SQUINT a little in the gloomy light, throw in a sizeable dollop of imagination, and you can picture you are in a jazz club cellar in pre-war Paris or Berlin. The walls are suitably dark and postered, the floor bare stone and woodwork, the tables small, the chairs flimsy.

This is Glasgow today though, so there is no cigarette smoke silently choking you. Instead it is the sound of a tenor sax that is enveloping you as it weaves through the air like a musical fast-growing vine, caressing you on the sadder notes like a lover saying goodbye. It is as if the hopes and dreams of the audience are being breathed out into the confined space, picked up by the saxophone, and blown melodically back at them. Beside it on stage is a double bass, and its vibrating chords seem to synonymously vibrate in your head turning your body into its own version of a double bass.

Did I mention that there are craft ales on sale upstairs? But you probably guessed that from the previous paragraph.

This is downstairs in The Hug and Pint on Great Western Road near St George's Cross. I knew it as The Liquid Ship, and yet again I plead for legislation to halt bars changing their names as frequently as underpants, thus confusing those of us resistant to change.

On stage playing the saxophone as part of the Glasgow Jazz Festival is 22-year-old Helena Kay from Perthshire. I was about to describe her as petite and blonde, which she is, but on reflection is of little importance. It is not her age, sex, or hair-colouring which has attracted the respectful crowd seated at the little tables. It is her playing. Not just the ability to play all the notes in the right order which in itself is a feat on a saxophone. But to then suffuse these notes with all the emotion that she somehow imparts. She and bassist Calum Gourlay and drummer David Ingamells take us through "The Folks Who Live on the Hill" composed by Jerome Kern. There are no lyrics, but they are not needed. The original had words by Oscar Hammerstein, which spoke of the longing a couple had to have a house built on a hill where they would raise a family, put down roots, and become known in a transient world as the folks who live on the hill.

Here in this Glasgow cellar that longing for stability comes across in Helena's playing as she knows when to hold a note, when to leave it lingering in the air, when to quickly move on. Is it jazz? I don't know, nor care. It is sublime music that stirs the senses and emotions. Other numbers are perhaps less structured, but with recognisable motifs. It's like the musical equivalent of gun dogs being sent out into the long grass. You are not quite sure where they are going, but every few seconds they pop up into view to reassure you, and after a while they satisfyingly come back to where they started.

On second thoughts, I will mention Helena's age again. A few will dismiss jazz as the musical indulgence of old men with beards. But the Glasgow Jazz Festival, celebrating its 30th year this year, took that landmark 30, and instead of just celebrating those who have been on that long road with them, made a point of naming “30 Under 30” – a collection of young Scottish jazz musicians already making a mark in the global jazz world. As festival director Jill Rodger explains: "It's vitally important to recognise the next generation of musicians."

One of them is of course Helena, now uprooted from Perthshire and in her final year at the famous Guildhall School of Music in London. She started, like many a young girl, with a violin, but then took up an alto saxophone. Her teacher gave her a Charlie Parker CD, and she was hooked. She joined the Fife Youth Jazz Orchestra, moved on to the tenor sax, and last year won the Young Scottish Jazz Musician of the Year competition. She hopes to continue playing full time as well as teaching in London when she graduates.

I ask her if she met any hostility because of her age or sex, but she tells me: "I feel I'm very lucky to be involved with jazz musicians who are very nice and open-minded people."

The Glasgow Jazz Festival is Glasgow's longest-running festival, pre-dating the goliath Celtic Connections festival of every January. Returning this year was the truly world-class Carol Kidd who performed at that first festival. And she recalls how it changed her. "I was absolutely petrified, because it was my first time singing with an orchestra. I looked down at my feet halfway through the second number and I realised that I had been so nervous, my shoes were on the wrong feet. So I took them off – and I’ve never worn them onstage since.”

Now I know people like the comfort of the large seats in the Glasgow Royal Concert Hall, or even don't mind sitting in the clouds above acts way below them in The Hydro just so that they can brag to pals about attending a landmark concert, but for sheer enjoyment, to really feel the musical shading of performers almost within touching distance, try out acts in the intimate surroundings of venues such as The Hug and Pint. Even if it is a jazz performer and you "don't like jazz" as you tell everyone even though you've never actually attended a jazz concert, it is music, and that can often move you even though you are not well versed in the art form. The tickets were only eight quid - the price of two beers.

When Helena, Calum and David were playing, I was lost in the music, and even forgot about the result of the EU referendum. How can you put a price on that?