That chord that you mention, has a really interesting history in jazz. Because it was often called or known (by Thelonious Monk and Dizzy Gillespie and Barry Harris and others) as a minor triad with the 6th in the bass.
So that ‘D minor b5’ ZeroZero mention would have been described by those I just named as an F minor triad with D, the the 6th, in the bass.
For more information about that, the best, most comprehensive source I know of is the Barry Harris Video Workshop series ... here’s a linkhttp://www.jazzschoolonline.com/ind...p;view=article&id=146&Itemid=521
It’s expensive but worth every penny. In it BH builds on what ZeroZero observed and goes all over the place (to good places) with it. Also, check out what Steve Coleman says about so-called “half-diminished chords.”http://m-base.com/the-dozens-steve-coleman-on-charlie-parker/
Here’s the relevant part, including a quote from Dizzy Gillespie’s autobiography about the so-called half-diminished or minor 7 flat 5 chord.
*** Copied and pasted from the link above which is an essay by Steve Coleman about Charlie Parker * * *
I realized by using the high notes of the chords as a melodic line, and by the right harmonic progression, I could play what I heard inside me. That’s when I was born.” ( c. 1939 quoted inMasters of Jazz)
“I found that by using the higher intervals of a chord as a melody line and backing them with appropriately related changes I could play the thing I’d been hearing. I came alive.” (1955 Hear Me Talkin’ to Ya)
However, Parker’s version of “higher intervals of a chord” was not in the form of flatted 9ths, 11ths and 13ths, but in the form of simple melodic and triadic structures that reside at a higher location within the tonal gamut which I refer to as the Matrix (who really knows how Bird thought of it?). In this case, simple minor structures such as Ebmin6, Amin6 and Fmin6 are the upper intervals of Ab7, D7 and Bb7, respectively. These minor triads with an added major sixth are very important structures in music, often mistakenly called half-diminished (for example Amin6 could be called F# half-diminished today). In this instance, the function of Amin6 is that of dynamic A minor, in the same sense that the function of D7 is that of dynamic D major. By dynamic I mean energized with the potential for change. Adding a major 6th to a minor triad has a similar (but reciprocal) function to adding a minor 7th to a major triad, and that function in many cases is to energize the triad, to infuse it with a greater potential for change, due to the perceived unstable nature of the tritone interval. Pianist Thelonious Monk was a master of this technique, and demonstrated this to many of the other musicians of this time (including Dizzy and Bird). Regarding whether to use the name half-diminished or minor triad with the added 6th, this is a case where a simple change in name can obscure the melodic and harmonic function of a particular sound. Dizzy Gillespie mentions this in his autobiography when he says that for him and his colleagues, there was no such thing as half-diminished chords – what is called a half-diminished chord today, they called a minor triad with a major sixth in the bass.
... [Here’s Dizzy Gillespie talking about the half-diminished or minor-seven flat 5 chord .... except he explains how his generation knew it as a minor triad with a 6th in the bass .... the quote is from Steve Coleman’s article ... ]
“Monk doesn’t actually know what I showed him. But I do know some of the things he showed me. Like, the minor-sixth chord with a sixth in the bass. I first heard Monk play that. It’s demonstrated in some of my music like the melody of “Woody ‘n You,” the introduction to “Round Midnight,” and a part of the bridge to “Mantaca.”…. There were lots of places where I used that progression… and the first time I heard that, Monk showed it to me, and he called it a minor-sixth chord with a sixth in the bass. Nowadays, they don’t call it that. They call the sixth in the bass, the tonic, and the chord a C-minor seventh, flat five. What Monk called an E-Flat-minor sixth chord with a sixth in the bass, the guys nowadays call a C-minor seventh flat five… So they’re exactly the same thing. An E-Flat-minor chord with a sixth in the bass is C, E-flat, G-flat, and B-flat. C-minor seventh flat five is the same thing, C, E-flat, G-flat, and B-flat. Some people call it a half diminished, sometimes.” (from the chapter Minton’s Playhouse in to BE, or not… to BOP)
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Lastly, take a G7 chord (G B D F) where the intervals in the chord are (ascending) a major third (G to B), and a minor third (B to D) and another minor third (D to F). Now invert those intervals, meaning instead of an ascending major third followed by two ascending minor thirds you have a DESCENDING major third (F down to Db ) followed by two descending minor thirds (Db down to Bb and Bb down to G).
What you have there is a chord we call G minor 7 flats 5 or G half-diminished 7. Convert it into the nomenclature used by Dizzy Gillespie and you could call that a Bb minor triad with a G (the sixth) in the bass.
Big deal? Coincidence? Go through enough Bill Evans transcriptions and you’ll find that sort of thing all over the place. So, for example, you’re playing the melody to Miles Davis’ Tuneup. You’ll quickly find a flat 5th over the second chord (which in fake books is shown as a dominant chord.
In particular, you’ll see for the second chord that D# moves to E natural and the chord underneath is A7. Use the logic above and don’t play Eb over A7. Instead play (from bottom to top) A G C Eb .... and then resolve that chord to A C# E G. All we’ve really done is taken the middle two voices from the A7, dropped them down a half-step to cover the D# in the melody, and then raised them back up a half-step (to follow the melody) so that we arrive back at an A7 chord. But if we want to get crazy about it, that first chord we got from the A7, simply by lowering the middle two voices ... we could just as well call it a C minor triad with a 6th in the bass. Of course, if we saw that written out in a lead sheet, we’d think the writer of said lead sheet had lost their mind!
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For anyone who’s still reading .... take our minor-seven b5 chord, perhaps built on D. So we have D F Ab C. Inner the intervals and now we have from top to bottom D B G# E (or from bottom to top, making it’s easier to recognise, we have E G# B D. Ok, so, what’s big deal and what do we get from this?
Well, if we know D min7 b5 inverts into an E7 chord, let’s just take the E as our new root and put the D F Ab C back on top. Now we’ve got (bottom to top) E D F G# C or an E7 with a flat 9 and flat 13.
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Think about this stuff as “shapes” rather than specific notes and chords that have be inverted. It’s much easier to work with it all like that. Steve Coleman more or less says the same thing in his essay. If you get the Barry Harris workshop videos, you’ll find he pretty much reduces everything to a 6th chord (major 6th or minor 6th) and then show how to put those on top of different roots to get whatever chord you might need.
But watch him explain this stuff in isolated videos on YouTube and it may make no sense whatsoever! You really do need the step-by-step explanation he gives in his Workshop video series.
And lastly, lastly, are there other ways to look at this stuff? OF COURSE THERE ARE! That place where ZeroZero began is a beginning. And there are a million jazz theory books that explain this stuff in a completely different way. All I’ve done here is to put it into the historical context that’s documented in SC’s essay and Dizzy Gillespie’s autobiography.
There is a lot more one could say about this stuff but it never ends!! Hope this is helpful!! And back to ZeroZero, what you discovered now your own with your ear is as good if not better than any theoretical explanation! Because now you have your own way to work with this stuff!!!!