Octaves and scale formation

Side Note

As you read this apply what you have learned to any instruments you have at your disposal. Things fall into place once you put them into practice.

Octaves

When you play an ocarina the air entering and leaving the chamber pushes on the air in your environment. This causes waves to travel trough the air much like those on the surface of a pond. When they reach your ears you hear a sound.

These waves can be visualized as a graph. High points represent pressure fronts and the low points represent the low pressure regions between them.

All waves have a frequency, the number of peaks that pass a point in space in 1 second. When two notes sound and one is exactly double the frequency of the other the human mind perceives both with the same tone. This is called an octave. Incidentally the phenomenon is not limited to a single doubling. If the high wave is again doubled, now 4 times the frequency of the first, all 3 are perceived equivalently. The following animation demonstrates the idea:

Because of this the notes used in music actually repeat. This repartition exists on all instruments but is most obvious on the piano keyboard. Western music divides the octave into 12 notes, 12 sequential white and black keys. After note 12, it returns to note 1 an octave higher or double the frequency.

The keyboard simply repeats these same 12 notes from left to right. This grouping can be identified easily by looking at the black keys, which are grouped into twos and threes.

If you pick any note within one octave and play a tune, then play the same sequence from that key in a different octave it will sound like the same tune. You can also play a sequence in two or more octaves at the same time. When a note sounds in multiple octaves the highest is heard as the melody and the lower ones create a richer tone.

Scales used in music

As mentioned above each octave contains 12 notes. From this point on things are easier to understand if the notes are simply considered in a line. The distance or 'interval' between any two of these notes in sequence is called a half step or semitone. note 1 to note 2 is a half step, Note 2 to note 3 is also a half step and so on.

Most western music is tonal, it is written to highlight a single note as it's focal point. This cannot be achieved using a scale comprised of half steps as they all sound the same, it sounds ungrounded.

To create a center point a selection of notes are chosen with an irregular pattern. This gives each of the notes a unique sound and gives the ear a hook so that it can tell where it is. To create an irregular pattern two intervals are used. The half step and the whole step, which is simply two half steps in sequence. Here are a few whole steps:

By using a mixture of these two intervals scales can be built. Among the most commonly used in music is the major scale which is defined as the following pattern:

Whole, Whole, Half, Whole, Whole, Whole, Half

Using this single pattern you can form a major scale beginning on any of the 12 chromatic notes. If you begin from note 1 the first two intervals are whole steps, you move forward to 3, then to 5. Instruction 3 is a half step so you move forward from 5 to 6. If you keep following this pattern you end up with: 1,3,5,6,8,10,12,1.

You don't have to start from note 1, you can start from any of the 12 chromatic notes. Because of this there are 12 major scales or 'keys'. Music can be written within any of these. The following tool allows you to scroll between all 12 patterns.

Many instruments are based on this pattern including the ocarina. It is actually visible in the sizes of there finger holes.

Naming the notes

As most music uses only 7 of the chromatic notes at a time It would be cumbersome to have to think about the additional 5 notes which you are not using. For example having to remember that the next note after 1 is 3, but that 6 follows 5 directly.

The standard note names are designed to hide these irregularities. The notes of the pattern built from note 1 are named using the first seven letters of the alphabet. Note 1 is called C, followed by D, E, F, G, A, B and finally C an octave higher. These are called the 'natural' notes. It is obvious that the note E follows D and F follows E despite the irregular spacing.

The other notes are called accidentals. They are named relatively using sharps (♯) or flats (♭). For now I'm only going to demonstrate sharps. Sharpening a note adds one semitone to it, 'C♯' is the note one semitone above C.

As it is the base of the system the scale of C major needs no accidentals. If you form a scale from any other note they will be included. For example if you start on D you have two sharps, F♯ and C♯.

Octave registers

To distinguish notes in different octaves each group of notes C to B are assigned a number called an 'octave register' starting from octave 1. The note C1 is C in octave register 1 and the highest note in this register is B1. After this the next note is C2 and so on. Following octaves are numbered sequentially. In total 7 full octaves are commonly used in music. C8 exists by itself at the top.

The following audio is the note C played in all 8 octaves.

Any single chambered ocarina can only access a small portion of this range. For example an alto C ocarina plays from C5 to F6. See 'Ocarina keys and pitch ranges' for more details.

Enharmonic notes

The system defined above is a convenient way to think about the notes of music but it does have a problem. In the tool below the numbers have been replaced with letters and sharps. Have a play and see if you can spot what's wrong:

In some cases there are repeat letters for example F major, if this scale is noted using sharps you get: F, G, A, A♯, C, D, E, F. The letter 'A' shows up twice while B is missing altogether. It is conventional to use each letter only once for clarity.

This problem can be solved by using flats (♭) instead of sharps. Adding a flat to a note lowers it by one semitone. For example if you begin from the note B and add a flat, you descend to the chromatic note between A and B. Using flats the scale of F major can be written cleanly.

f, g, a, b♭, c, d, e, f

Because of this the chromatic notes actually have two names, one raising the note below and one lowering the note above, i.e. C♯ and D♭. These are called enharmonic, a music term that means two names for the same thing.

In some cases the natural notes can also be enharmonic. For example here is C sharp major as displayed by the above tool:

C♯, D♯, F, F♯, G♯, A♯, C, C♯

The names 'F' and 'C' appear twice, while E and B are not used at all. In this case it is better to call 'F' 'E sharp' and 'C' 'B Sharp'. Now every letter us used once:

C♯, D♯, E♯, F♯, G♯, A♯, B♯, C♯

Transposition and other scales

Because all of the major scales are based on the same pattern they are equivalent, you can take a melody in one key and 'transpose' it into a different key. It will sound like the same tune despite being higher or lower in pitch.

Keys exist to create variation. If music remains in the same key during a long performance it begins to sound monotonous. Because of this it is a good idea to vary the key that you play in. A really easy way to do this is to change to an ocarina in a different key. You can play using the same fingerings but the sounded key will be higher or lower.

Keys also come in different types. The pattern used to form the scale can be changed. For example the minor scale is built from the pattern: whole, half, whole, whole, half, whole, whole. An easy natural minor scale to play on an alto C ocarina is D minor. You only have to add one flat, D flat. D E F G A Bb C D. Try looking up these notes in a fingering chart.

Exercises

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