WebHexIso: A Customizable Web-based Hexagonal Isomorphic Musical Keyboard Interface Hanlin Hu David Gerhard University of Regina University of Regina [email protected] [email protected] ABSTRACT The research of musical isomorphism has been around for hundreds of years. Based on the concept of musical iso- morphism, designers have created many isomorphic keyboard- based instruments. However, there are two major con- cerns: first, most instruments afford only a single pattern per interface. Second, because note actuators on isomor- phic instruments tend to be small, the hand of the player can block the eye-sight when performing. To overcome these two limitations and to fill up the vacancy of web- Figure 1: Euler’s Tonnetz based isomorphic interface, in this paper, a novel customiz- able hexagonal isomorphic musical keyboard interface is introduced. The creation of this interface allows isomor- In addition to the limitation of square isomorphism, there phic layouts to be explored without the need to download are two main constraints of isomorphic keyboard design: software or purchase a controller. additionally, MIDI de- firstly, most of the interfaces can provide only one par- vices may be connected to the web keyboard to display the ticular isomorphic layout, which means the layout is not isomorphic mapping of note being played on a MIDI de- changeable or in the other word, the device is not customiz- vice, or to produce control signals for a MIDI synthesizer. able, therefore the performers or composers are “locked in” to a single layout. Although learning a single layout may be desirable in some circumstances, one of the main advan- 1. INTRODUCTION tages of isomorphic keyboard design is the fact that many Since Euler introduced Tonnetz in 1739 [1], mathemati- different layouts with different harmonic relationships are cian, composers, computer scientists and instrument de- available in the same framework. For this reason, we think signers are interested in musical isomorphism, which presents that the limitation of a single isomorphic layout on most algorithms of arrangement of musical notes in 2-dimensional hardware instruments is a significant disadvantage which space so that musical constructs (such as intervals, chords should be addressed. and melodies, etc.) can be played with same fingering Secondly, when performers or composers play on the phys- shape regardless the beginning note [2]. ical appearance of an isomorphic keyboard, their hands Based on this concept of musical isomorphism, there have can easily block the display so that the name or colour of been a number of keyboard-based interfaces (instruments) keys is not easy to see. For traditional single-layout instru- being built over the last hundred years. At the beginning, ments, this is not an issue because performers memorize the keys on the keyboard were designed in the shape of a and internalize key-actuator positioning, but for reconfig- rectangle resembling that of the traditional keyboard. This urable digital instruments, where colour may be the only is called “square” or “rectilinear” isomorphism. Since the indication of the function or note of an actuator, the prob- limitations of the square isomorphism (e.g. the degenerat- lem of actuator occlusion may be considered significant. ing of layouts, which is passing by some notes in a equal One possible solution would be to separate the display of temperament with particular layouts [2]), interface design- the reconfigurable keyboard from the actuators. Although ers prefer hexagonal shaped keys on the keyboard over the this separation may be considered a step back in terms of last decade. They can be categorized to hardware and soft- usability and control/display integration, it may serve to fa- ware. As for hardware, there are the AXiS keyboards, cilitate exploration of this new class of reconfigurable in- Opal, Manta, Tummer and Rainboard [3]; As for software, terfaces. Further, although it is possible to plug a MIDI there are Hex Play (PC) [4], Musix Pro (iOS) [3], Hex OSC device into an iPad and play isomorphic software such as Full (iOS) [5] and Hexiano (Android) [6]. Musix Pro, practically speaking, because many MIDI de- vices draw power over the USB port, it is sometimes im- practical or impossible to connect a MIDI device to an iPad Copyright: c 2016 Hanlin Hu et al. This is an open-access article dis- or other external display. tributed under the terms of the Creative Commons Attribution License 3.0 In this paper, we present a novel web-based hexagonal Unported, which permits unrestricted use, distribution, and reproduction isomorphic musical keyboard interface, which is customiz- in any medium, provided the original author and source are credited. able, scalable, and MIDI enabled. It can be used as a soft- ware instrument, a composition device, an educational tool of musical isomorphism, and an assistive screen interface C# D# F G A B C# D# F G A B ... for performance. C D E F# G# A# C D E F# G# A# ... 2. MUSICAL ISOMORPHISMS C# D# F G A B C# D# F G A B ... The word “isomorphism” has the prefix “iso,” which means “equal,” and an affix term “morph,” which means “shape.” C D E F# G# A# C D E F# G# A# ... Isomorphism, then, refers to the property of having an iden- tical shape or form. The concept of isomorphism applied to music notations is that for an isomorphic arrangement Octave Octave of notes, any musical construct (such as an interval, chord, 1 2 or melody) has the same shape regardless of the root pitch Figure 2: Janko´ Keyboard tessellation of the construct. The pattern of constructs should be con- sistent in the relationship of its representation, both in po- sition and tuning. Corresponding to transposition invari- C# D# F G A B ance, tuning invariance 1 is another requirement of musical isomorphism. Most modern musical instruments (like the C D E F# G# A# piano and guitar) are not isomorphic. The guitar in stan- C E G dard tuning uses Perfect Fourth intervals between strings, (a) C-Major on Piano (b) C-Major on Janko except for the B string which is a Major Third from the G C# D# F G A B string below it. Because of this different interval for one F# pair of strings, the guitar is not isomorphic. C D E F# G# A# Isomorphic instruments are musical hardware which can D A play the same musical patterns regardless of the starting (c) D-Major on Piano (d) D-Major on Janko pitch. Isomorphic arrangements of musical notes intro- duce a number of benefits to performers [7]. The most Figure 3: Isomorphism in the Janko´ keyboard as compared notable of these is that fingerings are identical in all musi- to polymorphism in the piano keyboard. cal keys, making learning and performing easier. Modern instruments which display isomorphism include stringed instruments such as violin, viola, cello, and string bass [3]. the desired notes. Each vertical column of keys to the ad- It should be noted in this case that although the relative po- jacent column are a semitone away, and the horizontal row sition of intervals is the same for every note on the finger- of keys to the adjacent row is a whole step away. This de- board of a violin, the relative size of each note zone may sign never became popular since performers are not con- change, with the notes being smaller as you move closer vinced of the benefits of this keyboard and they would in- to the bridge of the instrument. The traditional piano key- stead have to spend more time learning a new system [9]. board is not isomorphic since it includes seven major notes This arrangement of notes on the Janko´ keyboard is iso- and five minor notes as a 7-5 pattern. morphic because a musical construct has the same shape Thanks to this 7-5 pattern design, performers can eas- regardless of key. Consider a Major triad (Fig.3). the C- ily distinguish in-scale and out-of-scale notes by binary Major triad has the notes C-E-G, while the D-Major triad colours, but the performer must remember which white has the notes D-F]-A. On the piano keyboard, these tri- notes and which black notes are in the scale in which they ads have different shapes, but on the Janko keyboard (and are performing. Because the piano is not isomorphic, dif- on any isomorphic keyboard) these triads have the same ferent fingerings and patterns are required when perform- shape. In fact, every major triad has the same shape on an ers play intervals and chords in different keys. This is one isomorphic keyboard. of the reasons that the piano is difficult to learn: each mu- There are three reasons why hexagonal shaped keys are sical construct (e.g. the Major scale) must be learned sep- better than rectangular shaped keys: arately for each key (e.g. C Major, G Major, F Major etc.) 1. The rectangular shaped keys of an isomorphic key- The first physical appearance of an isomorphic layout board does not meet the requirement of transposition in- was decided by Hungarian pianist Paul von Janko´ in 1882 [8]. variance perfectly, because the Euclidean distance between The Janko´ keyboard shown in Fig.2 was originally de- two keys is not identical. For example, in Fig.2, the dis- signed for pianists who have small hands that can cause tance between C and D in horizontal direction does not fingering difficulties when stretching to reach the ninth in- equal the distance between C] and D in vertical direction. terval, or even the octave, on a traditional keyboard.