I recently embarked on a new university subject - an introduction to Java programming - as part of my CS/IT degree, and cringed slightly when I heard we were advised (though not forced, thankfully) to use Eclipse. I've had some experience with Eclipse already, using it for Android development, and my overall impression was that it has almost as many features as it does bugs/'features'.
I wasn't looking forward to battling with that again, but it occurred to me that a lot of the things I find annoying about Eclipse could probably be customised/turned off in the preferences, so I decided to give it a go. After all, it does have some useful features, and I thought manually compiling code from the command line would be impractically tedious for assignments later on in the course.
In spite of some ridiculous issues which I can't be bothered relating (long story short: the only version of Eclipse I can use crashes if I try to modify the preferences), for the first week of my new subject I did, in fact, use Eclipse. If I'd been able to do so without it crashing, I might have turned off a lot of its autocompletion features and other things that save typing and make for lazy coding. However, it's hard to resist being lazy, and the way Eclipse is designed also means it's almost difficult to write classes and main methods yourself. Eclipse wants to do everything for you. That's very nice - and very bad for a newbie like me. I'll explain why in a minute.
Today I finally decided I wasn't going to put up with Eclipse anymore, so I moved all my source code out of the Eclipse workspace into appropriate folders for each week of my uni subject, opened up a terminal and Sublime Text, and tried to write a main() method.
I realised I had no idea how to.
It's not like I haven't seen hundreds of them by now; it's just that I've never had to remember how to write them because I've never needed to write them. Eclipse auto-generates these things.
I spent all day manually compiling and running Java code, and I've learnt more than I did in a week of writing similar programs in Eclipse. I consider it a privilege to be able to learn by trial and error, see exceptions and syntax errors pop up and try to figure out what's going on all by myself without the little lightbulbs and red 'X's that Eclipse gives you. I relish the fact that I can leave a variable unused for as long as I like without being given a wiggly yellow line and a warning that says 'you haven't used this variable yet!' I enjoy being able to make mistakes without being admonished. But most of all, I love having to remember how to do things.*
It turns out that Sublime Text - an excellent programmer's text editor - has many of Eclipse's better features, including autocompletion, so perhaps it's not so humble after all. However, the fancier features are unobtrusive enough that I barely noticed they were there.
The only autocompletion I use is for variables and methods I've already typed out at least once; Sublime Text doesn't seem to offer autocompletion for things you haven't already typed. I discovered an exception to that rule (and there are probably others) - it does offer autocompletion for the main() method, which I only allowed
myself to use once I was confident I knew how to write it by myself. There's also an option for auto-closure of brackets and strings, but that was one of the features I hated in Eclipse so I'm leaving it off. For now, closing brackets and quotes are too firmly embedded in my muscle memory.
It's slightly scary to realise that if I'd gone on letting Eclipse practically write code for me, if someone had sat me down in front of Vim and asked me to write a Java program I probably wouldn't have been able to.** Until I know enough about Java to be able to work on the kind of big projects that Eclipse is essential for, I refuse to succumb to laziness.
*the whole 'not crashing' thing is pretty great, too.
**without googling anything!
Friday, 14 March 2014
Saturday, 22 February 2014
Lazy piano technique
While practising the piano recently, I observed something in my technique which I'd never really paid much attention to before, although I know it's always been there. It struck me as interesting enough to blog about, although it may bore you to death.
For the purposes of this post, I'm going to coin 2 terms to describe different kinds of piano technique: "controlled" technique and "free" technique. The former is very precise and conscious, while the latter is very automatic and probably best described by the word "lazy". This is a massive over-simplification of piano technique, but I think it's a good summary of the two main techniques I find myself utilising. Both have their place, with different passages and even entire pieces sounding better with different techniques.
Controlled technique is what I use whenever I'm learning a new piece or section of a piece, especially in the early stages of metronome practise at very slow speeds, which is the technique I use to learn particularly challenging passages. The controlled technique essentially means thinking about precision, about where exactly where each finger needs to go, leaving nothing up to chance. It also means a small amount of tension in the fingers - ONLY in the fingers, not in the wrist or arm, which would be catastrophic and lead to RSI.
During the early stages of learning a passage, since I won't have developed muscle memory for that passage yet, playing it requires a certain amount of thinking (not something I normally do much of when playing the piano), so controlled technique would be inevitable even if I wasn't making an effort to hit exactly the right notes in order to learn the passage accurately.
Even once I've learnt a passage, initially - usually during the memorisation process, if I haven't automatically memorised it by that time - I'll play using this 'controlled' technique. This is probably mostly due to the need to maintain absolute accuracy while memorising, so I don't memorise mistakes.
While controlled technique greatly increases accuracy and clarity, it is also very risky. I believe many pianists, myself included, rely largely on muscle memory when performing. For me at least, this is something that happens without thinking - it's automatic, and being conscious of where to put my fingers or what's happening in the music actually gets in the way of letting the 'automation' take over. So once I've developed muscle memory for a piece, controlled technique feels uncomfortable, because even that tiny bit more consciousness that's required to be absolutely precise about where your fingers are going can result in a memory lapse. I can't speak for anyone else, but for me thinking really is my worst enemy when it comes to playing from memory.
Contrast this with what I'm going to call "free" technique (you might as well call it "lazy" technique). This is how I usually play something I know well from memory. It involves absolutely no conscious thought, allowing muscle memory to take over completely, and this is aided by complete relaxation of the hand and fingers, which results in a very different (though not always desirable) tone.
The downside of free technique is that over time, accuracy tends to suffer: when I've just learnt a new passage using controlled technique I've practised accuracy a lot, but once I start playing using free technique mistakes creep in and become embedded in muscle memory, accumulating until eventually I'll need to revert to controlled technique for a bit - or even do some slow metronome practise - to get back to the original standard of accuracy that I had immediately after first learning the passage.
The advantage of free technique, however, is that it greatly reduces the risk of memory lapses, as long as my muscle memory is sufficiently well established. Under pressure, such as when performing, I'll tend to fall back on free technique to get me through, which results in lower accuracy but a much greater chance of reaching the end without forgetting anything. It's a sort of mindlessness which is very useful to have when you're nervous.
That was a very long preamble to what I've been meaning to write about all along. For over a year I've been learning Rachmaninov's 2nd piano concerto, specifically the 1st movement (the 2nd I've already performed, albeit without an orchestra). A year is a long time to have something memorised, and for the reasons mentioned above my accuracy has been deteriorating slowly over that period, in spite of improvements in my technique as a whole.
The other night I was practising this movement and suddenly became aware of something which I never really took note of before: while struggling with a passage whose accuracy needed improvement, I found myself playing with a very different technique in order to try to get the notes right. My fingers became tenser, I found myself thinking more about which keys I had to hit, and the tone I was getting out of the piano changed completely (in a good way). In other words, I was playing using controlled rather than free technique, and I much preferred the result.
Once I realised this, I tried to play everything using controlled technique, but felt on the verge of a memory lapse constantly because I was THINKING about the notes for once, rather than letting muscle memory carry me along.
Normally in the course of playing something from memory, I'll constantly switch between controlled and free technique, using free technique most of the time but changing to controlled technique for passages I know are particularly technically challenging. I can actually provide some specific examples of this in the concerto I'm learning: I always use controlled technique in the fast "Un poco piú mosso" section, and always use free technique in this subsequent section. It was the 2nd example here that I was having trouble with the accuracy of, and which from now on I am going to try to play with controlled technique (as I did initially, when I first learnt it).
Although it could be very difficult to strike the balance between passages of the concerto I know well enough to safely be able to play them with controlled technique and passages where controlled tehnique is likely to result in a memory lapse, this is what I would like to try to do before performing it in a piano competition later this year.
For the purposes of this post, I'm going to coin 2 terms to describe different kinds of piano technique: "controlled" technique and "free" technique. The former is very precise and conscious, while the latter is very automatic and probably best described by the word "lazy". This is a massive over-simplification of piano technique, but I think it's a good summary of the two main techniques I find myself utilising. Both have their place, with different passages and even entire pieces sounding better with different techniques.
Controlled technique is what I use whenever I'm learning a new piece or section of a piece, especially in the early stages of metronome practise at very slow speeds, which is the technique I use to learn particularly challenging passages. The controlled technique essentially means thinking about precision, about where exactly where each finger needs to go, leaving nothing up to chance. It also means a small amount of tension in the fingers - ONLY in the fingers, not in the wrist or arm, which would be catastrophic and lead to RSI.
During the early stages of learning a passage, since I won't have developed muscle memory for that passage yet, playing it requires a certain amount of thinking (not something I normally do much of when playing the piano), so controlled technique would be inevitable even if I wasn't making an effort to hit exactly the right notes in order to learn the passage accurately.
Even once I've learnt a passage, initially - usually during the memorisation process, if I haven't automatically memorised it by that time - I'll play using this 'controlled' technique. This is probably mostly due to the need to maintain absolute accuracy while memorising, so I don't memorise mistakes.
While controlled technique greatly increases accuracy and clarity, it is also very risky. I believe many pianists, myself included, rely largely on muscle memory when performing. For me at least, this is something that happens without thinking - it's automatic, and being conscious of where to put my fingers or what's happening in the music actually gets in the way of letting the 'automation' take over. So once I've developed muscle memory for a piece, controlled technique feels uncomfortable, because even that tiny bit more consciousness that's required to be absolutely precise about where your fingers are going can result in a memory lapse. I can't speak for anyone else, but for me thinking really is my worst enemy when it comes to playing from memory.
Contrast this with what I'm going to call "free" technique (you might as well call it "lazy" technique). This is how I usually play something I know well from memory. It involves absolutely no conscious thought, allowing muscle memory to take over completely, and this is aided by complete relaxation of the hand and fingers, which results in a very different (though not always desirable) tone.
The downside of free technique is that over time, accuracy tends to suffer: when I've just learnt a new passage using controlled technique I've practised accuracy a lot, but once I start playing using free technique mistakes creep in and become embedded in muscle memory, accumulating until eventually I'll need to revert to controlled technique for a bit - or even do some slow metronome practise - to get back to the original standard of accuracy that I had immediately after first learning the passage.
The advantage of free technique, however, is that it greatly reduces the risk of memory lapses, as long as my muscle memory is sufficiently well established. Under pressure, such as when performing, I'll tend to fall back on free technique to get me through, which results in lower accuracy but a much greater chance of reaching the end without forgetting anything. It's a sort of mindlessness which is very useful to have when you're nervous.
That was a very long preamble to what I've been meaning to write about all along. For over a year I've been learning Rachmaninov's 2nd piano concerto, specifically the 1st movement (the 2nd I've already performed, albeit without an orchestra). A year is a long time to have something memorised, and for the reasons mentioned above my accuracy has been deteriorating slowly over that period, in spite of improvements in my technique as a whole.
The other night I was practising this movement and suddenly became aware of something which I never really took note of before: while struggling with a passage whose accuracy needed improvement, I found myself playing with a very different technique in order to try to get the notes right. My fingers became tenser, I found myself thinking more about which keys I had to hit, and the tone I was getting out of the piano changed completely (in a good way). In other words, I was playing using controlled rather than free technique, and I much preferred the result.
Once I realised this, I tried to play everything using controlled technique, but felt on the verge of a memory lapse constantly because I was THINKING about the notes for once, rather than letting muscle memory carry me along.
Normally in the course of playing something from memory, I'll constantly switch between controlled and free technique, using free technique most of the time but changing to controlled technique for passages I know are particularly technically challenging. I can actually provide some specific examples of this in the concerto I'm learning: I always use controlled technique in the fast "Un poco piú mosso" section, and always use free technique in this subsequent section. It was the 2nd example here that I was having trouble with the accuracy of, and which from now on I am going to try to play with controlled technique (as I did initially, when I first learnt it).
Although it could be very difficult to strike the balance between passages of the concerto I know well enough to safely be able to play them with controlled technique and passages where controlled tehnique is likely to result in a memory lapse, this is what I would like to try to do before performing it in a piano competition later this year.
Saturday, 11 January 2014
Algorithmic atonality
WARNING: I have no idea what I'm doing and errors probably abound.
I recently came across this incredible graphical and musical representation of sorting algorithms.
It got me thinking about the musical possibilities of such algorithms, and I immediately set about experimenting, taking a pseudo-random sample of 8 notes (the 5 notes of the pentatonic scale plus 3 arbitrary ones) to create an 8-tone sequence or tone row (aided by Python's random module.)
The sequence is split over 2 bars in rather the manner that hexadecimal splits bytes into two 4-bit groups (nibbles). No note is ever repeated within the 2 bar sequence.
The random sequence is first copied and pasted into another 2 bars, before sorting starts.
Each 'nibble' is then processed separately. In the case of my particular tone row, it takes 3 repetitions to sort a bar.
We start by sorting just the 2nd bar of the sequence, meaning the 1st bar remains the same for 3 iterations. The final note in the 2nd bar is compared with the previous note; if the previous note is of a higher pitch, the notes are swapped. The sequence is then copied and pasted again, and the following algorithm is used (in this context, 'greater than' means 'at a higher pitch than'). For demonstrative purposes, let's label our 4 notes A, B, C, and D (this has no relation to actual note pitches!)
D > C > B >A
If this statement is false, the first note to break the rule is compared to each of the previously processed notes to determine its place in the sequence.
This is repeated for the final iteration, by which time all the notes in the 2nd bar in the sequence are sorted. The process is then repeated with the first bar in the sequence, while the 2nd bar remains the same for three iterations.
The LH starts off in the same direction as the RH, but after a few repetitions it retrogrades (is flipped horizontally, in visual terms).
3rds, 5ths and octaves are added to the left and/or right hands at various points. Sometimes 5ths are added below the pure tone row, and sometimes they are added above it. These patterns can also be flipped vertically so that 5ths that were added below the 'melody' are now on top of it, meaning their intervalic relationship changes.
There are rules for these 'filler' notes:
The note must be either a major or minor third, or a perfect fifth, apart from the lowest note in the chord. it must not be the same as any other uppermost or lowermost note in the bar. This means that sometimes (although very rarely), where the overall pattern is using thirds, it becomes necessary to subsitute a 5th in to avoid doubling a note that already exists in the 'melody'.
The fact that this occurrence is so rare - only starting near the very end of the sorting process - fascinates me, although I don't know the reason behind it yet.
The result of my experiment - which I never ended up doing anything interesting with - can be heard here. I cannot stress enough that I don't know what I'm doing. This was just for fun.
I recently came across this incredible graphical and musical representation of sorting algorithms.
It got me thinking about the musical possibilities of such algorithms, and I immediately set about experimenting, taking a pseudo-random sample of 8 notes (the 5 notes of the pentatonic scale plus 3 arbitrary ones) to create an 8-tone sequence or tone row (aided by Python's random module.)
The sequence is split over 2 bars in rather the manner that hexadecimal splits bytes into two 4-bit groups (nibbles). No note is ever repeated within the 2 bar sequence.
The random sequence is first copied and pasted into another 2 bars, before sorting starts.
Each 'nibble' is then processed separately. In the case of my particular tone row, it takes 3 repetitions to sort a bar.
We start by sorting just the 2nd bar of the sequence, meaning the 1st bar remains the same for 3 iterations. The final note in the 2nd bar is compared with the previous note; if the previous note is of a higher pitch, the notes are swapped. The sequence is then copied and pasted again, and the following algorithm is used (in this context, 'greater than' means 'at a higher pitch than'). For demonstrative purposes, let's label our 4 notes A, B, C, and D (this has no relation to actual note pitches!)
D > C > B >A
If this statement is false, the first note to break the rule is compared to each of the previously processed notes to determine its place in the sequence.
This is repeated for the final iteration, by which time all the notes in the 2nd bar in the sequence are sorted. The process is then repeated with the first bar in the sequence, while the 2nd bar remains the same for three iterations.
The LH starts off in the same direction as the RH, but after a few repetitions it retrogrades (is flipped horizontally, in visual terms).
3rds, 5ths and octaves are added to the left and/or right hands at various points. Sometimes 5ths are added below the pure tone row, and sometimes they are added above it. These patterns can also be flipped vertically so that 5ths that were added below the 'melody' are now on top of it, meaning their intervalic relationship changes.
There are rules for these 'filler' notes:
The note must be either a major or minor third, or a perfect fifth, apart from the lowest note in the chord. it must not be the same as any other uppermost or lowermost note in the bar. This means that sometimes (although very rarely), where the overall pattern is using thirds, it becomes necessary to subsitute a 5th in to avoid doubling a note that already exists in the 'melody'.
The fact that this occurrence is so rare - only starting near the very end of the sorting process - fascinates me, although I don't know the reason behind it yet.
The result of my experiment - which I never ended up doing anything interesting with - can be heard here. I cannot stress enough that I don't know what I'm doing. This was just for fun.
Monday, 16 December 2013
notes vs. tones, digits vs. numbers
There is a little linguistic problem that I've been puzzling over quite a lot recently. It concerns what can probably be best described, in abstract terms, as differentiation between quantity and value in sets.
I first ran into this with number theory, working with the different numerical bases - hexadecimal, binary, decimal - that are relevant in computer science, as I needed to be able to refer to the length of, say, a bit pattern or hexadecimal number separately to the actual values that appeared in it.
In binary this is pretty easy, as there are only 2 possible values. However, if I said 'a byte has 8 digits', and you didn't have the assumed knowledge about binary, it could be misunderstood to mean a byte has 8 values, which would be incorrect, since a byte can only contain some combination of 2 values: 0 and 1. This confusion arises out of the ambiguity of the term digit: does 'digit' refer to the value of an item in the byte, or to the number of items in the byte regardless of their value? In this case, if you know anything about binary, the meaning is obvious, but there are other similar situations where it may not be.
It seems that most often digit is understood to refer to a quantity of items and number is understood to refer to the value of any item. However, all the dictionaries I've checked in seem reluctant to make such a clear distinction, the two words are listed as synonymous, and in reality they are often used interchangeably, making use of either one subject to misinterpretation.
The problem crops up again in music. For example, when we say '4 notes', are we referring to any 4 instances of an item (for example, four B flats), or are we referring specifically to 4 unique values (for example, a set of 10 items in which only four values, say A, F, D and B flat, occur)?
Officially there are separate words to describe quantity and value in music: note is to tone* what digit is to number - the former describes a quantity, the latter a unique value. But again, the two terms get used interchangeably, making it difficult to ensure any description of musical patterns is absolutely unambiguous. What am I missing here?!
In writing this blog post, I made an unsettling discovery: I kept trying to use general words that describe quantity or value, only to discover they could potentially be misinterpreted. Range is one such word. I was initially going to use this term instead of quantity, until I realised it could be misinterpreted in much the same way as digit or number. Are we referring to the number of items in the set, or the number of values occurring in the set? Range is perfectly correct in either context.
Also note how it's almost impossible to discuss these issues without using that pesky term number. In this post I've replaced as many occurrences of the word as possible with quantity, but I've left the ones in the previous paragraph untouched to demonstrate how much we rely on potentially ambiguous language.
One final thought, venturing into even more abstract territory: consider that we say 'number of digits'. This requires some recursive thinking: the digits are a set in which various values, known as numbers, can be stored. Another set, called a number, contains the digits which contain the numbers...see the problem with this terminology?
*gotta love that tone is an anagram of note eh
I first ran into this with number theory, working with the different numerical bases - hexadecimal, binary, decimal - that are relevant in computer science, as I needed to be able to refer to the length of, say, a bit pattern or hexadecimal number separately to the actual values that appeared in it.
In binary this is pretty easy, as there are only 2 possible values. However, if I said 'a byte has 8 digits', and you didn't have the assumed knowledge about binary, it could be misunderstood to mean a byte has 8 values, which would be incorrect, since a byte can only contain some combination of 2 values: 0 and 1. This confusion arises out of the ambiguity of the term digit: does 'digit' refer to the value of an item in the byte, or to the number of items in the byte regardless of their value? In this case, if you know anything about binary, the meaning is obvious, but there are other similar situations where it may not be.
It seems that most often digit is understood to refer to a quantity of items and number is understood to refer to the value of any item. However, all the dictionaries I've checked in seem reluctant to make such a clear distinction, the two words are listed as synonymous, and in reality they are often used interchangeably, making use of either one subject to misinterpretation.
The problem crops up again in music. For example, when we say '4 notes', are we referring to any 4 instances of an item (for example, four B flats), or are we referring specifically to 4 unique values (for example, a set of 10 items in which only four values, say A, F, D and B flat, occur)?
Officially there are separate words to describe quantity and value in music: note is to tone* what digit is to number - the former describes a quantity, the latter a unique value. But again, the two terms get used interchangeably, making it difficult to ensure any description of musical patterns is absolutely unambiguous. What am I missing here?!
In writing this blog post, I made an unsettling discovery: I kept trying to use general words that describe quantity or value, only to discover they could potentially be misinterpreted. Range is one such word. I was initially going to use this term instead of quantity, until I realised it could be misinterpreted in much the same way as digit or number. Are we referring to the number of items in the set, or the number of values occurring in the set? Range is perfectly correct in either context.
Also note how it's almost impossible to discuss these issues without using that pesky term number. In this post I've replaced as many occurrences of the word as possible with quantity, but I've left the ones in the previous paragraph untouched to demonstrate how much we rely on potentially ambiguous language.
One final thought, venturing into even more abstract territory: consider that we say 'number of digits'. This requires some recursive thinking: the digits are a set in which various values, known as numbers, can be stored. Another set, called a number, contains the digits which contain the numbers...see the problem with this terminology?
*gotta love that tone is an anagram of note eh
Friday, 29 November 2013
The CHORD of resignation
Before you read any further, please be aware that none of this post will make sense unless you've read this first.
The minor 7th chord consists of a stack of alternating major and minor thirds: min 3rd, maj 3rd, min 3rd, maj 3rd. It's always been my favorite chord, and at the time of writing the post linked above I was even vaguely aware that there was some connection between this chord and the chord progression I was analysing. However, I was so new to harmonic analysis at that time that I was happy to leave the analysis at a series of chords.
It's only very recently that I've been able to piece together and understand some of the connections I've always sensed existed between a handful of musical patterns and elements. This post is an attempt to explain these connections, with the aid of some examples. I still have much to learn about this topic, and I'm sure there will be many more blog posts to write as I make new discoveries.
Let's say we're in the key of B flat minor. In this key, the notes which correspond to the degrees of the scale that form the Chord Progression of Resignation are B flat, D flat, E flat and G flat, from the bottom up:
Let's now invert this chord to the 2nd inversion, so it starts on E flat (note that the dominant of E flat is B flat...) The resulting chord is E flat minor 7th:
The notes used in the examples above are 4 of the 5 notes of the pentatonic scale. If we were still in B flat minor (which we're not, since E flat is our new tonic), the missing note (an A flat) would form the 7th degree of the scale - a fairly common addition to the 'pure' chord progression of resignation.
The pentatonic scale is the mode you get from playing only the black keys of the piano (although it can be transposed into any key). It's an interesting scale in that it's very pure sounding - you can combine any of its 5 notes, or play them all at once, and as long as you stay within that mode nothing will ever sound jarringly dissonant.
It's also quite tonally ambiguous - shifting from major to minor and between keys is effortless. I've yet to figure out what gives the pentatonic scale this ambiguous quality, as - depending on which note you begin it on - the degrees of the scale that are 'missing' vary.
The pentatonic scale is prevalent in the traditional music of many vastly different and geographically separated cultures. This can hardly be attributed to coincidence, and the discovery of its relationship to the 'chord of resignation', and by assosciation the chord progression of resignation, has only reinforced my impression that there's something fundamentally significant about the pentatonic scale.
Below are some examples of the 'chord of resignation'. As with the chord prog list, I'll add to this over time, so check back! (Quite a few examples I could easily include here would double with ones already in the chord prog list, so I'm leaving some - though not all - of them out.)
To make collecting examples easier, I'm attempting to group them by harmonic structure a little.
The following examples simply use the minor 7th chord in its purest form:
1. Leo Ornstein - Piano Sonata No. 4, 2nd mvt (see 0:07, and probably most prominently 0:14) Aside from the timecodes noted, the opening of this appears to make use of the minor 7th constantly in other ways too complex for me to try to analyse yet. This piece already appears on the chord prog examples list, but I had to repeat it here because it has such a wealth of interesting harmony.
2. Ravel - Le Gibet (see 13:42 and several times again until the end)
3. Gershwin - Summertime (see 9:11)
4. Leo Ornstein - Piano Sonata No. 4, 4th mvt The opening of this is practically built out of minor 7th chords (or stacks of 3rds, in any case).
5. Steve Reich - Six Marimbas (see 6:15 onwards) The uppermost note of this chord shifts constantly between the 7th and 8th degree of the scale, while the underlying 3rds remain 'fixed'. Interestingly, the tonic doesn't appear in the bass until 6:32, and it dissappears again at 13:42. The inversion of the minor 7th created by this is the one shown in the first image above - the degrees of the chord prog of resignation stacked on top of each other in order: I, III, IV, VI.
6. Ravel - Une barque sur l'ocean (see 4:47)
7. Ravel - Noel des Jouets (see 2:26)
8. Ravel - Ondine (see 5:20) This example is really in a class of its own, as the chord is not only broken into a myriad of semiquavers and tuplets with a scattering of arbitrary notes in between, but it also isn't even a minor 7th. Nevertheless, a Chord of Resignation it undoubtedly is. A far more conventional example can be found at 5:49.
A very common way in which the minor 7th chord manifests - especially in minimalism - is where a particular interval or combination of intervals are maintained over the top of a changing base chord progression, resulting in the 'Chord of Resignation' seeming to grow naturally out of a pure tonic triad. The following examples demonstrate this.
9. Stellardrone - In Time This is a fairly simple example - harmonically and texturally - so well suited for explanatory purposes. The bass is progressing as follows: I, [V], VI, VII. To start with the...er, constellation of notes being repeated over the top is simply part of the tonic triad, but as it remains the same while the bass changes, it forms a minor 7th over the VI chord.
10. Porcupine Tree - Trains As with the previous example, the upper notes in the harmony here remain constant over a changing bassline, resulting in a minor 7th forming over the VI chord. However, there are other relevant complexities to the harmony which you can read about in the chord prog examples list.
11. Steve Reich - Electric Counterpoint III This is an interesting example because the underlying chord progression consists only of the degrees of the scale that form the minor 7th - IV, VI, Im. As a result, in this instance it's impossible to say that a minor 7th is only formed over, say, the VI chord, as was the case with the previous 2 examples. The harmony just morphs organically, an effect intensified the gradual introduction of each degree of the scale in the bass at the start of the piece (you have to listen to the whole thing to get what I'm talking about). PS in case you're curious what happens when it briefly modulates, the progression is III, IV, V, but effectively that III chord becomes the new tonic.
12. Steve Reich - Music for large ensemble Initially, the uppermost note of the chord is simply the 3rd degree of the tonic triad (i.e. the dominant), but each time the bass plunges down a third it becomes a minor 7th.
Yes, there is a lot of Ravel on this list. :P
The minor 7th chord consists of a stack of alternating major and minor thirds: min 3rd, maj 3rd, min 3rd, maj 3rd. It's always been my favorite chord, and at the time of writing the post linked above I was even vaguely aware that there was some connection between this chord and the chord progression I was analysing. However, I was so new to harmonic analysis at that time that I was happy to leave the analysis at a series of chords.
It's only very recently that I've been able to piece together and understand some of the connections I've always sensed existed between a handful of musical patterns and elements. This post is an attempt to explain these connections, with the aid of some examples. I still have much to learn about this topic, and I'm sure there will be many more blog posts to write as I make new discoveries.
Let's say we're in the key of B flat minor. In this key, the notes which correspond to the degrees of the scale that form the Chord Progression of Resignation are B flat, D flat, E flat and G flat, from the bottom up:
Let's now invert this chord to the 2nd inversion, so it starts on E flat (note that the dominant of E flat is B flat...) The resulting chord is E flat minor 7th:
The notes used in the examples above are 4 of the 5 notes of the pentatonic scale. If we were still in B flat minor (which we're not, since E flat is our new tonic), the missing note (an A flat) would form the 7th degree of the scale - a fairly common addition to the 'pure' chord progression of resignation.
The pentatonic scale is the mode you get from playing only the black keys of the piano (although it can be transposed into any key). It's an interesting scale in that it's very pure sounding - you can combine any of its 5 notes, or play them all at once, and as long as you stay within that mode nothing will ever sound jarringly dissonant.
It's also quite tonally ambiguous - shifting from major to minor and between keys is effortless. I've yet to figure out what gives the pentatonic scale this ambiguous quality, as - depending on which note you begin it on - the degrees of the scale that are 'missing' vary.
The pentatonic scale is prevalent in the traditional music of many vastly different and geographically separated cultures. This can hardly be attributed to coincidence, and the discovery of its relationship to the 'chord of resignation', and by assosciation the chord progression of resignation, has only reinforced my impression that there's something fundamentally significant about the pentatonic scale.
Below are some examples of the 'chord of resignation'. As with the chord prog list, I'll add to this over time, so check back! (Quite a few examples I could easily include here would double with ones already in the chord prog list, so I'm leaving some - though not all - of them out.)
To make collecting examples easier, I'm attempting to group them by harmonic structure a little.
The following examples simply use the minor 7th chord in its purest form:
1. Leo Ornstein - Piano Sonata No. 4, 2nd mvt (see 0:07, and probably most prominently 0:14) Aside from the timecodes noted, the opening of this appears to make use of the minor 7th constantly in other ways too complex for me to try to analyse yet. This piece already appears on the chord prog examples list, but I had to repeat it here because it has such a wealth of interesting harmony.
2. Ravel - Le Gibet (see 13:42 and several times again until the end)
3. Gershwin - Summertime (see 9:11)
4. Leo Ornstein - Piano Sonata No. 4, 4th mvt The opening of this is practically built out of minor 7th chords (or stacks of 3rds, in any case).
5. Steve Reich - Six Marimbas (see 6:15 onwards) The uppermost note of this chord shifts constantly between the 7th and 8th degree of the scale, while the underlying 3rds remain 'fixed'. Interestingly, the tonic doesn't appear in the bass until 6:32, and it dissappears again at 13:42. The inversion of the minor 7th created by this is the one shown in the first image above - the degrees of the chord prog of resignation stacked on top of each other in order: I, III, IV, VI.
6. Ravel - Une barque sur l'ocean (see 4:47)
7. Ravel - Noel des Jouets (see 2:26)
8. Ravel - Ondine (see 5:20) This example is really in a class of its own, as the chord is not only broken into a myriad of semiquavers and tuplets with a scattering of arbitrary notes in between, but it also isn't even a minor 7th. Nevertheless, a Chord of Resignation it undoubtedly is. A far more conventional example can be found at 5:49.
A very common way in which the minor 7th chord manifests - especially in minimalism - is where a particular interval or combination of intervals are maintained over the top of a changing base chord progression, resulting in the 'Chord of Resignation' seeming to grow naturally out of a pure tonic triad. The following examples demonstrate this.
9. Stellardrone - In Time This is a fairly simple example - harmonically and texturally - so well suited for explanatory purposes. The bass is progressing as follows: I, [V], VI, VII. To start with the...er, constellation of notes being repeated over the top is simply part of the tonic triad, but as it remains the same while the bass changes, it forms a minor 7th over the VI chord.
10. Porcupine Tree - Trains As with the previous example, the upper notes in the harmony here remain constant over a changing bassline, resulting in a minor 7th forming over the VI chord. However, there are other relevant complexities to the harmony which you can read about in the chord prog examples list.
11. Steve Reich - Electric Counterpoint III This is an interesting example because the underlying chord progression consists only of the degrees of the scale that form the minor 7th - IV, VI, Im. As a result, in this instance it's impossible to say that a minor 7th is only formed over, say, the VI chord, as was the case with the previous 2 examples. The harmony just morphs organically, an effect intensified the gradual introduction of each degree of the scale in the bass at the start of the piece (you have to listen to the whole thing to get what I'm talking about). PS in case you're curious what happens when it briefly modulates, the progression is III, IV, V, but effectively that III chord becomes the new tonic.
12. Steve Reich - Music for large ensemble Initially, the uppermost note of the chord is simply the 3rd degree of the tonic triad (i.e. the dominant), but each time the bass plunges down a third it becomes a minor 7th.
Yes, there is a lot of Ravel on this list. :P
Wednesday, 6 November 2013
A compositional project
Link to the project
About a year ago I wrote what I suppose you could call a 12-track piece for percussion ensemble. I say '12 track' because, although it used 10 separate instruments, I feel like 'track' is a more appropriate way to describe the way in which each stave was a whole composition unto itself.
I named this piece 'Mechanism No. 1', with the aim of writing more pieces in a similar style in the future. I recently completed Mechanism No. 2, which also has 12 'tracks'. You can find both pieces here:
Mechanism No. 1
Mechanism No. 2
I write most of my music in Sibelius, which has a mixing panel. While writing
anything with more than a few instruments, I usually mute or solo tracks and adjust volumes to hear how different combinations of instruments sound together and to make sure there aren't any unwanted dissonances.
With these very large, complex scores, such as the Mechanisms, often things come out in a reduced combination of instruments that are completely lost when all parts are blaring away at once. For example, just the marimba, vibrophone and harp together can convey a completely different mood to the work as a whole, and sound almost like a separate composition in their own right.
Often this has to do with each instrument's place in the harmony: with the combination of instruments just mentioned, you might never hear the tonic, so the whole key of the piece sounds different. In the work as a whole, these instruments might be filling in the 4th, 6th, or 7th degree of the scale (perhaps all at the same time!), but on their own, they create a new scale altogether.
It made me sad to think that my listeners would never get to hear all these different combinations of instruments I encountered while writing the Mechanisms. Short of uploading a Sibelius file to the web and hoping that everyone who wanted to hear the piece HAD Sibelius, there was no way of providing the same 'customizable' listening experience that I had from within the software during the composition process.
For this reason, I've decided to export several extra audio files of Mechanism No. 2 using a couple of different instrument combinations which I think are particularly interesting, and plan to do the same with Mechanism No. 1. I'll upload these to a Soundcloud playlist in the coming week. A link will be posted here when it's ready!
P.S. I originally considered exporting and uploading EACH STAVE individually, making them downloadable, and letting people remix. While I love projects like this, it would take a lot of time and probably not be worth it, since nobody knows I exist :P
About a year ago I wrote what I suppose you could call a 12-track piece for percussion ensemble. I say '12 track' because, although it used 10 separate instruments, I feel like 'track' is a more appropriate way to describe the way in which each stave was a whole composition unto itself.
I named this piece 'Mechanism No. 1', with the aim of writing more pieces in a similar style in the future. I recently completed Mechanism No. 2, which also has 12 'tracks'. You can find both pieces here:
Mechanism No. 1
Mechanism No. 2
I write most of my music in Sibelius, which has a mixing panel. While writing
anything with more than a few instruments, I usually mute or solo tracks and adjust volumes to hear how different combinations of instruments sound together and to make sure there aren't any unwanted dissonances.
With these very large, complex scores, such as the Mechanisms, often things come out in a reduced combination of instruments that are completely lost when all parts are blaring away at once. For example, just the marimba, vibrophone and harp together can convey a completely different mood to the work as a whole, and sound almost like a separate composition in their own right.
Often this has to do with each instrument's place in the harmony: with the combination of instruments just mentioned, you might never hear the tonic, so the whole key of the piece sounds different. In the work as a whole, these instruments might be filling in the 4th, 6th, or 7th degree of the scale (perhaps all at the same time!), but on their own, they create a new scale altogether.
It made me sad to think that my listeners would never get to hear all these different combinations of instruments I encountered while writing the Mechanisms. Short of uploading a Sibelius file to the web and hoping that everyone who wanted to hear the piece HAD Sibelius, there was no way of providing the same 'customizable' listening experience that I had from within the software during the composition process.
For this reason, I've decided to export several extra audio files of Mechanism No. 2 using a couple of different instrument combinations which I think are particularly interesting, and plan to do the same with Mechanism No. 1. I'll upload these to a Soundcloud playlist in the coming week. A link will be posted here when it's ready!
P.S. I originally considered exporting and uploading EACH STAVE individually, making them downloadable, and letting people remix. While I love projects like this, it would take a lot of time and probably not be worth it, since nobody knows I exist :P
This blog will no longer be limited to music...
Almost ever since I started this blog I've been itching to post about things other than music. However, I did initially set it up to be music-specific, and I didn't think I'd be posting frequently enough about other topics to justify changing that.
However, I recently changed my mind in light of the amount of stuff I have to say about technology (although literature is also a possible topic). I'm studying IT, and increasingly finding myself wanting to air my views or share my discoveries in relation to this pursuit.
So from now on, this blog is no longer exclusively music-themed. I'm going to have to think of another title! I'm also working on a widget to create navigation that elegantly divides it into sections based on post labels, but until that's finished, a flat link list will have to do.
However, I recently changed my mind in light of the amount of stuff I have to say about technology (although literature is also a possible topic). I'm studying IT, and increasingly finding myself wanting to air my views or share my discoveries in relation to this pursuit.
So from now on, this blog is no longer exclusively music-themed. I'm going to have to think of another title! I'm also working on a widget to create navigation that elegantly divides it into sections based on post labels, but until that's finished, a flat link list will have to do.
Subscribe to:
Posts (Atom)