Intro to tonal harmonic theory Part 2: Stuff you have to learn.

Stuff you have to learn

Disclaimer:

This post contains dubious amounts of hand-waving and opinion, and you might get more from it by ignoring the text and just playing with the table below, and the harp from the previous post. For audio to work you need a Web-Audio-API compliant browser like desktop Chrome or Safari.

Introduction

Western music notation is not the de-facto standard in music notation... there are many standards. But western musical terms are the most prevalent, and more often than not, when attempting to collaborate with anyone, you will find yourself needing to communicate using western conventions. So you might as well learn it. It looks hard at first, but you'll get the hang of it!

Next up, a table with the basics of western tonal harmonic theory. In this table you will find the common chords and scales. The discussion part will gloss over why these are the "common" chords and scales. I will sometimes refer back to part 1..

The Table

Choose a dominant note, and then press the buttons to hear the intervals, chords and scales (if you have a Web-Audio-API-compliant browser). The darker rows represent the black notes on a piano, and a "X" in a row means that note will be played. Intervals and chords are played simultaneously, whereas scales will ascend. You will have to use the scroll-bar at the bottom of the table to get to the scales. The source code for the table is here if you are interested.

Discussion

Unlike many tables like this you might have come across, I followed the piano-roll convention used in popular sound production software... where "one row up" translates to "one semitone up".

The "note numbers" column is consistent with the interactive harp in part 1. Choosing a "Dominant note" is analogous to setting the "Base String" in part 1.

This file contains the meat of the table above. It is in essence the first principle starting point for deriving much of western tonal harmonic theory. Hopefully it is enough to get you going.

Western pitch encoding.

This is the naming scheme still in use today to describe the 12 semitones : A, A#, B, C, C#, D, D#, E, F, F#, G, G#.
After G# it "loops" back to A, but an octave higher.

The reason western music theory is filled with oddities in naming conventions is because of historical conservatism. We could have ended up with a pitch encoding which used Arabic numerals instead... in fact, music teachers are forced to do this to get many concepts across (eg. counting out 7 semitones from "B" to show its "5th" is a "sharp"( more on sharps just now). ). The seemingly strange lack of mathematical consistency becomes consistent once you ignore the western conventions and just count out the semitones.

Intervals are just relative spacings between two notes played together. A "5th" will always be some base note and a note 7 semitones above it.

The choice of terms for intervals demonstrate a lack of mathematical proficiency in its originators since the 6th semitone interval is assigned, not a number but, a mystical sounding name instead... "The Tritone". Imagine counting like this in maths class: "One, kinda two, really two, kinda three, really three, four, MAGIC THREE!, five, kinda six, really six, kinda seven, really seven, eight!" (when what you really meant was to count from zero to twelve). People will think you're mad, or worse, an idiot. That is kinda the point to western music theory though... a lot of it is convention rather than sense... which is why, if you wanted to communicate your compositions or play in a band, unfortunately, you just have to learn this... which, once you learn it, you realise that even though it is a bit clumsy (like doing calculations using Roman numerals), it still remains systematically consistent... so at least useful.

Why are only some pitches a "#"

In western music theory they have two operators called "sharp" (♯) and "flat" (♭). Basically a "sharp" is a shift "up" by one semitone. A "flat" is one semitone shift "down".

Back in the day they still thought there were 7 tones (not counting the octave) in an octave (hence the name "octave" from Latin for 8). The tones were not logarithmically equally spaced and looked a lot like the octatonic scale set-up in part 1.

Once it emerged that 12 tones would be a better idea, instead of adopting a 12-toned scheme, they instead adopted the concept of a "semitone" (which you should be familiar with by now). In other words: a semitone is what a tone would have been had western music theory adopted a 12-tone scheme. Instead they kept the 7 tone system and kludged in the missing tones with "semitones". From part 1 it should be clear that the missing notes will make up another pentatonic scale.

That is why only some notes are sharp: the "sharps" make up the "semitones" that were missing from the original octatonic scale. They make up the black notes on a piano.

Scales

The family of Major scales was similar to earlier octatonic scales and they remain prevalent in modern music. The harmonic minor scale is the odd-one-out... it is common for reasons outside the scope of this post... basically, it is around because it has a pleasant sounding system of chords associated with it.

Resonance

I mentioned previously that I would go into this, but I will really only be touching on it. Resonance is the ability of something to sympathetically vibrate with something else which is also vibrating. A String will most strongly resonate with vibrations that are the same as its harmonics. Most strongly with the 1st harmonic, and then progressively less with each harmonic after that. So, looking back to part 1, intuitively, early iterations should produce a set of strings with strong resonances (up to 4 iterations), but then quickly become less resonant (from 5th to 7th iteration), and then progressively more resonant again just before the iterations loop back (the last 4 iterations).

So, using this grossly-over-simplified-hand-waving explanation it seems that chords based on the pentatonic scale will resonate the strongest. Significantly, the Major and minor chords exist in the pentatonic scale and they happen to make up the bulk of popular compositions. Diminished and Augmented chords are basically extensions of the Major and minor into the 12-semitone scheme, and are examples of "dissonant" chords... important in Jazz compositions.

More?

This post has become large enough... If there is enough interest, I might do another post expanding on sets of chords within a scale... but I think you've been sufficiently "introduced" to tonal harmonic theory that I can leave that as an exercise for you, the reader.

Intro to tonal harmonic theory Part 1: Why are there 12 semitones?

Why do we have 12 notes in an octave?

Disclaimer:

This is not a definitive source. Please forgive all the links to wikipedia. I studied physics, electronics and computer science. My understanding of music isn't the same as someone formally trained in, say, western classical music, though I understand enough of it to get by. This represents more an attempt to get across an intuition I've had about the question "Why do we have 12 notes in an octave?". It also acts as a means to test my intuition by actually implementing it. So, I won't bother with historical references, not only because they don't interest me, but since the confirmation to this post is in the code (which is still a work in progress, so I make no claims, etc...) hopefully running in front of you ( if you have the right browser... sorry). I leave the historical referencing and digging to wikipedians and people who are more passionate about that kind of thing. I'm more interested in the types of truths one can confirm through simulation... and music happens to be filled with those...

Introduction

In this post I present an interactive harp using an iterative construction method following a version of the Pythagorean construction method. The construction method will be presented visually rather than mathematically. The source is here if you are interested in the mathematics.

From using the interactive harp it should become clear why there are 12 semi-tones in the modern "chromatic" scale, and some further discussion will show how they became "tempered".

Note though that using some other scheme, or just arbitrarily, you could divide an octave up however you want, with as many notes spaced however you want...

This post specifically deals with the question of the origins of the tempered 12-tone chromatic scale which is most prevalent at any music store or almost standard in any music production software... and to provide an intuitive grasp on the physical origins of the modern tempered 12-tone chromatic scale.

The interactive harp

What follows is a harp made with strings that are "ideal"... meaning strings that might only exist by virtue of mathematics (so no problem for synths). The important attribute of ideal strings is that their harmonics are "perfect"... meaning; the 3rd harmonic is exactly a 3rd of the fundamental wavelength. Real Life strings actually have a 3rd harmonic which is dependant on the mass distribution properties of the string, and is not exactly a 3rd... but more on this later.

Also, these ideal strings are all under equal tension, so only their length need be considered: i.e. Longer strings have a "lower" fundamental (or 1st harmonic), and shorter ones have a "higher" fundamental.

The figure below is playable on browsers that support the Web-Audio-API (Currently only desktop versions of Chrome and Safari).

The figure above starts off as a pretty boring harp. The harp was constructed by taking some base string, and constructing 2 more strings whose fundamentals are the same as the base string's 2nd and 3rd harmonics... which in this case is simply 1/2 and 1/3 of the base length.

The choice of colours for the strings is arbitrary (in this case the hue value is incremented in 12 steps). The string's colour's is mainly a visual means to identify "new" pitches. You will notice that the 1st and 2nd strings are the same colour... this is because 2nd harmonics are so fundamental to music theory that they are assigned the same pitch. The 2nd harmonic also signifies what is known in western music theory as an "octave". Therefore, only the 3rd string will get a new colour... and is therefore the only "new" pitch. Historically, the 2nd harmonic and 3rd harmonic produce the interval referred to as a "5th".

Time to play...

Select a desired western base note with the "Base note" to be the largest string on the harp. Note though that in RL, we can select any base note with any frequency, and the results will look the same. The origins of the western naming scheme is hinted at in the interactive harp, but we'll go more into that in part 2.

What the buttons do:

• The figure can be reset to its initial state by pressing the "Clear" button.
• The "Iterate" button does all the magic... but it is quite easy to follow. Basically, it takes any newly coloured string, and doubles the length of that string until it falls within the initial octave's range (the first two red strings). Using the new long string's length as reference, another string is constructed which is a 3rd of that length. This final string will have a new colour, and will be the input for the next time you press the "iterate" button.
• The "Draw L_n=L₀.2^n/12; n=0..31 ("tempered" scale with 32 notes)" button does what it says... draws the "tempered" scale as reference. The tempered chromatic scale is what you will commonly find with non-sliding modern instruments (fretted guitar, piano, flute, bassoon, etc...). Specifically here I followed the conventions of concert pitch... which means I arbitrarily specified A4 to be 440Hz. There was no other reason for this choice than to make it relevant to western music theory. More on tempering later.
• The "Show Note Values" button displays the western pitch codes: (A, A#, B, C, C#, etc..)
• The "Pentatonic Scale" button resets the harp and iterates 4 times. This produces the well-known and cross-cultural pentatonic scale. The pentatonic scale also contains the musically fundamental major and minor chords, but more on this in part 2.
• The "Octatonic Scale" button resets the harp and iterates 6 times. This produces the well-known family of major scales (i.e. the Major, Natural Minor, Mixolydian and Dorian scales).
• The "Non-tempered 12-tone Scale" button resets the harp and iterates 11 times. This produces the well-known chromatic scale. This specific scale is a sub-set of just intonation tuning. You can press the tempered scale button to compare the difference. More on tempering in the discussion.
• The "Many iterations later" button resets the harp and iterates 52 times. This is to show the limit of this construction method. Any more iterations will over-step the initial chromatic set-up( Non-tempered 12-tone Scale).

Discussion

This version of the Pythagorean construction method can conceivably be performed visually or by ear. Given some basis string, this iterative method will eventually cycle back to somewhere very close to the initial string after 11 iterations (not counting the set-up as an iteration); dividing an octave into 12 (almost logarithmically equal) semitones. Repeated iterations will repeat this cycle every 12 iterations after that until it becomes a bit of a mess... So, in short, the reason there are 12 semitones, is because of the 3rd harmonic... A iterative construction based on the 3rd harmonic will produce 12 distinct bands which appear to "loop" back every 12 iterations. This construction will produce a pattern consistent with the circle of 5ths ( remember, the 3rd harmonic produces a interval on the harp historically referred to as a 5th (More on intervals in part 2))..

Small mathematical detour and tempering...

In Real Life, a string's 3rd harmonic is dependent on many factors, and generally isn't "perfect". Generally the factors string manufacturers take into consideration are tension, length, diameter and mass (length, diameter and mass = mass distribution.). So, is there some different 3rd harmonic that would make this iterative process cause the 11th iteration to loop exactly back to the beginning? The answer is in the definition of the semitone.

The semitone:
An octave is a doubling or halving of length or frequency... so, an "octave" isn't a length, or anything physical. It is a ratio. What we've been doing here is dividing lengths by 2 or 3, and sometimes multiplying by 2. So, the semitone is therefore some value, which if we multiplied some original value by that value 12 times, it would produce exactly 2 times the original value.
So, lets say x is the magic semitone value, then x*x*x*x*x*x*x*x*x*x*x*x*L = x¹²L = 2L,
or simply, x¹² = 2.
Therefore the semitone ratio, x = 2^1/12.

In 12-toned set-up, the 3rd harmonic would occupy the 19th string from the base string. For 12 equal semitones to exist, instead of the upper 5th being the base note times 3, it should rather be the base note multiplied by our semitone ratio, x, 19 times. Which is x¹⁹, or 2^19/12, which on your calculator would give 2.99661415 (rounded to 8 digits). Notice how that number is damn near 3.

Now, since you can't get a string with a 3rd harmonic which is "perfect", this at least gives one a physically attainable target. By tailoring mass distribution properties on strings and getting close to this target, manufacturers are "tempering" the string to fit into the 12-tone tempered chromatic scale, resulting in superior harmonising. Historical experimentation into the tempered scale often only considered the tuning of the instrument, but modern manufacturing takes into account the physical manifestation of harmonising (tempered string vs. tempered scale), which in essence is resonance. But more on that in part 2.

Battle of the audio APIs

TL;DR: Native Web Audio API is better if you're making games.

Which is better? Google's Web Audio API [1] or Mozilla's Audio Data API [2][3]?

 Well, actually that is not a question which can be easily answered since the two, though sharing some use-cases, are quite different. Also, to emphasise the difference, Mozilla's Audio Data API specification, officially since 15 December 2011, falls under a more general "MediaStream Processing" API specification [3]. Just browsing the two specifications will show you that they are quite different animals and that the Web Audio API specification is currently more mature (less likely to change).

To really get at the core difference between the two APIs, known that Google's Web Audio API can be,(and has been [4]) implemented in JavaScript using Mozilla's Audio Data API. So, immediately it is apparent that the Mozilla API is a lot more "low-level". That is, it gives you some core functionality which allow access to HTML "audio" elements' internal data. The specification, now more generalized for "MediaStream Processing", also allows for access to HTML "video" elements' internal data.

So, the specification championed by Robert O'Callahan and Mozilla is great for managing media assets, and performing streaming, extracting, injecting or mixing operations on raw data from audio and video elements. Microphone input would be considered a media element under this specification. The big use-case will be for in-browser video-conferencing or web-casting applications.

What is the Web Audio API then? It allows the user to build complex audio graphs, place sound sources spatially (including features like Doppler effects and HRTF ), trigger sound sources in a timely fashion, and comes with a set of pre-defined filters and effect generators. So, everything you need to make a soft-synth or a computer game's audio.

Now, since you can implement Chris Rodger's Web Audio API specification on top of the Mozilla specification in JavaScript, why have native support for it? Answer: Performance.

A JavaScript implementation of the Web Audio API, though functional, will run much slower than a native implementation. When making a game, you need processing time for game logic. You don't want CPU cycles tied up performing a set of computationally expensive convolution operations in JavaScript. Also, since the API is only a specification, a good implementation can hand off processing to hardware accelerated back-ends (e.g. on a Creative EAX card), or a browser maintained audio thread to help boost performance. For a complex scene with many filtered and spatial sound sources playing simultaneously, like in a game, you'll need all the performance you can get to keep the user experience responsive.

 Also, since the audio sources in the Web Audio API are easy to fill with custom buffers, there is little reason why both specifications can't live side by side. AudioContext's MediaElementAudioSourceNode method seems like a move in the direction of inter-operability between the two specifications. The  MediaStream  API can manage audio streams between peer-connected clients while the Web Audio API "renders" the received data in interesting ways.

So, in conclusion, for me, there is no battle, though I personally prefer using Web Audio API since it is more geared toward the game use-case. I hope that both specifications are refined to be more complementary and get accepted and endorsed by W3C [5].

 Links:

• [1] http://www.w3.org/TR/webaudio 
• [2] http://wiki.mozilla.org/Audio_Data_API 
• [3] http://www.w3.org/TR/streamproc 
• [4] https://github.com/corbanbrook/audionode.js
• [5] http://www.w3.org/TR/audioproc/

Almost done with audio

TL;DR: Still no pretty pictures. Sorry.

Since last post:

• Mixer.  Per-source volume and pan.  It can have multiple modules as sources, and forces any mono sources to fill all output channels (dependent on pan setting). 
• Stk Voicer support. Can essentially make polyphonic versions of any Instrmnt and trigger it from the script environment.
• Started on Stk Filters, but apart form delay, most of them seem ill-fitted for my purposes (see below).

Currently only stereo linear-cross-fade panning is supported by the mixer module. I'll re-visit multi-channel placement later. Audio positioning for game objects will only rely on volume and pan for now.

What's still left to do?

• Ignore all Stk Generators for now... they are too low-level to merit script instantiation.. They might make a comeback as LFO-type control inputs in the future...
• Ignore most Stk filters. Filters in Stk seem to be meant as helper classes for internal workings in custom Instrmnt derived classes. Many filters do not normalize and without extreme tweaking aren't useful in an intuitive real-time modular fashion. Compromise: Script instantiated filter which can be set up as a HP,BP,LP or BS filter. Internally an IIR Stk filter can be used with a known calculated set of normalized coefficients for Butterworth filters. This will be sufficient for games.
• Ignore score files for now... The effort which will have to go into creating a scoring environment is beyond the scope of a gaming project. It is a love of mine, hence the long interlope. I will come back to this, but not yet. 
• Ogg file loading/playback for music needs to happen (Easier to compose music in Renoise for now).
• Stk Effects to support : Chorus, JC-Rev, Echo ... the rest can come later.
• Implement tying motion-states to audio sources.

Tick these off and I'll have enough audio tech to my liking. 

After that? Menu GUI and exposing the keyboard-map to the script environment, then we'll be close to ThingMaker version zero point something!

Ok, so it is still a way to go, but an end is in sight.

No pretty pictures here, please move along...

TL;DR: I made a sound from within the scripting environment, and it was hard!

Disclaimer: programmers only.

It has been almost a month since the last post and no "visible" progress has been made...
Lots of code have been committed for the purpose of making a couple of extra lines of script work.

Basically, I had to write an interface class for an abstract "sound module"... which is something with an internal audio buffer and references to inputs and outputs to other sound modules. Script interfaces had to be written for connecting modules together with logic to detect any feedback between modules. The only sub-classed objects so far is a master module, which abstracts the "default" audio output device, and a Stk Instrmnt wrapper class.

When I designed for using Stk, I planned around the Stk base interface classes as much as possible, and being obsessed with the sound module idea I settled for the most common audio processing virtual function shared by all higher level Stk interface classes... namely : StkFrames &tick(StkFrames&frames).

Since this most common tick function processes a block of audio frames, I thought it best to have the algorithm which processes the audio frames in as large a chunk as "real-time" permits... Stk defaults to 512 frames, which at 44k1Hz equates to about 11ms (good enough for games!).

Wasting of time, feeling stupid and doing more work than necessary happened when I decided to design for feedback support after already having "chunk" optimizations in place.

What am I talking about? Say you have an instrument which you plug into a mixer. That mixer goes through an EQ and into a splitter. That splitter then has an output to a chorus effect and another to a re-verb effect. The chorus goes to the master output, but the re-verb goes back to the mixer the instrument is plugged into. Why do you want to do this? Well, why not? It might sound cool... who knows, but the point is you might just NEED it somewhere.

The problem is now apparent since it is clear that the mixer's second input is dependent on the output of some later stage which is in turn dependent on the mixer's output. The best you can hope for in a digital system is to allow the mixer to do a single frame's tick, propagate that tick though all modules until you update the module the mixer input is dependent upon which will then serve as the input to the mixer's next single-frame tick operation.

So, if like me, you went ahead optimizing for chunks, and then wanted to go and have a special feed-back case which just does single ticks, then you're probably also half-wasting your time (I'm sure it's possible, just probably not with the way I went about it.).

What I kept from this misadventure was just the ability to detect if there is feedback when a connection is created, and throw a script exception if so, not allowing the connection. A lot can be done still with just feed-forward modular audio networks, so apart from the wasted time, I'm not too bumbed.

So, I now have the master module which is the entry point for connection to other modules and the Stk Instrmnt wrapper  (which currently supports all the sub-classed instruments Stk has to offer). Further sub-classed modules still need to be added to complete the whole sound experience, but the minimals are coming together nicely.

The basic functioning of the audio engine is like:

• audio callback requests buffer
• audio engine processes the master module
• master module processes its source modules recursively

...still not noticing any non-stupidity-induced breaking sound artefacts, so all is still well and real-time(ish).

Hopefully the next update will have some video with "actual" sound. In the distant future, I hope to re-visit the modular feedback issue. 

What went wrong this time? (Adventures with STK)

Sorry, no pretty pictures in this post... Also, this post is moderately technical in nature, so browse away now if you are not interested in audio-programming jargon. You'll be happier for it. If you know Qt and STK well, you might find this post slightly amusing. If you are new to Qt and STK, you might not know what I'm talking about at all. This post is personal, I guess.

I've made the first steps for physics, interaction and graphics, and since I'm interested in making desktop games, it is only natural to do audio at some point...

I thought it would be easy to integrate Qt's audio functionality when using the qmake tool-chain... add qtmultimedia to the config in your .pro file, and include a QAudioOutput class somewhere and trigger sounds from that... Right?

Well, it kinda is... but not really... QAudioOutput is a reasonably low-level interface class and can read from a custom QIODevice derived class (pull mode, good for streaming... limited real-time application) or you are provided with a QIODevice which you can write to once a notify interval has elapsed (push mode... more real-time).  A QIODevice "talks" in raw bytes... so either way you still need to take care of formatting your audio data correctly to match the stream parameters (code for this can be seen in the Generator::generateData method in the Audio Output Qt example ). Also, no mixing/routing functionality is provided... you're expected to implement that or use some third party library like STK. So, although the QAudioOutput class provides a solid cross-platform starting-point, it still requires you to implement a lot of the low-level, broiler-plate, byte-array, endian-conscious code. Also, this part of the Qt framework is under active development so it might drastically change  in the main Qt distribution as projects become merged into it. It is inevitable that technology will pass you by... but it is all part of the learning process.

For a while I've wanted to use Perry Cook & Garry Scavone's STK (https://ccrma.stanford.edu/software/stk/) to provide the basis for a soft-synth audio framework for my game engine. As a preference I decided on RtAudio and STK over PortAudio and CSound, though I know much is interchangeable and CSound has a great deal more features. I was drawn in bySTK's well balanced compromise between latency (#1 consideration for games), footprint and readability.

The aim was to have an audio engine class which gets instantiated along with the script environment, which would also provide script interfaces into a range of STK classes and to dynamically connect them in a modular fashion... Since STK can be compiled without RtAudio dependence I though it best to stick with the QtMultimedia module since I was relying heavily on Qt already.

One can conceivably tie STK's non-real-time build in with a push mode implementation involving QtAudioOutput, but, after wasting much time, in the end experimentation with RtAudio  made me decide to use it instead of QtAudioOutput. The biggest factor for me was that RtAudio already deals with floating point samples and transparently does the conversion to raw audio for a wide range of audio formats. Also, it has a relaxed open source license and is cross-platform (Linux/Mac/Win). My DSP courses dealt mostly with audio signals represented as numbers in the range -1.0 to 1.0, so RtAudio is a more intuitive fit in this regard also.

On the plus side, choosing RtAudio over QtMultimedia also provided the additional ASIO support in windows ( although ASIO support is compiled and tested, I'm  defaulting to dSound on Win32 platforms for now) and RtMidi cross platform MIDI IO support ( which has also been compiled in but is waiting untapped). The STK source files have been statically incorporated into my project not because I planed it, but because I was initially only using some elements of STK... Eventually all of STK source got included. I might eventually move back to just linking to the STK library. Right now I don't care much because the code footprint is small and all the STK classes are pre-compilable, so they don't affect consequent compile times much (exception is lesson 1).

Lessons learned:

1. Complacency can make you forget the classics: Changed a define in your project file? CLEAN! REBUILD! (And don't forget the cleaning part. Too embarrassed to say how much time I wasted dealing with puzzling bugs after forgetting to do this).
2. RtAudio's closeStream() method should never be called from a destructor of a class your RtAudio instance is part of... safer to have a pointer to a RtAudio instance which you manually delete after step 3.
3. You need the "bool done" tick-data element you see in all the STK code examples... no escaping it if using the tick() callback functionality. In the main tick() callback check for data.done and return -1 if it is true; The audio engine class destructor should set the "data.done" value to true and should sleep for a couple of microseconds to allow any pending callbacks to return a -1... only then is it safe to delete the RtAudio instance without a hang (on my system at least).
4. Building STK with Qt(Qt Creator/qmake) MINGW: If like me, you added all the stk/include and stk/src files to your Qt project, you'll need to add some defines and library dependencies to your .pro file to get everything linking and compiling right. To get the compiler setting and project defines for STK, run STK's configure script from within a msys shell to generate a makefile. Reading this makefile will tell you what defines and libraries you need to add to your Qt .pro file (you can also look at the VC project files that come with STK but it is more verbose and the linker syntax is different). 

So, what do I have?

Not much really, just getting everything compiled together and first steps of simple integration for now. Tones are generating; instruments are playing; filters are filtering; effects are effecting even... but only C++ tests hacked into the audio engine's initAudio() method for the interim. The initial tests show promise. No audio script interfaces or script definable modular flow graphs have been implemented yet... that is next.

I still have a lot to do with the sound-programming before my next update... sorry, I know I can ramble sometimes. This post went on for longer than intended.

Useful links:

• http://www.mingw.org/ (msys doesn't come with Qt Creator installer)
• https://ccrma.stanford.edu/software/stk/ (STK Home page)
• http://www.music.mcgill.ca/~gary/rtaudio/ (RtAudio Home)
• http://web.mit.edu/carrien/Public/speechlab/marc_code/ADAPT_VC/rtaudio/doc/html/ (MIT RtAudio Tutorial)
• http://www.music.mcgill.ca/~gary/rtmidi/ (RtMidi Home)