The Power of the 3rd Rail!

( A shorter version of this video is here: https://youtu.be/_GrkDEKBHAU ) A paradigm change: The fretboard starts between the G and B strings. These two strings comprise the "3r Rail" which is the center of a primary diatonic symmetry. As a metaphor derived from electric rail systems like the NYC subway, the "third rail" is usually characterized as a thing that is too dangerous to touch, usually in business or politics. But while the 3rd rail is lethal to the touch, it also powers the train. So it is a double-edged sword, to mix metaphors. Locating the positions of the natural tones (the key of C major/A minor) becomes more logical when recognizing the inherent symmetry of the Diatonic keys starting with C. This is most clear when starting from the 3rd Rail. Index: 00:00 — Intro ... What is the 3rd Rail? 00:53 — Why is the 3rd Rail? ... How does the tuning of renaissance viols pertain to the tuning of the guitar? ... The standard guitar tuning is not all about playing barre chords! 03:26 — The Pentatonic Axis ... Every fret on the guitar is a pentatonic scale. ... There is only one major 3rd in a pentatonic scale. 04:45 — How Can We Use the 3rd Rail? ... The key of C major is built around the 3rd Rail. ... The three major 3rds in the key of C are positioned symmetrically on the 3rd Rail. 07:27 — 3rd Rail Major and Minor 3rds ... Three major 3rds and four minor 3rds in every key. ... The symmetry of major and minor 3rds on the 3rd rail. 8:57 — Mapping Diatonic Symmetry ... The symmetry of diatonic intervals. ... 7th arpeggios on the four top strings. 11:08 — The Primary Symmetry ... Animated diagrams of the rotational/palindromic symmetry from several perspectives. ... Comparison between the guitar symmetry and that of the piano keyboard. 15:32 — The fretboard begins on the 3rd rail C major 3rd ... at the 5th fret. ... What better way to understand the symmetry of the system than to start at the center of the system? 18:53 — Mission Statement and Thanks! ... A paradigm shift: Thinking about the guitar fretboard that begins at the 5th fret, on the 3rd string. ... More to come. © 2024 Mark Newstetter https://marknewstetter.com ================ More about the Renaissance guitar: https://www.laguitarra-blog.com/wp-content/uploads/2012/03/strining-and-tuning-the-renaissance-four-course-guitar.pdf The Metropolitan Museum Instrument Collection: https://www.metmuseum.org/art/collection/search?department=18&showOnly=highlights&q=guitar

Diatonic Map of the Guitar Fretboard

I will be updating this post with text and diagrams pertaining to this video. If you've already watched the video, check back soon. If you haven't ... please watch and study the video and let me know if any questions or thoughts.

Thanks!

Long Version:

Short Version:

In this video I present a method of mapping the diatonic system on the guitar fretboard in standard tuning. I've been using and refining this method for decades with many hundreds of private students to excellent results.

I was motivated to develop this map because, while there are many guitar methods which cover various aspects of playing scales, chords, arpeggios, riffs, etc ... there is no standard method for mapping and identifying the structures of the diatonic keys in their own right.

As the guitar presents the player with the challenge of simply knowing were all the notes are within each key, I became focused on finding a way to delineate key structures in a way that would be clear and accessible so that I could find any note in a key by knowing their relative physical positions.

Since all keys have the same structure, they also have the same geometric arrangement on the fretboard. It's just a matter of deciding how to depict and identify these structures. Having been unable to find any such map after years of searching, I created my own, which I make available here:

A page from my forthcoming book: "Commonalities" ...

More Modal Madness Galore!

Before you venture into this ... please study the previous post: 

https://fretography.blogspot.com/2023/03/diatonic-symmetry-galore.html

Now ... where were we?

Ok ... we're making connections between modes and keys across the diatonic system. Modes do not only exist in separate keys with walls around them. The cross key relationships we find in so much music have their own logic, grammar and flow.

The character of each mode becomes a pathway from one musical idea to another. We sense when the key has changed, and it is modality that provides the framework of coherence of the harmonic and melodic threads. 

Since Dorian mode is diatonically central, lets see how it connects to the seven keys drawn from its traverse of natural tone finals ...

The natural tones across the top, bottom, left and right of each diagram are the finals of seven modes in  seven keys. The tonic of each key is found where the blue lines cross.

The blue lines are anchored on each mode with D as the final.

Since all the modes stem from natural tones, it's easy to trace the connections between the keys through their modes. Each mode receiving this treatment will yield a different patter.

Particularly relevant is the connection between the placement of the secondary keys (blue lines) and the common tones (grey lines) and the symmetrical modal relationships.

Look at the palindromic pairs of modes ... those modes who's interval structures mirror one another: 

 

It becomes clear that while there are symmetries to be found in the treatment of the natural tonic (shown in the previous post), the symmetry is far clearer when applying the logic to the natural supertonic ... D.

Notice that all seven converged keys have natural tonics, where using C as the finals of all the modes led to the keys of C, G, F, Db, Eb, Ab and Bb. Also notice the the blue line crossings always converge with a grey line, which does not happen with the yellow lines in the previous post.

The symmetry is clear, which is to be expected with Dorian mode, and why this mode is so essential as a starting place for understanding the Diatonic System

Modal Symmetry Galore

The symmetry built into the Diatonic system has many manifestations. One of the most compelling is the phenomenon of modal common tones.

Deep Symmetry

The modes form palindromic interval groupings ...

Ionian and Phrygian, 

Locrian and Lydian, 

Aeolian and Mixolydian,

... and Dorian mode ...

The intervals within each mode are part of the overarching Diatonic symmetry. Study the interval structure of the modes ... notice the palindromic pairings:

Common Tones connect seven keys in a modal continuum ...

Modal Common Tones

When the notes of Major scale (Ionian mode) each become the tonic of a new key there is but one note common to them all. In the Key of C are the notes C D E F G A B ... the scale will include the complete octave — C D E F G A B C.

Make each of these natural tones the Tonic, and you have seven keys, and within each of them is the note 'E' ... the III of the original key. There will be no other note to find a place in all seven keys.

That's interesting enough, but there's more!

Do this with all of the seven Modes, and you'll find the correlation between Mode's interval symmetry and the Common Tone Counterpart groupings.

Common Tone Counterparts are those notes that link the diatonic symmetry due to their corresponding key degrees.

Just as Ionian and Phrygian are a palindromic pair, the notes C and E are positioned symmetrically around the central note of the key: D ... as are B and F, as well as A and G ... and their respective modes.

These images show the common tones in each mode. In each case — within seven keys which have Natural tones as their tonics:

(The tonics are always found in the column with C at the top and bottom, i.e.: the tonics for the Phrygian mode above are C Db Eb F G Ab Bb. The tonics for Aeolian mode below are C D Eb F G Ab Bb.)

The reciprocal relationships between modes and their counterpart common tones is profound!

... It reinforces the centrality of the Tritone ...

... and of the Dorian mode which stems from the 2nd Key Degree ...

All of this plays out on the fretboard with absolute consistency.

Notice the rotational symmetry of Key Degree relationships on the fretboard within the upper and lower string groups:

I is opposite III

VII is opposite IV

VI is opposite V

and II is opposite II

Just how the fact of this symmetry can factor into music in practice is a complex subject. Save to say that awareness of a thing naturally generally precedes one's understanding of it. 

The Modal Common Tone can be a pivot between keys. It has a different function in each, but ... there it is. Is there a difference between key transitions with or without common tones?

There must be a mathematical formula which expresses all this. Since I'm about as good a mathematician as I am a brain surgeon, I'll leave the math to others.

Also of interest is how these commonalities align with the Circle of 5ths and 4ths. 

On the left side of the circle are flat keys (keys containing one or more flat) and on the right side are sharp keys (keys with one or more sharp). The interval symmetry of counterpart modes plays out in the incidence of flat and sharp keys expressed by each mode. Since the key of C is all natural tones, the remaining keys are an equal number, with  F# and Gb each occurring only once — through Lydian and Locrian respectively — among the common keys ...

Common Keys

C Ionian: C, D, E, F, G, A, B

E Phrygian: C, Db, Eb, F, G, Ab, Bb

________________________________

F Lydian: C, D, E, F#, G, A, B

B Locrian: C, Db, Eb, F, Gb, Ab, Bb 

________________________________

A Aeolian: C, D, Eb, F, G, Ab, Bb

G Mixolydian: C, D, E, F, G, A , Bb

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D Dorian: C, D, Eb, F, G, A, Bb 

Among keys which are not found within each mode is the following array ...

Non-common Keys:

 

C Ionian: Bb, Eb, Ab, Db, and Gb or F#

E Phrygian: B, E, A, D, and Gb or F#

________________________________

F Lydian: Bb, Eb, Ab, Db, F

B Locrian: B, E, A, D, G

________________________________

A Aeolian: B, E, A, Db, and Gb or F#

G Mixolydian: B, Eb, Ab, Db, and Gb or F#

________________________________

D Dorian: B, E, Ab, Db, and Gb or F#

A careful analysis of the balance of sharp keys and flat keys within counterpart modes will reveal a clear symmetry vis-a-vis the Circle of 5ths as they are equally distributed.

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What do we do with this knowledge? 

That question can best be answered by asking another question:

"What do we do with nouns and verbs?" 

On the most basic level, these ideas are simple matters of fact ... like the Circle of 5ths. The interlocking relationships between common modes across multiple keys builds upon the Major key-Minor key paradigm usually associated with the Circle of 5ths. What applies to Ionian and Aeolian modes also factors into connections between all the other modes, and that's not limited to I - IV - V patterns.

The common tone connection brings chromaticism into the mix. How does that relate to, say, Melodic and Harmonic Minor ?

Recapping: Modal Logic

Any mode, when used as the source of seven tonics (or finals), will share with all of them one — and only one — common tone. That common tone will be the final of its palindromic counterpart mode.

For example:

The common tone of Ionian mode is its 3rd degree. That note is the final of Phrygian mode, which has a common tone on its 6th degree ... which is the final of Ionian mode.

The final of Lydian mode is its 4th, and the final of Locrian mode is its 5th. 

The final of Aeolian mode is its 7th degree, and the final of Mixolydian mode is its 2nd ...

Since Dorian mode is its own palindrome, its common tone is its own final ... note number 1.

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Secondary Source Keys*

The Secondary Source Key (or 'Parallel Source Key') for each modal group is the major key built from the modal scale with the note C as its final. There is an inverse relationship between the place of the tonic of each Secondary Source Key and the degree of the mode itself in the major scale overall. (*This terminology is original. I'm unaware of any existing term for this precise phenomenon.)

The Secondary Source Key for each mode:

C Ionian (tonic mode) =  C ... its own tonic.

C Phrygian (mediant mode) = Ab ... it's own submediant.

 C Locrian (leading tone mode) = Db ... its own supertonic

C Lydian (subdominant mode) = G ... its own dominant

 C Aeolian (submediant mode) = Eb ... its own mediant

 C Mixolydian (dominant mode) = F ... its own subdominant

and for C Dorian (supertonic mode) = Bb its own subtonic.

Here are the diagrams with the major tonics indicated by yellow highlights. Notice that the major tonic of the secondary source key, in each case, is where the two lines converge:

 

These layers of diatonic symmetry — each layer being balanced within itself — form overlapping asymmetries which in turn reveal interesting commonalities. Though the modal common tones follow the intervalic mirroring of mode pairs, the secondary source key relates the degree of the mode final within the original source key, to its own internal degrees. 

Put another way; the diatonic place of each mode's final has an inverse interval relationship to its relative major tonic. II is the inverse of bVII, III is the inverse of VI, IV is the inverse of V ... I is, of course, is own inversion.

The particular aspects of modal commonalities across keys delineated here are by no means the only possibilities, but they represent a way into this realm harmonic complexity.

...

Next: https://fretography.blogspot.com/2023/03/more-modal-madness-galore.html

Fretboard Landmarks ... Know the Notes (and More)

A wide-ranging lesson on several methods of note-knowing along with a healthy portion of music theory geekery. Index: 00:00 — Intro 00:27 — Up and down each string with Natural Tones 01:00 — Half Steps and Whole Steps on Each String 02:06 — Open Strings as a Landmark - E A D G B E 03:05 — Open String Intervals " 4 4 4 3 4 " 04:11 — 5th Fret Intervals " 4 4 4 3 4 " = A D G C E A 05:09 — 10th Fret Intervals " 4 4 4 3 4 " = D G C F A D 06:13 — Graphic: Where the Natural Tones Line Up 07:10 — Graphic: The Piano Keyboard Half Step Connection — BC EF 10:36 — Graphic: EF BC EF BC EF BC ... 11:05 — A D G 11:45 — Quick Review ------------------------- Other Methods: 13:16 — The Big Box 13:35 — Graphic: The Box Rooted on the 6th String 15:24 — Graphic: The Box Rooted on the 4th String 15:36 — The "3rd Rail" 18:11 — Graphic: The Box Rooted on the Open 3rd String 19:03 — 3 Shapes / 4 Positions of the Big Box 19:15 — Graphic: Comparison of the 6th String and 5th String Big Boxes 20:30 — The Big Big Box 20:50 — Graphic: All the Natural Tones between the 3rd and 7th fret 23:30 — Graphic: The III Zone 26:53 — Graphic: The VII Zone 28:14 — Do it in Both Directions — the 'Backwards' Alphabet 29:44 — Outro ------------------------- 30:18 — End Title Music: "Wisest Dreams" excerpt © Mark Newstetter

Guitar Interval Truth

A minor 2nd is always a half-step ... but so is an augmented 1st! A whole-step is two half-steps and a major 2nd is always a whole-step, but a whole-step is not always a major 2nd ... a whole-step can also be a diminished 3rd! A minor 3rd is three half-steps, but so is an augmented 2nd ... How can that be? We look at the perils of counting intervals by half-steps only ... and we'll emphasize the importance of the alphabet!

Intro music excerpt: "Lucky Number" by MN - https://youtu.be/hOCNoxzA6jY Outro music excerpt: "The Only Color in the Sky" by MN - https://youtu.be/Xph8wfuzfgo Guitar, piano and bass : M. Newstetter Drums: Joyce Baker Recording Engineer: Rob Preston Link to Interval Chart: https://fretography.blogspot.com/p/di...

The Symmetrical Guitar!

 

This video highlights an essential navigational element on the guitar fretboard. The juxtaposition of the Diatonic Axis positions and the 3rd Rail.

__________________________________________ Index of Highlights: 00:00 — Intro 00:25 — 'Four-top-string' 7th chord arpeggios — key of C 01:49 — Diagram of 7th chord symmetry 02:12 — The same arpeggios in D 02:38 — Finding the middle of the middle 03:51 — Fingering tricks 04:34 — Palindrome of the V and the viiº chord 05:23 — Landmarks on the 3rd Rail ( I - IV - V ) 08:05 — The four minor 3rds 08:10 — Counting 'Fret Spans' 15:19 — What comes after C? (high volume issue?) 18:52 — Visualize the keys 20:21 — Summing up (high volume issue?) 21:44 — Outro __________________________________________ More about Symmetrical Arpeggios: http://fretography.blogspot.com/2011/12/7th-chord-symmetries-around-3rd-rail.html http://fretography.blogspot.com/2011/12/7th-chord-symmetries-around-3rd-rail_18.html http://fretography.blogspot.com/2011/12/7th-chord-symmetries-around-3rd-rail_19.html http://fretography.blogspot.com/2011/12/red-diagonals-indicate-minor-3rds.html Tab and Notation: https://fretography.blogspot.com/p/symmetrical-arpeggios-7ths-upper-string.html __________________________________________ Musical excerpts from my songs: 'Lucky Number' * ( 00:07 and 22:18 ) 'Can't Blame it All on the Drug' ** ( 05:23 ) 'Tea and Cactus' ** ( 15:19 ) 'Wisest Dreams' ( 18:52 ) Personnel: Guitar, Bass, Percussion: Mark Newstetter * Drums: Joyce Baker ** Drums: Dave Scheff  

Special thanks to Lucy Hudson All music and visuals © 2022 Mark Newsetetter