Three-peat

Last fall I kicked off a series of math-y posts with On the Count of Three, some thoughts about the groupings of three that occur around us, both naturally and in things we create. The idea of triplets is an obvious progression from the idea of binary opposition — quintessentially expressed in the metaphor of Yin and Yang.

Ever since that post, I’ve been noticing (and then noting) various instances of triplets. It really is a fundamental way reality expresses itself. (And more than just metaphorically — matter literally has three-ness!)

Here are some of the other triples I’ve noted…

A key aspect of Yin-Yang is the tension between the poles, especially when the poles are balanced rather than being “cup” pairs (where one pole is something and the other pole is the absence of that thing).

That tension tends to be absent with triplets, although in bi-polar mode, there can be tension between the two extremes as well as between the center and the extremes. Usually there’s a Yin-Yang, along with a center marker, underlying the mode, and the tension is more from that.

For instance:

• high — (middle) — low
• big — (medium) — small
• left — (center) — right
• forward — (still) — backward
• for — (neutral) — against
• yes — (maybe/unknown) — no

These can all be case as Yin-Yang (balanced) pairs, but as triples we elevate the center as having the same metaphorical weight as the poles. And, for example, big–medium–small is a different metaphor than big–small.

With regard to our stories, I mentioned The Trilogy and the general rule of three writers often use when listing things (like lions, tigers, and bears).

Storytelling has many other triples:

Traditionally, a witch coven has three members: Maiden, Mother, Crone.

(In Terry Pratchett’s Discworld Witches books, the head witch, Granny Weatherwax, is quite testy about that last label. The other two witches have learned, under Granny’s glares, to say: “Maiden, Mother, and … the other one.”)

And speaking of witches, there is the well-known Rule of Three, which says that whatever energy you put into the world is returned three times over. There may be some tie to how triples show up in a lot of spiritual contexts.

Or, for that matter: Animal, Mineral, or Vegetable?

Something I’ve observed for a very long time is that storytellers have three options when it comes to telling stories involving the supernatural (ghosts, angels, Santa Claus, and so forth).

Those options boil down to: Yes (it’s real), No (it’s not), or Maybe (I’m not saying; you decide).

The delightful old TV series Night Court makes an interesting case study (in part because this was one place where I really began noticing these choices).

At first the writers went with: “Maybe!” Various apparently supernatural things that happened in Harry’s courtroom (and life), but neither we nor the characters ever knew for sure it all didn’t have a natural explanation (including being actively tricked).

But later in the series they began to go with: “Yes!” Harry got involved with a real witch, and Santa Claus really did appear in his courtroom.

The “No” option is reflected in Sherlock Holmes as well as in the Scooby Doo cartoons (it’s always a trick). Contrast this with the early Night Court, which left the matter open — no natural explanation is ever discovered to resolve the matter.

This triplet is very similar to: Theist (yes, it’s real), Atheist (no, it’s not), or Agnostic (I’m not saying (’cause I don’t know); you decide). It boils down to Yes–Maybe/Unknown–No.

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In the world of electronic hardware, last time I mentioned bi-polar power supplies and signalling systems.

That just scratches the surface. With both vacuum tubes (“valves”) and transistors, an amplifier circuit basically has three electrical connections: Input, Output, and Common (think of that last one as a “tether” keeping the circuit in place).

The reality does involve more connections (at least with tubes), but fundamentally, any amplifier has those crucial three. (And transistors do have only three leads.)

In the software world, a very common top-down way of decomposing a problem and building a system to solve it is called IPO — Input, Processing, Output.

You start with a box labeled: “The System” (or whatever you’ve named your system).

Coming from that are three boxes with lines connecting them to the first box (like a hierarchy chart).

The first new box is the input(s) to your system, the next one is the output(s), and the last one is the processing.

You repeat this process, breaking each box down into the IPO for that part until you’re down to a level where the boxes become obvious modules you can write.

It turns out that many software problems resolve to Input, Processing, and Output. (Not all, so it’s not a universal technique, but it’s a pretty good one. There are others that fit as: Initialization, Processing, and Clean-up. Or, with files and other resources: Open, Use, and Close.)

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A, A♯, B, C, C♯…

Lastly, the world of music has a number of interesting triples.

Firstly, there are note triples, a series of three notes played against a time signature that expects two.

And, of course, there is music written with a three-beat time signature. Waltzes are famous for it (one-two-three, one-two-three). The Christmas carol, Silent Night, is written with a time signature of six beats.

Digging deeper, we find three-ness in basic music theory. For now, I’ll only touch on this. I plan to get more into it some other post.

The Western music scale has twelve notes, which is 2×2×3, so there is both two-ness and three-ness already (double two-ness, even). These notes are repeated over and over in musical octaves (where the notes have double or half the pitch of the ones below or above, respectively).

A musical key (for instance, the key of C) has seven notes (also repeated over and over). Many, many melodies are comprised of only the seven notes within the key (rather than all twelve). When this is true, the melody can be arranged with only three chords.

Key of C

Exactly as in: Three-chord rock and roll. (Those with a bit of musical theory background know them fondly as the I, IV, and V7 chords.)

Further, a musical chord requires at least three notes, and those required three define the root name and basic nature of the chord (for example, a C chord or an E chord).

Adding more notes makes the chord more interesting, but doesn’t change its root.

(Two notes just forms a musical interval.)

I’ll get more into this some other time. I’ve been thinking of digging out my old keyboard, seeing if it still works, seeing if I can still play, and seeing if I can record some samples of what I’d write about.

Seems like a post about music theory needs examples.

(But don’t hold your breath waiting for me to get around to it. I’m still working through a large backlog of notes and post ideas.)