Friday 13 July 2012

Metallizing Phi - By Phil Moriarty

Professor Phil Moriarty and YouTuber Dave Brown (boyinaband) created a "math metal" song based on the Gold Ratio (Phi).

Here's the track (with music video!):

Below, in his own words, is Phil's explanation of what they did:

(note timings are mapped to start of the song, not the YouTube videos)

Here are all the gory details for the musicians amongst you...

Guitar tuning: Bb F Bb Eb G C

(This is traditional “drop D” tuning, i.e. D A D G B E, dropped two tones in order to approximate the math metal/Djent sound without a seven string guitar.)

We stick almost exclusively to riffs derived from the Bb harmonic minor scale (although the chorus is based around the natural Bb minor scale).

I used Guitar Rig to record the riffs (both clean and effected) which I then sent to Dave who used his studio wizardry and musical acumen to arrange and structure the song.

This involved quite a number of e-mail exchanges to hone the structure of the song during which Dave had to rein in my old school metal tendencies on more than one occasion.


0:00: We kick off with a clean picked piece which looks like this:

The digits of phi are “embedded” in the notes played on the 4th and 3rd strings.

I make use of octaves and finger picking to embellish the riff.

0:08: Dave comes in with sixteenth note “chugs” (on Bb) which are timed to match the digits of phi (as explained in the video).

00:16: All hell breaks loose. Same idea as for ‘chug’ pattern starting at 0:08, except this time matched by kick drums.

(All drum programming by Dave – visit his website for tutorials on how he lays down those impressive drum tracks).

00:40: The riff for verse 1 is basically power chords given by the digits 161803398, as follows (where ^ represents a higher octave):

1 - Bb
6 - Gb
1 - Bb
8 - ^Bb
0 - ^Db
3 - Db
3 - Db
9 - ^C
8 - ^Bb
8 - ^Bb

00:55: The chorus is a similar idea but this time in Bb minor (not harmonic minor).

1 - Bb
6 - Gb
1 - Bb
8 - ^Bb
0 - [rest]
3 - Db
3 - Db
9 - ^C
8 - ^Bb
8 - ^Bb
7 - Ab

1:11: Here we switch to ‘encoding’ the [1 + sqrt (5)]/2 representation of phi in the riff.

It’s a much more old school metal riff and involves lots of use of the open sixth string (first note of the Bb harmonic minor scale) to incorporate ‘1’.

The digits of sqrt (5) are then encoded as shown in the tablature below.

I wanted to get a somewhat Mastodon-esque feel here so used lots of octaves (and slides into octaves).

I tried to down-pick as much as possible to ‘drive’ the riff . The ½ of (1+sqrt(5))/2 is built in as half-time on the drums.

1:27: I very much wanted to have a heavily Tool-influenced riff in the song. Tool are math metal pioneers and, as many of those who have watched the “Golden Ratio – Making a Math Metal Anthem” video have pointed out, their song Lateralus has lyrics which are based around the Fibonacci sequence. So, the following is my ‘homage’ to Tool...

The digits of phi are encoded in the notes on the sixth and fifth strings and I ‘pedal’ around Bb notes on the third, fourth, and fifth strings.

2:15: As explained by Dave in the video, his riff here is also derived from (1 + root 5 )/ 2. Root 5 is embedded in the number of chugs again and the drums are half time.

The “1” is a sustained and ringing Bb note.


Real but uncountable
At the root of the problem 
Patterns will 
Emerge from the equation 
Golden Angle 
Sprials out of control 

The proportion is divine 
You'll find your way to Phi (to Phi) (to Phi) 
The ratio defined 
You can’t deny it's Phi 

The five-fold way
Forbidden symmetry 
Crossing points define 
Demonic geometry 

--- Verse 1 is fairly self-explanatory. Verse 2 above is a little more obscure. It refers to the pentagram which, of course, is a key piece of metal ‘iconography’. The verse refers to five-fold symmetry which is directly linked to phi ---

Phi = root(1 + Phi = root(1 +Phi = root(1 +Phi = root(1 +... 

--- This stems from the equation φ = sqrt (1 + φ) which, of course, is recursive – hence the looping lyric ---




  1. Very cool! I wondered if Tool was an influence. They are amazing. Will this kick off a whole new genre of Mathmetal?

  2. This comment has been removed by the author.

  3. Nothing short of awesome. Before you, the only real experience I've had with math metal is Mudvayne's: "Trapped in the Wake of a Dream" and, of course, Tool. That damn song has a 17/9 time signature. Anyways, what time signature(s) do you use throughout the song? Also, with the structure of the song, it sounds like the drums proceed the guitars. Either way, cheers and thanks.

    1. The song is in 4/4 the entire time.

    2. Mudvayne is nu-metal and not that good of a band.

  4. Hey. Loved your Golden Ratio song! Shared it on my Facebook. ^_^ I also make mathematically based music, though in a more electronic style.
    Here's one I made on the Fibonacci Sequence Modulo 13:

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