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. Hola amigo te escribo ya que veo que usas adsense, tengo un trato para ti por el cual puedes ganar muchisimo dinero por adsense si te interesa que te de mas detalles contactame:


  5. 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:

  6. Mashup music is the latest term of music, in which hard, soft, fast, emotional, batle and every kind of music touch dominate in this music world."Mp4 video bollywood

  7. the music is very good feeling it have a great power for uneltic passion.
    the theme of this site blog is very nice i like it and its color.
    ai submit here my website,
    PTCL INTERNET TESTING SPEED Checking Site now available, latest mechanical term of our website giving a fine relief you to sort out or handle Internet speed testing problem. You can now stable your net within two easy steps, just open our website, and one click our PTCL SPEED TEST SOFTWARE and you will get success of your internet problem. Encounter your Internet speed problems from our latest software of Internet speed issues.

  8. Metallized label provides an attractive and memorable way for manufacturers to draw attention to their products in the marketplace and differentiate their brands. Metalized Labels which are high on quality and they are made using the latest technology available in the market. Metalized labels have very high temperature resistance and suits most label requirements pertaining to printing projects that are suitable for printed images for example barcodes etc.

  9. Winter snow storms Hockey Safeness For Young ones and Infants. The accurate equipment, understanding and even training are essential to that safe and even fun winter snow storms hockey go through for young ones and infants.

  10. Within Playground rubberized mats we now have a huge assortment of mats associated with different dimensions, colours, designs and grabs. You may choose the following rubberized mats for the play ground for example Rubber Lawn Playground Pads, Playground Rubber Mats

  11. Fantastic articles is post by you in this blog. You give a nice thing. Thank you for such a nice article. Every word og this blog helps me to give detail to me.
    Visit: Scaler handpiece

  12. We offer superb quality Rubber matting that is produced from pure and finest quality rubber mats.The Rubber matting uk offered by our organization is genuinely the solution against the slipping over the ground. We are truly the industry leaders.

    You can vise my Of Luck.

  13. I hope, one day I'll have chance to record my own single in such record, but now I'm just trying to visit amazing concerts and enjoy great music. If you have the same case, see all concerts to find the best and go there with me.