Harmony & Scales
Contents:
1. Modal Mixture
2. Parallel Harmony
3. Resonance & the P5
4. deadmau5ian harmony
Modal Mixture
Modal mixture is "...a chord borrowed from the parallel key (minor or major scale with the same tonic). Borrowed chords are typically used as "color chords", providing variety through contrasting scale forms, major and the three forms of minor."
'Some Chords'
Image from Hooktheory.com, click on image to visit site.
One common colour chord in deadmau5 is the Major variant of the tonic chord. In this Song, g# minor is the home key, but the 4th chord of each group is a G# Major chord. The "deciding note" is the 3rd of the triad:
minor major
G# G#
B B#
D# D#
...which is in the melody, producing quite an emphatic colour change.
'Clockwork'
Brilliant harmonic sorcery by deadmau5.
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The chord groups move around the circle of 5ths, starting the home key of B minor
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The Dominant (V) of each chord group changes one note to become the minor tonic (i) chord of the next group, as demonstrated in "Some Chords" above.
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​The Major Dominant V (eg. F#major in B minor) implies a #7 scale degree (leading tone), and thus the effusive harmonic minor scale.
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So, each chord group is in a different key; but, two adjacent chord groups properly share one chord, the tonic chord of the previous key.
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This makes for gradual but consistent colour change throughout the progression, low key cycling through all the harmonic minor scales.
Clockwork - harmonic diagram
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Each chord group consists of 3 chords, of which the last chord lasts for two bars, for consistent 4 bar phrasing.
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Each chord group contains chords within the key of the first minor chord (diatonic harmony).
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The n+1th chord group is in the minor key of the final (V) chord of the nth group. Refer to the above diagram.
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...So, the n+1th chord group is a 5th higher than the nth group.
In music theory terms, this is a chain of 12 tonicizations, eventually leading back to the home key (for which reason I don't call each shift a modulation.) Tonicizations are brief modulations based on a harmony from the original key,
Considering that this song does move like clockwork, perhaps we can create a function explaining what is going on.
Define function Clkwrk:
4 bars
1st bar: i (tonic triad)
2nd bar: iv (subdominant triad)
3rd bar: V (Dominant triad)
4th bar: V (Dominant triad)
Program:
for n = 0 to 11
Clkwrk(n)
n = n + 1
end
the n+1'th iteration of Clkwrk is a tonicization of the n'th iteration, and so on until we make our way around the clock and return to n = 0, for the next section.
Map (minor) keys to integers, ordering in 5ths:
B - 0
F# - 1
C# - 2
G# - 3
D#/Eb - 4
Bb - 5
F - 6
C - 7
G - 8
D - 9
A - 10
E - 11
'Channel 42'
A minor is clearly the tonic, and is not tweaked to create a colour chord. Mau5 uses different variants of the Dominant (E = V) and the Subdominant (D = 4) harmonies.
Use of both major and minor variants of significant chords (tonic, subdominant, dominant) can also be understood in terms of alterations implied scales.
E minor // E Major
E E
G G#
B B
G-natural implies A natural minor // G# implies A harmonic minor
The E major triad is the major Dominant (V), and is the most cadential since it contains #7, the leading tone. This is why the listener feels such a strong pull back to the A minor chord at the start of the cycle.
Similarly, the presence of both D major and minor imply different modes.
D minor // D Major
D D
F F#
A A
F-natural implies A natural minor // F# implies A Dorian minor (#6)
D major contains F# (Dorian mode), which is substantially brighter than the natural minor mode due to the major IV chord.
Does this Dorian harmony (D major in A minor) remind you of anything?
'Ghosts N Stuff'
Image from Hooktheory.com, click on image to visit site.
One of the most famous songs in all of electronic music. In the key of Bb minor, the Eb major sonority is a borrowed chord (Gb -> G), creating a strongly Dorian sound. This warped plagal (IV - i) cadence is a captivating harmonic tool, since it plays with the listeners expectations.
'Avaritia'
Image from Hooktheory.com, click on image to visit site.
Again, we have a strongly Dorian (D minor with Bb -> B) sound. The B-natural is sounded in E minor and G major, as well as in the melody.
However, as in Channel 42 , deadmau5 alternates between the natural minor and Dorian modes, by using a Bbmaj7 sus2 (Bb-D-F-A-C). Considering melodic placement, this Bb7 chord is used similarly as the tonic d minor triad, and in fact contains the notes (D-F-A). This section does not go into further detail, but click here for a wider and deeper analysis of this song. (link to melodic analysis)
'Maths'
Here we have an 8 note E minor scale with:
F natural: flat scale degree 2
Bb: flat scale degree 5
C natural: natural minor mode
C#: sharp scale degree 6
D natural: no leading tone
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The closest formal classical mode would be Hypophrygian/Locrian, with flat 2 and 5, borrowing (adding) C# (#6) from the Dorian mode.
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It could also be understood as a modified Octatonic scale. Counting the number of half-steps between each note, -1-2-2-1-2-1-1-2 (E-1-F-2-G-2-A-1-Bb-2-C-1-C#-1-D-2-E), we can see that it doesn't follow the 1-2-1-2 pattern expected from an Octatonic scale.
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...which makes it so much cooler! There are quite a few patterns deducible from the sequence 12212112, but we know that the only useful numerical patterns would be ones that reflect how we hear the song.
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Strong beats (1&3): grouping each half bar, we have 12/21//21/12, a mirrored/inverted pattern about the tritone! (Each side adds up to 6, and the middle (5th) note is Bb, a tritone away from E)
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Bars (each downbeat 1): grouping each bar, we have 1221/2112. Each side adds up to 6, showing the importance of the tritone Bb as the cornerstone of the scale. It is clear that the sequence of half steps is inversed in the 2nd half of the phrase, with all 1's and 2's swapping places. How lovely!
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We also see an interesting property of Consecutive Semitones, in this case 3 (C-C#-D). No scale should have 3 consecutive semitones so...
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...Clearly, this is a carefully concocted scale. Looking at notes on the strong beats, we have:
E diminished 7th chord
Which explains the crunchy, dark but not quite minor tonality of the overall song.
Parallel Harmony
Parallel Harmony is the "Simultaneous, parallel movement of at least two voices." This technique is often called "Planing". There are 3 types:
Diatonic Planing: Retaining the general interval type (eg. 3rd, 4th, 6th), but modifying the specific (major/minor) interval to fit the key of the song.
Chromatic Planing: Retaining the same interval structure, allowing for notes outside the scale.
"General Planing": A mixture of the two
'Maths' (cont.)
During the 'chorus' part of the song, deadmau5 develops this scale by adding a major 3rd parallel melody on top of the original theme.
Cycling through the major chords of each note in his scale through parallel motion. This is a prime example of modal mixture through parallelism. Identifying which chords belong to which keys:
E major: E major, A major, D major
E minor: G major, C major
Neither scale: F major, Bb major, C# major
From context and rhythmic placement, we hear E major as the tonal center, but that's about all that anchors the listener in this section. Using Chromatic planing, deadmau5 'suspends tonality'.
'Move for Me'
This song abounds with Parallelism. The interval being planed is the Perfect 5th, whose size is fixed. Omitting/Supressing the 3rd forces the listener to hear the harmony in context, but more importantly brings out the open 5th sound so integral to deadmau5' music. This will be discussed in more detail in the next section.
The progression of this song is
C minor F minor F minor 7 Bb minor 7
i iv iv7 vii
This looks standard at first, until you realize that Db is not in the C minor scale, D-natural is. The vii Roman numeral is wrong, actaulyl describes the wrong chord. So, whats going on here?
The progression of this really song is:
C minor C minor F minor F minor 7 Bb minor
C C F F Bb
The Neapolitan ('N') is such an awesome chord. It is build on a flattened scale degree 2, a note foreign to the home key (Db in C minor). It is a tritone away from the Dominant (G = V), and can be used as a substitution for this chord.
In minor keys, the VI chord can act as a Dominant to the Neapolitan. In this case, Ab major, (VI in C minor) is a 5th above the Neapolitan Db major harmony. The gravity of the V-I progression is probably the strongest in all tonal music (recall Right this Second), which is why approaching this seemingly unrelated 'N' harmony using its dominant (which conveniently is within the C minor key) is so effective.
A little more about the power of the V-I and the Dominant chord: (link to Right this Second, talk about all ombinations of dominant-tonic variants)
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Only true, Major Dominant chords have this strongly suggestive power.
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The minor dominant isn't just any old chord, but has much less suggestive power.
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For instance, when the harmony in Move for Me changes from C minor to F minor, the listener may feel that this is a solid resolution chord, but would not have been as strongly pulled towards this specific resolution of the C minor chord.
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On the other hand, the Db major harmony seems like the most appropriate resolution of the Ab major chord.
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Lastly, Dominant chords are at their most powerful when they contain the 7th, (Dominant 7th chord), which is not the case here.
Another important aspect of parallelism is the resulting Voice Leading. The goal of good voice leading is to move smoothly between chords, by using the shortest path to the closest voicing of the chord. In a lot of instrumental music this is important to avoid "the dreaded parallel 5ths and Octaves", as well as to not be leaping all over the place and sounding chords in different registers.
This is a very different music we are talking about, however. The open 5th sound is so integral to the sound.......
Chords:
Bassline:
Resonance & the Perfect 5th
Alone with you - 5th relations
Resonance: Faxing Berlin (G minor doesn't have D for most of the song to avoid parallels)
I remember - How does he make the song in B minor without ever using a B minor tonic triad?!
deadmau5ian harmony
deadmau5ian modes
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