Fractions and Parts

The use of fractions and parts is familiar to dancers starting somewhere between Mainstream and C1. There are a few special aspects we will discuss here.

How Parts of a Compound Call are Divided

If a call is defined as having four parts done in sequence, one can do 1/4, 1/2 or 3/4 of that call in a natural way. For example, Split the Difference has four parts, so 3/4 of Split the Difference is clear.

Beware: Some calls naturally have a fraction at the beginning of their name. 3/4 Mix is not the same as 3/4 of a Mix. The caller must be careful to make the meaning clear.

Some calls (Hot Foot Spin and Settle Back, for example) are defined as a sequence of parts, some of which are themselves sequences of parts. When this happens, the parts subdivide uniformly at each level. The last 1/3 of Hot Foot Spin is Spin the Top. The last 1/2 of that last 1/3 is Fan the Top. That's the last 1/6, even though the call doesn't have 6 parts.

If we do 1/2 of a Hot Foot Spin, we stop halfway through the middle third.

\sxvlines{b1e,g1w,g2e,b2w}	\shonebythreedmd{b1s,g1n,g2s,b4e}

before 1/2 Hot Foot Spin	after

If we do 5/6 of a Hot Foot Spin, we stop halfway through the final third, that is, after the first half of the Spin the Top.

As a somewhat extreme example, we could do 9/12 of a Hot Foot Spin, that is, 3/4. That would be 2/3 (the first two parts) followed by 1/4 of the final part. 1/4 of the Spin the Top is 1/2 of the initial trade, that is, Hinge. The result is columns. This application would have to be considered obnoxious. An even more extreme example would be (from waves with boys on the end) Boys work 17/18, Hot Foot Spin. The boys would change their final Cast Off 3/4 to a Cast Off 1/2.

Some parts of compound calls are, by convention, a single part, even though they consist of doing something twice. These are the two "O" Circulates of Bits and Pieces, Outpost, and Settle Back, and the two "Diamond Counter Rotates" of Alter the Wave and Alter the Diamond. Of course, those two items can be broken apart with the correct fractionalization. For example, 5/8 Alter the Wave, or Boys Work 5/6, Outpost.

There used to be an alternative formulation for breaking calls apart, called "flattening". Under flattening, all parts at all levels were simply strung out in one list. Hot Foot Spin would have 4 parts. Flattening had logical problems — one needed to analyze a call all the way to the bottom before one could do anything, and it didn't work properly with meta-concepts like Initially. It is no longer used. One notable exception to the rule that we don't flatten is the call Swing and Mix. If it logically followed the conventions that we make for compound calls of this type, it ought to have two parts — Swing, and Mix, the second of which has 2 parts. However, by long-standing convention this call is construed to have 3 parts.

How Parts and Fractions Differ

One can do a Grand Swing Thru 1-1/4, resulting in columns. Does that mean that Grand Swing Thru has 4 parts? No. In addition to the natural subdivision of calls that have parts, a call that doesn't have parts can be stopped or interrupted at a fractional part, if that is sensible in terms of the call's action. For example, one can to 1/2 of a Wheel Around, 3/4 of a Do-Sa-Do, or 3/4 of a Mix. One can also stop non-compound parts of compound calls, as we saw with the 1/2 Hot Foot Spin.

When we fractionalize a call in a way that doesn't divide it on part boundaries, the number of parts in the result is not well defined. 1/2 Change the Centers has two parts, but the number of parts of 3/8 Change the Centers is not well defined. As another example, Initially Stable 3/4 Run Wild is improper.

How These Things Interact with Other Concepts

Some concepts work with parts, but not with fractions. The Interlace concept is a good example. You can't interlace a Do-Sa-Do, but you can interlace a Hot Foot Spin. The interlace occurs at the top level only — no interlaced call can come between the parts of the final Spin the Top.

Some operations, like Interrupt, can exploit either parts or fractions — one can interrupt Alter the Wave after 2 parts, or after 1/2. (But if you want to interrupt after 5/8, that is, between the Diamond Counter Rotates, you must specify it by fraction or use a powerful concept like Thirdly.)

The "Replace" concept is only specified by parts, because it is too cumbersome to say "Hot Foot Spin, but replace the material between 2/3 and 5/6 with an Ah So."

There are also meta-concepts that direct the application of some other concept over some part of a call. These can be done by parts:

Do the 3rd part Stable, Split the Difference

or by fraction:

Do the first 1/6 Tandem, Turn the Key (or just First 1/6 Tandem, Turn the Key)
Last 7/8 Tandem, Change the Centers

The meta-concepts "First M/N", "Middle M/N", and "Last M/N" mean to apply the concept to the indicated part of the call. They can, of course, break up parts.

Nested Meta-Concepts

The meta-concepts "Initially", "Finally", "Evenly", "Oddly", "Random", "Reverse Random", "Piecewise", "Firstly", "Secondly", and so on, are extremely powerful and extremely complex. They go down one level in the structure of a compound call, and cause the concept to be applied to the selected part or parts. When nested, they can go down multiple levels. If the concept after the meta-concept operates on parts or fractions, it operates on the parts or fractions of that subcall, and things can become quite complex.

Consider the case of "Initially Finally Echo Concentric Settle Back". The meta-concepts nest as though it were "Initially (Finally Echo Concentric) Settle Back".

Settle Back has two parts. The second of those (Cross Back and two O Circulates) will not be affected. But the first part is Reset 1/2, and has "Finally Echo Concentric" applied to it. Reset 1/2 has two parts — 1/2 Zoom and Hinge. The second of those parts, Hinge, has "Echo Concentric" applied to it.

\syhlines{b2n,g2n,g3s,b3s}	\sxhlines{b4n,b3s,g3s,g4n}

before Initially Finally Echo Concentric Settle Back	1/2 Zoom

\sxvlines{b4w,g4e,g3w,b3e}	\syhlines{b1s,g1n,b4s,g4n}	\sxvlines{b3n,b2n,g3n,g2n}

Concentric Hinge	Hinge	finished

Re-evaluation

When the application of a concept is broken up through the use of a meta-concept such as "Random", we say that the concept is "Re-evaluated". This means that any special things that we needed to think about for the concept (lines-to-lines, the Once-Removed axis, the Split Phantom Lines axis, with whom one is in a Twosome or a Tandem, etc.) are completely evaluated and processed at each interruption point. Normally we think about the lines-to-lines rule for Concentric only at the beginning and ending of the complete call. We don't apply it to each part of a Split the Difference. To do so would be incorrect.

\sxvlines{b3s,g3s,b4s,g4s}	\sxvlines{g2s,b2s,g3s,b3s}	\syvlines{g2e,b1w,b2e,g1w}	\syvlines{g2e,b3w,b2e,g3w}	\syhlines{g2n,b2n,g3s,b3s}

before Piecewise Concentric Split the Difference	after 1/4	after 1/2	after 3/4	finished

By applying the Concentric rule specifically to the last part of the call, we got 2-faced lines instead of the columns that we would get on a normal Concentric Split the Difference.

Under normal circumstances, we don't re-evaluate between parts of a call. But, if we interrupt the call, we have to re-evaluate.

While dancers are doing a Concentric Split the Difference, if we ask someone where she is at some intermediate point, she might say "I'm working around the outside, and I'm going to make columns when I'm finished". Now suppose we interrupt after 1/4 with a Transfer the Column. The preceding answer isn't good enough. She has to make precise columns after part 1, applying the "columns to columns" rule. After the Transfer the Column, people need to re-evaluate the setup again and proceed from there.

Similarly, the Once Removed axis might change, or whether a person's Twosome is Tandem or As Couples might change. During an interruption, or during a part of the call without the concept, these things are meaningless, so they need to be re-evaluated when the concept is resumed.

The Piecewise meta-concept forces a re-evaluation on every part, as well as causing the concept to be applied to each part separately. For example, Piecewise Twice Change the Wave is not the same as Change the Wave Twice.

Concepts That Present Parts

Since knowing exactly how things are broken into a tree structure of parts and sub-parts is so important, one needs to be aware of some concepts that themselves impose part structure. A prime example of the is "Crazy".

The Crazy concept, applied to anything, always has 4 parts.
N/4 Crazy has N parts.
Echo and Reverse Echo have 2 parts.
Initially, Finally, Random, etc. have as many parts as the underlying call.
Interlace has the sum of the parts of the constituents.

So, if we interlace a Crazy Circulate with The Difference, we do a total of 7 things — 4 Circulates in various places, interlaced with the 3 parts of The Difference.

If we do an Initially Echo 1/2, 3/4 Crazy Roll Away, from a tidal 1-faced line, there are "officially" 3 parts, but we do 4 things:

1/2, Roll Away (now in facing lines, re-evaluate)
Roll Away
centers Roll Away
Roll Away

The first two of those things constitute the first part.

How about Random Crazy Change the Centers?

The Random concept picks out the first and third of the four parts of Change the Centers for special treatment. The fact that doing those parts Crazy turns those actions into 4 actions makes no difference — Random doesn't see them. It sees only four things. There are a total of ten things to do, but the whole operation has four parts: Crazy Trade, Slip, Crazy Centers Cross Run, Slip.

The "initially" meta-concept (and others like it) give rise to similar issues. These meta-concepts do not change the number of parts of the subject call, even if the concept is something like "twice" or "crazy". "Initially Twice Mix" has 2 "official" parts:

Centers Cross Run twice
Centers trade

So Initially As Couples, Initially Twice, Mix is done as:

As Couples do a Centers Cross Run twice
normally do a centers trade

Things like this can be quite confusing.