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I am slightly overwhelmed by all of the lovely comments on last weekโs #MedEd #TheoryThursday thread. Thank you all for nerding out with me!!
Right, now on to PARADIGMS
What are paradigms, why are they important + whatโs their relationship with theory?
๐งต
Right, now on to PARADIGMS
What are paradigms, why are they important + whatโs their relationship with theory?
๐งต
Paradigms are assumptions, values, beliefs + practices that form distinct ways of viewing the world. They are usually shared by people in a community. They inform how we view + discuss reality and knowledge.. + this shapes how we try and find out about experiences/our environment
Theories are not paradigms, and paradigms are not theories.
Theories help us explain the connections between what we observe.
Paradigms tell us how we might go about observing those connections in the first place.
Theories help us explain the connections between what we observe.
Paradigms tell us how we might go about observing those connections in the first place.
Ok, #MedEd theory nerds โ you asked for #TheoryThursday, so here we are.
Before we launch into the weird + wonderful world of various theories, we need to think about what theory is + what it can do.
A thread ๐งต
Before we launch into the weird + wonderful world of various theories, we need to think about what theory is + what it can do.
A thread ๐งต
What the heck is theory?
Well, theory is so confusing because people donโt really agree on what it is! My fave definition is from @LaraVarpio + colleagues
Well, theory is so confusing because people donโt really agree on what it is! My fave definition is from @LaraVarpio + colleagues
Theories explain the relationships between concepts. Prepositions are statements that might be โ
or โ (they are statements made as โfactsโ that can be true, or may be disproven as false).
So theories have to make statements of โfact โabout how concepts connect.
So theories have to make statements of โfact โabout how concepts connect.
Today is #TheoryThursday ๐ง!
The most important question in all of Computer Science is probably whether P equals NP. That is, are all problems easy to validate also easy to solve?
How can we even start to ponder this question? ๐งต๐
The most important question in all of Computer Science is probably whether P equals NP. That is, are all problems easy to validate also easy to solve?
How can we even start to ponder this question? ๐งต๐
๐ In case you're just hearing about this, here's a short refresher on what we are talking about:
Let's think now about what would it mean to properly answer this question. ๐
Let's think now about what would it mean to properly answer this question. ๐
Say we want to answer "yes". How can we do that? Do we have to check that *all* NP problems are actually in P?
๐ To begin, there are infinitely many problems in Computer Science.
There must a better way...
๐ To begin, there are infinitely many problems in Computer Science.
There must a better way...
Today is #TheoryThursday ๐ง!
I want to talk about what is, possibly, the most important question in all of Computer Science: Does P equal NP?
If you have heard of this and want to learn a bit more, read on... ๐งต๐
I want to talk about what is, possibly, the most important question in all of Computer Science: Does P equal NP?
If you have heard of this and want to learn a bit more, read on... ๐งต๐
Computer Science is all about finding clever ways to solve difficult problems.
We have found clever algorithms for a bunch of them: sorting stuff, finding shortest paths, solving equations, simulating physics...
But some problems seem to be way too hard ๐
We have found clever algorithms for a bunch of them: sorting stuff, finding shortest paths, solving equations, simulating physics...
But some problems seem to be way too hard ๐
One example is the Travelling Salesman problem.
โ Find a cycle starting in your home city to visit all major cities in your country and return home with the least fuel cost.
This is the kind of problem we expect computers to solve easily, right? That's what computers are for!
โ Find a cycle starting in your home city to visit all major cities in your country and return home with the least fuel cost.
This is the kind of problem we expect computers to solve easily, right? That's what computers are for!
On musical form; sixth instalment: Sonata Form
What is sonata form? For many people, the term sounds perhaps daunting, associated with the loftiest flights of imagination as it is, and with musical minds of the greatest renown, like Beethoven, Brahms, Haydn and Mozart.
1/30
What is sonata form? For many people, the term sounds perhaps daunting, associated with the loftiest flights of imagination as it is, and with musical minds of the greatest renown, like Beethoven, Brahms, Haydn and Mozart.
1/30
In a structural sense, however, sonata form is not too hard to explainโespecially seeing that I have already spent so many words on other forms of a similar construction.
2/30
2/30
The sonata form is a ternary form. In essence, therefore, it differs not significantly from any other ternary form; not from the simple ternary form, not from the minuet or scherzo and neither from the rondo forms.
3/30
3/30
Hey, guess what, today is #TheoryThursday ๐ง!
A silly excuse I just invented to share with you random bits of theory from some dark corner of Computer Science and make it as beginner-friendly as possible ๐
A silly excuse I just invented to share with you random bits of theory from some dark corner of Computer Science and make it as beginner-friendly as possible ๐
Today I want to talk about *Algorithmic Complexity *.
To get started, take a look at the following code. How long do you think it will take to run it?
Let's make that question more precise. How long do you think it will take to run it in the worst-case scenario?
To get started, take a look at the following code. How long do you think it will take to run it?
Let's make that question more precise. How long do you think it will take to run it in the worst-case scenario?
We can see that the code will run slower if:
๐ your computer is older;
๐ the array is longer; or
๐ x happens to be further to back, or not present at all.
Can we turn these insights into an actual formula? We will have to get rid of ambiguous stuff like "old computers".
๐ your computer is older;
๐ the array is longer; or
๐ x happens to be further to back, or not present at all.
Can we turn these insights into an actual formula? We will have to get rid of ambiguous stuff like "old computers".
On musical structure; fifth instalment: Rondo Forms
To outline the structure of the rondo forms, we will need to resort to discussing its technical trappings. A general portrait of the rondo forms can be painted, however, by defining a few key characteristics.
1/27
To outline the structure of the rondo forms, we will need to resort to discussing its technical trappings. A general portrait of the rondo forms can be painted, however, by defining a few key characteristics.
1/27
The rondo forms capitalise upon one of musicโs most fundamental principles, namely repetition. They are primarily defined by the repetition of the primary idea, its secondary sections acting as digressions from this primary idea.
2/27
2/27
The repetitions of the rondo's main idea, often varied, provide the development of the musical idea. As outlined in Schoenbergโs words on the form I shared last week, the subordinate sections are merely there to prevent the monotony of hearing repetitions all the time.
3/27
3/27
For today's #TheoryThursday, a few words from Arnold Schoenberg as a prelude to the discussion of Rondo form.
Schoenberg disputed the popular notion that the musical rondo is more than superficially an imitation of the poetic โrondeauโ (i.e. a repeated refrain and couplets)
1/8
Schoenberg disputed the popular notion that the musical rondo is more than superficially an imitation of the poetic โrondeauโ (i.e. a repeated refrain and couplets)
1/8
He notes that, in the poetic form, the refrain underlines the common factor of juxtaposed elements, while in the musical form, the repeated section is the main ideaโand intervening sections only subordinate digressions.
2/8
2/8
The difference is thus, that the stanzas of the poetic โrondeauโ develop the idea stated in the refrain, while the digressions from the refrain in the musical rondo serve as complements, to save the repetition of the refrain from the danger of becoming monotonous.
3/8
3/8
Today, on #TheoryThursday, (I know it is Friday but as I wrote the text yesterday, I refuse to change it) allow me to say a few words on musical theory itself, on the textbooks which have been used throughout the ages, and on their influence on the music of the masters.
1/16
1/16
Schoenberg denounced theorists and proclaimed the Living Art as the source of ever-evolving musical lawsโ'tis not for the theorist to decide which rules music should adhere to. Debussy said that โLes oeuvres d'art font les rรจgles, les rรจgles ne font pas les oeuvres d'artโ.
2/16
2/16
In part, I subscribe to this view, in that theorists should not be lawmakers, that they do not decide the course of musical historyโbut they can document it, and in this regard their work is very valuable, as long as their advice is not heeded like tables of the law.
3/16
3/16
๐๐ง ๐ฆ๐ฎ๐ฌ๐ข๐๐๐ฅ ๐ฌ๐ญ๐ซ๐ฎ๐๐ญ๐ฎ๐ซ๐; ๐๐จ๐ฎ๐ซ๐ญ๐ก ๐ข๐ง๐ฌ๐ญ๐๐ฅ๐ฆ๐๐ง๐ญ: ๐ฅ๐๐ซ๐ ๐๐ซ ๐ญ๐๐ซ๐ง๐๐ซ๐ฒ ๐๐จ๐ซ๐ฆ๐ฌ
Onwards to more extensive forms, we come to larger ternary forms, the most prevalent of which are the dance forms; the minuet and the scherzo.
1/22
Onwards to more extensive forms, we come to larger ternary forms, the most prevalent of which are the dance forms; the minuet and the scherzo.
1/22
Both the minuet and scherzo can either be independent pieces or movements of a larger structure, like a suite, sonata or symphony.
They are essentially identical in form, though one can speak of differences in a general sense, especially in character and tempo.
2/22
They are essentially identical in form, though one can speak of differences in a general sense, especially in character and tempo.
2/22
The minuet, generally in 3/4 time, has a more or less stately character and an average metronome marking of 60-70 to a bar in Haydn and Mozart. Still, the variations in mood are myriad, as proven by the difference between this minuet by Haydn...
3/22
3/22
๐๐ง ๐ฆ๐ฎ๐ฌ๐ข๐๐๐ฅ ๐ฌ๐ญ๐ซ๐ฎ๐๐ญ๐ฎ๐ซ๐; ๐ข๐ง๐ญ๐ซ๐จ๐๐ฎ๐๐ญ๐ข๐จ๐ง ๐๐ง๐ ๐๐ข๐ซ๐ฌ๐ญ ๐ข๐ง๐ฌ๐ญ๐๐ฅ๐ฆ๐๐ง๐ญ: ๐๐ก๐ ๐๐จ๐ญ๐ข๐ฏ๐
In musical masterpieces, it is impossible to see a single part or fragment as independent of any of the other parts.
1/23
In musical masterpieces, it is impossible to see a single part or fragment as independent of any of the other parts.
1/23
Even where musical phrases are simply juxtaposed, such as in a Bach chorale, they could not have been presented in any other way.
2/23
2/23
For the musical work comes to the master as a whole, a composer, then, has not the freedom to pick a theme and vary it here and thereโthe master must carry through the consequences inherent in the theme his mind conceives.
3/23
3/23
๐๐จ๐ซ๐๐ฌ ๐ข๐ง ๐ฆ๐ฎ๐ฌ๐ข๐
Throughout musical history, there have been countless forms which composers have employed in order to express their musical ideas, like symphonies, concerti and operas for orchestral forces and quartets, trios and sonatas for smaller ensembles.
1/34
Throughout musical history, there have been countless forms which composers have employed in order to express their musical ideas, like symphonies, concerti and operas for orchestral forces and quartets, trios and sonatas for smaller ensembles.
1/34
These are only a few of a vast array of musical forms, and I have only mentioned a few predominant mainly in the Classical and Romantic eras; there are a host of others!
To illuminate their merits would take countless hours and countless Tweets.
2/34
To illuminate their merits would take countless hours and countless Tweets.
2/34
Today I would therefore like to direct your attention to a musical form which has been almost a constant throughout the entirety of history.
When humanity first made music, they did so using the instrument born within virtually every human body; the voice.
3/34
When humanity first made music, they did so using the instrument born within virtually every human body; the voice.
3/34
#TheoryThursday
The resources a composer can use to communicate their music are not confined to notes and markings alone. Often, words are written over their music, especially at the beginning, in order to convey more clearly the musical thought.
1/12
The resources a composer can use to communicate their music are not confined to notes and markings alone. Often, words are written over their music, especially at the beginning, in order to convey more clearly the musical thought.
1/12
There are pieces which have only a metronome marking, like the pieces in Schumannโs โKinderszenenโ. The character and mood of the pieces is to be discerned in the notes themselves.
2/12
2/12
Before the invention of the metronome, composers had to communicate a tempo to the performers by means of words. Through a shared frame of reference between composer and performer, the tempo could be fairly exactly communicated.
3/12
3/12
On this fine #TheoryThursday , I would like to share with you a little bit of insight into something that many consider one of musicโs most important components, namely MELODY.
1/34
1/34
A melody is nothing more than a linear succession of pitches conditioned by rhythmic factors, yet we tend to ascribe great value to melody. Why is this? What makes this aspect of music so important that people judge music on the perceived absence or presence of a melody?
2/34
2/34
The concept of melody is quite intimately linked to the possibilities and limitations of the human voice. This is, after all, our primeval musical instrument. This immediately explains too why we value melody so highly.
3/34
3/34
The title of a musical composition can be descriptive and refer to the musicโs extramusical influences, like the title of a symphonic poem by Liszt which tells us basically what the music is about, or that we should keep in mind a certain programme.
1/24
1/24
More often, a compositionโs title denotes form, like with the sonata or rondo, or implies a certain character without presenting an explicit programme.
2/24
2/24
Other times still, the title refers to the instrumental forces for which the piece is arranged (a symphony being, almost invariably, a work for orchestra, while a piano sonata speaks of both the form and the instrument employed).
3/24
3/24
Today I would like to talk about something in music which is utterly laughable, but nonetheless of such an influence that we must take it seriously, although we would want to declare it ludicrous.
This is the influence of notation on music, especially on HARMONY.
This is the influence of notation on music, especially on HARMONY.
In conventional harmony, there is an assortment of chords which are treated as โchance harmoniesโ, as sonorities which occur because of the voice leading or as appoggiaturas, and these are not classed with traditional chordsโgiving rise to the notion of โadded-tone chordsโ.
Compare the following two harmonies; neither is traditionally classified amongst the consonances.
The first is a seventh chord, and therefore has a name and description in harmonic theory. The other is, at first glance, a c major triad with a d added above it.
The first is a seventh chord, and therefore has a name and description in harmonic theory. The other is, at first glance, a c major triad with a d added above it.
