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What is the fastest way to identify chords?

When reading a chord quickly, read the root/lowest note and then the intervals above it and place them in the key. With experience you will be able to recognize common voicings by shape alone.

music.stackexchange.com - Fast Chord Identification - Music: Practice & Theory Stack Exchange

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From what I see, you are a "working backwards" personality. You are like a painter who just mix your colors to get your desired shade and then just paint. After that, you ask yourself: "What did I do just now and how did I get that color?" You get the desired sound first and then try to decipher it. So, to achieve your end, learn the below and then work backwards to decipher the names. I will explain as we go along:

I am assuming that you already know the fundamental Major Chords for all the scales already, am I right?

Now, just think in terms of semitones (or half-steps in American Terms) and sharps and flats. With only 9 formulas, you can create at least 144 chords. There is absolutely nothing complicated with forming chords if you do it this way. You already learnt that Chords are formed by pressing the Root note, next note 4 half steps up and then 3 half steps up. ie. C E and G in C chord. You can get every other major chords by using this R - 4 - 3 formula. Now, to get the minor chord, just flatten the middle note (i.e. E flatted to E flat). So Cm chord = C Eb G. I do not want to use R - 3 - 4 because by doing so, you end up memorizing 12 formulas at least. I just want you to remember 9 for the time being) For the suspended chord, just sharpen the middle note (i.e. E sharpened to F) Sharpen means raise the note 1 half step. So for Csus or Cs4 or Csus4 = C F G. You will get this is "McGyver's theme" For the Diminished Fifth chord, just flatten the rightmost (fifth) note (i.e. G flatted to G flat). So Cm chord = C E Gb. It is most commonly used in m7-5 like in Cm7-5 which is C Eb Gb Bb. It will most commonly be used as Bm7-5 when playing songs in A minor key. Bm7-5 = B D F A. When playing Dm E7 Am progression, replace the Dm with Bm7-5 and you will get the an even more beautiful color to your song. For the Augmented 5th chord, just sharpen the fifth, rightmost note (i.e. G sharpened to G#) So for CAug or C+5 or CAug5 = C E G+. You will find this is "Greatest Love of All" and "James Bond Theme"

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Now for the 6th, 7th and Major 7th. Basically it means:

For 6th ADD a note 2 half steps from the 5th note. C6 will result in C E G A. You will find these sweet sounding chords prevalent in Hawaiian songs. For 7th ADD a note 3 half steps from the 5th note. C7 will result in C E G Bb. These chords with "unfinished" feelings alway appear in pairs with root chords. I.e. G7 with C chord in C key; C7 with F Chord in F key; etc. For Major7th ADD a note 4 half steps from the 5th note. CMaj7; CMaj;CM7 will result in C E G B. You will find these big broad sounding chords prevalent in Movie Themes to give you the big countryside feelings. You will also find it in songs with minor keys long root chord progressions like Feelings which goes Am - AmM7-Am7-Am6-Dm... For Diminished Chords, this is a special exception. All the 4 notes are 3 half steps apart. ie. Cdim = C Eb Gb A. You will find these weird sounding chords prevalent in Hawaiian and Jazz songs as a passing chord ie. C C#dim Dm G7.... or C Ebdim Dm G7..... One of Bach's songs also uses this (I forgot the name) which is commonly used in Dracula Vampire movies. Try it out and see. For all the above, you will see that all these adds to the color of sound and like an artist, these are your shades that will help you paint your masterpieces. How you use them will determine the quality and output of your music. With the above, you can create 144 chords at least. Test it out as below

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Major (try out all the 12 chords) Minor (try out all the 12 chords) 7th (try out all the 12 chords) m7th (try out all the 12 chords) m7-5 (try out all the 12 chords) dim (try out all the 12 chords) 6th (try out all the 12 chords) 7th (try out all the 12 chords) Maj7 (try out all the 12 chords) Dim (try out all the 12 chords) Aug5 (try out all the 12 chords) Sus4 (try out all the 12 chords) Now, for the final crunch!: Assuming you pressed F Ab C# E and you like the sound to fit that section of your song, then just take the F as your root note and know that F Major is F A C. With reference to that, find out what happened to the other notes: ie. Ab is lower than A, therefore it should be a Minor; C# is higher than C, so it should be Augmented and E should be 4 halfsteps above C, so it should be Maj7. Putting it all together, it should be FmMaj7Aug5! Get it? Get this first. Then we deal with the 9th, 11ths and 13ths once you have grasped this.