The tradition of Mouth Music or Puirt a Beul (literally tunes from the mouth) is still kept alive today. It is usually unaccompanied music. It was said that if you couldn't get a piper for an occasion, then puirt à beul was used instead.
It's good to learn about the culture as well as the language, and that applies to all languages.
These two websites are absolute treasure troves for anyone wanting to look up this (or any other) type of Gaelic music.
Tobar an Dualchais - http://www.tobarandualchais.co.uk/gd/. I can go on here and hear my great and even great great granny singing. Really special.
http://www.bbc.co.uk/alba/oran/orain/list/a_u/ - Bliadhna nan Oran has loads of recordings sorted by theme. Many of them have recordings.
Is Mairi MacInnes related to Kathleen Macinnes ? I didn't find the information , and there is a Maggie too, arghh 3 singers with the same last name !! :) Thanks for the link I only knew Kathleen so far :)
Can I also suggest Catherinne-Ann Macphee ? I don't know if it's also Mouth Music but I like this kind of singing too.
I agree with CIMacAonghais, Tobar an Dualchais is a great resource, and I have dipped into the BBC site too from time to time. Have several CDs by Cathy Ann McPhee, Runrig. A family member was very involved a couple of decades ago in preparing two song/music books for the Fèisean nan Gaidheal - Ceòl nam Fèis books 1 and 2, lots of favourite tunes, including Puirt a Beul. This site might also be worth a look - https://dasg.ac.uk/en
The more you start to listen to Uibhisteach and Leodhasach musicians, the easier it is to find =)
Julie Fowlis (Uibhisteach) makes it a point to have at least one Puirt-a-Beul set on pretty much every CD she releases and most of her music is available on Spotify and YouTube. Manran also tend to do Puirt sets and Ewen's voice is very clear so it's been easier for me as a beginner to pick out where words should start and stop, even if I don't know what the words actually mean or how to spell them (yet).
To deviate slightly from Puirt-a-Beul but staying on-topic for the culture:
If you're anywhere near the Hebrides, July is basically a Month of Trad Music. A nearly week-long festival in Tiree followed by another nearly week-long festival in Stornoway (HebCelt is 25 this year!!). Sure there is a lot of English but Gaelic performers always make up a sizable chunk of the programme. So far I believe Julie Fowlis, Tide Lines and Trail West are committed for HebCelt and there are always free sessions by smaller groups at Stornoway Town Hall, the community centre in Tarbert, etc. Just grab the line-up from the websites and start searching for bands, your ears will thank you! =)