Inconsistencies in Common Western Music Notation

Introduction

The benefits of the ThumMusic (Pitch) System arise from its use of isomorphism – specifically, an isomorphic note-layout (the ThumField) and tonnetz (the ThumLattice). Using isomorphism more widely could produce even greater benefits, although at the risk of incompatibility with existing systems. Before discussing the ThumMusic PLUS System and its benefits, let's examine the inconsistencies of the traditional approach to displaying musical information.

The Five Inconsistencies of the Common Western Music Notation (CWMN)

Despite the central and pervasive role of intervals in music, the Common Western Music System is focused on pitches. In Common Western Music Notation (CWMN), for example, each line and space represents a specific pitch (in Hz), with the A above Middle C representing (by international treaty) the pitch 440Hz.

Figure 11 shows the traditional hymn “Amazing Grace” notated in the key of C using CWMN's treble clef.

Figure 11

Figure 12 shows the same song notated in CWMN's bass clef. A comparison of the two shows that the notes from identical pitch classes are placed in different vertical locations in the treble and bass clef – thus demonstrating CWMN's inconsistency between clefs.

Figure 12

Figure 13 shows the same song as that in Figure 11, in the same key, written in the same clef but an octave higher. A comparison shows CWMN's inconsistency between octaves.

Figure 13

Figure 14 shows the same song written in the treble clef in the key of F and comparison with Figure 11 shows that individual pitch is notated differently, even if the intervals between them are the same. This demonstrates CWMN's inconsistency between keys.

Figure 14

Figure 15 shows a chromatic octave in CWMN's treble clef from middle C upwards, also showing the note that is a major third (four semi-tones) above each chromatic note, using sharps as necessary. Thus the musical interval between each pair of notes is identical and yet the spatial distance between vertical pairs is inconsistent.

Figure 15

A completely different pattern of vertical spacing emerges from the use of flats instead of sharps as can be seen in Figure 16. This demonstrates CWMN's inconsistency of interval spacing.

Figure 16

Common Western Music Notation has another inconsistency, rarely recognized: an inconsistency across meantone tunings. A notational system which was consistent across meantone tunings would facilitate the creative exploration of such tunings, whether historical, cross-cultural, or novel.[13]

Four of these five inconsistencies – between clefs, octaves, interval spacing, and keys – are well-known. New notation proposals have flourished ever since Guido d'Arezzo invented the first four-line staff (denoting the pitches of the diatonic scale in the key of C (although Guido would not have described it that way) in roughly 1026 AD. Over 500 alternative music notation schemes are described in Music Notation Modernization Association's “Directory of Music Notation Proposals.”[14] None of these proposals has provided a sufficiently-compelling benefit to become broadly popular (except for guitar tablature, for reasons that will be discussed below).

These inconsistencies appear most prominently in CWMN's staff notation, but are equally present in traditional musical instruments including the piano-style keyboard, the guitar fret-board (in standard tuning), and in almost all other musical instruments.

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