Neo Riemannian, Neo Riemannian

Following up from the last blog on Neo Riemannian theory especially in the area of Triad Transformation I've played around with extending these essential moves because each new transformation has these 3 possibilities and so on. These examples could be done in various other ways... It is probably predicted in my friend CKM equations that are for another day.

To review: RPL—remember that major triads transform to minor triads and vice-versa.

In R:  C major (triad) transforms to Ami by raising the 5th 'G' to 'A' creating Ami triad.
In P:  C major (triad) transforms to Cmi by lowering the third 'E' to 'Eb' creating a Cmi triad.
In L:  Cmajor (triad) transforms to Emi by lowering the root 'C' to 'B' creating an Emi triad'

In R: Cmi (triad) transforms to Ebma by lowering the root 'C' to 'Bb' creating an Ebma triad.
In P:  Cmi triad transforms to Cma by raising the minor 3rd 'Eb' to 'E' creating a Cma triad.
In L:  Cmi triad transforms to Abma by raising the 5th 'G' to an 'Ab' creating an Abma triad.

Here's a few examples starting in C major:

C........Ami......C.......Cmi..........Ab............Abmi..........E...........Emi.........C ||


R      R          P L P L           P        L
CEG —CEA - ceg-  CEbG  – CEbAb —CbEbAb— BEG# — BEG —CEG etc.  


I didn't use R very much so here's another:

C.........Ami.....C.....Cmi..........Ab (Ab/C)....Fmi............Db...........Dbmi.
        

R       R       P L R L                P

CEG——CEA -ceg- CEbG——CEbAb——CFAb——DbFAb——DbFbAb

My super math friend CKM says:  ..... "Ok.  All of these are "kosher" R, L and P transforms. 
My only point ........(which you got) was that it is IMPOSSIBLE ever get anything except a major and minor triad using R, L, and P in any combination.  For that, new transformations and/or new "rules" of transformation need to be invoked.  But that's okay.  All RLP can ever do is move to one of the adjacent triangles on the Tonnetz Torus or (equivalently) a neighboring point in Dancing Cubes." 


Dancing Cubans I've seen, but "dancing cubes" sound like they might be electron microscopic images:)....  But makes a little more sense when the Revolving Torus from the last blog is viewed. Some links available to me explain this more but, they are quite involved and lengthy with lots of side links to both educate and distract so I will be following this up later.


I'll try a couple more:


  C..........Ami.......A..........C#mi...........Db........Bbmi..........Gb.........Ebmi..............B............Abmi              


                    R            P            L              P            R              L                 R             L              R                
|| CEG—CEA—C#EA—C#EG#—DbFAb—DbFBb—DbGbBb—EbGbBb—D#F#B—EbAbCb—


...E............Emi.....C...


  L          P        L
EG#B—EGB—CEG ||


So one could spend hours just making little moves and learning them in all keys and inversion starts: that's the trick. I've tried one move at a time through all keys and then just tried to improvise using them in whatever progression it lead to.


I've found an interesting aspect of the Transformational procedures can be imposed on major or minor triads use as extension color changing on the fly. Some are very obvious and are worth pursuing.

For example on a Cma7 chord Ctriad transforms to Emi (through L). If you hold on to the root of C in the left hand it becomes Emi/C = Cma7. The same for Ami/C (through R) = C6.

C/C—Emi/C—C/C—Ami/C creates a Cma7 and C6. With the pedal held down it ends up sounding Cma13 'ish'.

In the same vein, with a Gtriad/ Ctriad the result is Cma9. If the 'G' triad transforms in the way proscribed above then other colors/extensions are generated i.e.

G/C = Cma9 || by imposing transformations on 'G' (/C) : G—Emi—G—Bmi /// all over the C triad the potential result is Cma13(#11) which can emphasis the extensions of the moment created by the sliding transformations of the G triad / C especially with the piano damper pedal discretely used. I'll outline these sorts of things further in the next blog.

Pitch Wrap

Whoa !! I never did claim to know anything. I taught at music outlining large yet essential (I still think so) ideas about harmony especially in jazz but it could be about music or aspects: rhythm, harmony, and melody. Of course they all go together in a simultaneous flow. Harmony appears vertical on the page and creates a large or small multi-colored, multi functional, impact soft or loud.

Stimulation has come from the outside (the net) for me to pursue musical topics with a more in-depth look at how harmony is really horizontal in its nature. Here's a theory that was first outlined in the late 19th century and has only really been developed within the last 30-40 years by present day theorists.

Neo-Riemannian theory refers to a loose collection of ideas present in the writings of music theorists ....... What binds these ideas is a central commitment to relating harmonies directly to each other, without necessary reference to a tonic. 

Here's this original link again:

http://en.wikipedia.org/wiki/Neo-Riemannian_theory

It has other highlighted links in there that are great too—very comprehensive and impressive.

One of the first and most easiest topics to understand (but quickly complicates through it's 12 note multiplicity), are the thoughts on Triadic Transformations and voice leading. This is a staple of song writers in the pop genre as in "Hallelujah" by Leonard Cohen in which at one point the lyrics themselves talk about the harmonic progression in the song: "The 4th the 5th the minor lift"

The 2 triads discussed are the major and minor. The major triad interval stack: 135 (Major 3rd - minor 3rd) and the intervallic inversion (upside down) from the major triad: the minor triad: interval stack 1b35 (minor 3rd-major 3rd). I find it kind of inspiring to pursue these routine moves because they sound good and one never knows when this knowledge might be needed. It's based on something we do all the time: go from chord to chord in an efficient voice led manner i.e. common tones held or repeated while the voice or voices moves in a stepwise motion. If these moves are identified and learned in keys there should be a positive result.

If you look up the link above you'll see that the moves are explored from the perspective of changes from major to minor triads and then secondly, minor to major: reversing the moves of the major to minor transformation. It doesn't really matter which inversion starting point, it's really about the shifts in the voices.

Individual transformations of triads through voice leading are given a  letter acronym
and a definition. They are obvious but good to know well.

The P transformation exchanges a triad for its Parallel. C major (triad) becomes a C minor triad by lowering the 3rd 1/2 step. And C minor becomes major by raising the minor 3 to major. 


The R transformation exchanges a triad for its Relative. C major transforms to A minor by raising its 5th a tone and conversely (good to remember), A minor transforms into C major lowering the root by a tone.


The L transformation exchanges a triad for its Leading-Tone Exchange triad. The C major triad transforms into an E minor triad by lowering the root of C 1/2 step. Conversely, E minor transforms to C major by raising the 5th 1/2 step. 


It's good to know both sides of that perspective. To summarize:


P (parallel) transformation the major triad "I" transforms to minor and vice-versa through the lowering or raising of the 3rd respectively.


R (relative) transformation refers to the "I" major transforming into it's relative minor triad (vi) by raising the 5th of the major and conversely transforming TO the major from the minor the root of the minor is lowered to the 5th of the major i.e. C major and A minor.


L (leading tone exchange) transformation refers to the I major triad transforming into the iii minor triad by lowering the root of the major 1/2 step to become iii minor. From the perspective of the iii minor (E minor using our example) it transforms into I major by raising its 5th by a 1/2 step.


There are a couple of other combinations there but these 3 transformations do relate to the Richard Cohn article on Richard Cohn:

MAXIMALLY SMOOTH CYCLES, ........  next time !!

Here is some more thoughts on this Torus design connecting apparatus that I wrote while writing to a friend on this matter— this all relates to the above link. <http://en.wikipedia.org/wiki/Neo-Riemannian_theory>

So is the tonnetz an infinitely square sheet with possible extensions of dimensionality ? :)

So looking at that spinning revolving-on-itself donut there, I've decided (I'm so glad it's color coded) that it is driven around more by the diagonals —like the turning of a screw.... The cycle of 5ths (blue diagonals) seems to drive it but the diagonal of the augmented triads (red diagona ls) eternally cycling would also be motivators in that they kind of represent the cycle enfolded on itself C—Ab—E resolves downward (that took me a minute to figure out even though they said that very thing in the article !!). This how it cycles or represents a cycle really of 4ths i.e. constant V7 resolution. Let's say C augmented is C7 and in the body of one of the 3 symmetrical diminished scales. C7 (represents Eb7, Gb7, and A7) resolves to Ab7 (representing B7, D7, and F7) and E is E7 representing G7, Bb7, Db7 so the cycle is truncated but still revolves on by the dynamic (here's a metaphor) of the lid that's just too big (or too small) for the coffee cup ... really its the +5/b6 interval that is providing the pressure for that lid to close but it only closes on two of the three points. Very tantalyzing !! The "vertical" (green lines) diminished 7ths are coiled along for the ride and of course are woven into the fabric of tension and release with the turning of that amazing magnetism created in that revolving sphere. In a way the diminished chord motivates the outward turning possibly due to the fact that each note of a Dim7 chord has the potential to fall 1/2 step and become the root of a Dominant 7th (of course this is just speculation on my part but logically it might hold true to some extent—perhaps 1/2:).


More later.

Ready, get Set, theory: Diminished perspectives 6

The thorny issue of writing diminished 7 chords into a minor 3rds stack has generated some conversation and is opening up a body of work that is being done under our noses: That is: methods to further understand and more deeply relate to the relationships between notes and chords—now we're calling them pitch collections, which has provided through this "Set Theory", a reasonable and more usable description of these relationships. Especially as applied to the diminished chord discussion under way in this blog.

My friend (he is possibly a mentor), Calvin Wong, a well known jazz musician about town who is a scientist by day and a pleasingly creative jazz pianist by night (and day too, no doubt), has some concerns about how the diminished was spelled and how it is used in diatonic tonality.

I quote:

Cal Wong

            I liked your new post but aren't we just fitting a square peg in a round hole in forcing a non diatonic scale (and it's subsequently derived chords) into diatonic notation? Consider the asymmetry of the tritone stack that makes up the skeleton of the diminished chord. B-F is a dim5. F-B is an aug4. It's just the diatonic sequencing fails us. If we write a B symmetrical scale without repeating a diatonic note name, we're going to end up on Cb. If we write a B whole tone scale in sequence we have to end up on A## unless we skip a note. Diatonic note names only will work for 8 note scales. Sadly the scales that make up our dim chords (as well as our aug chords) as well as the subsequent chords will have to carry enharmonics or skipped intervals). Just because they aren't 8 note scales. imagine a musical notation where the interval between two note position on the leger actually reflected the actual interval. The problem is our notation has B-C written indistinguishable (for a non musician) from A-B.

Unquote.

I came up with this response from what I had learned from conversations with Dr. Bill Richards @ MacEwan University Music. Dr. Richards basically introduced me to set theory and I was fascinated but also wondered where it might be useful. My response to Cal Wong gave me a small eureka moment when I realized that this theory of pitch collections numbered like the clock was a good way to circumvent the problem. My response:

That's a timely observation Cal. Sometimes I confess I yearn for no chromaticism, but then again I don't like to "force" the square peg into the round hole but try only to persuade it. The articles I've been doing are just to outline the potential for chromaticism through the diminished structure and then perhaps later: augmented structure. In practical terms How something is played has a lot to do with success or failure in the application of this. I'm just trying to share my efforts in this area. It often comes down to context. The way I've been trying to add harmonies/extensions and density is a personal evolution in harmonic application. I've got plenty to learn about the niceties of voice leading and still strive to learn about that. 


The problem with notating diminished 7th chords is mollified by the real symmetrical inversion of these chords. I think historically at one time Cb and B were tuned differently which was truly audible. With the advent of the "Well Tempered Scale" championed by J.S. Bach and now the advent of the equal interval system imposed on the piano gives rise to an actual equality of the notes of the Dim7 chord which when combined with an equally "equal" interval set—(It sounds like you know this already). The practise of "Set theory" dispenses with note names and assigns the numbers of the clock to an ascending set of "pitch classes": pitch class "0" (i.e. 12) is C, pitch class Db (C#) is 1 and so on.... Using this Set Theory system, a "B" diminished chord consists of p.c. 11, p.c. 2, p.c. 5, p.c. 8 thereby eliminating the need to write so diatonically—granted this is often (as in my case studies) married to a diatonic system. It's my hope that this exploitation if you will, can be used in a tasteful way and add to the richness/colors of a musical painting. Sorry to go on but I do agree with you on this—it's just a direction/exploration and it is totally worth talking about and is especially applicable to the improvisation of chord voicings and melody using the diminished stacks etc. 

Unquote.

Like I said this opens up new exploration territory, not that I ever wanted to be a theorist but reading about the great body of work being done in this area by some brilliant people is encouraging. I was reading a Doctoral dissertation on John Coltrane and I can't believe that I don't own the Slonimonsky's Thesarsus Of Chords and Scales. I think I always intended to own a copy but never got around to it. I'm going to correct that asap. There's some high math being done in another dissertation that ties in with the Torus concept with one graphic using the cycle called: Spiral Array: cool. I'm not going to be looking for things to do.

The bottom line for most people when it comes to music is: do I like it? That can be intuitive for a music maker but if the intuition at play is informed, the chances are good for playing music for people to "like" it and that's what it's all about. It's about growth and understanding, and, it is really for our souls.

Divergent links: Thoughtful information

So I'm cruising these music sites trying to PR things and publish a few pertinent facts re: jazz piano theory. One of my first forays was into the area of diminished 7th chord function and I actually got a comment from a deeper music theory guy and I quote:

Even though the author so liberally uses the idea of symmetrical divisions of the octave, it's interesting to know that this kind of symmetry, while clearly audible, is in fact not possible to notate. For example, B-D-F-Ab is a set of pitch-classes for a diminished seventh chord, each separated by a minor 3rd interval. But if you consider the wrap-around interval Ab-B, you've got a augmented 2nd interval. If one were to continue stacking minor thirds to that collection, it would look like B-D-F-Ab-Cb-Ebb-Gbb-... etc. The same issue arises in the so-called symmetrical divisions of the octave by major 3rds. Richard Cohn talks about this in his Maximally Smooth Cycles article, if anyone's interested in some more thoughts on the matter.


unquote:


Now that's cool actually and I hope I responded graciously especially since I ran down a couple of his leads and found some interesting and even inspiring graphic theory stuff that related to the world of improv piano (i.e. jazz). My response:


Thank you for your comment re: the notation of diminished "7th" pitch classes. Yes, a so-called B diminished 7th chord can't be written as successive minor 3rds, without producing enharmonic descriptions of the same thing i.e. Bdim7, Cbdim7, Dbbbdim7 ect. and this is a written musical fact, a thorny issue in an "equal" interval system to be sure. From an improviser/composer's point of view, especially a pianist's point of view, the beauty of this symmetrical/enharmonic/aural pattern phenomena whether described as stacked augmented 2nds or minor 3rds (or "double diminished" 4ths?) or combinations of the above will still allow, through the symmetrical diminished scale (2 minor tetrachords a tritone apart), all the potentialities for chord voicing, melody, and harmonic function within a given chord progression and voicing texture that the symmetrical diminished scale has to offer. The idea of the article was to discuss the flexibility of this set of pitch classes. It's a difficult enough task as a jazz pianist to obtain these useful diminished scale textures between the hands without being concerned about the infinite possibilities of writing them in a certain intervallic way. However it is worth exploring. There is, no doubt, some benefit that can be gained by studying this notation aspect. Thanks again for your comments which are educational and helpful. I hope that the point I was making can be recognized in the context intended. I will read the article by Richard Cohn with interest.


 Here's the link I found relating to this:   http://en.wikipedia.org/wiki/Neo-Riemannian_theory

Now in this first page scrolling, down low and behold: an active "torridial" graphic which links major and minor triads augment triad, the diminished 7ths, and the cycle of 5ths all in this spinning/revolving  TORUS structure, not unlike the Torus device described in the controversial video: Thrive. In this case it's color coded to make it more accessible. There's another graphic just above which is kind of the prep course for the major—minor—augmented—diminished 7ths—5ths-cycle Torus demonstration.  It's really quite brilliant. There's some interesting "transformational theory" (an academic sounding name that codifies little musical moves that we all make) that has piqued my interest too.

So given this Torus graphic I feel confident regarding the diminished 7th numbers game and the exploration of the Symmetrical Diminished Scale (i.e. 3 separate diminished 7ths each containing the 4 rotations that themselves are diminished). On to the augmented chords of 3 equal intervals (ma 3rd) with a total only 4 different augmented triads.  So this is starting to get good !!

No Perceptible Waves

OK I got a gig (Yeh!). I had to sing O'Canada (: not an Irish tune although it was St. Patrick's Day). I chose not to sing in Rap style although I felt like it. Now that there is danger from the government of Canada visa—vis erosion of rights and the privatization/incorporation of essential services et al, my enthusiasm for the traditional way of singing Oh Canada has been modified. Normally it's straight ahead—Oh Canada, Our Home and ..... with an appropriate gusto... True Patriot Love in all our sons.. (politically corrections needed there? re: female soldier fatalities and all). Let me say that this gig was part of a larger gig i.e. I was there 6+ hours doing solo piano background in two different places in the hotel—doin' it for the money yeah but also I had fun.

Back to Oh Canada. One of the requirements for this (well-paying, what a change) gig was that I had to "lead" the assembled ATCO (speaking of privatization) workers in the singing of OH Canada while playing the piano. Now when I sing it I felt like emphasizing: The True North Strong and FREE !! ..... We stand on GUARD (in a different way than before) for Thee. .... Glorius (yes) and FREE...... So it has a different meaning than before.

Once that "task" was done. I got to play a refurbished Kawai, which isn't too bad. I heard that since the piano was so old—I've been playing gigs there on this same piano on and off for close to 40 years (it was new then), that they're going to sell it and of course NOT going to replace it. We will now hear the (not so) dulcet tones of electric pianos — ones that pianists (Keyboardists) have to buy, bring, and set up. So that is a big loss right there. As for the Kawai grand ("old") it had just been tuned by a fine tuner (Josh S.C.) and really it's very good, especially in the "business" area of the piano. The bass was not as fine as the mid—treble but it is a relatively small grand piano. There is still plenty Plenty of beauty in it and I had a many a spiritual experience on that gig. It was fun to play material one knows well—There's always a discovery waiting for you especially when you just have to take a chance and revel in the acoustic piano experience on a gig like this. So like most people in a situation like this, I learned a thing or two about upwardly mobile capacity at the piano. So it was fun.

But that gave me an idea: To see if I could buy (what they think is a clunker) this piano... store it... and work out a deal that it could be set up at a gig somewhere on some special occasion and it could be played there... cartage is not the only cost but perhaps I could get a break on the tuning. There may be ways for that to happen. That would be exciting to play a small venue like the Blue Chair, Noala or even Jeffreys it might not make so much money but it would be worth it to give one's all on an "accoustic" piano in places like that. A person could build something on that perhaps. Playing music on piano is the funnest !!

Now I'm playing dinner music but it's not an intimate dinning alla Sabor Dinning but a bigger hall...people are farther away. I still tried to hold down the horses and play jazzy classical hotel style but as impulse would have it, free rein ravished the musical picture now and then.... Sometimes I looked up to see if I'd gotten away with it but no one gave me a dirty look so away I went. The thing is that in this particular setting they're definitely not there for you the piano player. They're there paying their dues at a company awards ceremony. The conversation is flat out. They are talking fairly loud and it's a steady stream of vocal noise. There isn't much opportunity to blend in and surge or hold a thought a little longer while someone laughs (See my blog "Tip See"), there are no perceptible waves of conversation—it's just one big Roaring Wave. So I appear largely useless to them, so therefor I try to become useful to myself in that case and get involved with the music—somebody might be listening, I hope, and that stretching out is good for me and good for anyone who happens to be listening (a faint hope in that crowd). It comes down to expressing that little edge of rebellion (which keeps my heart beating) even if it's hardly discernible it's still in operation and that's the important thing. I did get acknowledgement from the M.C. with a nice applause—they didn't ask for my CD's or anything :) and two personal compliments given at the end with some heartfelt conviction. I think people are shy, (Canadians) and sometimes I like it that way. Don't ask me to play AC/DC (who I admire: That scream/sing voice the crazy dancing guitar man: but, I don't know any of their tunes). I could play Kurt Cobain a little but I think that's on everyones list. Anyways I will refer to T. Monk's list of behavioral hipness ideas that's floating out there in FB land and apply it to all my activities, Yeah !!

Thriving on: perspectives.

The Thrive video. There would be a modicum of disbelief, re the technology evolution: Torus et al from the Thrive video. It was taken off Face Book per say but was still available in fragments on You Tube. The skepticism would focus mainly on the unproven concepts outlined: free energy and extra-terrestrials and so on. At first I thought it might be an "ahHah" moment but apparently it was taken off by the company that created the video in the first place. I guess they're trying to get a wave of feeling going on this topic. Selling it in order to promote the ideas to groups of people. Very interesting—high production values makes some question: Just get the point out etc. Although it is slightly suspicious that it has come under extreme attacks again on You Tube.

Most I've talked to about this video message, do indeed agree on the banking monopoly news if not the technology side—still it is tantalizing. Maybe that's not such news after all: there was this other video going around called Connect The Dots On You Tube. In this one we have a gentleman who tries to project this weighty topic re finances/incorporation of currency with connections directly to inflation. The poor man sort of giggles nervously while spelling out the raging inferno of the decline of value and worth of labor i.e. intentional inflation by the a collusion of Government (income tax initiated in 1913) and private banks. It's a very good clip. My comment on his delivery style is merely that he would rather laugh than cry—in his astonishment and disbelief that this could be happening !! It does tell it like it is though.

So the passion remains steady. My friend and long time philosophical mentor, Bob T. from Vancouver really summed it up by saying the bottom line should be based on two things: Equality and Justice !! We all continue to hope for, and try to contribute to those very things. This involves the truth of course, which will come out. It also involves fair play and good intentions. Something I continue to humbly learn more about.

The # R's:

How do you like this: my new 3 R's (not readin' 'riitin' and 'rithmetic) as applied mutually to life and to people in general: (Thought up while driving home from choir night)

Respect, Responsibility, and Reverence.


On with the Music !!

Diminished Perspectives 5: Polarized Passing chords with Extensions

I thought it might be fun to do a little exploration of the (Bebop type scale) where there can be essentially 2 polar harmonic entities: 1) tonic 2) dominant. Chord extensions are also explored using the Diminished Whole/half scale. At the end of the pages I introduce a passing tone/chord with "polarized components" using Auxiliary Diminished with extensions. It's not totally thorough but will give those who want to or feel the need to work with this a point of departure for their own explorations of this topic. Please enjoy. Next x a few pages on dominant 7th and an application of stacked diminished (ii/i).

Thrive arrive alive bee hive Behave

Interesting devolopments in the You Tube: "Thrive" clip (over 2 hours long) and I'm not through it all yet. Talks of technology and further proof of ancient extra terrestrial visitations. I'm not totally convinced but this clip is tantalizing in its connections to that very thing. They're talking about discovering primary patterns found in every aspect of creation. Spinning rings of light i.e. Torus/vector equalibriam and the magnetic sphere et al. Look at the clip and decide for yourself. I put it on my FB. If true, this will likely be suppressed.

I'd rather be Whirling Dervish !! The clip is amazing and inspiring though !!

Any new technology will be manipulated and "owned" by armed force. This new technology if real, would threaten those invested in Carbon storage—the piggy bank for them. Who's power is threatened? ... like he says on the clip: follow the money. That reminds me of the RCA CEO ripping off the guy (i.e. out-maneuvering) that invented TV... he was on "What's my Secret show" in the 50's and that was his secret.... he didn't look mad only thin and riven—part of his prize was a carton of the show sponser's cigarettes. I wouldn't think that anyone would want to emulate this CEO guy: the look on his face a reflection of the hardness of his heart. But, I judge him not and can only try like everybody else, to emulate those with grace (as long as I don't forget).

A monopoly of influence. How can we respond docilely to the perpetuation of big money, big power, (and big 'worse')? and, the intellectual Trolls at the bridge entrances (CEO/BP...from Chris Hedges: "Death Of The Liberal Class). Unless those in power can exploit this emerging technology they will attempt to suppress it. So, true cancer cures are suppressed as being unexploitable?

Two personal things:

As an infant (2-3 years old).

I had a reoccurring dream just about every night that machines in the form of "truck" cranes etc. monsters would come to our house and devour my mother (I was born during WWII). Maybe I saw cement trucks at working outside I think. It was very stressful and the reoccurring dream affected me. The thing that is weird about it is that we expected them to come and in some painful way accepted it as fact — haunting really! and here it is tending to be true (Mom's 95 and fine —I pray) —(Mother Earth is struggling—and I pray).

Raindrops are unlikely to be blue.

As a 5-6 year old in the local kindergarten, we had a good time and I think learned how to read. I could certainly read in Gr. 1. The kindergarten teacher was well intentioned and for the most part was a good teacher. One day she asked us to draw a landscape of our neighborhood or something and oddly, told us to indicate raindrops as the color blue (it rained in Vancouver a lot). Something of a silent rebel i.e. seeker of painful truths, within me made me think about that and I realized that rain was not blue but really transparent and reflected the colors of it's surroundings So— what did I do: I colored (crayons) the rain yellow and brown and green and orange etc. I guess to symbolize that. Bless her heart and soul but the teacher asked all the kids in the little class to come and look at what a mistake I had made and basically shamed me for not painting the rain blue. My feelings at that moment were: I'm not really here... and it had no immediate effect on me. But, it made me think about that and of course I was right about that. How could rain be blue... of course it can I suppose if reflected by a patch of blue somewhere—we all know you need clouds for rain to happen or? We try to fight this with little acts of rebellion: giving to charity, and if possible, support to those who need it.


I still have a dream: Martin Luther King....

The dream is that we will all wake up to who we really are. Those who follow the so called "golden rule": 'them that has the gold makes the rules'—they can wake up to that fact also. That is a dream worth trying to fulfill. I just think it's great that we can see clips like "Thrive". Of course ever leery of being lied to, being ever gullible, still, I like what he is saying—he is brave and a truth seeker just by putting his thoughts out there is putting his life on the line while no doubt, perplexedly preturbing the brain waves of the (you know).

One last thought from Hariharananda: If you are absorbed in the workings of the mind, then emotions, judgements, dislike, and other negativities arise and are reflected back to you in people, nature, and the world. However, if you are constantly absorbed in the soul, then only love and goodness is reflected back. (Amen) !!

Diminished Perspectives 4 Piano score, Symmetrical Dim

This is a piano score of the previous lead sheet example (found in Diminished Perspectives 3) of Diminished 7th function and voicing and voice leading.

The diminished chords with extensions as "slash/chords are derived mostly with the symmetrical diminished whole/half scale in mind. They are primarily auxiliary in function. The lower "denominator" of these slash chords are usually a diminished chord on the root of the next change except where there are voicing considerations and inversions of the auxiliary diminished are used. The "numerator" part of the slash chord will be a chord or chord voicing which will carry the melody and are also derived from the whole/half scale. For example in the 4th full bar on beat 4 (Emi7/Ddim7), both of the chords found in this slash/chord are derived from the same whole half symmetrical scale. The D diminished chord in this case, is an inversion of Ab diminished 7 which is on the same root as the chord that follows, i.e. Abdim7—Abmi7. 

Life in Time

Monday, I played for a friend's funeral (Bryan Foster).

This makes one contemplate about all that's going on. The reading I've been doing (Chris Hedges' "Death Of The Liberal Class")... makes one very introspective and even introverted, not that I don't appreciate deeply everyone I know. One feels the need to address any personal issues while proceeding in this life. Someone just asked me how I was doing and I replied:

"'can't complain... it's all amazing and tragic and scary and beautiful all at once... I'm seeking the inner man...it's seeking me...pulling me, goading me, but not abandoning me. Forgive me I think it's the books I'm reading (not enough).... Played for a friend's funeral the other day...in the St. Joseph's Basilica on 13th and Jasper.. a very timeless experience... the piano a Steinway grand) was wonderful... I could've played all day... but played to my friend and his family..very sad.... 62/cancer... 5 year fight ...suffering badly at the end. ... A really interesting and wise guy... very musical... I should've hung with him more... we were on the road together in the early days...So it has me thinking, for one thing, about the feeling of being in that huge tall cathedral-like church... the feeling of quiet and devoted respect... a very fine young priest... I may convert yet.... I will at least go there sometime: where other people respect and sincerely pray to Holy God....I was deeply moved and won't forget it ... I think I will go back and just sit there myself and contemplate...


Monday played for a friend's funeral—and juxtapose that with some tragic video footage about the most meaningless of meaninglessness actions of an African Despot (Joseph Koni) engaged in the worst disregard for human life and human suffering as he synonymously lends his very name to Atrocity. There is some action against this man but he has yet to be brought to task although there is more of a concentrated effort to find him. Judge the act and not the abysmally deluded man I remind myself. As Chris Hedges says that violence leaves one in a moral VOID !! Judgement serves all.



On a lighter note. I've discovered my piano records very well and has great qualities. A friend dropped by to record some tracks for a demo they are creating and thanks to the lap top ... he recorded me playing to his background tracks. The nice thing about it is that he was genuinely delighted and I found that inspiring— in a way and was able to seek the introversion and the surrender to real feeling, suspending my angst, nerves, and ego to get the reward of a truly deep feel for the groove which seemed to simultaneously refine the chord changes/voicings, tone, and musicality in general —even in the key of "E". So that was a great experience. I liked it so much that I'm hopping to have him over to record a few things of my own. Somehow it's about chemistry. I felt relaxed, and motivated and really took my time to let the beautiful sound of my piano linger and gel into the moment.

Diminished perspectives 3 Auxiliary Dim used in rhythm context..

So does this get easier? My friend CKM casually laid out the solution for making sense of Auxiliary Diminished and I quote:

"The whole auxiliary diminished thing makes more sense when rhythm is involved. Like one common pattern in that song is:

C7 Cdim C7 rest | bang! -- bang! ...if you know what I mean.

And there's also ....C9 + 2 + 3 + 4 B9 | C9 2 3 4 (with the B9 on the and of 4, in case my quasi-notation is not crystal clear)

Which I didn't interpret as an auxiliary dominant the first time round. They are both kicks kind of."

Thank you CKM !!

So Auxiliary Dim tends to create a rhythmic play of tension and release—release (at rest) on to beat one maybe or to any downbeat.

The diminished chords with extensions as "slash/chords are derived mostly with the symmetrical diminished whole/half scale in mind. They are primarily auxiliary in function. The lower "denominator" of these slash chords are usually a diminished chord on the root of the next change except where there are voicing considerations and inversions of the auxiliary diminished are used. The "numerater" part of the slash chord will be a chord or chord voicing which will carry the melody and are also derived from the whole/half scale. For example in the 4th full bar on beat 4 (Emi7/Ddim7), both of the chords found in this slash/chord are derived from the same whole half symmetrical scale. The D diminished chord in this case, is an inversion of Ab diminished 7 which is on the same root as the chord that follows, i.e.
Abdim7—Abmi7. I'll write this out in a piano score in the next blog.

Diminished perspectives 2

Please re-read Diminished perspectives .... chords that is for updated edits which I hope will add some sanity to my disjointed take on the dim 7 chords from last time.

We've had a bit of a forum on FB re: the observations on how a dim7 chord function is determined.

From Robert O.G. who (paraphrased) thinks of the diminished passing chord (iiimin7-biiidim7-iimin7) as an auxiliary diminished. More like (Imaj7/III-idim7/biii- iimin7) makes more sense. I think that has utility and is good to keep in mind when approaching improv or arranging. In fact the diminished chord comes after the iiimi7 and is leading to the ii mi7 and by virtue of that can be classified as a passing dim.

This thought was taken up by Marcus W. (many apologies) who confirms: Re: iiimin7 equalling Imaj7- This makes sense in both realms. Classical tonality says that the iii min is too weak and therefore a manifestation/prolongation of 1maj, so the dim. chord functions as passing.

My response was to affirm the idea of direction of the progression. Where is it going... in this case from iiimi7—iimi7 with the biii dim7 between i.e. iiim7—biiidim7 –iimi7...

To Quote:

Ima/iii—biii dim passes to iimi7 and the relation that biii dim has to iiimi7 is not considered auxiliary because it no longer relates to iiimi7 but relates and travels to ii ...I think that principle is valid. The auxiliary idea of biii is a moot point. But, the auxiliary dim 7 idea applied to the iiimi7 (or Ima7/iii) is also good to keep in mind I think.

I'd like to repeat the idea of Auxiliary Dominants. I don't hear people in the know defining these chords that way but it appears to have some wheels... (as they say) at least from the perspective I'm developing.

OK: C6—B7—C6 is a classic maneuver and is derived from C6—Cdim7—C6. Cdim being the derivation of B7(b9) etc. This has "release" C6 (tonic) i.e. at rest !! traveling to B7, a chord out of the tonality of C major— .... and then resolving that "out of key sense" back to C6...

This is how all 4 of the Auxiliary Dominants work.... they are derived (per say) from the root diminished chord (Cdim 7 in this case)..

in C or C6:

C6—B7—C6 acts like a lower neighbor chord

C6—F7—C6.... use in blues and boogie etc.... with utility in jazz rock too..

C6—Ab7—C6 ...(as in Bye Bye Blues)...forms a basis for use in so-called augmented 6th chords ..German 6h etc.

C6—D7—C6.... offers a milder form of tension and release but as D7(b9) this chord is derived essentially from C dim7..

More on this later...

This Music: Melody That Is—Chris Gestrin Trio

I wrote this word-piece after a couple of hearings of Chris Gestrin's trio album: Melody That Is. It's the title track.

I was in Vancouver about 2 summers ago and heard Chris sit in one of the fabulous jam sessions at O'Doul's on Robson St.... I had a chance to play a tune with Mike Allen's simultaneously stunning and reassuring rhythm section (Julian MacDonough-drums). and Adam Thomas on Bass). I had a revelatory time —really comfortable as I played a tune I knew fairly well: Embraceable... They didn't know it but let me play the changes a time or 2 and leaped in and ecstasy followed. Before I knew it, it was over.

But I digress. (My apologies to Chris Gestrin)

Chris Gestrin was there and sat in on the session and did about a 3 second casual piano warm up that was so sleek, musical, breathtaking on a miniature scale—he has a touch-less touch, if you know what I mean. That got my attention!

I had met him a couple of times before and had his original recording of quartet with tenor sax entitled: Times That Do Not Belong To Us...It's Impeccable, beautiful, spiritual, meditational and moving —not to mention swingin'... all original material. It's a stunning album and I highly recommend it (I had talked to him about it and he was considering re-releasing it).

His manner in person is an understated projection of clarity—in his thinking and talking. As a matter of fact he reminds me of all people: Glenn Gould. A very deft and to-the-point thinker. He is well known as a B3 Hammond player which reflects his funkier bluesy side. You can hear Chris Gestrin and his B3 on a recently released album "The Maverick" by the Edmonton wunderkind saxophonist Jerrold D. to get a pretty good idea of what Chris does there (I own and enjoy a copy).

I have most of Chris Gestrin's albums and this particular track caught my ear and resonated in the mind. So, being inspired as I am impressed I decided to put it down in this form... Dear reader, thank you for bearing with me.

This Music:

(For Chris Gestrin’s Trio recording: featuring Andre Lachance, Dylan Van Der Schyff)

“Melody That Is”

This Music, like spiritual glue, binds

vertical/horizontal dimensions to the Heart

supports

fractality, a continuing event-

horizon superimposed

In the now, the nowness

Of the ever-present.

Fracticallity evolving involvement involving

urgency in the play of vibration

ever an evocation ever true

intelligence in the perfect

means of golden means detail

informs the broader form: informing-synchronicity

generates a continual flow

of proof, proving pure intention

and informed moving touch

moving dimensions

from place to place in place

in a naturally natural

committed dance of pure

thought:

a complimentary issuance of beauty.

Ode to: Oops I did it again..

I like the song, it has that interesting tritone leap to an interesting chord change for a pop tune.

Then there is the lyric: I'm basically commenting on that in the dreaded poetic form (sorry in advance).

Ode to Oops I did it again…(Brittany)

The song speaks of matters of the mind (heart and soul). Therein lies a shallowness of the intention in the heart/mind that is revealed…. for some it seems popular to ridicule this song and the intent of the lyrics… Stepping back from that, one can be sympathetic and realize that the inattention to the intent of the moment happens more often than one might realize….. considering:

That we are

a part of

the infinity

of time and

eternal consciousness

and in a moment

we give that away.

without seemingly

knowing

but we do know

but we do forget

timelessness

that we can know:

will know;

Distractions attraction:

Indolence

amounts to insolence

to one’s own

life

Diminished perspectives...chords that is

Diminished chord function..... 3 (or more) essential kinds and approaches... My friend and colleague Bobby Cairns (my hero/mentor) said the diminished chords were essentially dominant 7 in their nature.

They are constructed symmetrically of minor 3rds. They are found diatonically in Harmonic minor and Harmonic major scales on VII (the raised 7th), and symmetrically in the "whole/half" diminished scale. This discussion is mainly about the symmetrical diminished scale and chord here.

This scale is "invertable" by minor thirds of course for example: Cdim inverts symmetrically to Ebdim, F#dim and Adim and the other remaining notes i.e. the 9, 11, b13, and Ma7 form ANOTHER dim7 chord and inversions that of course are a whole tone away from the original dim7 (Cdim). The chord used for this scale would be a form of Cdim7. The second of the 2 only modes would be "half/whole" and would be used for the roots of Dominant 7th chords with extensions b9, #9, #11, and 13 (which for in this case, Ddim7— i.e. Ddim7/Cdim7).

Functions of the Diminished 7th chord:

1) Leading tone function or dominant function popularly called VIIdim/ii.... where the leading tone diminished chord functions as if it were the 3rd of the dominant, for example: C#dim—Dmi7..... The C#dim acts or projects, as the 3rd of the dominant of Dmi7 i.e. A7(b9)—Dmi7. This is included as a secondary V7 within a given tonality. The scale used could be C# Sym-Dim but mode VII of D harmonic minor would be a probable first choice.

2) Passing chord function of dim7 are voice-led phenomena that uses 1/2 step voice-led motion to achieve a chromatic root motion. The common example (in C major) is Emi7—Ebdim7—Dmi7—G7 etc. Here the Ebdim7 is resolving by voice leading to Dmi7. If Ebdim7 can be interpreted as D7(b9) [and it can !!].... it is as if D7(b9) "resolves" to Dmi7 ... a slightly different chord quality on the same root !!

3) Auxlliary dim7 function is very useful and has many applications especially when the dim7 chord is assumed to be a part of the 4 dominant 7th chords it represents: i.d. Cdim/D—/F—/Ab—/B creates respectively: D7(b9), F7(b9), Ab7(b9) and B7(b9).

The Auxiliary dim7 CHORD FUNCTION acts like a "release" ( C6)—"tension" (Cdim7)—"release" (C6)....device.

C6 [or CMa7 or C7] — C dim (with extension possibilities) — C6 [or CMa7 or C7]....etc... can be and is used in many ways that one might not think come from Auxiliary dim.

In this example Cdim7 is the Auxiliary dim and can derive 4 dominant chords that could be called Auxiliary Dominants

i.e C6—B7—C6.....

or C6 (or C7)—F7—C7.....

or C6 etc.—Ab7—C6 etc... and even

C6 etc. — D7 —C6 has a milder tension...and release effect.

This becomes a lot of fun when one starts using some of the possible extension/slash/chord derivatives in passing chords. Why use them? because they help to harmonize melodic notes that aren't in the scale of the moment i.e Cmajor, for a very much denser and "active" harmonic sound.

The beauty of the Sym-Dim (whole —1/2) and Sym-Dom (1/2—whole) scales is the astonishing choices of extension color and slash chords available.

For example IN the Cdim scale (whole-1/2) on 9, 11, b13 and (ma)7 there resides 7th chords D7, F7, Ab7, and B7.....

Other chord qualities that are found in this scale also on the same 4 roots are: mi7(b5), 7(b5), mi7.

These are available as slash/chord components (don't forget inversions) of Cdim itself. Of course the C dim and inversions have extension possibilities which mix in the roots of D dim (F dim, Ab dim and B dim) to form for example: C dim9, C dim11, C dimb13 and popularly: CdimMa7 to name only a few. Ideally you can stack the two diminished chords in the make up of the symmetrical diminished scale to make a powerful if slightly crowded vertical chord as in Ddim7/Cdim7.

I have tried doing this on the fly and it works but to get to any sort of familiarity, these ideas should be written out in a tune context even if only with slash/chord symbols. A good tune— example of where this really come in is Benny Golson's Stablemates.... any tune will do if it has some "out-of-the-chord" tones the might need a reharminization. Reharminziation certainly is not restricted to these extended diminished concept chords and is a whole topic unto itself (endless really). The melody of Stablemates has some notes that are not very close to the harmony but Can be usually subsumed if played in a musical dynamically sensitive manner without any added passing changes. I'll try to get that idea of passing harmony both in the horizontal and vertical sense across in a graphic example the in the next blog—using extended dim 7 harmonies. These harmonies are used mostly as approach chords.

Cheers, everybody !!

listenism ..

Music day... listened to some nice tracks that came my way by facebook.

'Got almost talked into purchasing an ipad re music storage with instant access for gigs etc... rather than all those books... Picked up a couple of gigs with Dino D. (Nolas Mar. 28/29 early show) who uses the ipad and of course has all his many things on there. Now if I could only read !! Apparently they are back-lit and are fairly easy on the eyes. It might be a good idea for gigs.. but for rehearsing/practising and developing arrangements on the fly might be less than productive than quickly pensiling in a cool sounding chord change that you just thought of. I probably will go the way of the ipad eventually... $900.00 is not small change so I better be gettin' a lot of gigs I guess (ihope).

A friend came for a "lesson" today re what does the "Book" (AATJP) say there? (he's got it)... that was fun for me too to work with an advanced person/player. Needless to say he had an ipad as well and had my book on file right there.. We still read from the copy that I have however.. but the ipad does look practical if not downright time consuming (is my fear).

I wanted to review the diminished chord function thing visa-vis extensions, function, and slash chord potential. I'll write more on that tomorrow.

Man! I've been reading Chris Hedges continuing on — he is so scathing at the corporate/governance with his concern for the working men and women and really outlines from his deep deep coverage of political events.

Here's a sample from "The Death Of The Liberal Class": To set this up he refers to a FedEx worker/driver (HENDERSON) who was hurt very badly in an accident while working for that company (not his fault or doing)... and was subsequently abandoned and shed piecemeal from this company."

"Our destitute working class now understands that the cloying feel-your-pain-language of the liberal class is a lie. The liberal class is not attempting to prevent wages from sinking, unemployment from mounting, foreclosures from ripping apart communities, or jobs from being exported. The gap between a stark reality and the happy illusions peddled by smarmy television news personalities, fatuous academic and financial experts, oily bureaucrats and politicians, is becoming too wide to ignore. Those cast aside are often willing to listen to anyone, no matter how buffoonish or ignorant, who promises that the parasites and courtiers who serve the corporate state will Disappear. Right-wing rage is becoming synonymous with right-wing populism."

"Obama, seduced by power and prestige, is more interested in courting the corporate rich than in saving the disenfranchised. Asked to name a business executive he admires, the president cited Frederick Smith. of FedEx, although Smith. is a union-busting Republican. Smith, who was a member of Yale's secret Skull and Bones Society along with G W Bush and John Kerry ........ Smith is rich and powerful, but there is no ethical system, religious or secular, that would hold him up as a man worthy of emulation. Such men build fortunes and little monuments to themselves off the pain and suffering of people like Henderson."

Chris Hedges is a brave, concerned and humble man who is deeply literate and knowledgeable. He's not just my hero d'jour but a true stalwart and tells it like it is. I seem to see it all around on the TV... Alberta's groovin' OK and the unions are not "busted" here so much ?? but the money pressure is definitely on. I can't say I know so much about that but there are social problems that can get very personal in a heartbeat. In fact the lack of skilled workers might slow things down too.... We DO hope for the best for everyone though (now even) Yeah !!