Last year’s council tax calculation shows a total local tax burden of £24.66 million and a council tax base of 45,512.

The council tax base is arrived at by aggregating the council tax bands of all the chargeable properties in the authority’s area and expressing them as "Band D equivalents".

So, a Band A property counts as 6/9 of Band D; Band B 7/9; Band C 8/9; Band D 9/9 (1); Band E 11/9; Band F 13/9; Band G 15/9; Band H 18/9 (2); and a new Band I whose ratio to Band D I am not sure about.

This means that every nine Band A properties are expressed in the council tax base as six Band Ds and so on.

The actual amount of a Band D council tax is calculated by dividing the total amount to be raised by the tax base.

The amount of tax to be paid on an individual property is then calculated by dividing the Band D tax by the appropriate ratio: 6/9 of the Band D charge in the case of a Band A property and up through the bands to Band H which pays double the Band D charge.

Suppose that, just before last year’s calculation was made, 3600 band D properties were upgraded from D to E.

All other things being equal, while that is bad news for the 3600 householders affected, it would benefit of the rest of us because it would increase the council’s tax base by 800 (3,600x 2/9 (the difference between Band D and Band E)).

On dividing the £24.66 million by the new tax base of 46,312 you arrive at a Band D charge of £532.57 compared to £541.93 on the old valuation.

And, as the charge to all the other bands is calculated as a fraction of Band D they too would show a corresponding fall (£6.24 for band A and £18.72 in the case of Band H).

The only people who would actually pay more are those whose properties had been moved to a higher band.

In the example given the newly graded Band E properties would pay £650.91 compared to £541.93 had they remained in Band D.

Or, put another way, the 3600 householders would have paid an extra £392,328 which would be distributed in various proportions among the rest of the tax payers..

However, it may be that all other things are not equal because, as I understand, an authority's tax base is factored into the calculation of the amount of Revenue Support Grant each authority receives from the government.
So, if property values in, say, Pembrokeshire had increased faster than the all-Wales trend then it could find some of its RSG being redistributed to other authourities.
The principle being that a higher tax base is linked to higher property values which in turn is linked to better off people who can afford to pay more tax.
As an example: a community with 1000 Band A properties would have a tax base of 666 while one with 1000 band H properties would have a tax base of 2000.
In order to raise, say, £100,000 in each community would require Band D charges of £150 and £50 respectively which would result in a Band A property in the poorer community would be paying exactly the same amount of council tax (£100) as a Band H property in the rich area.
I have calculated this the long way round but the same result can be obtained by dividing the £100,000 between the 1000 properties in each area.