Chord inversions and consonance

Question

So the way I understand chords is based on the interval of the individual notes present in them. This is what gives the chord a consonant or dissonant quality.

However, this doesn't seem to sit well considering how people handle chord inversions.

For instance, if i play a C and the G a perfect fifth above it, that's a very consonant chord as a result of the perfect fifth interval. Sounds good.

But now if I invert the chord and play a C with the G below it, i have an chord with a perfect fourth interval, much less consonant than the first one.

As I read about inversions, people seem to consider these to be the same chord, but in some inversion. But it's clearly not the same chord any more, since the intervals have changed.

So why even have the concept of inversions? Just call it whatever you would call a G with the C a perfect fourth above it. It's a different chord with different intervals.

Answer 1

...So why even have the concept of inversions?

A real answer is a deep delve into music theory history. One very important thing to read about is Rameau's theory of the Fundamental Bass. The essential idea is that harmony is based on chord roots rather than the lowest tone in the bass voice. Understanding chord inversions allows you to identify a chord root. Modern harmony analysis is based on chord roots using Roman numeral analysis.

...Just call it whatever you would call a G with the C a perfect fourth above it.

You can. Figured Bass was the system used before Roman Numeral Analysis and chord inversions were used. You need staff notation to actually write it, but in English it would be described just as you suggest: "a G with a perfect fourth and a (diatonic) sixth above."

...It's a different chord with different intervals.

Prior to the concept of fundamental bass that's sort of what people thought. But we should not overstate things or overlook how important counterpoint was in the system of harmony.

Musicians could obviously see that (from bass to treble) ECG was the same collection of tones as CEG and in the key of C major clearly are a collection of the tonic chord. Rather that thinking of it as a E chord, it was something like: an E bass should be harmonized with a chord of the sixth (meaning a first inversion chord.) The progression of the harmony was then a question of stable perfect chord & unstable chords of the sixth within a scale, voice leading, and tonal goals rather than the movement of roots.

A chord inversion concept in necessary to define chord roots and do RNA harmonic analysis (a music analysis purpose.)

Chord inversions are not necessary to do figured bass or 18th century counterpoint based harmony (a music performance and composition purpose.)

Answer 2

Inversions of a chord do have the same root but do not have the same uses in general. A major or minor triad (C-E-G or C-Eb-G or 1-3-5) in root position is considered stable (in itself it does not imply other chords to follow.)

In first inversion (with the 3 in the bass or E-G-C) the chord is nearly as stable; it doesn't often end a piece but is used to end phrases. Another use is to make a smoother sounding bass line. Take the Romanesca pattern (which is still being used though four or five hundred years old): C-G-a-e or in minor c-g-Ab-Eb; the bass rises a fifth (or falls a fourth), rises a second (or drops a seventh), and repeats. (Pachelbel's Canon among others.) By using inversions one has C-G/B-a-e/g or c-g/Bb-Ab-Eb/G which gives a stepwise descending bass line. Similarly for the circle of fifths (or cycle or fourths depending) one can alternate root position with first inversion chords to yield smoother bass lines.

The second inversion major or minor chords are a bit less stable. According to "strict" counterpoint, this chord is dissonant because of the fourth between the bass and middle note. One use is in arpeggios a C-E-G-C-E-G-C-E-G (in different octaves of course) doesn't sound much different from (E-G-C-E-G-C... or G-C-E-G-C-E...). Another use is as a neighbor chord C-G-E followed by C-F-A then C-G-E. A more idiomatic use from the Common Practice Period is similar the the previous but with a dominant seventh chord. The common chord progression (again 500 or so years old) of ii6-V7-I or ii06-V7-i or ii6-V-I, etc. is often has a I64 (sometimes notated as V64) between the V and I chords. Thus one gets the chord progression ii-I64-V7-I (or in C major D-F-A, G-C-E, G-B-D, C-E-G with voice leading adjusted). The G-C-E acts as a neighbor to G-B-D, similar to the other neighbor usage. Another (common in the 1700s but often discussed at present) occurs in the Romanesca (Pachelbel's Canon) C-G/B-a-C/G-F-C/E-F-G (or variants like C-G/B-a-C/G-F-C/E-d/F-G).

So the inversions are root (53)(most stable), first inversion (63) a bit less stable, second inversion (64) dissonant. The more unstable or dissonant, the more careful one tends to be in using that inversion.

Answer 3

I want to give a different view for why chord inversions are useful.

Why do chords exist? Because by playing multiple notes at the same time you're able to manipulate the feeling of harmonic context in the listener's mind more effectively than you can by playing just one note at a time. With harmony voices, music feels fuller, has the possibility to create stronger emotions, and can re-direct the interpretation of melodies. The lead melody can consist of only C notes, but when accompanied with different harmony notes, each C is felt from a different point of view. And musicians have noticed that the note combinations are not at all arbitrary or chaotic, but there's a certain logic to them... So, simultaneous note combinations are called chords, which are used as handy reusable building blocks for harmonic changes. And we have a system for naming chords based on their structural patterns ... So now we can accompany the C note with e.g. Bb11, Am, Ab, G11, Dbmaj7, and it will sound much more interesting than just C all the time, making it feel as if there was a progression.

If you take a melody and harmonize it by placing chord notes below it, you create inversions. Pianists and organists will inevitably end up doing this, if they want to play both the melody and accompanying harmony notes at the same time, with just one hand. (or two hands, but with one hand it's more obviously seen that you're playing chord inversions)

Maybe you've noticed that when the lowest note is moved, it creates a different sensation than when the highest note moves. If you want to move the bass line, and place chord notes above it, you create inversions.

If you want to keep the bass note and the melody note, but move the notes in between them, you create inversions of some chords.

If you want to do all this at the same time: move the highest note along a melody line, move the bass note, and the notes in between, you create inversions. In whatever way you want to place more than one note, it can always be seen as some inversion of some chord.

All inversions of C major can be used to perform essentially the same harmonizing function of a C major chord. No matter which inversion you pick, it will work as accompaniment. Or, can you find a way to order the notes C, E and G so that it just completely won't work as the first accompaniment chord of Yesterday, spoiling the whole thing?

It is useful to look at the group or "class" of chords consisting of inversions of a chord as practically the same chord, because any chord inside the same class can be used in the same basic harmonic role. There are other aspects to harmony like bass movement and movement of inner voices, but they can be considered secondary aspects, because they cannot completely ruin the big overall story line.

Answer 4

Let's think of the harmonics in the sound. Most musical sounds consist of a fundamental and then further overtones at (roughly) integer multiples of the frequency.

For the sake of simplicity, let's imagine that the instrument timbre we're using has 3 overtones - and that rather than C, we're playing a note of 100Hz. That means it has partials at 100, 200, 300, and 400Hz.

A fifth is a frequency ratio of 3:2, so our fifth will have its fundamental at 150Hz - and then have energy at 300, 450, and 600 Hz.

So the resultant sound has components at 100, 150, 200, 300, 400, and 600 Hz.

But now if I invert the chord...

Ok, let's play the 'fifth' an octave lower. It now has partials at 75, 150, 225, and 300 Hz.

So the resultant set (added to our 100Hz note) is 75, 100, 150, 200, 225, 300, and 400Hz.

What's the difference? Well, 75 and 225 are new, and we've lost 600. But five of the original 6 frequency components (100, 150, 200, 300, and 400 Hz) are sill there. So there's still a lot of similarity between the new sound and the original one.

As I read about inversions, people seem to consider these to be the same chord, but in some inversion. But it's clearly not the same chord any more, since the intervals have changed.

Of course you're right in that it won't sound the same. But because

• notes are named in an "octave repeating" way
• two musical tones an octave apart will have some overtones in common, because a note's harmonics themselves are an octave apart

...there will be some similarity in the resulting frequency spectrum. The amount of similarity depends on the timbre of the actual notes you're playing.

So why even have the concept of inversions?

It's mainly an expression of similarity, rather than saying that they're actually "the same". They may be "the same chord" in terms of the name of the chord, but the fact that the name is the same shouldn't be taken to mean that they necessarily sound the same.

That's even true with chord names in other senses too - a 'C' chord in the bottom octave of the piano doesn't sound the same as a 'C' chord played in the middle of the piano keyboard, or on a guitar, or on an instrument tuned with a different temperament.

Answer 5

There are a few reasons that come to mind. First, a chord is a by definition set of notes and while voicings and the inversion shape the exact, knowing the set of notes played gives a lot of information for things like function, improvisation, and reharmonization. Don't get me wrong, the inversion does play a part in harmony, but it's one of many aspects that shape it.

If you are coming from classical harmony, building chords in 3rds is the bread and butter of harmony so looking at sets of notes as inversions rather than new constructs is helpful. It's also the source of most names we come up with. There is a more post tonal way to look at chords, but even then they tend not to take voicings into account and they have a much more mechanical inversion simplification called prime form where major chords [0, 4, 7] and minor chords [0, 3, 7] end up having the exact same prime form due to them containing the same exact intervals.

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In general, there's a lot more to chords outside the inversions. For example, if you were to try to harmonize a C chord in close position and you did it in a lower octave, most people would call it more dissonant than a close position chord in higher octaves.