Wednesday, July 11, 2012

Arvo Pärt’s secret sauce

I fell in love with the music of Estonian composer Arvo Pärt (b.1935) right away. I was seduced by his meditative and contemplative style, it was a new sound. Upon performing an analysis on some of his pieces for my masters thesis, I found some interesting characteristics about his music.


One of the major sources of information on Pärt is Paul Hillier’s biography on Arvo Pärt published in 1997. Hillier discusses Pärt's obsession with patterns. If you listen to Spiegel im Spiegel it really sounds like just a series of arpeggiated triads over a stepwise scale.

Let's look at text patterning in another piece, Summa.

Example 1

You could probably guess how the rest of the song patterns out. One could come up with various reasons for the apparent anomaly in the first line containing only 7 syllables not aligning with the 9-14 patterning. Pärt might have wanted the first line to be thought of something separate, like perhaps an incipit sung by a cantor? When we take a closer look at his music, we see that the patterning is more intensive.

Tintinnabuli style

Another compositional technique Pärt employs is the tintinnabuli style. A technique that allows for only a limited number of harmonies. This might help explain the minimalist (though some people don't like lumping him in with minimalists John Adams and Philip Glass because he did not come from that tradition) quality in his music.

Example 2

Tintinnabuli, meaning “a small bell,” is a relatively simple technique consisting of a pairing of two voices, a melodic voice (M-voice, scalar) and a tintinnabuli voice (T-voice, arpeggiated). The M-voice in the example is represented as the black noteheads, usually stepwise and in some kind of pattern, and the T-voice voice is represented in the example as the white noteheads.

According to Paul Hillier the T-voice can only be the first or second nearest note in the triad above or below the M-voice pitch or in alternation note by note. Taking that into account, example 1.1a has all the possible positions of the T-voice in relationship to the M-voice.Tallying up the number of unique harmonies possible from this restrictive system, one realizes that it is quite limited indeed.

So far, we have two important compositional elements to Pärt's music - patterns and the restrictive tintinnabuli system. However, these elements are incredibly different from one other. Patterns can go on forever. One might expect (quite reasonably so) patterns to generate a diverse collection harmony. However, the tintinnabuli system seems so restrictive that you wouldn't think that there would be much room for patterning. I found it hard to imagine that Pärt could execute both elements cleanly at the same time. Does he favor one over the other?

Pärt’s Fratres seemed like a good candidate for analysis. It is a simple and repetitive piece that sounds like it was composed out of patterns and a restrictive harmonic system. I analyzed every vertical slice of harmony in Pärt’s Fratres using set class theory (where you measure the distance from the bottom note by half steps, ie. [C, C#, E] = [0, 1, 4]). (This happened while I was dating my wife Margaret. I would sit in the coffee shop at Capers in West Seattle while she worked 8 hour shifts – I did analysis the whole time, it was tedious work.)

Before discussing the results of the harmonic analysis, here are the rules Pärt sets up:
1. Three different pitches. No doublings.

2. Two M-voices in tenths (or thirds) from the C-minor "harmonic" collection against one T-voice (tintinnabuli voice), member of the G-minor triad.

My plan was to create two lists - one with the possible harmonies based on the patterning Pärt sets up and another with the actual harmonies. In Fratres, there are eight possible harmonies [013], [014], [015], [024], [025], [026], [036], [037], of which Pärt only uses five [015], [025], [026], [036] and [037]. See example 3. (To understand the set class notation, make sure you put the notes in their closest arrangement). The T-voice is on the bottom staff.
Example 3

We see that Pärt avoids certain harmonies by breaking the pattern he sets up. Pärt manipulates the T-voice to maintain a restricted sound world that contains only five of the eight possible harmonies. In other words, Pärt doesn’t really follow through on the patterning completely, just only if it doesn’t create unwanted harmony.

What is the Arvo Pärt secret sauce? Sketchy patterning with a side of 5 harmonies.


Why go through so much trouble creating complex OCD-like patterns and not follow them through?
Does it lessen a composer's work when not following through on self-imposed compositional rules? Perhaps that is why some call Pärt a "pop" minimalist and don't like seeing his name next to true minimalists - Riley, Glass, Adams, etc.

It may not fall into traditional minimalism (which I don’t think a lot of people listen to for pleasure) however, people love Pärt's music. Some call his music mystic minimalism, a musical style uniting classical music with contemplative spirituality. Mystic minimalism challenges the prevailing intellectual approach of composition which evolved out of 400 years of musical tradition, in favor of a radically simplified framework resulting in an austere and transparent sound world focusing on music's most basic elements - sound and silence. Perhaps music composed out of these philosophical tenants should not be analyzed and judged using the theoretical models that have informed the development of western music for centuries.

“The most beautiful and most profound emotion we can experience is the sensation of the mystical. It is the sower of all true science… to know what is impenetrable to us.” -Albert Einstein


If you would like to read the full chapter on my thesis about this, please feel free to download here:


  1. This is really a nice and informative, containing all information and also has a great impact on the new technology. Thanks for sharing it

  2. This is a great article thanks for sharing this informative information. I will visit your blog regularly for some latest post. I will visit your blog regularly for Some latest post. buy genuine instagram likes uk