3rds and 4ths together in chords

Q: Why is it that major 3rds and 4ths in the same chord is prohibited? In your book (p.49) You say that simultaneous presence of a major 3rd and perfect 4th in the same chord is undesirable – so, why exactly? Because it’s said to be cacophonous? And that’s all? Hmm… Maybe there are some reasons which are more objective? "Cacophonous" is too subjective to my mind (especially regarding modern music)… As I understand it, any two notes a min2nd (or min 9th) apart never should present in the same chord simultaneously. But later in "The Infinite Guitar" while regarding different modes You give a lot of examples of chords with simultaneous presence of one and even two pairs of notes min 2nd (or min 9th) apart. How could You explain all this?

A: 3rds and 4th together in the same chord is not prohibited, just not a great sound. Sometimes minor 2nds together in a chord sound better than others, like between the 7th and root in a maj7 chord or between the #11 and 5th in a maj7#11 chord. Even between the 3rd and #9 in a 7#9 chord. So why not in a sus chord? Because:

1. It throws the nature of the chord into question. In a maj7 chord the B and C notes are important to the nature of the chord (the chord sounds crappy with the 7th as the bass note but eliminating either, would change it from what it is), same with the #11 and 5 in a maj7#11 chord. A 7#9 chord without both the major 3rd and #9th would turn the chord into something else. But the 3rd and 4th in a dominant chord are conflicting to the nature of the chord. It makes the ear wonder if something is wrong and confuses us.
2. It isn’t necessary. The 4th is way more important in a sus chord and there are better notes to add to the chord than a 3rd.

By the way, theory is just common practices to specific genres and, although sometimes based on laws of nature, is not musical law. You can add a third and there are some interesting voicings. Like a IV–V in G (C–D). Play an open position C chord and slide it up a whole step leaving the 3rd and 1st string open. Nice sound as long as you are arpeggiating and not bashing the chord (look at the chord up on top of this post).

Q: C-E-G-B-D-F-A (maj13 chord) = also impossible? Why? For the same reason, the 3rd and 4th can't be included together in the same chord? But is the 11th note is necessary for the 13th chord?

A: No, theoretically the only notes that must be included in a 13 chord (major or minor) is the 1-3-5-7 and 13. 9ths and 11ths are options. But the general rule is that the 11th, if you were to include it should be raised, as in C-E-G-B-D-F#-A. But once again, they are options and regardless, you couldn’t play a 7 note chord on the guitar. If you were playing with a bassist, you could technically just play the 3rd, 7th and 13th.

Links:

• Chord Construction Formulas
• Chords and Their Symbols
• The Infinite Guitar Instructional Book