A shape-note notation for a Jankó keyboard

This is to introduce the ChromaTonnetz-2 notation for a Jankó Keyboard.
I’m attaching a couple examples. One is an old hymn and the chromatic scale.
The other is a representation of jazz chords.
dtdChromaTonnetz2-Hymn-ChromaticScale
dtdChromaTonnetz2-QuietRevolution
Note that I changed color schemes and stem-side placement between the two examples.
This notation is a synthesis of various alternative notation ideas. For background and recent discussion of these ideas, see previous posts in this blog, and the Music Notation Project at http://musicnotation.org.

1. Klavarskribo, by Cornelius Pot.
Pot invented a “piano music typewriter” that produced a cross between a piano-roll and conventional notation. He used vertical staff lines with 5 lines and 7 spaces per octave, arranged as on the piano, with lines for the black notes and spaces for the white notes, the EF and BC spaces being double width. Note stems are directed sideways, and time is linear, that is, the vertical distance between note stems corresponds to the duration of time between the notes.

Recently, Antoon Dekker suggested adapting this notation to Jankó by placing the notes of the two whole-tone scales on opposite sides of the stem, and making the distance between adjacent notes equal. For example:

Eb  F   G   A   B   C#  
--------------------------------
          Ab  Bb  C   D   E   F#     
See: https://en.wikipedia.org/wiki/Klavarskribo

2. ChromaTonnetz, by Joseph Austin.
Roy Pertchik, a vibraphonist, developed a two-row “Jankó” vibraphone with two rows of bars a whole-tone apart. In addition, he developed a three-color scheme to highlighting intervals used in the “diminished scale” jazz theory of Barry Harris. Each of the three diminished chords, whose notes are a minor third apart, are a distinct color: white, black, or red, so the bars cycle among those colors. Pertchik has patented the tri-color scheme.

Centuries earlier, the mathematician Leonard Euler organized the musical scale into a hexagonal pattern called the Tonnetz, or Tone Network, in which notes are arranged in a three-axis honey-comb pattern, where notes on the horizontal are a fifth apart, notes on one diagonal are separated by a major third and those on the other diagonal are separated by a minor third, e.g.

Gb  Db  Ab  Eb  Bb  F   C   G   D   A     
  F   C   G   D   A   E   B   D   F#    
G   D   A   E   B   F#  C#  G#  D#  A# 
I was interested in creating a 12-symbol “shape-note” system in which each note of the chromatic scale would have a different symbol. And I wanted the scheme to be “isomorphic” with respect to key, not the ad-hoc collection of shapes of conventional shape-note system such as Sacred Harp and Aikin. To make the symbol-scheme isomorphic, I applied Euler’s idea of cycling major and minor thirds. I used Pertchik’s coloring, red, white, black, for the minor third intervals, as he did. For the major thirds, I wanted a representation that would cycle with period 4, and chose the triangle shape in four orientations up, right, down, left. Applying simultaneous (not nested) cycles in color (Red White blacK) and orientations (Up Right Down Left) gives the following sequence for the chromatic scale: Ru Wr Kd Rl Wu Kr Rd Wl Ku Rr Wd Kl. O. E. Soriano has recently suggested a different coloring scheme of Ivory, Navy, and Blue, and colored his Chromatone accordingly, so I’m using his scheme in the examples.
see: http://drtechdaddy.com/2010/09/24/tonnetz-based-4×3-notation/

3. Clairnote, by Paul Morris
One problem with a 12 position staff vs. the traditional 7 position staff is that it takes more space to represent the same music. Paul Morris (among others) began experimenting with ways to use color to distinguish pitch to reduce the physical space. (Of course this also requires a change to the method for distinguishing half- and quarter-notes, which previously used color.) He started with a systems that used two different colors or shapes on the same staff position to represent two different pitches, allowing a chromatic scale it fit in 6 staff positions rather than 12. This evolved into the notation he calls Clairnote, is which successive semitones are placed about a third of a note-head height apart, successive semitones are alternately colored black and white, and the staff has lines at E and G#/Ab and a ledger-line at C, lines being thus 4 semitones, or a major third apart.

Clairnote has recently become popular for the Chromatone because the color distinction, and staff lines separated by an even number of semitones, matches the Jankó separation of notes into two whole-tone rows. See: http://clarinote.org

Combining these ideas results in a new notation which I call ChromaTonnetz2: 1. It uses the note-head shape/color system from ChromaTonnetz 2. It uses the vertical staff and note-stem ideas from Klavarskribo as adapted for Jankó by Antoon Dekker 3. It uses the major-third-lined high-density staff from Clairnote.

Advantages of the new notation:

1. The shape of the notes matches the shape on the keyboard. The above-stem notes correspond to one row on the Jankó, the below-stem notes to the alternate rows. The horizontal separation of notes is isomorphic, in the same proportion as the Jankó keyboard.

2. Harmonic intervals are highlighted by note-head shape, note-head color, step position, and staff position:
– major thirds are on the same side of the stem, nearly touching, have the same orientation, and are in the same position relative to staff lines (on, above, below, between)
– minor thirds have the same color and are “diagonally adjacent” on opposite sides of the stem.

3. Being an isomorphic notation, all intervals, melodies, and chords appear exactly the same in any octave.

4. All intervals of the same harmonic distance have the same size, similar shape, and the same relationship among stem sides (same or opposite), staff line position, color sequence, and orientation sequence.

5. Software: I am developing a JavaScript program to produce ChromaTonnetz2 notation from a MIDI file or from a “piano-roll” spreadsheet. I plan to offer it as an open-source project on GitHub. Music in the attached examples was created with this software. As the examples illustrate, the system is adaptable to various choices of note-head coloring and stem-side positioning.

I am currently experimenting with coloring the staff lines, each of which has a different associated color in the tri-color system, and coloring only the keyboard keys that correspond to the staff lines. I had found that on a six-row Jankó, it was difficult to distinguish rows when all keys were colored with the same hexagonal pattern.

Given the features listed above, I believe this notation would be suitable for use in a Jankó curriculum.

Joe Austin, DrTechDaddy.com

About DrTechDaddy

Dr Tech Daddy is a retired computer science professor with additional interests in music, robotics, STEM education, model railroading, mathematical physics, congenital heart disease and heart transplant, and Christian theology.
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