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Old 03-16-2012, 03:35 PM
John825 John825 is offline
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Serialism and retrograde.

I was reading something online and it said how some musicians utilize serial composition in their music or serialism. What is serialism? Also, what is retrograde and retrograde inversion and could you give an example? I'm very curious as to what these terms mean. Thank you, it is appreciated.
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Old 03-24-2012, 10:45 AM
James.Erickson James.Erickson is offline
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Originally Posted by John825
I was reading something online and it said how some musicians utilize serial composition in their music or serialism. What is serialism? Also, what is retrograde and retrograde inversion and could you give an example? I'm very curious as to what these terms mean. Thank you, it is appreciated.

Serial composition is a way of organizing reoccurring elements of music (such as melody or harmony) in a way that gives a piece unity. Serialization is not a style or a way of composing, but it is a technique of composing. It is often used in 12-tone music, and a great example of it would be Arnold Schoenberg's work.

Serial composition utilizes what are called "pitch classes" and "pitch sets," which put simply means that a number is assigned to each pitch based on their organization within the pitch-space (the infinite collection of pitches possible). These are often mathematical relations that yield non-tonal harmony, but it does not necessarily have to be limited to non-tonal harmony, as tonal harmony is actually often described as a subset of the total collection of the pitches.

An example of a subset collection is actually the "Circle of fifths," which is an organization of the total set of pitches described by sets of 7 in relation to their most direct modulation between nearest key centers. It only takes one note-change to move from G to C or from G to D, and so on. Thus the circle of fifths provides an organizational tool that provides a method of moving between keys in an musically coherent way. This is a simple example of serialization because serialism takes this concept and applies it to different collections and pitch-sets, not just the tonal scales that we are used to. This example would be applicable if one used the circle of fifths two move from a specific point on the circle two another specific point on the circle as a part of one's organization of the composition. Like if you moved from C through the 12 different keys back to C every twelve bars, that would be a small use of serialism in tonal music.

Retrograde Progressions in tonal music on the other hand is a type of progression. Normal progressions typically have tonic, preparatory chords, dominant, tonic. This is the typical motion in most tonal music, but there is a tool called retrograde which yields interesting results, which means you reverse this sequence: tonic, dominant, preparatory chords, tonic. For example: I IV V I (standard), I V IV I (Retrograde). Because the nature of the dominant-tonic relationship, the ear wants/expects the tonic to follow, and so by delaying the tonic resolution by placing other chords in its way (like the ii, IV, etc), than the progression becomes retrograde, and gives you a different emotion than what the normal progression. A I IV V usually sounds happy, where as a I V IV I sounds almost melancholy. Same chords, but different order.

Yet there is a retrograde that can be applied to rhythm (a backwards rhythm of an earlier used rhythm).

There is also a retrograde that applies to serialism, which is where the ordered series of pitches that I talked about earlier is reversed. So if the composition made its way, for example, linearly up the chromatic scale for the first half of the composition, a retrograde of that would descend down the chromatic scale during the second half. Yet don't misunderstand the simple example: this does not mean simply going up and down a scale, but a reversal of the melody and harmonic elements. You can think of it this way: like a mirror was placed on the sheet of music paper and created the next section of the music. This is probably what you meant more by what is retrograde, but I included the tonal retrograde progression answer as well, because it is more directly applicable to most musicians.

Retrograde inversion is taking the organized series of pitches and not only reversing it, but inverting it as well. This is not as simple as the "mirror' example, because inverting involves a particular pitch around which pitches are mathematically mapped from one pitch to the next. It is more involved than reversing the organization, it takes a deeper understanding of how the organization of pitches works, which would require a much deeper exploration. Inversion does not necessarily mean flipping it upside down, even though that is what the name implies, because you could invert the music around any point on the collection.

I hope I did not confuse you further, because these topics are very expansive and mathematically-heavy, so I hope you were able to glean some understanding. If you have further questions, I would be happy to make things more clear as your understanding of these dense topics unfolds.

James Erickson

Last edited by James.Erickson : 03-24-2012 at 11:04 AM.
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Old 03-28-2012, 06:39 PM
Slipin Lizard Slipin Lizard is offline
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That was an excellent explanation... I tried out the retrograde thing.. very cool! I'm struggling to "visualize" serialism.. a YouTube example would be great... thanks for the effort with that in-depth answer!
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Old 04-24-2012, 01:22 PM
MarcusWiesner MarcusWiesner is offline
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music of the 12-tone variety is very interesting. Here is a good example of some pretty good stuff for a beginner to listen to While this has a very pleasant sound, some twelve tone music, like this, does not have quite so accessible of a sound:

The idea was that in order to completely destabilize tonality, they would use all of the twelve tones in music equally. Notice that it is fairly impossible to find "do" in all of these examples. They use a tone row, its inversions and retrogrades, and even its inverted retrogrades, to compose the piece of music. You can generate your own matrix here:

This will give you a pretty good understanding of how this music is frequently organized. The most helpful thing is if the composer includes a key with his piece, otherwise it is incredibly difficult to analyze and figure out what the tone row is. The chords and everything in this type of music are frequently analyzed on a clock face with every tone being represented by a number from 0 to 11 (because when you get back to 12, you are at the same pitch class again).

To get the prime form of a chord, you find the smallest 3 integers that will represent it. A minor or major triad, for instance, is 0,3,7 which is a right triangle. Pythagorea's theorem of a right triangle states that the smallest whole number integers which fit the formula are 3,4,5, and if you check the prime form 0,3,7 on the clock face, the distance from 0 to 3 is 3; the distance from 3 to 7 is 4; the distance from 7 back to 0 (base 12) is 5. There is also an idea of inversional (and retrograde) equivalence. This means that in 12-tone theory, the major and minor triad are essentially the same.

I hope that this answers a lot of your questions but I also know that it will leave you with many more, so my suggestion is to study music theory and 12-tone theory to answer whatever other questions you have about it, because me telling you is not as helpful to you as you learning about and intellectually experiencing it and applying it for yourself. happy studies
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