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A note and its flat or sharp do not sound good played together. The sound is as dissonant as it gets.

How is it that placing a 3rd and 5th between a note and its major 7th (flat of its octave), then playing the four notes as a chord, makes a consonant sound? Is there some mix of frequencies that makes the dissonance blend into consonance?

On the contrary, play the major 7th note as the lowest note of a chord, at least on guitar, and it sounds terrible. Example: C E G B sounds nice, pretty, airy, even though C and B are being played together. Play B C E G and is sounds so dissonant (sour/off) a listener would think a mistake has been made.

How does putting the E and G between C and B quell the dissonance to the point a very pretty chord is played, and why are E and G no help if the chord is inverted with B as the lowest note? (On guitar at least) Please note: I know only elementary math. Math algorithms, equations, etc. have no meaning for me.

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    In classical harmonic theory, a major seventh chord is not consonant.
    – phoog
    Sep 5, 2023 at 16:18

2 Answers 2

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It's pretty straightforward; it's a matter of "distancing and diluting" the dissonance.

This is "very dissonant"*:

enter image description here

... and this is "less dissonant":

enter image description here

The "clash" of the two notes has been reduced by distance. (Disclaimer: the explanation that follows may be inaccurate; the math confuses me.) Insofar as there is any objective math to "dissonance,"** that's because the first example has "beats" that are less frequent and therefore more noticeable. That is, when the two sound waves play at the same time, some times they "add up" to a louder moment and sometimes they cancel each other out. If we had this:

enter image description here

... then for each wave of the bottom C, exactly two waves for the top C would fit into it, and they'd line up nicely and sound "smooth." Or, if we had this:

enter image description here

... then both waveforms would be identical***; their peaks and valleys would line up, and we'd hear one pitch. But if we de-tune one C just slightly, then its wave would become longer; they'd start in sync, but every so often, after X milliseconds, it would wind up in a valley while the other one is in a peak, and they'd cancel out. And after another X milliseconds they'd be back in sync and reinforce each other again. At intervals smaller than a half step, the X unit of time can take so long that you can hear each individual "beat" and it can be quite noticeable. As the pitches diverge and the beats speed up, at some point we describe it as sounding "rough."

So anyway, the major 7th fits in twice as many Bs into each C, so the beats are more frequent, less additive, and less noticeable.

Meanwhile, making a seventh chord out of the whole thing:

enter image description here

... "dilutes" the dissonance because there are a bunch of consonances present as well. We could see this basically as a C major triad plus an e minor triad, superimposed. For modern sensibilities, both major and minor thirds are consonant, and we've got three of them! In subjective terms, the clash is "softened" by all these "nice intervals." (In some ways, this major seventh chord is even better than the dominant seventh because we lack the dissonant tritone we'd find between E and B flat.) In more objective terms as well, the other pitches add their interference patterns, and any beats between the C and B get softened by the interaction of all the other notes.


* But "as dissonant as it gets"? That's tricky, and depends on context and subjectivity. Plus, of course, if we step outside the equal-tempered 12-tone scale, for instance, two pitches separated by a quarter step will clash much more than a half step.

** There isn't always. "Dissonant" is a subjective and cultural word, and is also influenced by factors other than pitch anyway.

*** Theoretically, and especially if artificially generated. Things like instruments, human imprecision, speakers, and sound moving from the speakers through a room to our ears could make them not truly identical.

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    I often wonder whether the actual instrument, with its peculiar, unique overtone system, has a bearing on the question.
    – Tim
    Sep 6, 2023 at 9:17
  • @Tim the overtone spectrum doesn't really impact this, since humans strongly tend to perceive only the spectrum's fundamental as the pitch. Even when the fundamental frequency is removed from the spectrum, we still hear it as the pitch (residual pitch phenomenon). So which consonances/dissonances are formed by the overlapping spectra of different notes does not matter to our perception, we just hear the consonances and dissonances formed by the fundamentals
    – Michel
    Sep 7, 2023 at 6:26
  • I get the distancing the dissonance concept but still wonder how this is possible. I am wondering what physically is going on with the sound waves that sweetens up the dissonance of two notes by adding one or two more notes (forming a maj 7) to a chord. I can easily demonstrate the phenomenon on guitar but cannot explain what is happening and wish I could in the most practical language possible.
    – ejbpesca
    Sep 7, 2023 at 14:45
  • @ejbpesca The math of wave interference confuses me too, but maybe some visual illustrations of it will help. I don't have time to draw right now, but maybe this page, although it's not a complete explanation, will help: physicsclassroom.com/class/sound/Lesson-3/… (or also ffden-2.phys.uaf.edu/webproj/211_fall_2020/Jared_Bowden/… ) Sep 7, 2023 at 14:53
  • @ejbpesca Your comment makes the assumption that something is "physically is going on with the sound waves". More likely it's something "going on" in our auditory system (ears and brains).
    – Theodore
    Sep 7, 2023 at 20:15
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It’s safe to say there is both objectivity and subjectivity when discussing dissonance and consonance. I do agree with your statement that a major 7th chord sounds much more consonant than just a M7 interval. I believe the reason for this is actually very simple. In its most basic form a major 7th chord is a pair of perfect 5ths, for example, Cmaj7, you have C-G and E-B. The M3 and m3 intervals contained within are also consonant. Even if you re-voice a maj7 chord it will usually yield intervals (4ths, 6ths, etc) that are more consonant and take the “sting” out of the M7 interval in the chord.

As for your comment about the Cmaj7 with the B below the C “at least on guitar”, this particular voicing is not guitar friendly at all unless some type of alternate tuning is used and is pretty much impossible for chords where you can not incorporate at least one open string. The only way I could think of to play that voicing is this: X-15-14-12-0-X. Regardless of that, it may sound bad to you but some people do like voicings that have clusters in them so I would say your statement is a bit subjective on this point.

The one thing you do want to avoid in terms of voicings and dissonances is placing the M7 a m9 below the root, that’s definitely a chalkboard scratcher!

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    "The one thing you do want to avoid in terms of voicings and dissonances is placing the M7 a m9 below the root": unless it resolves or is a passing dissonance.
    – phoog
    Sep 5, 2023 at 16:34
  • @phoog I’ll buy that. I was thinking in terms of a static voicing for my answer. Sep 5, 2023 at 18:32

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