The Modes in “Circle of Fifths” Order

I won’t be analyzing the modes in their traditional order, since I’m be analyzing how lowering a regular pattern of notes by a half-step each enables us to walk through every mode on every key. A few notes (pun intended):

• A♯ and B♭ represent the same pitch. Likewise B and C♭, C♯ and D♭, and so on. However, in terms of music theory, A♯ and B♭ can be semantically quite different in some contexts – be careful.
• Key signatures with seven sharps or seven flats exist, but I’ve omitted them. (There are even monstrosities with double-sharps [𝄪] and double-flats [𝄫] … which I’ll mostly be ignoring. I can at least tolerate the double-flat symbol, but the double-sharp symbol is a monstrosity that doesn’t even bear any resemblance to the thing it’s supposed to be doubling.) I feel it was pretty extravagant just to include six-flat and six-sharp key signatures alongside each other.
• If we start from Lydian mode, lowering the correct pitches one at a time by a half-step each gives us the next mode in the cycle. I’ll use C Lydian as an example to demonstrate the principle:

• In other words:
  • Lowering C Lydian’s F♯ to F gives us C Ionian (i.e., C major).
  • Lowering C Ionian’s B to B♭ gives us C Mixolydian.
  • And so on, until we reach C Locrian – whence the pattern repeats for C♭/B, the key below C on the chromatic scale.
• Lowering Locrian’s root gives us Lydian mode in the key below it on the chromatic scale.
  • In other words, lowering C Locrian’s C to C♭/B gives us C♭/B Lydian.
• The sequence repeats from there:
  • Lowering B Lydian’s E♯ gives us B Ionian.
  • Lowering B Ionian’s A♯ gives us B Mixolydian.
• This sequence will repeat for every note on the chromatic scale: C, C♭/B, B♭/A♯, A, A♭/G♯, G, G♭/F♯, F, F♭/E, E♭/D♯, D, D♭/C♯, and back to C.

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The Principles of Inverse Operations

• Now, note that we’ve effectively been subtracting 1 from a regular pattern of values in a sequence:
  • 4, 7, 3, 6, 2, 5, 1, 4, 7, 3, 6, 2, 5, 1…
• As a result, if we consult the mathematical properties of inverse operations, we can infer that converse of everything we’ve just done will apply if we add 1 to the same notes in the reverse order:
  • 1, 5, 2, 6, 3, 7, 4, 1, 5, 2, 6, 3, 7, 4…
• In other words:
  • Raising C♭ Lydian’s C♭ gives us C Locrian.
  • Raising C Locrian’s G♭ gives us C Phrygian.
  • Raising C Phrygian’s D♭ gives us C Aeolian.
  • And so on.

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An Audio Demonstration

• None of this will mean much to readers in isolation, so I put together a crude demonstration of the above principle ⟨aaronfreed.github.io/c_lydian_to_b_lydian.flac⟩ in Logic Pro. For the following modes, in order:
  1. C Lydian
  2. C Ionian
  3. C Mixolydian
  4. C Dorian
  5. C Aeolian
  6. C Phrygian
  7. C Locrian
  8. C♭/B Lydian
  you’ll hear the following, in order:
  1. the scale in ascending order
  2. arpeggiated and block versions of:
     1. the root (I) chord
     2. the subdominant (IV) chord
     3. the dominant (V) chord
     4. the root (I) chord
  (I could make a version going down the entire chromatic scale, but the entire thing would take thirteen and a half minutes to play through. Even I think that’s overkill, and I submit this exact page as exhibit A for what my definition of “overkill” must entail.)

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Further Notes

• It might help solidify your conception of this principle to understand that while we’re lowering (or raising) a pitch on our scale, we’re also, in a sense, jumping down (or up) a fifth. F Lydian is in the same key signature as C Ionian, not F Ionian. This is why so many of these patterns mirror the circle of fifths.
• In “Modes Descending from Lydian” above, the mode number and the pitch we lower to get it are exact mirrors of each other. This is not coincidental – it’s the direct result of a mathematical pattern.
• The modes are also always either three steps on the scale below their predecessors (usually, but not always, a perfect fourth), or four steps above (usually, but not always, a perfect fifth). In this context, they’re equivalent, since the scale repeats every octave.
  • Although this is only somewhat relevant here, one pair of intervals always constitutes an exception to the “perfect fourths” and “perfect fifths” rules: one fourth is always augmented, and one fifth is always diminished. These are actually the same interval, a tritone. The following steps on each scale are tritones in either direction:

    Diabolus in mūsicā
    #	Mode	Tritone
    4	Lydian	4	1
    1	Ionian	7	4
    5	Mixolydian	3	7
    2	Dorian	6	3
    6	Aeolian	2	6
    3	Phrygian	5	2
    7	Locrian	1	5

    Note that the third columns of “Diabolus in mūsicā” and of “Modes Descending from Lydian” are identical. This is also not coincidental.

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The Major Scale’s Modes & the Circle of Fifths

12 Major Scales × 7 Modes = 84 Combinations

• I’ve printed the C major scale’s modes in bold, blue type to make them stand out. These are the only scales played using only the white keys of the piano (this is also why music notation can express these specific keys without accidentals, either in the key signature or after it). The differences between their numbers are always multiples of twelve; this is also not a coincidence.
• Halfway between C major’s modes, I always print a mode twice, in orange, with its key signature first using six flats (G♭ major), then six sharps (F♯ major). I don’t really like either option (E♯ is F♮! C♭ is B♮!), but both avoid a repeated letter in a scale, and thus a rash of accidentals in the notation of any piece that uses them. G♭/F♯ major’s modes are also always separated by multiples of twelve, for the same reason: this progression separates all seven modes of each scale from each other by multiples of twelve.
• I’ve listed these descending by pitch so higher pitches will be, well, higher, which may confuse some people since we read from top to bottom and are used to thinking of harmony in ascending order. Someday, I plan to write a JavaScript add-on to give readers an option to reverse the order – and eventually, to give them then option to create similar tables for different scales (at the bare minimum, ascending melodic minor, harmonic minor, and chromatic Hypolydian; possibly others as well).
• “RM” is an initialism for “Relative Major”, and “KS” is for “Key Signature”. A cheat sheet for what modes use what key signatures can be found in the section immediately following this one.
• I’ve used zero-based indexing for these tables, so they’re indexed from zero to eighty-three. This is partly because I prefer zero-based indexing, but to be honest, it was mostly to give C Ionian an index of one.

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Key Signature Cheat Sheet

• The twelve-note chromatic scale has fifteen key signatures (𝄪 and 𝄫 monstrosities notwithstanding):

• Legend for the above:
  • Lyd = Lydian
  • Maj = major (Ionian)
  • Mix = Mixolydian
  • Dor = Dorian (if you’re not sure why it’s grey, ask your English teacher about the picture)
  • Min = natural minor (Aeolian)
  • Phr = Phrygian
  • Loc = Locrian
  • KS = key signature (highlighted because it’s the key to the table – pun coincidental, though I definitely didn’t even try to avoid it)
• Additional notes:
  • 5♯ and 7♭ express the same pitches.
  • 6♯ and 6♭ express the same pitches.
  • 7♯ and 5♭ express the same pitches.
  • As in the tables above, I’ve printed C major’s modes in blue and F♯/G♭ major’s modes in orange.
• Accidentals also fall onto the circle of fifths (e.g., B♭ to E♭ and E♭ to A♭ are both perfect fifths).

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Why is this happening?

The simple answer: whether we realized it or not, we’ve been traversing the circle of fifths this entire time. In the introduction, I mentioned that traveling from C Lydian to C Ionian was, in a sense, traveling from G major to C major. Here’s the C table again. Note how “relative major” traverses the circle of fifths downward:

The explanation is that each of these modes, apart from C Ionian, has been rearranging a different major scale. Reshuffling each mode back into its Ionian form may explain the cause:

Every note of every scale in this table is, in fact, a perfect fifth below its counterpart in its predecessor. Almost every other pattern we’ve observed that follows the circle of fifths in some way is a direct consequence of this.

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Chord Analysis by Mode

• I’ve printed the root (I), dominant (V), and subdominant (IV) chords of each mode in bold – they are especially important to the mode’s tonality.
• I’ve printed the seventh chord in lighter text because it’s diminished in the major scale.
• Minor chords are blue; diminished chords are orange.
• Printing the chords this way makes it clearer why Ionian became the standard major scale and Aeolian became the natural minor scale: the root, dominant, and subdominant are all major in Ionian mode and all minor in Aeolian mode. This makes them feel, respectively, especially major and especially minor.
• Since their root chords are major, Lydian and Mixolydian still sound more “major” than the other modes (except Ionian), and Dorian and Phrygian still sound more “minor” than the others (except Aeolian). Locrian, as mentioned, is the oddball because it’s the only mode of the scale whose root chord is diminished.

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Beyond the Major Scale

Other Scales & Tonalities

Although this page focuses on modes of the major scale, numerous possible scales (and modes thereof) don’t fit its pattern, such as:

• The twelve-note chromatic scale (though works that use the entire twelve-note scale for non-colorative purposes are quite rare and are mostly considered avant-garde).
• Numerous seven-note scales that aren’t modes of the major scale. I’ve rooted the following examples (many of which are common in jazz) in C to make it clear how they change the diatonic major scale:

  Other Seven-Note Scales
  Scale		1	2	3	4	5	6	7	Intervals
  Chromatic Dorian	Kanakangi	C♮	D♭	E𝄫	F♮	G♮	A♭	B𝄫	½	½	1½	1	½	½	1½
  Mixolydian ♯1	Super-Locrian ♭7	C♮	D♭	E♭	F♭	G♭	A♭	B𝄫	½	1	½	1	1	½	1½
  Locrian ♭4	Super-Locrian	C♮	D♭	E♭	F♭	G♭	A♭	B♭	½	1	½	1	1	1	1
  Locrian ♯6	Maqam Tarznauyn	C♮	D♭	E♭	F♮	G♭	A♮	B♭	½	1	1	½	1½	½	1
  Dorian ♭2	Jazz minor inverse	C♮	D♭	E♭	F♮	G♮	A♮	B♭	½	1	1	1	1	½	1
  Phrygian ♯3	Phrygian dominant	C♮	D♭	E♮	F♮	G♮	A♭	B♭	½	1½	½	1	½	1	1
  Major Phrygian		C♮	D♭	E♮	F♮	G♮	A♭	B♮	½	1½	½	1	½	1½	½
  Aeolian ♭5	Half-diminished	C♮	D♮	E♭	F♮	G♭	A♭	B♭	1	½	1	½	1	1	1
  Harmonic minor ♭5		C♮	D♮	E♭	F♮	G♭	A♭	B♮	1	½	1	½	1	1½	½
  Aeolian ♯7	Harmonic minor	C♮	D♮	E♭	F♮	G♮	A♭	B♮	1	½	1	1	½	1½	½
  Ionian ♭3	Ascending melodic minor	C♮	D♮	E♭	F♮	G♮	A♮	B♮	1	½	1	1	1	1	½
  Double harmonic minor		C♮	D♮	E♭	F♯	G♮	A♭	B♮	1	½	1½	½	½	1½	½
  Dorian ♯4		C♮	D♮	E♭	F♯	G♮	A♮	B♭	1	½	1½	½	1	½	1
  Mixolydian ♭6	Aeolian dominant	C♮	D♮	E♮	F♮	G♮	A♭	B♭	1	1	½	1	½	1	1
  Ionian ♯5	Augmented major	C♮	D♮	E♮	F♮	G♯	A♮	B♮	1	1	½	1½	½	1	½
  Phrygian ♭1	Lydian augmented	C♮	D♮	E♮	F♯	G♯	A♮	B♮	1	1	1	1	½	1	½
  Lydian ♭7	Lydian dominant	C♮	D♮	E♮	F♯	G♮	A♮	B♭	1	1	1	½	1	½	1
  Chromatic Dorian inverse		C♮	D♯	E♮	F♮	G♮	A♯	B♮	1½	½	½	1	1½	½	½
  Chromatic Hypophrygian		C♮	D♯	E♯	F♯	G♮	A♯	B♮	1½	1	½	½	1½	½	½
  Lydian ♯2	Aeolian harmonic	C♮	D♯	E♮	F♯	G♮	A♮	B♮	1½	½	1	½	1	1	½
  Superlydian augmented		C♮	D♯	E♯	F♯	G♯	A♯	B♮	1½	1	½	1	1	½	½

  Since it would be impossible to alphabetize scales with more than one name (note that many scales have more names than I’ve printed here), I’ve applied the principles of alphabetization to the intervals, with the first interval counted as the most significant. Bold, orange text denotes raised notes and minor thirds; thin, blue text denotes lowered notes and minor seconds (doubly lowered notes are also fainter).

  Note that this list is far from exhaustive; it doesn’t even delve into scales with different ascents and descents. Also, none of these scales use B♯ because, while it is semantically different in music theory from C, the two notes represent the same pitch in twelve-tone equal temperament. Likewise, none of these scales use D𝄫 because it’s the same pitch as C.

  In any case, one thing distinguishes these scales from modes of diatonic scales: we can print any mode of any diatonic scale with no accidentals outside the key signature, but every single scale in the above table would require accidentals for at least some notes. Key signatures are strictly based on major scales and the circle of fifths; using three flats that weren’t B♭, E♭, and A♭ in a key signature would just confuse readers.

  One additional advantage of printing Chromatic Dorian first: It’s directly relevant to the section below on ancient Greek harmony.

• Note that several sets of the above scales are modes of each other. In particular:

  Harmonic Minor & Ascending Melodic Minor’s Modes at a Glance
  Scale		1	2	3	4	5	6	7	Intervals
  Aeolian ♯7	Harmonic minor	C♮	D♮	E♭	F♮	G♮	A♭	B♮	1	½	1	1	½	1½	½
  Locrian ♯6	Maqam Tarznauyn	C♮	D♭	E♭	F♮	G♭	A♮	B♭	½	1	1	½	1½	½	1
  Ionian ♯5	Augmented major	C♮	D♮	E♮	F♮	G♯	A♮	B♮	1	1	½	1½	½	1	½
  Dorian ♯4	Lydian diminished	C♮	D♮	E♭	F♯	G♮	A♮	B♭	1	½	1½	½	1	½	1
  Phrygian ♯3	Phrygian dominant	C♮	D♭	E♮	F♮	G♮	A♭	B♭	½	1½	½	1	½	1	1
  Lydian ♯2	Aeolian harmonic	C♮	D♯	E♮	F♯	G♮	A♮	B♮	1½	½	1	½	1	1	½
  Mixolydian ♯1	Super-Locrian ♭7	C♮	D♭	E♭	F♭	G♭	A♭	B𝄫	½	1	½	1	1	½	1½
  Ionian ♭3	Ascending melodic minor	C♮	D♮	E♭	F♮	G♮	A♮	B♮	1	½	1	1	1	1	½
  Dorian ♭2	Jazz minor inverse	C♮	D♭	E♭	F♮	G♮	A♮	B♭	½	1	1	1	1	½	1
  Phrygian ♭1	Lydian augmented	C♮	D♮	E♮	F♯	G♯	A♮	B♮	1	1	1	1	½	1	½
  Lydian ♭7	Lydian dominant	C♮	D♮	E♮	F♯	G♮	A♮	B♭	1	1	1	½	1	½	1
  Mixolydian ♭6	Aeolian dominant	C♮	D♮	E♮	F♮	G♮	A♭	B♭	1	1	½	1	½	1	1
  Aeolian ♭5	Half-diminished	C♮	D♮	E♭	F♮	G♭	A♭	B♭	1	½	1	½	1	1	1
  Locrian ♭4	Super-Locrian	C♮	D♭	E♭	F♭	G♭	A♭	B♭	½	1	½	1	1	1	1

  We can apply similar principles to them as we applied to the diatonic major scale’s modes, though certain things may not line up as neatly with some of the scales. I leave ascertaining which other sets of scales are modes of each other as an exercise for the reader. (I didn’t list every mode of most other sets of scales.) The next two sections analyze these modes in much greater depth.

• There are also, naturally, scales that use fewer than seven notes; pentatonic (five-note) scales are quite common in rock, blues, and jazz music, though they’re much older than that and exist in many cultures. Six-note scales are also fairly common (including whole-tone scales).
• Scales may also have more than seven notes; blues and jazz often use eight- and nine-note scales.
• And of course, all of the above is based on the twelve-tone equal temperament (12-TET) ⟨en.wikipedia.org/wiki/12_equal_temperament⟩ used in the vast majority of Western music from the last five centuries. Plenty of other tunings have been and still are used, though; there’s nothing even restricting the number of notes per octave to twelve. For instance:
  • A twenty-four-note scale ⟨en.wikipedia.org/wiki/Quarter_tone⟩ is common in Arabic and Turkic music.
  • Indian rāgas ⟨en.wikipedia.org/wiki/Raga⟩⁽²⁾ typically use anywhere from four to seven svaras⁽³⁾ (roughly comparable to the notes of a Western diatonic scale) selected from the twenty-two śrútis ⟨en.wikipedia.org/wiki/Shruti_(music)⟩⁽⁴⁾ (roughly comparable to the Western twelve-note chromatic scale, except with ten more notes).
  • Experimental Western musicians also occasionally use alternate temperaments. Here are a few recent rock and metal examples, in increasing order of heaviness:
    • Flying Microtonal Banana ⟨kinggizzard.bandcamp.com/album/flying-microtonal-banana⟩ by King Giz­zard & the Lizard Wizard (24-TET)
    • Nowherer ⟨votsband.bandcamp.com/album/nowherer⟩ by Victory over the Sun (17-TET)
    • any metal album by Jute Gyte ⟨jutegyte.bandcamp.com/music⟩ since Discontinuities (24-TET)
  • The Ancient Greek enharmonic genus, as we’ll see after our examinations of harmonic and melodic minor, also used microtonality.

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Harmonic Minor’s Modes in Detail

Since learning the modes of harmonic minor and ascending melodic minor is absolutely essential for anyone who wants to play jazz, I’ve created several sets of tables to help people visualize them better.

Thus, as the first set of mode names suggests, harmonic minor’s modes respectively raise by a half-step:

• Aeolian’s seventh degree,
• Locrian’s sixth degree,
• Ionian’s fifth degree,
• Dorian’s fourth degree,
• Phrygian’s third degree,
• Lydian’s second degree,
• C-C-C-C-COMBO BREAKER!

Since we’re transposing every mode to C, we can’t raise Mixolydian’s first degree, because it’s the first degree! Instead, we must lower every other degree by a half-step. Say wha?

Somehow, it’s actually both even weirder than that, and not weird at all: what we do in the above table is the equivalent of raising the first degree. Since we’re constraing ourselves to a root of C, raising the first note of a scale by a half-step requires us to lower every note of that scale by a half-step. This results in the first note being the only scale degree we don’t lower: ½ − ½ = 0.

In practice, though, harmonic minor has already raised its seventh degree for us. Let’s represent these modes again, but this time, we’ll root each mode in its respective note within its parent C minor scale:

Thus, B♭ Mixolydian is to C Aeolian as B Mixolydian ♯1 is to C harmonic minor: each starts from its parent scale’s seventh note. There’s actually nothing odd going on here at all; it’s exactly how modes are supposed to behave. C Mixolydian ♯1 equates to lowering every note of C Mixolydian except C by a half-step – and to raising only the B in B Mixolydian by a half-step.

Observant readers may have noticed that the “rooted on C” table above actually appears to contain several shifts. The missing puzzle piece is that it lists the modes in ascending order rather than “circle of fifths” order, which I did to make the scales’ intervals easier to relate to each other. So let’s return to “circle of fiths” order.

We now see that, broadly speaking, in all except one case, each scale has one fewer sharp or one more flat than its predecessor two entries above. The clear outlier is Mixolydian ♯1, and this table may further clarify why the mode corresponding to Mixolydian is the one thus affected. Mixolydian corresponds to Ionian’s fifth scale degree, Dorian’s fourth scale degree, Phrygian’s third scale degree… and that’s the degree that harmonic minor’s modes raise. For completeness, here are the modes in “circle of fifths” order, rooted to their respective notes within their parent C minor scales:

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Ascending Melodic Minor’s Modes in Detail

Ascending melodic minor is perhaps better related to the modes starting with Ionian. I haven’t drawn borders this time, because… well, it’s probably better to just show the table first.

The dual mnemonics for each mode of ascending melodic minor in this table effectively show how we can derive ascending melodic minor and each of its modes in two different ways:

1. Ascending melodic minor is Ionian with a flat third or Dorian with a sharp seventh.
2. Jazz minor inverse is Dorian with a flat second or Phrygian with a sharp sixth.
3. Lydian augmented is Phrygian with a flat first* or Lydian with a sharp fifth.
4. Lydian dominant is Lydian with a flat seventh or Mixolydian with a sharp fourth.
5. Aeolian dominant is Mixolydian with a flat sixth or Aeolian with a sharp third.
6. Half-diminished is Aeolian with a flat fifth or Locrian with a sharp second.
7. Super-Locrian is Locrian with a flat fourth or Ionian with a sharp first*.

Asterisks are necessary for the first scale degree when transposing every scale degree to C. When improvising on an existing scale, the same principles apply as with harmonic minor’s Mixolydian ♯1 – the mode’s root will already be transposed within the scale you’re playing, so you just have to bear that in mind when thinking of what notes to play above it. This may be clearer in the following table, which shows how the above modes relate to C ascending melodic minor and C Ionian:

In short, E♭ Phrygian ♭1’s root note is already flat in its parent scale – you don’t have to flat it again!

“Circle of fifths” order makes it clear that the big note shift from Phrygian to Lydian augmented occurs in the “rooted on C” chart for the same reason the note shift between Mixolydian and Mixolydian ♯1 occurs with the harmonic minor scale: rooting everything to C means we can’t lower the first note and must instead raise the other notes by however much we’d have lowered the first note.

Phrygian mode corresponds to Ionian’s third degree; that’s the note ascending melodic minor lowers from Ionian. Thus, Phrygian is the mode that undergoes the note shift in the above table. Moreover, C Lydian augmented raises every note of C Phrygian except its root because its parent scale lowers its corresponding note.

For completeness, here’s “circle of fifths” order without transposition.

Of course, as the orange names in the “rooted on C” table suggest, we can also get ascending melodic minor by raising a different set of notes on a different series of modes. I’ve changed the first set of scale names accordingly, and since this interpretation of ascending melodic minor raises pitches from its parent modes instead of lowering them, I’ve printed it first in this table. Note also that the diatonic scale has a different key signature here (B♭ major instead of C major).

Here’s a comparison of these transformations in “circle of fifths” order, rooted to C:

And in “circle of fifths” order rooted on their parent scales:

The Diatonic Major Scale’s Stability

Let’s use a slightly more flexible root to show how ascending melodic minor’s modes relate to the diatonic major scale’s in both directions – modes of Ionian, modes of ascending melodic minor, and modes of Dorian. Note, particularly, how much stabler the diatonic major scale’s root is.