84ed2 (1): John Cage and Microtonality

Cage’s final period was notable, unsurprisingly, in at least two or three respects: he devised a system of time bracket notation with varying degrees of rigidity and looseness, he entitled his works with a dry, basic numbering system, and three of his last works were microtonal.

His time bracket notation concerns rhythm in a loose manner. Instead of using standard notation with quarter-notes, half-notes etc., and instead of using graphic notation as he had for much of his output, where 1 horizontal inch might represent a time value of, say, 1 second, he devised a compact form whereby bars begin and end at the performer’s discretion within values given by the composer; some freedom is allotted to the performer.

For example, Section A–Part 1 from Four, for string quartet, begins anytime in the first twenty or so seconds: the first bar contains two whole notes (A and B, above middle-C) but no conventional indication of meter or tempo. Instead there is a beginning bracket, 0’00″–0’22.5″, and an ending bracket, 0’15″–0’37.5″. The player must begin and end within these ranges (and the player must not end before he has begun). In this work each of four parts and each of three sections has identical brackets but different material within.

The third bar, or system, has no range but, instead, specific starting and ending times: 1’07.5″ and 1’22.5″. Cage differentiates these ‘fixed’ brackets from the other ‘flexible’ brackets. There are many articles that explain this with more examples, or that offer other details (such as his compositional periods with and without computer software as an aid—see here), and there’s even an article out there showing geometrical properties of this treatment of time.

His titles became austere in that he wrote many works with simple titles such as One7, the ‘7’ being a superscript [not possible to display with internet/HTML]. Rather than “1 to the power of 7” he means a seventh piece for one performer. We shall look at an aspect in common within the series Two4, Two5, Two6, and Ten, that they are not only some of his last but, more relevantly, his microtonal pieces.

I’m mainly going to point to others’ writings but before I do so I want to clarify that Cage wrote microtonal music with very small intervals. I perused some CD booklets at the local library and most simply described this music as “microtonal” and one unhelpfully said that he wrote with “quarter-tones.” Often people use ‘quarter-tone’ as a blanket term to mean ‘anything but normal tones.’ I also looked online, of course, and saw that the John Cage Trust describes the microtonal writing as having ‘six notes, degrees or steps between each half step.’ Yes but… potentially misleading and I would like to clarify.

It would be better to say that Cage divided each semitone into 7 steps, meaning there are twice as many per whole tone, 14 steps. You may call it 1/14th-tone music (but not 1/4-tone).

What I find remarkable is that the other—more normal?—choices for dividing a semitone so finely are somewhat more established, as much as microtonal praxis can be. 1/16th-tone music, i.e. dividing each semitone into 8 tiny steps, was—believe it or not—being done to pianos a century ago.

The Mexican composer and inventor (and Nobel prize nominee) Julián Carillo patented pianos able to play in various tunings, the 1/16th-tone piano being one example that was manufactured. Instead of 88 keys it requires 97, and that’s just to play one octave! (I tried one belonging to Bruce Mather for a few moments at the conservatory in Montreal. You play a chord… and a single, warbling tone is the result.) Sixteenth-tone music was commissioned in the roaring ‘20s and played by Stokowski and the Philadelphia Symphony Orchestra. It could have become a new standard of tuning but then musical developments evolved in other directions and such microtonal music faded out of the picture.

The other choice, 6 tiny steps per semitone was also not chosen by Cage. This scale is very popular (as much as microtonal music can be). Georg Friedrich Haas writes in this scale and they teach this scale in Boston in sight-singing classes! There are also at least two good notation systems for representing it. Twelfth-tones, better known as the 72ed2 scale.

But Cage marches to the beat of a different drummer. Below is text from a festival programme in Frankfurt twenty years ago, which I enjoyed translating (as an exercise for my German language acquisition—please indulge me):


“In July 1991 John Cage composed three works for the japanese shō instrument, a mouth organ using reed pipes: One9 for shō, alone; Two3 for shō and 1 percussionist, who plays five water-filled mussels [shells]; and—a commission from the McKim Fund in the Library of Congress—Two4 for shō and violin, a piece in which a piano can partake instead of the shō. The musical outcome’s material, that Cage employs, is entirely different for both instruments: The shō has 17 pipes and, from them, up to 6 can be blown simultaneously. The composer uses here all possibilities from single tones up to hexachords, and builds rather vast phrases in which the tones either detach from one another through breath-marks or, alternatively, are linked through legato arcs. By way of contrast the violin plays a maximum of 3 tone pitches per system but, instead, with constantly varying timbre.

“Remaining is the violin part—like all the voices besides piano and percussion in Ten (October 1991)—written in a fourteenth-tone system:


“From the notation’s kind and manner one can distinctly discern how immediate are the sonorous characteristics of this work by Cage, coming at once from the possibilities of the refined notation system: The decision for 14 intervals per whole tone is not owing to melodious considerations or general, theoretical deliberations, but because Cage uses upward- or downward-pointing arrows as notation symbols: This allows one to apply, without optically taxing the player, three different positions (high, middle, low) before a conventional note; also two notes come without arrows, those boundaries marked by semitones; so 7 intervals per semitone, 14 intervals per whole tone, and 84 intervals per octave emerge. The dynamic of the half-hour work stays in the range of pp.

Martin Erdmann

[transl. Todd Harrop]

(Rausch, Ulrike and Martin Erdmann. “4. Number Pieces II”, pp. 198–200. Schädler, Stefan and Walter Zimmerman, editors. John Cage: Anarchic Harmony. Frankfurt Feste ’92/Alte Oper Frankfurt. Mainz: Schott, 1992.)

Cage continued writing microtonal writing in Two5, Two6 and Ten with the same scale, 84 tones per octave, hence the title of this article, “84ed2”, meaning 84 divisions of the 2nd harmonic (which is the octave, a.k.a. 84edo). So, Part 1 has introduced the full, ‘chromatic’ set of pitches and one composer’s employment of them. (See this page for more information on the 84-tone scale and YouTube links to performances of Cage’s works.) The next article will compare this microtonal scale with the standard 12-note scale by constructing pentatonic- and diatonic-like subsets inspired by the writer George Orwell.


About th

musician, thespian
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One Response to 84ed2 (1): John Cage and Microtonality

  1. Pingback: 84ed2 (2): George Orwell and Microtonality | th muses

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