Why are the changes in the tune “I Got Rhythm “ considered so important in learning Jazz standards?
First, “I Got Rhythm” is one of the most well known classic songs from the American Songbook which should be high on the list of tunes one should memorize. It is in a bright tempo, has a lot of harmonic movement in the A sections and a string of dominant chords going through part of the cycle of 5ths in the bridge. These elements challenge the player to develop advanced improvisational skills that will serve them well when playing other jazz and American Songbook standards.
Another reason is the harmonic structure has become a template for dozens of other songs such as Cottontail, Lester Leaps In, Anthropology and many more. By knowing this tune you will also know how to improvise over the many other tunes that are based on this harmony. When on a gig or at a jam session it is almost inevitable that this or one of its many spinoffs, or contrafacts (if you want a fancier term) will be played at some point.
That tune, and those changes, contain two specific progressions that are common in all Western music. To be fair those changes existed probably 100s of years before that tune and the popularity of the tune made them forever associated with it!
The two progressions are (1) the I --> vi --> ii --> V7, which is almost identical to I --> vi --> IV --> V and is the progression for Heart and Soul, and many rock ballads, and (2) III7 --> VI7 --> II7 --> V7, or the circle of 4ths. This latter one can be found in 100-150 yo classical guitar pieces and standard work books so I doubt that I Got Rhythm is really the beginning of this pattern.
There is a third progression, v --> I7 --> IV --> iv --> I. But IMO most of that is just repeat of the first moved to the IV chord. The resolution IV --> iv --> I is very nice and distinct from the V7 --> I.
Both of these progressions embody a standard movement found Western classical movement. The first is a subset of a larger progression called circle progression which goes like...
I --> IV --> vii --> iii --> vi --> ii --> V --> I
This follows as closely as possible the circle of 4ths without leaving the key signature, the deviation being the jump from IV to vii, an aug 4th (dim 5th). So I would really say that the importance or perceived importance of I Got Rhythm is a red herring. The progressions are used every where and have been in use for a lot longer than that song is old. Again, perhaps the popularity of it is what made it stick.
I would guess that about half of the tunes in the Real book (or more) have these changes. But another equally important set is the 12 bar Blues, and other variations of the Blues (8 bar, 16 Bar, etc).
One could ask "Why are the changes to The Lemon Song by Led Zeppelin" so important in Rock. Analysis would show that (1) the song is really an old Blues standard, (2) that those changes have been in use for a lot longer than Zep existed, and that many other artists before and after used them and probably never heard that song.
Those chord changes have been adapted by jazz musicians as the harmonic basis for other songs.
The chord progressions are common in tonal music.
The basic patterns involve roots by descending fifth.
ii7 V7 I in the first part and a chain of secondary dominants
V7/vi V7/ii V7/V V7 in the second part. Both are common progressions in tonal music. In basic harmonic terms you can't tell from those symbols if you're dealing with Mozart or Gershwin!
Another interesting point about the song is the use of a French augmented sixth chord. This chord appears at the end of the second part (the "old man trouble..." part) in my copy of the tune from Girl Crazy. In classical style the augmented sixth chord resolves to a dominant chord. Labeling the song in the classical style it would be
F: Fr+6 V7 | I. In jazz harmony that augmented sixth chord is called a tritone substitution and it's often seen between a
I chord as
ii7 bIIalt7 | I6 or something similar where importantly the resolution is to a tonic rather than a dominant. Gershwin used the chord in the "classical' manner where it resolves to a dominant.
Lots of variations on basic rhythm changes exist and many use tritone substitutions, so it seems worth mentioning the connection to the augmented sixth chord appearing in the original song.
Of course I don't literally mean you couldn't tell the difference between Gershwin's harmony and Mozart's. Gershwin uses inversions, added ninths, sixth, chromatic embellishments, etc. that Mozart didn't. But the basic chord qualities and root progressions are the same.
So, rhythm changes are important because they are used in a lot of jazz songs. But they are also important, because on a basic level they are chord progressions ubiquitous in tonal music.