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An article on the origin of the "delta" symbol has been doing the rounds recently. It quotes a book by Yusef Lateef, which claims that John Coltrane introduced the "triangle notation" for a major 7th chord:

"DELTA (△) SYMBOL. Introduced into music notation to symbolize a major seventh chord by the late John Coltrane."


Chart for Naima, probably written by Coltrane himself in 1959

The second part of the article does some more sleuthing, but is inconclusive:

I'm not sure we can draw any conclusions here, but [for what it's worth], it looks as though both Coltrane and Shorter were using the symbol by 1959. In Coltrane's case, perhaps not earlier. Wayne used a "△7", Coltrane just a "△".

It would seem that the symbol was not in use (in jazz, at least) before 1959.

I understand that the symbol "originally meant 'triad'", although I'm not sure whether it was ever used extensively in charts. When did its meaning change to maj7? Who popularized it?

Edit: I've contacted Shorter's publicist who relayed my question and gave me back this (disappointing) answer:

Unfortunately Wayne really doesn't know the answer to this question!

He thinks it came around around the time when Modern Jazz and Be Bop emerged, but he doesn't know who came up with it!

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    This is a good question and I wonder if the best answer we are going to get is contained in the question (e.g., perhaps Coltrane popularized it). – Todd Wilcox May 12 '17 at 18:07
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    Here is a discussion from a few years back that seems to get nowhere with this. One person in the thread claims to have seen the triangle notation used in charts in the '50s. – David Bowling May 12 '17 at 18:38
  • I agree that this is an extremely interesting question. I wonder if Wayne's response is at all revealing. His answer would certainly be compatible with a history where the ∆ symbol was used frequently enough in some circles before 1959 that its origin wasn't memorable to Wayne. (Of course, this isn't the only possibility. His answer would also be compatible with a history where a single person invented the idea and explained it to Wayne, and then Wayne forgot about that conversation...) – jdjazz Jun 12 '17 at 16:59
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There are a few extremely interesting questions asked here, including "what's the origin," "who popularized its usage," and "when did its meaning change from major triad to major 7." I'll try to shed some light on the question in the title, "what's the origin?"

If you draw an equilateral triangle inside the circle of fifths, its vertices connect an augmented triad. These and other similar triangle-shaped drawings within the circle of fifths were well known long before the 1950s, and they are documented within classical music and music theory. I haven't seen any evidence that these drawings were or weren't known by the relevant jazz musicians in the 1950s, but I haven't done much digging. I do know that Charlie Parker discusses studying classical theory in his interviews from the 1950s, which suggests he and perhaps also other jazz musicians could have been familiar with pictures like the one below.

http://www.playukulelebyear.com/wp-content/uploads/2010/08/A5.jpg

The first documented usage that I have seen of the ∆ symbol in jazz is from Charles Mingus in 1957. The Civil Rights Digital Library contains this entry for a trumpet score handwritten by Charles Mingus and dated 1957 according to the record:

http://www.loc.gov/exhibits/brown/images/br0131s.jpg

In the B section, we see these chords: C–∆7 and A♭–∆7. As you surely know, the minor major seventh chords contain an augmented triad like the one drawn inside the circle of fifths. In C–∆7 the augmented triad is E♭ G B. Perhaps the equilateral triangle symbol, which earlier in history was synonymous with an augmented fifth, was first used in jazz to indicate the major minor seventh chord (e.g., C–∆7)--a chord which at the time had no other symbol associated with it. This is consistent with the documented history of the ∆ symbol, which shows its first usage in a minor major seventh chord, not a maj7 chord.

In one of the links you included, Matt L. cites the book The Chord Scale Theory & Jazz Harmony by B. Nettles and R. Graf as evidence that the ∆ symbol originally meant "major triad." But that's not what the text states:

the ∆ originally meant "triad" and if written with haste may appear as a circle. (Nettles and Graf, p. 23)

This is in a section about common chord notations. It's not a history book, and Nettles and Graf do not provide a citation for their claim. They also don't clarify whether the original meaning of ∆ was major triad or simply triad (as in augmented triad). So I don't think that text is very useful in answering your question about the history and origin of the ∆ symbol in jazz.

Just to clarify, I'm piecing together parts of history to try and provide a possible explanation. This normally wouldn't be appropriate, but I think it's useful in this case since it would appear that the only way to answer the question about the origin of the ∆ symbol in jazz is through some original research. Interesting areas of further study would include some of your other questions, along with some other question like "was Mingus/Coltrane familiar with drawing the triangle inside the circle of fifths?" To uncover more of the history, perhaps it would be instructive to look at historical records of songs from the 1950s that contain major minor seventh chords.

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    Wow, really interesting answer. Do you know of any charts by Mingus around that time that use augmented triads? If so, how does he label those? I see he labels the "G+" scale along with the A♭–∆7; does he also use + for augmented triads? – Richard Jun 12 '17 at 18:55
  • That's a great question, and I wish I knew the answer. It would be telling if he had used ∆ for augmented triads, although I'd probably to expect to see the + notation given that this was common practice at the time and there was no need for a different/new notation for augmented chords. Reserving the ∆ for minor major seventh chords and the + for augmented chords also could have had the benefit of distinguishing between the two scenarios. – jdjazz Jun 12 '17 at 20:21
  • Here is a manuscript from Tony Zano where he is seen using G+5 for an augmented chord (m. 17) and D–(M7) for a minor major seventh chord (m. 11). I cannot for the life of me find a year this was written, but I would guess around 1957. It couldn't be earlier than 1957 because that's the year Berklee Press began operating. – jdjazz Jun 12 '17 at 20:46
  • And here is a [manuscript of Monk's Mood] (d2jv9003bew7ag.cloudfront.net/uploads/…) where Monk writes a major 7th chord as D♭ ♮7 (m. 4). This manuscript is supposedly from 1956-57. – jdjazz Jun 12 '17 at 20:54
  • Lastly, here's another manuscript of Fables of Faubus that appears to have the Library of Congress stamp in the top right corner. This manuscript is written with E+7 in the B section (this would be a E G♯ C D chord). I'm also not sure when this was written though, and the handwriting definitely appears different from Mingus's. – jdjazz Jun 12 '17 at 21:01

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