Why are diatonic chords the way they are?

Question

Why are diatonic chords the way they are?

Answer 1

Some very good answers above me. Just to add a little more insight:



From what I remember, Jean-Phillipe Rameau (in his Treatise on Harmony) is the one who wrote about the move from the horizontal writing used in the Renaissance and earlier (basically, using scales as the basis of composition) to vertical writing (using chords and triads instead as a basis). When we say horizontal/vertical, we're talking about the notes on the staff paper - was it written left to right (melodic/scalar/contrapuntal) or 'up and down'/beat by beat ("chordally").



But everyone else is right in saying by asking this question, you're actually asking a bunch more, deeper questions ;), i.e. why does western music rely on the major/minor scale/triad? And how did we get there?



Well here's one theory: when the Roman Empire adopted Christianity as its religion, the priests would have sung chant that's probably more reminiscent of Greek Orthodox chant today (what we might perceive as "Arabic"-sounding) - after all, they would have gotten the tradition from Judea, in turn from the Jews. Anyway, after the Empire fell, missionaries were sent up western Europe, to the Franks, a Germanic tribe that are the namesake of France. There is an account that when they were trying to teach their chant to the Franks, they couldn't sing it right - the Franks kept singing large intervals like 4ths, 5ths, and 6ths when the Romans were singing really small intervals and probably "eastern" or "Arabic"-sounding melodies (this is most likely because of linguistics - there's something about Germanic languages that makes them prefer larger intervals). Because this was lost in translation, Gregorian chant developed using wide, perfect intervals like the 5th as its basis. Harmonization in 5ths came after that, and finally the 3rd made its appearance at cadence points (thanks to the English). The rest is history.



TL,DR: Rameau wrote about it, but wasn't responsible for it. Our music might sound the way it does because of Roman chant being sung wrong by the Franks in the Dark Ages. In any case, we owe our musical tradition (rock, classical, country, you name it) to the Catholic Church.

Answer 2

The names "major" "minor" and "diminished" are really somewhat arbitrary. While there are reasons they have those names, it doesn't really matter what they are called.



The question you're not asking is the important one: what makes these chords different? How is a minor chord different than a major chord? or a diminished chord?



Well let's take a look! We'll just use the key of C major, since it's easy. Out I chord is C major, and consists of the notes C E and G. How far apart are those notes? Well from C to E we have, C-C#-D-D#-E... that's 4 semitones. Then from C to G we have C-C#-D-D#-E-F-F#-G... that's 7 semitones. So a major chord is made up of the root, a note 4 semitones above it, and another note 7 semitones above it.



Now what about a minor chord? We'll just use D minor. Your little formula up there tells us that a D minor chord has the notes D F and A in it. So from D to F we have D-D#-E-F... 3 semitones. So already we've got a difference between the major and minor chord! Let's check the distance to the A. D-D#-E-F-F#-G-G#-A... 7 semitones. So it looks like the only difference between a major and minor chord is that middle notes. It's only one semitone different, but it makes a big difference in sound.



Check the intervals for all the other major and minor chords. They are all the same... that's what makes them major and minor! What about that diminished chord? Well, in C major, we get a B diminished chord, and it has the notes B D and F. So from B to D is 3 semitones, and from B to F is 6 semitones.



So now that that is out of the way, we could probably use some better terminology to refer to this stuff by right? Well, read this article here and learn all about it: http://library.thinkquest.org/15413/theory/intervals.htm



Now that you've read that, you're probably realizing why the chords are called "major" "minor" and "diminished". The major chord has a major 3rd in it, while the minor chord has a minor 3rd. The diminished chord also has a minor third, but it also has that diminished 5th, so we name it after that interval.



Nobody just "decided" one day that these were the harmonies we would use, and nobody just "decided" on their names. It's something that developed over a LONG period of time, composers mainly did things (and continue to do things) because they sound good, not because of some arbitrary, nonexistent rulebook.



Here are some videos I made about chord construction. What them and you'll learn how all sorts of chords are built:

http://www.tinyurl.com/lucasmanchords1

http://www.tinyurl.com/lucasmanchords2

http://a.1asphost.com/LukeSniper/ccc.html

Answer 3

The major chord comes from the overtone series.

The first tones of an overtone series on C are:

C C G C E G



The dominant seventh chord probably comes from the overtone series too,

since the next tone is Bb.



Minor modality probably comes from the pentatonic scale.

In the pentatonic mode, the only two possible triads are the tonic and the relative major or minor.



Betcha Septimal Minor Third is going to answer this question--

betcha he'll have a real good answer, too!

Answer 4

Here is a very general answer without music-theory.



Why are triads constructed this way?

Composers/musicians found that stacking thirds was a "satisfying" way of putting notes together(harmonizing) the major scale.



Who decided what is what?

Each of these triads you listed have a distinct sound to the human ear. Theorists came up with names for these groups of notes.



All theory is an attempt to explain why we hear things the way we do; and why, throughout western history, we seem to consistently "like" or "dislike" certain sounds.



For a more in-depth or scientific explanations, I would recommend looking up Pythagoras(who "invented" the western scale), common-practice period, tertian harmony, and the overtone series(or even acoustic physics!)

Answer 5

If those lengthy answers don't help here's a tutorial on diatonic chords:

http://www.musictheorysite.com/major-diatonic-chords/

Answer 6

First off, I would like to say that I applaud your curiosity. These are the kind of questions that prompt us into a deeper understanding of music than simply blindly following rules and conventions can bring. It really isn't too complicated in the end, and in fact, the only real reason it is very complicated at all is because you have to unlearn some things that are simplified in conventional music theory to understand it well, but it is more complicated than I can explain on this post, so I will do my best to try and explain as much as I can.



The term "diatonic scale" is often used generally to refer to the set of 7 notes (starting on any one) on the white keys of the piano. So either C major, A minor, or any of the modes (E.A, D Dorian, which is D to D on the piano keyboard) or any of their transpositions are part of the diatonic scale, which strictly speaking is not a scale, as it does not designate a single tonic, therefore I prefer the term "Diatonic set" and from here on out will use that term to refer to it.



As suhwahaksaeng points out, the major chord is found in the harmonic series, this is probably the best evidence we have as to how triads themselves came about in western harmony. The minor triad can be though of as the mirror image of the major triad. (a major third inverted inside a perfect fifth is a minor third)



As to why (how) the scale itself came about, there are a lot of different explanations, but this is one I like, and find very illuminating;



When you stack 4 perfect fifths on top of eachother and then rearrange them within an octave you obtain the major pentatonic scale. This scale obtains all the resources for both a major chord, and a minor chord separated by a minor third. Now, these major and minor chords are not the same as those found in the harmonic series, but that is another discussion, so for our intents and purposes, let's assume that they are.



When you stack 6 perfect fifths on top of eachother and rearrange them within an octave, you now have 3 distinct sets of major pentatonic scales, each containing a major and a minor chord, therefore there are 3 major chords, and 3 minor chords in this scale of 6 stacked perfect fifths, but there are 7 tones. Starting from the seventh tone, there are not the right tones to build either a minor or major chord, so a diminished chord is substituted, and it just so happens that in order to construct a diminished chord, one requires a stack of 6 perfect fifths, so now we end up with;



3 major chords

3 minor chords

1 diminished chord



This is the diatonic set, and that is why we have the arrangement of triads that we do in the scale. But, you may be asking yourself why we use 7 tones. Well, it turns out that this scale of 7 tones has exactly two sizes of step; a major second, and diatonic half step. This property seems to be appealing to humans, and is also found in a 5th generated scale of 5 notes, and 12 notes. 5 note pentatonic scales (generated by fifths) are the most popular scale in the world, the diatonic set is less popular, but is also found in many places all around the world, and the 12 tone chromatic set is not only the basis of our tuning, but long before western civilization, the chinese used this as their master scale, along with the arabs and babylonians. Another reason that these scales became so popular could be explained by their abundance of consonant harmonies by the nature of stacked fifths approximating triads.



As for why we use the major mode of the diatonic set (the exact arrangement of major, minor, minor, major, major, minor, diminished), that is mainly for historical reasons, but also because the major mode has an objectively strong tonic.



Another note; this does not illegitimize the use of non-diatonic scales, but simply puts forth that scales from stacked fifths form a natural FOUNDATION for music, there is nothing wrong with adding onto that foundation for expressive purposes. For example, the arab system of modes nowadays has some lovley non-diatonic scales. (the arab 12 note chromatic scale was used in the past, but not so much today)

Answer 7

Musicians talk about the overtone series, physicists call it the harmonic series. Why? different priorities. The first harmonic is the fundamental, the second harmonic is the first overtone. I'll use the terms interchangeably, but number harmonics with the physicists' system, because the interval between two harmonics is exactly equal to the ratio of their harmonic numbers. (Pythagoras figured that out in the sixth-century-or-so.)



The pitches in a harmonic or overtone series can be produced by touching a vibrating string to divide it in parts.. The fundamental is the lowest pitch, the first overtone is an octave higher. The series (with harmonic numbers) with each successive overtone expressed as the interval above the previous overtone is:

1 Fundamental (the lowest tone you can produce, hence, not expressed as an interval above anything)

2 octave

3 fifth (making it an octave and a fifth above the fundamental)

4 fourth (this is two octaves over the fundamental)

5 Major third ( 2 octaves and a third above the fundamental)

6 minor third ( 2 octaves and a fifth)

7 subminor third (2 octaves and a very flat seventh)

8 supermajor second (3 octaves)

Now something interesting happens:

9 "Greater Tone" (the 'large' second, 3 octaves and a big whole tone)

10 "Lesser Tone" (the 'small' second. I'm not going to bother with the interval over the fundamental any more.)

11 and 12, the Greater and Lesser 'Undecimal Neutral Second's

13 amd 14, the Greater and Lesser 'Tridecimal 2/3rd tones'

15, septimal diatonic semitone

16 just diatonic semitone.



From these can be built a scale of 7 tones (the 8th being the octave of the first, etc.) The usual makeup of the scale is a large tone, a small tone, the diatonic semitone, a small tone, a large tone, a small tone, and a diatonic semitone.



Remember interval = ratio of harmonic numbers, so the greater tone is 9/8, the lesser tone is 10/9, and the diatonic semitone is 16/15. If you start on A=440, and multiply it by each of these intervals:

440 (A)

440 * 9/8 = 495 (B)

495 * 10/9 = 556.875 (C#) (Just major third 9/8 * 10/9 = 10/8 = 5/4, note fourth to fifth harmonic=M3)

556.875 * 16/15 = 594 (D)



556.875 * 16/15 = 660 (E) (Perfect fifth, 3/2, ie 660/440)

And so on, since the next three intervals are identical to the first three (and, in fact, would be the bottom half of an Emaj scale.)



The ancient Greeks constructed scales of this variety, and did it without a clear concept of frequency or devices to measure them.



Stacking fifths (as Pythagoras) produces the scale called Pythagorean. In this case, each note's pitch (frequency) is 3/2 to the previous one, and reduction by octaves can bring all 12 tones within the spam of an octave. Again, the intervals are related by whole number ratios: it is worth noting that whole-number-ratio (WNR) intervals are 'beatless', in the sense of being "in tune". (Equal Temperament intervals are decidedly not in tune, and are purposely mis-tuned: the theory we use with regard to equal temperament is based on the foundational theory work done before Equal Temperament was developed!) In the case of Pythagorean scales, the notes that fall on diatonic steps as derived from the harmonic series are close enough to be called by the same name. (Heck, even the pitches derived from equal temperament do!)



Once the diatonic scale is established, and the existence of the major and minor triads are seen in the same harmonic series (1, 2, 3, 4, 5 form a Major triad, although octave divisions are needed to get the third between the fundamental and fifth; 5, 6 and 8 form a minor triad) it was simple work to ask what you'd get if you built triads on successive scale degrees, using nothing but notes in the diatonic scale. Observation quickly shows that a major triad is a major third with a minor third stacked on it, a minor triad is a minor third with a major third stacked on top of it, the triad on vii is two stacked minor thirds (hence, diminished, because it is the one chord where the fifth is smaller than pure) and from this, it's a short step to wondering what two stacked major thirds would be (augmented, actually.)



At this point, no one actually had to decide what was major, minor or diminished: it's built into the diatonic scale and inescapable.



The Greeks went on to develop a system of modes: instead of transposing the diatonic scale intervals to new fundamental tones, they just took seven-note sequences from the diatonic scale starting on successive diatonic scale degrees. In the Medieval and Renaissance periods, this Mode system was resurrected...but they got it upside down! (It didn't hurt their music though!)