Maybe you're a bit old-fashioned, and you still enjoy the famous artists of previous centuries. The spread of phonographs/grammophones during/after WWI, followed by the spread of radio in the 1920s, made new recordings of old compositions available at a reasonable price. If you can tolerate a little modernity, you might put down that Bach or Sousa record and listen to some George Gershwin: https://www.youtube.com/watch?v=ynEOo28lsbc (1924)

Maybe you enjoy music from the previous couple of decades, like someone today who listens to 80s and 90s music. It's a lot of piano solos for you, since recent classics were more likely to be published for self-playing piano than expensive record players. https://www.youtube.com/watch?v=pMAtL7n_-rc (1909) EDIT: /u/Whizbang points out this is probably not a Joplin recording, and the date is suspect. But this one is by Joplin: https://www.youtube.com/watch?v=Hr_VXR0GWhQ (1916). The song was composed in 1899 and remained popular enough that Joplin was contracted to make some piano roll recordings in 1916, while he was suffering the effects of the syphilis that would kill him the following year.

This period was a great time for blues, which would eventually form the basis for rock: https://www.youtube.com/watch?v=ZOTTYTGv22k (1924)

Country's been around forever: https://www.youtube.com/watch?v=0yMgOZ6gw1I (1923/24?)

You might enjoy swing / big band music: https://www.youtube.com/watch?v=teJfuKdzbOo (1939) my favorite: https://www.youtube.com/watch?v=0NigiwMtWE0 (1937)

Unfortunately big band requires, well, lots of band members. It fell out of style when the massive troop enlistment needs of WWII made it prohibitively expensive to employ dozens of musicians for a simple dance event. Edit: Probably an over-generalization, see https://www.reddit.com/r/AskHistorians/comments/4zyne3/the_popular_conception_of_the_popularmusic/d70wsea

But hey, it's a great time to be a showtunes enthusiast! Annie Get Your Gun, Oklahoma, The Wizard of Oz. People were into vibrato, who knows why: https://www.youtube.com/watch?v=PSZxmZmBfnU (1939)

Some of these might seem like variants on jazz. That's due to the technology/instruments available, and the fact that styles tend to look more similar after time has passed. Think about this: to a lazy historian a century from now, Elton John and Dragonforce are probably both "rock artists of the late 20th century." There are people today who aren't into classic rock but still listen to metal; or who aren't into mainstream electronica but listen to dubstep or other variants. My grandmother would never understand why we think her exciting, dance-worthy big band music sounds similar to her dad's boring old jazz records!

What is commonly lumped in as jazz now might not have been considered such at the time. Think of the song "White Christmas". That remained the most popular song, based on the common metrics of requests and sales, for a surprisingly long time. It was a vocal performance with the instruments of jazz, but devoid of the beat that one associates with mid-forties Jazz.

It's easy to see the distance between the clatter of Glenn Millers orchestra and the tissue smooth stylings of Bing Crosby's White Christmas and compare that to say, the Foo Fighters and Sarah MacLachlan, yet no doubt the future would lump both together based on chronology rather than contemporary appeal.

We tend to lump anything that is primarily brass and woodwind instruments with drums as jazz, but during that time, that's the noisemakers you had, and beat and volume would have been the factors of attraction. When growing up I knew friends of my parents that strongly preferred Benny Goodman over Tommy Dorsey, would discuss it at parties, break out records and I didn't see the difference.

It is worth mentioning as well that the popularity of nineteenth century classical music continued well into the twentieth century, and it dominated early radio broadcast programming. In more remote parts of the country, one might find blues or early mountain music, but a city person may not be exposed to it. It could remain isolated for decades. Much like today, the music of a previous generation was broadcast as "popular", whereas one would have to go to parties or clubs to hear "today's" music.

And that's looking at it from a city perspective. Prior to WWII it was common that someone would live and die within a modest radius of where they were born. Radio stations would cull local music and broadcast it in addition to the aforementioned "classical" music. Music tastes at that time were spread beyond ones locality mainly by stage shows and especially movies, which were able to share the identical tempo and dance moves with people thousands of miles apart. This was utterly new and helps explain the appeal of Hollywood musicals. Music videos are nothing more than those in concentrated form.

The wars of the forties and early fifties changed the radio landscape as they began to offer programming suited to soldier-age tastes. Radio programming became more pre-recorded, and live shows could be linked and broadcast far and wide. But appealing to the young who were making sacrifices was considered patriotic. This effectively reduced the target age of their audience by a decade or two, and station owners found that it's affect on advertising revenue was negligible, if not positive. In the early days of advertising it simply made sense to advertise to those who had money, rather than to those who have no discipline with money.

This model remains in place to this day. One can look at television programming and see it followed a similar model, and you can see a shift of the target audience to a younger age over time.

With all this said, you simply had the instruments available, which save for electronics do not differ from what's available today. How they were employed was what you were attracted to. No one in that period would have considered music as "wall to wall" jazz, that is a lazy genre label applied by middle school music teachers, like how the four centuries prior to that "wall to wall" classical.

Someone in r/music recently bemoaned the requirement to add a "genre" along with your post. Genre's are stifling ghettos that keep musically tastes corralled, and do not encourage one to venture out and find something new. Music should be a collection fetish and should reflect one's ever changing tastes as well as what's available at the time. I mean, I might like powdered wigs, but I'm not going to wander into Macy's and find one.

Bear in mind, tastes are not some internal organic eruption. It is a choice made of what is available at the moment. My preference for powdered wigs would not have come about if they weren't available at some point prior to now

One hundred years from now Celine Dion's "The Heart will go On" will be lumped in with Rock and Roll, or maybe even Hip Hop by a middle school music teacher, based on some shitty text book. Everything we've created in the last fifty years will fall into the categories you see in a music shop...Rock, Rap, Country, Jazz, Other. Guh...

My apologies to all contemporary middle school music teachers! I have one in mind, and for affect I'm painting all with the same brush. Please forgive my literary license. You do God's work.

Folk music was absolutely huge. In the 1920s and recording technology expanded, people could finally hear their traditional music recorded. This is absolutely one of the most revolutionary things to happen to folk music, and it led to people like Harry Smith in the US and Cecil Sharp in the UK obsessively recording and collecting everything they could. It had quite the effect on classical music too, with composers like Vaughan Williams encompassing these strange new (old?) sounds into their music. This is why the folk music of the 60s is often referred to as 'folk revival'.

This is also why Oh Brother Where Art Thou is a masterpiece.

Not mentioned in any of the responses here is that the period between the 20's and 40's was the incubator for what today is known as country-western music. Harry McClintock and other hobo themed music, Gene Autry, Jimmie Rodgers, The Carter Family, Hank Williams, western swing, "hillbilly", Woodie Guthrie, Bill Monroe and the Bluegrass Boys, the early black country jug bands, etc.

Since there already have been some great answers, I'll take the risk (and please call me to order if you consider this an insufficient answer) and simply point you to "The Rest is Noise: Listening to the Twentieth Century", by Alex Ross, which is a popular overview of the music of the 20th Century. It's an easy read, and might give you some additional insight.

Question for OP? What is your idea of the "popular perception of the popular-music landscape in the 1920s-40s" based on? I ask because both blues and country - driven by technological advances like the jukebox and the radio - were extremely popular in large swaths of the U.S. at this time - particularly in the American South.