Your computer or phone likely runs with a clock speed on the order of around 1 GHz (gigahertz) or faster (the iPhone’s A8 processor runs at 1.1 GHz). That means that there are one billion pulses per second controlling instructions inside it. This equals one pulse every nanosecond, which is just one billionth of a second.

One nanosecond compared to one second is the same as one second compared to 32 years. Every second there are as many pulses of instructions in your phone as there are seconds over the span of 32 years. Many computers run faster than this. My Intel i7 processor runs at around 3.5 GHz, so, we multiply the 32 years by 3.5, getting as many pulses per second as there are seconds in 112 years.

We can use this information to begin to understand large distances. In one nanosecond, light can travel just short of 30cm, the length of a standard school ruler. So this distance is 1 lightnanosecond. If we scale that up to one full second, a billion times more time, that light can now travel almost 299,792 km. 1 lightsecond.

How many seconds are there in a year? Let’s work it out: There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365.25 days in a year (the .25 is to account for a leap day every four years). We multiply all those factors together to get 60×60×24×365.25 = 31,557,600 seconds in a year. That’s 31 million, 557 thousand and 600 seconds.

In astronomical terms, we talk about lightyears as one base unit of distance. One year is 31,557,600 times longer than one second, so one lightyear is 31,557,600 times further than one lightsecond. So we multiply: 299,792 km × 31,557,600 = 9,460,716,019,200 km. That’s 9 trillion, 460 billion, 716 million, 19 thousand and 200 kilometers!

Now, in the world of astronomy, we’re dealing with distances so big that those 200 km at the very end of that figure really don’t make much of a difference either way. Actually, what we really care about is only the first few digits, which leads to the scientific notation of numbers. We write one lightyear as being equal to 9.641 × 10^12 km. This means that we take the first part, 9.641, and move that decimal point twelve places to the right, adding zeros as we go, like this: 9 641 000 000 000. But rather than writing these things out all the time, astronomers use the lightyear as a unit by itself (the same as we use meters or kilometers), so we write 1 ly.

Now 1 ly is a long way compared to what we normally see and experience in our day-to-day lives, but really it’s not all that far when you look at star systems, let alone the whole galaxy. In fact, the very nearest star system to us (Alpha Centauri) is a little more than 4 lightyears away. This is a three-star system, with two stars orbiting each other close together, and a third star much further out, taking more than 500 000 years to orbit the other two.

But Alpha Centauri is just our nextdoor neighbour. Even if we go out to a distance of 10 lightyears, we’re still just strolling around the cul de sac with 9 star systems that close by. Our whole street might be out to 15 ly around us, which includes about 45 star systems, and our suburb might encompass 50 ly in any direction, with around 1400 star systems.

50 lightyears is a long way in human terms, but when we consider the Milky Way, our galaxy, we’re still only just scratching the surface. In fact, the centre of the galaxy, which is occupied by a supermassive black hole, is around 25,000 lightyears away from us here on Earth. The whole disc of our spiral galaxy is more than 100,000 lightyears across, with hundreds of billions of stars contained within it. Hundreds. Of billions.

We’ve certainly shot past the point of numbers that I can actually comprehend, and possibly you too, but why stop there? Our galaxy is not the only galaxy in the universe. In fact, we are part of a group of galaxies local to us which has the creative name of the Local Group. The Local Group comprises more than 50 individual galaxies, and the Milky Way is the second biggest of these. The biggest, the Andromeda Galaxy, is 2.5 million lightyears away from us. If we wanted to write that out in kilometres, we’re looking at something like 23 650 000 000 000 000 000 km, much more easily written as 2.365 × 10^19 km, or 2.5 Mly (the M stands for mega-, and like megabytes in a computer means a factor of one million).

Until recently, we thought that in the entire universe, there might be hundreds of billions of galaxies, each containing billions, or hundreds of billions, or trillions of stars themselves. Last year, a study was published that suggests that we actually underestimated the number of galaxies by a factor of 10 or so, which means that our current estimate is that there are at least a trillion galaxies in the universe. That’s 1 000 000 000 galaxies, each with about 100 000 000 stars.

In the last couple of decades, astronomers have confirmed the existence of planets around other stars – extrasolar planets, or exoplanets – something that was assumed to be true for centuries but not proven until 1995. Since then, thousands of exoplanets have been discovered (as of this month, 3,667 confirmed), and looking at the regularity of these across different types of stars in different parts of the sky, it is suspected that every star in our galaxy has at least one planet.

We even suspect that one out of every five stars like our Sun has an Earth-sized planet in its habitable zone, where liquid water is stable on the surface of the planet, conditions that we suspect may be conducive to the development of life.

Considering all of this; the magnificent scale of the universe around us, the unimaginable number of possible worlds around an unimaginable number of other suns, and that’s in just one galaxy out of an unimaginable number of other galaxies. Over the span of billions of years, with billions more to come, the universe is constantly surprising and awe-inspring.

And we’re down here arguing about who should be allowed to marry each other, and whether some people should be allowed to kneel when a particular song is sung. Go figure.

# Biomusic, Music in Nature and Musica Universalis

The following post is an edited version of the third of four chapters from my honours thesis, originally written in 2013. The thesis as a whole acts as a kind of “how to” guide for composing in a few different styles, each of which somewhat removes human aspects of music composition, at the same time exploring ideas of musical universals – those aspects of music that seem to be ubiquitous across all cultures or even found to be in common across different species! This chapter details one method of musical data sonification, which I used in order to create musical representations of the orbits of planets around distant stars.

Chapter 3: Biomusic, Music in Nature and Musica Universalis

Universals are rooted in nature, but have effects in culture” (Leman, 2003, unpaginated)

Given that music can exist in numerical data, and in the sounds produced by animals, naturally occurring patterns can also hold musical information, and could have had profound impact upon the creation of early music. Natural patterns such as the rhythms of heartbeats, the natural walking pace of an individual, the night/day cycle and the changing of seasons are all examples of patterns that hold potential musical information and are all intrinsic parts of life.

Biomusic here differs from zoömusic in that it refers to sounds, pitches or rhythms created biologically, but without an intended aesthetic aspect. While the ‘voices’ of many animals used for mating calls are widely considered to have an intended aesthetic aspect, other sounds that are purely functional or biological come under the heading of biomusic.

Musica Universalis is an archaic philosophical concept relating the movements of celestial bodies – the Sun, the Moon, and the planets – to a form of music. This ‘music’ is of course not audible, but rather it can be described in the same terms as music – through mathematical and harmonic principles. The implications of this have historically been thought of as astrological rather than purely mathematical (Kepler, 1997). The harmonically described motions of celestial bodies (the rotations, orbits and resonances with other objects) are yet another example of patterns in nature which contain musical information that can be used in compositions.

# Zoömusicology: Music in the Animal Kingdom

The following post is an edited version of the second of four chapters from my honours thesis, originally written in 2013. The thesis as a whole acts as a kind of “how to” guide for composing in a few different styles, each of which somewhat removes human aspects of music composition, at the same time exploring ideas of musical universals – those aspects of music that seem to be ubiquitous across all cultures or even found to be in common across different species! This chapter is all about creating music that is based on birdcalls, and the technique could be altered for any natural (or non-natural) tuneful sounds.

Chapter 2: Zoömusicology: Music in the Animal Kingdom

Zoömusicology is part of a framework within biomusicology, first described by Wallin (1991), which combines the fields of evolutionary musicology (dealing with the origins of music, animal sounds as music, and ‘selection pressures’ resulting in the music we hear today), neuromusicology (the brain areas and cognitive processes involved in music making and interpretation), and comparative musicology (looking at the functions and uses of musical systems, as well as universal traits; comparative musicology was the precursor to modern ethnomusicology). In this chapter, I have looked at bird song.

No sound in nature has attached itself so affectionately to the human imagination as bird vocalisations. In tests in many countries we have asked listeners to identify the most pleasant sounds of their environment; bird-song appears repeatedly at or near the top of the list. And the history of effective bird imitations in music extends from Clément Janequin to Olivier Messiaen. (Schafer, 1977, p. 29)

Mâche notes the similarity between human music and animal music,

There is not a single musical procedure which does not have its equivalent or its prototype in one or other of the innumerable signals of animals. The simplest, in animals as in man, is naturally repetition. (Mâche, 1983/1992, p. 115)

# Music By Numbers

The following post is an edited version of the first of four chapters from my honours thesis, originally written in 2013. The thesis as a whole acts as a kind of “how to” guide for composing in a few different styles, each of which somewhat removes human aspects of music composition, at the same time exploring ideas of musical universals – those aspects of music that seem to be ubiquitous across all cultures or even found to be in common across different species! This chapter details the creation of an alternate tuning system for musical notes which is based on phi, a mathematical relation found in art and nature.

Chapter 1: Music By Numbers

Music is numerical by its very nature. The subdivision of time into rhythms, beats and pulses; the subdivision of frequency into myriad distinct scales and tonal systems, the mathematical principles underlying the combination of frequencies and notes in the creation of harmony. Many aspects of music are based on numbers, but is there a correlation between the numbers that define musical theory, and those that can be used to define natural phenomena? If such a correlation exists, implications could be drawn regarding the development of musical systems, as well as the ideas of musical universals.

There are several ways in which number patterns can be used to describe natural phenomenon. The self-similarity of fractals can describe the growth of plants, logarithmic curves and Fermat’s spiral can be used to describe the shapes of spirals in ram’s horns, the arrangements of leaves on plant stems, and the spiral curves in nautilus shells; chaos theory can explain the flow and shape of rivers, and the shapes of seashells can be described through the use of cellular automata. One pattern that can be found in nature as well as art to a great extent is the Fibonacci sequence.

# Score Analysis – Star Wars Episode V: The Empire Strikes Back

George Lucas’ Star Wars (1977) is considered a groundbreaking work in modern cinema, particularly within the science fiction genre, and particularly also with respect to film scores and sound design – John Williams’ score to the film is often credited with reviving the practice of symphonic scores – and particularly the use of Wagnerian leitmotif. The film’s sequel – The Empire Strikes Back (1980) – continued this tradition, using many musical motifs from the first film, while also introducing others. The series’ sound design, led by Ben Burtt, has also been praised as a shining example of what could be done with pre-digital technologies, and both the score and the sound design are major reasons why these films have stood the test of time as well as they have.

While the original Star Wars and its second sequel – Return of the Jedi (1983) – both feature sequences with specifically composed diegetic music, all music in The Empire Strikes Back is non-diegetic.

Musical Score Analysis

20th Century Fox Fanfare (0’00” – 0’19”)

The first cue in the film, and one that became something of a tradition in Star Wars films, is the 20th Century Fox Fanfare, originally composed for the studio by Alfred Newman in 1933. For Star Wars in 1977, director George Lucas wanted to use the fanfare, which was, at the time, being rarely used in films from the studio. Composer John Williams wrote the iconic Star Wars Main Title in the same key as the fanfare (Bb) to act as an extension and to blend the fanfare into the score for the film more seamlessly. For Star Wars, the 1953 CinemaScope recording of the fanfare was used, but for The Empire Strikes Back, John Williams conducted the London Symphony Orchestra in a new recording for the film. The fanfare plays over logos for both 20th Century Fox and Lucasfilm.

R1Pt1: Star Wars Main Title/R1Pt2: The Imperial Probe (0’27” – 4’14”)

As with each of the six films in the Star Wars saga (as well as related TV shows and video games), the film opens with the words “A long time ago in a galaxy far, far away….” on screen in silence. The Star Wars logo appears on screen in synchrony with the opening full-orchestra chord of the Star Wars Main Title, a march-like, heroic theme that is one of the most recognisable music cues from the series, and perhaps from cinema as a whole, and represents the main protagonist of the original trilogy, Luke Skywalker (figs. 1 & 2)The musical style is similar to that of ‘Golden Age of Hollywood’ composers such as Alfred Newman, Max Steiner, Erich Korngold and Franz Waxman. This was primarily by design, as director George Lucas wanted John Williams to compose music that already felt very familiar, and that was reminiscent of serial adventure films from the 1930s and 1940s such as Dick Tracy, Flash Gordon, Zorro, and Tarzan. This familiarity and style creates something of a contrast between the music and the exotic and futuristic locales, characters and settings seen in the film.