Flat-5 (or flat-V) is a technique for chord substitution using the Cycle of Fifths.
Let's say we have a song in the key of C that has the following sequence of chords: C, Dm, G and C. (A more likely set of chords would be C7, Dm7, G7, C7, but for simplicity, we are going to leave out the 7s.)
Hearing these chords, in sequence, will be very helpful. If you play piano or guitar or some other chording instrument, just play the chords one after the other as described below. If you play a single-note instrument, you'll need to play the individual notes of the each chord in fairly rapid sequence to hear the chord, then play the notes of the next chord, and so on.
Play the chords, in the sequence below, and see how each one feels in relation to the chord that came before.
Once my ear has heard the C chord several times and then the Dm chord is played, I feel like something else must follow: a sequence has started but isn't done. The Dm makes me want something next.
And when I hear the G chord, I'm very aware that something else must follow. I want more: I want the next thing: I want release: I want it to finish.
Finally, when the C chord is played, I feel relief. The tension is gone and my ear tells me we are home.
Playing the C chord at the beginning established the "home" for the sequence. Then, my tension went up a little (Dm), reached a peak (G), and then quickly slid back down to peaceful rest (C).
This sequence of chords is called "Harmonic Resolution." Once a key is established, the chords cause many listeners to feel that the chords must move, and in a particular direction. Looking at the Circle Of Fifths in the drawing, if you move clockwise around the circle, you will always be moving in the direction of Harmonic Resolution, and although the chords will always feel like the tension is still there, complete relief will be found when the song's tonic chord, C in our case, is reached in the sequence.
This can be taken to greater lengths. For example, we could play an Am chord before the Dm, G and C chords and be following the Circle of Fifths. (One song whose title escapes me at the moment goes all the way around!)
And we could even insert new chords in-between existing ones: If a chord rooted on A is coming up in the music, we could insert the appropriate E chord just before it. If the song were in the key of C, the chords would be the new Em chord inserted before the existing Am. Whether the new chords are Major or minor will depend on the key of the song and whether we need a Major or minor third (or even a diminished chord) to comply with the "diatonic" notes ("in the scale based on the key"). And whether we add the 7th (and the 9th, and maybe even the 13th) will depend on how fancy or "embellished" we want the chords to sound.
Finally, the Circle of Fifths can also be used when changing keys. Let's say our song is in C and we want to modulate up a full step to D to add a little life to the song for a final verse. Looking at the Circle of Fifths, an A appears before D so, to make the transition into the new key, one measure before the verse starts in the new key, we actually start playing in the new key with an A7 (A Major 7) chord, the dominant in the new key, that then resolves to the tonic in the new key, D. And in the final verse in the new key, the ii-V7-I chords would be Em, A7, D.
And if you want to be really clever about the key change, see if any of the chords in the original key near the end of the chorus are similar to the "ii" or the "V" in the new key. For example, in the key of C the chord progression might be Am, Dm, G, C where we've inserted an Am before the Dm by looking at the Circle of Fifths. Well, in the new key (of D), we're going to use an A7 so, at the end of the old key, instead of playing Am, play an A7 instead followed by the D chord. The A chord, A7 instead of Am, will be both "expected" and "surprising" to the listener, it will get their attention. And then by resolving to that chord's tonic of D (the A7 serves as the "dominant" chord in the key of D), listeners hear (and feel) the Harmonic Resolution, but into the new key.
Inserting chords using the Circle of Fifths is a way of changing the harmony of a song. Another alternative is to change the chords based on the original chord's function in the song. (Two other ways are to change the melody, and to change the rhythm.) The function of a chord relies on the fact that the "I", "iii" and "vi" chords have approximately the same feeling -- they are all "tonic" in feel, and "ii" and "IV" chords have similar tensions -- they are slightly tense or "sub-dominant", and "V" and "vii0" chords have a lot of tension -- they are both "dominant" chords.
In the key of C:
So, if we decide to improvise by changing some chords, we could do so by substituting chords with similar tensions. Let's say we want to try some an alternative to the "ii" (Dm) chord. A "IV"  chord, F (or IV7, F7) might work since they are both sub-dominant. And instead of the "I" (C) chord, sometimes a "vi" (Am) or, less often, a "iii" (Em) might be used. Again, they all have a similar feeling. And, on occasion, a vii0 (Seven-Diminished) chord might be substituted for the V (G) chord.
Another substitution is the flat-5 or, if you prefer, bV (where "b" denotes "flat"). To find the flat-5 substitute of a particular chord, find the original chord in the Cycle of Fifths and follow the straight line through the center of the circle. The chord opposite the original is its flat-5 substitute. For G, that would be Db. G's flat-5 substitute is Dbm (and vice versa!).
In the example song above, the revised chord sequence would be Dm, Dbm7, C.
If you play this new progression, you'll notice the flat-5 chord lends a Chromatic feeling to the progression. This works very well in this place in the sequence.
Not all flat-5 substitutes will have that same feel, however. Nor will they all work as well. Indeed, depending on what the melody is doing, there are places where nothing but the original chord will work. In some cases, no substitute can be used. To take an extreme example, if the melody line has the notes G, B, D and F in rapid succession, it would be very difficult to use any chord other than a G.
And you may have noticed that, in many cases, we've actually been working backwards by figuring out what chord should come before another. This means that when you decide to make a substitution, the chord that comes before the new one may also need to be changed. Just how much substitution you can do before the original gets lost completely is a judgement call.
As you can imagine, this only scratches the surface on chord substitutions, and chords are strongly related to the melody, to the feeling the composer or arranger wants you to get, and often to the notes available to a jazz musician when improvising. Trying different substitutions is easiest if you play an instrument that plays chords (accordion, piano, guitar, etc.) or if you have a computer program that can generate the notes (and rhythms) automatically. (I have used "Band In A Box" for many years since its earliest releases and give it my unqualified, highest recommendation if this is an area that interests you. A link to PG Music appears in our links -- see below.)
Two books I found particularly useful are "Improvising Jazz" by Jerry Coker (Fireside Book, Simon and Schuster, 1964, ISBN 0-671-62829-1) and "Inside the Music" by Dave Stewart (Miller Freeman, 1999, ISBN 0-87930-571-1). Both are for performing musicians.
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