Parallel Dyads in Megadeth’s Holy Wars

One of the more common procedures found in metal music is harmonization in parallel thirds.  We often hear this in the guise of two guitars playing a melody or dual guitar solos (with one guitar playing in parallel thirds above the line of the other guitar), and we also hear this harmony being used within riffs (with the harmony being played within a single guitar part).  This type of harmony is an example of a dyad—an instance of two different pitches being played together—and the reason it is classified as parallel thirds is because the notes of the harmonic line are consistently played a third above the root melodic line.

When parallel third harmonies are constructed, they are typically based rather strictly on the notes of whatever mode is in play.  As a consequence, the quality of the parallel third harmony—i.e. whether it is a major or minor third—may change from note to note (the reason being that the notes of common modes aren’t uniformly spaced, so the quality of particular harmonies fluctuates with the change in root note).  For example, in the case of E natural minor, parallel third harmonies appear as a succession of major and minor thirds as below:

An alternate, and interesting, way to approach parallel harmonies is to play strictly one quality of the harmony, such as strictly major thirds or strictly minor thirds.  The consequence of this is that the coherence of the underlying mode may be sacrificed, and this could be a very useful and desirable effect as it may produce some unexpected and unpredictable notes for the listener.

We find examples of this type of effect in Megadeth’s “Holy Wars…The Punishment Due”, which is among the finest metal songs ever written and exemplifies the incredible riff-writing of guitarist Dave Mustaine.  In some of the song’s riffs, parallel thirds are played strictly in one quality, which adds an unusual flavor to the E minor setting.  Additionally, we find power chords—i.e. parallel fifth dyads—being juxtaposed to parallel third dyads based on the same root note, which offers the listener two different versions of a dyadic progression.

The first example occurs in the riff that appears at 1:08 in the song.  The riff opens with power chords on a progression alternating between F# and G.  The notes that fall above the F# and G—namely, the C# and D—are notes that belong to the E Dorian mode and are somewhat ordinary within a traditional E minor key setting.  Hence, we hear them without perceiving any disruption to the E minor key:

When that progression returns, the power chord dyads are replaced by major thirds:

The switch to major thirds offers a different flavor of this riff.  The chief culprit is the A# that falls above the F#, for this A# is classified as the tritone to the tonic note of E and does not fall within the traditionally-expected setting of the minor key.  Because of that, we perceive the A# as disrupting the otherwise normal E minor key setting.  (Even though we are accustomed to tritones being utilized freely in the minor key fabric of metal songs, our ears still respond to their inherent dissonance).  Hence, between the two versions of the F#-G progression, we hear a juxtaposition between the normal-sounding power chords and the slightly discordant major-third setting.

There is an even greater mixture of dyads in the verse riff (starting at 1:28).  The verse riff is characterized by a recurring, ascending, three-note chromatic motive and gallop attacks on the low E string, with dyads interspersed throughout.  The dyads in each measure appear as follows:

  • First measure: major thirds on G-F#.  As with the riff at 1:08, the A# that falls above the F# sounds dissonant within the E minor tonality.
  • Second measure: minor thirds on A#-B-A#.  The notes that fall above A# and B—namely, C# and D—are themselves acceptable in the E minor tonality (as part of E Dorian mode).  However, the root note of A# is, as explained above, dissonant in E minor.  Furthermore, though the minor third on B is reasonable within E minor, it is less expected and less powerful harmonically than the major third on B minor that we are accustomed to hearing. (The major third is part of the full major triad on B that constitutes the dominant V chord in E minor).
  • Third measure: minor thirds on E-D#.  All of these notes are expected in the E minor tonality (as part of the harmonic minor mode).
  • Fourth measure: major thirds on F#-G (similar to first measure)
  • Fifth measure: major thirds on A-G-A.  All of the notes are reasonable in E minor (as part of E Dorian mode).
  • Sixth measure: major third on Bb.  The Bb is enharmonically equivalent to A# and hence also represents a tritone to the tonic of E.  The D that falls above is normal within E minor.
  • Seventh measure: major thirds on Bb-A.  Again, the Bb is a tritone to the tonic E.  We could possibly explain the Bb-A motion as indicating the Locrian mode, but the C# above A is not part of the E Locrian and hence would upset that definition.
  • Eighth measure: perfect fifths (“power chords”) on Bb-A.  With the F and E that fall above the Bb and A, the notes now fully correspond to the E Locrian mode (unlike the previous measure).


These various dyads contribute to an impressive diversity of sounds within this riff.  Not only do the different dyads (major thirds, minor thirds, and perfect fifths) have unique sonic qualities, the different approaches to the minor tonality (Dorian modality, harmonic minor modality, free usage of tritone, and Locrian modality) also create a mixture of different modal and harmonic references.  Similar to the example at 1:08, there is also juxtaposition between two progressions on Bb and A: in the seventh measure, on major thirds; in the eighth measure, on perfect fifths.

As complex as the impact of these dyads seem, they are the result of the rather straightforward approach of using parallel harmonies of a particular quality.  This strict parallelism undermines the concept of an overall modality and allows for unusual results, some of which can be partially explained within other modal contexts and some of which are just plain quirky and inexplicable within a traditional modal framework.  And when different qualities of parallel dyads are used in combination with each other, the results can be even more intriguing.

“Holy Wars” demonstrate how the diverse usage of strict parallel harmonies can arranged with particular artistry and to great effect, and the manner in which this technique is used likewise contributes to what makes “Holy Wars” one of the true masterpieces in metal.



Tonality in Mastodon’s “Blood and Thunder”

Mastodon has emerged as one of the premiere bands in prog-metal today.  Their past three studio albums, Leviathan (2004), Blood Mountain (2006), and Crack the Skye (2009) have all been met with critical acclaim and growing commercial success.  Like other prog-metal bands, Mastodon’s music is characterized by performance virtuosity and compositional complexities.  One area where they distinguish themselves is in their approach to tonality, in which they deftly weave in disparate elements with sophistication and artistry.

Their famed song “Blood and Thunder” from Leviathan exemplifies this process.  E minor serves as the overarching key for the song, but they use different scales and non-harmonic tones that either compliment or contrast with that key.  The result is a rich tapestry of tonal colors, a more sophisticated manner of presenting and interpreting the E minor key. (Note: the song is played with the guitars downtuned to D, but for purposes of interpreting this song as it is conceptualized on the fretboard, we’ll consider it in E minor).

The opening riff, (0:00 in the song), which also serves as the verse riff, is based on power chords on D – E – F with the power chord on E emphasized.  This chord pattern, with the F used in lieu of the F#, refers to the Phrygian mode that is commonly used in metal music.

Blood and Thunder - Intro

The first unusual tonal shift occurs in the chorus riff (0:31), which includes power chords on E – G – Bb – C#.  These notes outline a type of symmetrical scale, meaning that each note is spaced evenly apart (in this case, by a minor third).  The presence of the G and Bb could lead one to interpret this chord pattern as suggesting the Locrian scale, which belongs to the family of minor modes.  However, the C# does not belong to the minor key at all, referring instead to E major.  Hence, even though this chord pattern supports the overall E minor tonality of the song, it also diverges briefly from that tonality with the power chord on C#.

The interlude (1:32) features a melody played with parallel harmonies.  The first half of the first riff plays that melody in E minor, and the notes of the melody with the accompanying harmonies combine to include each note of the E minor scale.  The second half of the first riff plays that same pattern again, only this time it is transposed down a whole step (i.e. in D minor instead of E minor).  This transposition does not constitute a formal change to D minor, nor is it particularly difficult to understand—truly, it is simply a shifting of the riff down two frets on the guitar.  Nevertheless, it does impact the tonal fabric of the song by briefly introducing the D minor scale in the E minor context. (note: the below examples rearrange and transpose the notes of the interlude riffs to put them in order and in a more readable position on the staff).

The interlude riff is followed by a variation (1:48) in which the essential melody is retained but one of the harmonic lines shifts to a different set of notes.  The result of this shift is that the notes of the melody and the harmonies combine to spell the E Phrygian mode instead (as indicated by the F being used in lieu of the F#).  Correspondingly, the second half of the riff is changed to D Phrygian (with an Eb instead of an E).  It is a subtle change, and one that works perfectly well within the confines of the overall minor tonality, yet it does present a different flavor.

The bridge (2:15) presents a power chord progression that does not fall so neatly within a modal definition.  Over the course of its four measures, the chords involve a descending melodic pattern that is sequenced downward twice.  With the chords rearranged from lowest to highest, their tonics spell out nearly all the notes of the chromatic scale (with only an A#/Bb and C#/Db missing).  Tonally speaking, we hear the overall E minor key perpetuated in this riff, but clearly the approach is very loose and free form, and the presence of the G# alludes to the E major scale.

The coda of the song (3:26) also fails to strictly conform to the E minor tonality.  The first riff features a parallel octave chord pattern that emphasizes E with neighbor motion coming from F and D#.  With the F referring to the Phrygian mode and the D# serving as an ordinary leading tone, both notes qualify perfectly fine within E minor.  Such is not the case with the following riff, which finds the parallel octave pattern shifted upward to an emphasis on G# with neighbor motion coming from A and G.  The note G# belongs to E major, and the prominence of the G# in this riff makes the reference to E major sound more powerfully than it has in earlier moments of the song.

In summary, the overall E minor tonality has either been complimented or challenged by the following aspects:

1. The E Phrygian mode of the intro/verse riff

2. The symmetrical minor 3rd scale of the chorus riff, with the C# referring to E major

3. The momentary shift to a D minor scale in the first interlude riff

4. The E Phrygian mode in the second interlude riff (and corresponding D Phrygian mode in the second half of the riff)

5. The nearly complete chromatic palette of the bridge riff, with G# referring to E major

6. The strong emphasis on G#, referring to E major, in the second riff of the coda

The result is an ever-shifting interpretation of the overall E minor tonality, one that freely weaves in a variety of non-harmonic tones and mixes traditional modes with more innovative and obscure note collections.  Many of the nuances, such as the Phrygian moments, are basic and perfectly reasonable within a metal song context.  Others, such as the symmetrical scale of the chorus and the pseudo-chromatic collection of the bridge riff, are out of the ordinary and pull in unexpected tones.  In addition, the combination of all these changes, slight or significant, put the E minor setting in a constant state of flux.

The subtle manner in which Mastodon make references to E major is particularly noteworthy.  At no point do they plainly articulate a formal shift to E major but instead make loose connections that are powerful enough to color the E minor core tonality without completely disrupting it.  This is in contrast to many metal band’s (particularly earlier ones) approach to using the major key; it is more usual to find the major key overtly stated and employing that key’s characteristics in a more obvious manner.  Mastodon, however, seems to be using modes and keys not by their strict definitions but simply as starting points from which they freely depart and explore uncommon combinations and applications.

In “Blood and Thunder”, Mastodon demonstrates how masterful they are in constructing the tonal fabric of their songs.  Many of their other songs exhibit the same characteristics, and examinations of their other works may eventually establish how distinguished Mastodon is from their peers in the treatment of tonality.

Proto-metal in Captain Beyond

One of the most compelling arguments regarding metal music is the question of metal’s birth.  Black Sabbath is commonly referred to as the first heavy metal band, though not without the argument for the inclusion of other late 60s/early 70s bands like Led Zeppelin, Deep Purple, Blue Cheer, and even the likes of Cream and Jimi Hendrix.  The basis of the advocacy for these latter musicians is that the elements of metal can be found in their music — Hendrix’s exemplary use of guitar distortion, heavy riffs in Led Zeppelin’s music, etc.  Though there are many who make claim that these groups deserve to be classified as “heavy metal,” it is typically maintained that they contributed greatly to the rise of the genre without meeting the pure definition of metal (at least, not in the same manner as Black Sabbath).  Hence, these early contributors are often segmented out as “proto-metal,” playing a mix of hard rock and heavy blues that precipitated the forthcoming genre and influenced the future generations of pure metal bands.

I was recently introduced by a friend of mine to one such proto-metal group: Captain Beyond.  The band had a strong rock pedigree — the original members included singer Ron Evans (the original singer of Deep Purple), guitarist Larry “Rhino” Reinhardt and bassist Lee Dorman (both of Iron Butterfly), and drummer Bobby Caldwell (formerly with Johnny Winter).  The album that my friend sent me was their 1972 self-titled debut album, Captain Beyond.  On top of being a consistently strong effort full of interesting riffs and excellent performances, the album is striking in its inclusion of many elements that would become common in metal music.  And unlike many of the other proto-metal bands whose works seem to influence only the first generation of metal bands, Captain Beyond anticipates later developments in metal.

The most obvious such element is the dominance of the minor key throughout Captain Beyond.  Most of the riffs are in minor, particularly in the traditional modes of Aeolian (e.g. natural minor), pentatonic minor, and the so-called “blues” scale.  The use of the blues scale is noteworthy in that it contains the tritone above the root note (which can be called either a flat-5 or sharp-4 scale degree, depending on the context); the highly dissonant tritone interval is, of course, one of the trademarks of the metal sound.  In the song “Frozen Over,” they use the “blues” scale with a strong emphasis on that tritone, creating a distinctly metal feel as opposed to a more “bluesy” sound to which the scale is most often assigned.

The music throughout the album also features a heavy dose of prominent riffs in five- or seven-beat subdivisions.  For example, the songs “Dancing Madly Backwards (On a Sea of Air)” and “Thousand Days of Yesterdays” open with riffs in  five-beat phrase lengths, and the songs “Mesmerization Eclipse” and “Thousand Days of Yesterdays (Time Since Come and Gone) begin with riffs in seven-beat phrase lengths.  These riffs are interwoven with more typical duple meters, which create sudden shifts in the metric feel of the song.  The significant usage of five- and seven-beat riffs foreshadows the rise of odd and irregular meters in later genres of metal, especially the thrash metal movement in the 80s and the progressive death metal subgenre that has proliferated in the 90s and 00s.

The “Dancing Madly Backwards” suite (which also includes tracks entitled “Armworth” and “Myopic Void”) contains a rhythmic element that has since become a cliche in metal.  At the 1:41 mark in the track “Dancing Madly Backwards” begins a riff in 4/4 and E minor, which is composed of pedal notes on the low E string interwoven with power chords on E, F#, and G.  The power chords create tonic accents (i.e. accents created by higher pitches), and the arrangement of the power chord-created accents outlines a pattern of three eighth-note subdivisions.  This three-note subdivision clashes with the expected beat pattern of the 4/4 meter, resulting in a temporary syncopation.  However, the three-note pattern is abandoned by the second measure, and the remaining rhythms restore the sync with the 4/4 meter.

Variations of this riff occur in the “Armworth” (0:00) and “Myopic Void” (0:24) tracks; in both cases, a similar rhythmic pattern is used.

This use of a series of three eighth-note patterns within a 4/4 context has since become common practice in metal.  For example, Iron Maiden’s song “2 Minutes to Midnight” opens with such a pattern, and the main riff in Metallica’s “Creeping Death” also features a similar rhythm.  In each of these cases, the riff involves a low pedal note with interspersed power chords outlining an initial three-note subdivision.  The 4/4 meter is momentarily challenged by these three-note patterns, yet the meter is re-established by the end of the riffs.  In this manner, the riffs maintain a straightforward duple meter while creating interest with internal syncopation.

The fact that “2 Minutes to Midnight” and “Creeping Death” were released a decade after Captain Beyond indicates not only how deeply metal’s roots go but also how much proto-metal bands like Captain Beyond have contributed to metal’s foundation.  Truly, the music from Captain Beyond is right on the cusp; if the gain on the guitar distortion was higher and the tempos were a little faster, the music would probably be accepted as straight-up heavy metal without argument.  As it is, Captain Beyond serves as a compelling reminder that metal’s ancestry goes far beyond the usual suspects of Black Sabbath and Led Zeppelin.

Iron Maiden’s “The Number of the Beast”

Iron Maiden’s famed song “The Number of the Beast” from the album bearing the same name contains a number of interesting analytical tidbits.  The aspect that is most often examined is the quirky phrase length of the opening riff, which is regularly interpreted as being in a 5/4 meter.  Such a meter is certainly appropriate for a song about an encounter with Satan; a five-beat subdivision can be read as being symbolic of the five-pointed star (i.e. pentagram) that is the traditional sign of the Devil.

It is also interesting to note that the initial riff, and much of the song, is in a major key (D major).  There are no shortage of songs about Satan, demons, and other forms of evil in metal music, and usually those songs express “evil” in the traditional fashion: minor tonalities heavy on lowered strings, tritones, flatted seconds moving down to the tonic, etc.  Yet in “Beast”, the major key, relatively high register, and tunefulness of the riffs invoke positive, almost happy energy.  We often think of tritones and other dissonances as tools for making a song sound “evil”, but there is something truly deviant about the joyful and anthemic riffs that Iron Maiden use in “Beast”—the sound is celebratory, as if they really are singing Satan’s praise.  Of course, any such effect is made with tongue in cheek, yet this presents a fantastic example of how the major key can be used in metal to create an ominous effect.

Finally, one of the most interesting aspects of the song is found in the chorus riff.  The basic chords of the riff are as follows (rhythm is not notated accurately in respect of copyright):

The first chord moves to the second chord with a slight change: the index finger on moves from the 3rd fret of the 5th string down to the 2nd fret, while the finger on the 5th fret of the 4th string remains stationary.  The notes of this second chord are B (the bottom note) and G (the top note).   Because the B is the bottom note, one might be inclined to interpret the B as the root note of this chord, in which case the G would have to be interpreted as a minor 6 suspension to the B chord.

However, even though the root notes of chords most often occur as the bottom note, that isn’t always the case.  In this case, the G is actually the root note of the chord, and the B is simply the major third of the chord.  If the B fell above the G, we would have no problem recognizing the major third.  The fact that the B occurs below the G does not change the relationship between the notes — the G is still the root and the B is still the third of the chord.

A chord in which the root does not appear as the bottom note is called an inversion.  Whenever the third of the chord appears as the bottom note, the chord is described as being in first inversion.  If the fifth of a chord appears as the bottom note, then the chord is described as being in second inversion.

Inversions are interesting because they affect the perceived stability of a chord.  The quality of a chord in inversion remains the same — major chords remain major, minor remains minor, etc. — but they present a slightly different sound and don’t offer the same sense of finality as a chord with the root at the bottom.  One reason for this is because inversions create an internal dissonance; in this case, the B below the G creates the internal dissonance of a minor 6.  The chord itself is still consonant, but we still perceive the internal dissonance as upsetting the stability of the chord.

The relative instability of chord inversions are helpful for keeping harmonic progressions moving.  Harmonic progressions thrive as long as instability is constantly introduced and allowed to resolve to stability.  This can be achieved with chords in root position (provided that dissonant chords like diminish or 7th chords are used), but chord inversions offer a more subtle level of dissonance and allows for consonant major and minor chords (which are perfectly stable in root position) to contribute to the fabric of instability.

Consider what this riff would sound like if Iron Maiden used a G chord in root position (as below).  The movement of the bottom notes between the first and second chords is now a somewhat shocking leap downward (from C to G) instead of an attractive half-step descent from C to B.  Even if the B is used as the middle note of the second chord to capture the C-to-B voice leading, the prominence of the bottom note would obscure that effect.  It would also obscure the internal dissonance of the B below the G, so all we would hear is a perfectly stable G chord that doesn’t have a strong momentum to move to the next chord.

It’s amazing what one minor movement of an index finger can do — kudos to Iron Maiden for using a chord inversion in such a simple yet powerful way.  This is also a lesson to all of us metal musicians to keep chord inversions in mind for writing our own music, for as this example shows, chord inversions can be very easily executed while contributing greatly to a harmonic progression.