Pedagogical Resources
“The true essence of humankind is kindness. There are other qualities which come from education or knowledge, but it is essential, if one wishes to be a genuine human being and impart satisfying meaning to one’s existence, to have a good heart.”
The 14th Dalai Lama1
This section of the website offers access to a variety of useful resources and documents, covering practical items such as printable blank manuscript paper and pitch matrices alongside pedagogical resources that could aid the learning and teaching of musical analysis, composition and theory. Some documents are more referential in nature and would be useful to researchers interested in the subject of composition, pitch organisation and form in the 21st century.
As with all the available resources on this site, this documentation and research is made available for public access and peer review, but Dr Ian Percy retains full ownership and copyright for all intellectual property, media resources and text, and should be appropriately accredited for any and all references to, or formal use of, these materials.
Dr Ian Percy
2019
1 Buddhist Offerings 365 Days: Danielle & Oliver Föllmi – Thames & Hudson, London.
Western Tonality
This is a collection of reference sheets illustrating the triadic diatonic Major/minor system of seventh chords that has served as the foundation for Western tonality, Classical functioning harmony and contemporary Pop, Rock and Jazz songwriting. The sheets also illustrate the changing chords of the two minor scale mutations: Harmonic and Jazz Melodic (Melodic Ascending).
The purpose of these sheets is to establish clarity for study and reference, so where there is an obvious preference in enharmonic key signature, only one example is offered: why illustrate something in C# Major (7 sharps) when one can illustrate the same point in Db Major (5 flats). The one exception to this is the six-sharp/six-flat key signature: F#/Gb Major.
This is a collection of reference sheets illustrating the seven modes found within the Western Major Scale written from each note of the chromatic scale: i.e. The Seven Modes of C Major (the scale). Alongside the modes for each major scale is a page of the modes written from the same specific individual note: i.e. The Seven Modes from C (the note).
These reference sheets were compiled in indignant reaction to having to decipher and explain the many over-complicated (published) worksheets undergraduate (and sometimes postgraduate) students regularly bought to me in befuddled frustration. One would often witness examples where the modes had been written with chromatics instead of key signatures (sometimes both were present …!!!), therefore displaying a complete lack of intuitive understanding of the modal system and its linear and vertical relationships to the ‘Parent Scale’ and completely confusing the reader.
Through following the format of these sheets, students can quickly learn to recognise repeated patterns (both visual and aural) and will be able to internalise the modal system to memory through reference to a parent major scale that can (of course) transpose to any note of the chromatic scale.
This document illustrates the complemental relationships which exist between modal mirror-inversions. It is a self-contained and self-completing process: Ionian inverts to Phrygian (and vice versa), Dorian inverts to Dorian (identical pitch palindrome), Lydian inverts to Locrian, and Mixolydian inverts to Aeolian.
For instance, one could be composing in F Lydian (C Major) and immediately modulate to F Locrian (Gb Major), effectively shifting key by a tritone through the pivot of a specific note (in this instance F natural). The work contained in this analytical exercise was an important link for the composer’s evolving philosophies of pseudo modulation (modal modulation) and modal sfumato.2
This sheet was presented to 2nd year undergraduate composers over a period of at least eight consecutive years, always with the expectation that its internal relationships would spark the interest and enthusiasm of the cohort … Nothing …!
It was always ‘just a little disappointing’. So …
Over the past five years, this work has also been given to PG and PhD composers, but again … Nothing …!
It has been a pleasure to teach many talented composers over the past two decades, but no-one has ever really noticed the potential analytical and compositional value of this self-contained cycle, or even ‘raised an eyebrow’ for the fact that Dorian Mode is a perfect pitch palindrome and therefore unique within western tonality/modality. The internal relationships highlighted on this sheet offer unusual options for pitch modulation, which can present a sense of false modulation (pseudo modulation) within key or offer ‘modal’ alternatives to traditional functioning harmony when modulating across keys.
2 Sfumato: Technique used by Leonardo Da Vinci for softening the transition between colours: Imperceptible transitions between colours and tones …
Blank A4 Resources
Having stopped purchasing printed manuscript paper well over a decade ago and although one can transfer music to digital software faster (and neater) than handwriting, it can still be very productive to compose with pen on paper (especially when weather allows work to be ‘taken outside’). It is by far the most tactile (and enjoyable) way of sketching initial thoughts and developing skeletal ideas.
One does not have to possess ‘the perfect ear’ to compose in this manner. Music has many strata and composition has many stages; work with phrase contours and harmonic approximations instead of specific pitch: Does the note move up or down? Is it a close interval or a wide interval? Consider elements of texture, pacing, rhythm, dynamic and articulation. Predetermined elements of pitch organisation (perhaps a specific chord, mode, key or pitch class cell), can inform the ear and help to internalise an aural approximation of the soundworld. Through reflective analysis and theory, one can begin to develop vertical relationships, micro units and macro forms. It is amazing how far the parameters of ‘what one can compose with one’s ear, instinct and imagination’ stretch with just a little practice.
Try working through pre-compositional plans and theoretical problems of progression, counterpoint and harmony in this way, using elements of graphic and traditional notation alongside written comments. Sketches do not always have to revolve around musical notation, but you should always have sheets of blank manuscript paper (and of course the obligatory Wi-Fi devices) at hand.
Print a handful of these sheets off and head out into the great outdoors (or at least away from the writing desk) next time you have an idea for composition. Try the analogue tactile method, you never know, you just might like it …
There is nothing wrong with composing by instinct, imagination and ear, but the best music tends to come from a symbiosis between soul and intellect. One should always engage in theoretical due diligence to inform the creative imagination and explore the many options available to the 21st century composer for developing preconceived pitch organisation and form.
Regardless of the initial material for a piece: tonal, modal, atonal, or how large the collection of notes: trichord, tetrachord, pentachord, hexachord, heptachord, octachord, nonachord, decachord or eleven and twelve-tone rows, it is always beneficial to compile pitch matrices of your material. This immediately shows the Prime [P], Retrograde [R], Prime Inversion [PI] and Retrograde Inversion [RI] (along with the literal transpositions) of the material within a neat little square (try it on your favourite chord spelling). Pitch matrices (and similar concepts) can be utilised for many parameters of compositional planning and process, but that is another story …
Through following the format of these sheets, students can quickly learn to recognise repeated patterns (both visual and aural) and will be able to internalise the modal system to memory through reference to a parent major scale that can (of course) transpose to any note of the chromatic scale.
If you are new to the world of pitch matrices, pitch-class sets and twelve-tone analysis, then the following link on this page offers a condensed introduction to the fundamentals.
Fundamentals
The Dodecaphonic System: The liberation of the western chromatic scale from the hierarchical qualities of the tonal system establishing twelve pitches of EQUAL importance: Twelve pitch-types, twelve pitch-classes, twelve interval-types and SIX interval-classes. A non-hierarchical and transposable system of pitch-organisation.
Useful for analysts, composers and musicologists, this document outlines a condensed introduction to the fundamentals of twelve-tone, atonal and pitch-class analysis through a series of written tutorials and practical worksheets growing progressively more advanced. The content is explained in an accessible vocabulary that can be followed by anyone with a basic understanding of music theory (and a little patience).
Twelve-tone composition is not inherently dissonant, this is a common misconception. The dodecaphonic system is a non-hierarchical and transposable system of pitch-organisation. Nothing more, nothing less. One can ‘compose’ the twelve-tone row as two overlapping keys and in doing so embed a precomposed sense of tonal or modal modulation, or one can adapt a short chord progression. The rules of twelve-tone composition state that no note can be repeated until all twelve have been played, they do not determine how one conceives (or composes) the initial row. Then there are the subcomponents of the row – the pitch-class sets. The musical possibilities remain endless …
Besides, who follows the rules anyway? Check out the modal stasis of Arvo Pärt and his post 1976 tintinnabulation style, you will find many elements of strict systemisation and precomposed elements of form and proportion comparable to the processes and concepts discussed in these sheets, even the presence of a primary row. However, Pärt chooses to work with modality and tonal stasis, repetition of notes (rhythm and time) is an essential element of his immediately recognisable style.
So … It is not ‘what you know’, but ‘what you do with it’ that counts here …
Twelve-Tone Analysis Further Resources
In an apparent hangover from the total serialist and new complexity scores of the mid to late twentieth century, exacerbated by the digital age’s ability for software to play in any speed and to convince the ear that it can hear the difference between crotchet equals 84 and crotchet equals 85 (I challenge anyone to count out the discrepancies between these tempi in the acoustic of the recital hall), one found oneself quite frustrated at the impractical (and quite abstract) tempo and time changes regularly appearing in student scores. For the last decade, I have pretty much insisted that all my student composers ONLY use the tempi available on the traditional Maezel Metronome.
I once tried to ‘reinvent the wheel’ and reconceive a list of tempi governed by the Golden Ratio (and other natural proportion theories). Weeks into the research came the realisation that this is exactly why the Maezel settings feel more instinctive, they have an inherent proportional relationship, and, from a practical perspective, they are still regularly recommended by conservatoires across Europe and the UK.
This list of tempi has been very useful over the years, one rarely hears comments on the way time is communicated within my scores during rehearsals (perhaps we are always too busy discussing the plethora of more pressing issues?). The music has never suffered as a consequence of a commitment to the value of this list, in fact, to the contrary, it often saves time procrastinating over (what used to be) agonising decisions concerning intricate tempi changes that would over-complicate rehearsals anyway.
The Maezel Metronome Tempi have long since been committed to memory, but this list is still one of the first documents copied and printed to the digital and hard copy ‘planning’ folders of each emerging composition. It is strongly recommended that you consider adopting this list for your own scores, and always ask yourself, ‘could I count out the changes I am asking for’ …?
The string quartet is one of my favourite classical ensembles. It is capable of intimate whispers and violent crescendi. The strings are theoretically tireless (unlike wind players who need to breathe), can perform acrobatic feats of virtuosic agility and yet change the emotion of a single sustained tone with empathetic subtlety. Professional string players are amongst the most phenomenal sight readers I have ever witnessed (an important skill for the UK musician).
It has been my privilege to host over thirty string quartet workshops, rehearsals and recitals for student composers since 2010, mostly working with professional musicians from the Royal Liverpool Philharmonic Orchestra during my time at University and they have always been one of the highlights of the year.
This document offers a reference to some of the available techniques when composing for strings. It is a referential document, so whilst a brief description is offered for most listed terminology, it is expected that the composer then ‘follows the thread’ to research correct notations and perhaps locate aural examples from instances in external scores (Berio’s Sequenza are always a good place to start).
The document also includes some essential and recommended listening, introducing examples of the many stylistic options one can utilise when composing for string quartet (an informed reference of current and historic repertoire for the instruments you are using is always an important element for planning a new composition).
Whilst the majority of the techniques listed are still in common use today, the old adage of ‘less is more’ seems a suitable way to end this written introduction …
Pitch Documentation
On the subject of diatonic pitch organisation and the composer’s evolving concept of Modal Sfumato …
An almost imperceptible modulation between colours and tones offering the potential for pseudo modulation within keys, an alternative route to using elements of traditional functioning harmony for modulation across keys and (in this instance) helping to navigate almost imperceptible semi-tone modulations and whole-tone pitch schemes.
This paper is a useful reference for any composer looking to extend their available palette for preconceiving and pre-composing pitch organisation or as a potential catalyst for analytical and musicological discourse:
The 21st century composer is no longer frightened of tonality and modality, nor intimidated by twelve-tone and pitch-class process; they are ‘informed eclectics’.
This document summates a period of theoretical and practical research on the subject of pitch palindromes3. This line of research has influenced many recent works and has provided the foundations for a current orchestral ‘work in progress’ but is extensively featured in the scores and theory for The Palindrome Triptychs.
Pitch Palindromes, and the potential for exploring palindromes within palindromes, adds another musical stratum within an evolving concept of Matryoshka Form4 and self-similar replication which emerged from recent consideration of pitch organisation and proportional subcomponents of internal architecture relative to the study of panoptic non-linear resonances, fractals and chaos theory.
The potential for the connectives outlined in this document seem limitless (one has only uncovered the tip of an iceberg here). This document simply lists observations about the inherent relationships between particular intervals and their vast universe of combinations. What style one chooses to embrace is not predetermined by the pitch organisation outlined here.
3 A word or phrase, the letters (or components) of which, when taken in reverse order read the same
4 A design paradigm indicating the existence of object within similar object, originating from the Russian ‘nested’ dolls design. It is important to note that Matryoshka dolls are traditionally hand painted. They are not exact replications, but self-similar replications. Their subtle differences make each unique …
Palindromes
This document contains a short definition, analysis and clarification of Messiaen’s Modes of Limited Transposition. The paper emerged from a period of contextual, analytical and practical research in planning and preparation for a large orchestral composition involving musical palindromes and has led to studies into non-linear acoustics, chaotic pairs and fractal self-similar replications.
Messiaen’s Modes of Limited Transposition are all self-contained pitch palindromes …
This document contains a short definition, analysis and clarification of Elliott Carter’s All-Interval Twelve-Note (AITN) Chords. This paper emerged from a period of contextual, analytical and practical research in planning and preparation for a large orchestral composition. This line of research has led the composer to studies into non-linear acoustics, chaotic pairs, fractals and musical pitch palindromes.
There are two types of AITN Chords: Symmetrically Inverted (SI AITN) and Parallel Inverted (PI AITN). Carter’s AITN Chords are all self-contained pitch palindromes within palindromes.
Analyses
This document outlines context and analysis of John Cage’s Three Dances No.1 (1944-45) and serves as a useful reference for EDEXCEL A Level study. The paper was presented as part of a lecture recital at Liverpool Hope University during 2018 and was followed by an acoustic performance of the movement (without amplification) by piano duo Ian Buckle and Richard Casey.
Three Dances No.1: Live
This document offers a brief introduction to Arvo Pärt’s post-1976 tintinnabuli style alongside a written analysis outlining the compositional landmarks and primary processes found within Summa (1977). This piece makes an ideal study analysis, as it is a score in which the composer strictly adheres to preconceived methods.