Tag: teach yourself

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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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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Teach Yourself Music Theory – 15.) Building Pentatonic Scales

As of right now, the only scales we have covered are those with 7 different pitch classes with a repeat of a note at the octave.

But there are other common scales that use less notes.

The pentatonic scale (the “penta” prefix meaning “five”) is a scale built from 5 different pitches within its pitch class collection with a repeat at the octave. This scale is commonly used in many genres of music from rock, to jazz, folk, pop, world, etc.

A good argument as to why these scales are so widely used is because they avoid certain dissonances. You will see why shortly.

First, let’s start by building the major pentatonic scale.

A major pentatonic scale is made up of a pattern of notes set apart from each other in an ascending manner of M2-M2-m3-M2-m3 from the root to the octave:

Notice how the scale and intervallic distances do not contain anything to form dissonances (m2, A4, d5, M7, etc.). Also, take a look at how the scale is very similar to that of a regular major scale, but is missing the fourth and seventh scale degrees.

Just like every major scale has a relative natural minor scale, so will every major pentatonic scale have a relative minor pentatonic scale.

To build a minor pentatonic scale, you just have to use the same pitch class collections as the relative major pentatonic scale, but start on the sixth scale degree. Or, you can also build it by using the intervallic pattern of m3-M2-M2-m3-M2:

Similarly, it looks like a natural minor scale, but it is missing a few members. Hence, that is why the pentatonic scale is called “penta;” because it is 2 pitches short of a major or natural minor scale, making it 5 instead of 7.

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Teach Yourself Music Theory – 14.) Key Signature

A key signature is a marking of sharps or flats found at the beginning of a piece of music (or section) right after the clef. It is used to tell the performer what pitches are to be sharpened/flattened throughout, which pitch collections are used, and what is the center of tonality.

First, let’s take a look at the sharp keys:

With every sharp, the respective major/minor key goes up a perfect fifth. Also, notice that the addition of sharps in the key signature form a pattern of { F# – C# – G# – D# – A# – E# – B# } and are placed in there respective place on the staff lines.

So, if the piece has one sharp in the key signature, we can tell that it is in either G Major / e minor and that we must play F# throughout the entire composition.

Now, let’s take a look at the flat keys:

Once again, we can see a similar pattern with the respective major/minor key going DOWN a perfect fifth with each flat added to the key signature. Also, the flats work in a backwards pattern from the sharps, going { Bb – Eb – Ab – Db – Gb – Cb – Fb } and still be placed on the correct line of the staff.

So, if the piece has four flats, we know to lower those notes down and play in the equivalent pitch collection of an Ab Major / f minor key.

Okay, so now how do we tell what key a piece of music is in?

  1. First, check the key signature to decipher how many sharps or flats it has.
  2. Second, look at the beginning and end of the piece and see what scale degree it lands on.
  3. Third from the information gathered, make a educated conclusion as to where the music is focused around – a major or minor key.

And there you go. Unfortunately, there are some exceptions to the guideline, but above all gather information and make a supportive conclusion as to where you think the piece of music lives in – being either a major or minor key within the given key signature.

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Teach Yourself Music Theory – 13.) Pitch-Class Collections of Natural Minor Scales

Continuing with the idea of pitch-class collections and how they can form scales, let’s introduce a new scale: the natural minor scale.

To make a natural minor scale, one has to have a collection of pitches that in ascending order go in an intervallic pattern of whole-step, half-step, whole-step, whole-step, half-step, whole-step, and whole-step back to the original pitch. One can also think of this as M2-m2-M2-M2-m2-M2-M2.

Take a look at the composition below, write the pitch-class collection, and then arrange the pitches into an ascending manner fitting the pattern of the natural minor scale:

If you did it correctly, you would get {F#, G#, A, B, C#, D, E, F#}, which means this composition uses a F# minor scale…

…but wait, don’t the same pitches used also make up the A Major scale?

That is correct! For every major scale, there is its own relative natural minor scale. All you have to do is go down a minor-third interval (or up a major-sixth interval) from the original major scale to find the relative minor scale. So C major is A minor, G major is E minor, E major is C# minor, etc.

Now, how can well tell if a song is using a major or minor scale? well, that will be saved as a topic for next time.

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Teach Yourself Music Theory – 12.) Pitch-Class Collections and Major Scales

Read, analyze, play, and/or listen to this compositional segment below:

Now, write out all of the note letter-names that you see where used in this small composition.

You should get (in order of appearance): { A, C#, E, F#, D, B, G#}

What we have written above is the composition’s pitch-class collection, or a collection of all the pitches listed by their letter-names used.

Time to introduce a new concept. A scale, which is a pitch-class collection but organized in a ascending/descending manner in an alphabetized way.

Which… using the same example above, if we put the pitch-class collection in an alphabetical order, it would be: {A, B, C#, D, E, F#, G#}

So, what kind of scale is this? Well, to spoil the answer – this is a major scale. But how can we tell? Just look at the intervallic distances between the notes.

A major scale is made up of a pattern of notes set apart from each other in an ascending manner of whole-step, whole-step, half-step, whole-step, whole-step, whole-step, half-step (which returns to the starting pitch). You can also think of this as M2-M2-m2-M2-M2-M2-m2.

So now, let’s take a look back at our pitch-class collection:

Does it match the pattern of the major scale interval formula? Yes it does!

Try now for an exercise by taking any starting pitch and see if you can build a major scale of your own!

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