The major scale (part 2)

How many major scales are there?

In the last article we learned how to build a major scale from any note. We can conclude that we just need to apply the formula:

WS  WS  HS  WS  WS  WS  HS

WS = whole step
HS = half step

As we saw, all major scales have 7 different sounds but we must begin and end with the same note, so in the end, all major scales will have 8 notes. For example, C major scale: C D E F G A B C (begins and ends with C). F major scale: F G A Bb C D E F (begins and ends with F). We also said that we cannot repeat nor skip note names in the same scale. This is why the F major scale cannot use A#:

F  G  A  A#  C  D  E  F

As we can see, A# is the same note that Bb on the piano (they are enharmonic), but it is technically incorrect to use A# in the F major scale. This is because we would use A twice and skip B. So, the right solution is to use Bb instead. In this way we will have all the note names in our scale:

F  G  A  Bb  C  D  E  F

Double accidentals

Technically speaking, we cannot build major scales from any note. For example, there is not a G# major scale but there is an Ab scale instead. Let's see why this happens:

1. We start on G#
2. Whole step ahead: A#
3. Whole step ahead: B# (we cannot use C because we can't skip the B note name)
4. Half step: C#
5. Whole step: D#
6. Whole step: E# (we cannot use F because we can't skip the E note name)
7. Whole step: ??? G?

As we can see, every note becomes "sharp" and it's harder to understand and visualize that way. Besides of that, we have to use E#. It would be easier to use F instead, but we cannot skip the E note name. Another problem is that one whole step ahead of E# is F double sharp! This situation is called double accidental and we write it Fx. Fx is enharmonic of G and, clearly, double accidentals make everything much more confusing! In a similar way, we could have a double flat, which is written bb (Abb, Cbb, etc.). Anyway, if we build our scale from Ab instead of G#, we won't get any double accidental nor enharmonic craziness:

Ab  Bb  C  D  Eb  F  G  Ab

This way is so much easier to read and understand. In a similar way, we should use Eb instead of D# major scale, and Bb instead of A# major scale.

The 15 major scales

On the other hand, there are also enharmonic "valid" scales. For example, we can use Db or C# major scales. Both are valid as they don't have double accidentals, but in this case, Db is more common as it uses less accidentals:

Db major scale: Db  Eb  F  Gb  Ab  Bb  C  Db

C# major scale: C#  D#  E#  F#  G#  A#  B#  C# (all sharp notes)

Following this, here there are the 15 major scales valid in modern harmony:

C, C#, Db, D, Eb, E, F, F#, Gb, G, Ab, A, Bb, B, Cb.

It's a great exercise is to build and play all of them in different ways. Every professional musician should be able to play well in any of these 15 scales. 

If you want to learn more about harmony and theory, check out my online course: Applied Modern Harmony, part 1!

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The Major Scale (part 1)

What is a major scale?

Perhaps the most important topic that we must understand in modern harmony is the major scale. We know that in the western tuning system we have 12 different notes, as we saw in the Chromatic Scale article. However, we usually need fewer notes when we are making music. This selection of notes is called scale. There are many kinds of scales, but the most basic one is the major scale, which has 7 different notes. There is a major scale for each note in the chromatic scale, that is, we have the C major scale, the C# major scale and so on. The most famous one is the C major scale, as it has the notes: C D E F G A B and C (all the white keys on a piano keyboard). As we can see, the scale has eight notes but only seven note names. This means that every major scale should start and end with the same note name.​

Using tetrachords

To build a major scale we must follow a formula like we did when we built tetrachords (S - S - HS). The major scale formula is:

S  S  HS  S  S  S  HS

S = step; HS = half-step.

If we compare both formulas, we can se that the major scale is built from two tetrachords:

S  S  HS  S  S  S  HS

This is why, if we can build tetrachords, we can easily build major scales. Let's see some examples.

G major scale:

1. We start from G
2. We move one step ahead: A
3. Another step ahead: B
4. Now a half-step ahead: C
5. Then, we move another step ahead: D
6. One more step again: E
7. Then another step: F# (a step above E takes us to F#, not F)
8. And finally, one last half-step: G

The G major scale has these eight notes: G  A  B  C  D  E  F#  G

Another example, the F major scale:

1. We start on F
2. One step: G
3. One step: A
4. One half-step ahead: Bb (we say Bb instead of A# because we cannot repeat consecutive note names)
5. One step: C
6. One step: D
7. One more step: E
8. Final half-step: F

So, the F major scale uses the notes: F  G  A  Bb  C  D  E  F. We can say we did a good job if the last note is the same than the first one. All major scales have a "definitive sound". If we play any major scale, we can hear this characteristic sound. There are more examples and interesting facts to mention about the major scale, so stay tuned for the next article! ;)

If you want to learn more about harmony and theory, check out my online course: Applied Modern Harmony, part 1!

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The tetrachord

Harmony tutorial

This time we are going to talk about harmony. A basic harmony concept is the tetrachord. This word means "4 notes". To understand tetrachords will help us to understand music scales later.

Steps and half steps.

The distance between two adjacent notes in the chromatic scale is called a half step. For example: the distance between C and C# or between F and F#. This is also the case between G and Ab and so on. This is easier to understand looking at a music keyboard. The closest key is a half step away, it doesn't matter if it's a black or white key. Now, two half steps make a step (whole step). For example, there is a step between C and D. From E to F there is a half step, but from Eb to F there's a whole step. Another example would be the distance from B to C#, a step.

The tetrachord formula.

Ok, so to create a tetrachord we have to use this formula:

S - S - HS

Where: S = Step and HS = Half Step. We can make tetrachords from any note. For example, let's start from C, following the formula we get:

1. Our first note: C
2. We count one Step ahead: D
3. We count another Step ahead: E
4. We count one Half Step now: F

The formula S - S - HS gives us the notes: C, D, E and F. These notes make the C tetrachord. Easy huh? Let's see another example. Now the D tetrachord:

1. We start from D
2. One Step ahead: E
3. One Step ahead: F#
4. One Half Step ahead: G

So, the D tetrachord is built with the notes: D, E, F# and G.

 
 Now, let's build the F tetrachord:

1. We start with F
2. One Step: G
3. One Step: A
4. One Half Step: Bb

So, the F tetrachord is made with the notes: F, G, A and Bb. A common question is why to use Bb and not A# instead? Well, the answer is that the tetrachords MUST be made with consecutive letter names, we cannot repeat nor skip any. So in a tetrachord we cannot find an A and an A#, nor an Eb and an E, etc. In the same way, we cannot have E and skip to Gb instead of F#. In this fashion, we can (and we should) create tetrachords from every single note. This exercise will give us a lot of fluency to better understand scales and other harmony topics later.

Finally, to grasp tetrachords requires practice. It's very important to play them with a musical instrument so we can hear how they sound. The tetrachord "sound" will be our base for the major scales. 

If you want to learn more about harmony and theory, check out my online course: Applied Modern Harmony, part 1!

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The chromatic scale

What's the chromatic scale?

Among the key elements of harmony, we can mention the scales. A scale is a set of notes that have some relationship to each other. Scales are the basis of modern harmony, because from them we can better understand the chords. Learning scales also help us to know what notes to use when we are making an arrangement, a solo or a composition.

The simplest scale is the chromatic scale. This is the scale on which Western music is based. It has the 12 notes that we use within our tuning system (there are other systems with different notes in cultures like India or China, for example). Below there is a list of each note expressed with English naming convention, which is the system that we will use from now on (the # symbol is called sharp):

C, C#, D, D#, E, F, F# G, G# A, A#, B 

This is the way to name the ascending scale, that is, from the lowest to the highest note. We can name the descending scale too, from the highest note to the lowest one (the b is called flat):

C, B, Bb, A, Ab, G, Gb, F, E, Eb, D, Db

As we can see, there are  notes that are 'equivalent' to each other, these are called enharmonics: C# and Db D# and Eb F# and Gb G# and Ab A# and Bb Using either case depends on the context and tonality of the music piece. It is also important to note that there are other enharmonics, e.g. E# and F, C and B#, etc.

Every musician must be familiar with all these enharmonics. We must know all the notes of the chromatic scale in ascending and descending order. Practice that! Try to do it on a piano or keyboard. 

Well, that's all for now. We'll talk about more topics on the world of music and sound the next time. If you want to learn more about harmony and theory, check out my online course: Applied Modern Harmony, part 1!

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Harmony, the basis for music creation

What is harmony?

This time we leave aside the technical information and focus on the artistic and musical part. A tonmeister (expert in arts and sciences of sound) must master both the technical and the artistic sides of music production. To learn music we must understand many concepts: melody, rhythm, harmony, instrumentation, etc. We'll begin with the basis for the music development: the harmony.

Harmony is the way we can combine the musical notes so that they generate some effect on the listener. Harmony has centuries of development, or rather, of discovery. In reality it is based on physical phenomena: vibrations, stationary waves and harmonic oscillations. (hence its name). These phenomena have always existed in nature. The human beings discovered that certain frequencies or vibrations sound good when combined. They analyzed and studied these combinations. This is the foundation of harmony.

In musical terms, harmony shows which notes can be used together in a "nice" way and which not. As I often say to my students: engineers and physicists call them 'frequencies' (Hz) and musicians call them 'notes', but they are two sides of the same coin. It's important to say that harmony will always be somewhat subjective. The idea of pleasant sound cannot be generalized at all.

In these days, we can name two basic types of harmony: the tonal or classical harmony and the modern harmony. Tonal harmony has strict rules that have been accepted for centuries and comes from ancient cultures like Greece or Rome. These rules were perfected in the Renaissance. Modern harmony is developed in the twentieth century and it is the basis of almost all popular genres today: blues, jazz, rock, pop, electronic, etc.

Traditional music schools, i.e. conservatories, teach tonal harmony. It shows the guidelines that have been used since the time of Bach and Mozart and remain valid in certain styles of music. Contemporary music schools often teach modern harmony. This is a less strict method and allows the use of resources that are forbidden in the classical field. Anyway these resources are an essential part of popular styles like jazz or rock.

You can get great results creating music from either of the two mentioned systems. That is, the music uses harmony and learning about it will allow us to develop our musical ideas. The goal is to master a tool that will be the basis to compose, arrange, improvise or play instruments. Harmony helps us to understand music in general.

In this space we will focus on modern harmony concepts. Stay tuned on my next articles about harmony. Next time I will talk about the basic building blocks of harmony: scales.

If you want to learn more about harmony and theory, check out my online course: Applied Modern Harmony, part 1!

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