Sight-playing part – 2

In the first part of the article, we have learned about many musical and technical concepts. Now it is time to use them to build an automatic composer.  Before doing so, however, we must make certain assumptions (or rather simplifications):

  • the pieces will consist of 8 bars in periodic structure (antecedent 4 bars, consequent 4 bars)
  • the metre will be 4/4 (i.e. 4 quarter notes to each bar, accent on the first and third measures of the bar)
  • the length of each motif is 1 bar (although this requirement appears restrictive, many popular pieces are built precisely from motifs that last 1 bar).
  • only C major key will be used (if necessary, we can always transpose the piece to any key after its generated)
  • we will limit ourselves to about 25 most common varieties of harmonic degrees (there are 7 degrees, but some of them have several versions, with additional sounds which change the chord colour).

What is needed to create a musical piece?

In order to automatically create a simple musical piece, we need to:

  • generate the harmony of a piece – chords and their rhythm
  • create motifs – their sounds (pitches) and rhythm
  • create variations of these motifs – as above
  • combinate the motifs and variations into a melody, matching them with the harmony

Having mastered the basics, we can move on to the first part of automatic composing – generating a harmony. Let’s start by creating a rhythm of the harmony.

Slow rhythm

Although one might be tempted to create a statistical model of the harmonic rhythm, unfortunately, (at least at the time of writing this article) there is no available base which would make this possible. Given the above, we must handle this in a different way – let’s come up with such a model ourselves. For this purpose, let’s choose a few “sensible” harmonic rhythms and give them some “sensible” probability.

rhythmprobabilityrhythmprobability
[8]0.2[2,2]0.1
[6, 2]0.1[2,1,1]0.02
[2, 6]0.1[3,1]0.02
[7, 1]0.02[1,1,1,1]0.02
[4]0.4[1,1,2]0.02
Table 1. Harmonic rhythms, values expressed in quarter notes – [6, 2] denotes a rhythm in which there are two chords, the first one lasts 6 quarter notes, the second 2 quarter notes.

The rhythms in the table are presented in terms of chord duration, and the duration is shown in the number of quarter notes. Some rhythms last two bars (e.g. [8], [6, 2]), and others one bar ([4], [1, 1, 2] etc.).

Generating a rhythm of the harmony proceeds as follows. We draw new rhythms until we have as many bars as we needed (8 in our case). Sometimes certain complications may arise from the fact that the rhythms have different lengths. For example, there may be a situation where to complete the generation we need the last rhythm that lasts 4 quarter notes, but we draw one that lasts 8 quarter notes. In this case, in order to avoid unnecessary problems, we can force drawing from a subset of 4-quarter-note rhythms.

Then, in line with the above findings, let’s suppose that we drew the following rhythms:

  • antecedent: [4, 4], [2, 2], [3, 1], 
  • consequent: [3, 1], [8], [2, 2]

Likelihood

In the next step, we will be using the concept of likelihood. It is a probability not normalised to one (so-called pseudo-probability), which helps to assess the relative probability level of different events. For example, if the likelihoods of events A and B are 10 and 20 respectively, this means that event B is twice as likely as event A. These likelihoods might as well be 1 and 2 or 0.005 and 0.01. From the likelihoods, probability can be calculated. If we assume that only events A and B can occur, then their probability will be respectively:

Chord progressions

In order to generate probable harmonic flows, we will first prepare the N-gram models of harmonic degrees. To this end, we will use N-gram models available on github (https://github.com/DataStrategist/Musical-chord-progressions).

In our example, we will use 1-, 2-, 3-, 4- and 5-grams.

In the rhythm of the antecedent’s harmony, there are 6 rhythmic values, so we need to prepare the flow of 6 harmonic degrees. We generate the first chord using unigrams (1-grams). Now, we first prepare the likelihoods for each possible degree and then draw while taking these likelihoods into consideration. The formula for likelihood is quite simple in this case

likelihoodX=p(X)

where

  • X means any harmonic degree
  • p(X) is the probability of the 1-gram of X

In this case, we drew IV degree (in this key of F major).

We generate the second chord using bigrams and unigrams, with a greater weight for bigrams.

likelihoodX=weight2gramp(X v IV)+weight1gram*p(X)

where:

  • p(X v IV) is the probability of the flow (IV, X)
  • weightNgram is the adopted N-gram weight (the greater the weight, the greater the impact of this N-gram model, and the smaller the impact of other models)

We can adopt N-gram weights as we wish. For this example, we chose the following:

N-gram12345
weight0.0010.010.115

The next chord we drew was: vi degree (a minor).

The generation of the third chord is similar, except that we can now use 3-grams:

likelihoodX=weight3gramp(X v IV, vi)+weight2gramp(X v IV)+weight1gram*p(X)

And so we continue until we have generated all the necessary chords. In our case, we drew:

IV, vi, I, iii, IV, vi (in the adopted key of C major these are, respectively, F major, a minor, C major, e minor, F major and a minor chords).

This is not a very common chord progression but, as it turns out, it occurs in 5 popular songs (https://www.hooktheory.com/trends#node=4.6.1.3.4.6&key=rel)

Summary

We were able to generate the rhythms and chords which are the components of the harmony of a piece. However, it should still be noted here that, for the sake of simplicity, we didn’t take into account two important factors:

  • The harmonic flows of the antecedent and consequent are very often linked in some way. The harmony of the consequent may be identical with that of the antecedent or perhaps slightly altered to create the impression that these two sentences are somehow linked.
  • The antecedent and consequent almost always end on specific harmonic degrees. This is not a strict rule, but some harmonic degrees are far more likely than others at the end of musical sentences.

For the purposes of the example, however, the task can be deemed completed. The harmony of the piece is ready, now we only need to create a melody to this harmony. In the next part of our article, you will find out how to compose such a melody.

Cloud computing vs environment

The term “cloud computing” is difficult to define in a clear manner. Companies will approach the cloud differently than individuals. Typically, “cloud computing” is used to mean a network of server resources available on demand – computing power and disk space, but also software – provided by external entities, i.e. the so-called cloud providers. The provided resources are accessible via the Internet and managed by the provider, which eliminates the need for companies to purchase hardware and directly manage physical servers. In addition, the cloud is distributed over multiple data centres located in many different regions of the world, which means that users can count on lower failure rates and higher availability of their services [1].

The basic operation of the cloud

Resources available in the cloud are shared by multiple clients, which makes it possible to make better use of the available computing power and, if utilised properly, can prove to be more cost-effective. Such an approach to resource sharing may raise some concerns, but thanks to virtualisation, the cloud provides higher security than the traditional computing model. Virtualisation makes it possible to create simulated computers, so-called virtual machines, which behave like their physical counterparts, but reside on a single server and are completely isolated from each other. Resource sharing and virtualisation allow for efficient use of hardware and ultimately reduce power consumption by server rooms. Financial savings can be felt thanks to the “pay-as-you-go” business model commonly used by providers, which means that users are billed for actually used resources (e.g. minutes or even seconds of used computing time), as opposed to paying a fixed fee. 

The term “cloud” itself originated as a slang term. In technical diagrams, network and server infrastructure is often represented by a cloud icon [2]. Currently, “cloud computing” is a generally accepted term in IT and a popular computing model. The affordability of the cloud and the fact that users are not required to manage it themselves mean that this computing model is being increasingly preferred by IT companies, which has a positive impact on environmental aspects [3].

Lower power consumption 

The increasing demand for IT solutions leads to increased demand for electricity – a strategic resource in terms of maintaining the cloud. A company maintaining its own server room leads to significant energy expenditure, generated not only by the computer hardware itself but also by the server room cooling system. 

Although it may seem otherwise, larger server rooms which process huge amounts of data at once are more environmentally friendly than local server rooms operated by companies [4]. According to a study carried out by Accenture, migrating a company to the cloud can reduce power consumption by as much as 65%. This stems from the fact that cloud solutions on the largest scale are typically built at dedicated sites, which improves infrastructure organisation and resource management [5]. Providers of large-scale cloud services can design the most effective cooling system in advance. In addition, they make use of modern hardware, which is often much more energy-efficient than the hardware used in an average server room. A study conducted in 2019 revealed that the AWS cloud was 3.6 times more efficient in terms of energy consumption than the median of the surveyed data centres operated by companies in the USA [6].

Moreover, as the cloud is a shared environment, performance can be effectively controlled. The scale of the number of users of a single computing cloud allows for a more prudent distribution of consumed energy between individual cases. Sustainable resource management is also enabled by our Data Engineering product, which collects and analyses data in order to maximise operational efficiency and effectiveness.

Reduction of emissions of harmful substances

Building data processing centres which make use of green energy sources and are based on low-emission solutions makes it possible, among others, to control emissions of carbon dioxide and other gases which contribute to the greenhouse effect. According to data presented in the “The Green Behind Cloud” report [7], migrating to public cloud can reduce global carbon dioxide emissions by 59 million tonnes per year, which is equivalent to removal of 22 million cars from the roads.

It is also worth considering migration to providers which are mindful of their carbon footprint. For example, the cloud operated by Google is fully carbon-neutral through the use of renewable energy, and the company promises to use only zero-emission energy around the clock in all data centres by 2030 [8]. The Azure cloud operated by Microsoft has been carbon-neutral since 2012, and its customers can track the emissions generated by their services using a special calculator [9].

Reduction of noise related to the use of IT hardware  

Noise is classified as environmental pollution. Though at first glance it may appear quite inconspicuous and harmless, it has a negative impact on human health and the quality of the environment. With respect to humans, it increases the risk of such diseases as cancer, myocardial infarction and arterial hypertension. With respect to the environment, it leads to changes in animal behaviour and affects bird migration and reproduction.

The main source of noise in solutions for storing data on company servers is a special cooling system which maintains the appropriate temperature in the server room. Using cloud solutions makes it possible to reduce the noise emitted by cooling devices at workplaces, which helps limit environmental noise pollution.

If you want to learn more about the available solutions for reducing industrial noise, check our Intelligent Acoustics product.

Waste level reduction 

Making use of cloud computing in business activities, as opposed to having traditional servers as part of company resources, also helps reduce the amount of generated electronic waste. This stems primarily from the fact that cloud computing does not necessitate the purchase of additional equipment or preparation of infrastructure for a server room at the company, which reduces the amount of equipment that needs to be disposed of in the long term.  

In addition, the employed virtualisation mechanisms, which entail the replacement of a larger number of low-performance servers with a smaller number of high-performance servers which are able to use this performance more effectively, optimise and increase server efficiency, and thus reduce the demand for hardware resources.  

Summary 

Sustainability is currently an important factor in determining the choice of technology. Environmental protection is becoming a priority for companies and for manufacturers of network and telecommunications devices, which means that greener solutions are being sought. Cloud computing definitely fits this trend. It not only limits the consumption of hardware and energy resources, but also reduces the emission of harmful substances into the ecosystem as well as noise emissions into the environment.  

References 

[1] https://www.wit.edu.pl/dokumenty/wydawnictwa_naukowe/zeszyty_naukowe_WITZ_06/0006_Joszczuk-Januszewska.pdf 

[2] https://rocznikikae.sgh.waw.pl/p/roczniki_kae_z36_21.pdf 

[3] http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.ekon-element-000171363539  

[4] Paula Bajdor, Damian Dziembek “Środowiskowe i społeczne efekty zastosowania chmury obliczeniowej w przedsiębiorstwach” [“Environmental and Social Effects of the Use of Cloud Computing in Companies”], 2018 

[5] https://www.accenture.com/_acnmedia/PDF-135/Accenture-Strategy-Green-Behind-Cloud-POV.pdf  

[6] “Reducing carbon by moving to AWS” https://www.aboutamazon.com/news/sustainability/reducing-carbon-by-moving-to-aws

[7] https://www.accenture.com/us-en/insights/strategy/green-behind-cloud

[8] “Operating on 24/7 Carbon-Free Energy by 2030.” https://sustainability.google/progress/energy/

[9] https://www.microsoft.com/en-us/sustainability/emissions-impact-dashboard