What are scales?

I wrote this response for another forum, and thought I'd post it here as well. Basically, someone asked about understanding why there are so many "different G major scales for example," because they were confused about how they could be playing the same scale over different places on the guitar.

I decided to break down their question to the more basic question of "what is a scale?" In my experience, lots of people are kind of confused about what scales are and how they work. This is a bit long, but I hope someone here finds it useful.

Also, if anyone sees something I said incorrectly, or could be phrased better, let me know :)

Thanks!
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This points to a standard issue: not understanding what a scale is in and of itself.

So, let's back up and just take part of your question: what is a scale?

A scale is an ordering of notes that cover an octave.

An octave is just the space in the sound frequencies between two tones where the rate doubles. Sound travels in waves, and frequency measures how many wave peaks and valleys happen in a span of time. The scale usually used for measuring frequency is the "Hertz" scale. One hertz (abbreviated Hz) is equal to the passage of the top of one peak to the summit of another peak over the period of one second.

1 Herz is a low frequency, so low that the human ear can't hear it.

Human ears can distinguish sound between the range of approximately 20 Hz to 20 kHz (a kHz is 1,000 Hz).

Low E on the guitar is 82.41 Hz, and high E is 329.64 Hz

The E on the fourth string and the second fret is 164.82 Hz.

So the first scale you can play on the guitar is the one which covers the range of 82.41 Hz to that frequency doubled or 164.82 Hz.

Similarly, the first G scale you can play covers the range of about 98 Hz to 196 Hz. Any ordered series of notes that cover that frequency range is called a "G scale." Any frequency that is a multiple of 98 Hz and a multiple of 2 is a G note. The name is just what we call those tones due to historical reasons.

Regardless of which G one starts on, it is G scale. We call it G because we name the scales based on the name of the first note. (There's an important distinction between a note and a tone, the tone we usually call G is also A double flat and F double sharp, for example, and one can write a scale based on any valid musical name for any particular tone.)

Now, it doesn't matter what the different intermediate notes are if the first and last notes are Gs one octave apart, and we're playing an ordered sequence of notes with no repeating notes, it is a G scale.

For tonal music, we break up the frequency distance between the doubling of frequencies into what we call "half steps." These are chosen to correspond with particular geometric relationships between the wave shapes over the distance of the scale. In tonal music, there are always 12 half-step tones that make up the range of an octave. These tones have 15 common note names. For example, the same tone that is a C# note is also the note Db.

In G, these would be G, G#, A, A#, B, C, C#, D, D#, E, F, F#, and the final G.

Note, that we use sharps to name the notes in the G scale because G is a scale that naturally has #s in the key signature. A scale that has flats in the key signature would use flats to name the notes.

These relationships result in a particular sense of consonance (notes that sound good together) and dissonance (notes that sound in conflict together) which lead to a consistent experience of the notes which make up any scale.

An example of this is that a note which has a frequency approximately 80% of the way between the scalar distance is known as the 5th of the scale, and has a strong consonance with the root tone.

The scale that uses every interval is called the chromatic scale.

Any combination of notes (in order) of the chromatic scale starting on any particular note is a "valid" musical scale with a tonic (or base) of the starting note.

So, for example, the scale "G, G#, B, D#, E, G" is a "G" scale. It may not be a very useful or common, but it is still a scale. The notes are ordered (in alphabetical order wrapping around from G to A, with each note appearing only once and covering one octave.

Some scales are extremely common. They appear over and over in music and are so useful that we gave them names to avoid having to spell out the scale each time we wanted to use it.

One such common pattern is the major scale.

As you probably know, the major scale has the particular interval pattern: whole step, whole step, half step, whole step, whole step, whole step, half step.

If you count up the intervals (2 + 2 + 1 + 2 + 2 + 2 + 1) it equals 12, so you know that it covers an octave.

The odd example scale I gave above also has 12 intervals (1 + 3 + 4 + 1 + 3) and you can see it adds up to 12 as well.

Now, on the guitar, each string has many intervals, a 24 fret guitar neck covers 2 octaves (24 being equal to 12 x 2). Since the strings are only a few intervals different from one another ( in standard tuning they are five half steps different except the G string to B string which is four), there is lots of overlap for playing notes in various locations.

High E for example, is playable in six different places on a 24 fret electric guitar.

Any one of those high E's is just as usable as any other for using a scale.

Across a fretboard, any given note will appear as many as six times in various octaves.

These two facts combine to mean there are many of ways to play any given major scale.

For a G major scale, for example, you can play it as follows:

6th string 3rd fret, 6th string 5th fret, 6th string 7th fret, 6th string 8th fret, open 4th string, fifth string 7th fret, 6th string 14th fret, 4th string 5th fret.

Now, that fingering is not exactly useful in most contexts, but it is a way to play the G scale starting from low G and ending on the equivalent of the open G (third) string!

This property of the guitar can make it quite challenging for new players, but it is also one of the features of the guitar that make it very useful in many musical contexts. The flexibility to move your scales around the neck gives you easy access to playing different combinations of notes and chords.