This post contains several completely improvised solo piano songs I recorded on GarageBand between February and April 2014.
In straight-ahead jazz (which likely includes a large portion of the jazz music a casual jazz fan would listen to), different composed songs are played . Each song has a composed melody and harmony, and the rhythm and general feel of the song usually come from one or more of few different styles (e.g. swing, bossa nova, waltz, and so on). During some portion of the song, some of the instruments will "solo", whereby they improvise a new melody on top of the composed harmony and rhythm of the song. The improvised melody may be similar to the composed melody, or not, depending on the feel of the song and the style of the improviser.
This is in contrast to Free Jazz, where the composition may offer less melodic, harmonic, and rhythmic guidance (sometimes absolutely none at all). The improvised portion of the song forces the soloist to improvise all of these musical elements. Generally, Free Jazz is more atonal and less accessible to someone new to the music .
The recordings below differ from straight-ahead jazz in that there is no underlying composition that I am using as a base for my improvisation. I improvised the melody, harmony, and rhythm. I had no pre-conceived ideas what I would play before hitting the "record" button. However, they also differ from what would be considered Free Jazz in that it the songs are mostly standard in their use of harmony, and are mostly harmonious .
Many of the rhythms are similar throughout each different improvisation. I find improvising rhythms to be the most challenging of the three musical elements, especially while focusing on melody and harmony. The harmonies are improvised. I tend to draw on common harmonic patterns, but sometimes not. The melodies are almost always improvised (on occasion you may here a familiar sounding melody if it happened to pop into my head).
The biggest influence for these improvised pieces comes from Keith Jarrett. He is famous for performing totally improvised, solo piano concerts. His most famous is the Koln Concert (you should listen to it). I don't know much about how he approaches these improvisations, and I have never received any formal training on this style of improvisation.
Most of the other music I have posted here is older; in other words, a few years passed before I posted it. In that regard, that music passed a sort of test of time to my ears. I'm not sure how I will look back on this music in a few years. In general, I tend to like music I record shortly after I record it, but over time I may come to dislike it.
As of writing (May 2014), I mostly enjoy this music. It is totally unedited, so you will hear some mistakes. It is rough around the edges at times. Parts of it I already don't care for. But there are also segments that I really enjoy. Regardless of whether or not I enjoy the music afterwards, I greatly enjoy playing it. It can be deeply meditative. Oftentimes, when I stop playing, I will have no idea how long I had been playing for.
Have a listen below.
 The compositions generally come from showtunes, classic swing or big band tunes, other popular music of the day, as well as compositions by the jazz musicians themselves.
 The seminal Free Jazz album is Ornette Coleman's The Shape of Jazz To Come. Recorded in 1959, relative to some of the Free Jazz that this album led to, it sounds rather tame and accessible.
 I say "mostly", because there are definitely some dissonant moments.