Are inverted scales a thing?

Question

Inverted chords are a thing. But are inverted scales a thing?

What do I mean with that? A scale is defined by a certain set of notes where one of them is the root key. Playing the root key feels like coming home and most melodies in that scale start with that note. So let's say in a song I'm using the notes of a certain scale. However, the note that it feels like coming home to and I often start a melody with, is another note than the root key of the scale I'm using. Could you say I'm using an inverted version of that scale? Is there any other name for it? Or doesn't it really matter and I'm still using the same scale? If that is the case, wouldn't that mean that C Major and A Minor are not two different scales with the same set of notes, but actually the same scale which just has two different names?

An example: For now, let's just assume C Major wouldn't exist as a named scale. Yes, weird, but bear with me. However I'm making a song in a scale that would be C Major. Since it has the same notes and I want to be able to communicate what scale I'm using, I'm would say that my song is in A Minor - second inversion. Of course, it's a bit weird that I'm using a major scale and I'm calling it a minor scale, but I think you understand my point.

Answer 1

We call these rotations (or modes) of a scale. We can rotate any scale such that any member of that scale can be a tonic.

The most common rotations are the seven diatonic church modes (see also this question), where we rotate the major scale to begin on each of its seven pitches.

But you can rotate every scale out there, and there's likely a name for it. Rotating the harmonic minor scale to begin on the fifth scale degree, for instance, creates the Phrygian dominant scale, something very common in Klezmer music.

Answer 2

There are seven of them. They're called modes. They use exactly the same notes as the 'standard major scale', but are rooted on each of the scale notes. And, there are many tunes which use them.

Let's take C major. CDEFGAB. As it stands, it's the C major scale. But if we reconfigure that abd go from , say D to D, it beecomes D Dorian. the root is now D, and the sound is minor. The scale now is DEFGABCD.

That same idea carries through with each 'root note'.

Answer 3

You have a lot of questions in your “question“ so I will try and hit on them in order.

So let's say in a song I'm using the notes of a certain scale. However, the note that feels like coming home to and I often start a melody with, is another note than the root key of the scale I'm using. Could you say I'm using an inverted version of that scale? Is there any other name for it? Or doesn't it really matter and I'm still using the same scale?

OK, 3 at a time, here goes: If your home key or tonality is the root of the particular major scale then you are playing just that scale and not an inverted scale. There is no rule stating that melodies have to originate or end on any specific note within a scale. If you are in C major and playing E to E you are still using a C major scale.

There is a name for what you are more or less describing, explore “modes”, which is the process of creating 7 different scales from one scale, say a C major scale, by using the 7 different starting notes, i.e. D to D, E to E, etc. In each of these cases though the starting note becomes the new tonality. There are MANY answered questions about modes on this site or you can do an independent search about them.

If that is the case, wouldn't that mean that C Major and A Minor are not two different scales with the same set of notes, but actually the same scale which just has two different names?

C major and A minor are two different scales which contain the exact same notes BUT they have different root notes and are also constructed very differently.

An example: For now, let's just assume C Major wouldn't exist as a named scale...

As for your example, C would be the 3rd inversion of the Am scale, not the 2nd (B is the second) if they were called inversions but this is really about what I mentioned before, “modes”. Actually the A minor scale (Aeolian mode) is built on the 6th degree of the C major scale (Ionian mode) Explore modes and I think you will see things more clearly. Here’s a wiki article to get you started:

https://en.wikipedia.org/wiki/Mode_(music)

Answer 4

You mention "inversion" in the context of chords and scales. Inversion means different things depending on the context so I though it might be helpful to list out some examples in notation (which makes it easy to see direction and position) ...including rotation/modes of a scale which I think is the crux of your question.

Chord inversions are about which chord tone is in the bass, regardless of how the tones are distributed in the upper voices...

Rotating through a scale will give you "modes" of a scale, each with a new "tonic" which is the starting/ending - or "home" - tone of the scale...

Finally, inverting (melodic inversion) means to change the interval direction of a melodic line, in other words: playing it upside down...

Answer 5

Like others have said, what the original question stated as "A minor, second inversion" is in fact 2nd rotation. The "melodic" inversion or maybe "horizontal" inversion is an important tool in set class theory. There, you would write a major scale as [0,2,4,5,7,9,E] (E for "eleven"). If you invert that set, you'll get [0,1,3,5,7,8,T] (T for "ten"), which actually is the same as "phrygian".

That "set class inversion" (for my personal lack of a better term) is something totally different than harmonic inversion can be seen by inverting the set class [0,3,7] which represents a minor triad. (with c=0: C, Eb, G) Inverting it gives [5,9,0], (c=0: F, A, C) which is actually the 5th transposition of [0,4,7]: a major triad. What is referred to as "inversion" of a triad in classical theory is rotation in set class theory, since you don't change the pitch class set content, but the order: [0,4,7] => [4,7,0] => [7,0,4].