The major 7th chord

[Bob Walance]

The major 7th chord can be very interesting. Musicians including Pink Floyd, Burt Bacharach, and The Carpenters have used it frequently in their tunes.

Simple chords are part of nature. Any instrument, including the human voice, creates a major chord with its harmonics (overtones).

After doing some spectral analysis of various instruments, the major 7th chord became obviously related to other notes - but in an unexpected way. In the picture, it's obvious that single notes create major chords and even the dominant 7th chord.

When multiple notes are combined to create a major chord, the major 7th tone is part of that chord. The major 7th of the C major scale is B.

 

[.Scott]

Since you're working with a guitar, you get to pick the temperament.
I asked google to generate wave clips of the C major 7th (264Hz) for well temperament, meantone, equal temperament, just tone. Apparently, PF doesn't support the inclusion of wav files in posts.

So here is what I heard. The values in the parenthesis are the cents differences between the notes in the chord in contrast to "just intonation". It's also worth noting that I was listening 21-second clips of pure tone (flute-like) chords:

Just (0, 0, 0, 0): This is what the chord "should sound like". It sound like a single pure chord. The notes blend together so there is nothing "extra" to hear. Google describes it as "pure, warm, and consonant". Too bad Google can't really hear it.

Well (0, 9.8, -5.4, 7.8): Very similar to Just, but you can hear the contribution of each note. The very slight discordance sounds slightly unstable to me. The clips are 21 seconds and with "Well", I find myself expecting a change. Google notes that the version of "Well Temperament" it has chosen is "Werckmeister III" and simply says that the effect is different for different chords.

Meantone (0, 0, -5.4, -2.7): I notice a beat frequency of about 0.25 Hz right away - I assume form that "2.7cent" flattening. The very slight flatting on two notes also makes it sound a bit darker to me. Google notes that it is using the Quarter-Comma Meantone and notes that the "0,0" should make it sound sweeter. (I didn't hear anything "sweeter)>

12-Tone Equal temperment (0, 13.7, -2.0, 11.7): I notice a rapid beat frequency (>2Hz). Google described this as "brighter, slightly more tense, or "pressed"". If you don't consciously catch the rapid beat frequency, I would expect you would feel it as "more tense". After playing it a couple of times, it does sound brighter to me. Google describes the beat frequency as a "shimmering".

 

[Bob Walance]

12-Tone Equal temperment (0, 13.7, -2.0, 11.7): I notice a rapid beat frequency (>2Hz). Google described this as "brighter, slightly more tense, or "pressed"". If you don't consciously catch the rapid beat frequency, I would expect you would feel it as "more tense". After playing it a couple of times, it does sound brighter to me. Google describes the beat frequency as a "shimmering".

Yeah, these various historical temperaments were a valiant effort, but they all failed for various reasons and we're stuck with equal temperament - unless everyone's playing violins and theremins.

Take a look and listen at:
bobwalance dot github dot io

The two 'Press for tones' sections will let you listen to (and play with) an equal-temperament chord and a natures-temperament chord.

 

[berkeman]

Apparently, PF doesn't support the inclusion of wav files in posts.

There are a number of file type suffixes that are not allowed (mostly for malware reasons, I think), but often you can change the suffix to ".txt" to be able to attach it and just tell others to download the file and rename the suffix. (if they trust you, obviously )