The notes outside the major scale form a pentatonic scale

Question

Something that woke me up in the middle of the night, realising that if you take the 12 notes in an octave in western music, and from that you remove all those belonging to a major scale, you are left with 5 notes arranged as a pentatonic scale! (the mode of the 7 note scale or the minor/major quality of the pentatonic is irrelevant here).

How come in twenty years of playing guitar I've never come across this fact? Not that is useful (or is it?), but even now doing a few Internet searches, I can't find any reference to this.

For example, take C major (all white keys in piano). You are left with Eb, Gb, Ab, Bb, Db (all black keys in piano), which is an Eb minor pentatonic.

I'm not very good with music theory, so maybe this is obvious to anyone that goes to music school. I just found very interesting that these two patterns, that are by far the most commonly used, more than any melodic, harmonic, or other exotic scale arrangements (always within western music), and their notes are arranged so that they add up to all twelve notes in the octave without overlapping.

Two questions: Is this just a coincidence? Is there a musical way to use this?

And if someone could point out to any website where this is mentioned, I'd be curious to know.

Answer 1

I think this seems surprising only when fixated on the black and white key layout of keyboard instruments, but lets unpack what is going on.

Using the C major scale we list out all the pitch letters in scale steps...

C D E F G A B C

Now rearrange those letters by ascending perfect fifths...

F C G D A E B

To get the pitches with sharps and flats, the ones that make the black keyboard keys, we can extent the pitches to the left and right, notice that each letter is repeated but with a sharps on the right and flats on the left...

F♭ C♭ G♭ D♭ A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯ E♯ B♯

That now gives us a series of all basic pitches including those with sharps or flats and allowing for enharmonic spellings like D♯/E♭ etc.

Technically both the left and right side of the series could extend infinitely using double, triple, etc. sharps/flats, but for practical purposes we will stop the series at only one sharp/flat. Again, notice that the series is listing all pitches by perfect fifths.

We can now make these observations:

• any five adjacent pitches in the series makes a pentatonic scale.
• any seven adjacent pitches in the series makes a diatonic major scale.
• any twelve adjacent pitches in the series makes the chromatic scale.

For the scale in your example we have...

C major:

F C G D A E B

G♭ pentatonic:

G♭ D♭ A♭ E♭ B♭

C major and G♭ pentatonic concatenated for a chromatic scale:

G♭ D♭ A♭ E♭ B♭ F C G D A E B

Those are the two parts so visible on a keyboard as the white keys and black keys. But it's important to note there isn't anything special about those two particular scales. It's just a coincidence that one is all white keys and the other all black keys. (Or at least is was just a choice to assign all white keys to C major and fill in the remainder of 12 chromatic tones with black keys, other choices could have been made.)

Just remember you can make many other combinations of 5 + 7 or 7 + 5 adjacent pitches in the same way.

For example you could point out that all the piano keys are a combination of F pentatonic F C G D A and B major E B F♯ C♯ G♯ D♯ A♯ where all the black keys are the pitches with sharps in B major and the white keys are the other pitches from the combined scales.

Answer 2

It is known, maybe especially to piano/keyboard players, that the black keys form the Gb major / Eb minor pentatonic scale. Given the structure of the major scale and the structure of the pentatonic scale it's of course no coincidence, but I don't think there's some deeper meaning to it; it's just a result of these structures.

The interesting question (in my opinion) is if there's a "musical way" to make use of this fact. The answer is yes, there is. Many jazz musicians know that the minor pentatonic scale a minor third higher than the root of a dominant seventh chord (or the major pentatonic scale a tritone away from the root of a dominant seventh chord) contains all possible alterations and the minor seventh of that dominant seventh chord. So, e.g., over a C7 chord the Eb minor / Gb major pentatonic scale contains

Eb -> #9 Gb -> b5 / #11 Ab -> b13 Bb -> 7 Db -> b9

So you can use that pentatonic scale over C7 to create altered or outside sounds. As an example, if you play over a II-V-I in C major (Dm7 - G7 - Cmaj7), you can play a different pentatonic scale over each chord. One way to do that is to move up chromatically, which gives you an altered sound over the V chord (G7):

Dm7: A minor pent. (Dm9 sound) G7: Bb minor pent. (altered) Cmaj7: B minor pent. (lydian)

Of course, this trick for playing outside can also be used over other chords, such as minor 7 chords. Check out this example of Chick Corea using a G minor pentatonic scale to step outside over an Em7 vamp.

Answer 3

Perhaps the closest thing to a “reason” for this is that both diatonic and pentatonic scales can be considered as approximate Pythagorean scales. Now observe how the 12 degrees are constructed from circle of fifths: for instance,

E♭  B♭  F   C   G   D   A   E   B   F♯  C♯  G♯  D♯≅E♭
└───B♭-major diatonic───┘   └E-maj pentatonic┘  └temperament

Note that the story doesn't necessarily end there: while 12-edo tuning tempers out the Pythagorean comma that would follow between D♯ and E♭ here, other tunings do not. 17-edo is pretty good as a Pythagorean tuning, here you get an additional pentatonic scale before returning to the start:

G♭  D♭  A♭  E♭  B♭  F   C   G   D   A   E   B  F♯  C♯  G♯  D♯  A♯  E♯≅G♭
└───D♭-major diatonic───┘   └G-maj pentatonic┘ └F♯-maj pentatonic┘ └temperament

Answer 4

There's a fairly intuitive reason for this--"intuitive" in this case meaning that I'm not going to give a formal music-theoretic reason, but rather try to simply provide some intuition about why this might be so based on the circle of fifths and how "close" and "far" particular tonalities are from each other.

First, some observations:

• Major and minor pentatonic scales are the "nicest" notes that can be grouped together (to Western ears). This is a fuzzy concept, of course, but it's easily formalized: notes (and keys/chords/scales) that are closer together on the circle of fifths sound more similar and are "nicer" together than notes that are further apart on the circle, and any five consecutive notes on the circle form a pentatonic scale.
• The major scale is a pentatonic plus the two "next-nicest" notes--i.e., any seven consecutive notes on the circle of fifths form a major scale. (Note that in order to take a pentatonic scale and form a major scale of the same key, you must add the two notes directly before and after the pentatonic scale group on the circle of fifths. More about this issue of "directionality" below.)
• Notes (/keys/chords/scales) that are a tritone apart are as dissimilar as possible; they are diametrically opposed (i.e. maximally far apart) on the circle of fifths. This typically means they sound the least "nice" together (hence the term "Devil's interval").
• This concept of "similarity" and "dissimilarity" is transitive. For example, C neighbors G on the circle of fifths, and G neighbors D, so C and D are fairly similar. On the other end of the spectrum, C and F♯ are a tritone apart and are thus maximally dissimilar; F♯ is next to C♯ on the circle of fifths, and so C and C♯ also clash (though not as badly as F♯ and C).

Now, sticking with our example of using C as the basis for our analysis (but, as mathematicians say, "without loss of generality"), we can see that:

• Notes in the C major pentatonic scale are "similar to" C (i.e. they are the next 4 notes going up the circle of fifths).
• Notes in the F♯ major pentatonic scale are "similar to" F♯, and F♯ is maximally "dissimilar from" C, so, transitively, we've now divided up the keyboard between "notes that are similar to C" and "notes that are similar to F♯ and maximally dissimilar from C."
• We've got two notes left over: B and F (E♯). These belong to both the C major scale and the F♯ major scale. Thus the property you noticed is (of course) reflexive: if we're in F♯ major, the unused notes are the C pentatonic scale, and if we're in C major, the unused notes are in the F♯ pentatonic scale.

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This leads to an interesting thought: we can evenly partition the keyboard into two 6-note "major-ish" scales. Presumably we'd want to give B to C major and F (E♯) to F♯ major to ensure that we have leading tones for both scales.

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The biggest "fuzzy" element of this analysis is that "similar" (as used above) doesn't precisely correlate with "nearness" on the circle of fifths, because going backward from C (i.e. moving up by 4ths or down by 5ths) quickly leads to B♭ (A♯), which is part of F♯ major pentatonic. But there's no particular reason why "closeness" on the circle of fifths shouldn't be considered reflexive (i.e. there's no reason to consider D closer to C on the circle than B♭ is). This part of the analysis could be made more rigorous by introducing a concept of directionality into the concept of "similarity" with which we've built the scales in question, i.e., by formalizing a reason for going up by 5ths when constructing our scales rather than going up by 4ths. This is well understood by applying the concept of the tonic-dominant relationship, but that's beyond the scope of this answer.

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Can we use this when playing music? Matt L. has already given one use-case, unsurprisingly coming from the world of jazz where the concepts of "nearness" and "farness" are bent pretty far from how they're used in Western classical music.

But even in more "traditional"-sounding music, and especially in pop songs and Broadway-style show tunes, there's another use-case: dramatic modulations. If you're in C major and you want to have a sudden radical shift that still sounds "right", why not modulate as far away from C as possible? If you start playing the F♯ pentatonic scale, suddenly, most of the notes you're using would have been (somewhat) out of place in C major, but in their new context post-modulation, they're as close as possible to your new tonic (F♯). The shift is so dramatic, and the pentatonic scale is so harmonically "clear" or "obvious" sounding, that composers will often simply modulate without any real transition chords; you can jump right from C Major to F♯ Major without preparing the listener, and the chordal structure will still remain clear.

Answer 5

THIS IS HOW TO USE IT. It can used to play "outside" and best works with Fusion jazz, or possible some weirder metal styles. If you are not into those styles or modern discordant classical it probably won't be useful.

It will work best over a grove if you want it to blend

So you play a solo in the main key and in the middle of it you start playing that pentatonic scale of the other 5 notes. You just sprinkle it in once in a while

As you said begin with the notes of a diatonic 7 notes scale

Now the unused notes form a pentatonic scale.

You had C. On youtube play a C Major vamp backing track

then Eb, Gb, Ab, Bb, Db

Now start on any of those and play the rest and end on two chord notes from CM ( "<" descending not follows)

Gb Ab Bb Db Eb E < C

Bb Db Eb Gb Ab A < G

Eb Gb Ab Bb Db C < G

Bb Db Eb Gb Ab A < E

Db Eb Gb Ab Bb < G > C

the last notes can be switched

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Or in descent (this one sounds good try it)

Db Bb Ab Gb Eb G C

etc always resolve to notes in the chord (if not in CM scale)

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It will take a couple of weeks to flow with this. The hardest part is smoothly going back to C major. It's disorienting to make the switch at first

Here's another technique that's easier take a not from CM, say G

now take a note a step above Ab and one below Eb put it all together Ab, Eb, G play the G on a down beat that's the last note resolution It's called "enclosure"