‘Assessment consists in evaluating or judging the value of something, or someone, in accordance with certain expectations, an idea or a reference, related to personal and/or shared values.’ 
One notable attempt to bring assessment under control was Derek Rowntree’s book ‘Assessing students: how shall we know them? first published in 1977. 
Reading the book in 2016 I am struck by how little has changed in the way assessment is thought about. Rowntree sets out systematically, chapter by chapter, the nature of assessment, its purposes, the question of what to assess, how to assess and so on.
In Rowntree’s chapter ‘How to assess?’ there is a section titled:
Idiographic vs. Nomothetic Assessment
Idiographic is about the individual while nomothetic is about the making of general laws. 
So in the case of assessment the idiographic is concerned with understanding the uniqueness of the individual, how the individual is thinking, how they are making music and what value they are seeking to give to their endeavour.
Set against this is nomothetic assessment that collects data about individuals and aims to understand people in general and this means measuring them against each other and against standards.
One obvious difference from the time when Rowntree was writing is the extent to which standards are no longer a matter of the local or national but a matter of international comparison leading to what for music teachers in the UK can be an overbearing and barely tolerable audit culture. (See https://jfin107.wordpress.com/2015/03/20/music-teachers-taming-the-audit-culture/ )
It is this culture that pushes against seeing the individual pupil and their musical work as ‘sui generis’ – in a class of its own. It is the audit culture that exasperates the long-standing tension between valuing the work of the pupil as sui generis and some external standard.
Rowntree cites William James on the tendency to classify and label the pupil.
‘’The first thing the intellect does with an object is to class it along with something else. But any object that is infinitely important to us and awakens our devotion feels to us also as if it must be sui generis and unique. Probably a crab would be filled with a sense of personal outrage if it could hear us class it without ado or apology as a crustacean, and dispose of it. ‘I am no such thing,’ it would say; ‘I am myself, myself alone.’’’
Writing in 1993 Ross et al. noted that:
‘For many children assessment means enduring a form of mental and emotional derangement, the morbid exchange of a warm, living experience for a cold, dead reckoning.’ 
For Ross et al., the radical solution found was to ensure that judgement in the arts ‘’must be and always remain ‘suspended judgement’’’ and thus provide the pupil with an experience that was uniquely freeing and empowering.
In this view assessment is quite simply a matter of sensitive conversation in which the personhood of the pupil matters greatly and far removed from being a unit of accountability.
 Beauvais, M. (2011) Assessment: a question of responsibility. UNIVEST. Retrieved from http://dugidoc.udg.edu/bitstream/handle/10256/3592/Beauvais_en.pdf?sequence=2
 Rowntree, D. (1977) Assessing Students: How shall we know them? Kogan Page.
 Greek words adopted by German philosophy.
 Ross, M., Radnor, H.,Mitchell, S. and Bierton, C. (1993) Assessing achievement in the Arts. Open University Press.