Originally Posted by: dlwalkeIn the music and songs I've seen, the fully diminished, non-diatonic, dim chord is way more popular than the half-diminished chord.[/quote]I don't know what music you've seen or haven't seen. So I can't speak to that. But I can say that both fully diminished & half-diminished chords in general are both widely used in classical, jazz & popular songs from earlier eras. The diminished chord is more widely used & that is related to function. See below. Neither are used much in contemporary modern music.
Originally Posted by: dlwalkeIs the fully diminished chord just especially useful, and/or is the half-diminished chord not very useful musically...or something else?[/quote]Most of this has to do with function.
The fully dim chord usually functions as a dominant chord or leading tone chord tonicizing the root or modulating to the temporary root. Diminished chords are also used in classical & jazz (& early pop & blues) as common tone color chords.
Classical examples
Beethoven
https://www.guitartricks.com/lesson.php?input=25577&s_id=2128
Tchaikovsky
https://www.guitartricks.com/lesson.php?input=10351
Jazz examples of voice leading motion
https://www.guitartricks.com/lesson.php?input=16449&s_id=1232
Classic blues turnarounds
https://www.guitartricks.com/lesson.php?input=10302&s_id=274
Common tone bluesy examples:
R&B style check out m.13
https://www.guitartricks.com/lesson.php?input=17453&s_id=1316
Deep River Blues m.2
https://www.guitartricks.com/lesson.php?input=25081&s_id=2082
The half-dim chord usually functions as a subdominant, setting up a dominant to tonic resolution. Examples:
Love Is Here To Stay (throughout!)
https://www.guitartricks.com/lesson.php?input=19125
Summertime
https://www.guitartricks.com/tutorial.php?input=2189
R&B m.1
https://www.guitartricks.com/lesson.php?input=18885
Fly Me To The Moon during "Life is like on ..."
Blue Bossa m. 5 of the main melody.
I cover these chords & their functions in this tutorial.
https://www.guitartricks.com/tutorial.php?input=1166
[quote=dlwalke]Related to this, the diminished chord also stands alone as a chord where the 7th form (either full or half-diminished) is the norm.
That's probably true for popular music forms (jazz, blues, early pop standards). But the basic diminished chord is very widely used in Baroque & Classical era music. Especially in the works of Bach.
[quote=dlwalke]I don't think I've ever seen a chord chart where a basic diminished triad (e.g., BDF) is called for. Not saying it doesn't happen, but in my limited experience it's always with the 7th. Again, not sure why that is.
It happens but not as often. I think that most of the time this is because a basic diminished chord is usually just treated as the extention of the V chord (upper notes of a G7 in this case). And of course if you can get more colorful sound from the full dim chord, then why bother with a small simple version?! :)[br][br]Hope this helps!