Ear Training

Wouldn't it be nice to be able to (instantly) recognize intervals when a song is played on the radio? If you have been playing music for years, it's probably easy but for the rest of us, mortals, it might be a tad difficult.

A good way to recognize intervals is to match what you hear with the beginning of a well-known song. If you have a browser (who doesn't?), there's this free web application that enables you to play an interval and find the matching song. Now, even if you ace the tests, it doesn't mean that you'll be able to play anything by ear but you'll probably be one step closer.

The web site where you can find this neat little web app is:

Free Online Ear Training

It's a nice little flash application which I really wish I had written. Of course, I know next to zero about flash, so that might have been a tad difficult. Below are a couple of videos that explain the finer points of this fine application.

Updated: Getting started using my free ear trainer from Jimmy Ruska on Vimeo.

ear trainer, statistics feature from Jimmy Ruska on Vimeo.

Tone Stability

A tone is not made up of a single frequency wave, it has many overtones (also called partials or harmonics). The main tone at the lowest frequency is called the fundamental. As you order those overtones according to the pitch, you form a harmonic series with the fundamental being the root (lowest tone). The amplitude, or strength, of an overtone depends upon how far it is, pitch wise, from the fundamental tone (in other words, how far it is in the harmonic series). The farther the overtone is from the fundamental, the weaker it is.

So, when you play a C on the keyboard, you get the fundamental at the C frequency but also quite a few harmonics at higher frequencies, several of them being themselves C notes, but at higher octaves. The more harmonics the tone has at higher octaves and the closer those are in the harmonic series, the more stable the tone is.

Looking at the major scales (if you need a refresher course on scales, feel free to go back to the scales post):

The degree 1 note has 4 harmonics at the same degree (at higher octaves): 2nd, 4th, 8th and 16th harmonics.

The degree 2 note has 1 harmonic: 9th harmonic.

The degree 3 note has 2 harmonics: 5th and 10th harmonics.

The degree 4 note has no harmonics.

The degree 5 note has 3 harmonics: 3rd, 6th and 12th harmonics.

The degree 6 note has 1 harmonic: 13th harmonic.

The degree 7 note has 1 harmonic: 15th harmonic.

As you can see, the degree 1 note is always the most stable. Only two other notes are stable: degrees 3 and 5, with 5 being more stable than 3. All other degrees are unstable. This gives us the following stability order (from most stable to least stable): 1 5 3 6 2 4 7.

So, if you are playing in the key of C major:

the notes C (degree 1), G (degree 5) and E (degree 3) are stable and
the notes A (degree 6), D (degree 2), F (degree 4) and B (degree 7) are unstable.

What does this mean for music composers? Well, unstable notes usually need to be resolved downward, except the 7th (in the stability order) that's commonly resolved upward. Unstable tones create a sense of expectation and give melodies forward motion until they get resolved (if they do get resolved).

Looking at the stability order:

2 resolves naturally to 1,
4 resolves naturally to 3,
6 resolves naturally to 5 and
7 resolves naturally to 1 (at next higher octave).

Unstable notes don't have to resolve to their natural resolutions, they certainly can "skip" resolution levels; they don't even have to resolve at all (if you don't want to). By generating expectation in the ears of the listener, unstable tones provide "kinetic" energy to melodies.


In this video, we show how an unstable tone at the end of a melody can leave a feeling of expectation or that's something is amiss. We resolve the unstable tone (D) by downward motion to the most stable tone of all (C) and everybody is happy again.

Arpeggios

An arpeggio refers to playing the notes of a chord in sequence, rather than at the same time.

If the instrument at your disposal is monophonic (can only play one note at a time), you cannot play chords the way they were meant to be played, so you need to play arpeggios instead.

Sounds familiar? Indeed, the (real) KORG MS-10 is a monophonic synthesizer. On the other hand, the Nintendo version (KORG DS-10) has two voices (SYNTH1 and SYNTH2) and four drum tracks so we could probably use three drum channels to play chords, I guess. It seems however to be quite painful and it kinda defeats the purpose of having drums.

If the the first oscillator, VCO1 plays the first note of chord, the second oscillator, VCO2 could be used to get the second note of the chord, by shifting the pitch of the first oscillator. If you don't mind devoting two synths for playing chords, then you could possibly play triads and quads that way.

Anyways, it seems that if we really want to play chords on the DS-10 without getting too complicated and tying up too many synths, we probably will have to "arpeggiate" them.


In the video above, we make use of arpeggios to simulate chords. The first voice (SYNTH1) has the first four pitches of the C major scale (C, D, E, F) played as quarter notes. The second voice (SYNTH2) accompanies the first voice with the corresponding first four diatonic chords (C, Dm, Em, F).

Rhythm

Rhythm is controlled by the note values (and rest values) and the time signature.

Note and rest values


From left to right, on the upper staff (treble clef), we have a whole note, half note, quarter note, eighth note and sixteenth note. On the lower staff (bass clef), we have a whole rest, half rest, quarter rest, eighth rest and sixteenth rest. This is by the way Music Studio from Activision on the Commodore 64.

Time signature

The time signature appears at the beginning of a music piece, as two numbers, one on top of the other. The top number indicates the number of beats per measure. The lower number indicates the note corresponding to one beat.

An heavily used signature is 4/4, also known as C, for common time. With 4/4, you have 4 beats per measure and one beat corresponds to a quarter note. So, within a measure, you can have one whole note, two half notes, four quarter notes, etc.

You of course have quite a few time signatures at your disposal. Another common signature is 3/4 where you only have 3 beats per measure. That's a signature used for waltzes for example.

It is usually pretty easy to tell the number of beats per measure (the upper number in the time signature) by just listening to when the kick drum is hit.

On the Nintendo KORG DS-10, we have 16 steps per pattern as the default. It kinda means the signature is 4/4 (assuming the pattern itself represents a measure) and that each step is a sixteenth note. The time signature on the KORG DS-10 is certainly not limited to 4/4. If we change the number of steps in the pattern to 12, we can possibly have a 3/4 signature and play waltzes (if we really want to).



In this video, we use the legato effect to change the duration of notes from sixteenth (default) to quarter notes. Note that the BPM (beats per minute) has been quite lowered so that we can easily follow the 16 steps of the pattern as the beat goes on.

Harmony

Harmony encompasses the study of chords and how they relate to each other. Here, we focus on diatonic harmony, that is, the study of chords of a given scale.

If you need to refresh your memory about all this, now would be a good idea to go back to chords, intervals and scales.

Major harmony

A scale contains seven chords that use the notes of a given scale. Just like diatonic notes, these seven chords are diatonic because they are said to belong to the scale.

In the following, we are gonna build those seven chords considering the C major scale:

1 2 3^4 5 6 7^8
C D E F G A B C

The first chord consists of the root, the 3rd and 5th degrees of the scale, that is, C-E-G, which we recognize as being the C major triad, or C. It is named the I chord. The roman numeral 'I' stands for one here. It is capitalized to indicate that this is a major chord.

The second chord is built with degrees 2, 4 and 6, that is, D-F-A, which we know is the D minor triad, or Dm. It is named the ii chord. The roman numeral is this time not capitalized to indicate that it is a minor chord.

The third chord in the progression is built with degrees 3, 5 and 7, that is, E-G-B. This is the E minor triad, or Em. It is the iii chord.

We do the same thing for the next degrees and get:
F for the IV chord,
G for the V chord,
Am for the vi chord,
B° (Bdim) for the vii° chord.

We have the following progression for the C major scale:

C Dm Em F G Am B°

This is the general sequence of chords for major scales (in terms of quality):

I ii iii IV V vi vii°

It indicates that the chord qualities go in the following order:

major minor minor major major minor diminished

We could write the chord progressions for all major scales (12 of them) and we would get the same exact progression in terms of quality. This is why these chords get their own roman numeral numbering, which indicates the position in the progression but also the quality.

Minor harmony

We can do the exact same thing we did for major scales to the minor scales. We would obtain the following progression:

i ii° III iv v VI VII

Just like with scales, the diatonic chords of a minor scale follow the same progression as those of a major scale, but starting from the 6th.

Major harmony with seventh chords

Why not do with four what we can do with just three? Seventh chords go to the next level by adding a fourth note to the triads.

To build a seventh chord, we consider the triad and add a seventh degree pitch. We also add a '7' at the end of the corresponding triad's name (if the chord is major, we also add 'maj' before the '7'). For example, the first chord of the C major scale is Cmaj7 made up of the 1st, 3rd, 5th and 7th degree pitches.

The chord progression becomes:

Imaj7 iim7 iiim7 IVmaj7 V7 vim7 viiØ7

In the C major scale (key of C), the corresponding chords are:

Cmaj7 Dm7 Em7 Fmaj7 G7 Am7 Bm7♭5

The V chord is a dominant seventh chord. The vii chord is called a minor seventh flat five chord also known as half-diminished (hence the Ø symbol).

This pretty much ends our delving into music theory. If you want to know more about it, you may want to read some music theory books, for example, Music Theory: a practical guide to all musicians by Barrett Tagliarino.

Chords

Before going into chords, it would be a good idea to go back (if needed) to intervals and scales.

Chords are notes being played at the same time, three notes or more. The simplest chords are chords built using 3rds (as in intervals), they are called triads. We are going to look into these first before getting deeper into chords and harmony.

Major Triad

The major triad consists of a root, a major 3rd and a perfect 5th. To build it, we consider the major scale rooted at the chord pitch and get the major 3rd and perfect 5th (just like we did when looking for intervals). A major triad is referred to by the name of the root.

Let's look at getting the F major triad:

1_2_3^4__5_6_7^8
F G A B♭ C D E F

The major 3rd is A and the perfect 5th is C, which gives us F-A-C for the F major triad (F).

Minor Triad

The minor triad consists of a root, a minor 3rd and a perfect 5th. A minor triad is referred to by the name of the root followed by 'm'.

If we look at how we obtained the F major triad, all we need to do is diminish the major 3rd by a half-step to get the minor 3rd, A♭. The F minor triad (Fm) is then F-A♭-C.

A minor triad could also be obtained using the natural minor scale with the same root as the chord. In that case, we would need to consider the root, 3rd and 5th degrees.

Diminished Triad

The diminished triad consists of a root, a minor 3rd and a diminished 5th. A diminished triad is referred to by the name of the root followed by 'dim' (or °).

If we look at how we obtained the F minor triad, all we need to do is diminish the perfect 5th by a half-step to get the diminished 5th, C♭. The F minor triad (Fm) is then F-A♭-B. Remember that there is a natural half-step between B and C, and therefore, if we diminish C by a half-step, we get B. We could have of course looked at the F major triad and diminish both the major 3rd and perfect 5th degrees.

Augmented Triad

The augmented triad consists of a root, a major 3rd and an augmented 5th. An augmented triad is referred to by the name of the root followed by 'aug' (or +).

Again, if we look at how we obtained the F major triad, all we need to do is augment the perfect 5th by a half-step to get the augmented 5th, C#. The F augmented triad (Faug) is then F-A-C#.

Suspended Triad

The sus4 chord consists of a root, a perfect 4th and a perfect 5th.

The sus2 chord consists of a root, a major 2nd and a perfect 5th.

As you have probably noticed, those are not really triads since they are not built using thirds.

Inversion

The way the notes composing the chord are arranged is called voicing. When the root of the chord is the lowest note, the chord is said to be in root position.

If the root is raised by an octave, the 3rd degree note (or 2nd note in the chord construction) becomes the lowest note of the chord. This is called first inversion.

If the root and 3rd are both raised by an octave, the 5th degree note (or 3rd note in the chord construction) becomes the lowest note of the chord. This is called second inversion.

A chord inversion is indicated by adding to the chord name a slash '/' followed by the lowest (bass) note.

Intervals

The interval (in pitch) between two notes has two parts: the quantity and the quality. Intervals are defined with a number (the quantity) and a name (the quality). Quality is either major, minor, perfect, diminished or augmented. Intervals are either going up (ascending) or down (descending).

If you have trouble with the notation and/or building major scales, please go back to the post about scales.

Major and perfect intervals

Intervals based on the major scale are either major or perfect. For ascending intervals, given the starting pitch (note), we use the major scale rooted at that starting pitch to find the pitch (note) that corresponds to the major or perfect interval we are looking for. The number in the interval, the quantity, is the degree of that pitch.

The term major refers to degrees 2 (major 2nd), 3 (major 3rd), 6 (major 6th) and 7 (major 7th).

The term perfect refers to degrees 1 (perfect unison), 4 (perfect 4th), 5 (perfect 5th) and 8 (perfect octave).

For example, to find the ascending perfect 5th from F:

1_2_3^4__5_6_7^8
F G A B♭ C D E F

Since we need to find an interval starting from F, we build the F major scale (major scale rooted at F, our starting pitch). Please, remember that there is a natural half-step between B-C and E-F (that's really fundamental to know). Once we have the F major scale laid out, all we need to do now is find the pitch corresponding to the quantity of the interval we are seeking, that is 5. The ascending perfect 5th from F is thus C.

To find descending intervals is pretty much the same thing except that we need to consider the major scale formula counting backwards from the degree indicated by the interval.

For example, to find the descending major 6th from C:

8^7_6_5__4^_3_2_1
____C B♭ A♭ G F E♭

To get the descending major 6th from C, we use the backwards major scale formula starting from C but at degree 6. This gives us E♭ as the descending major 6th from C.

Minor, diminished and augmented intervals

When we diminish the quality of a major interval (by a half-step), it becomes minor.

When we diminish the quality of a perfect interval, it becomes diminished.

When we diminish the quality of a minor interval, it becomes diminished.

When we augment the quality of a major or perfect interval (by a half-step), it becomes augmented.

When we augment the quality of a minor interval, it becomes major.

Notice that a major interval is diminished first to a minor while a perfect interval goes straight to diminished. On the other hand, both major and perfect intervals become augmented when increased (by a half-step).

In practice, to obtain an interval that is either minor, diminished or augmented, we look for the corresponding major or perfect interval and modify the obtained pitch by a half-step.

For example, let's try to get the ascending minor 6th from F:

1_2_3^4__5_6_7^8
F G A B♭ C D E F

First, we get the major 6th, D. Since a minor interval is a major interval diminished by a half-step, we lower what we found by a half-step to get D♭.

Another example, let's find the diminished 5th from A:

1_2_3^_4_5_6__7^_8
A B C# D E F# G# A

The perfect 5th starting from A is E. To get the diminished 5th, we lower the pitch by a half-step which gives E♭.

Compound intervals

Compound intervals are larger than an octave. They are considered equivalent to the corresponding intervals at the lower octave.

A major 9th interval is a major 2nd plus an octave.

A major 10th interval is a major 3rd plus an octave.

A perfect 11th interval is a perfect 4th plus an octave.

A perfect 12th interval is a perfect 5th plus an octave.

A major 13th interval is a major 6th plus an octave.

A major 14th interval is a major 7th plus an octave.

A perfect 15th is a perfect octave plus an octave, that is, two octaves.

Well, that's about it about intervals. Learning how to build intervals and recognize them seems a bit (a lot) tedious at first glance but it's the foundation we need to build chords.

Scales

Scales are fundamental to music and in particular, to people that create music. This is because songs, in most cases, are written with just the notes of a given scale. These notes (or more exactly, the tones associated with them) are called diatonic because they belong to a scale.

A scale is a series of increasing (or decreasing) pitches. The first note in the series is called the root. A scale has 7 pitches and the repeated root, one octave higher.

Let's look at the white keyboard keys, say from C4 (middle C) to C5 (one octave higher). From left to right, the white keys are named C, D, E, F, G, A, B, C. If there is a black key in between two adjacent white keys, it means the interval between the two white keys is a whole step. If there is no black key, the interval is just a half-step. The white keys have two natural half-steps: E-F and B-C. This is fundamental in music theory.

Major Scales

Major scales obey the following progression in terms of intervals:

1 2 3^4 5 6 7^8

The number (1 to 8) is the degree, that is, the position with respect to the root of the scale (the first note). A space between two degrees indicates a whole step and a caret (^) signifies a half-step.

If we look again at the white keyboard keys, starting from C4 (or any other C), the progression:

C D E F G A B C
1 2 3^4 5 6 7^8

is a major scale because we have half-step intervals between keys E-F (degrees 3-4) and B-C (degrees 7-8). This is the C major scale and C is its root (degree 1).


C major scale on the Korg DS-10 keyboard.

The root of a major scale can be any note we wish among the 12 possible pitches. Recall that the sharp accidental ♯ increases the pitch by a half-step while the flat accidental ♭ decreases the pitch by a half-step. For two natural pitches separated by a whole step, the lower note with a sharp accidental is equivalent to the higher note with a flat accidental.

For example, the F major scale would look something like this:

F G A B♭ C D E F
1_2_3^4__5_6_7^8

Because A-B is a whole step and B-C is a natural half step, you need to lower B by a half-step to get the half-step between degrees 3 and 4 and the whole step between degrees 4 and 5.


F major scale on the Korg DS-10 keyboard.

If you play major scales one after the other, they will all sound similar to the C major scale, in terms of progression. Major scales are often described as being joyful (as opposed to minor scales).

Major scales are extremely important to know and understand because intervals between pitches (major, perfect, minor, diminished and augmented) are based on the major scale. Since chords are built using intervals, you can fully measure the importance of those major scales.

Minor Scales

There's only one major scale but several minor scales. We'll focus here on the natural minor scale which is the one to remember.

The natural minor scales obeys the following progression in terms of intervals:

1 2^3 4 5^6 7 8

There is one natural minor scale that can be played with just the white keys: the A natural minor scale. Indeed:

A B C D E F G A
1 2^3 4 5^6 7 8


A natural minor scale on the DS-10 keyboard.

Here is the G natural minor scale:

G A B♭ C D E♭ F G
1_2^3__4_5^6__7_8


G natural minor scale on the DS-10 keyboard.

There is a relationship between major scales and natural minor scales. The sixth degree of a major scale is the root of the relative (associated) minor scale. Similarly, the third degree of a minor scale is the root of the relative (associated) major scale.

If you listen to any natural minor scale, it sounds quite different from a major scale. Minor scales often express sadness (as opposed to major scales).