The Pentatonic scale is often described as being the major scale with the 4th and 7th notes removed. E.g The C major scale is C D E F G A B C, so the C Major Pentatonic scale is C D E G A C.
Why are the 4th and 7th scale degrees removed why not say the 2nd and 6th? it would still be a pentatonic (5 notes) scale.
What's so bad about the 4th and the 7th degrees?
What we call THE pentatonic scale really wasn't created by removing the 4th and 7th notes from a major scale! It pre-dates the major scale. People have sung on pentatonic scales since they lost interest in tetratonic ones! "The five-note system was already considered archaic by the Greeks in 350 B.C. and [was] employed long before that by the Chinese." [Pentatonicism in Hungarian Folk Music, Zoltán Kodály, 1917.]
The five-note scales Kodály found in Hungarian folk music were anhemitonic (without semitones), but pentatonic scales exist in countless cultures and they often DO include either semitones or intervals roughly similar to equal temperament semitones. Javanese Gamelan orchestras, for example, generally use five-note (Slendro) scales or five-note subsets of the seven-note (Pelog) scale. These tunings certainly include small intervals - sometimes as many as three.
I think there may be some truth in the idea that semitone intervals are harder to sing than larger ones. That might account for the appeal of the 'all black notes' type of scale.
The fourth and the seventh are the only tones that distinguish the different major and minor modes (not including locrian). The pentatonics represent the common tones in all these modes.
Ionian, Lydian, and Mixolydian all have (1, 2, 3, 5, 6) in common. Only the 4th and 7th are altered. Similarly for the minor modes. Aeolian, Dorian, and Phygian all have (1, b3, 4, 5, b7) in common the second and sixth are removed in the minor case but these are the seventh and fourth in the relative major modes. This allows one to move freely between keys that are off by a fourth. This is a very common modulation and keys that are a 4th apart are often called compatible keys in classical music theory. Going up or down by a 4th involves only one note change. In any key the 4th above (Fa) is a compatible key and has the Lydian mode occurring on it relative to the original key. To change key up a 4th you just drop the 7th of the original key. For example, modulate from G maj to C maj involves moving F# to F (flat seventh). To move down a fourth to the key of D (which is also the 5th of G) one raises the 4th of the original key. So you see that the I, IV and V in any key are "compatible" and differ only by the seventh and the fourth. This is one significance of these two tones. It is not uncommon for songs to be harmonized with the I, IV, and V (and/or V7) chords. Additionally it is common for songs to modulate to these keys. That is to say we don't only use these four chords to harmonize in the original key but often change key in a song by moving through he circle of fourths (or fifths). Removing these tones from the diatonic scale reveals the common tones. for a guitarist it reveals common patterns that can easily be moved around.
Keep in mind that the description you have provided might be a bit of a red herring and somewhat ethnocentric. In many cultures 5 tone and 6 tone scales are used and they are not derived from western music by removing notes. The description might be an atempt to explain to the scales of other cultures from a Western point of view, to provide a simple algorithm for westerners to understand other scales. This does not always help.
A pentatonic scale isn't a major scale with the 4th and 7th removed any more than it's a minor scale with the 6th and 2nd removed or a major scale is a chromatic scale with C#, D#, F#, G#, A# removed, etc. etc.
A pentatonic scale is a five note scale. Nothing is missing or removed.
One way to generate a pentatonic scale with an additive process is to build the scale from ascending perfect fifths: C G D A E. That can be re-arranged as C D E G A or A C D E G for either major or minor pentatonics. With this method there are no removed tones.
Ascending perfect fifths is not necessarily how the scale evolved, but it's one way to describe it. No one can explain the origin. It's prehistoric so any explanation is speculation. Personally I like thinking of it as two tones a perfect fifth apart (very resonant) with auxilary tones a major second above and a minor third below those two starting tones...
______(P5)_____
| |
A (m3) C (M2) D E (m3) G (M2) A
| | | |
-----(P4)---- -----(P4)----
...which also gives us two tetrachord-like perfect fourths that are a kind of musical universal.
Michael Curtis's answer makes the point that the pentatonic scale is what you get if you make a five-note scale by adding successive perfect fifths (and also makes the good point that this is not necessarily how the scale evolved). What I would add to that answer is that five notes is a natural stopping point in the process of adding perfect fifths.
If you start with a single note, F, and a single interval (the octave),
2
________________
| |
F F
then addition of the note a fifth above F gives C and subdivides the octave into two unequal intervals of a fifth (frequency ratio 3/2) and a fourth (frequency ratio 4/3):
3/2 4/3
________________ ____________
| | |
F C F
We've already added the fifth above F; if we now add the fifth above C we get G and the fifth between F and C gets subdivided into a major second (9/8) and a fourth:
9/8 4/3 4/3
____ ____________ ____________
| | | |
F G C F
Adding the fifth above G gives D, and subdivides the fourth separating C and F into a major second (9/8) and a minor third (32/27). If, instead of stopping there, we add the next fifth, A, both fourths get subdivided in the same way. In the resulting scale there are two intervals between consecutive notes: the major second (9/8) and the minor third (32/27):
9/8 9/8 32/27 9/8 32/27
____ ____ ________ ____ ________
| | | | | |
F G A C D F
Had we stopped at only four notes, there would be three unequal intervals separating consecutive notes of the scale.
We can stop here, but if we do continue adding fifths, the next point at which our scale has two unequal intervals rather than three is the seven-note scale:
256/243 256/243
9/8 9/8 9/8 | 9/8 9/8 |
____ ____ ____ ___ ____ ____ ___
| | | | | | | |
F G A B C D E F
The minor thirds of the pentatonic scale have been subdivided into a major second (9/8) and a minor second (256/243). (The stated frequency ratios are those of Pythagorean tuning, which, of course, is not what is actually used these days.)
The next such stopping point would be a 12-note scale. The five added notes would subdivide the minor seconds into two different types of semitone (ratios 256/243 and 2187/2048 in Pythagorean tuning). Note that the five added notes themselves form a pentatonic scale.
This answer is a somewhat abbreviated version of the related discussion here.
The fourth and seventh degrees of the major scale are the basis for the dominant harmony.
The interval between these notes is the tritone interval. They are incorporated into the dominant chord; for instance G7 in the key of C major.
These notes create a tension which drives toward resolution to the tonic: in C terms, the B "wants to" move to C, while the F also wants to move to C. This dominant to tonic resolution creates a lot of the sense of forward motion in Western music.
If we remove these notes, we remove the source of tension and forward motion, which creates are more relaxed, ambiguous mood, which in turn assists in improvising.
Note that the same major pentatonic scale you are thinking of isn't the only pentatonic scale by any stretch. And even that pentatonic occurs within the major scale at several locations. In the key of C major, there is one starting on C, one starting on F and one starting on G. These major pentatonics have their relative minor pentatonics. So that is to say, even if we specifically want a major pentatonic scale in the key of C, removing F and B isn't the only way to get it; that just specifically gets us that one which starts on C.
The pentatonic major scale is the diatonic major scale without half-steps, therefore allowing for simpler transitions between scale tones.
When mathematician Pythagoras plucked the string and discovered the natural harmonic overtone series, he used those first three perfect intervals of octave, fifth, and fourth to make the pentatonic scale:
[root] + P8va + P5th + P4th
This link has a helpful graphic: http://hyperphysics.phy-astr.gsu.edu/hbase/Music/just.html#c3
No, I'm not saying the pentatonic scale only has three notes in it ... I'm saying the five-tone scale was composed using three intervals (much like the circle of 5ths [or 4ths if you go the other direction] is made using the perfect 5th interval).
No, P4 is not "way down" the list of harmonics. The first overtone is the octave. Then the 5th, and then the 4th which yields the second octave.
Yes the interval of perfect 4th is in the pentatonic scale. The 4th is complementary to the 5th, so any time you have a perfect 5th you also have a 4th going the other direction.
Finally, to moderator Dom, please do not delete my answers. If you don't understand them leave a comment and I'll be happy to explain.
The 4th and 7th were not removed to get a pentatonic scale. In opposite they rather have been added to the pentatonic scale to have a heptatonic by constructing 2 tetrachords ("scales" of 4 strings (tones). The 7th, (leadtone to the root tone) was one of the last tones as there have been only six degrees (hexachords) before. (But the Greek 2000 years ago had much more tones between the whole steps we use today!).
