Musical Chords: What are majors, minors, 7s and 9s?

[RM_Mentock]

@Tripler

I’m an engineer, and may be looking at this a little too hard.

paison!

@friedo

C-major is called “major” because it sounds full, happy and complete. The notes also come directly from the C-major scale, C, D, E, F, G, A, B, C.

And the “reason” it sounds that way:

Whenever something with a natural resonance is sounded, we hear harmonics. There may be a fundamental note, but various overtones may also sound. So, we might hear an A, but also to varying degrees the 2nd, 3rd, 4th, 5th, 6th multiple of the frequency of that A. So, since we’re used to them, or maybe there’s even an underlying physical reason, they sound good together. The 2nd and 4th multiples are just A, one and two octaves higher. The 4th, 5th, and 6th multiples are the major chord. (The 6th is the same note as the 3rd, as well, one octave higher.)

In the C major chord described above by friedo, the E has a frequency 5/4 times C, and G has 6/4 times C.

You may be wondering why these intervals seem not to be directly related to the number of semitones between things. Why does a perfect fifth have seven semitones, for example? The reason is because our modern tuning system with 12 notes per-octave is a compromise based on historical tuning systems which are a fascinating subject in their own right.

In that twelve semitone scale, a note four semitones above has about 5/4 the frequency, and seven semitones above has about 6/4 the frequency. They form a major chord.

The distance between such notes as I described them are not exactly equal, but we can “adjust” them slightly so that the steps are all equal. That makes it easy to transpose scales. So, that’s often what we do, “tempering” them.

The ratio between each semitone is then 2^(1/12), so that 12 semitones would be an octave ( 2^(1/12)^12, which equals 2 ). So, in the tempered scale like we might use on pianos, the fourth semitone is actually 2^(4/12) higher, or 1.26 instead of 1.25 (5/4). The seventh is actually 2^(7/12), or 1.498 instead of 1.5, but it’s close!

[GorillaMan]

This ‘simple’ explanation of harmonic resonance giving rise to the chords with which we are familiar doesn’t entirely hold true - and there’s previous threads discussing it. One obvious thing it doesn’t give any explanation for is the way the major and minor chords have come to sound ‘equivalent’ to each other, because nothing so conveniently resembling a minor triad crops up anywhere in the overtone series.

(Relevant nitpick - the 6th overtone is somewhere between a minor & major seventh, but sounds like neither. The 7th is the next octave.)

[Musicat]

@+MDI

I’ve also seen it referred to that the ninthis the second of a scale but raised an octave. Indeed, I’ve seen Cadd9 referred to as Cadd2 if the “ninth” is in the same octave. Same with eleventh and thirteenth. Is this correct?

Our western harmonic system, with roots in 18th Century harmony, is based on 3rds – root, 3rd, 5th, 7th, 9th, 11th, 13th (15th would be the same pitch as the root, so there’s no point in continuing). For a C triad, for example, the (dominant) 7th is a B-flat.

From a theoretical harmonic standpoint, that B-flat can occur ANYWHERE within the range of human hearing and it will be considered the 7th of the chord.

Something that has not be discussed in this thread yet it voicing or inversions. harmonically, C[sub]1[/sub]-E[sub]1[/sub]-G[sub]1[/sub] (reading from low to high pitch) is the same structure as G-E-C, E-C-G, C-C-E-G-E-C-C if octave repetition is present. Or, if each member of the orchestra is playing either a C or E or G in the native range for their instrument, that is still a C major triad.

In a practical sense, the note at the bottom of the stack, usually played by an instrument of the bass persuasion, is important for the overall sound. Also, due to human hearing characteristics, clusters of notes in a low pitch range sound muddy and are more commonly placed higher. Although none of these items will change the name of a chord, there are some notators who try to indicate (clumsily) that the 9th is to be played close to the root by calling the 9th a 2nd.

In popular music, the root of the chord is typically played in the bass, with the 5th often used as an alternate for less-accented beats (think ump-cha, ump-cha or simple country or folk songs). Popular music notation since the 1950’s has attempted to indicate any other notes in the bass with a slash notation following the chord name, such as C/E, which indicates a C major triad with E as the lowest note. (C/C would be redundant.) If the bass note exists in the chord already, guitarists typically ignore the bass indication and play a chord that fits best in their hand regardless of that note ends up at the bottom. If the note is not part of the chord (C/D = C major triad with D in the bass), a guitarist may try to include the bass note.

Note that the slash notation is not the same as polyphonic notation, where there is a horizontal instead of a diagonal line between two independent chord names. Rarely seen.

Another notational convention you may see is the “added” note, as “C add 2” or “C add 9” or “C add D”. This usually means to literally include with a C major triad the extra note. So a C11 chord, (C-E-G-B flat-D-F) would be different from C add 11, (C-E-G-F). The added notation does not imply intermediate tones while the C11 implies the intermediate 7 and 9.

[Tripler]

@deevee

If simply learning how to play is what your after then I would suggest you not get bogged down in the specifics of why things are the way they are, just accept it. Many people are quite adept musicians without knowing the theory behind it in the same way that many people can speak quite beautifully without knowing parts of speech.

This is my plan. I simply didn’t understand the terminology, and through the descriptions here on this thread, the terminology as well as the “construction” of chords (that is, their relationships) is a helluva lot clearer. . . even to a simple sparkchaser like me.

I do admit though, that this thread makes for good reading. I thank you guys!!

Tripler
Now if I could only just learn to read music. . . :rolleyes:

[friedo]

@Tripler

Now if I could only just learn to read music. . . :rolleyes:

Don’t worry. I have yet to learn an instrument!

[minor7flat5]

Take your guitar and bar the top three strings at the first fret. Play the top four strings.

The lowest note is D, naming the chord.
The highest note is F, which is a minor third up from D, giving the chord a minor feel.
The second highest note is a C, the (flatted) seventh of the D Major scale, making our chord a 7 chord.
Those notes alone are enough for a traditional D minor 7.

Throw in the second-lowest note in this chord, a G#. This is a half step down from the fifth note of the D Major scale, aka flatted fifth or diminished fifth.

It’s an interesting chord, often referred to as a “half diminished” chord.

Of course, there’s another name for it that escapes me now ;).

[pulykamell]

@GorillaMan

I’d recommend this site to be able to hear some of what’s being described here.
Heh heh, nitpick time…a two-note chord obviously isn’t a triad, but is surely no less of a chord? What about the open-fifths endings of plenty of medieval music, do they not end on chords? I’ve rarely come across a ‘3-note-minimum’ definition. And an interval is a theoretical construct to describe what’s happening, but isn’t the notes itself. (Am I being awkward enough? )

I am speaking of course from a classical Western theory point of view. And in classical Western theory, a chord must have at least three notes. Sometimes the third note, major or minor, is implied by context. I don’t really pay attention to such distinctions. From a practical standpoint, it doesn’t really matter to me whether a combination of notes is an interval or a chord; (and in guitar music, these root fifth intervals are called “power chords,” because I suppose “power intervals” wouldn’t sound quite as cool.)

When it comes to learning music, though, don’t get too entrenched in theory to start with. You can learn this way, but it’s slow, confusing, and unnatural, in my opinion. Learn to listen, play, imitate. It’s like learning language. Most people learn quickest when immersed in it, and when they naturally pick up language through trial-and-error, listening, and imitation, not through slogging through grammar books (which is what theory essential is, a descriptive musical grammar.)
A little theory is okay, but don’t get too bogged down in it.

And let’s not get into quartal and quintal harmony.

[RM_Mentock]

@GorillaMan

This ‘simple’ explanation of harmonic resonance giving rise to the chords with which we are familiar doesn’t entirely hold true

It certainly gives rise to the notes, and things have been taken from there. We’ve gotten used to it–some of what is considered music today, used to be called noise.

• and there’s previous threads discussing it.

I’ve seen a few of them, posted in a few.
Music and Mathematics
12-step Harmonics
Are harmonics in music related to harmonics in mathematics?
but I didn’t find any discussion like that. You have some links?

One obvious thing it doesn’t give any explanation for is the way the major and minor chords have come to sound ‘equivalent’ to each other, because nothing so conveniently resembling a minor triad crops up anywhere in the overtone series.

Equivalent? You mean, a major chord sounds like a minor chord?

(Relevant nitpick - the 6th overtone is somewhere between a minor & major seventh, but sounds like neither. The 7th is the next octave.)

?

[GorillaMan]

@RM Mentock

It certainly gives rise to the notes, and things have been taken from there.

It doesn’t fully explain even the earliest tuning and harmonic systems.

You have some links?

This thread is one that touches on it: http://boards.straightdope.com/sdmb/showthread.php?t=296023

Equivalent? You mean, a major chord sounds like a minor chord?

We hear a major chord and a minor chord as closely-related and interchangeable. This cannot be explained by reference to the harmonic series - and is contradicted by an explanation of the existence of the major chord based only on the overtone series.

?

From C, the overtones go (approximately): C G C E G B-flat-ish C. The ‘major chord’ within this series isn’t as important as is sometimes made out.

[Musicat]

@GorillaMan

We hear a major chord and a minor chord as closely-related and interchangeable.

We? Speak for yourself, Sir! Major and minor chords to a professional musician, and I am one (or used to be), are not interchangeable in any way I can imagine, but quite distinctive.

This cannot be explained by reference to the harmonic series - and is contradicted by an explanation of the existence of the major chord based only on the overtone series.

The idea that our western, 18th-century-based harmonic structure must or can be explained by similarity to acoustic phenomena is a philosophical one. It is interesting to note, but there is no reason why our ears must adhere to the theory. And oriental (1/4 or 1/3 tones), primitive (pentatonic scales), experimental (12 tones, etc.) and other harmonic schemes differ even more from the overtone series.

[RM_Mentock]

@GorillaMan

It doesn’t fully explain even the earliest tuning and harmonic systems.

Which ones?

This thread is one that touches on it: http://boards.straightdope.com/sdmb/showthread.php?t=296023

I see your comment there (“Where this has been talked about earlier is in respect to intonation systems other than equal temperament.”) but I don’t see anything else in that thread related to it. Did I miss it?

We hear a major chord and a minor chord as closely-related and interchangeable. This cannot be explained by reference to the harmonic series - and is contradicted by an explanation of the existence of the major chord based only on the overtone series.

What do you mean by interchangeable?

Of course they sound related–they have two of the same notes, right?

From C, the overtones go (approximately): C G C E G B-flat-ish C. The ‘major chord’ within this series isn’t as important as is sometimes made out.

The ratios between the C E G are 4:5:6. That’s not important, musically?

[GorillaMan]

@Musicat

We? Speak for yourself, Sir! Major and minor chords to a professional musician, and I am one (or used to be), are not interchangeable in any way I can imagine, but quite distinctive.

Interchangable in that you can swap a C minor chord for a C major one while retaining the recognisable features of its context…but you couldn’t replace it with a diminished chord, or an augmented one, or the Tristan chord, etc., without a far greater alteration being perceived. None of those chords are derived from the harmonic series, and nor is C minor. But minor triads have acquired a special place - completely unexplained by simple refernce to overtones.

The idea that our western, 18th-century-based harmonic structure must or can be explained by similarity to acoustic phenomena is a philosophical one. It is interesting to note, but there is no reason why our ears must adhere to the theory.

Absolutely agreed.

Of course they sound related–they have two of the same notes, right?

C E G#, or C E F#, or C F G would all have two of the same notes. Again, my point is that the minor chord has acquired a specific and important role not because of its inherent acoustical properties. Which is an indication that the major triad’s equal importance is solely not due to physics.

The ratios between the C E G are 4:5:6. That’s not important, musically?

Nope, not especially. Exact ratios don’t sound right in the context of western harmony - indeed, adherence to exact ratios damages the functional roles of chords. Tune a string section to exact-ratio fifths, and they’re noticably out of tune with one another.

And if ratios were so important, what’s so special about 4:5:6? Why not 4:5:6:7, or even just 5:6:7? If the answer is ‘because they don’t sound right’ (and they certainly don’t sound anything like western harmony), then you’re back at square one.

[Musicat]

@GorillaMan

Interchangable in that you can swap a C minor chord for a C major one while retaining the recognisable features of its context…but you couldn’t replace it with a diminished chord, or an augmented one, or the Tristan chord, etc., without a far greater alteration being perceived. None of those chords are derived from the harmonic series, and nor is C minor. But minor triads have acquired a special place - completely unexplained by simple refernce to overtones.

I’m not sure what you’re getting at RE: interchangeable. I don’t think a playing musician would feel comfortable with this concept – maybe you’re thinking in a theoretical sense. If so, since the interval from 1-3 is the defining interval of a major or minor chord (the 5th is not essential for its major- or minor-ness), then an augmented triad – which has the same 1-3 interval as a major triad – could replace it without a great alteration being perceived, or a diminished triad could replace a minor one using the same logic.

In any case, I don’t see why common musical chord structure – developed first by human ears, not the physics lab – needs to be explained in terms of the overtone series.

[GorillaMan]

I’m struggling to see what’s so hard to understand about major-minor equivalence. All I’m doing is responding to RM Mentock’s post, that the “reason” the major scale & triad sounds ‘right’ is because of its relationship to the harmonic series. We hear minor triads & scales as equally ‘right’, despite their absence from that series. Both major & minor chords are essential and integral to western harmony - that it is possible to describe one as being directly derived from overtones, and not the other, should put a big question mark over the explanation.

[Heart_On_My_Sleeve]

I enjoyed reading this thread, and now I understand why my 9 chords sounded like there was something missing. The flatted 7th. I really need to get myself to a jazz piano class.

[pulykamell]

@Heart On My Sleeve

I enjoyed reading this thread, and now I understand why my 9 chords sounded like there was something missing. The flatted 7th. I really need to get myself to a jazz piano class.

Yep. Any extended chords like 9ths, 11ths, and 13ths all include the thirds leading up to that extension. (the 9th includes the 7th, the 5th, the 3rd, the root; the 11th includes all that plus the 9th, etc.)

When playing these chords, however, it’s most important to play the root, seventh, and the last note of your extended chord (and any altered notes). So, for a 13th, you can get away with just playing the 13th, the 7th and the 3rd, providing the bass is giving you the root. For a C13#11, for example, you want the third, the 7th, the 13th, and the #11 (because it’s an altered note).