The Macaulay Duration

Dear Sir,
Regarding the Macauley duration, in the notes it’s written that:
The following should be clear for each of the variables:
– Time to maturity: as the time to maturity increases, the Macaulay duration will also increase
– Coupon rate: as the coupon rate increases, the Macaulay duration decreases
– Yield to maturity (or gross redemption yield): as the yield to maturity increases, the Macaulay
duration decreases

For Time of maturity and Yield to maturity, the impact of changes to MD is clear.

I need further elaboration over the impact of changes of Coupon rate – as the coupon rate increases, the Macaulay duration decreases!

I simulate increase of Coupon rate in xls and see that really the MD decreases, but could you explain more thoroughly why this happens? Both numerator and denominator (MV) of MD formula increase in absolute values when the coupon rate rises (which is OK), but also I see that denominator MV is increasing relatively higher than the numerator.

Please explain in more details why as the coupon rate increases, the Macaulay duration decreases?

Thanks in advance.