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Parallel Chords

To put it concisely, both relative and counter parallel chords are those that have a strong connection to the main chord. For example, considering the Cmaj7 chord, its relative chord is Am7, and the counter parallel chord is Em7. Why?

Parallel Chords

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The logic in this case is verysimilar to the previous case, except that everything will be the other wayaround. As a rule, the relative and counter parallel chords of a minor chordwill always be major, and to find them just do the following:

In the study of harmonic functions, you may notice that the relative and counter parallel of strong function chords result in medium-strong or weak function chords. And you will also discover that the IIIm7 chord can be considered both of weak tonic function and of weak dominant function, after all it is relative to V7 and counter parallel to Imaj7.

In a circle, parallel chords of lengths 2, 3, and 4 determine central angles of , , and radians, respectively, where . If , which is a positive rational number, is expressed as a fraction in lowest terms, what is the sum of its numerator and denominator?

All chords of a given length in a given circle subtend the same arc and therefore the same central angle. Thus, by the given, we can re-arrange our chords into a triangle with the circle as its circumcircle.

Understanding the concept of relative and parallel keys is a must for any decent musician. Relative minor? Parallel major? These music theory terms are a lot easier than they might seem. Let's learn about relative and parallel keys now.

It's worth looking at relative chords a little closer. With a C major chord and an A minor chord side by side, we immediately see that they both share two of their three notes: C and E. If we extend these triads to four notes, they even have three notes in common: C, E and G. From this it's easy to understand how closely related relative chords are. They're so closely related that in functional harmony, a relative minor chord can take the place its relative major chord. Both C major and A minor play the same "harmonic function" (e.g. a tonic function in C major or a pre-dominant function in G major).

Some scientists even believe the 251 progression was the original cadence that later developed into the classic 451 by replacing the first minor chord with its relative major (see next section)! This theory sounds convincing, because 251 not only has the functional progression of pre-dominant to dominant to tonic, but also has a sequence of falling fifths in the bass - one of the strongest forces in music theory. Anyway, we only need to remember: 251 and 451 are related via the magic of relative chords.

That seems a lot simpler than it is. While the root stays the same in a parallel key relationship, the accidentals change dramatically. You can see this when looking at parallel keys in the circle of fifths:

You can view parallel keys as the cousins of relative keys: While relative keys keep all accidentals the same, but change the root, parallel keys keep the root the same, but change the accidentals.

Using parallel keys can sound more sophisticated due to the drastic move along the circle of fifths. It is certainly the more obvious sound compared to relative keys. So use parallel keys for the more impactful effect and relative keys to be more subtle.

Instead of just substituting a chord with its minor parallel chord (e.g. C major with C minor) many songs "borrow" chords from the entire parallel key. This is why you encounter non-diatonic chords like Eb major, F minor or Ab major in the key of C major quite frequently. Two examples might illustrate this:

It sounds familiar to our ears, yet these chords come from two different keys: C major (chords C and F) and C minor (chord Eb). While you could just say rock guitarists are lazy and just slide the major chord voicing up the fretboard ?, the underlying music theory actually makes sense: The Eb chord is a borrowed chord from the parallel C minor key.

With parallel minor we tend to think more about the whole parallel key instead of single chords (as we do in relative relationships). This is in the nature of parallel minor, since it actually has different chords due to the different accidentals.

I have seen less use of the parallel major key in actual songs compared to parallel minor or relative keys. Nevertheless you should know about this twin of parallel minor to extend your harmonic choices when writing in a minor key. And if you know any songs that use parallel major, please send me a message with the song!

You might have noticed that we can talk about relative/parallel keys and relative/parallel chords. Sometimes the distinction is important, sometimes it's not - but I thought clarifying this matter briefly does not hurt.

Talking about the relative minor key of C major doesn't give us any new chords to choose from. The chords of A minor (the relative key) are exactly the same as those of C major. If we apply the concept of "relative" to single chords, however, we get a possible substitution chord for each major chord in the key. So with "relative" we mostly think about relative chords.

Talking about the parallel minor key C major, however, gives us a whole set of shiny new chords we can borrow! So with "parallel" we mostly talk about the whole key instead of single parallel chords. Simply replacing a major chord by its minor parallel chord can certainly work (like in the plagal cadence Fm C), but in actual songs it is far more common to borrow other chords from the entire parallel key (like C Eb F).

Sometimes it pays to combine the concept of a parallel and relative chords to pick the right chord from a parallel key. For example substituting a borrowed Eb major chord for a C major chord can be explained in these two steps: First replace C major with its parallel minor chord C minor, then replace C minor with its relative major chord Eb.

An important topic with parallel keys is the idea of borrowing chords. Borrowing a chord means to widen your set of harmonic choices by also using ("borrowing") chords from the parallel key. In C major for example, you would only have seven chords to choose from (aka diatonic):

So instead of harmonizing a melody note G with the chords C, Em or G, you can also harmonize it with Cm, Eb or Gm. We already saw the example of the "rock progression" above. The awesome backdoor progression is another example of borrowing chords from parallel minor.

If you are a non-native English speaker or you have been trained in functional harmony, you might be surprised that the abbreviation for "Tonic relative" chord is Tp!? This comes from the German origins of functional harmony and it can be pretty confusing: "parallel" in German means "relative" in English ?. Check out this interesting fact in my article Parallel or Relative minor? (coming soon).

Understanding relative and parallel keys is a basic skill for any decent musician. Now you have a thorough understanding of the two concepts "relative" and "parallel" as well as their application to whole keys or single chords.

While a using chords from the relative key does not change the sound a lot, borrowing chords from the parallel key has more drastic effects. This is because of relative keys having the same accidentals (and thus the same chords) as their relative counterpart (e.g. C major and A minor). The chords of A minor are still diatonic to C major (e.g. the chords Em or F). Parallel keys however have different accidentals than their parallel counterpart! They essentially shift you around the circle of fifths by three steps (e.g. C major (no accidentals) and C minor (3 accidentals).

To practice the concept of relative chords and keys, try to substitute an occasional chord with its relative counterpart. Take your favorite song or one of your own compositions. Randomly replace a few chords and listen to the effect.

To practice the concept of parallel chords and keys, try to substitute the occasional chord with any chord you borrow from the parallel key. Again take your favorite songs or any of your own pieces. Get used to the sound and the effects you can achieve.

In a circle, parallel chords of length $2$, $3$, and $4$ determine central angles of $A$, $B$, and $A+B$ radians, respectively, where $A+B

In this explainer, we will learn how to use the parallel chords and the parallel tangents and chords of a circle to deduce the equal measures of the arcs between them and find missing lengths or angles.

While it is outside the scope of this explainer to prove this theorem, it can be proven in a minimal number of steps using the inscribed angle conjecture and properties of angles in parallel lines. We will now apply this theorem alongside other properties of chords to find the measure of an arc.

In our previous examples, we have applied the theorems of parallel chords and tangents in a circle to find missing values given information about their chords and tangents. These properties can also be applied alongside geometric properties of polygons to help us find missing values. We will demonstrate this in the next example.

Since ???? is a rectangle, ?? is parallel to ?? and ?? is parallel to ??. Since these line segments are chords of a circle, we can use the following theorem: the measures of the arcs between parallel chords of a circle are equal.

A chord progression is a set of chords following each other in a specific order. There are certain patterns as well as certain pairs of chords that do not sound especially good together. Regardless, there exist thousands of ways to combine a limited number of chords.

You can combine the Tonic, Subdominant and Dominant chords (degrees I, IV and V; 1st, 4th and 5th degree) in any order you like. They will always make harmonic sense and have been staples of western musical vocabulary for many centuries. 041b061a72


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