
• Archive 4: Modes, scales, tonoi, and thingimajiggs (2014); Conflict with article "Chord (music)" (2014); Notation Systems (2014). Archived 7 January 2015.
• Archive 5: Clean up of the intro (2014); Quarter tones (2014); You said "scales"? (2014); History of Music Theory (2014); Theories of Harmonization Problems (2014). Archived 11 August 2015.
• Archive 6: Alternative Outline (2014). Archived 15 August 2015.

Most of these archives, especially archives 3-6, remain important for the ongoing discussions and should often be reread.

Hucbald.SaintAmand (talk) 16:24, 15 August 2015 (UTC)

What is a chord?

I open this new section because I consider it necessary to widen the question posed in the previous one.

If one can argue, against the statement discussed above, that the concept of chord may not have existed before common-practice tonality (or, say, before the 17th century), then what is one to do of this statement in the article?

• Chords and sequences of chords are frequently used in modern Western, West African, and Oceanian music, whereas they are absent from the music of many other parts of the world.

In what sense would series of chord in, say, West African or Oceanian music be called "progressions"? Are they ever represented by Roman numerals, as described soon after? It is not only the phrase discussed above that is problematic, but also the one that follows:

• Although any chord may in principle be followed by any other chord, certain patterns of chords have been accepted as establishing key in common-practice harmony. To describe this, chords are numbered, using Roman numerals (upward from the key-note), per their diatonic function.

Obviously, the chords numbered "per their diatonic function" are not those of West African or Oceanian music, nor those of Carl Ruggles, Edgard Varèse, Olivier Messiaen, or Michael Finnissy.

This really is a complex matter and, now that many of us may have not much else to do, we might find the time to try and clarify matters. We should be able, I think, to explain the distinction that must be made between, say, vertical aggregates, stackings of thirds, and chords "properly speaking" (i.e. functional?). There is a complex balance to be found between the need to remain understandable to everyone, and the requirements of precision.

Once again, any opinion about this would be welcome. — Hucbald.SaintAmand (talk) 09:37, 16 March 2020 (UTC)

Maybe the best place to start is at Chord (music)? Pretty much any simultaneity is considered a chord in that article, which we could reference with a hatnote. —Wahoofive (talk) 03:21, 19 March 2020 (UTC)

This topic is also related to Harmony. This overview page isn't really the right place to go into detail on this. —Wahoofive (talk) 03:22, 19 March 2020 (UTC)

Yes, indeed, Wahoofive, or better: the definition should be more detailed in all three pages. On the other hand, it seems to me that Chord (music) deals almost exclusively with common-practice chords and mentions other simultaneities only in passing. We should first decide, I think, whether "any simultaneity" can be called a "chord". Only after that would we be in position to decide where to begin. — Hucbald.SaintAmand (talk) 18:41, 19 March 2020 (UTC)

I think this is a major area of "dispute." Traditional (mostly pre-20th century) theorists would codify chords based on previous practice. In the last chapter of his Harmonielehre (1911) Schoenberg described the possibility of any simultaneity being a chord; though it took a long time, I think many post-WWII practitioners (not so much theorists) have taken the point of view that almost any simultaneity can be a chord. Thus when you get to Elliott Carter's Harmony Book (early 1960s I think), he methodically goes through all the possible chords based on intervals, not harmonic practice.. - kosboot (talk) 21:45, 19 March 2020 (UTC)

I kept thinking of this, kosboot, and I think indeed that we must say what you say: today, any simultaneity may be considered a chord, but it was not so in former times. This being said, we must state at each point in what particular sense we discuss chords and "progressions" (Schoenberg does the same, he mentions quartal chords progressions, progressions by common tones, or on the contrary by changing tones, etc., always indicating the context). This reminds me of instructions we had received when working on the first edition of the New Grove (you all are too young to remember that), that controversial issues had to be presented as such, as controversial issues. In the WP articles concerned as they are now, one jumps from one meaning of "chord" to another without any indication that one does. — Hucbald.SaintAmand (talk) 09:17, 20 March 2020 (UTC)

List of software

Because of the virus threat I'm working from home. It occurred to me that Wikipedia has so many lists of software products, why not have a list of music theory software. I've done a few searches, but I'm sure people out there know more (especially programs that are now obsolete but which should be included). I'd be most appreciative if people could list products they know. Thanks! - kosboot (talk) 17:57, 17 March 2020 (UTC)

kosboot, the research center IReMus, in Paris, assembled a list of softwares for music analysis, listed in this page. They describe about 70 softwares (not all of them really available). — Hucbald.SaintAmand (talk) 17:53, 23 March 2020 (UTC)

Thank you, Hucbald.SaintAmand! - kosboot (talk) 19:38, 23 March 2020 (UTC)

Oxford Companion definition as lede?

I think the current beginning of the article starting with the Oxford Companion definition is confusing from a North American context, in which "music analysis" is a part of the field of "music theory." The 3-part definition given by Oxford does not include a large portion (perhaps even the majority) of academic "music theory" research published by major journals titled with that term such as Music Theory Spectrum or Music Theory Online, research which is concerned with description of stylistic idioms and the analysis and interpretation of existing pieces—rather than rudiments, general principles, or historical understandings of music. But I wouldn't want to remove an opening line in such a big article without a consensus opinion and a new lede to replace it! Shugurim (talk) 04:55, 3 February 2021 (UTC)

There was a discussion years ago on SMT Discuss to the effect that music theory is not the same thing as music analysis. — Hucbald.SaintAmand (talk) 11:26, 3 February 2021 (UTC)

Revised Music Theory - Based on geometric logic, namely, the tetrahedron

I have grown tired of the confusion, so I thought I'd start a new article. But I want to talk about my theory first and see what kind of responses I'll get. I'm still developing it.

However I think my theory is pretty solid and I would like to share it.

Introduction

In geometry, the tetrahedron, which is comprised of 4 equilateral triangles stuck together, is the most basic, simplest 3-dimensional solid that can be created. No other solid has less faces or total sides than the tetrahedron. Because of this, I thought to use this shape as a basis for my revised musical theory.

Firstly, I posit that music DOES have objective universal laws that it must follow. Music is a structure, and like all structures, there are rules you must follow and there are things that simply should never be done when building a structure. Many people will say that "music is subjective, there is nothing objective about it", but I disagree. I'm not going to delve too deep into philosophy, but subjectivity is not the opposite of objectivity, rather, subjectivity is when something requires uniqueness for a specific function, whereas the objectivity are the universal rules that must be followed regardless of any special circumstance. Paradoxes can't truly exist by default, so there is no reason to separate subjectivity from objectivity.

Now with that out of the way...

My theory is that, like colors that can be mismatched, so can notes. Therefore, there must be notes you can play, and notes you cannot play, at least at certain times. While this is already a part of traditional music theory, it has historically failed to clearly demonstrate why this is. But let's dive deeper into the comparison of notes and colors.

So we have a TRIANGLE of primary colors in nature. Blue, Red and Green. Together, they can create any color you can imagine. You could say the same for *additive* CMY, cyan magenta and yellow, but those colors can be broken down into RGB, whereas you cannot do the reverse. Also, being that blue is the darkest of all non-gradient colors, and green is the brightest of them all, (not on modern computer screens they do not have the power/watts to show green properly) it makes sense to use RGB as the primary colors.

So, like RGB, I believe musical notation follows a very similar pattern. Now I can prove this with a modified, corrected color wheel, but we'll deal with that some other time. I believe that 3 notes are necessary to create all musical structures. Just as with a equilateral triangle having 3 sides, which is the minimal amount of sides you can have in any shape, (circles don't count because curves have "infinite" or many sides), we need 3 primary notes to complete a section of a song. This tells the listener not only what key you're playing in, but what to feel about it, and which direction the song is going.

With the understanding that out-of-key notes don't sound right unless fixed, as mismatched colors do, we can be sure that we need a music scale so we can avoid that from happening.

Tetrahedronic Scale

We make an abstract tetrahedron here. The idea is to create 4 triangles of notes, with each triangle built on top of the last, and each one getting more spaced out and larger. A growth pattern if you will. So the idea is to land on THREES. And count by threes.

First Triangle

The first triangle is the base in our scale. We have 1,2,3. While in our scale we will skip the 2, it's necessary to build the first triangle. Now, we have 2 notes in our scale so far. The first note is used because you have to start somewhere, and we also use the third note. (land on threes).

Second Triangle

The second triangle is 1,3,5. It does the same thing, except when we get to 3, that becomes "1" triangle. So we overlap a "1" on top of it and do the same thing we did with the first triangle. So now we start at 3, skip over 4 (2) and land on a 5. So now we have 1,3,5 out of the notes we can play. That's three notes and that creates a triplet that allows for the next triangle to do something a little different.

Third Triangle

The third triangle is 3 triplets. We had one triplet last triangle, which was based on skipping over the "twos". So now we are going to do 3 of those.

The pattern now becomes: 1,3,5 (first triplet) and now we overlap 5 to a "1", and we get 5,6,8 (second triplet) and then finally 8,10,12 (third triplet).

These three triplets complete our THIRD TRIANGLE. But to clear something up, the reason we have a 6 instead of a 7, is despite what we did with the first two triangles, we already have a base set of THREE notes we can PLAY in our scale, therefore we don't need to build another "3" above that, as it is it's own triangle. Therefore, we can just do a half step up and get 6. Now that we start from 6, we skip over 7 and get to 8. (the idea is to build threes like we did with the first two triangles). Now that we are at 8, and is both a "3" therefore an overlapped "1", we now start ALL OVER again, and do the same thing to get 8,10,12. This creates the entire major scale, although we overlapped the notes.

Fourth Triangle

The fourth triangle is very straightforward. Just like in the other three triangles, we skipped some notes to create three. Aha, but we want this one to be bigger to continue in our little growth pattern. So that means, instead of skipping over notes we DON'T play in our scale, we skip over notes we CAN play in our scale. So instead of 1,3,5, we'll skip over 3 and get 5. Start from 5, skip over 6 and go to 8.

Now we have: 1,5,8

This completes our tetrahedron. It is these 3 notes, which you may call Blue (1), Red, (5) and Green (8), if you desire, that are necessary components of all songs. I believe this means that per each key in the song, you must play, in any order or in-between other notes, 1,5 and 8. Or your 1st, 3rd, and your 5th of the major scale.

To recap:

Tetrahedronic Music Scale:

 1,2,3
 1,3,5, (playable triplet)
 1,3,5  5,6,8  8,10,12 (three playable triplets)
 1,5,8

This is our completed musical tetrahedron.

Deeper Understanding

Colored Notes

If you play all three 1,5,8 notes (1st, 3rd, 5th) at the same time, you get what is called a regular "major chord". It's just those 3 notes. Notice how neutral and flat they seem to sound. Very "middle ground" and pleasant to hear. This is because, like when you mix RGB together you get a comfortable and neutral, flat, WHITE color, when you mix these three notes together, you get a WHITE chord. It's a "white canvas" of sound.

Direct Comparisons to the Tetrahedron

Musical Note Count Comparison:

To compare our notes to a physical tetrahedron we can use the following picture:

This is a pentagonal bipyramid, only problem is it was built using equilateral tetrahedrons. So it leaves a small gap in between the FIRST and the FIFTH triangle. If you count the amount of exposed triangular faces, it's a total of TWELVE faces. If you count just the top faces and the 2 faces in the small gap, you have SEVEN faces. There are 12 notes in the chromatic scale, and 7 notes in the major scale. We can do more with these equilateral tetrahedrons, however.

We can put 5 more on top of them and 5 more on the bottom, for a total of 15 tetrahedrons. So now you have 3 layers of 5 tetrahedrons. At this point, you are unable to stack anymore tetrahedrons onto our strange creation. The first correlation I noticed between this and our music scale, is that if you count the triangles we had earlier, and only the triangles that have 3 notes we can PLAY, you end up counting 15 notes.

1,2,3 is skipped because you only get 2 notes you can play. The idea is to count 3 PER TRIANGLE. 1,3,5 = 3 notes 1,3,5 5,6,8 8,10,12 = 9 notes total 1,5,8 = 15 notes total.

15 notes, 15 tetrahedrons.

Physical Comparison

Yes, and another correlation is the 1 tetrahedron, and then the 5 tetrahedrons stacked together. That's obviously correlated to our notes, but where's the 8? Well the idea is to attempt to do something similar to what we did with our music scale. So we start at 1, and then we count to 5 for the next shape. Now we start at FIVE, and count a total of 3 x 5 tetrahedrons. So, 5, and then immediately 6 for the second layer, which we then start over at 6, the middle layer becomes "7" which then gets covered up by the last layer, our magic "8". I know that sounds strange, but it's perfectly logical. With our music scale, we grew the notes based on all of the prior triangle, correct? So we can do the same thing with our tetrahedrons. Only problem is people aren't used to thinking that way. But it works.

Song Structure

There are so many things people get wrong about song structure. They think you can pretty much slap whatever sections you want in a song together, but this rarely has a pleasing effect to the ear. In fact in can be downright cringeworthy, and teeth grinding.

All songs have a main melody. This melody is what the song is *supposed* to revolve around, but like I said many musicians tend to randomly slap different sections together that have nothing to do with each other. Now, the way I see it, is we should continue growing our song with a tetrahedron.

Fundamentally, an AAAA song structure works perfectly well. It is simply 4 main melodies, as it's the only melody in the song. 4 main melodies, much like 4 triangles. Now we have another tetrahedron!

What if we wanted to add other sections though? That's where it gets a bit tricky. Like I said most song structure have very obvious flaws. But first of all, you always need 4 main melody instances in every song. For the purpose of this explanation, we will automatically designate ALL MAIN MELODIES as "A".

Examples:

Ex 1:
AAbAA

This works. You have your 4 main melody sections (tetrahedron), but we have a b in the middle. This is allowed because it's symmetrical and does not interefere with our main melody therefore.

Ex 2:
AABBAA

This is correct for the same reason as above, just with an extra b.

Ex 3:
AAABBA

This works because the pattern becomes a decrement of 1 for each section switch. We start with 3 As, then decrement by 1 and get 2 bs, and then back to A and get 1 a.

You could even draw it like this to see the pattern more easily:

  A
 B B
A A A

Ex 4:
ABABABAB

This one is the simplest. You just alternate until you get 4 of each. There's many variations of this, but all simple.

Ex 5:
ABAABA

Another example that is self-explanatory.

So you see, even song structures look better when stringing them together in a pattern. I think if everyone did this instead, we'd have much better sounding songs. But that is not all.

Notational Patterns

Within your main melody, you can be as creative and wacky as you want, as long as you have 1,5,8 being played somewhere somehow for each key, doesn't matter the octave or instrument arrangements, as long as they are played the same way in the next instance of the A (main melody). The hard part is getting your other sections (b,c,d .... etc.) to revolve around your A.

This means we need to "patternize" our sections to reflect the main melody in a certain way. This requires more and more work the crazier and wackier the main melody is. But it can be done.

Examples:

STANDARD C MAJOR EXAMPLES:

Ex 1:
A (main melody ) = 1st, 3rd, 5th, 5th
B = 3rd, 5th, 7th, 7th.

So what is the pattern here? Yes we went from start at 1 to starting at 3. Makes sense doesn't it? We then just have the same pattern of skipped notes. So we get 3rd, 5th, 7th, and 7th.

This works because we can EASILY attribute it to what the A (main melody) did.

Ex 2:
A = 1st, 3rd, 5th, 5th
B = 1st,3rd,5th,5th,1st,3rd,5th,5th

Now the only way this works is to play B twice as fast as A. Otherwise you're just getting 2 more of A. The reason this works is because it is a factoring of A. You're doing A sped up 2x in tempo. Why not 3 times? Because in order to reflect our A, it must be a factor of A in some way, because you can easily derive a pattern simply by copying what A does in some way. So if A is played at 60 bpm, then you can play b at 120bpm. You're just copying A's tempo twice. Now again, the factoring is done in the first example, but it can also be done with tempo, even with octaval changes. There are many ways to do this. But you must either multiply a property of A, or divide it in half. It is always a "n2" (number x 2) algebraic equation if you will. Or n/2. (division).

That's all for now I'll update this later. Thanks for reading.