2N3055 has already answered most of it, yet I want to summarize...
For calculating the frequency a full period is all you need, when you calculate it manually (f=1/T).
A DSO can´t do it ?
But it can measure/calculate amplitude, mean and all other "vertical stuff" ?
Interesting..
Of course one period is sufficient. The problem is, the measurement algorithm needs to know what a period is. For this, it requires at least one sample before and after the relevant zero crossing (or 50% level). If you position the measurement gate precisely, you will miss the samples outside the period, hence the period cannot be determined.
It can measure amplitude, because the transition in the middle of the measurement gate is relevant for this.
It can measure mean, because it doesn't need to detect any transition to calculate that.
When you don´t specify the measure gate, it will measure on the whole screen(lecroy, siglent).
Frequency then will be measure correctly, but mean for example not*.
When you specify the measure gate, about one period, mean will be correctly measured, but frequency not.
interesting, again..
Over the entire record, frequency measurement will indeed be correct as long as at least two complete transitions in the same direction are present.
Amplitude measurement would be correct too.
Mean measurement cannot be correct, as long as the record does not contain an exact integer number of periods. The error decreases with record length; if you measure one and a half period of a standard waveform, then the error will be at its maximum. The difference between e.g. 10 or 10.5 periods will be much smaller.
And why can the "hardware counter" get it ?
Because it gather the "information" over the whole memory and not what´s on the screen ?
Interesting, the third..
The trigger frequency counter is independent of the waveform acquisition.
The trigger frequency counter, as its name implies, counts the trigger events. It analyzes the continuous data stream that goes to the trigger engine. So, it doesn't care for record lengths or measurement gates.
Simple solution to get it all right:
Forget about the measurement gate - it looks like this is not needed for your application. But for the amplitude measurements, like Mean, RMS, Stdev, use the corresponding Cycle-measurements. I.e. "Cycle Mean", "Cycle RMS", Cycle Stdev". This way you'll get a correct frequency measurement
and correct amplitude measurements at the same time.