Transfer Function, What's Your... uh... Function?

Having a good mental model of how an unfamiliar piano responds helps you know how to adjust (or not adjust) your playing. For example, if a piano's action seems relatively stiff, you might be more careful to avoid notes not sounding. If a piano is voiced more brightly than you're used to, you might want to beware the tendency to underplay to compensate.

Both of these examples illustrate the importance of sensing how effort applied translates to sound out. I think of this relationship as a Transfer Function: different amounts of energy in (effort applied) produce different changes in energy out (volume, roughly). When playing an unfamiliar piano, if you can build a mental model of this transfer function, you're more likely to be able to exploit its dynamic range effectively. It's also easier to avoid overplaying a piano whose sound is smaller than what you're used to or underplaying a piano whose sound is bigger.

The graph below shows how energy out might vary depending on how much energy goes in for three hypothetical pianos.

The yellow curve is the transfer function for a hypothetical "linear" piano, where doubling the effort produces exactly double the volume over the entire dynamic range. The red line would be a piano where small changes in effort produce larger changes in volume at the soft end, but more effort is required to produce changes in volume at the loud end. For example, a small increase in effort (from a to b) might be required to go from pianissimo to piano, whereas a large increase in effort (from e to g) might be required to go from forte to fortissimo. The green curve represents the transfer function of some wacky imaginary piano where the louder it gets, the easier it becomes to play even louder.

Real pianos would have transfer functions more like the red curve. Eventually, the curve flattens out to the right, meaning that as you hit the keys ever harder, you don't get much more volume.

The next graph shows how transfer function might account for differences in big pianos versus small pianos. One of the most surprising things when playing concert grands, for example, is how they continue to respond dynamically at the loud end. That is, even when playing loud, the piano has power to get even louder. The transfer function of smaller pianos flattens out faster than that of larger pianos. In the graph below, the red curve would be a larger piano, the green curve a smaller piano.

Any given piano may have a unique shape to its transfer function. The red curve in the graph below represents the transfer function for a piano that requires little effort to get from piano to forte, but then flattens out quickly. On such a piano, the risk to the player is in reaching high volumes with little effort, but then having no headroom left for louder passages. The tendency then would be to over-exert on loud passages, which can affect clean technique and result in fatigue. Keeping a model of this piano's transfer function in mind while playing would remind you that wide dynamic variation requires little change in effort in the soft and middle dynamic ranges, that forte comes easier than expected, and you should be careful not to hit the flat part of the curve before the loudest passages of the piece.

Action!

I was excited by the title of a recent post on the Dallas Steinway blog: The Importance of Good Action on Pianos. I guess I was expecting a technical article about the motion and interaction of elements of a piano's action and how they affect playing. But the article seems more aimed at piano buyers, with the message: "don't be put off by a firm action... it's good for you".

The reason for my excitement (and disappointment) is that I spend a lot of time thinking about how pianos sound and feel. And I think there's more to action from a player's point of view than just "firm or not firm". So why not write about it on my blog?

When a piano requires relatively more energy to play, people often describe its action using words like "heavy", "stiff", "firm", etc. But I've played lots of pianos that felt "heavy but loose", or "light but stiff", suggesting there's more than one dimension. So here are the elements I think of when describing a piano's action:

1. Weight (heavy vs. light)
   
2. Stiffness (stiff vs. fluid)
   
3. Tightness (tight vs. loose)
   
4. Response (responsive vs. sluggish)
   

These may or may not map simply to physical differences in the machinery of the action. And they're all closely related to the subjective perception of how effort produces sound. I think of this effort-in-to-sound-out as a kind of Transfer Function, which I'll describe in another post. For now, I'll say a little more on each of the four elements.

I see weight as a perception of how much matter it feels like you're moving when you press a key. This may correspond to the actual weight of the moving pieces. It may also be affected by a sense of inertia (how much effort it takes to get things moving, and how much it feels like they keep moving once in motion).

Stiffness to me seems more similar to friction. How fluid is the motion of the key? The action can be stiff but light (like pushing an empty cardboard box across a table), or heavy but fluid (like pushing a heavy stone across ice).

The tightness of an action is more about the amount of extraneous motion. The motion can be lateral (for example, extraneous side-to-side motion if the guide pin is too loose in the bushing) or vertical. Two kinds of vertical looseness are excessive bounce on key-up and excessive mushiness at the bottom of the key bed. It's easy to imagine an action being heavy or light and loose, and fluid and loose. I'm not sure I can imagine stiff and loose.

For me, the response of an action is about the perceived directness of the connection between motion and sound. More than the other elements, response seems temporal to me. Is there a feeling of delay in the action? How quickly are notes available for repetition? Does the key motion seem synched with the note sounding (especially when playing softly)? Informally, does the piano do what you want it to without hesitation?

So where do various pianos stand on the four dimensions? I'd say the action on my piano (an Essex 183) is medium-weight, somewhat stiff, nice and tight, and extremely responsive. The Steinway D I played at my last recital was fairly heavy, but fluid and a little loose, making it feel overall a little sloppy to me (the lack of stiffness and tightness failing to hold the inertia of the heavy action in check).

Of course, all of these perceptions are in the context of how the piano produces sound in response to force exerted, which is the topic of my next post.