::  Posts  ::  RSS  ::  ◂◂RSS  ::  Contact

Diatonic modes as progressive flattening

September 10th, 2018
music  [html]
Most tunes are built around a diatonic scale. The most well known diatonic scale is the major scale, C D E F G A B, but all seven cyclic permutations of those notes are named scales:
  • C D E F G A B: major (I)
  • D E F G A B C: dorian (II)
  • E F G A B C D: phrigian (III)
  • F G A B C D E: lydian (IV)
  • G A B C D E F: mixolydian (V)
  • A B C D E F G: minor (VI)
  • B C D E F G A: locrian (VII)

Even though seven of these are possible, the only ones you generally run into in traditional music are major (I), minor (VI), mixolydian (V), and dorian (II).

Another way to think of these is as adding flats:

  • no flats: C D E F G A B (I, major)
  • add a flat seventh: C D E F G A Bb (V, mixolydian)
  • add a flat third: C D Eb F G A Bb (II, dorian)
  • add a flat sixth: C D Eb F G Ab Bb (VI, minor)
  • add a flat second: C Db Eb F G Ab Bb (III, phrigian)
  • add a flat fifth: C Db Eb F Gb Ab Bb (VII, locrian)
You'll notice that IV (lydian) is missing. Following the pattern, this would give us:
  • flat first: Cb Db Eb F Gb Ab Bb (IV, lydian)
And then, I guess:
  • flat fourth: Cb Db Eb Fb Gb Ab Bb (I, major)

This is correct, except that we switched down to Cb once it came time to flat the first.

The problem is that the major scale (I) isn't actually a great place to start: if we instead start with the lydian scale (IV) everything works:

      C  Db D  Eb E  F  F# G  Ab A  Bb B
IV    1     2     3     4  5     6     7
I     1     2     3  4     5     6     7
V     1     2     3  4     5     6  7
II    1     2  3     4     5     6  7
VI    1     2  3     4     5  6     7
III   1  2     3     4     5  6     7
VII   1  2     3     4  5     6     7

You can see that starting with the lydian scale each scale degree in turn is flattened: 4, 7, 3, 6, 2, 5. For more symmetry, each note to be flattened is a fifth down from the previous note to be flattened.

If we follow this pattern, flattening one note at a time, we can run through all the modes of all the keys:

       A  Bb B  C  Db D  Eb E  F  F# G  Ab A  Bb B
C IV            1     2     3     4  5     6     7
C I             1     2     3  4     5     6     7
C V             1     2     3  4     5     6  7
C II            1     2  3     4     5     6  7
C VI            1     2  3     4     5  6     7
C III           1  2     3     4     5  6     7
C VII           1  2     3     4  5     6     7
B IV         1     2     3     4  5     6     7
B I          1     2     3  4     5     6     7
B V          1     2     3  4     5     6  7
B II         1     2  3     4     5     6  7
B VI         1     2  3     4     5  6     7
B III        1  2     3     4     5  6     7
B VII        1  2     3     4  5     6     7
Bb IV     1     2     3     4  5     6     7
Bb I      1     2     3  4     5     6     7
Bb V      1     2     3  4     5     6  7
Bb II     1     2  3     4     5     6  7
Bb VI     1     2  3     4     5  6     7
Bb III    1  2     3     4     5  6     7
Bb VII    1  2     3     4  5     6     7
A  IV  1     2     3     4  5     6     7
A  I   1     2     3  4     5     6     7
A  V   1     2     3  4     5     6  7
A  II  1     2  3     4     5     6  7
A  VI  1     2  3     4     5  6     7
A  III 1  2     3     4     5  6     7
A  VII 1  2     3     4  5     6     7

Turning this on it's side, it's really quite a pretty pattern:

Stepping back, this makes it easy to think about what notes to expect in a mode:

  • major: no extra flats
  • mixolydian: one extra flat
  • dorian: two extra flats
  • minor: three extra flats

I find this framing much more useful than the cyclic permutation approach of thinking about starting the major scale on different notes.

(This also gets more elegant if we rename "F#" to "F" and "F" to "Fb". Then the lydian scale is C D E F G A B and all the other scales add flats from there.)

Comment via: google plus, facebook

Recent posts on blogs I like:

Incoming Gantz-Led Government to Invest in Israel’s Infrastructure

Israel’s incoming prime minister Benny Gantz unveiled an emergency government, to take power following an upcoming confidence vote in the Knesset. The last two MKs required to give Gantz a 61-59 majority, two members of Gantz’s own Blue and White Party wh…

via Pedestrian Observations April 1, 2020

Finding home in the time of coronavirus

Disclaimer: I’m going to say this once. Obviously, I am not happy about the coronavirus’s threat to public health or the economic toll it’s taking. I do not think the existence of this pandemic is good. Just so happens that social distancing and remote wo…

via Holly Elmore March 31, 2020

Massachusetts should shut down immediately

We’ve been running 30x fewer tests than other states, and have been extremely tardy in responding to the Biogen outbreak.

via benkuhn.net March 15, 2020

more     (via openring)

More Posts:


  ::  Posts  ::  RSS  ::  ◂◂RSS  ::  Contact