# Is the IV chord a perfect fifth in disguise?

They say the root of the IV chord is a perfect fourth away from the key's tonic. But isn't it a perfect fifth from the tonic (if we go the other way)? let's for the sake of coolness, call it a perfect fifth shadow.

So if we take the key of C:

F F# G G# A A# B [C] C# D D# E F F# G

If we go 7 semitones (perfect fifth) from the right of C then we get G, the root of dominant V chord.

If we go 7 semitones (perfect fifth) from the left of C, then we get F, the root of "sub-dominant" IV chord.

Now the root of the chord. essentially defines the sound of the chord. So I'll just talk about the actual chords..

According to hooktheory, the IV chord is equally as popular as the V chord in music (and they are both more popular than the I chord), so that makes the V and IV the most used chords in all of music. http://www.hooktheory.com/blog/i-analyzed-the-chords-of-1300-popular-songs-for-patterns-this-is-what-i-found/

So I think the IV chord is as popular as the V chord because they are essentially both perfect fifths, so maybe they're both dominant (?)

But we usually call the IV a sub-dominant perfect fourth. But it's equally as popular as the fifth. Maybe because it's just a reflective image of it. It's just the perfect fifth shadow raised an octave. I've heard from a variety of sources that the perfect fifth is the most important interval in music. according to mathematician Pythagoras, he said that after the octave, the most consonant interval in music is the perfect fifth which has a musical ratio of (3:2), whereas the octave has (2:1). Also in the wikipedia "Perfect Fifth" page, it says "The perfect fifth is more consonant, or stable, than any other interval except the unison and the octave." So people just gravitate towards consonant sounds.

And so in the key of C major (or any other major or minor key?) we're essentially just playing the tonic, and perfect fifth (G), and a perfect fifth shadow (F). Am I right on this or completely off?

• Your question is confused betwee chords (IV and V) and intervals (perfect fifth). The IV chord contains a perfect fifth, of course, but that doesn't seem to be what you're asking about: you're asking whether IV is some kind of a dual of V, which it is, by symmetry. – user207421 Apr 21 '17 at 10:12
• I'm was mainly talking about the root of the chord. and chords essentially sound like their roots. so the root of F is F, root of G is G and I was comparing them to their key of C. but yeah.. good point. – user34288 Apr 21 '17 at 12:33
• Certainly an interesting theory. Not sure if anyone would be able to confirm it, seeing as we haver difficulty even confirming the more common explanations... +1 – user45266 Apr 1 '19 at 14:55

F is a perfect fifth from the root, but obviously in the other direction, so it's a bit like "moving the goalposts." If you're measuring G as up a perfect fifth from C, you have to measure F up from C as well, otherwise your system lacks consistency.

That said: you're homing in on the concept of harmonic dualism. This is a nineteenth-century German idea, and one of the outgrowths of it is that the IV chord is in some ways equivalent to the V chord because of this very reason: if the V chord is a perfect fifth above C, the "harmonic dual" is a perfect fifth below.

There are a lot of ways to explain this, but here's one:

The perfect fifth is one of the first intervals in the harmonic series, and this is why the fifth is so closely related to its parent pitch. In short, the parent pitch generates the fifth. One of the questions in dualism is: if we're emphasizing the fifth that is generated, let's look at the fifth below tonic, because it is what actually generates the tonic in the first place.

However, there's an added issue: one of the ideas with harmonic dualism is symmetry. And as it turns out, major and minor triads are symmetrical reflections of each other. So the connection is not between V and IV, but actually iv (minor!). The claim is thus that, while B (the chordal third of V) is the leading tone of C, A♭ (the chordal third of iv) is a different type of leading tone that leads down by half step to scale-degree 5:

Another outgrowth of this is that the plagal cadence (IV or iv to I) is "equivalent" in some way to the authentic cadence (V to I).

• Hm, I am not familiar with the idea of major and minor triads being "inversions" of each other. Clearly you don't mean "inversions" in the sense of changing the bass note, but I'm not sure what you do mean. – Kyle Strand Apr 20 '17 at 17:48
• "Inversions" in this sense means "symmetrical reflections." Major triads have a M3 on bottom, m3 on top, but minor triads have the m3 on bottom, M3 on top. – Richard Apr 20 '17 at 17:49
• Ah, got it. I am still not quite clear on how that implies a relationship between V and iv, though I do see some similarity to the borrowed vii°, which incorporates the flat-6th leading to the 5th scale degree that you describe. – Kyle Strand Apr 20 '17 at 18:29
• You're not the only one that doesn't see the implied relation; harmonic dualism is one of the lesser-respected branches of music theory. – Richard Apr 20 '17 at 19:27
• Actually, now that I've googled it, the picture provided on the Wiki page makes everything clear. I'd suggest simply adding a link to your answer! – Kyle Strand Apr 20 '17 at 19:31

Fifths and fourths are inversions of each other. A perfect fifth and a perfect fourth add up to an octave. Note that in a typical "cycle of fifths" (also called a "cycle of fourths"), the bass line often moves up and down by fourths and fifths alternately (or fifths and fourths).

C up to F down to B up to E down to A up to D down to G then up to C. The moves are short and the range of the bass line is less than an octave (G to F) and so easy to sing or play.

Intervals that are inversions of each other have similar harmonic "meaning," differing in which is the bass note. The who thing of fourth vs fifth in the original question is essentially just a matter of terminology.

• F down to B? That's a tritone, did you mean Bb, which then throws out the rest. To get back to C, there needs to be all 12 keys/chords in the loop. – Tim Apr 20 '17 at 6:20

Not completely off. But a fourth is still a fourth. If you play it a fifth below the tonic, yes, it's a fifth down, and yes, it has the same intervallic relationship therefore to the tonic. But the tonic stays the tonic in any case, due to the construction of the chords themselves.

The reason (probably) that certain intervals "sound good" is that their frequency ratio is simple. Octaves "sound alike" because their frequency ratio is 2:1, meaning that a sound an octave higher than a note vibrates twice as fast as that note. Ratio for a fifth is 3:2, and a fourth is 4:3. (I'm leaving out the concept of "equal temperament"; feel free to look it up if you're interested.) For contrast, a half step has a ratio of about 18:17.

So, not only do the notes have a close frequency relationship, they also share overtones, which are additional components of a sound that give it its character or timbre. (For example, overtones are what makes a violin sound different from an oboe when they are playing the same note.) Unless a note is a pure sine wave (a single oscillation between two points; a close approximation is running your finger around a wine glass), then it will have overtones.

If you pluck a guitar string, it will vibrate not only along its entire length, but simultaneously in twos, threes, fours and so on. This means that two notes an octave apart share a lot of overtones, and as the interval ratio becomes less simple, the two notes share less overtones.

Wandering around looking for pictures of a string vibrating in twos, etc. led me to this page, which has a diagram that lays it out very well. It also has some beyond fascinating (to me at least) recordings of "Tuvan throat singers" who are able to emphasize overtones in their voice so strongly that it sounds like they're singing two notes at once. You might be interested in giving it a listen.

I don't think any interval can be called the most important interval. They are all important. But, more to the point: I think you are mixing up the interval of the bass movement with the identity of the chord. In your example the important thing is that you are moving to the subdominant (IV) chord. It's important to understand that the bass moving down a fifth does not mean you are moving to the IV chord. The bass could move from DO to FA - down a fifth - but if the upper voices above FA move to RE and LA the chord is the supertonic (ii) chord. If the bass didn't move and stayed on DO you could sill move to the IV chord - a I V6/4 chord. There is no bass movement of a fifth, but we still get a IV chord. It isn't the interval of the bass movement that defines the harmony, it's the root movements and the chord identities (tonic, subdominant, dominant, etc.)

As to the popularity of the IV chord. It depends on style. In classical style you should look into the idea of functional and pre-dominant harmony. In functional harmony the IV and ii 6/3 are both pre-dominant chords and are very commonly used to lead to V. Functional harmony basically says the IV will precede the V by convention. For this reason the IV is very common found.

• I would argue that the octave is objectively the most important, since without it you can't even have the concept of pitch-classes. – Kyle Strand Apr 20 '17 at 17:44

Here's a simple way to see it. A fourth and fifth are the same notes, but not necessarily the same interval in the same key. The IV chord of a C key is C F A all together. If you raise the C, it is now F A C which is a one chord, which has a fifth. The answer is yes. A perfect fourth and fifth are really quite similar.

You are conflating multiple concepts. A "perfect fifth" is an interval, whereas a "IV chord" is a triad built on a scale degree. The interval is a more primitive "unit" of harmonic analysis than the scale-degree-triad.

When you say that the IV and V chords "are" perfect fifths, it appears that what you mean is that the root of each chord is a perfect fifth away from the tonic of the scale.

This is absolutely a reasonable thing to take note of! But on its own, it doesn't really mean much. Here are some questions you ought to ask yourself:

• Why does the interval between the root of a chord and the tonic matter?
• Why does the interval between any scale degree (whether used as the root of a chord or not) and the tonic matter?
• What gives different scale-degree-triads different "functions" in harmonic theory? (Or, with less music-theoretical terminology: why do we differentiate between I, ii, iii, IV, ... chords?)

The important thing to take note of here is that the concept of "intervals" is insufficient to answer any of these questions, because they involve harmonic context, which is not included in our idea of an "interval".

So, let's start by eliminating the concept of chords from your question, and ask:

Is the 4th scale-degree really a "perfect fifth" in disguise?

When phrased that way, it's not clear what's "in disguise" here, because the obvious answer is yes, the 4th is a perfect fifth away from tonic. The next step is to ask about the connection with the 5th scale degree (which we'll need to consider if we want to eventually understand the relationship to the V chord):

Is the 4th scale-degree really "equivalent to" the 5th scale degree?

Well, here we need some notion of "equivalence". Yes, each scale degree is a perfect fifth away from the tonic. But the 4th degree is a fifth down, whereas the 5th degree is a fifth up.

In other words, in order to understand scale-degrees, we need to recognize that although our idea of "interval" doesn't include a direction, we need an idea of interval with direction. This is similar to how numbers don't have "direction" in mathematics, but it's sometimes necessary to discuss a "number with direction", which we call a "vector".

Let us take a step back and consider what harmony is. A musical harmony is not just a collection of pitches; it is a collection of pitches that change over time. Thus, the "direction" in our "interval with direction" is the direction in which a pitch moves over time. A "fifth up" is found when a voice starts on a particular pitch, and then moves to a pitch a 5th above that.

So, the relationships between scale degrees have something to do with when the scale degrees are played in relation to each other. If we imagine a voice moving from the 5th degree to the tonic, that is a "fifth down"; and if we imagine a voice moving from the tonic to the 4th degree, that is also a "fifth down".

Since we can take this idea of moving between scale degrees and apply it by chordal movements by simply discussing triads built on the scale degrees instead of scale degrees on their own, we have enough context to create a less misleading version of your original question;

Is the (function of the) harmonic movement V -> I equivalent to the harmonic movement I -> IV?

The answer is, essentially, yes, depending on context! The movement I -> IV could be considered an opportunity to recontextualize IV as the new "tonic", with I as the new "dominant" (V). Though note that in most contexts, I is preserved as the tonic. This is part of why the sequence I -> IV -> V -> I works well; I -> IV "sounds good" in the same way that V -> I does, but it introduces an ambiguity, since IV may now be treated as the "new" I. The IV -> V demonstrates that IV is not functioning as the tonic, since V includes the seventh scale degree, which would be a half-step lower if the 4th scale degree were the tonic. (Concretely: in C major, C M -> F M implies that we might be moving to F major, but F M -> G M shows that we can't be in F major because we have B natural.)

A lot of great replies here. I love theory, but it all comes down to sound. There is most certainly a connection, but they are not the same. If you add a harmonic layer and turn each of the chords into dominant 7 (FACEb , CEGBb, GBDF) then it adds a direction to the progression. So to reiterate what another person said, the intervals between the pitches G C & F are all 4th or 5th inversions, but attaching harmony to the pitches creates a definite direction which makes each chord function differently in relation to each other.

Here is a fun interval experiment to try which helps show the difference between a static interval, and one in context.

play the notes C and B together (middle C) sounds awful! add an E below, and a G above, and now what does it sound like? (EBCG) Answer: a beautiful major 7 chord in 1st inversion. great question!

If a person hears a combination of frequencies, the brain will generally try to identify groups of frequencies that share common factors, and those factors will themselves be perceived as pitches. For example, if someone hears 220Hz (A3), 330Hz (E4), and 440Hz (A4), the brain will often perceive those together as a tone with a frequency of 110Hz (A2). This effect is especially strong in the presence of distortion, which is why power chords are so popular on the electric guitar (an A power chord in a guitar's upper octave would have the above frequencies).

If the brain hears just two frequencies 220Hz and 330Hz (a fifth apart), the same effect will occur, though it's not as strong as with all three frequencies. Likewise (though to an even lesser extent) if the brain hears just 330Hz and 440Hz (a fourth apart). Note that with notes a fifth part, the perceived pitch will be that of the lower note, one octave down, but with notes a forth apart the perceived pitch will be that of the upper note, two octaves down.

Things get more complicated when chords are built up that include thirds, so I wouldn't say a IV chord is a perfect fifth in disguise, but intervals of fourths and fifths are very strongly related. The relationship between a I and IV is the same as the relationship between a V and I, but the relative popularity of the V and IV perhaps best be expressed by thinking of them as being on opposite sides of the I; music which harmonically flits around both sides above a restful state can be more interesting than music that only deviates to one side of it.