[abstract] Distortion is an important and essential property of timbre, and it is the timbral property that defines hard rock and heavy metal. However, most analyses and analytic theories of compositions from this repertoire focus solely on pitch-class relationships because pitch-class theories can produce powerful explanations or structural descriptions, such as, functional harmonic or Schenkerian style analyses of pitch-class relationships. The preeminence of pitch-class theories is further enhanced by the limited power analytic theories of timbre have had in analyzing timbre relationships. Unfortunately, most tonal theories of pitch-class relationships applied to hard rock and heavy metal produce analyses that lack the complexity found in the analyses of classical compositions, so hard rock and heavy metal works often appear to be structurally simplistic. However, the complexity that would put compositions from this repertoire structurally on par with classical compositions is often found in the domain of timbre. In this paper, I will present a theory of distortion. The theory presents a quantized view of the distortion continuum based on spectral analysis that produces a series of transformations connecting an absolutely linear signal to a signal containing 100% total harmonic distortion. The theory also incorporates contour theory. I will use the theory to demonstrate how distortion motives are developed and how distortion can create form in a composition. Specifically, I will present an analytical model of distortion motives and distortion structuring in the compositional design of two Metallica songs, ‘Enter Sandman’ and ‘Nothing Else Matters’, as well as other compositions from the repertoire.
Ciro Scotto’s research in music theory includes creating compositional systems, producing analyses and theoretical models of the music of the 20th and 21st centuries, mathematics and music, and rock music (specifically hard rock and Heavy Metal). His research in rock explores the structural role of timbre and the pitch- class compositional connections between Heavy Metal and Contemporary Classical Music. He has published articles in Contemporary Composers, Perspectives of New Music, Music Theory Online, and the Journal of Music Theory, and has delivered papers at SMT, SMA, IMS, AMS, and the American Mathematical Society conferences. He was also twice selected to attend the Mannes Institute for Advanced Study in Music Theory (2003- Transformation and 2007-Schoenberg and His Legacy). Besides his theoretical work, he is an active composer. His latest composition, ‘Between Rock and a Hard Place’, a concerto for electric guitar and percussion, was written for the USF Percussion Ensemble.
Ciro begins with a specific (October 1992) issue of Guitar Player magazine, which is thematically devoted to distortion, and noting the magazine’s mutli-faceted approach to the subject. Our first example is James Hetfield, whose take on distortion is cited thus;
“Distortion always starts with the amp. Pedals just sit on top of the sound. They don’t feel like a full part of it, just some fuzz on top. You can fiddle with parametric EQs and all that shit for days, but it still won’t have the smooth distortion of an amp.”
[here’s the rest of the interview].
His first graphic example 1 is Everett’s voice-leading and harmony values for thirty selected 1999-2000 albums. He acknowledges that distortion may not require definition, but nonetheless undertakes a [necessary I feel] attempt to define ‘chunk’ and ‘crunch’.We then get some electronics/physics regarding waveforms – the transfer function for a noiseless system. This leads to a discussion of linear and non-linear distortions. Non-linear distortions change the shape of a waveform, and he notes that they add additional harmonics according to amplitude [as a fellow electronic guitar player, I contend that one of the drivers – pardon the pun – of this sound is the ferocity of pick attack, which is why in practice the ‘bite point’ is so essential when setting gain levels].
We now look at the clipping characteristics of distortions, with sine/square waves as the input. We now turn to asymmetrical clipping, and Ciro notes that the additional harmonics are still related to the input, but become hugely more complex when diads [or even, we may fear, triads!] are introduced. So what’s going on in physics terms is that the upper harmonics are being amplified and turned into a square wave. He briefly describes his gear list (ESP with high output EMGs into Mesa/Boogie).
The range of distortion can be scaled as a waveform, morphing from triangle to square wave, and he cites the Thema from Symphonie Op.21 by Anton Webern as a non-rock example.
Pleasingly, Ciro discusses pink noise outputs of cymbals and notes the way a [crash] cymbal can bond with a guitar sound in a mix. He notes the methodological problem of categorising distortion, it being a continuum based on a contour. So he looks at ‘C-space’ (from contour theory) and speculates that we could assign linear values to ‘clean’, ‘overdrive’, ‘crunch’ and ‘distortion’. He proposes a ‘dist-space’ graph, suggesting that such a 2D array would be a useful categorisation tool.
[JB note – by this point, around 15 minutes in, I was getting worried that Ciro would omit discussion of dynamic transients – the envelope/compression of the guitar attack (and release) being an essential characteristic of rock and particularly metal. Thankfully he dives into this in lots of detail, playing us Blackened from And Justice For All by Metallica. Indeed he makes the point explicitly “dynamics and distortion are intrinsically linked”].
We now discuss Meshuggah and Dream Theater, and Ciro briefly namechecks the relatively new genre of Djent. The Dream Theater example is spectrally analysed twice, noting the harmonics (and non-harmonic frequencies) added as the drive level is ramped up (particularly the ‘fizz’ around 2kHz). Intermodulation distortion is demonstrated, in harmonic form and in music notation terms to show the added harmonics. E5 power chords and E/B dyads are sonographed, and he notes the [musically/aurally apparent] dissonance in the sonogram when we analyse E/Bb.
The next example is Freak on a Leash (Korn), analysed from the PoV of its macro structure, noting the way distortion contributes to song form. The relationship between distortion levels in chorus and verse is analysed in detail, with reference to ‘chromatic saturation’ within the form – there being only one note out of the entire chromatic scale that is omitted.
He finally plays us some of Freak On A Leash, and laments momentarily the sound system in the room – “this should really be louder”. To paraphrase Ciro’s earlier Tap reference, we really need lecture rooms that go up to 11.