Music Theory Tree

The A Minor Scale: All Natural Pitch Classes From ‘A’

This will be the first of many posts showing excerpts from my upcoming eBook, tentatively titled: “Music Theory Tree: An Introduction to Visualizing Music Theory”.

The A Minor Scale may also be referred to as the “A Natural Minor Scale”, or even the “A-Natural Natural Minor Scale.” Usually people just use the simple name. The reason the other two names may be used is that there are other kinds of “A’s”, like A-sharp and A-flat, and other kinds of minor scales, like the harmonic minor and melodic minor scales, to name two. One could have an “A-Sharp Harmonic Minor Scale” and if one were discussing it in comparison to the A Minor Scale, more explicit labeling might help the audience keep things straight. Though, most people who routinely speak about such scales don’t require such explicit labeling. Using the word “natural”, meaning “unaltered”, in music theory is generally unnecessary, because it’s implied. This is consistent with typical English language.

In any case, with this formality out of the way, let’s explain what the A Minor Scale is, where it comes from (in brief), and why it’s important. We’ll leave the question of “How does one apply this to composition and analysis?” to later posts with videos so I may demonstrate and we can discuss that directly.

Most simply, it is a scale consisting of seven pitch classes, labeled as the letters A through G. Pitch classes are sets of pitches that are considered equivalent under the Octave Equivalence Relation. For more on that, please visit my essay, “Meet the 12 Pitch Classes of 12-Tone Equal Temperament, aka “The Musical Alphabet”, or “The Chromatic Scale” here: https://www.facebook.com/musictheorytree/posts/1401253997494056 published on my page.

Typically people use the term “note” where I use the term “pitch class”. This is a formality, and these terms may sometimes be considered interchangeable, but technically speaking, in Western music theory, the latter is more precise when discussing the letters A through G, and their altered versions. I try to reserve the term “note” for discussions of musical notation in sheet music. These two spaces are importantly connected, but distinct, in my view. My arguments for this are described in the aforementioned essay. I welcome any edits and criticisms one may have of it.

It is common to teach Western music theory with a piano keyboard, because the pitches of natural classes are produced by striking white keys, and those with sharps or flats, with black keys. This convention is reflected in these diagrams. The naturals are on white backgrounds. The others (not listed here) would be on the black backgrounds. The colour coding of the pitch classes will be discussed in the next post.

If one takes the Chromatic Scale of 12 pitch classes in 12-Tone Equal Temperament, beginning from A, and removes all of those with sharps or flats, one is left with the A Minor Scale. It may be also described as all of the natural pitch classes, beginning and repeating from A, because pitch classes repeat at multiple registers, due to the Octave Equivalence Relation. In short, the Octave Equivalence Relation exists because we hear certain pitches as especially similar to one another; so much so, that they receive the same pitch class symbol. So, a scale may be observed as a linear system or a cyclic system. This combination of being both linear and cyclic makes the A Minor Scale, and all musical scales “Periodic”. Therefore, one can confidently define musical scales as “periodic sequences of pitch classes”.

It is common for music theorists to use little arches to connect two pitch classes together, demonstrating the distance between them. These little arches are called “cycloids”. They resemble the trail of a bouncing ball from one object to the next. These cycloids represent what are called “intervals”, often described as “the distance between two notes” but may be more precisely described as “the difference in frequency between two pitches, in accordance with a given tuning system”.

There are two types of intervals shown here: whole steps (W’s) and half steps (H’s). These may also be referred to as “whole tones/tones” and “semitones”, respectively. I prefer the former, because the word “tone” in music theory is overloaded, and could cause more confusion. They may also be called “Major Seconds” and “Minor Seconds”, respectively. More on this naming convention later.

If we run through the intervals between the natural pitch classes of the A Minor Scale, skipping over those from the Chromatic Scale with sharps or flats, we get the “Minor Scale Interval Formula”: (W, H, W, W, H, W, W). This pattern of intervals may be applied to any pitch class, and a distinct ordered set of pitch classes will emerge. For example, if we apply this intervallic formula to the pitch class C, the resulting scale is (C, D, E♭, F, G, A♭, B♭). This is known as the “C Minor Scale”.

Again, the reason why the A Minor Scale is so important, is that if and only if one begins a minor scale from A, does one get the letters A through G, with no sharps or flats. That makes it especially easy to work with. The A Minor Scale is therefore a member of a distinguished set of seven scales I like to call “The Diatonics of All Natural Pitch Classes (DOANPC’s)”. The A Minor Scale is a super important scale in Western music theory, second only to the next scale we will look at; namely, the C Major Scale.

What does “diatonic” mean? More on that soon, too.

The most important takeaway from this post is that if one wants to learn music theory, one must remember that all pairs of neighbouring natural pitch classes have a pitch class separating them, except for the pairs (B, C) and (E, F).

Please let me know if you have any questions. I am here to help.

Let’s reimagine music theory.

Steve Evans From Winnipeg