When writing a primer on learning and understanding modes (using Roy G. Biv), I discovered some interesting curiosities about modes that I had never seen or read about, at least not through this particular thought-process. I wanted to share them, but that article was getting pretty long, and these things aren't particularly useful or practical, just interesting, so I made two separate pages to share them, this one, and one on reading a parallel mode chart vertically.
This article can also be read in conjunction with Modes Quiz / Flashcards and Mode Calculator and Mode Chart.
Frankly, I can't tell if this is complicated, or extremely simple. Either way, I'm pretty sure I took the long route to get there, but I'll explain the path I took, and you tell me what you think.
Take a look at the table below. It lists 1) the order of sharps in notes, 2) the corresponding major scale, 3) the order of sharps in scale degrees, and 4) the corresponding "C" scale. Nothing particularly interesting here, just look it over and keep reading below.
| Order of Sharps | Major Scale With associated Key signature |
Scale Degrees of the Order of Sharps |
Order of Sharps as applied to "C" modes |
|---|---|---|---|
| F# | G major scale | 7 | C scale with F#: C Lydian |
| F#, C# | D major scale | 7,3 | "C" scale with F#, C#: C# Locrian |
| F#, C#, G# | A major scale | 7,3,6 | "C" scale with F#, C#, G# C# Phrygian |
| F#, C#, G#, D# | E major scale | 7,3,6,2 | "C" scale with F#, C#, G#, D# C# Aeolian |
| F#, C#, G#, D#, A# | B major scale | 7,3,6,2,5 | "C" scale with F#, C#, G#, D#, A# C# Dorian |
| F#, C#, G#, D#, A#, E# | F# major scale | 7,3,6,2,5,1 | "C" scale with F#, C#, G#, D#, A#, E# C# Mixolydian |
| F#, C#, G#, D#, A#, E#, B# | C# major scale | 7,3,6,2,5,1,4 | "C" scale with F#, C#, G#, D#, A#, E#, B# C# Ionian |
Now, if you're like me, then the order of sharps represented in scale degrees stood out to you. If not, look at that column again. They don't actually look like they represent sharps, do they? They look like they represent the flats of the modes!
When I see "7," "7 and 3," and "7, 3, 6," etc., particularly in that order, I don't think "oh, that's the order sharps in scale degrees as applied to the major scales," I think "Modes!" Here's why:
Cool! But... 7, 3, 6, 2, 5,... and 1? Yup, the pattern continues! Write out a C scale (C D E F G A B) now flat those scale degrees (7, 3, 6, 2, 5, 1) and you get this Cb Db Eb F Gb Ab Bb. What's that? Cb lydian!! Next, if you flatten 7, 3, 6, 2, 5, 1, and 4 you get Cb ionian!
This is all perfectly logical, but I had never given serious thought to it until I made this chart for the other article and noticed the order of sharps in scale degrees. So, in short, the order of sharps is not just the order of flats in reverse, but also the order of flats in modes...but why?
Continuing, I added that row to the table, and that just made things worse.
| Order of Sharps | Order of Sharps in Scale Degrees | Associated Major Scale | "C" mode | If the order of sharps (scale degrees) were flats |
|---|---|---|---|---|
| N/A | N/A | C | C ionion | C ionion |
| F# | 7 | G | C Lydian | C mixolydian |
| F#, C# | 7,3 | D | C# Locrian | C dorian |
| F#, C#, G# | 7,3,6 | A | C# Phrygian | C aeolian |
| F#, C#, G#, D# | 7,3,6,2 | E | C# Aeolian | C phrygian |
| F#, C#, G#, D#, A# | 7,3,6,2,5 | B | C# Dorian | C locrian |
| F#, C#, G#, D#, A#, E# | 7,3,6,2,5,1 | F# | C# Mixolydian | Cb lydian |
| F#, C#, G#, D#, A#, E#, B# | 7,3,6,2,5,1,4 | C# | C# Ionian | Cb ionion |
I mean, those right two columns both start on C ionian, but end up on ionians that are a doubly augmentd / doubly diminished prime apart!?
Now that we have this extra set of modes, how do they relate to everything else on that table -- it doesn't seem to make much intuitive sense. To figure this out, let's start by removing all the columns but the two in question so it's a bit easier to navigate:
| "C" modes created by the order of sharps | If the order of sharps (scale degrees) were flats |
|---|---|
| C ionian | C ionian |
| C lydian | C mixolydian |
| C# locrian | C dorian |
| C# phrygian | C aeolian |
| C# aeolian | C phrygian |
| C# dorian | C locrian |
| C# mixolydian | Cb lydian |
| C# Ionian | Cb ionion |
Here are the connections I made when thinking about these lists:
1. These two "lists" go in opposite directions. Read the modes of the "left list" from the top down: ionian, lydian, locrian, etc. Now look at the second list and read it from bottom to top: ionian, lydian, locrian, etc. Interesting... but why? It still doesn't answer any of our questions about how those two columns are related.
2. Another interesting and related aspect I noticed was that the left column ascends in perfect 5ths, and the right column ascends in perfect 4ths. On the left side (bottom to top), ionian to mixolydian is perfect 5th, and mixolydian to dorian is also a perfect 5th, this continues throughout the table. The right column is the same, but it ascends in perfect 4ths. What's interesting is that they start and end on ionians in "unison." What happens if we keep going on each side? A perfect fifth above ionian, and a perfect fourth above ionian is mixolydian and lydian. Ah, of course...we're looping (sort of... keep reading!). Again, interesting, but does this satisfactorily explain how these two lists are related? No.
3. Let's try looking at individual rows instead. Ignoring the C ionians for now, how might C lydian to C mixolydian, be related? Well, they both obviously have one alteration from their parallel major (#4 for lydian, and b7 for mixolydian). Additionally, as noted in point 2, lydian is a mode that is found a perfect fourth above, or a perfect fifth below, it's relative major, while mixolydian, on the other hand, is found the opposite directions: a perfect fifth above and a perfect fourth below. Furthermore, C lydian "belongs" to G major, while C mixolydian "belongs" to F major. Hopefully you've caught on by now: their associated major scales are moving in opposite directions around the circle of fourths/fifths -- in fact, they create the circle of fourth/fifths!
So now, let's add their associated major scales on either side.
| Associate major scale | "C" modes created by the order of sharps | If the order of sharps (scale degrees) were flats | Associated major scale |
|---|---|---|---|
| C major | C ionian | C ionian | C major |
| G major | C lydian | C mixolydian | F major |
| D major | C# locrian | C dorian | Bb major |
| A major | C# phrygian | C aeolian | Eb major |
| E major | C# aeolian | C phrygian | Ab major |
| B major | C# dorian | C locrian | Db major |
| F# major | C# mixolydian | Cb lydian | Gb major |
| Cb major | C# ionian | Cb ionion | Cb major |
Notice how the outter most columns literally create the circle of fourths/fifths?
Now, because we can, lets continue this chart in both directions at once -- up and down! I'll highlight the rows where the ionians match.
| Associate major scale | "C" modes created by the order of sharps | If the order of sharps (scale degrees) were flats | Associated major scale |
|---|---|---|---|
| Cbb major | Cbb ionian | Cx ionian | Cx major |
| Gbb major | Cbb lydian | Cx mixolydian | Fx major |
| Dbb major | Cb locrian | Cx dorian | B# major |
| Abb major | Cb phrygian | Cx aeolian | E# major |
| Ebb major | Cb aeolian | Cx phrygian | A# major |
| Bbb major | Cb dorian | Cx locrian | D# major |
| Fb major | Cb mixolydian | C# lydian | G# major |
| Cb major | Cb ionian | C# ionian | C# major |
| Gb major | Cb lydian | C# mixolydian | F# major |
| Db major | C locrian | C# dorian | B major |
| Ab major | C phrygian | C# aeolian | E major |
| Eb major | C aeolian | C# phrygian | A major |
| Bb major | C dorian | C# locrian | D major |
| F major | C mixolydian | C lydian | G major |
| C major | C ionian | C ionian | C major |
| G major | C lydian | C mixolydian | F major |
| D major | C# locrian | C dorian | Bb major |
| A major | C# phrygian | C aeolian | Eb major |
| E major | C# aeolian | C phrygian | Ab major |
| B major | C# dorian | C locrian | Db major |
| F# major | C# mixolydian | Cb lydian | Gb major |
| C# major | C# ionian | Cb ionion | Cb major |
| G# major | C# lydian | Cb mixolydian | Fb major |
| D# major | Cx locrian | Cb dorian | Bbb major |
| A# major | Cx phrygian | Cb aeolian | Ebb major |
| E# major | Cx aeolian | Cb phrygian | Abb major |
| B# major | Cx dorian | Cb locrian | Dbb major |
| Fx major | Cx mixolydian | Cbb lydian | Gbb major |
| Cx major | Cx ionian | Cbb ionian | Cbb major |
Now obviously there's no true "circle," but this was a cool train ot thought to explore, and ultimately show to myself that the "circle" is just two small parts of a potentially endless list wrapped around eachother.
Obviously the reverse is the same. I won't rewrite the entire thing, but I'll go ahead and reproduce the "flat" version of the frist two tables so you can see how you would arrive at the same conclusion.
| Order of Flats | Associated Major Scale | Scale Degrees of the Order of Flats | Order of Flats as applied to "C" modes |
|---|---|---|---|
| Bb | F major scale | 4 | C scale with Bb: C Mixolydian |
| Bb, Eb | Bb major scale | 4, 1 | C scale with Bb, Eb C Dorian |
| Bb, Eb, Ab | Eb major scale | 4, 1, 5 | C scale with Bb, Eb, Ab C Aeolian |
| Bb, Eb, Ab, Db | Ab major scale | 4, 1, 5, 2 | C scale with Bb, Eb, Ab, Db C Phrygian |
| Bb, Eb, Ab, Db, Gb | Db major scale | 4, 1, 5, 2, 6 | C scale with Bb, Eb, Ab, Db, Gb C Locrian |
| Bb, Eb, Ab, Db, Gb, Cb | Gb major scale | 4, 1, 5, 2, 6, 3 | C scale with Bb, Eb, Ab, Db, Gb, Cb Cb Lydian |
| Bb, Eb, Ab, Db, Gb, Cb, Fb | Cb major scale | 4, 1, 5, 2, 6, 3, 7 | C scale with Bb, Eb, Ab, Db, Gb, Cb, Fb Cb Ionian |
The pattern here is a little less clear becuase lowering scale degree 1 ends up being the second flat we add in terms of the order of flats (think of the circle of 4ths... C, F, Bb, Eb, etc.). However, the pattern is still there, it's just harder to recognize at first since we rarely think in terms of a "flat 1."
So again, look at the table above and rather than think of the order of flats in scale degrees, look at them as if they were sharps. The first row has just 4, which would become #4, and that's obvious: lydian. Next is #4 and #1. A bit confusing perhaps, so let's write out a "C" scale with a sharp 4 and 1: C# D E F# G A B. Ah, C# locrian! And the pattern continues: Lydan, Locrian, Aeolian, Phrygian, Dorian, Mixolydian and ending with C# Ionion.
Cool!
Here's one more table that spells it all out:
| Order of Flats | Order of Flats in Scale Degrees | Associated Major Scale | If they were sharps instead of flats |
|---|---|---|---|
| Bb | 4 | F | C lydian |
| Bb, Eb | 4,1 | Bb | C# locrian |
| Bb, Eb, Ab | 4,1,5 | Eb | C# aeolian |
| Bb, Eb, Ab, Db | 4,1,5,2 | Ab | C# phrygian |
| Bb, Eb, Ab, Db, Gb | 4,1,5,2,6 | Db | C# dorian |
| Bb, Eb, Ab, Db, Gb, Cb | 4,1,5,2,6,3 | Gb | C# mixolydian |
| Bb, Eb, Ab, Db, Gb, Cb, Fb | 4,1,5,2,6,3,7 | Cb | C# ionian |