Music Theory De-mystified BlogBasic Music Theory Lessons 2

B3. Melodic And Harmonic Minor

This post is one of a growing series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here. Please feel welcome to make a comment or ask a question.

A Potted History Of Modes And Scales

Early Western music was based on modes. Religious music favoured those modes which had a solemn quality appropriate for worship. Secular music favoured modes suited to dance music and ballad singing.

The earliest recorded Western music, back in the 9th century, is Medieval plainsong; religious chants which were sung in unison. In Medieval times, secular music was somewhat more innovative, first by accompanying a melody with a drone and percussion, and later by layering several melodies on top of each other to form pieces called motets. The resulting “harmonies” were quite different to what we consider harmony to sound like nowadays.

During the Renaissance era, from the 14th century to the beginning of the 17th century, everything was done on a large scale, and music was no exception. Famous composers were commissioned by the Church to create ever more grandiose works, to be performed in the great cathedrals of Europe. By now, the combined melodies were crafted to produce rich harmonies. Renaissance music was still based on the Medieval modes but notes were organised harmonically as well as melodically, producing a more sophisticated sound.

By the 17th century we had entered the Baroque period, where music was sponsored as much by the royal court as the Church. Secular music flourished in high society and the sombre tone of some of the modes became unfashionable. The Ionian mode, most frowned upon by religious society for its frivolous nature, became the prominent mode of the time, to the point where it became known as the major scale.

The major scale is different to most of the other modes in that there is only 1 semitone between the 7th note and the octave, whereas in most other modes it is 2 semitones. From the Baroque perspective, this provides a sense of resolution that most other Western modes lack.

Harmony as we know it had developed, with melodies now being accompanied by chords. Along with this came the sense of key. It became possible for a piece to start in one key and visit another key.

Baroque music has many of the characteristics we can recognise in popular music of the 50’s and 60’s such as simple rhythmic structures, chord progressions, parallel (close) harmonies, and in particular the popular use of the major scale.

As popular as the major scale was, there was still a need to express the darker musical emotions. The Aeolian mode provided this to some extent and became known as the minor scale. However, it was still considered too reminiscent of the starker sounds of earlier times.

Three Types Of Minor

During the early Baroque period two variations of the minor scale were developed, called the melodic minor and the harmonic minor. As their names indicate, they were initially developed for use in melodies and harmony respectively.

To distinguish between these and the original minor, we often refer to the Aeolian mode as the natural minor.

Collectively, regardless of which variation is in use, we just use the term minor, based on the key signature.

Melodic Minor

Below are the scales of A major and A natural minor. By having both on the same root note, we can compare their character.

Listen to the the Aeolian scale, the natural minor. As a melody, it doesn’t arrive very strongly at the octave compared to the major, due to the 2-semitone interval from the 7th note to the octave. It’s a bit reminiscent of the modal sound of medieval times.

It turns out that, although parallel major and natural minor scales have 3 different notes, the most musically significant difference between their modes is the 3rd note. The 3rd is 4 semitones above the root note in the major scale and 3 semitones above the root note in the minor scale.

As long as we have the minor 3rd, the character feels like minor.
If we start to play a minor scale but finish like the major scale, we get the best of both worlds. We still have the essential character of the minor mode but a more “melodic” flow up to the octave at the end.

The problem is, when you play these notes descending, it sounds weird. It feels like we’re listening to the major scale until suddenly, right near the end, we hit the minor 3rd. It’s a bit of a shock!

The solution composers settled on is a hybrid.

On the descent, the natural minor flows quite well. The 2-semitone jump from the 7th to the octave that made it so ungainly (from the Baroque perspective) on the ascent isn’t an issue when descending. If anything, it helps the descent get started. Have a listen:

This leaves us with a new kind of mode, unlike any other mode we’ve seen so far; one that goes up one way and comes down another way. The 6th and 7th notes of the minor are sharpened while ascending but are returned to their key signature while descending.

Because the changed notes are temporary, they can’t be shown in the key signature. Instead, they are written as accidentals. If you’ve forgotten how accidentals work, see 9. Accidentals, Sharpen And Flatten.

Courtesy Accidentals

Note that on the descent, the 7th and 6th notes are written with natural signs, even though that’s part of the key signature. This isn’t strictly necessary because they’re not in the same bar as the sharpened notes, but it’s common practice to put them in when they’re in the following bar. These are called courtesy accidentals or cautionary accidentals. We will learn more about how accidentals are used in the next lesson.

How To Find The Notes Of The Melodic Minor

Start with the natural minor
When ascending, sharpen the 6th and 7th notes. Remember, a flat becomes a natural, a natural becomes a sharp and a sharp becomes a double-sharp
When descending, cancel the sharpened notes (a double-sharp becomes a sharp, a sharp becomes a natural and a natural becomes a flat)

Try These…

Write out the following melodic minor scales for 1 octave ascending and descending, in 4/4, in either the treble or bass clef
Use the rhythm of the example below
For each scale, write the key signature and use accidentals as needed

Example

G melodic minor
E melodic minor
Bb melodic minor
C# melodic minor

For bonus points, name the relative major of each scale…

Answers at the end of this post.

The Harmonic Minor

The harmonic minor was developed to make it possible to play a major chord on the 5th note of a minor scale. As we haven’t looked at chords yet in this course, I will leave the full explanation of the harmonic minor till a later lesson.

Unlike the melodic minor, the harmonic minor’s notes are consistent. Only the 7th note is sharpened, both while ascending and descending.

Because only the 7th note is sharpened, the harmonic minor has a 3-semitone interval between the 6th and 7th notes. As a melody, this gives it a rather exotic quality, as none of the standard Western modes have a 3-semitone interval between consecutive scale notes. Hence it is less-often used for melodies than the melodic minor.

Like the melodic minor, the sharpened note is not reflected in the key signature. Both melodic and harmonic minors are considered variations of the natural minor and in fact, often the same piece can incorporate both variations.

How To Find The Notes Of The Harmonic Minor

Start with the natural minor
Sharpen the 7th note, both when ascending and descending

Try These…

Write out the following harmonic minor scales for 1 octave ascending and descending, in 4/4, in either the treble or bass clef
Use the rhythm of the example below
For each scale, write the key signature and use accidentals as needed

Example

D harmonic minor
B harmonic minor
F harmonic minor
G# harmonic minor

For bonus points, name the relative major of each scale…

Answers at the end of this post.

Augmented 2nd

The harmonic minor is a good example of the need for alternate interval names.
As intervals, consecutive scale notes are called 2nds. When they are 1 semitone apart the interval is a minor 2nd and when 2 semitones apart the interval is a major 2nd.

The interval between the 6th and 7th notes of the harmonic minor is 3 semitones. Consecutive scale notes have consecutive letters so the interval must be called a 2nd but it is 1 semitone larger than a major 2nd. In other words, it’s an augmented 2nd.

We can’t call F – G# a minor 3rd because then G# would have to be renamed as Ab, implying that there is a possible scale note in between, F – G – Ab.
The difference between a minor 3rd and an augmented 2nd is quite noticeable when hearing the same pitches in different contexts.

Key Signature Shortcut

To this day, the melodic and harmonic minors are more popular in most genres than the natural minor. Since both involve the use of accidentals, either on the 6th and 7th note or just the 7th note, the frequent or early presence of an accidental in the part would likely indicate that the piece is in a minor key.
A key signature can equally represent a major and a minor key. Usually we look for clues in the first and last bars to find the root note, so we know whether the key signature represents the major or minor key for that key signature.
If there’s a recurring accidental, the piece is probably in the minor key of that key signature.

You can check this by seeing if the accidental is the 6th or 7th note of the key signature’s minor key.

For example, in the key signature of 1 sharp (F#), the key could be G major or E minor. If the part contains a C# or D# in the first few bars, the piece is most likely in E minor rather than G major.

Sing Along

Almost all voices and pitched instruments can sing or play one octave starting on C. Listen to all three minors on C and compare their character. Learn to sing and play all three.

Once you’ve learnt these, try singing or playing them in different keys (on different root notes).

If you found this post helpful, please feel welcome to like, share or leave a comment. If you have any questions, leave them as a comment and I’ll respond as soon as I can. To stay up to date with new posts, please subscribe.

NEXT LESSON: B4. Accidentals Etiquette: How And When To Use Accidentals

PART 2 CONTENTS: Basic Music Theory Course Contents

Answers to Try These…

B2. Intervals 2: Augmented And Diminished Intervals

Context

There are times when intervals of the same number of semitones require alternate interval names.

When taken out of context, this difference can’t be heard, and in fact, without the right context there’s no reason to use an unusual interval name. However, the same size interval can sound unrecognisably different in different contexts and requires different note names and interval names to reflect this.

Even if you don’t use note names in your practice, it’s worth becoming acquainted with augmented and diminished intervals. You can definitely feel the difference in the appropriate context.

Augmented And Diminished

In 16. Intervals 1: Major, Minor And Perfect Intervals there was one interval which was unnamed; the interval of 6 semitones. There isn’t a note 6 semitones above the root note in either the major or minor scale so we can’t call it a major, minor or perfect interval. Instead, we describe it as being 1 semitone larger than a perfect 4th or 1 semitone smaller than a perfect 5th.

Just as a note can be sharpened or flattened, an interval can be augmented or diminished.

Augmented means that the interval is 1 semitone larger than the corresponding interval in the major scale (major or perfect).
Diminished means that the interval is 1 semitone smaller than the corresponding interval in the minor scale (minor or perfect).

Let’s look at the interval ruler on A:

The note 6 semitones above A could either be called D# or Eb.

If the interval is A-D# we call it an augmented 4th; a perfect 4th plus 1 semitone.
If the interval is A-Eb we call it a diminished 5th; a perfect 5th minus 1 semitone.

The same applies for other intervals with unusual note names. Most notes have two or more possible names, resulting in different interval names.

For example:

A to C# is a major 3rd
A to C double sharp is an augmented 3rd, 1 semitone larger than A to C#
D is a perfect 4th above A
Db is a diminished 4th above A, 1 semitone smaller than D to A

NOTE: Remember to always count intervals from the lower note to the upper note. Use the major and minor scales of the lower note to find the upper note and name the interval.

Example:

Interval names are based on note names as well as size, so even though A-C# and A-Db are the same number of semitones apart, they can’t have the same interval name.

A-C#

C# is the 3rd note of A major, so
A-C# is a major 3rd

A-Db

There is no Db in A major or A minor. There is a D natural, though, the 4th note of both A major and A minor.
A-D is a perfect 4th.
Db is 1 semitone lower than D, so A-Db is 1 semitone smaller than A-D.
A-Db is a diminished 4th.

In general, if the upper note of an interval doesn’t fit either scale of the lower note, look for the nearest note in the scale with the same letter.

If the upper note is 1 semitone higher than the equivalent note in the major scale, the interval is augmented.
If the upper note is 1 semitone lower than the equivalent note in the minor scale, the interval is diminished.

NOTE: Augmented and diminished intervals can involve the occasional double-sharp or double-flat, depending on the lower note.

If the lower note is a sharp, an augmented interval will most likely require the upper note to be a double sharp. Similarly, if the lower note is a flat, a diminished interval would probably require the upper note to be a double flat.

Don’t be concerned. Just stick to the method:

sharpen = 1 semitone higher without changing the note name
flatten = 1 semitone lower without changing the note name

Interval Names Summary

2nds, 3rds, 6ths and 7ths have four possible qualities. From largest to smallest they are augmented, major, minor, diminished.
4ths, 5ths and 8ths have three possible qualities. From largest to smallest they are augmented, perfect, diminished.

It’s possible to have an augmented 1st but a diminished 1st is meaningless. There’s no such thing as a negative interval. Intervals are absolute…
8ths can be diminished or augmented but they should be called eighths, not diminished or augmented octaves. By definition, an octave is a perfect 8th.

Here’s a list of all intervals within an octave, with examples on C showing all the interval names including augmented and diminished intervals for each degree.

Here’s the same list of intervals shown as an interval ruler on C.

Just a reminder: the scales used to count intervals are built on the lower note of an interval and serve as a ruler to measure the name of the interval, in this case an interval whose lower note is C. For an interval with a different lower note we use scales on the new note to measure the interval.

The interval ruler is no indication of the actual key of the piece! The actual key is determined by the key signature and the overall root note.

Why have two names for the same size interval?

Good question! Interval names are based on note names. Note names reflect a specific musical context. The same size interval can sound unrecognisably different in different contexts.

An interval name describes both the size of an interval and how many letters there are from the lower note to the upper note. This allows us to “reverse engineer” an interval name and arrive at the right note names as well as the right sound.

In the next lesson we will see a practical example of the use of an alternate interval name.

Why are there two note names for most notes?

There are actually more than two if you count double sharps and double flats…

The choice of note name depends on the context.

If a note belongs to the key of the piece, its name is determined by the key signature.
If a note doesn’t belong to the key, its name is based on which note in the key it replaces.

When reading a new piece, the reason for some note names may not be apparent. In the coming lessons we will encounter some examples where an unusual note name is required. You can see and hear two of these in Sleight Of Ear.

In the meantime, let’s assume that unusual note names are used for a reason, so interval names need to be able to reflect which note name is used.

How To Name An Interval

Write out the interval ruler; the major and *minor (phrygian) scales built on the lower note of the interval. One way to do this is to write out the major scale then flatten the 2nd, 3rd, 6th and 7th notes to get the *minor.
Look for the upper note of the interval in these scales.
If the upper note is in either scale or in or both scales, name it as we’ve already learnt, as a major, minor or perfect interval. You have the answer.
If it’s not in either scale, find the note of the same letter that’s closest in pitch to the upper note of the interval.
If the upper note is 1 semitone higher than the note of the same letter in the major scale, the interval is augmented.
If the upper note is 1 semitone lower than the note of the same letter in the *minor scale, the interval is diminished.

The degree is always the number of letters from the lower to the upper note, inclusive.

Try These…

Below is a blank interval ruler you can use as a template. For each of the following exercises, first write the scales of the lower note as per the template.

A. Name the following intervals, keeping the above method in mind:

A-G
A-Gb
C-C#
C-E
C-E#
Bb-Ab
Bb-Abb
D-A
D-Ab
D-G#

How To Name The Upper Note Of An Interval

Write out the interval ruler; the major and *minor (phrygian) scales built on the lower note of the interval.
For major, minor or perfect intervals, find the upper note by following where the degree and quality of the interval name intersect.
If the interval is augmented, sharpen the same letter note in the major scale.
If the interval is diminished, flatten the same letter note in the minor scale.

Try These…

B. Name the upper note of the following intervals. For the degree, count letters (including the starting note).

If the interval is augmented, sharpen the equivalent note in the major scale.
If the interval is diminished, flatten the equivalent note in the minor scale.

major 6th above G
augmented 6th above G
major 7th above G
augmented 7th above G
minor 3rd above E
diminished 3rd above E
perfect 5th above E
diminished 5th above E
minor 6th above C
diminished 6th above C

Answers at the end of this post.

Shortcuts

It may seem laborious to have to write out scales every time you want to name an interval.

If you know your keys well, you can do this in your head. In part, I have encouraged the learning of at least the key signatures of the major keys for this very reason. As we’ve seen, you can find the *minor by flattening the 2nd, 3rd, 6th and 7th notes. Key relationships also provide some shortcuts for remembering keys. Have a quick look at the relevant lessons from Part 1 if you’re not sure…

The good news is that there are a number of shortcuts to help us to name intervals without writing out scales. These will become apparent over the next few lessons.

NEXT LESSON: B3. Melodic And Harmonic Minor

PART 2 CONTENTS: Basic Music Theory Course Contents

Answers to Try These…

minor 7th
diminished 7th
augmented 1st
major 3rd
augmented 3rd
minor 7th
diminished 7th
perfect 5th
diminished 5th
augmented 4th

major 6th above G = E
augmented 6th above G = E#
major 7th above G = F#
augmented 7th above G = F##
minor 3rd above E = G
diminished 3rd above E = Gb
perfect 5th above E = E
diminished 5th above E = Eb
minor 6th above C = Ab
diminished 6th above C = Abb

B1. Syncopation Basics: Playing Off The Beat

A time signature has an inherent hierarchy of strong and weak points within the bar. Syncopation is the emphasis of weak parts of the time signature. This introduces a dynamic interaction between the time signature’s implied rhythm and the rhythm of the part; a sense of going “against the grain”.

The Back Beat

The simplest form of syncopation is to emphasise the weak beats instead of the strong beats. The classic example of this can be found in many popular music genres since the advent of rock & roll; the snare drum playing the “back beat”, emphasising beats 2 and 4 in a 4-beat bar.

A similar effect can be achieved on any instrument by accenting the weak beats. Below is an example of a quaver rhythm, first with accents on the strong beats, then on the weak beats.

Tap, clap or play along to the following rhythms:

Playing Off The Beat

The back beat is only syncopation in the broadest sense. The term syncopation typically refers to emphasising weak parts within the beat a rather than just the weak beats.

The most common example of syncopation within the beat is to emphasise the 2nd quaver of each beat, the “off-beats” or “and”s, instead of the beat itself.

The following example of a bar of quavers uses accents, first to emphasise each beat, then to emphasise each off-beat quaver. Listen to the rhythms then tap, clap or play along:

Listen again and this time, only tap on the accented notes.

Syncopation adds excitement to a rhythm. Even in rhythms which are largely on the beat, the odd syncopated moment adds life to a part.

In the drum rhythm below, there is a brief syncopation is in the second half of bars 2 and 4.

Ways To Syncopate

Syncopation can be achieved in 2 ways:

by emphasising a note or notes on a weak part of the bar as above, with an accent.

by de-emphasising a strong part of the bar, in particular by not playing a note there at all. This can be because there’s a rest or because the previous note is still sounding.

Note that when clapping or tapping, there is no audible difference between these two bars.

Zooming In

Syncopation doesn’t just refer to emphasising the off-beat quavers. A more aggressive version would be to syncopate by a semiquaver.

A couple of the rhythms we learnt in 20. How To Read Rhythms 1 had semiquaver syncopation within the beat, by not playing a note on the “and”, the 2nd quaver. We can see now why these felt harder to learn than the others… Here’s an example of a bar with these two rhythms. Tap or play along:

Once you’ve experienced it, syncopation feels quite “natural”. In many popular genres, singers seldom sing exactly on the beat, even if that’s how the melody is written. Instead, they instinctively apply a degree of syncopation so the melody doesn’t sound too rigid. Rhythmic players rely on syncopation to add dynamics and drive.

Learning To Syncopate

Like many rhythms, syncopation is best learnt initially using a metronome. The secret to being able to syncopate is to feel the beat – to know where the beat (or strong beat) is, and then to know what relationship your note has to the beat.

Some musicians find it easy to tap the beat with their foot while playing. If this works for you, then by all means tap instead of using a metronome. However, many find it awkward to tap on the beat while playing off the beat, especially when first learning a new rhythm.

Foot Tapping Tip: In simple time, use the action of lifting your toes between taps to represent the half-beats; the “and”s.

If the rhythm seems tricky, remember to slow down the tempo and zoom in, as discussed in 20. How To Read Rhythms 1.

Ultimately, once you know a rhythm well enough to be able to feel it, you will no longer need the metronome. Metronomes can become quite annoying over time(!) so it’s worth weaning yourself off it as soon as you can feel the rhythm properly.

Mixed rhythms

Many parts, rhythmic as well as melodic, have a degree of variation in their rhythm, often achieved by brief syncopations in between overall on-beat rhythms.

Try These…

Play the movies below and tap the rhythms with your hand on a bench top, or if you prefer, clap. Listen carefully to the metronome click so you remain aware of the beat…

Once you’ve learnt each rhythm, play it to a metronome at 60 bpm without the movie. Gradually increase the tempo to 100 bpm or more. You can play along to the following movies of the rhythms at 100 bpm to see how you went.

Being able to tap the beats with your foot while playing is a useful skill. Practice tapping the beats with your foot, together with the metronome, while playing or tapping/clapping the above rhythms with your hands. As you settle in, stop the metronome and try it by yourself.

Notation Tip

Rhythms are usually notated so that it’s clear to see where the beats are. For shorter notes, this is indicated by beaming. For longer notes, the note is split into shorter notes and joined by a tie (see 21. Note Values 2: Ties).

When crotchets fall halfway between beats, on the “and”s, they can be written as crotchets: it’s such a common occurrence that most musicians, once they see a crotchet after a single quaver or quaver rest, are familiar with this shortcut.

However, crotchets which are a semiquaver off the beat must be split and tied to show where the beats are, otherwise the music is too hard to follow.

In the correct example above we can see that the next note starts just after each beat. The position of each beat is clearly shown by the beaming.

This post is one of a 2-part series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here. Please feel welcome to make a comment or ask a question.

NEXT LESSON: B2. Intervals 2: Augmented And Diminished Intervals

PART 2 CONTENTS: Basic Music Theory Course Contents