Why is the hexatonic scale that can be derived via a chain of perfect fifths so little-known?

Question

When learning about European classical music, it's heptatonic scales. The pentatonic scale is also very well known and widely used in folk music in different parts of the world. However, before I started reading in Wikipedia about hexatonic scales, the only hexatonic scale I had heard about was the whole-tone scale. The hexatonic scale that you get by throwing out one of the notes from the diatonic scale so that it becomes atritonic (or by adding one note to the pentatonic scale) seems to be less well known than its neighbors. Although, just like those other two, it can be derived from a chain of perfect fifths.

What I mean is the scale which has the following intervals between notes: 1 semitone, 2 semitones, 2 semitones, 3 semitones, 2 semitones, 2 semitones.

I started thinking about it in the context of algorithmic composition. This 122322 scale is much more flexible and rich than the 22323 pentatonic scale. There is this semitone and you can get more interesting melodies out of it. But, unlike with the 1221222 heptatonic scale, you do not have tritones anywhere. If I want to avoid tritones in melody and harmony, this is a very good thing since it ensures that any random bunch of notes that my algorithm outputs is guaranteed to not contain a tritone.

There are of course some disadvantages... The one that I notice is that it's not possible to play two major or minor chords that are two semitones apart. However, for example, if we want to play F major and G major chords, we can just play A-C interval and G major chord, or F major chord and G-D interval, and to my musically untrained ears, those compromises sound almost as good as the two full chords. And, whatever the disadvantages are harmony-wise, in pentatonic it's even worse, right?

Are there any practical or historical reasons why the 122322 scale is so little-known, while the two nearest neighbors 22323 and 1221222 are in wide use? Does it have something to do with the fact that 5 and 7 are prime numbers while 6 is not? Does it have something to do with the history of musical instruments?

Or IS hexatonic little-known? I do not have much music background, only took a couple of music theory and harmony classes at the uni, so maybe I am mistaken and the hexatonic scale is actually more widely used than I think? Do you know any pieces that use this scale? (Especially folk melodies, early music or classical compositions.)

Answer 1

The premise isn't really true, since such hexatonic scales are actually very common in folk and country music. In particular, the “missing ⅶ scale” 221223. An important source are Scottish tunes, e.g.

X:1
T:The Athole Highlanders
L:1/16
M:6/8
K:D
V:2 clef=treble
|: A6 A3FD2 | A3FD2 E3FG2 | A6 A3FD2 | E3FG2 F3ED2 |
A6 A3FD2 | A3FD2 E3FG2 | Ad3A2 B3AG2 | F3GE2 D6 :|
%

Celtic music is strongly dominated by a single melody, which is often mostly pentatonic but adds in the remaining diatonic notes occasionally.

This tendency to keep a lot to the major pentatonic (as well as the Blues one, though that is actually quite different) has had a lot of influence on American Folk and through that on country, rock and pop music. However, those genres have much more emphasis on a chordal accompaniment, using the Ⅰ and Ⅳ chords most often, so country can hardly be called pentatonic. Hexatonic it is.

The situation is very different in classical music. This too is dominated by melodies, but there is a fundamentally different approach. Whereas Celtic music likes a “constant floating feeling”, classical music is all about building up, constructing cadences that have clear resolutions. And the most powerful melodic resolution is the ⅶ-Ⅰ step, which is therefore all over classical music.

But even classical music may use hexatonic scales, in particular when going for a folky feel. But it's usually limited to short motifs:

X:1
T:Sinfonie No. 6, “Pastorale”
C:Ludwig van Beethoven
Q:"1: All. ma non troppo"
L:1/8
M:2/4
K:F
V:2 clef=treble
z .A.B.d | (cB/2A/2 .G).C | .F.G (AB/2A/2) | .G.A (Bc/2B/2) | Accc | c2
%

A bit longer:

X:1
T:Finlandia
C:Jean Sibelius
L:1/4
M:C
K:Ab
V:2 clef=treble
z (c B c) | (d3 c) | (B c A z/2 B/2) | B (c3 | c) (c B c) | (d3 c) |
(B c A z/2 B/2) | (c4 | c) ( !tenuto! e !tenuto! e !tenuto! e) |
(f3 c) | (c e) (e3/2 B) | B (d3 | d) ( !tenuto! d !tenuto! c !tenuto! B) |
(c3 A) | A (B2 z/2 A/2) | A
%

I'm a little hesitant about that example, because the theme doesn't span an entire octave, and it's homophonically harmonised with voices that do include the G note. So it might well be argued that it's actually heptatonic but simply keeps in a small range of the scale.

A hexatonic mode that's rather more natural for classical music is the “missing Ⅳ” 223221 scale. A prime example of this is the gorgeous Andante Maestoso from Holst's Planets:

X:1
T:Jupiter, the Bringer of Jollity
C:Gustav Holst
L:1/8
M:3/4
K:Eb
V:2 clef=treble
z4 G,B, | C2 (CE) (D3/2B,/2) | EF E2 D2 | CD C2 B,2 | G,4 G,B, |
C (CE) (D3/2B,/2) | EF G2 G2 | (GF E2) F2 | E4 (BG) |
F2 F2 EG | (F2 B,2) BG | F2 F2 GB | c4 cd | e2 d2 c2 | B2 e2 G2 |
FE F2 G2 | B4
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Answer 2

It should also perhaps be mentioned that the hexatonic scale derived from a chain of perfect fifths is probably not often found, because Pythagorean thirds sound so bad. And in the hexatonic scales derived from removing the second note of the major scale (CEFGAB), you can have two chains of perfect fifths, F C G and A E B, with A and G separated by 10/9 (rather than the 9/8 demanded by a continual single chain), and all thirds are also perfect. Sounds much better.

(this is just a parenthetical answer for just intonation freaks)