~ Bach's instrumental arpeggios ~

~ here we examine a timeless Euro Bach musical puzzle and discover Americana pieces for forward motion, melodies and chords all combined into four bar phrases while learning to hear the changes ~

wiki ~ Johann Sebastion Bach


'I was obliged to be industrious. Whoever is equally industrious will succeed equally well.'

wiki ~ J. S. Bach


Johann Sebastion Bach (1685-1750), was the unheralded King Of The European Continent at the close of the Baroque era. As often quipped on this side of the Atlantic, in Bach's own day he was 'the greatest keyboard player that we never heard of.'

At this key historical juncture, the loud / soft key mechanism for the piano forte was just perfected. Composers had already been demanding more key centers of the 12 pitch cycle, some of which were more successfully in tune than others, depending on their piano tuners.

As Europe was still coming to terms with equal temper tuning, Bach comes along and writes his collection titled the "Well Tempered Clavier." While there's still controversy today of the tuning of Bach's keyboard in creating this work, there's zero argument about that fact that his music is 24 unique pieces, each written in one of the 12 major or minor key centers. Once this work was reintroduced to a wider range of players, having all of the key centers on the one piano not made total sense, but composers wrote more music and modulations to 'remote' keys.

Once this full 12 key range was available through the equal temper tuning of the pitches, we've really never looked bach ... I mean back :) Here's JS, the master himself, working the magic.

So this bit of the story provides one half of the theory of our Americana musics. Was there a piano on the Mayflower? Or one floated down the eastern U S A seaboard? If so there's a chance it was equal temper tuned. As such, Americans now had the full range of key center, harmony and modulation that all of Europe had too.

In regards to our Americana musics, we catch up with Herr Bach's magic towards the apex of his career. For in the early 1720's he's composing his collection of songs for the WTC. By it's completion, while we Americano's have all the harmony we'll ever need to create all of our indigenous 'folk musics' for ever after, 200 years later 'jass' comes along. For in this collection we find all the changes. Bach's exhaustive searching of the harmony is as complete as any we might have today. That is until Parker and Coltrane come along to add their own magics to the pitches and take the Americana jazz to new vistas.

Bach as a bookend / diatonic progressions of chords. Bach is a bookend because all of the cool changes we play today, spanning all of our styles, he had them too. And put them together with melodies that ring Bach true. Triads, voicings, progressions, cadence, form, no stone unturned for Herr Bach.

the changes
the styles

Today, we have Bach's now 300 year old double volume WTC, a towering pinnacle of masterful musical art achievement. Perhaps as thorough an examination of harmony, from a single composer, that has ever been created? What encouraged and energized Herr Bach to want to exhaust the potentials of 12 'equal' pitches, 12 major and 12 minor key centers?

Having all the changes to explore, that's my guess :)

the changes
chord progressions
chord substitutions
Ted Greene

Bach today. In all of our styles and genres, near all of our chord progressions and chord colors are included in WTC first song. Hear it here and follow along. Search and find a chart, a written score, if so inclined. The links at the right are the various 'theory highlights' as the musical art is crafted and evolves through the entire piece. We can hear these highlights in one place or another, or in one form or another, somewhere on our Americana radio dials every day :) In 'C' major. Here's the rhythmic / arpeggio motif that is filtered through the events listed to the right. Example 1.

Here's the complete song. Example 1a.


Cool or what ? And yea, it all applies. Same pitches, same tuning, same cycles, some of the same tricks, just different historical eras. And blue notes ? That's the melody magic our own Americana palette brings into the European harmony tuning and systems.

A closer look. With so much of the philosophy of this book arpeggio evolutionary based, take a closer look at a reduced score of of this Herr Bach masterpiece. Measure by measure, the arpeggiated figures as they move through the changes are clear as day.

So the new tuning precision of the 12 pitches, as brought forth by equal temper tuning, 'encouraged and allowed' the scope of Bach's masterwork? In theory, that's the idea put forth here. And as such it becomes a bookend for our theory studies. For while the organization of our melody notes go back to the early mists of antiquity, the chords as we know and enjoy them today only go back 300 years or so. And yet ... and surely by now ... you've heard the rumor ... that yes indeed its be true that ...

'there was an old pian'er ... on that fancy Mayflower, when it bumped on into ol' Plymouth Rock ... :)

For guitar. We guitarists here can also ponder along these lines with Ted Greene's "Chord Chemistry." Which becomes another dear bookend for many a six stringer. Beyond amazing, back when published in the 70's, it was a true 'awesome.' That of course is still true today, even if awesome now can describe a cup of coffee. Seriouso six string cats should find a copy for a new perspective on whatever is currently under the fingers.

the changes
chord progressions
chord substitutions
Ted Greene

J. S. Bach. 'Come one come all and marvel at a master maestro's musical call. To open our ears to the sounds of the day, from way back when to our present of today.' :)

For the following music is a 'reduced score' of J.S. Bach's "Preludio I" from his Well Tempered Clavier. A perfect piece for this book, it's all arpeggios, spelling out each chord with a startling clarity. Presented here in two bar phrases, each measure's harmony magic is super clear to hear, providing us an easy aural access to theories of harmony and chord progressions, and create various artistic links to common elements in Americana music. In 'C' major, here's Bach's motive. Example A.

Thinking in the key of 'C' major and in 4/4 time, examine the chord changes for Bach's opening opus in this collection. Nearly all the measures have just one chord per measure. In 36 bars, it closes with V to I at 32, and then there's a 4 bar tag of sorts. Example Aa, each letter name is followed by its classical theory 'Roman numeral' designation in parenthesis. Thinking 'C' major, 32 bars.

C ( I ) D - ( ii ) G 7 ( V 7 ) C ( I )
A- / C ( vi ) D 7 / C ( V7 of V ) G / B ( V ) C ( I )
A- ( vi ) D 7 ( V7 of V ) G ( V ) E dim 7 / G ( iii dim 7 )
D - / F ( ii ) G 7 b9 / F ( V7b9 ) C ( I ) F maj 7 ( IV maj 7)
D -7 ( ii-7 ) G 7 ( V 7 ) C ( I ) C 7 ( V 7 of IV )
F maj 7 ( IV maj 7 ) F# dim 7 ( #iv dim 7 ) C- maj 7 /G ( i - maj 7) B dim 7/Ab (vii dim 7)
G 7 ( V 7 ) C / G ( I ) G 7 sus 4 ( V 7 sus ) G 7 ( V 7 )
C dim 7 / G ( i dim 7 ) G 7 sus 4 ( V 7 sus ) G 7 ( V 7 ) G 7 ( V 7 )
C 7 ( V7 of IV ) F / C ( IV ) G 7 / C ( V 7 ) C ( I )

Wow, looks like a page from "Chord Chemistry!" Of course, analyzing changes is super subjective at times. Measure one ? Zero worries, root position tonic chord in Herr Bach' chosen key center. But then ... once it rolls on to Four in bar 25, its 'game on' as they said in the day. The #4 dim in 26 is super common in jazz advanced blues, we hear it all the time. Followed by tonic minor / major 7th ? In the 1720's ... ? Thank goodness that for the most part, 'burnings' we're scheduled, but thankfully cancelled. And we all love the 'sus' chords yes? Especially towards the end of the song.

Instrumental music. In our Americana theory and art musings here, this next discussion is woven through a completely worked out instrumental piece, a Bach prelude written at the keyboard. So we've a distinction to make between instrumental musics or musics with words and vocals. So just to avoid confusion as we go through the measures, there'll be threads of thoughts, as links to other discussions of styles, that include vocals, poetry, and lyrics of words etc. In doing so we get to explore the commonality of similar music elements across the span of a couple of hundred years. And maybe pick up a lick or two along the way too :)

Measures 1 through 2. In 'C' major, the Roman numerals represent the diatonic scale degrees, One through Eight. Starts on One, and will probably end on One, then stepwise to Two, with triad pitches in melody, over tonic pedal. Example 1.

Measures 3 through 4. Preceded by Two, moving to Five in first inversion, to root position One. So a Two / Five / One cadential motion right out of the gate ... from 1722 or thereabouts? Yep. 251. And Two / Five is the 'cell' that motors the jazz in Americana for the last 100 years or so ? Tis is indeed. Blues too. Then add a seventh for chord type and we have a bingo. And then 'b9' to any V7, to open up the leading tone potential of the diminished 7th chord, and another bingo depending. And a substituting we will go :) V7 to One in major, hear it ? Recognize it? Label it? Cool. Example 2.

Catch the fairly 'wide intervals' in the arpeggio? Perfect 4th then perfect 5th. It can makes for tricky, somewhat unorthodox lines to speak, but they sure are a way to rocket right on through the full range of your horn, either way down or up.

Measures 5 through 6. Our first accidental, signals and event. Here we get a quick nod to the relative minor color possibilities, so 'A' minor. Followed by the soon to be famous, Five of Five motion. For in this pairing we get another Two / Five cell, and can kick in the theory of cycling, and cycles of our dominant chords. Example 3.

While the two chord is 'sans' a 7th, the V7 of V is clear. Even in third inversion? Yep, anytime we've the old tritone interval between pitches in a chord, blues music excepting as it is V7 based, chances are its aural 'rub' wants to move towards a spot to resolve and rest a spell.

Measures 7 through 8. Basic V to I cadential motion. Our most common way to bring tension to resolution within a chosen key center. One point of interest here is the softer cadence of first inversion V7, and its carry over to the tonic chord sounded in bar 8. Sounded through the measure, super clear tonic major triad pitches arpeggiated in the melody, over a major 7th colortone. Example 4. We modernes, flip this around, using root position major with the major 7th colortone on top. Example 4.

We modernes, flip this around, often using a root position major triad with the major 7th colortone on top. Example 4a.

wiki ~ "Color My World"

Measures 9 through 10. From a bit unsettled tonic One Bach is off to the relative minor. First a minor 7th Two chord type followed by V7 of V. So, a super clear Two / Five cell of modern times. Example 5.

Measures 11 through 12. Have we modulated to the dominant ? To 'G' major ? Seems so ... until the diminished color sounds in bar 12. Then there's some uncertainty in the aural predictability of the music. Often termed a 'temporary' modulation, we get to officially visit the 'dominant V' as a key center, thanks to the Two Five / One cadential motion. Very common in our jazz and pop musics. Jazz once was Americana's pop music wasn't it? Example 6.

Let's cherry pick the # i dim7 chord. While the chord in bar 12 above is a chromatic passing chord between diatonic destinations, as a '#1dim7' chord, it's also an 'accelerator' chord of super jazzy dimensions.

Labeled here as passing '#1', in relation to our tonic note 'C', for in our next measure we find a diatonic Two chord in 'C.' As a 'passing diminished 7th', it becomes for us modernes an 'accelerator' in our jazz musics. For in brighter tempos, '#1 dim 7' color propels our sense of moving between the diatonic positions in our chord progressions. We've #1, #2, #4 which are jazz common. A '#5' going to the minor Six is available but not too common. The '#4' choice is the most common of these fully diminished 7th chords in the blues.

And in theory, we can 'soften' this 'dim 7' color to a plain old V7 chord, actually four different V7's. And in this 'softening' begins the explorations into 'V7b9', creating new possible motions in minor 3rd intervals, the perfect 4th motion in Two / Five's, the two minor 3rd's and whole tone stepping of a tritone interval, and new combinations of all these towards Coltrane's 1960 release of "Giant Steps."

Modulation to the dominant. We can also cherry pick from this last idea the common 'classical' feature of modulation from the tonic / One to the dominant / Five. An essential compositional feature / component of the 'sonata allegro' form of Euro classical music. This modulation, changing key centers to Five, is found in a wide range of Euro composition, from the baroque and on through the classical eras, thus spanning well over 100 years of succeeding generations of composers.

The idea is to simply start in a chosen key, like 'C' here, and work out the motif in such a way as to change keys to its dominant note, 'G.' Once there, we usually get the same motif again with the pitches of 'G' major. Eventually the music will 'recapitulate' or 'recap' and modulate its way back to the original key center.

As one of the old time 'rules of properness', 'modulation to the dominant' has historical precedence in crafting musical works deemed appropriate for the drawing rooms and concert halls. For a 100 years and more, the 'sonata allegro form' was the opening 'movement' form for the symphonies, concertos, and string quartets of the Scarlatti's, Haydn, Mozart, Beethoven and beyond.

Need a PH.D topic? In just the Beethoven string quartets alone, curious readers here have a combined tonality and musical form 'evolutionary study' through this important compositional form. In four sets of four, each written together, provide a glimpse of Beethoven's own evolutions in theory, form, tonality, and what's acceptable as a V7 chord :) Wouldn't happen to need a Ph.D. topic by chance ?

We Americana modernes have abbreviated this 'opening movement sonata allegro form', over the centuries now into our own 32 bar, 'song form.' In four sections of eight bars each, it's a larger form for composing, so mostly in the jazz 'standards' realm of songs.

"There was no one near to confuse me, so I was forced to become original."

wiki ~ Joseph Haydn

Measures 13 through 14. Picking up from measure 12, we arrive on Two, of our original key of 'C.' The harmony of bar 13 is again fully diminished 7th. Peeking ahead our next chord is a 'C' major chord. Knowing this next chord, the diminished 7th on Two could also be viewed as an 'incomplete dominant 7th chord. Example 7.

Its 'incomplete' because while we're thinking it's a 'G7' chord, yet there is no 'G' note in the chord. Thus, it is incomplete, no root note. With fully diminished 7th, we jazzers quickly shift to V7b9 and its off to the races' as to where this theory can take us harmonically through the chord substitution properties of V7b9.

Measures 15 through 16. Half step descending motion in the bass brings us back to a softer One chord, as it is in first inversion. Holding over this bass note in his motion to Four, these combined pitches give us that major 7th coloring again as in measure 8 above, a distinctive color of stability, love and devotion often found in our jazz and pop musics. Example 8.

Have a clear sense of the direction and flow of the tension and release of this music ? No ? Good, we're not supposed to :) For all throughout our literature, motion to Four is indeed the center of near every song we have. And just must say here, tis indeed quite uncommon to have the major 7th as the lowest pitch of a chord, even and maybe even especially so, in motion to Four. As it cores the gospel woven through all our Americana, this subdominant Four chord in 3rd inversion is rare, maybe hen's teeth rare indeed.

Measures 17 through 18. Well back to the Two / Five motion, and this time both chord's have a 7th added to their triad base. Example 9.

Cool huh? So with a '3rd and 7th' in any chord, our theory of 'chord type' manifests. And '3 and 7' in V7, brings the tritone into play. So now all bets, both deep in the blues and jazz, are on. Any guesses as to the next chord in the song?

Measures 19 through 20. And voilà ... wouldn't ya know it, a 'root position tonic One chord, with the bass note sounding on the downbeat of the new measure. Example 10.

Back in Kansas ? Yep, home safe.

... for by sounding the root of the tonic chord, on a down beat in a new bar, and its triad pitches are in the arpeggio = we've created a resting moment in our diatonic realm of 'C' major in this piece of art.

Now, ready for our next adventure ? Where to go ? We did go off to Five a few measures back. Catch the 'Bb' in measure 20? And the 'V7 of IV' Roman numeral letters designation between the bass and tab clefs? Ok with the idea that 'Bb' is a 'borrowed' pitch, a note that is not diatonic to the pitches of 'C' major? So adding a 'Bb' pitch into our mix of pitches, where might that take us? Let's see what Amigo Bach does.

V7 of IV. The 'V7 of IV' of bar 20 gives away our harmonic direction every time, sets in motion the direction of our next tonal destination, clear as day. For in our Americana musics, and especially the jazzier styles, 'V7 of _____ ' anything can signal a myriad of different events.

One note. And that one note change, from the diatonic 'B' natural, of the key of 'C' major, to 'Bb', is the secret. For in theory, this 'B' natural leading tone major 7th of 'C' major momentarily becomes a true blue minor 7th', which shifts the chord type of our harmony. From 'tonic' to 'dominant' chord type.

tonic One / C E G B to dominant V7 / C E G Bb

While this evolution to V7 is probably 'theory 101' for most, the concept of 'chord type' is anything but '101' level theory. So, a super theory game changer then ? Yep. Maybe even a 'kaboom level stgc.' And if you're brand new to all this mumbo jumbo? Welcome to a whole new world of musical art / theory to discover.

Chord type becomes chord function, chord function gets boring, so we begin to 'substitute' new chords that function the same way, that have the same chord type. And it just turns out that some of these substitute chords are are a bit sleeker than the original, sleeker moves faster, and faster and faster still, till it is all a blur of seemingly chromatic color.

Measures 21 through 22. Four ! Of course. Wait ... that's for golf ... and now music too ! Regardless, we're arriving at Four and in root position too. So, solid as a rock landing. Root position works like a charm, every time. You know, bass line story and all of that. Ex. 11.

Four it is, with some added major 7th color, and then a #iv diminished 7th chord? Jazz it up a bit why don't ya ?

Sharp One diminished 7th. Here built up on the sharp (#) 4th degree from our root pitch 'C', the fully diminished 7th color is most often a passing chord between diatonic destinations. Americana blues / jazz artists often include this in their chord progressions. For it's been a fairly common passing chord all along through history in our jazz musics. And when a fully diminished 7th chord sits atop V, becoming V7b9, then all bet are off, to where this magical V7b9 will direct the music.

Measures 23 through 24. Continuing by half step, our bass line arrives at Five. In plain figuring, we've an augmented major triad. Not quite done yet, Bach moves by half step again, hinting that we might be going on to Six, the relative minor. Example 12.

Moving from an augmented to diminished color is a sure way to obscure our tonal direction. For both are not only non-diatonic but are a bit unstable themselves as chords in their own right.

Measures 25 through 26. Back to the dominant Five with an added 7th we go, so root position V7, and sure enough cadentialing on to One, though voiced in second inversion, continues to give us still a bit of wobble in our sense of tonal center. Example 13.

The Five to One is an authentic cadence, so we get that sense of resolution. It's just not quite perfect, as our tonic / One chord is not in root position.

Measures 27 through 28. Continuing to pedal on the dominant, and back to Five we go, Bach brings us another first in this piece, by including a 'suspension' of the pitches to create a new sense of 'floating' or hovering near our tonal center, yet not quite ready to land. The 'sus' does settle to V7 though, setting up a tritone tension that will direct the music towards a resolution, or not, as the case may be. Stay tuned and we'll see. Example 14.

With both V7 chords in root position, and we've already counted the number of measures in this song ... we're getting close to the finish, and surely want to resolutely resolve back to where we started yes? 'C' major ? Yep.

Measures 29 through 30. We keep the dominant pedal tone but slide back into the diminished color on sharp Four. Just a sort of oscillation around the dominant. Followed by One, yet still with the dominant pedal, which again puts our tonic chord in second inversion, so the 5th of the triad as the bass pitch. We're stable again, but not quite perfectly stable, at least as far as these pitches go. Example 15.

Measures 31 through 32. Back to V7 and our 'sus' color, all still floating over the dominant pedal tone. There's an 'event' coming up, signaled by the pedal tone now sounded over the last eight measures. Example 16.

Measures 33 through 34. And the event is ? A 'V7 of Four' again ? We're going back to Four? No, and then some yes. Surely there's a bit of Four followed by a hint of Two? All over a tonic pedal. Example 15.

When Four becomes Two in our Americana musics, we can create the Two / Five / One cadential motion. Near every bit as convincing as Four / Five / One. In this harmonic evolution, using Two instead of Four, we 'free up' the Four chord to become more of a destination in composing songs. Do recall, that motion to Four is in near every song, somewhere. And while a principle chord of 'three chords and the truth', when we swap a Two chord for Four, we've a sleeker cadential motion. And sleeker is generally quicker. And quicker leans us towards the jazz stylings of our style spectrum, and ways to jazz things up, in any of our styles. , in doing so, Four .

Measures 35 through 36. And to close out the piece, Herr Bach sounds root position Five to root position One. That the last chord has its tonic pitch in both the root and top, soprano voice, we've a perfect authentic cadence to confirm yes indeed, we're home. Ex. 16.

Review. Well in 36 bars we sure covered some theory ground. All sorts of links out to explore, bringing new vocabulary and new ways to use the same musical components. Pick up a new pathway or two for further explorations? As time permits, do find a reading of this piece by a classical pianist reading the score. Presented here as a 'version', it gives us a chance to scrutinize a simpler score, to watch and hear how the arpeggios and bass line tell the story. So what's next in your curriculum?

Learning to hear the changes. Bach's magics with chord progressions are a sort of mirror image to our own Americana ways of doing. As they were written way before ours, from like 1700, we borrowed a lot of essential coolness straight off the scores. Same letter names, triads, colortones, all of it we have with Bach. And further into the study of one or two Baroque sequences, one in major one in minor, is a super solid kaboom for 'by ear' players to get hip to the changes.

The unique Americana color we add to the world of Bach's chords is of course the blues. And because our blues is based on the V7 being the tonic chord, a lot of the theory that lines up to create the Bach need bending to create the blues. Know the theory is tricky to keep straight. Canadian Jazz pianist Oscar Peterson's penned "Hymn To Freedom" captures the essence of both styles; Bach and the blues, in a perfect capture.

Today, we have Bach's now 300 year old double volume WTC, a towering pinnacle of masterful musical art achievement. Perhaps as thorough an examination of harmony, from a single composer, that has ever been created? What encouraged and energized Herr Bach to want to exhaust the potentials of 12 'equal' pitches, 12 major and 12 minor key centers?

Having ... all the changes in tune to explore on one keyboard instrument ... that's my guess :)

"You have to be at the right place at the right time with the right stuff, and then you got a chance."

wiki ~ Jimmy Cobb

References. References for this page's information comes from school, books and the bandstand and made way easier by the folks along the way.

References academia Alaska. And when you need university level answers to your questions and musings, and especially if you are considering a career in music and looking to continue your formal studies, begin to e-reach out to the Alaska University Music Campus communities and begin a dialogue with some of Alaska's own and finest resident maestros !