Piano Note Layout
LinnStrument Fourths String Layout
When I (Roger) first started designing LinnStrument, I considered making its flat 3D-sensing rubber pads in the shape and arrangement of piano keys. However, I soon discovered that the piano note arrangement presented too many problems for the performance of expressive pitch gestures. So after researching a variety of note arrangements, it became clear that a stringed instrument layout--multiple rows of consecutive semitones overlapping in pitch-- was superior and solved the piano's problems:
Problem 1: The piano's pitch intervals aren't uniform and the black keys are located behind the white keys
On an expressive controller, the most intuitive way to perform pitch slides and bends is to slide your finger directly from one note to another. Because of the uneven pitch intervals of a piano's white keys, a pitch slide from B to C results in semitone pitch change whereas a slide from C to D (the same distance) results in a whole tone pitch change. (Imagine the difficulty of bending strings on a guitar if bending an inch on one fret produced a whole-tone pitch change, but bending the same distance on the next fret produced a half-tone pitch change.) Plus, sliding up an octave results in a series of uneven pitch jumps. Further, sliding from a white key to a black key requires a diagonal movement, which requires changing your Y-axis position.
This also presents a problem for vibrato, a common expressive pitch gesture. If a white key has a half-tone interval on one side and whole-tone interval on the other, a performed vibrato will be asymmetrical, with twice the pitch movement on the whole-tone side than on the half-tone side.
Also, because the black keys are about half the length of the white keys, they have only half the Y-axis range of the white keys. Finally, it's not isomorphic--for each chord or scale, you must learn a different fingering for each of the 12 musical keys.
Some keyboards have worked around this problem by adding a linear pitch-control strip above or below the key area. But this doesn't work because you must move your fingers from the key area to the pitch strip in order to perform pitch bends or slides. Imagine the difficulty of playing bends on a guitar if doing so required that you move your finger to a pitch-control strip on the side of the neck in order to bend pitch.
LinnStrument's stringed-instrument layout has none of these problems. Because the interval between adjacent notes is always a semitone, pitch slides are always uniform, pitch slides are intuitively performed by sliding from fingered note to fingered note, vibratos are always symmetrical, each note has exactly the same Y-axis range, and when the rows are tuned to the same interval (as in the default Fourths String Layout), it is fully isometric-- for each chord or scale, the same fingering is used for all 12 musical keys.
Problem 2: The piano's notes are arranged in one long single line
Why? Because a few centuries ago, there needed to be a string behind each key, a requirement that no longer exists in electronic controllers. This presents a few problems.
First, if the left hand is playing bass notes and the right is playing treble notes, the hands are too far apart to watch both at the same time. Second, there is only one instance of each pitch, so you can’t play the same note in different hands at the same time, or play chords and melody in the same pitch range. Third, you can't stretch more than a musical tenth interval in one hand. Fourth, it's not very portable.
LinnStrument's stringed-instrument layout has none of these problems. Because of its overlapping rows of notes, the hands are always fairly close together and therefore easy to see both, each pitch has multiple locations making it possible to play the same note in both hands, and you can stretch up to 3 octaves in one hand. In the default Fourths String Layout tuning, the large LinnStrument model's 200 note pads provide a five-octave range (due to the overlapping pitches), same as a standard MIDI keyboard. The smaller LinnStrument 128 provides a four-octave range. And at 22.5 inches long by 8.25 inches wide by 1" thick and only 5 pounds, it's much lighter and more portable.
Like strings on a guitar, LinnStrument's rows of consecutive semitones can be tuned however you like. But the most popular tuning—and LinnStrument's default tuning—is in intervals of musical fourths (five semitones between rows), which is like a bass guitar or the lower four strings of a guitar. The name for this is the "Fourths String Layout". This note arrangement turns out to provide the ideal note density for chords and scales, yet still provides a full five octaves of pitch range on LinnStrument, same as a standard MIDI keyboard, or four octaves on LinnStrument 128.
And others have noticed this too. It's a standard note arrangement in Ableton Push, ROLI Blocks and the GeoShred, GeoSynth and Musix Pro apps for iPad. Plus, of the few MPE controller available today, four of them--LinnSrument, Continuum, SoundPlane and Eigenharp—abandoned the piano layout because of its problems for expressive performance.
What makes the Fourths String Layout worthy of so much attention? Two reasons:
1) The most natural and intuitive way to perform pitch bends and note-to-note pitch slides is to slide your finger directly from the starting pitch to the ending pitch. This requires that the semitones are arranged consecutively in rows, just like a string of a stringed instrument.
2) Like a stringed instrument, multiple strings/rows of consecutive semitones permit easier chords and scales than a single string/row. So the only question is "What is the best pitch interval between rows?" Guitar tuning may seem like a good idea, but without open strings and therefore open chords on LinnStrument, the isomorphic advantages of a uniform row interval outweigh the familiarity of guitar tuning. Assuming isomorphism is a primary goal, then the question becomes "What is the best uniform row interval?". Fifths tuning (7 semitones as on violins and cellos) is too great an interval to finger many common chords in one hand. An interval of 6 semitones provides the advantage of aligned octaves on alternate rows, but moving up by 6 semitones on adjacent rows is not so intuitive, and the relatively large interval makes common chords difficult to finger in one hand. Thirds tuning (4 semitones) permits playing most chords in one hand, but the total pitch pitch range of the playing surface is too limited. But fourths tuning (5 semitones) permits easy fingering of any chord or scale, provides a very good total pitch range, and is highly intuitive, given that fourth intervals are common in most musical forms. .
Another option is a matrix of hex keys. However, if you want the want the advantages of intuitive pitch gestures explained in #1 above, you still need horizontal rows consisting of consecutive semitones. If so, then a hex keyboard is merely a grid with alternate rows shifted over by 1/2 column then squished down between the keys of the adjacent row to form hexagons. Instead of integer pitch intervals between grid rows (4, 5, 6, 7, etc.), the hex row intervals would be 3.5 or 4.5 or 5.5 or 6.5, etc. To illustrate this, here is a picture of what LinnStrument might look like with a hex-key playing surface and with a row offset of 4.5 semitones. While this layout has merit, I (Roger) find it less intuitive to form chords or to play single lines than a grid and therefore don't see an advantage.