The Diatonic Scale and Musical Empowerment

Phil Nice
7 min readOct 8, 2017

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Western music is built up over a sequence of tonal steps with a distinct signature. This sequence is generally referred to as “the diatonic scale” and is arguably known to one and all as the seven tones pertaining to the syllables “do, re, mi, fa, sol, la, ti” (or variations hereof) and ending on the eighth note “do” again, completing the eight note cycle we call an “octave.” We would recognise it as the pattern of notes sounding from the white notes of the keyboard. In its original, pure form, it builds on natural phenomena, occurring as the product of a chain of six perfect fifths and described mathematically as a set of consonant frequency ratios like the octave (2:1), the perfect fifth (3:2) and the perfect fourth (4:3). This results in a sequence of whole tones and half tones (semitones) in a set pattern.

The diatonic scale (just intonation) with tonal ratios expressed as factors. The steps are not uniform, but describe a pattern of whole and half steps. If do were 260Hz, for example, (approximating to modern middle C), then sol (G), a perfect fifth above it, is given by 260 x 3/2 = 390Hz, whilst do’ (C above it) is 260 x 2 = 520Hz. In other words, for every vibration of do (whatever actual note it is), fa will vibrate 1 1/3 times (4:3), sol will vibrate 1 1/2 times (3:2) and do’ will vibrate exactly twice. These pure relationships occur naturally as overtones or partials in vibrating materials like stretched strings or the air in pipes, horns, whistles etc.
In the key of C (on the white notes, where C is do), the differing steps are easily identified by the distribution of the black keys. From E to F (mi to fa) and B to C (ti to do) are half steps or semitones, identifiable by the lack of a black note in between. Whilst the alphabetical note names (A, B, C, D etc.) are fixed to specific piano keys and pitches, the steps of “Solfege” (do, re, mi etc.) are moveable to any key. If do is moved to D, for example, mi must become the black note F# instead of F, whilst ti must become C# instead of C in order to maintain the constant pattern of whole tones to semitones up the scale.

Use of the diatonic scale appears to date back to prehistory. Babylonian and Sumerian inscriptions have been found describing this tuning system, as have ancient Chinese flutes whose holes are positioned so as produce a close approximation to the diatonic scale. Even though musical systems have evolved and diversified into much more complex forms, this basic, original sequence, like a piece of musical DNA, still underpins most of the music we sing, play and listen to today, not only in the West, but the world over.

In the middle ages and up to the baroque era, the diatonic scale could be weighted in various ways, resulting in seven different “modes” (an early concept of “key”) depending on the starting note or “tonal centre,” of which six (three major and three minor) were in regular use, whilst the seventh (regarded as bereft of musical value) was discarded. After the advent of the 12-tone, chromatic octave and a different concept of “key” (in the later Baroque and Classical periods) most music now operates within two broad modes: major (tonal centre: do) and minor (tonal centre: la), each of which are subject to chromatic variations, i.e. where the scale gets modified by the use of other tonal steps, foreign to the diatonic pattern. Arguably the major development of the Classical period was the harmonic theory now known as “common practice” or “functional harmony” in which notes and harmonies (chords) operate within a system of both weight and direction, perhaps best understood as a kind of “grammar” within music. This grammar has its roots directly planted in the internal relationships of the diatonic scale.

Chromaticism, essentially the free movement between varying scales and keys within common practice, is therefore not a rejection of the diatonic system, but rather an extension of its basic tenets within a 12-tone equally tempered octave. Within intellectual spheres of Western art music, systems have grown up that do reject the diatonic system, like serial music (all 12 tones have equal weight) or modern modal music (non-functional harmony). These operate on other rules than common practice, but are still built on the tonal framework (12-tone equal temperament) and many harmonic elements (chords) that have their origin in the diatonic system.

A section of keyboard, showing the modern 12-tone octave (from any note to the next with the same name). This is a relatively modern development of an ancient instrumental surface. For most of its history, the keyboard comprised only the “white” notes, until Bb was added as an alternative to B (or B as an alternative to H), gradually followed by the rest of the “black” notes as the modern concept of musical key evolved. The black notes have two alternative names, depending on the key/context in which they are used. This double naming also reflects the fact that the 12-tone octave is the product of a compromise in tuning or “temperament.” Any single piano key plays a note that is a compromise between two naturally occurring ones. If just intonation (the natural tuning that produces the diatonic scale) is extrapolated the 12 tone octave, a mismatch arises between the natural intervals and the octave.
In just intonation, a semitone (like mi to fa or ti to do) is given by the ratio 16:15. Stacking 12 semitones on top of each other should make an octave, but there is a problem. 16/15 ^ 12 ≠ 2. The natural semitones are too large and therefore incongruous with the octave. A similar mismatch occurs between natural fifths and the octave, where a stack of 12 perfect fifths (3/2 ^ 12) should equate to seven octaves (2 ^ 7) but doesn’t. This incongruity, known as the “Pythagorean comma,” is large enough to render certain of the 12 musical keys out of tune. To make up for this, many temperaments have been tried, culminating in 12-Tone Equal Temperament (12 TET), in which the octave is the only pure or just interval (2:1) and is divided into 12 equal semitones by the ratio 2 ^ 1/12. This compromise sacrifices the purity of just intervals for a 12 tone octave that “resolves” a cycle of fifths, i.e. giving 12 fully equivalent musical keys.

As both a natural phenomenon and the cultural basis of Western music, the diatonic scale would seem a natural starting point for the teaching of musical skills. Indeed, in my own approach to teaching music, I have made the assumption (based on the available research) that the diatonic scale is prior knowledge for any normal, musically receptive person. It is not necessary to teach the sound pattern of it. Like one’s native spoken language, it has been acquired in early development by exposure and some form of predisposition.

It is the implicit knowledge of this pattern of tonal steps, the ability to discern between tonal relationships, that is normally referred to as “the musical ear.” Without it, we would have no recognition of melodic and harmonic content in music, be unable to discern between one tune and another. People who claim to be “tone deaf” in most cases aren’t. If they listen to music, glean pleasure from it and can tell one tune from another, then they possess a musical ear. Studies show that true “tone deafness” or amusia (the scientific term for the congenital or acquired inability to process music) occurs in under 4% of the population. Singing out of tune or having difficulty accessing or using one’s musical ear for musical activities (other than just listening) are not in themselves evidence of tone deafness.

The fact that many people claim this or otherwise undervalue their musical prowess would seem to be evidence of a disservice done them by their cultural environment, neglected or possibly even exacerbated by whatever music teaching they have had. In my daily contact with adult pupils and amateur choristers I hear all sorts of mythologies about the nature of “musicality” or musical “talent,” which bear witness to a generally pessimistic discourse about musical potential and ability. My impression is that much music teaching seems to have mystified rather than enlightened the subject of music. It appears to suit the Western ego to see musical ability as something unattainable, bestowed only upon the anointed. This excuses the less capable from the disconcerting thought that their own potential could be wasted by lack of conviction. It puts the more accomplished on a pedestal where any kind of celebrity is more agreeable than the less glamorous status of craftsman.

Pulling musical ability down from this pedestal, treating it as acquirable skills based on a universal predisposition, proves to be a hard pill for many to swallow.

Many pupils dodge putting in the work, preferring to let mystical, media perpetuated ideas like “talent” or “X Factor” be the decider. This “make or break” attitude, the idea that you either already can or never will, is mostly destructive to real potential.

Many in the teaching profession uncritically perpetuate the same approaches and methods they themselves were taught by, or else lack the strength of conviction or confidence to challenge the pupils’ culturally borne misconceptions and mythologies. It has been my impression that the musical education communities I have been in contact with are inherently conservative, doing much the same thing the same way they always did. Progressive movements in education have tended to affect superficial elements like instrumentation, technology and repertoire, but have left core understandings of musical development unchallenged. If anything, they have lowered the bar on some quite useful skills like music reading. I doubt whether the contributions of genuine progressives like Suzuki and Kodaly — how ever prominent in their day — have survived the millenium as much more than a few materials and tricks, adopted and incorporated into existing practice. In fact, it is my impression that this inherent conservatism is actually exacerbated by a self-image of hipness and progressivism within music culture, eclipsing true criticism of underlying systems and perceptions. Numerous studies and projects linking music education to all manner of positive knock-on effects in other educational subjects (e.g. music improving performance in maths) are great news for these other subjects and for the image of music as “the new black,” but do nothing for the standard at which music itself is taught.

The teaching of music and music theory should surely take the (presumably innate) musical ear into account, rather than perpetuating notions of the beginner as an “empty vessel” or the musical ear as some rare attribute or talent. The not unreasonable assumption that any beginner has usable prior knowledge profoundly changes music teaching in core ways when put into practice. It changes perceptions of skills and where they arise from, as well as the order in which these skills can be developed and through what means. It is the basis of an approach that I think of as “musical empowerment,” because it is about guiding the pupil in taking his musical development into his own hands with his musical ear as a basis. Its central ideas are essentially the same ones that informed earlier progressive movements like those of Suzuki and Kodaly during the last century and Curwen in the one before that, so it is by no means new. But it takes a critical look at the role notation plays and can play in musical learning, for better or worse, and suggests a modified symbol system as a tool for building musical skills. This musical notation, using the numbers 1 to 7 as symbols, is also far from new, with versions proposed in the 18th century by Jean Jacques Rousseau and Pierre Galin, a variation of which is in widespread use in China today. Similar musical terminology can also be heard among Western jazz and country musicians. I feel that this type of symbol system has not been adopted to its full potential as a teaching aid and general musical tool, a matter which I will explore in the next article.

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