Difference between deltat and frequency in R ts() function

Question

This is something that has been bugging me for a while. I've been working with (monthly) ts() objects a bit recently, and I cannot for the life of me figure out the difference between frequency and deltat in the R Documentation:

frequency: the number of observations per unit of time.
deltat: the fraction of the sampling period between successive observations; e.g., 1/12 for monthly data. Only one of frequency or deltat should be provided.

In my case, I have tried setting frequency=12 and deltat=(1/12) in separate cases with the same data, and I cannot tell any difference in the resulting time series objects.

From the way the descriptions are worded, I get the feeling that there has got to be a difference in their uses, I just can't put my finger on it.

Examples of cases where only one would work and not the other would be great.

Answer 1

The question is a bit old, but I answer the same to put more informations. The focus of these functions are to provide to describe informations about the structures and patterns in your time sereis. You have to consider also that in the ts() (years time series) aren't always the exact same (think about the business days), just the hours in a day are always the same. We can say that we have three operations about ts The first one is the deltat() function that returns the fixed time interval between observations. The second one is the frequency() function that returns the number of observations per unit time. The last, but not least we have the cycle() function that returns the position in the cycle of each observation.

Example: 

AirPassengers
     Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1949 112 118 132 129 121 135 148 148 136 119 104 118
1950 115 126 141 135 125 149 170 170 158 133 114 140
1951 145 150 178 163 172 178 199 199 184 162 146 166
1952 171 180 193 181 183 218 230 242 209 191 172 194
1953 196 196 236 235 229 243 264 272 237 211 180 201
1954 204 188 235 227 234 264 302 293 259 229 203 229
1955 242 233 267 269 270 315 364 347 312 274 237 278
1956 284 277 317 313 318 374 413 405 355 306 271 306
1957 315 301 356 348 355 422 465 467 404 347 305 336
1958 340 318 362 348 363 435 491 505 404 359 310 337
1959 360 342 406 396 420 472 548 559 463 407 362 405
1960 417 391 419 461 472 535 622 606 508 461 390 432 

deltat(AirPassengers)
[1] 0.08333333

frequency(AirPassengers)
[1] 12

cycle(AirPassengers)
     Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1949   1   2   3   4   5   6   7   8   9  10  11  12
1950   1   2   3   4   5   6   7   8   9  10  11  12
1951   1   2   3   4   5   6   7   8   9  10  11  12
1952   1   2   3   4   5   6   7   8   9  10  11  12
1953   1   2   3   4   5   6   7   8   9  10  11  12
1954   1   2   3   4   5   6   7   8   9  10  11  12
1955   1   2   3   4   5   6   7   8   9  10  11  12
1956   1   2   3   4   5   6   7   8   9  10  11  12
1957   1   2   3   4   5   6   7   8   9  10  11  12
1958   1   2   3   4   5   6   7   8   9  10  11  12
1959   1   2   3   4   5   6   7   8   9  10  11  12
1960   1   2   3   4   5   6   7   8   9  10  11  12