Charles' solution is exemplary!
The best thing to do with microphones in front of singers is to turn them off.
This assures that the sound of human voices in song will be pure, genuine, and professional.
It is the organist's responsibility to register any accompaniments accordingly.

What sort of microphone(s) can amplify the sound of the singers without picking up the big organ behind them?

https://www.youtube.com/watch?v=NFQCYpIHLNQ

There likely are specialist microphones that can do what you ask - however they may require very close micing of your singers, which is often not a good approach in a choral situation. I would not be asking here for them. Find yourself a skilled acoustic consultant, who starts with understanding the goals of your music programme, and ask them for recommendations.

This assures that the sound of human voices in song will be pure, genuine, and professional.

Provided they were pure, genuine and professional in the first place.

They will also be inaudible to people shut-ins etc who receive recordings of the service, and perhaps also some people in your church building too, depending on how well built it is.

Say that you have a loft.
Then, you put a big organ in that loft.
In front of that organ, you place some singers.

What sort of microphone(s) can amplify the sound of the singers without picking up the big organ behind them?

Why?

If they are singing while the organ is playing, the organ should be balanced to support them, not overpower them. If they are incapable of projecting sound due to a ability or lack of training, they shouldn't be singing...

Much of the bad singing is people who can't sing being heard.

I heard a very lovely piece last night in which a person introduced it by speaking over a microphone when they could easily have been heard without it and it was disconcerting to hear this loud sound followed by the choir singing beautifully.

At the risk of answering the original question and incurring the wrath of the microphone haters (and let me say that I'm not particularly in favor of them in church, but I have no agenda to push here, either), there are microphones that will do the job you ask. At one time, I worked in various studios (where some very talented musicians, including vocalists, sang or played in front of -- gasp! -- microphones) and was exposed to many microphones and their subtle and not-so-subtle differences.

If you have two sources of sound (granted, one is a choir and so itself 'multiple') and you wish to capture one but not the other in a microphone in a live situation where they are near to one another, your best bet is to have them facing different directions. The difference doesn't have to be much, but if you can get them at 90 degrees to one another, so much the better. Then use a cardioid or hypercardioid mic in front of the singers. It will pick up sound directly in front of it, but very little from the sides, and little to none from the back. (Hypercardioid are prone to pick up a bit more from the back than cardioid.)

If you have many singers, you will probably need multiple mics because cardioid and hypercardioid (there is also a 'supercardioid' type which is in between) are quite directional, and with just one, even with well-positioned singers, you are likely to pick them up very unevenly. Still, if all of the mics have the organ significantly off-axis then the organ will not be heard much through the mic. Getting the singers close to the mic also helps because the 'amount' that the mic picks up is not a linear function of distance from the mic. (With singers close to the mic -- not 'eating it', but close -- you can turn the gain on the mic way down and it will still pick them up but not hear the organ almost at all.)

Any decent microphone will specify its pick-up pattern (some are capable of multiple patterns, selected with a switch). For a specific example, the Shure SM58 is a workhorse cardioid mic made for vocalists, not expensive, reliable for decades at a time, and easy to find. (They grow on trees.)

Amplification systems in 99.9% of American Catholic churches are like the lighting in a typical house. You turn it on and take what it gives you.

Subtle? No.
Artistic? No.

Effective? Well, things get louder, but not always clearer - and rarely well regulated for volume or equalization. Also rarely effective in making the sound appear to come from whoever is making the sound. So the homily does not sound like it is coming from the ambo, it sounds like it is coming from the speaker cluster/column/whatever as do the presidential prayers from the chair, etc. Virtually never with the kind of subtlety and flexibility the OP asks about.

Is it possible for amplified sound to be subtle and artistic? Yes.
Effective? Yes

Will it take more time and money? Yes and yes.

Will it happen? Not likely.

Why? (WARNING! Massive generalization coming!) Because the celebration of Mass (in either OF or EF) is not taken very seriously as a human sensory experience. This is why so little attention is paid to art, music, sound, homily preparation, lector preparation, everything preparation. It doesn't matter what the experience actually is, it only matters that we go through the proper motions. (The proper motions are different in the OF and EF.)

Clearly (from the state of amplification (and American building acoustics) in Catholic churches) it really is not that important to the church what kind of sonic experience Catholics have at Mass.

Question: What percentage of Catholic churches that install or renovate their amplification system hire a reputable acoustic engineer to advise and then actually follow the advice. My guess is less than 10%.

Another question: How often do Catholic churches include a study of the building's acoustics and how to improve them when a sound system is being installed and what percentage spend money to follow the study's recommendations. My guess is less than 5%.

The other extreme? Over 20 years ago I heard beautifully modulated choral singing and spoken word in a live performance of Man of La Mancha. The sound was amplified, even though the singers could have projected into the (rather dry) theater. The amplification helped keep the sound even through the theater. What I heard was part singer (original source) and part amplification (from well located speakers). If they could make a complicated staged presentation sound great 20 YEARS AGO - now so much more is possible.

I would prefer the entire liturgy to be unamplified, with natural sound emanating from speaker, singers, instruments, and aspergilla. Where factors such as building size or acoustics (not, however, poor singing or speaking skills) indicate that amplification may be useful, it could be done well if taken seriously.

And by the way, to wrest open another bag of worms, I really detest fake electronic tower bells (including the older style amplified "bell generators").

If they are singing while the organ is playing, the organ should be balanced to support them, not overpower them. If they are incapable of projecting sound due to a ability or lack of training, they shouldn't be singing...

Life should be so simple. I have some singers who are pretty good, I also have 2 or 3 who are really bad, but I can't get rid of them for political reasons. I suspect that is not unusual and in that case, you deal with it and go on.

Microphones are not needed in my reverberant building. I have been in places so acoustically dead that no one would be heard without them. It's like the old rule with organs, placement determines everything.

The amplification I use is a couple of monitor speakers in the loft to boost the sound level from the ambo and altar. It doesn't help that priests and readers can't seem to get the hang of correctly speaking into a microphone. They talk into their chests while reading, so everything gets muffled. Some of my older choir members don't hear as well anymore, so the monitors benefit them.

Question: What percentage of Catholic churches that install or renovate their amplification system hire a reputable acoustic engineer to advise and then actually follow the advice

I haven't found many really qualified sound technicians. Most are folks who decided to set up shop based on what they thought they knew about sound. I know of churches that spent thousands on systems that were badly designed, installed, and simply don't work.

Yes bonniebede, but you will probably want the organ heard as well in that case.

We hired a sound engineer for our new church. He recommended ceiling accoustic tiles. The committee has decided to trust that advice and try without the tiles first. All I can do is pray that they will not deaden the sound too much that we need to add microphones.
Tiles are installed but Windows, pews and floor tiles are not yet. Ill keep you posted. It sounds pretty dead to me currently.

donr

I am assuming that your "sound engineer" is an electronic equipment salesman or, slightly better, a public address system designer. Probably not either an acoustician or a sound designer familiar with Catholic worship.

Given that..

My two cents on acoustic deadeners: there are two common sources of this (almost always) pernicious idea.

1. The "sound engineer" knows only one solution for every situation: add deadener, then amplify enough to overcome the created deadness. (As MJO said above.)
2. The "sound engineer is actually capable of designing an appropriate system for your church (assuming it really needs one) but the church has not given a clear specification of what is desired. In general, I would ask for some genuine room (not electronic) reverberation and sound directivity IE that the sound appear to emanate from the speaker or singer. If the engineer doesn't know what the church wants, or if the church doesn't know what it needs, then - out comes the acoustic tile.

In most situations, musicians have limited input on this decision. This is another indication of the lack of seriousness with which our churches take the sensory experience of the liturgy. I wish you the best. Sometimes these things turn out quite well.

It is true that some engineers have engineered positive acoustical environments for liturgy and its music. I have heard of a number of such encounters. The important factor is to be certain that one's 'engineer' understands what a positive environment for making music from the classical tradition is, and is enthusiastic about making it a reality in one's church. A certain reverberation suitable for one's church, which will enhance music making, both choral and instrumental, should be a non-negotiable desideratum. In securing the services of such a person one would be wise to seek a recommendation from an organ builder of repute, or someone responsible for acoustics in university or municipal concert halls. Any PA systems, if at all necessary, should be strictly engineered to enhance musical sound, not compensate for the lack of sound nurturing and reverberant acoustics. I'm sure that there are others here who are more competent than I to address these matters. But, one thing is an unassailable certainty: carpeting, pew cushions, and so-called 'acoustical tile', any sound-deadening materials, are in any situation acoustic destroyers. Without these I would dare assert that by far most PA systems would be unnecessary.

In securing the services of such a person one would be wise to seek a recommendation from an organ builder of repute, or someone responsible for acoustics in university or municipal concert halls.

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