Hexadecile

The assessor can then be asked to successively divide an interval into equally likely segments yielding the octiles (X_(.125), X_(.875)), hexadeciles (X_(.0625), X_(.9375)), etc., etc.

With each of the above methods, the quartile values are always either one of the data points, or exactly half way between two data points. Those methods involve only simple arithmetic and are easily extendable to octiles (eighths), hexadeciles (sixteenths), etc. They are not, however, extendable to quintiles (fifths) or percentiles (hundredths), etc. Furthermore, they tend to have a high bias. (That is, the quartile values calculated on subsets of the data set tend to vary more, and are not good predictors of the quartile values of the entire data set.)

But becauſe ſome Aſpects are more Effectual than others, therefore they are (reſpectu graduum, Scientiæ and Congruentiæ, necnon Efficacitatus) thus to be Diſposed: viz. ☌. ☍. ◻. △. ⚹. SS. Q. Bq. Vc. Dec. Td. Sq. SSq. whereunto are added (as in the laſt and loweſt degree of Dignity and Efficacy) the Quindecile, Hexadecile, Vigintile, and the Icoſiteſſeragonall, (or figure of 24 ſides), which are only considered in Venus and Mercury with the Sun.

Parameters are then non-linearly re-scaled to the range of 0 to 15 to create a 4 bit acoustic vector component. Empirical non-linear scales were pre-determined for each parameter such that, over the long term, their values distributed evenly across a set of hexadecile bins representing the full range of the parameter. In the current system a separate non-linear scaling was established for each individual speaker, and, given the extent of the ANDOSL data used, this amounted to deriving equiprobable bins from approximately 10 minutes of spoken phonemically-rich sentence data.

Several algorithms were tested for the equi-population transform. The simplest consisted of dividing the total population by 16 and then, in a single linear scan, the parameter histogram was divided into hexadecile units. This approach performed poorly where parameter distributions were peaky, which is often the case.