The 5-Against-Powers-of-2 Cycle in Yes's Our Song

A year ago, I blogged about a 23-second passage in a progressive rock song that does something rather special, but did not reveal the passage, instead promising to reveal it this month.

That blog post a year ago investigated how powers of 2s and multiples of 3s can interact in different ways in music, so, to complement that presentation, I will explore in this post how powers of 2s and multiples of 5s can interact in different ways in music.

If an even division of time with inter-onset intervals of 5 units aligns its first onset with the beginning of pure duple music (straight eighths, 4/4, 4-measure groups, etc.), a subsequent onset will never coincide with a power-of-2 beat, as shown below with the eighth note as the unit. Such a coincidence could be produced if the music broke from the quintuple regularity, like 5+5+6 = 16 or 5x12+4 = 64. This adjustment, what Richard Cohn calls a comma, converges the otherwise divergent quintuple and pure duple divisions of time, much like a leap year day—like today—helps to reconcile the otherwise incommensurate daily and annual divisions of time.

A corollary of this observation is that a rhythm that is the unit complement of the quintuple rhythm above will always place an onset on a power-of-2 beat. The spoken-word music below—simulating a group of folks both sporting and evaluating neckwear—demonstrates this corollary by stringing together a series of four-unit four-syllable phrases with a unit rest in between. The phrase "I like your tie" is used when at least one of its syllables coincides with a power of 2. Notice that the coincidences cycle through these four syllables in the following order: LIKE on 2, TIE on 4, YOUR on 8, and I on 16. The four-element cycle begins to repeat with LIKE on 32; the reader can verify that, if this pattern continues, the next power-of-2 coincidence will be TIE on 64, YOUR on 128, and so forth. (I'm also using this cycle to showcase, as many others have, how emphasizing different words in a sentence can change its meaning, as is sometimes done with the phrase "I never said he stole your money.") This four-cycle is analogous to the two-cycle that results when a complement of a 3-unit rhythm interacts with pure duple moments, as in "I know" from Bill Withers's "Ain't No Sunshine."

The simultaneity of multiples of 5 and powers of 2 are not as common as that of multiples of 3 and powers of 2, but, of those I have heard, most align the beginning of each pattern; therefore, these two ways of dividing time subsequently never align, unless adjustments are made later. One example of this is from the first track entitled "Shofukan" from the 2014 album We Like It Here by the American jazz fusion group Snarky Puppy. The simultaneity starts at 4:48 in the video below. Listen for the 5-note ostinato in the keyboard and guitar parts, with the highest note (a B) marking its beginning.

Now for the reveal: the aforementioned 23-second passage starts at 3:25 in the song "Our Song" by the English progressive rock group Yes from their 1983 album 90125.

Vocals, bass line, and a keyboard ostinato are transcribed below, with some annotations. This passage is pure duple: 128 eighth-note units sandwiched in between the last statement of the chorus (which ends with the line "Music has magic / It's good clear syncopation") and a return to the opening 7/4 instrumental introduction.

The ostinato iterates a three-note motive (B-A-D) that is five eighths long: both its registral contour—like the Snarky Puppy ostinato (which also has the same starting note and close to the same tempo)—and durational content—long, long, short—clearly emphasize the first of its three notes. However, the ostinato does not begin until three eighth notes into the passage. This sets up a cyclic, rather than divergent, relationship between the ostinato's beginning and the 6 powers of 2 in this passage that remain after timepoint 2. Although it starts with a misalignment (the +1 in red between timepoints 3 and 4), it realigns right away (the 0 in green at timepoint 8). But then it continues on the four-element cycle, passing through differentials of +3, +4, and +1, before returning to realignment at timepoint 128. For me, this realignment creates a powerful arrival, very much akin to a strong attainment of the G-major tonic harmony after so much subdominant and dominant, and the conjunction of the ostinato's B with the intro's first-note B. The lyrics appear to reference this well-planned coordination as well.

Next month I'll blog about an earlier n-against-powers-of-2 cycle in the same song that becomes dislodged soon before a moment of convergence, prohibiting a realignment. I believe that this suppression makes the later cycle even more satisfying.