It isn’t a church, but if you are ever in Austria, you can hear the Kufstein Heroes’ organ daily at noon.
You can hear it all over town. You don’t want to be too close. It is loud.
I heard it once while traveling. My wife and I stopped in Kufstein on our way back to Germany from Lofer in Austria. We were in Kufstein around noon. I don’t remember what it sounded like, except it was loud and I wasn’t expecting it.
We were on the walkway shown in the last panorama on this page. That’s in the fortress, not too far from the organ.
If your tastes run to the French organ repertoire perhaps the most famous builder was Aristide Cavaillé-Coll and a list of extant organs by him is in Wikipedia at Existing Cavaillé-Coll organs.
There are even a few in the UK rather to my surprise so when travel becomes easier in the UK you can sample a few without a passport.
I live in the Netherlands and there are so called ‘open monumenten dagen’ (in English Heritage days). On such days, many churches (and other cultural places like windmills, old farms, historic buildings) are open to the public. A few years ago I visited a number of churches in Alphen aan den Rijn en Leiden where the organ was played almost the whole day so your chances of finding a place where the organ is actually played is much higher. These heritage days are at the same moment all over Europe so perhaps you could plan your visit around those days, the Wikipedia page (Heritage days) shows you those dates.
Wikipedias article on Arp Schnitger includes a list of his surviving works: https://en.wikipedia.org/wiki/Arp_Schnitger.
They are located mainly in northern Germany and the Netherlands.
A number of the constituent colleges of the University of Cambridge have good organs and good organ scholars to play them. In consequence they have some very good organ performances, many of which are open to the public, many of those being free of charge. Primus inter pares is probably the King’s College chapel organ, on which free organ recitals are given every Saturday in term-time, and which has been sounding particularly good since the restoration finished three years ago.
Once the world gets back to normal, that is.
In the UK, a good place for "binging" would be the annual St. Albans International Organ Festival. Two weeks of wall-to-wall listening to the world’s best young (under-30, or thereabouts) players competing against each other. https://organfestival.com/
There are similar festivals (both competitive and non-competitive) in many European countries. As well as the obvious locations (e.g. in France, Holland, Germany, Spain) check out Eastern Europe (Poland, Slovakia, Estonia, etc) which have many fine instruments.
The Monastery/Palace of Mafra, Portugal is one of the largest of its kind in Europe and can have 6 organs playing at the same time.
The six organs of the Basilica of the National Palace of Mafra
constitute a unique ensemble in the world, not because of their
number, already remarkable, but because they were built at the same
time and originally conceived to play together, they were built by the
two most important Portuguese organ makers of their time – António
Xavier Machado and Cerveira and Joaquim António Peres Fontanes.
Right now the Municipal Townhall of Mafra, supported by the Portuguese Ministry of Culture is promoting a contest open until the 16th of April 2021,
"International Composition Prize – Organs of the National Palace of
Mafra"
which aims to create a new repertoire for this magnificent instrumental set, classified as World Heritage by UNESCO.
So stay tuned for some magnificent concerts in 2021
edit: the first concert 2021 "Concerto de Reis for 6 organs", January 9th, 2021 at 21h00 UTC. Live at: https://www.facebook.com/camaramunicipaldemafra
Performed by the Schola Cantorum of Santarém Cathedral, under the
direction of Pedro Rollin Rodrigues, accompanied by the six organs,
which will be played by André Ferreira, Daniela Moreira, Diogo Rato
Pombo, João Santos, Margarida Oliveira and Sérgio Silva, with musical
direction by João Vaz. The concert will be transmitted through the
Facebook of the Municipal Townhall of Mafra.
update: unfortunately, due to new COVID-19 travel restrictions in Portugal on weekends, in force as of today January 7th, 2021 23h59, the concert was cancelled
You might try to find "organ associations" in various countries and see if they can give recommendations or ideas. I know that in Gothenburg there is an active such, https://www.organacademy.se . They did a festival October 2020. I would believe that members there might be as interested as you and could give long lists of interesting places and organs.
Several cathedral/church locations in Europe are listed here https://www.classicfm.com/discover-music/latest/organs/, for example:
Freiberg Cathedral in Germany
Basilica of Valère in Sion, Switzerland
Church of St Pierre des Chartreux in Toulouse, France.
From a comment it seems you are in the Midlands, UK. The Victoria Hall in Stoke-on-Trent is renowned for its acoustics and has a world-class organ dating from the 1880s http://www.victoriahall-organproms.co.uk/organ_d.htm (disclaimer: my home town!)
All main European cities have cathedrals and most of those use the main organs in the main services. Maybe not every Sunday but almost all of them will have them in use for the Easter and Christmas services.
You will need to research which of the main churches in really big cities will do the best or longest organ playing around the services.
When you look up organ concerts in the city you happen to be in, do not discount concert halls, as some of them have organs that are as good as most of the church or even the cathedral organs. And it they are happy to organize an organ concert, it will be worth your time and money.
I am not a lover of organs, will escape out of a church as soon as the organ starts. The last event was an organ playing while I was still in the RC (Roman Catholic) cathedral in Haarlem, the Netherlands (called St Bavo, as is the old/former cathedral in the same city) and this had been posted locally in the concerts list of the ‘things to do’ website.
In London I would check the concert list as well as the ‘activities’ list of St Pauls, Westminster Abby as well as Westminster Cathedral (which is the RC cathedral for the area.)
In Paris, again the same listings and for all the main churches. I remember my father telling very enthousiasticly about the organ in the Saint Eustache, but he did mention organs in many of the main churches and cathedrals he visited in France. And not just at the main church holidays but also on random Sundays.
In Germany I have only visited one main church, the Dom in Cologne and indeed, it had a main organ and they played it.
In short, each main church in Europe is likely to be worth visiting.
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