This paper examines the elements of music that can be learnt, that students want to learn, that can be taught and that are traditionally taught. It focuses on the fundamentals of learning music (not on learning the fundamentals), mainly ‘musicianship’ - and will not touch upon the aesthetic aspect.
There are studies claiming that perception of music makes use of the dual nature of human thinking mechanisms; the instinctive part of the process taking place in the right, whilst the logical part in the left hemisphere of the brain. Although it is not the object of this paper to argue the physiological validity of above hypothesis, for the purpose of easier distinction between the two types of processes, the labels (bR) and (bL) (right or left hemisphere of the brain) shall be used in the paper.
This paper aims, based on the author’s music teaching experience, to conclude that, though music in its entirety is perceived/reproduced by the brain’s two hemispheres simultaneously, an efficient music learning/teaching method should clearly separate and set the learning tasks to one side or the other at any one time. Both these (bR) and (bL) processes should use a common interface (iF) of consistent terminology; that enables the student to interpret one side’s reference in terms of the other and vica-versa.
General objectives of music learning: to acquire an efficient method that provides the student the ability to playing, singing or inner hearing written pieces of music.
Expectations from music teaching: to help the student to acquire skills that include sight-reading, aural recognition and understanding the theory of music at a level appropriate to his instrumental/singing/music appreciation.
Assessing the achievement of the above objectives (music exams):
Apart from the aural test and the pieces [bR], even the deaf could pass the rest, the [bL] written exam, with honours.
This traditional assessment implies a closed system of integrated progress grades, retrospective learning objectives and teaching methods. The progress grading from simple to complex structures both in theory and practice raise internal contradictions in the apparently consistent curriculum. A simple example is that the use of the ‘black keys’ is considered ‘more advanced’ than using just naturals (a totally unfounded argument for singing, strings or wind). Thus, according to the theory curriculum, playing a D, A, or E Major triad (root-position) on a keyboard (which, in effect, follows the natural anatomy of both right and left hands) should only follow the learning of the ‘easier’ C, F and G Major triads (all white keys, albeit with less natural hand-position). These contradictions themselves between theory and its alleged didactic objectives would justify an overall review of the theory of music – but this present paper only aims to refer to traditional theory from the aspect of its relevance to learning.
The general lack of a real integration of the methods associated with this system is clearly seen as most students fall, to an extent, into one or the other class: having problems with hearing/sight singing (whilst knowing the theory well) or having problems with musical notation (whilst their instinctive music-making reaches an advanced level) – in other words, their music studies only result in the amplification of their initial abilities and shortcomings.
Elements of music
The problem with learning music arises from the unique nature of time, the medium of music. Music itself is a sequence of intangible real-time events, whilst identification or recollection (i.e. the description, analysis or labeling of the events) of tangible sets may take shorter or longer time than the events themselves. In the course of listening to, or playing a piece of music, the musician (music student) associates the tangible sets to the intangible events, ideally not interfering with the overall timing of the real-time sequence of events.
independent tangible sets
Whilst the intangible events1,2,3…n are perceived by (bR), the a), b), c) tangible data or processes are (bL) sets, and time-independent, and are the result of previously learnt processes. Experienced musicians have their skills so developed, that the result is the instantaneous recollection of past processes – therefore (bL) takes less time, than the real-time event it is associated with.
Music teaching should lead the student to this level of instantaneous recollection of tangible sets (e.g. recognition of a pattern of written music) and its linking to the associated intangible event (e.g. singing or playing the given note) with the least effort, in the shortest possible time.
Simplified model of learning music:
(bL) (iF) (bR)
logical thought Interface imitation, motoric
processes links memory
A sight-singing example of and the traditional model of performing it:
break-down path of the compressed-time thought processes
· The first note has already been sung (bR);
· Already heard note’s name (‘Every-Good-Boy-Deserves-Favour’): E (bL);
· Next note’s name: B (bL);
· Interval (7 semitones): Perfect 5th (bL)
· Pitch association (Perfect 5th sounds like: “Twinkle, Twinkle”) (iF).
· Pitching (‘inner hearing’) the “Twin1-Twin2“=Perfect 5th (bR)
· Singing the “Twin2“=B (bR).
Every thought process of this example have to be mastered first, otherwise the completion of the different steps would take much longer than the time available before singing B.
Model of an efficient thought process of pitching the B:
This model shows how an experienced musician would perform the same task. He would totally rely on the interface label, as the result of previous repetitions of all the (bL) and (bR) processes – thus developing an instant visual recognition of a perfect 5th, and an instant pitch image associated with a perfect 5th. It takes practically no time for him. If we asked, how he did it, he would, most probably, detail the thought processes of the first model with the additional advice: ‘practice, practice…’. But, in fact, he had been practicing the association of a “Perfect 5th” (iF) between one or the other side. In his mind he had, ultimately, two images only:
Here, he uses the interface “Perfect 5th that is both visually decoded and associated with the pitch as a result of having practiced them both in the past.
This result of instant recognition is desirable, but the means of achieving it is inefficient, unnecessarily long-winded and its foundation is questionable.
Tonic sol-fa is a practical approach to learning pitch with mnemonic interfaces
Guido d’Arezzo could not foresee that his (bR) set of incidentally chosen mnemonics (ut-re-mi…) and its translation (c,d,e..) shall be considered as the basis of an ‘absolute’ standard – whilst his truly ingenious teaching method (using graphical and hand-sign interface links to the sung pitches) has only been revived by Curwen and Kodály, around a thousand years later. These latter considered their tonic sol-fa as a means to, ultimately, learn the intervals as the basis of theory (harmony, counterpoint and analysis).
Tonic sol-fa uses the seven syllables (‘doh-ray-me…’), as a set of mnemonics to express the seven degrees of the scale. It exploits the concept that the (interval) structure of a scale is the same related to any chosen tonic. So much so, that if one (like the overwhelming majority of us) does not have ‘perfect pitch’, cannot hear the difference whether a piece is performed in C or Bb Major. However, he can sing Doh for the tonic, Soh for the dominant – for him, as they constitute the same interval, the relative pitch is right in both cases! Learning pitch with tonic-solfa is based on a ‘Pavlovian’ development of conditional reflexes. Thus the (bR) physiological pitch-sensation (relation to a given doh) is consistently associated with the same mnemonics (syllable sung) – further reinforced with a (teacher) interface: a set of hand-signs for the mnemonics. Its efficiency is still unrivalled from the point of (bR) development.
Tonic sol-fa only uses the (bR), and the mnemonics provide an (iF) link.
The problem with tonic sol-fa is that, whilst it solves the more difficult task of learning music (i.e. direct labeling of the intangible pitch), no convincing method is associated with it to translate the acquired (bR) skills to the (bL) expectations of theory, for example, with musical notation. Attempts always try to relate sol-fa to the traditional terms of theory (e.g. intervals), and, as a result, make the method seem impractical for ‘serious’ learning.
Progress in learning music should simulate the natural perception order: the 3 dimensions of the intangible elements 1. Rhythm, 2. Melody, 3. Harmony
Chords and Harmony
Metre: bar: one cycle between 2 downbeats [tension-] release to tension [-release], beat: 1 unit of time between up-beat and down beat.
(time signature: the number of beats per bar.
Rhythm: the start and duration of sound events [notes or rests] in terms of coinciding or not with the beats
Pitch: the ‘height’ of the note assuming a set of relations (tonality): scale: the set of the likely notes to be used within the given tonality – in alphabetic order. Degrees: the ordinal number of notes within the scale
Melody: a sequence of sound events, where the pitch of the notes defined by the rhythm is defined in terms of the degrees of the scale.
Chord: a frozen moment of several notes sounding together, where only the relationship between those notes is considered.
Harmony: ’colouring’ of melody with different chords.
(Tonal function: the reinforcement of tension or release by the use of notes in the melody, further underlining by the use of chords of harmony of the appropriate ‘colour’.)
Myths built in the theory of music
The myth of ‘understanding’ rhythm’
A scholar in the Middle Ages, whether he perceived or not (bR) how time was divided to form rhythm, knew (bL) that, 3 units (as in the Holy Trinity) formed tempus perfectum, therefore, 2 units must be imperfectum. But, is our modern explanation different on ‘why’ 34 is not the same as 68, just because the terms used (‘simple’ and ‘compound’ times (bL)) seem more objective? The object of rhythm is time, and as such, is intangible. Beats and the notes of different length in relation to those beats only exist in time, thus in (bR), whilst a description of those in mathematical fractions only exists in (bL). The unfortunate practice of blurring the border between the two leads to the establishment of misconceived expectations (such as: ‘now, tap two quavers’).
The myth of intervals as a measure of pitch
In the 18th century, nearly all musicians had perfect pitch. Their students, however, did not. Therefore, the teachers of the time invented a method: the intervals. Practically nobody has ever challenged (or proved) the validity and purpose of this concept, in spite of the fact, that the originator (the teacher) did not offer an emulation of his own perception process (as, having perfect pitch, he knew the name of the new note and associated its pitch with it, and did not measure the interval from the previous note). The other problem with intervals is that the name is an indirect (bL) label, and for making sense of it for the (bR), usually a part of a known melody is given as a third stage of reference. For instance, a Perfect 5th sounds like the beginning of ‘Twinkle, twinkle, little star’. Therefore, in sight-singing or aural recognition situation, the student initially associates ‘Twinkle, twinkle, little star’ with a Perfect 5th. Obviously, this is a long-winded, inefficient method – where, with time, the process with the distinct tasks is long forgotten. A music student is expected to pitch a Perfect 5th directly, thus establishing a false belief that it is possible.
The myth of ‘hearing the notes’ of a chord
When a student is asked to identify the 3 notes of a triad in the course of an aural test, he is asked something that would physically only be possible, if he had 3 ears (on a separate skull each – and the notes produced in 3 isolated atmospheres). The traditional expectation of ‘hearing out’ the components of a complex sound (the triad) is really based on the past learning of different chord structures (bL) and on hearing of different chords (bR) and on a long scan of trial-and error processes. Most often, the final answer (the chord’s name) never reaches an interface stage that could be meaningful in real time (in either direction).
The above examples demonstrate that traditional music teaching uses didactically unfounded, tedious methods – yet many achieve reading rhythm, sight-singing and aural recognition. The purpose of searching for alternative teaching methods is to achieve the same objectives with a more sound foundation (from the student’s aspect) and with a higher success rate.
The arguments, so far, focused on learning musicianship (loosely: theory, music reading/writing, sight-singing and aural recognition) that, according to many (including the author), should be integrated to learning instrumental skills. Although the author has experience only in teaching piano (keyboard), the following generalised findings of discussions with other musicians/music teachers is most probably true in respect of all instruments (including singing).
The traditional model of learning a piece of instrumental music
Built-in inefficiencies of this model:
The instrument is a physical extension of (bR)
A more efficient model for learning an instrument would be breaking down the process into:
Digesting: the real-time image of the sound events that is expected as the ultimate output from the instrument (this may be: e.g. singing [inner hearing] the melody, etc). It is the end-result of (bL) and (bR) musicianship processes.
Planning: a sequence of (bL) and (bR) preparation steps particular to the instrument and to the physical implementation.
Example (learning a piece for recorder): the student
Performing the piece. In this way, he learns the piece he wants to play with little or no practice at all; the only task left for him is to shape it to his liking. In other words: to enjoy his music making - after all, that is his ultimate objective for learning music, anyway.
· be consistent (using thought processes based on the same principles)
· be progressive (new elements built on previous ones)
· clearly address the tasks to the appropriate type of process (bL) or (bR)
· use a common set of (iF) labels for both (bL) and (bR) processes
· simultaneously develop sight-singing, aural recognition, inner hearing, relevant theory and musical memory (and assume a similar approach to instrumental/singing skill development)
· be vectored (follow the order of the dimensions of natural perception) therefore should include, from the very beginning, both (bL) and (bR) development of the relevant
o pitch, and
o harmony patterns.
· (provide a set of interface processes tailored to the particular instrument and to the appropriate motoric implementation
The general structure of the curriculum follows the expectations listed in the conclusion of the previous part.
The particular structure of the curriculum is based on the objective, that the student must develop both his visual and aural ‘vocabulary’ to such a level, that the compressed time taken by recollection/identification of the appropriate pattern is shorter than the given real time in the flow of music.
ZNK achieves this by practicing distinct visualisation based on (bL) structural processes, and practicing the auditive implementation of the visual pattern (bR) using the same (iF) terms.
Interface devices in ZNK:
For the consistent coding/decoding of (iF) elements a set of terms are laid down from the very beginning.
Visual (bL): Picture gallery, with separate halls according to the time signature (i.e. with the value of one beat; hall of a [crotchet] [quaver] [minim] [dotted crotchet] etc.)
Auditive (bR): practicing one or several voice rhythm exercises, melodies and harmonised melodies
Example: (learning crotchet notes, rests and quavers)
1. (bL) learning process (visualisation and naming ‘pictures’)
2. (bR) reading process (left to right, pictures of whole beat’s length only)
3. (bL) memory development (remembering a longer sequence of several pictures)
4. (bL) development of reading (copying) patterns in context, not symbols out of context)
1. The student, by tapping the beats, should be able to follow through visually any piece of music consisting of crotchets and pairs of quavers (ignoring pitch for the time being). He could sing most (or all) of it without stopping.
2. If there are unknown ‘pictures’ in the piece, the student could ignore them, and pick up from the next known picture.
Method of singing and ear training: (bR): using a kind of tonic sol-fa. Visual (iF): unique mnemonic graphic symbols used in practicing the above.
Note: the 7 mnemonic syllables are different from tonic sol-fa: Zoo-Vah-Nay-Yaw-Koo-Pah-Tay. Two reasons justified the change of mnemonics: a) using ‘doh-ray-me’ for relative pitch would confuse students having do-ré-mi as absolute pitch in their mother-tongue, b) in the mnemonic expression of chords (see later), the syllables will change, anyway.
Visual (iF): unique mnemonic graphic symbols used in practicing
[*with the optional help (teacher emulation) of an audio-visual aid (computer program) displaying unique ‘ZNK’ graphic symbols, staff notation and playing the different pitches providing both sight-singing and aural recognition exercises]
Visual (bL): using and applying the 6 rules [of the diatonic scale] by the application of logical thought process and visualisation.
1. singing (auditive) process: (bR) by imitation of an external source (teacher or AV. aid) zoo-koo to different given zoo
2. visualisation (bR) process:(and verbal reinforcement) of the Zoo-Koo distance on the 5 lines of the staff (e.g.: if the Zoo is on the middle line [‘zoo clef’], the Koo is on the top line; or, if the Koo is on the space above the bottom line, the Zoo is on the space below the first lower leger line, etc.)
The visual image of Zoo-Koo is always either [zoo-]line to 2 lines up, or [zoo-]space to 2 spaces up.
3. absolute names:(it is assumed that the student already knows the ABC-names in treble clef)
4. application process (bL) of the rule: if the ‘zoo’ is natural, then the ‘koo’ is natural too. Except, when ‘zoo’ is ‘B’, then ‘koo’ is sharp
5. practicing process (that is: [bL]-driven visualisation) of the 7 possible Zoo-Koo pairs (not singing), cannot take longer than a few minutes – leading to an instant visual recognition of “Zoo-Koo” as an [iF] label.
(bL) visualisation processes can be practiced anywhere, anytime – as it does not need any external device. The author usually advises his students to practice those on the Tube or Bus on their way home. In the course of the visualisation process it is recommended to exaggerate the (inner) image (for instance the size of visualised notes could be that of the underground station symbol): as, according to memory experts, that would leave a deeper impression– thus the pattern could be recollected/ identified much faster.
6. identification process of the pattern (iF) both as (bL) E-B= “Zoo-Koo” and (bR) i.e. what “Zoo-Koo” should sound like.
7. reinforcement (iF) exercises
already visualised pattern already practiced conversion already familiar pitch image
8. sight-singing (bR) melodies (‘pitched’ rhythm) using Zoo-s and Koo-s.
9. re-writing them from memory (see the process above, re. Rhythm)
10. transposing them from memory (by changing the Zoo)
1. The student, by tapping the beats, should be able to follow through visually any melody using rhythm of the level of his knowledge. He could sing most (or all) of the zoo-s and koo-s without stopping.
2. The student could instantly recognise zoo-s and koo-s aurally – and decode them to absolute-name notes if necessary/could play them on their instrument in real time
3. If there are unknown notes in the melody, the student could ignore them, and pick up from the next zoo or koo.
The (bR) process development treats harmony as a ‘colour dimension’ to a melody-note. ZNK’s monosyllabic (thus real-time) chord mnemonics are composed of two elements:
Everybody hears, in real-time, the two different colours of ‘Long’ and ‘live’ in the second line of ‘God Save the Queen’. The two chords, according to the rudiments of music, are: we sing (in the melody) the 3rd. degree (of a Major scale) is accompanied by a (tonic) Major triad 2nd inversion, followed by the same melody note, accompanied by a (relative, or sub-mediant) root-position minor triad. This type of labeling is extremely tedious, and can only be speeded up to become useful (iF) labeling through serious efforts, and at a fairly advanced (near-professional) level of music studies, and, in the majority of cases, never reaches the real-time identification speed.
But, emulating the actual perception process, there are two elements only:
a) the note we sing (that here, happens to be : ‘nay’ in ZNK), - which we could express as ‘n’;
b) the ‘colour’ of that note (‘Long’ or ‘live’) - which we could express as ‘-o’ or ‘-i’ respectively,
either of which we could sing in one syllable per chord, in real time!
Thus, using such monosyllabic compound labels could solve the real-time labeling of the real-time event, emulating the dimensions of perceiving the music. These compound mnemonics in ZNK first use the consonant of the melody (top)note [nay] followed by a vowel, expressing the ‘colour’ (the accompanying chord) of the melody-note. The vowel ‘-oo’ stands for Zoo Major triad, and the ‘-ah’ for pah minor triad. Thus ‘Long-live’ would sound: ‘Noo-Nah’ in ZNK. It is quite easy to imagine that, singing the Noo-Nah sequence with simultaneous hearing of the appropriate chords (in different keys) can develop firm Pavlovian reflexes within a 5-minute practice session. This concept, associated with the (bL) visualisation processes can develop instant chord recognition in the student (together with the instant knowledge of the [component] notes). The author knows of no other method for chord recognition with such scientific foundation and one which has been tried and tested for decades in practice, with a near-100% success rate.
1. (assumed stage: the student already knows instantly Zoo-Koo as was detailed above, and also that [Zoo-Nay are line-to-line or space-to-space] and [Rule 2: if Zoo is natural, then Nay is # except when zoo=C, or F or G; then Nay is natural too])
2. listening/singing (bR) Major triads by imitation from an external source (teacher or audio-visual device [computer]) to different given zoo-s
3. visualisation (bL) of (Zoo-) of Major triads: line-to-line-to-line or space-to-space-to-space
4. (bL) thought processes and visualisation of the 3 types of Major triads:
Nay # #
Triads: B Major C,F,G Major A,D,E Major
5. aural recognition and sight-singing (bR) exercises of the different notes of different Major triads
1. (bL) learning process (logical processing, visualisation of chord patterns)
2. (bR) sight-singing/aural recognition of notes within Major triads
3. (bL) feedback patterns in melodic reading (of the ‘skeleton’ [Tonic triad] notes of tunes in Major keys)
4. (bL) memory development (memorising in larger-scale context)
1. The student could think of a pattern and could recognise it without analyzing what context (here, Major triad) would the component notes make up
2. Even if there are unknown notes in the melody, the student could ignore them, and return to zoo or nay or koo (skeleton-notes) instantly, when they are used by the melody.
General process of practicing
An efficient practicing process (both in musicianship and on an instrument) has the following steps:
Example: (new picture: ‘off-beat quaver’ [second bar, first beat])
Although the author strongly believes, but it is not proven that the method works at all levels, as his experience is limited to teaching the first year for beginners (for 5-6 years at Morley College and Goldsmith’s College in the ‘70-80s).
Problems with traditional methods
A beginner, traditionally, is loaded with a large number of tasks (recognition of rhythm patterns, hands, notes, relating those to the keyboard, fingers, hand-position or ‘touch’) – which is impossible to solve in real time. Nevertheless, students are encouraged to repeat it until they can manage it [that is called: practicing - some tutors even try to make the task ‘easier’: practice the hands separately….] This method implies:
first, your hands should learn the piece;
then, you can hear what you play.
The student picks up bad musical and manual habits – unlearning of which provides a good excuse for further practicing for years to come.
Learning the keyboard through an alternative approach turns the process round:
first, you should learn what you want to do, when you get to the keyborad;
then, you should play, and enjoy playing and shaping the already known piece.
Anyone, never having played the piano before, could be instructed to go to the piano, open the lid, find a pattern of two black keys (around the middle) hit the white key in-between the two (which we call:D) with his middle finger. He should be able to do it, without any ‘practice’
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