~ sharp Eleven ~ # 11 ~

~ #11 theory rub ~

'simply moving the tritone up an octave ...'

the core of the theory the most popular spot for natural 11in voice and guitar examples also on every page

 

 

In a nutshell. With a perfect octave and a half interval above our root pitch we locate the sharp Eleven / #11. Retaining its essential tritone DNA from #4 / b5, it lends itself in similar ways to it's octave down counterpart yet in melody and chords adds some new twists. Where as the lower tritone tended to diminish ours sounds, with #11 we tend to augment and open up polytonal ideas.

So why an augmented 11th? When altering our three perfect intervals; the fourth, fifth and octave, traditional theory dictates that we use the musical term 'augment' to enlarge or 'diminish' to reduce their size. This initial change is always by half step up or down.

So in creating our sharp Eleven interval, we simply augment or increase the natural 11 by half step. As with the natural 11, harmonies written to include the #11 will in theory have a 7th and 9th also. Examine the pitches to locate the #11 above our root pitch C. Example 1.

numerical scale degrees
1
2
3
4
5
6
7
8
9
10
11
#11
12
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15
two octave C major scale
C
D
E
F
G
A
B
C
D
E
F
F#
G
A
B
C
arpeggio degrees
1
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3
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5
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7
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9
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#11
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15
C major arpeggio
C
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E
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G
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B
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D
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F#
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C

Theory names: augmented 11th, sharp 11. Increasing the natural 11th by half step opens up a new series of colors which lean towards the whole tone / polytonal landscape. Surely this is mostly in the jazz domain as our sense of tonal gravity and aural predictability evolve. On occasion these #11 colors will find their way into well crafted pop songs, nearly always as an altered Two chord. Example 1a.

Sounds like a tritone. And indeed it is. Hear the tritone quality in both the #4 / #11 intervals? Measure three whole steps ( tri-tone ) up from our root pitch and we're at the tritone. We simply transpose up an octave to sharp Eleven and voila, we've got us another tritone.

So where is this #11 colortone in the music. While occasionally in pop music, sharp Eleven is truly a jazz color. For there are players who base their thinking along these lines of the theory and their music is rather quite stunning in many many ways.

In both style settings, we most commonly find #11 as a colortone for tonic or dominant type functioning chords. For once we alter the diatonic natural 11 to #11 we no longer have the half step / b9 interval sharply dissonant pairing with the major third. Examine the pitches and sounds of sharp Eleven. Example 2.

arpeggio degrees
1
3
5
7
9
#11
13
15
C major / #11 arpeggio
C
E
G
B
D
F#
A
C

A subtle difference. Initially there's not too great an aural difference in these two colors. Of course both their triads are major, the key pitch shift in the arpeggios is the tonic major 7th lowering to the b7 of the dominant chord. This one pitch is the theoretical game changer between these two essential American components. Let's explore each one a bit and see what's what. Example 2a.

arpeggio degrees
1
3
5
b7
7
9
#11
13
15
C major / #11 arpeggio
C
E
G
Bb
B
D
F#
A
C

Tonic type chords / sharp (#)11. Tonic chords that feature the sharp (#)11 can open up and 'legally' expand the sense of tonal center beyond its diatonic boundaries. Did you pick out the D major triad in the upper part of the chord in measure two if the example just above? Check it again for the D major triad pitches; D F# and A.

arpeggio degrees
1
3
5
7
9
#11
13
15
C major / #11 arpeggio
C
E
G
B
D
F#
A
C

Pop / #11 on Two. Excluding for the moment the range of these colortones in jazz, a most common spot of the #11 is to use it to alter the diatonic minor Two chord to major. Our chord progression can thus evolve in the following manner. Example 2b.

Catching something a bit 'out there' in bar four? This basic alteration is not uncommon as it also becomes a Five of Five motion when 7th's are added. In the last idea just the triad makes it more of a pop sound. "Against All Odds', which went #1 here for Phil Collins back in the 80's, features this chordal color. "Somewhere Out There", which went to #2 for Linda Ronstadt also features this unique chordal color in the hook.

While written music that would thoroughly explore this 'two tonic realm' is clearly off the bigger picture radio playlist radar for most, it's far more common in modern day to day improvisations among advancing players. Some cats will find it and get there in every solo (?). For when sounded, it creates a respite from the original key center and its sphere of tonal gravity. Which for some artists is just where the hang is.

Generally available compositions such as the jazz essential "Blue In Green", by pianist Bill Evans opens with a written tonic #11 chord, using its 'floating' environment to gently set the piece in motion towards its core center of D minor. As it is the top of the tune, it re-invents each new chorus of its written 10 bar form.

Its recording on leader Miles Davis' "Kind of Blue" captures what was then something sounding quite new and astonishing for the times. As a ballad, there's just such a aural clarity that was captured of such essential American music artists and their art. Since its creation, intermediate to advancing jazz artists have thoroughly explored this composition and full album when seeking new enlightenments and to reset artistic defaults.

"Goodbye Again." This next composition was written to capture and portray the heartbreak of a love lost, then refound yet then lost again, creating a cycle of rebirths of love between soulmates. The opening chord in this work is along these lines of #11 and polytonal to create the unknown yet curious atmosphere for what is to come. Click the gitfiddle to hear the piece.

Tonic type sharp (#)11 voicings. The following #11 shapes are root position chords from the 6th, 5th and 4th strings. All these can work as tonic function / #11 chords, combining a tonic sense plus an easy way beyond. As like chord shapes will do, they themselves make for a cool 'mix and match' group for creating phrases as the counterpoint of the inner voices suggests possible combinations. In C, example 3.

arpeggio degrees
1
3
5
7
9
#11
13
15
tonic #11 arpeggio
C
E
G
B
D
F#
A
C

Hear anything cool? These chords may take time to assimilate onto your palette.

Tonic #11 chords in action. A fairly common spot for these chords is on the final hold of a jazz arrangement. The absence of a solid resolution leaving the listener with just a wisp of future expectations and artistic explorations. We can also use the tonic #11 to delay a resolution, so in a sense a suspension that often occurs on the downbeat. Modern cats use these tonic colors as the tonic and revel in the sense of an ambiguous sense of tonic. Which of course to them it is not :) Here's the delayed resolution idea. Example 3a.

Tonic #11 chords sure make a lovely modern Four chord too. It's been said that motion to Four is as gospel as it ever gets. Well, these last few voicings work rather nicely as diatonic Four chords. In this next idea we do just that. Create a vamp between One and Four by simply moving just our bass pitch. Although not really too gospel any more perhaps more of a modern bossa nova vamp. In G major. Example 3b.

Hear anything cool?

Dominant type chords / sharp (#)11. With the flip of one pitch we change our basis, from tonic to a dominant type chord. These dominant #11 chords can potentially possess two tritone intervals and can clearly have an augmented triad in their configuration, thus the wholetone possibilities. Examine the pitches and their sound from the root pitch C. Example 4.

arpeggio degrees
1
3
5
b7
9
#11
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C7 #11 arpeggio
C
E
G
Bb
D
F#
A
C
tritone interval
C
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tritone
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F#
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tritone interval
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E
tritone
Bb
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Bb augmented triad
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aug. triad
Bb
D
F#
.
.

Sound the same? Do these chords sound mostly the same to you? No surprise really as when the whole tone color is involved, it truly can dominate the sonority of a chord. So these last few chords are essentially the same, just different shapes starting from different strings.

The chord in the third measure is perhaps the most common augmented chord shape. Here in first inversion, so the major third of the chord is its lowest pitch. It also moves up easily up in whole steps as a constant structure, advancing its capabilities.

In this next idea, we first resolve the V9#11 chord in a fairly common manner then use its whole tone properties to ascend to the tonic minor. Example 4b.

Sharp Eleven (#11) as the final hold. In the world of day to day jazz performance, oftentimes it is based on the idea of 'arrangements while you wait.' All this really implies is that the leader of the gig creates the arrangement for the song. While this may sound open ended, which of course it can be, oftentimes seasoned players of really any style who have worked together will know how this thing is going to mostly work out.

Standard format for standard tunes. A standard format would be to use the last four or eight bars of the song as an intro, read the tune down, oftentimes twice for brighter tempo melodies or 12 bar blues, a round of solos, then head just once and tag or coda.

The tag could be many different things. Last four bars played three times is common. Creating a Three / Six / Two / Five vamp is cool going out as it gives another chance for players to blow over a common cycle of chords and find an idea to end with. Maybe the melody? Maybe, there's lots of ways.

Final hold / tonic birds eye. Thinking in a major key, the close of an arrangement is usually a cadential motion to the original tonic key of the song being performed. Once that chord is struck and held, it's not uncommon for jazzers to slip a tonic #11 chord as the final hold. It just creates that wee bit of something that gently trails away and fades to black. Example 5.

Final hold with V 9#11. In this next idea we do a similar thing with our #11 color with a few twists. We use a very common lick to end the tune and the V 9#11 as the final hold. The voicing might be a lot to quickly grab, I know it was for me. So if you've a bass player on the gig, maybe leave the root out or assign the root pitch to another. As a single I would play the grab-able for moi top part of the chord then reach over and thump the bass with me right hand. So, whatever it takes right? Ex. 5a.

Cliche. With or without the V 9#11 chord, we can find this lick and near endless variations throughout our Americana songbook. No style is immune from its presence. Well, probably. Not sure if the metalist cats ever use it. Regardless, perhaps learn it from a couple of different string sets and plug it in when Ya need it to close out a tune. Variations? Potentially endless based on your chops but even the vanilla version included above and properly sounded most often will work like a charm.

Tonic sharp Eleven arpeggio symmetry. Another neat thing about our tonic sharp #11 color is the perfect weaving of the major and minor 3rd intervals in it's creation. Termed tertian harmony, while the vast majority of our arpeggios and chords are constructed with the major and minor thirds, rare is the alternating interval symmetry as found with our tonic #11 colors.

We can verbalize the following chart by thinking that C up to E is a major 3rd, E up to G is a minor 3rd etc. Dig the pitches, the interval symmetry and their sound in C major. Example 6.

arpeggio degrees
1
3
5
7
9
#11
pitches
C
E
G
B
D
F#
intervals
maj 3rd
min 3rd
maj 3rd
min 3rd
maj 3rd

That last chord is a piano voicing yes? Pretty much. With so many pitches so close to one another it's either a piano or an orchestra to sound these combinations!

Symmetrical interval construction. Our system of music theory and its modern tuning allows for us to create evolutionary new and exciting artistic ideas with perfectly uniform patterns of construction. Like "Giant Steps" was in the later 1950's? Yep.

So we can we open up new avenues for theoretical and artistic exploration with the perfect interval symmetry of and between the pitches. Does the symmetry of the thing make it sleeker? It might. And is sleeker faster too? As when the Four chord evolves towards Two? Setting up the chromatic bass motion of the tritone sub? Can we accelerate the perception of time without actually going faster by the clicks? The arpeggiated symmetrical sequencing of major and minor thirds, is perhaps another such component to explore.

We've just a few more stops along our numerical discovery pathway and two will have this uniform symmetry of construction. While one will provide another unique and modern tonic functioning color, the second will enable us to open an entire new realm of theoretical potentials. Stay tuned :)

That last chord voicing. So the chord at the end of the last idea is quite a handful for guitar. So to sound it out we can split it into a few parts. Once divided we can choose the when and how to reconnect it up back together. This one idea or approach to sounding these 'pitchier' colors can open up a vast portal for the modern, evolving guitarist.

In another discussion here in Essentials we'll employ this technique as we create a new system for tonality and composition. Here's the above tonic #11 chord broken down into three note sections and sounded out. Ex 7.

Just superimposing triads? Yep, pretty much but the trick of it is in the perfect symmetry of the interval construction and how this symmetry can lead us from one tonal environment into another. That we can do this without any real sense of the tritone cadential motion we've enjoyed and employed for the last four centuries or so is what I think is the evolutionary direction of our future musical system. Evolve from within.

Is there a flip side to this major 3rd / minor 3rd symmetry? Absolutely. Our Yin / Yang, major / minor two part dichotomy is the mirror image of this last idea. A sequence of minor 3rd / major 3rd yields the beautiful Dorian arpeggio beloved by so many. The 'modal period in American jazz during the later 1950's and forward featured this Dorian color. Examine the pitches of this sequence from the root pitch A, the diatonic relative minor of C major. Example 8.

That chord belongs in an orchestral score. Sure does or even just a piano. Special coolness lives in that last pitch. By correctly following the sequence of intervals, that last C# signals that we're really not in Kansas anymore. So we've symmetrically arpeggiated ourselves right out of our key center? That appears to be the case mon ami and while the loop closed itself at 'A' two octaves up our next pitch is its major 3rd. So from minor into major? Yep.

Review and forward. Our #11th chords can create that sense of floating, of something not quite finished. Perhaps that's why we often find a dominant chord type V9#11 as the final chord of a jazz arrangement, to leave things up in the air a bit as to what might be coming next.

Tonic #11 chords often are used to simply delay the resolution to a more definite sense of tonic. Although in more modern music, the #11 is the tonic color as the artist is wanting that sense of being not quite settled or resolved in their tonal destination.

The interval / arpeggio symmetrical sequence we use in creating our #11th chords, if continued just a wee bit more, will ascend to create a portal which opens up into a new dimension for our creative endeavors. Not really sure of what is there but perhaps the next generation of music theorists and composers will create the music that heals our world of the often senseless tragedies and unrelenting sadness for so many in our times.

"The greatest discovery of my generation is that you can change your circumstances by changing your attitudes of mind."

wiki ~ William James
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Footnotes:

(1) Isacoff, Stuart. Temperament ... The Idea That Solved Music's Greatest Riddle, p. 40-42. USA Alfred A. Knopf, New York. 2001

(1)Duffin, Ross W. How Equal Temperament Ruined Harmony, p.32. USA W.W.Norton and Company, NY, New York. 2007.
(2)Aebersold, Jamey and Slone, Ken. The Charlie Parker Omnibook. New York: Atlantic Music Corp., 1978.

Russell, George. The Lydian Chromatic Concept Of Tonal Organization. USA Concept Publishing Company, Cambridge, Mass. 1982