Teach Yourself Music Theory – 21.) Polyrhythms and Hemiolas

As you can see from the title, we are going to talk about some new concepts and add new vocabulary into our musical terminology usage.

Polyrhythm, is the juxtaposition of two different beat divisions happening at the same time. This will create an interesting composite rhythm of the combining beat divisions. Let’s take a look:

Above is a piece of music with a lot of beat divisions working together to create one polyrhythm. We can see that the C4 pitch is played on every down beat of the 3/4 measures, but the arpeggiation (breaking apart of a chord) of the C major triad below is in a division pattern similar to a 6/8 time signature. Play it out and you will hear it.

In the melody line, we see four notes in equal length of a dotted eighth-note. Within the 3/4 time signature, we have four notes of even value going against the quarter-note pulses and 6/8 division grouping arpeggiation. So that too is another addition to the overall polyrhythm.

A hemiola, is similar to a polyrhythm in that it goes against the conventional beat division – but it is more defined of when normal groupings of three become groupings of two:

Here is another exaggerated version of a hemiola, going from odd to even groupings:

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Tip #174 – Reimagining Purpose of a Circle-Of-Fifths Progression

To some people, a circle-of-fifths progression (a sequential chord progression with root movement all done by perfect fifths) is a very artistic way of composing music. Others may find it predictable because you know well in advance where the next chord is going to.

Take a look at this one for example:

You can view this as a simple circle-of-fifths progression, but how about another way:

You can also reimagine this as an overlay of IV – I – V movements. And now when you are in this mindset, you can control how to get out of the predictable pattern into a set key with the understanding that you have the momentum of a IV – I – V progression.

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Teach Yourself Music Theory – 20.) Mixing Beat Divisions

To remind: when you are in simple meter (4/4) the beat is easily divided into 2s or 4s, and when you are in compound meter (12/8) the beat is divided into 3s or 6s. Review old posts if you are not familiar with these concepts.

However, just because you are in simple meter doesn’t mean that you can’t incorporate compound meter divisions.

Take an example below:

We know that this piece is in duple meter because the time signature is 4/4, but there is a figure notated with a “3.” This is called a triplet, and it appears in duple meter pieces to tell the performer to divide the beat into three eighth notes of even length instead of two – just as you would find in a compound meter.

This can happen in reverse, too…

Thae a look now at this example:

This piece is in compound meter (12/8 and the beat is divided into 3s), but there are two figures – one noted with a “2” and the other with a “4.” They are called duplets and quadruplets respectively, and they divide the beats in compound meter pieces into even divisions.

Practice performing switching between these different divisions.

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Teach Yourself Music Theory – 19.) Tetrachords and Pentachords

Okay, so we have learned a lot of scales so far. This can become confusing and jumbling trying to remember them all and how different they are from each other.

A way to remember is to break them apart into smaller pieces. This is so you can compare and contrast between the scales – essentially see what makes them similar and different.

We can break them up into different groups.

A tetrachord (tetra – meaning “four”) is not a chord, but a group of 4 consecutive notes.

Take a major scale for example and split it down the halfway. Compare the two different tetrachords:

You will see that they are formed of the same interval pattern of W-W-H (or M2-M2-m2). These are major tetrachords, because they are distinctive of the major scale.

Another way to break scales into smaller groups is into pentachords, groups of 5 consecutive notes.

Once again, this is to help understand and memorize the structure/functions of scales.

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Teach Yourself Music Theory – 18.) Harmonic and Melodic Minor

Review time! What scale is this?:

If you said “a natural minor scale” you are correct! Don’t worry if you didn’t get the answer correctly, you can review on all the past posts on music theory.

We can tell that this is a natural minor scale because…

1.) The key signature has no sharps or flats, and it starts on the A pitch

2.) The scale is built in the intervallic pattern of all natural minor scales of M2-m2-M2-M2-m2-M2-M2.

Now, it is time to introduce two different kinds of minor scales.

The first is called the harmonic minor scale, and it is made by raising the seventh scale degree (the subtonic) up a half-step (the leading tone). It would look like this:

As the name goes, it is used for harmonic purposes to achieve a dominant V sound. More on that soon!

The second is called the melodic minor scale, and it is made by raising the sixth and seventh scale degree up a half-step. HOWEVER, that is only when you are ascending up the scale. Those scale degrees return back to their natural position as you descend down the scale:

As the name goes, it is used for melodic purposes to retain a “minor” sound with the lowered third degree, but have leading motion in the sixth and seventh degrees to resolve to the tonic.

Play those scales in different keys to see how they sound.

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Teach Yourself Music Theory – 17.) Solfège Syllables

Cue The Sound Of Music

Anyways, this is a continuation once again of explaining the jargon used amongst musicians when referring to scale degrees.

Solfège Syllables is a practiced used commonly with sight-singing (singing a musical work for the first time without prior rehearsal or practice) to train the performer how to recognize the intervals between pitches just by looking at a piece of sheet music.

“How is this done,” you ask?

Well, many of you might have heard of “do-re-mi-fa-sol-la-ti-do,” and that is basically solfège singing. The purpose of it is that when you assign any pitch to “do” (or to any syllable as a matter of fact) you can figure out how to sing the other syllables because the muscles in your vocal chords know the sonic distances between each syllable.

Still sounds complex?

Okay, let’s take a C Major scale. Play it and sing it. Now sing it with “do-re-mi-fa…”

Good! Now, choose any pitch you want (other than C) and make that “do.” From there, if you copy exactly what you did when you sang solfège syllables, you will be able to sing a major scale from any key!

Below is the list of solfège syllables and the chromatic alterations:

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Teach Yourself Music Theory – 16.) Calling Pitches by Scale-Degree Name

Today’s topic is more so about covering jargon used in music than actually understanding of music. However, the use of this terminology can help clear-up some confusion from previous lessons as well as aid in helping understand the next lessons.

When we talked about the major and natural minor scales, we talked about how they are made up of 7 different pitch classes with a repeat at the octave. Previously, we have just been calling the pitches of the scale just by there ascending number.

So, for example: we call the second note of the scale the second degree.

Well, there are some specific names for those pitches that make up the scales:

Now, going back to our previous example: when referring to the second scale degree of the major or natural minor scale, we would say the “supertonic” of the scale.

To further drill-in this terminology, let’s review the major pentatonic scale.

Remember that the major pentatonic scale has the same pitch class collections as the major scale… but 2 pitches less (hence how “penta” means “five”).

What scale degree names are in common with the major scale AND the major pentatonic scale?

Looking at the chart above, it would be:

  • The tonic
  • Supertonic
  • Mediant
  • Dominant
  • and submediant

And there you! That’s how you name pitches by their scale-degree names.

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