More travels have brought me new flavours. This is a beverage typically found in Turkey. Although I rarely drink sweetened beverages, this is worth the calories.
Start with fresh or frozen tart cherries. They should constitute ~35% by mass for your recipe (I know, I know, just get a kitchen scale and everything works perfectly).
If you haven't got fresh tart cherries, frozen pie cherries are perfectly fine.
More math: ~5% should be sugar. Ex: ~250g cherries needs 50g sugar and ~750ml water. The total mass is ~1kg, but after straining the pulp, the volume yield is a bit less than a litre.
Blend it up!
Strain it through progressively smaller sieves. The more pulp that remains the more astringent, or dry, it will be.
Serve chilled.