For some time I have been wanting to write a few things that I've learned along the years about music, theory and other sort of things. Go ahead and hate me for if this gets very basic sometimes but I can't go deeper without stating the starting point. So here I go.
Hopefully you'll know that music is an art based on sounds and silences, with changes of rhythm, pitch, melodies, harmonies, dynamics, etc. Many may have different opinions about its bases, whether it's a complicated science or art, or a free artistic way of expression. Truth is it may be less complicated to understand than what you may think, or on the contrary there may be more to it than you thought. Let's go slow.
Musical Notes
There are musical notes. You probably have heard of them. They can be named in two different ways and it's easy to learn both. These are the ones hopefully you already know.
Do___Re___Mi___Fa___Sol___La___Si___Do
In english we know them as:
C___D___E___F___G___A___B___C respectively.
You can see that this nomenclature seems to be alphabetical, and that A or La should be the first ones. There is a reason to that but I won't get in there just yet. Now, it seems we have 7 different notes. The last C is the same note as the first one however this one has a higher pitch than the first, this is called an octave (it's the 8th note of the scale). But saying that there are only 7 notes is wrong. There are more, they're the so called accidental notes that are between some of the above.
Musical Notes, accidentals
What we really have is 12th notes. With all notes included we have
(note that all the notes are one semitone away from each other)
C___C#___D___D#___E___F___F#___G___G#___A___A#___B___C
The # on C# means it's a C sharp. A sharp notation is used to indicate that the note that is shown there is not the one that is really meant to be used, but instead the note that is a semitone (also called half a step) higher.
But that is not the only way we can express accidentals. We also have this.
C___D♭___D___E♭___E___F___G♭___G___A♭___A___B♭___B___C
The ♭ on D♭ means it's a D flat. A flat is the exact opposite of a sharp, its pitch is one semitone lower. It's important to take notice that C# is exactly the same note as D♭.
Now, hopefully you might have noticed that between B and C, and E and F there are no accidental notes. That is because they are already a semitone apart in distance, whilst for example C and D are a full tone (or whole step) away from each other.
The use of a sharp and the flat depends, but most of the time we use them in a way in which we use every single note once without repeating and without skipping. So let's say we have a scale with C, C# or D♭, and E (and F, G, A, B etc, it's a made up scale). We must use then D♭ instead of C# because otherwise we would be skipping D and repeating C.
They could've called each note by a different name instead of using this notation for accidentals, I don't know. Probably at the beginning they didn't saw them as different notes but as they are called, "accidentals". Instead of hitting the one they wanted they hit one semitone higher/lower.
C___D___E___F___G___A___B___C
The reason we are taught these notes in particular is because they are a scale, and the easiest ones to learn. This is the C major scale to be precise.
Musical Scales
A scale is a sequence of notes that have certain harmony with each other. But they are only a mold that includes certain notes and excludes other for the sake of harmony. The chromatic scale is the scale that includes all possible notes, so when I wrote above all the notes with all the accidentals included, I wrote the chromatic scale.
Scales are more like a mathematical formula which tells us which notes are included. The most important scale is the Major Scale. It is used as reference for all the other scales, therefore it's the first you should learn. The Major Scale of C is so popular because it doesn't includes any accidentals.
So let's get to the formula. What we can observe is that the notes included in the C Major Scale are C D E F G A B. Let's start.
- C is the tonic, meaning that it's the first note and that all the notes used in the scale are used relatively to this one.
- Between C and D we have a full tone.
- Between D and E we have a full tone.
- Between E and F we have a semitone, remember that there are no accidentals between this two.
- Between F and G there is a full tone.
- Between G and A, another full tone.
- A and B, a full tone.
- Finally, since a scale is a sequence that repeats itself indefinitely we must go back to the tonic. Between B and C there is a semitone (remember, no accidentals between this two either).
So the formula for a major a scale is... Tone, Tone, Semitone, Tone, Tone, Tone, Semitone. Use it with any note and there you have that note's major scale. Let's take then G.
G(tone)A(tone)B(semitone)C(tone)D(tone)E(tone)F#(semitone)G
For future reference, A is G's 2nd, B is G's 3rd, and so on until F# is the 7th. (This is for G)
Music and physics
This part is of little use, however it's pretty cool.
As some of you know, sound has physical properties. To keep it simple, the frequency of a sound wave determines its pitch. Each note has its own frequency measured in hertz. The lower the frequency, the lower the pitch. We use a couple of constants for the calculation of the frequency of any note, one is the frequency of A.
A4 (or La4) has a frequency of 440 hz. Now, the other constant is the 12th root of 2, which is about 1.0594630943593... The importance of this second constant is that this is the ratio of the frequencies between two half tones.
This means that A# is the 12th root of 2 times A's frequency.
440 x 1.0594630943593 = 466.16376.. or so.
For the next note, which would be B, then we need to take A#'s and multiply it by the 12th root of 2. Do it until you reach A's next octave and you'll get 880. Which means that an octave's frequency is the double of the note's frequency. Pretty much as expected.
For a more complete formula, use this:
* don't forget that 12th root of two can be written like 2^(1/12) [^means powered]
f= 2^(n/12) * (440 Hz)
Where f is the note's frequency that we are looking for, and n is the amount of semitones between A and the note. When it's higher pitched n is positive, negative if lower.
Let's try it with F4 then (which is lower than A4) which is 4 semitones from A. Therefore n=-4
So F4 is at 349.2 Hz
(I know images are messed up with the background...sorry about that)
Cheers.
