Picture Chord Encyclopedia: Photos, Diagrams and Music Notation for Over 1,600 Keyboard Chords

Since the thing in music harmony is muh simpler, in that it is simple to observe that each chord within tonal music has a function:
1 - Fundamental or tonal rest where everything ends or die, named "I chord".
2 - A dominant chord of which causes instability and expectation to the fundamental "I chord".
3 - Minor chords that are excellent dominant's preparers, so we call them sub-dominant, or we use the minor chord also to escape the tension caused by the dominant chord. If you want to spruce up all these chords adding the 7ths is your problem, Jazz and Pop do this way.
4 - Semi-diminished chords that inaugurate in human hearing the sensation of the '9th', that is easy to listen in the chord vii of the major tonal field, producing a semi-diminished chord, it was perceived by the romantics in the early 19th century that if you are in the vii chord, works exacly like you drop the 3dr on the bass and add a 9th, so it will be a 'V9/3dr' [ex.:G9/B], then by cromatism it's easier to fall this '9th' to flatted 'b9th' to achieve the 5th, that together with the tritone descends in equal proportion by tonicization to the boring 5th, in which became the main ingredient to be used in the late 19th century by Russian Scriabin and French composers, whose French migrated to New Orleans-USA to influence all the African-Americans of what later we will call it Jazz Harmony.
Hence American standards composers will begin composing in the 20th century, like 'Laura by David Raksin' who begins his melody using the major 9th on the minor chord and and goes resting on the 9th of each progression and interspersed with the 6th, which seems to be a joke to be a 9-headed.. '9 6'.

As a good example of this is to use in the dominant V-chord the 6th and b9th, creating an incredible sound much used in Jazz, especially in the style Cool Jazz: V6,7,9b.
Ex: in the key of Ab [V = bass: Eb - chord: G-C-Db-Fb] going to Ab6,9,10,12: [bass: Ab - chord: F-Bb-C-Eb].

Note that the function of the dominant V chord remains the same, and 'G' and 'Db' form the tritone that since the baroque resolve to the fundamental and the third of chord I.

The same happens if we make that chord that many unprepared books call a 13th chord. Whose notes in the key of Ab are: [V = G-B-Db-F #]; note that G is the third of the Eb chord, and Db is the seventh minor, so we have the same tritone of the V = Eb7 chord, but the 5th was augmented and the 9th became also augmented. Soon Eb7 5+ & # 9 +, the tritone of the dominant chord remains intact, however the bass can be solved by chromatism, using the natural ♮A prior to arriving at the Láb: [V5 + 7, # 9 = bass: ♮ A chords : GB-Db-F #] and solve in the same Ab6,9,10,12: [bass: Ab-chord: F-Bb-C-Eb].

Or finish this chord in the key of Ab: [G-B-Db-F #] with a just a perfect 5th interval '♮D and ♮A' on the bass.

It is good to remember that tritone, meaning, 'three tones', therefore, are not just two notes, the 5th also counts. This sound caused revulsion in Catholics, and at the 'Council of Trent' in Italy it was banned from being used because it was classified in the sound of the devil in the music, 'Diabolus in Musica', for causing repulsive tension in harmony, hence the musicians continue using the hidden places, therefore, everything that is forbidden seems to be more delicious, then they called it by joke of Tritono, that was the three-pronged fork of the devil, used to pierce evil humans who go to hell, according to the Catholic threats of the time.

For what the 6ths are used in the chords, simply to take a useless note that human hearing does not differentiate, the fair perfect fifths in the chords that only serve to fill an empty space, because, to any fundamental note already adds the 5ths naturally to the chord, thus causing the "invisibility" auditory when the 5th is added, which is why Jazz moves so much with the 5th, to get rid of something useless. All respect to Beethoven's 5th, that's just a numbering of a symphony, joke.

6- And the diminutive chord, that appears in the minor key tonality, can also be said to have 50% of the DNA of the two full-tone scales within one octave: [C, D, E, Gb, Ab, Bb and Db, Eb, F, G, A , B that contains two tritones in its nucleus to be played and or to tone modulations or more conclusive arrivals. ie it continues at the same V-I rate.

If the musician is to decorate the chords with dimished or augmented 5th or replace with 6th, and to add to it the minor or major 9th together with the major or minor 13 th, is simply to add to what already exists in the harmony functions that has always existed, the harmonious functions continue the same, that is, the major and minor 3rds and 7ths can never be modified, otherwise the tonal music loses its structure and goes to other musical strands, that is why some wanted to go to the atonalism and dodecafonism that is the first form of the serialism.

It is amazing that to sell books, some authors play to make money with the ignorant who spend with useless books.