Bjorklund Rhythm Device


Try out a my bjorklund M4L:

A rhythm comprises a number of sounded pulses played in each set of steps. The algorithm distributes these pulses as evenly as possible throughout the number of steps.The rhythm names and origins are copied from the paper by Godfried Toussaint. The javascript algorithm is based on work by Jack Rutherford (


G. T. Toussaint, The Euclidean algorithm generates traditional musical rhythms, Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science, Banff, Alberta, Canada, July 31 to August 3, 2005, pp. 47–56.

E. Bjorklund. The theory of rep-rate pattern generation in the SNS timing system. SNS ASD Technical Note SNS-NOTE-CNTRL-99, Los Alamos National Laboratory, Los Alamos, U.S.A., 2003.


Letter to Julian Leeser MP

Julian Leeser MP
Member for Berowra
PO Box 743
Pennant Hills, NSW, 1715

Dear Mr Leeser,

Congratulations on being re-elected to the federal seat of Berowra.

As the representative of my family in the Federal Government there are several issues of concern that we would like you to know about and act on in parliament and with your colleagues in the government.

Our three main concerns are: the avoidance of armed conflict, the progress of reconciliation and improvement of the lot of Indigenous Australians, and positive action on climate change and species loss.

Successive Australian governments have made rash, ill-informed and negligent choices in their response to the alliance with the United States through committing the lives of Australian soldiers and innocent civilians in other countries to death, physical and psychological injury and loss of livelihood. As our representative we demand that you use your influence, common-sense and moral power to help your colleagues avoid these decisions and their awful consequences.

We commend you for your work with the Joint Select Committee on Constitutional Recognition relating to Aboriginal and Torres Strait Islander Peoples. We were disappointed by the former Prime Minister’s response to the Uluru Statement from the Heart, but we note that positive action is being taken by government in progressing these issues. We encourage you to help your colleagues to speak in more positive and constructive language about their plans to make practical changes to the administration of Indigenous affairs in this country. Please do not be afraid to insist that Prime Minister Scott Morrison change his rhetoric of self-int
erest and help him to develop a more compassionate form of public discourse. It is essential that Government seeks advice from Aboriginal Australians and avoids adopting uniform measures that cannot be applied effectively in each community.

The Federal Government must stop attempting to second-guess opinion polls and start taking responsibility for the environmental impact of fossil fuels. Our family expects leadership from our leaders. This must include both a positive and constructive public discourse and firm and decisive action to support the development of a post-carbon economy.

We wish you the best of luck in taking our concerns forward and using your influence over your fellow parliamentarians. Please be a voice for compassion and reason amongst the less wise members of the federal coalition. For our children’s sake help us to be proud of our Australian Government.

Yours sincerely,

Ian Stevenson


Almost Dead Right

In the recent Quarterly Essay, in which he attempts to demolish the prevailing neoliberal status quo, economist Richard Denniss misses the mark in two important respects. Firstly, he dramatically overstates the population’s rejection of neoliberal ideas. Secondly, he underestimates the all-pervasive power of ideology. A careful re-reading of Marx and Althusser, would help him to understand how the neoliberal ideology insinuates itself into every aspect of our personal and social relations. A brief examination of the ways in which neoliberal thought arises in our everyday attitudes and decision making, in the dictates and orientation of our institutions, in the desires and aspirations of our selves, co-workers and students, reveals the ways in which our realities are coopted and formed through ideology. Denniss’s intervention is an important first step, but to reverse four decades (I think his historical calculation is wrong by nearly 10 years) of indoctrination will take more than overoptimistic journalism. However, in Denniss’s defence, the method of stating as facts, states of affairs that are clearly not supported by the evidence, has been a potent tool in the arsenal of the powerful, and he co-opts this strategy effectively in his essay.


Hello Pythagoras

In their recent polemical article “A Psychocultural Theory Of Musical Interval: Bye Bye Pythagoras””, Richard Parncutt and Graham Hair seem to have forgotten the technological dimension of musical practice.

The article has a perceptual and cognitive bias that ignores the utility of “ratios” or more fully “theory” in the production of the physical artefacts of musical culture, namely instruments. Some form of mensuration must be applied in the reproduction of successful instrumental designs. This is where ratios come in handy not as the basis of tuning but as a starting point for measurements in the crafting of musical devices.

While I applaud the author’s understanding of musical scales as matters of “social and cultural” practice; leaving out artefacts and material culture, reducing culture to some kind of perceptual and cognitive process produces an inadequate account of musical culture and the scales and tuning that are the focus of their paper. Ratios or other numerical or computational approaches fit into that other important aspect of culture, namely “regulation”. The regulated adoption of a concert tuning standard and of the EDO or equal temperament tuning system have allowed a wide range of standardised musical practices. Many would claim that this form of regulation has caused the downfall and decay of musical culture in the second half of the 20th century. Many artists in the world of popular (and not-so-popular) electronic music might argue otherwise. Whether or not regulation of cultural practice is good or bad it is a key ingredient in the adoption of a tuning system. The author’s claim that “Musical intervals belong to the subjective world of human culture, not the objective world of mathematics and physics.” This division is fundamentally wrong, and is clearly not true.

Ultimately it is the blending of theory and practice (praxis) that produced musical culture. An example of confusion over this point is given in the authors’ reference to David Hykes’ harmonic chant. Their statement “The ultimate reason for just tuning in this kind of music may not be ratios themselves but overlapping harmonics. The ratios emerge when harmonic partials line up and not because the brain is processing ratios.” begs the question of where ratios fit into a so-called Pythagorean conception. A Pythagorean might rightly assert that “we choose low-order ratios because of the sounds they produce”.

The article is exceptionally comprehensively referenced (references extend to 7 pages), however the authors occasionally draw an extremely long bow in their combinations of ideas. For example a somewhat misplaced quote from Gyorgy Lukacs attacking empiricism does little to support their position.

Overall, I agree with the position taken by the authors that scales are a reflection of musical practice, a common sense position supported by Percy Scholes’ eminently practical entry on scales in the Oxford Companion to Music. My complaint is about the overly cognitivist position that the authors take to support their argument which ignores large aspects of material musical culture.