UPDATED - Harmonic Implications of the Overtone Series, Part I

This is a re-visit to my earlier Musical Philosophy post, which generated some hilarious responses, all from proponents of adding atonality to the definition of music, and all rather infantile. If I think a comment is worth responding to or worth a viewer's read, I'll post it; if not I won't. So, there were none worth responding to, obviously. And here's a hint: If you use dummy e-mails and obviously idiotic names, I won't even read the comment when it comes in. This is primarily directed at a fan of mine named, aptly, U.R.N. Idiot (I did get a laugh out of the name though. I mean, "Dear Mr. Urine Idiot, Sorry about the bad luck with that name of yours, but as they say, if the shoe fits...").

There are strange people on the internet.

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Anyway, I've revised my terminology a tad to tighten up the consistency, and I think all lovers of music theory will be able to derive some use out of this post.

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UPDATE 09/17: I suppose I ought to take a moment to describe the logic behind my analysis symbols, as they are slightly different than "normal," if there is such a thing in music analysis. I developed these with the idea that they would be 1) Consistent, 2) Unambiguous, and 3) Executable on a QWERTY keyboard.

A bold capital Roman numeral denotes that the fifth has a major third, while a bold small case Roman numeral indicates that the fifth has a minor third. Fifths are perfect by implication. In the case that the fifth is diminished, a small case "d" will appear in parenthesis after the analysis symbol, and if the fifth is augmented, a capital "A" will appear in the parentheses. To be extra-clear on major thirds with diminished and augmented fifths, the numeral "5" will appear after the modified fifth designator.

Senenths (and ninths &c.) will be described with the M, m, A, d symbology as well, with the numeral following the modifier.

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The first section will be using the following example:



As always, every discussion of music must begin with the harmonic series, which has been true since the first music theorists investigated it with their monochords. The entire history of Western Art Music has been the ongoing investigation into the implications of this series.

Today I want to discuss the harmonic implications of the series. Obviously, the series makes a major minor-seventh chord, also called a dominant seventh chord, and it generates the gravitational force in music. The first and most obvious implication of the series is the primordial progressive root motion, as seen on the second system. This decending fifth or rising forth progression is statistically the most common type of progression in Western Art Music, and popular forms as well.

The technologically correct voice leading for this progression is a crosswise transformation in which the root of the first chord becomes the fifth of the target chord, the third of the first chord becomes the seventh of the target chord, and vice versa, in a purely tetradic environment. Traditionally, the target has been a triad momentarily, as I'll demonstrate shortly.

The implications of this progressive root motion lead to major tonality, which is the most perfect in accordance with the implications of the series for a triadic system. The root is the point at which arrivals or departures can be made in a progressive root motion to and from major triads, as you'll see on the third set of staves. Note that where the texture is triadic, there can only be clockwise or counterclockwise circular transformations between chords. In progressive root motions in a triadic texture, the transformations are counterclockwise: Root becomes fifth, fifth becomes third, and third becomes root.

If you simply read the third system backwards, you get the opposite of progressive motion, which is regressive. Regressive root motion types go against the dominant resolution impulse of the harmonic series. This in no way implies that these root motion types are inferior, rather they are just a resource and are necessary for variety and balance, as you'll soon see.

Note also that I not only analyze the degree and gender of the chords, but the root motion and transformation types as well. I have found this to be of great assistance in composing harmonic continuities, because I can visually check the paterns I'm creating.

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UPDATE 09/17: Again, I developed these symbols to be easily executable on a QWERTY keyboard, so ---> = clockwise transformation, <--- = counterclockwise transformation, and <-^-> = crosswise transformation. For the root motion types, P = progressive root motion, R = regressive root motion, .5P = a half-progression, .5R = a half-regression, SP = a super-progression, SR= a super-regression, Ptt = a progressive tri-tone root motion, and Rtt = a regressive tri-tone root motion.

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If we take the notes of the major triads of the cardinal degrees and put them into a scale, we get the Ionian or Major mode. It is important to understand that it is the harmonic implications of the series that generate the scale, and not the other way around (Technically, the series itself creates a Mixolydian Augmented Fourth scale). Historically, the melodic and contrapuntal implications of the series were worked out first, but this was because the original medium was vocal, I believe. The archaic Church Mode system also held back musical development for centuries, and this lineal thought lead to a poly-lineal musical conception, or counterpoint. As early as the 1300's though, the common musicians were using the Ionian mode in many of their pieces. In any case, what I'm discussing here today was not initially intuited until just before the time of J.S. Bach, and it was Rameau who first attempted (poorly) to explain it theoretically.

Not until Schoenberg's "Structural Functions of Harmony" were root motion types first categorized (Again, poorly: He obviously hadn't a clue about the implications of the harmonic series), and it was Joseph Shillinger who first correctly worked out the transformational nature of harmonic voice leading. Until Schillinger (And still among most traditional tonal composers of today) harmonic voice leading was a watered down form of counterpoint, gleaned primarily from the chorale harmonizations of Bach (Which explains the situation perfectly).

On the bottom staves you see the resulting harmonized scale, and unfortunately, this is what students are often given first. Without the preceeding understanding, confusion is inevitable: For years I thought scales generated harmony. They don't. It's exactly the other way around.

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Instead of presenting the root progression types in sterile isolation, I decided to use some phrased continuities. In the first example, after a super-regression from I to vii(d), the phrase has all of the chords in the diatonic system arranged in progressive order.

It is important to note that the constant root bass part is just a checking tool: The triadic continuity exists solely on the upper staff of each system. After the super-regression's clockwise circular transformation, all of the progressive root motions generate counterclockwise transformations. I turned the phrase around in the last measure with a super-progression from IV to V.

The reason for the terminology of super-progression and super-regression is simple: What is actually happening in these cases is that there is an implied root not present a third below the "root" of the first chord, which progresses or regresses to the target chord. By comparing every root progression type to the primordial natural progression, their various effects can be well understood. In part two, I'll clarify this further with secondary diminished seventh chords, which are actually major minor-seventh chords with a minor ninth and a missing root (If you want to prove this to yourself, try to write a four voice continuity employing these chords over a constant root bass: You'll end up with parallel octaves unles you put the REAL root in the bass line).

Note also that in a triadic texture, the voice leading is not totally smooth where super-progressions and super-regressions are used: The series actually implies a four part texture.

In the example on the second system, I have arranged all the chords in the system in half-progressive order. In a half-progression the two chords only go half way to the fifth the series desires to go to. As you can see, If you were to go directly from the I chord to the IV chord, not only would the root fall the required fifth, but the triadic continuity would make the progressive transformation all at once as well. Again, a half-regression would simply be reading that section backwards.


So, there are only seven types of root motions:

1) Progressive root motion (Falling fifth/rising fourth)

2) Regressive root motion (Rising fifth/falling fourth)

3) Half-Progressive root motion (Falling third/rising sixth)

4) Half-Regressive root motion (Rising third/falling sixth)

5) Super-Progressive root motion (Rising second/falling seventh)

6) Super-Regressive root motion (Falling second/rising seventh)

7) Tri-Tone root motion (Which is Ptt if it is a falling diminished fifth, or Rtt if it is a falling augmented fourth).


In example III, I used all of the root motion types in a single phrase with the exception of the Rtt (Regressive tri-tone). Note that the Ptt breaks the phrase up into two four measure sub-phrases, and that these sub-phrases have mirrored root motion types: The initial regression from measure one to measure two is answered by a progression from measure four to measure five; then the super-progression from measure two into measure three is answered by a super-regression from measure five into measure six, &c. Well ordered root motion patterns separate good progressions from bad ones, for the most part, and using the extended analysis symbol sets that I do makes the patterns easier to create and to see.

As I said, the series really implies a four-part texture, so the first tetradic example is the same as the first triadic example with the exception of the number of voices. Note that in a purely tetradic texture even the super-progressions and super-regressions have a common tone. Progressions and regressions have two common tones, and half-progressions and half-regressions have three common tones. The number of common tones also has a huge effect on the nature and effect that the various root motions create, obviously.

Now for the (Insert horn fanfare here) parallel perfect fifths in the super-progressions and super-regressions: They are perfectly natural and are not an issue in harmony at all, unless the chordal functions of the tones do not transform! In other words, parallel perfect fifths only sound "crude" when the root remains the root and the fifth remains the fifth (Or the same relationships involving the thirds and sevenths).

If you get the impression that I'm calling jazz vioce leading crude, well, yeah, on a certain level, but not transforming the chord tone functions is simply an aspect of that style. No doubt in my mind that the "proper" transformations sound "cooler" though, which is why I use them (Some of the "style" listeners percieve in the late music of George Gershwin is due to his being a student of Schillinger and employing some of these techniques).

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UPDATE 09/17: But, one thing the jazz musicians did properly intuit is that the overtone series implies a four-part texture. This actually began with blues tonality, which is simply a musical system built upon overtone chords on all of the cardinal degrees (I7, IV7, V7 in traditional parlance, I(m7), IV(m7), V(m7) as I designate them).

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Finally, as with the primordial progression implied by the series, progressive root motion creates crosswise transformations (As does regressive tetradic motion).

The second tetradic example at the bottom of the page is just a four voice version of the second triadic example. Note all the common tones: This series of falling thirds and one-at-a-time note movements in the transformations creates a very mild effect.

If you want to make a four voice version of the third triadic continuity, that would be good exercise, but I want to go back to the first example for my last point today.

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UPDATE 09/17: Also notice that in triadic textures the series of progressive and half-progressive root motions cause the voices to rise in pitch through time (And, regressive/half-regressive root motions in triadic textures would cause them to fall), but in tetradic environments, the same root motion types have the opposite effect. Imbalanced progressions, like these examples, can get you in "trouble" with ranges if they are not balanced out by alternating three and four voice episodes. Noticing all of these details enables the composer to gain total control over his work, and freedom is control.

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The pull of the dominant resolution/progressive root motion force in music - well, in sound, actually - lead to composers intuiting overtone chords on every degree of the diatonic system over time. The original continuity was written with this demonstration in mind.

After the super-regression from measure one, the thirds of the chords are raised and/or the sevenths are lowered to get an overtone chord. I did not raise the fifth of the V(d5m7)/iii to show you the harmonic origin of the so-called French Augmented Sixth Chord: In the second inversion, you get the Augmented Sixth interval, but in reality there is nothing "French" about this chord, and that description is useless insofar as explaining what it is. What it is, is merely a secondary dominant seventh chord with a diminished fifth in a particular inversion. All inversions of it are available, however, and on any degree, I might add.

Note that the secondary leading tones are allowed to resolve to the new roots-of-the-moment in this example. This is the traditional way to deal with these chords, but it is not the only way: The secondary leading tone can come down chromatically to give seventh chords as targets (Another thing that sounds vaguely Gershwinian in abundance, but composers have done this as far back as Bach's time in isolation). What this more traditional example's resolutions do is to demonstrate that inserting triads as target chords only delays the transformation type (crosswise), it does not negate it entirely (Or rather, that's the way that the series implies it ought to go).

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UPDATE 09/17: Yet another thing to note is that if the continuity started out with a minor seventh chord instead of a diminished minor seventh chord, and the remaining targets were also all made into minor seventh chords (On the dominant, tonic, and subdominant degrees), a very simple harmonic double canon would be created. I have covered that subject in depth previously, but I guess I'll hit it again in the next post (Because it really is a super-cool musical technology).

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Please understand that this is something I have been pondering recently, and I wrote this post in a stream-of-consciousness kind of way to put my own mind in the driver's seat with these concepts. I will study and re-read this a few times and try to clear up and points that might be confusing with a summary at the beginning of the second part of this subject.

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Remembering 09/11/2001

Five years ago today, I was living in Adelphi, Maryland. At the time, I was working at the FEMA National Processing Service Center in Hayattsville, a mere three mile commute. That morning was crystal clear - not a whisp of cloud from horizon to horizon - and a crisp nip of Autumn was in the air. I rode my pride and joy, a BMW K1200LT motorcycle, to work that AM, and it was a pleasant little start to the day.

At the office, I logged in and began my morning by processing cases in the queues, just as I always did when I wasn't deployed to the field. As I was working, I overheard someone say, "An airplane just hit the World Trade Center!" I was thinking in terms of a small private aircraft, and not a comercial jetliner, so while I thought it bizarre, I just kept on processing cases.

A few minutes later, I heard another person say, "Another airplane hit the Trade Center!" And I got a real deep, sick feeling. All of us went downstairs to the lunchroom, where the TV's were tuned to the CNN coverage. I walked in just a few minutes before the first tower came down. Somehow, stunned doesn't quite cover the way I felt.

I couldn't really wrap my brain around what was transpiring, so I numbly walked back upstairs to my desk and sat in silence. Within minutes, the news spread that a third aircraft had hit the Pentagon. I had a south facing window, so all I had to do to confirm that was look over my left shoulder. Sure enough, there it was: A black cloud of smoke streaming up from the Pentagon, which was several miles across town.

I'll never forget that day, nor will I forget the aftermath. For over eighteen months after 09/11, since I was a FEMA employee, I worked cases related to that terror attack. It changed me. Forever.

One of the main reasons I got out of the disaster business and returned to music is because of my work on the 09/11 aftermath. I had no problem dealing with natural disasters, but the unmitigated evil that is terrorist mass murder is another thing entirely. I was totally unprepared for that.

These photos were taken at Ground Zero by a FEMA employee who was one of the first FEMA people allowed on the scene. Unfortunately, I cannot recall the person's name, but I thought they were worth saving when they were forwarded to me.

Never forget who did this, and why: They hate freedom, they hate love, they hate the God of Abraham, Isaac, and Jacob, and therefore they hate all of us. "Allah" is historically a pre-Islamic diety who was god of the moon, and now "Allah" is simply another mask that Satan hides behind. If you have a problem coming to terms with that truth, then you have a problem. God is love; "Allah" is hate, and that list of opposites goes on forever.













When I lived in NYC, I used to take summer jobs as a bicycle messenger. I went up those towers to make deliveries all the time. If the weather was nice, I'd always stop on the observation deck and enjoy the spectacular view. Another thing I enjoyed was standing between the towers - where they came together edge-to-edge - and I'd tilt my head back and laugh at the incomprehensible vanishing-point effect.

Nobody ever has to worry about me forgetting that day, or the miserable aftermath.

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It's Official: I Have a Management Contract

The Lord works in mysterious ways. Many years ago I was under contract while in a rock band, and it was a disaster. I learned a lot from the experience, but I swore I'd never have a manager again. You know what they say: Never say never.

As I have been rebuilding my neglected music career over the past two years, one thing has become apparent to me: I can't do it all alone, despite my most fervent desires. Doing all my own booking is not only a distraction that keeps me away from practice and composition, but I also do not enjoy it, and so, consequently, I'm not very good at it.

Realizing I needed a partner in this effort, I decided to ask a friend of mine who is a musician - I don't wish to name drop, but he has been a friend for over twenty years and you would recognize the name of his jazz band instantly - how he managed his booking. He turned me on to his manager, and within a couple of e-mails, I knew that this lady understood artists on a deep and fundamental level. She also has an IQ which could instantly vaporize vast seas.

The first draft of her proposed contract - THE FIRST DRAFT! - was all but flawless, and was sensitive to any outcroppings of differences which might arise, so... I signed it.



The contract runs from February, so I have a few months to collect gear, tools, get the press materials together, etc.

I. Am. Psyched.

I'll be touring the college circuit, with higbrow dinner gigs and piano bars thrown in, and she wants to start me off in... ski lodges. Too cool. Er, cold (I hate cold weather and wouldn't ski on a dare, as one of my childhood friends broke both legs on his first day out, and paid for that with several months of rehab). But, I have a bad@$$ 4x4 pickup, so I think I'll get there OK, and sitting by a fire with ski babes sipping warmed cognac in the evenings sounds like my sort of "thing."

What better way to celebrate than with a redhead pinup girl? Exactly.

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Whirwind of Activity

Been holding off for a certain post I'm anxious to make, but like all watched pots, this one is taking longer to boil than I expected... but it's getting there.

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Major progress in the perfomance department, as I've integrated the Murray with the Carlos CP-1 High End with the Godin Multiac into my set now. As it stands now, I play the Murray for the A minor and C major suites, and then I switch to the Godin for the E minor, and G major suites (The E minor and G major suites end with tap-technique pieces, which are easier to play on the Godin, with its lower action). Then I return to the Murray for the D major suite, in which all of the pieces use a dropped-D tuning. By lowering the E down to D when I switch guitars the previous time, with one further tweak, the tuning stays much more stable. I raise the D back to E when I move to the Multiac for the F-sharp minor suite, and stay with the Godin until the break at the end of the A major suite. I've tried this out at a couple of gigs, and my students and regualrs really love the Murray's sound, and the guitar exchanges are quite smooth.

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The key to getting the CP-1 integrated tuned out to be using the EQ effect section in the Lexicon, and matching the levels between the two guitars using a combination of the internal input gain, and the EQ's gain as well. The problem I was having with the Murray turned out to be feedback on the C, B, and B-flat on the low A string. Fortunately, all of the original sounds for the Godin Multiac used no EQ because the RMC Polydrive doesn't need any, so I had that entire block free. The only problem I ran into is that some of the more complex programs were too large, and there wasn't any memory space for the EQ. In those instances, I simply deleated the pitch-shift doubler, which gave the needed space for the EQ.

Keeping in mind that I tune to Philosophical Pitch (A= 432), and that the open A string is therefore at 108 Hz, by using a single band EQ and reducing 127 Hz to -27 (Out of a silly range of 72 for that parameter: Why Lexicon used such a dizzying array of parameter ranges in the MPX-G2 and MPX-1 I just don't understand) with a Q set at 1.8, I was able to eliminate the hump in that range and ended up with a woodier sound to boot.

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Once I figured this out for the Murray, of course, I started in on the Glissentar/CP-1A sound programs, and am going through those right now. It too wants a tad cut at 127Hz.

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Cool timewaster site: That Image Site.

A couple of grabs:



I'm not sure who this is. Anybody know? I'd like to hear the guy play it.



This guy, however, I do know: Rick Nielsen of Cheap Trick. Too funny.

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Now that's a glamorous babe.

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Strings: Just When You Think You Have It All Figured Out...

... you have to develop an entirely new worldview.

Installing the Carlos CP-1 High End transducer into my trusty old Murray has required... a whole new learning curve with respect to string choice. Over the years I had gone for bigger and bigger bass output, and the best strings in that department - for this particular guitar - ended up being D'Addario Pro Arte' EJ46C Composites. Using the composite G gave great balance, and the regular nylon B and E gave a smooth upper register with no carbon fiber harshness. Well, guess what? Those strings suck for the Carlos transducer: The A and D strings, especially, simply overwhelm the others. back to square one.

Square one, in this case, is the old standby red card Savarez set. Why? Middle of the road everything: Bass output, response, upper register; just an all-around good point of reference. Talk about hitting it in the sweet spot! I'm wondering, in fact, if Carlos developed his transducer with these strings. One minor major bugaboo: The G@& D@%*#> F#&%^#& G-string! Talk about wimpy-@$$ pound-testage! Methinks that G weighs in at less than 12 pounds in an A=440Hz tuning (And, I tune to A=432/"Philosophical Pitch"). I love happy accidents.

I just happened to have ten nine Savarez red card metal wound G strings laying around from an earlier experiment, and voila'! So, low E through G are now dialled in. High B and E, however, suck unholy @$$! The balsy output of the wound lower strings now makes the old fashioned nylon strings sound, well, old fashioned.

Savarez Alliance Carbon Fiber trebles to the rescue! I had a gazillion of these laying around for the Glissentar, so no problemo.

Oh yeah: I have to re-do all the EQ settings in my Lexicon's too.



And, I have a management contract offer, which I'm going to accept, so Hucbald may be coming to a town near you in 2007!



Just for you, Peg! ;^)

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Sid and Nancy

One of my favorite movies of all time. For reasons you may not expect.



In 1983 I was a roadie/driver/guitar tech for Johnny Thunders, who was formerly in The New York Dolls, who were on the Anarchy in the UK tour with... The Sex Pistols and The Clash back around 1976 (The Year I graduated from high school). This was immediately after Johnny Rotten's "Fuck the Queen" quotation hit the headlines of every rag in Europe. It was the dark flip-side of the Beatlemania phenomenon. Very intense.

Sid Vicious and Johnny Thunders were birds of a feather and long-lost-brother soul mates (A relationship which was absolutely platonic, I can assure you). Johnny Rotten, by comparison, was - and remains - a pathetic poseur.

I used to get enraptured by Johnny's "Sad Vacation": A wrist-slitting nihilistic punk-rock ballad about his sense of loss when Sid died. Sadly, Johnny has joined Sid now, along with Jerry Nolan, the drummer for that tour and for The Dolls, and I'm almost the only one left who remembers any of it.

Except for the bass player, Billy Rath. Wish I could find him. He was cool. Last I heard, he had a Swedish wife half his age. Rock on, Billy.

This was long before I re-emerged as an All-American boy. Long before.



You can call me Huc, you can call me Bald, but don't call me late for dinner.

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Hazy, Lazy, Crazy Days of Summer

Please forgive the light blogging, but there has actually been almost too much going on in my life to be blogging for the past week or so. No "wucking furries" - as an Aussie pal of mine would say - because it's all been good. Very good. So good, in fact, that I don't want to jinx some of it by talking about it. Let me begin by saying that I have spent many man-hours getting the Glissentar/CP-1A and Murray/CP-1 guitars ready for giggage, and that project is now in the pocket.

What I had to do there was develop twelve "virtual acoustic environments" - one for each of the suites in my set - in my Lexicon MPX-G2... for each axe. That required modifying the twelve I had already developed for the Multiac/RMC Polydrive guitar - and which began their evolution back when they were for a Gibson Chet Atkins CEC guitar (There are, without exaggeration, literally hundreds of man hours in these programs) - and renaming/storing them down the user program address chain. I have gotten that done for the MPX-G2 I use in my recording settup, but I still have not entered them in the MPX-G2's I use for my small venue and large venue performance rigs (Remember, I need three MPX-G2's to make my life work).

This has to be done by hand: I have to stack the units and modify the programs one-at-a-time by comparing the new ones to the old ones in the other units because there is not data dump or sysex function in those units (Well, that I can figure out, anyway). That's for each and every parameter of each and every effect in each and every program! So, the reast of this week will be spent getting that done, because I have to re-EQ all of those programs for the various amp/speaker configurations. It's a freaking nightmare.

A nightmare that I must get through, however, as events seem to be conspiring to make me even busier (I'll have to leave it cryptic, as I don't want to count my chickens before they hatch).

I have some seriously cool guitars now.



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I want to take a moment to thank Carlos Juan for putting up a nice splash page for me at his site. It is no exaggeration to say that his CP-1A and CP-1 pickups have changed my entire musical life for the better, and I'm proud to be associated with his awesome products.

I'm too good to be true, and I get better looking every day, don't you think?



(Don't answer that!)

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The Great Irony: While the north, and then the north east, have been suffering with a record-setting heat wave, we out here in the desert chapparal have been having fabulous monsoon rains this year. Here's a pic from a couple of days ago, taken at about 6:30AM, from the back porch of El Rancho Ucobaldo.



"Red sky at morning, sailor take warning!"

It rained furously that afternoon.

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One other thing I'll have to be elusive about is a potential new location for my "Rancho": This will be the fulfillment of a thirty year dream if it pans out, as I have been offered a "sweetheart deal" on some acreage a couple hours north of here. I'm going to scope it out next week. Most of the land sold out here is never listed with a broker: You have to be part of the community for a while, and put out feelers. If folks like you and wouldn't mind having you as a neighbor, then - and only then - will you get some offers. I love that.

Remember this?



Just a couple of miles away.

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Perhaps I'll end up with some neighbors like this?

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