Hi everyone. I’m a self-taught amateur pianist.
I’m trying to make sense of scales— beyond just memorizing them— and understand the patterns. I was under the impression that the circle of fifths would help understand scales and why they are what they are.
Eg:
*Why is a C scale absent of sharps, when the G scale isn’t?*
I’ve been trying to learn to read music and understand theory through a combination of watching YouTube videos and studying sheet music, but the ads on Youtube are totally intrusive, and I keep seeing explanations that seem to contradict each other because of my limited understanding of the background information. There is so much information out there and most of it seems to hinge on context that I don’t understand.
To learn and apply information, I generally need to watch people do something or look at thorough diagrams/charts; as well, I really benefit from actual conversations with other people in which they’re talking to me and I am able to ask them questions directly. I want to start taking lessons as soon as I can afford it so I can have one on one conversations with a trained teacher.
Edited for clarity!
Thanks so much♡
*Edited again: THANK YOU, really, I wish I could give all of you a million reddit awards. Seriously, so many of you have given me totally thorough answers that have still been easy to understand. I love it.*
In: 12
In a way, the circle of fifths is more fundamental than the idea of keys and scales.
Suppose for a moment that we had no concept of a musical scale, but wanted to build one from scratch. We don’t know how many notes we should use, or what their pitches should be. All we know is that we want a collection of pitches that “sound good” together.
One way we might do this is by starting with some random pitch, and stacking consonant intervals on top of it. In general, two sounds are consonant with each other if their pitches form a simple ratio. The simplest ratio (besides 1:1) is 2:1, so the most consonant interval is one where the higher note has twice the frequency of the lower note. We call this interval an “octave.”
We could try to build a scale by stacking octaves. However, due to a quirk of how humans hear sound, pitches an octave apart sound roughly “the same”. They sound like higher or lower copies of each other. As a result, a scale built from octaves, while highly consonant, would also be extremely boring.
So we move on to the next most consonant interval. After 2:1, next simplest ratio is 3:2, and we call the corresponding interval a “perfect fifth”. What happens when you create a scale by stacking fifths? This is equivalent to repeatedly multiplying pitches by 3/2 (or 1.5). Let’s say the lowest note in our scale has a frequency of “1”, and see what happens:
1 = 1
x 1.5 = 1.5
x 1.5 = 2.25
x 1.5 = 3.375
x 1.5 = 5.0625
x 1.5 = 7.59375
x 1.5 = 11.390625
x 1.5 = 17.0859375
x 1.5 = 25.62890625
x 1.5 = 38.443359375
x 1.5 = 57.6650390625
x 1.5 = 86.4975585938
x 1.5 = 129.746337891
That last pitch is interesting–notice how close it is to 128, a power of 2. The deviation is around 1.3%, almost imperceptible. This means that if we go up a perfect 5th twelve times, we end up back at the same note we started on, just 7 octaves higher. And what do you know, twelve is also the number of notes in the chromatic scale! This is not a coincidence. Looking at this another way, let’s start at a note, say, F, and see what happens if we keep going up by fifths:
F -> C -> G -> D -> A -> E -> B -> F# -> C# -> G# -> D# -> A# -> (E# = F)
We end up hitting all the notes in the chromatic scale, before returning to our starting note. Or, in other words, the chromatic scale is just a tightly re-ordered version of the circle of fifths.
So, that’s where the chromatic scale comes from.
What is a major scale, then? The seven tones of a major scale are just seven consecutive steps in the circle of fifths, which we re-order so that they fit into an octave. For example:
F -> C -> G -> D -> A -> E -> B becomes C D E F G A B, which we call the C major scale.
C -> G -> D -> A -> E -> B -> F# becomes G A B C D E F#, the G major scale
G -> D -> A -> E -> B -> F#->C# becomes D E F# G A B C#, the D major scale
and so on.
You may have noticed that the circle-of-fifths sequence for a given major scale starts one step early (e.g. the sequence for C major starts with F, not C). So why not take the same notes F -> C -> G -> D -> A -> E -> B, rearrange them to FGABCDE and call that the F… something scale?
It turns out, you *can* do that. It’s just that the result is called an F Lydian scale, not an F major scale. Same idea as how if you take the C major set of notes but start on A, you get A natural minor. For any major scale, there’s a set of 7 “modes”, each containing the same notes but starting at a different place.
One might also ask “why seven notes?” In fact, there are other scales that are built by cutting out and compacting different sized chunks of the circle of fifths. If you take five consecutive notes from the circle of fifths like F# -> C# -> G# -> D# -> A# and rearrange them to fit within an octave, that gives you a major pentatonic scale like F# G# A# C# D#. Specifically, this is F# major pentatonic, which you may recognize as the black notes on a piano.
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