# Share and Learn About Techniques of Modern Music



## Torkelburger (Jan 14, 2014)

I wanted to post a thread about appreciating modern music from a different angle. I wanted to have posts share pieces which give examples of modern musical techniques so that those who are wanting to appreciate modern music on a more in-depth level will come to perhaps enjoy modern music even more (since they will have learned something about it and it won't be so foreign to them).

So please post pieces in this thread that illustrate a modern musical technique. Do not post genre examples (like a minimalist piece as an example of "minimalism"). It must be a technical subject. Take a sentence or two to describe the technique. If you wish, say what you like about the technique and what you like about the piece that illustrates it.


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## Torkelburger (Jan 14, 2014)

In the 20th century, composers developed a new type of harmony to express themselves with called Quartal Harmony. Instead of building triads with the intervals of thirds (C, E, and G to build a C Major triad), the discovery was made to build a chord by fourths (C, F, and Bb) (or fifths (quintal) Bb, F, and C).

What I love the most about this sound is that it sounds modern and even atonal at times, but is consonant, not dissonant (the fourth is a consonant interval). Whenever I hear quartal harmony I immediately picture images of cubism and art deco in my mind. It has that great 20th century austerity to it. One thing to note is the more fourths you add to the chord, the more "dissonant" it becomes, however, it still maintains an essence of quartal consonance and has a kind of unique "in between-ness" to it, a sort of liminal ambiguity.

The first example is Leonard Bernstein's Seven Anniversaries second movement (for his sister Shirley) which starts at 1:16.





The second example is Paul Hindemith's Six Chansons (Un Cygne (A Swan)) which starts at 1:23. This piece shows just how beautiful this type of harmony can get and how well it blends when occasionally interrupted with regular triads by thirds and open fifth chords. It also shows the quartal chord in inversion (C, F, Bb is "root position" and first inversion would be F, Bb, C and second inversion would be Bb, C, F).





The third example is a brilliant short song by Charles Ives titled "The Cage". It uses the large quartal chords described earlier in this post.





The last example is Aaron Copland's Piano Fantasy. The beginning has quartal writing sprinkled throughout and is very effective, powerful, austere, etc.


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## Larkenfield (Jun 5, 2017)

Great subject for a thread.

For those interested, here is an excellent overview of a number of modern compositional techniques. Look for sub-headings under each lesson. It might be worth seeking out an example of each:

https://online.berklee.edu/courses/contemporary-techniques-in-music-composition-1

For example, Bartok's two five-tone scales from his Mikrokosmos... I love their unique ethnic and colorful flavor... fantastic... (and any contemporary composer can make up his or her own scales):


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## Phil loves classical (Feb 8, 2017)

Bartok's Mikrokosmos is chock full of different techniques. Here is one I just recorded myself playing (edited a few mistakes out ). Regular bar in traditional music typically has the stress on the first beat (and 3rd in 4/4 time), but in modern music, the stresses were put in different places.


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## Torkelburger (Jan 14, 2014)

Composers in the 20th century developed a new type of harmony where you combined at least two chords from varying harmonic areas at the same time. The technique is called Polychords. An example would be writing a single chord that consisted of C-E-G (a C Major triad) and D-F#-A (a D Major triad) that sounded at the same time.

What I like about this technique is that while it sounds modern, it still has roots to tonality and sounds as such. It is versatile in that it can be used anywhere as soft background sustained chords in strings, or percussive punctuations in brass.

Who can forget the effective opening bars of Honneger's Symphony No. 5 with its dramatic use of polychords?





Vincent Persichetti was a composer who used polychords extensively. The first example has polychords in the brass in the first movement punctuating the phrases in the winds.













William Schuman also has a piano piece with polychords. They start at 0:28


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## Torkelburger (Jan 14, 2014)

One more example at 4:26


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## Torkelburger (Jan 14, 2014)

Composing with at least two different modes simultaneously either on the same tonal center or varying tonal centers is called polymodality. An example follows where Francis Poulenc uses Bb major in the left hand and Bb Locrian in the right (bars 10-13).






Closely related to polymodality is polytonality, which is using more than one tonality or keys simultaneously as seen in the opening movement here.






Again, I like the modern sound of these techniques but like how they still hold a footing in tonality and consonance. You have control over the amount of dissonance by how distant you place the modes/keys apart from each other.


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## millionrainbows (Jun 23, 2012)

One of the concepts of modern musical thinking is the idea of dividing the octave into parts in a different way than traditional tonality does it.
In traditional tonality, in which the 12-note octave is divided according to a 7-note diatonic scale, the 12 notes of the octave are divided as "7" (C to G) and "5" (C to F). These are the main intervals of tonality, the fifth and its inversion, the fourth.

The mid-point of the twelve notes of the octave is really "6" (12 ÷ 2 = 6), and this is the "tritone" (C-F#) and is unsettling to tonality, since tonality needs that fifth to make stable triads.

Since modernism is not as concerned about stable fifths, many composers have chosen to ignore tonal considerations and base their division of the octave on purely arithmetical values, as shown above.

A good example of this division is the whole-tone scale. It is a six-note scale, and there are only two of them: C-D-E-F#-G#-A#, and C#-D#- F-G-A-B. Composers have used the symmetrical properties of the WT scale, as it is formed out of a succession of whole-steps (hence the name), and is completely symmetrical. A whole tone scale sounds the same no matter what note you start on. Thus, a WT scale can have six possible starting points as a scale, and will exhibit the same characteristics, and generate the same set of chords, and inversions, regardless of which note is chosen as the start-point.

Schoenberg used rows with tonal implications in his Op. 26 Wind Quintet:

[The row is (first hexad) Eb-G-A-B-C#-C, which gives an augmented/whole-tone scale feel, with a "resolution" to C at the end, then (second hexad) Bb-D-E-F#-G#-F, which is very similar in its augmented/whole-tone scale structure, which only makes sense: there are only two whole-tone scales in the chromatic collection, each a chromatic half-step away from the other.

I've heard Debussy use the two whole-tone scales in this manner, moving down a half-step to gain entry to the new key area.

This is why Schoenberg used a "C" in the first hexad, and the "F" in the second; these are "gateways" into the chromatically adjacent scale area. Chromatic half-step relations like these can also be seen as "V-I" relations, when used as dual-identity "tri-tone substitutions" as explained following.

Another characteristic of whole-tone scales is their use (as in Thelonious Monk's idiosyncratic whole-tone run) as an altered dominant, or V chord. There is a tritone present, which creates a b7/3-3/b7 ambiguity, exploited by jazz players as "tri-tone substitution". The tritone (if viewed as b7-3 rather than I-b5) creates a constant harmonic movement, which is what chromatic jazzers, as well as German expressionists, are after.

So Schoenberg had several ideas in mind of the tonal implications when he chose this row.]


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## Torkelburger (Jan 14, 2014)

Secundal Harmony and Clusters

Chords built on the interval of the second is called secundal harmony. A secundal chord may have open spacing in the voicing and defined inner voice movement between chords. An example of a secundal chord would be B,C, (up a fifth to the…) G,A.

Clusters are closely related to secundal chords but feature a greater number of chord tones in closed spacing with a lack of inner voice movement. An example of a cluster would be C, Db, Eb, E, F, G.
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My favorite example of secundal writing comes from Leonard Bernstein's _Symphonic Suite from On the Waterfront_ starting at 7:14 here:






What's great about it is that it shows that secundal harmony does not have to be dissonant just because it is made up of seconds (and sevenths). It can sound very beautiful. It gives the music a highly original, distinct, and unique flavor using a modern vocabulary without sacrificing beauty.

Another example of secundal harmony is Bartok's _String Quartet No. 3_ at 1:00 in the 2nd violin, viola, and cello.






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A great example of cluster writing is the opening of Rautavaara's _Piano Concerto No. 1_. Very beautiful and dramatic.:






Another cluster example is a piece by Henry Cowell. A very musical effect, representing the crashing and rolling of ocean waves.:






And finally, perhaps the most famous example of clusters is Varese's _Ionisation_. Clusters occur in the piano starting at 5:24.


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## Torkelburger (Jan 14, 2014)

What did modern composers do with triads (tertian harmony)? Instead of only utilizing the circle of fifths chord progressions, they also moved triads by third relationship, second relationship, and tritone relationship. They also carried on the impressionist technique of extended harmony (seventh (C-E-G-B), ninth (C-E-G-B-D), thirteenth chords (D-F-A-C-E-G-B), etc.).

Prokofiev used triads by third relationship (roots are the interval of a third apart) throughout the March from _The Love of Three Oranges_.





Samuel Barber utilized chords by second relationship (roots are the interval of a second apart) throughout the score for Adagio for Strings.





An example of a chord progression in tritone relationship occurs at 2:43 for 1 bar here:





For examples of extended harmony (sevenths and ninths), there is the following:
Occurring at :23 and throughout





And starting at 2:00 here


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## tdc (Jan 17, 2011)

Torkelburger said:


> What did modern composers do with triads (tertian harmony)? Instead of only utilizing the circle of fifths chord progressions, they also moved triads by third relationship, second relationship, and tritone relationship. They also carried on the impressionist technique of extended harmony (seventh (C-E-G-B), ninth (C-E-G-B-D), thirteenth chords (D-F-A-C-E-G-B), etc.).
> 
> Prokofiev used triads by third relationship (roots are the interval of a third apart) throughout the March from _The Love of Three Oranges _


_

Interesting information thanks and btw very nice interpretations of the Prokofiev and Barber pieces there. :tiphat:_


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## Torkelburger (Jan 14, 2014)

Modern composers use a wide range of scale materials to compose with, including modes, pentatonic and hexatonic scales, synthetic scales and so on (and whole tone scales have already been touched upon).

Modes

The first of two examples of Dorian writing (DEFGABCD) comes from Ernest Bloch's Concerto Grosso No.1, right at the beginning.





And Ralph Vaughan Williams Oboe Concerto at the beginning (A,B,C,D,E,F#,G,A)





An example of Lydian writing is Darius Milhaud's Protee, right at the beginning





An example of Mixolydian writing is Erik Satie's Gymnopedie No. 2 (entire piece)





An example of Aeolian writing is Carl Orff's O Fortuna from Carmina Burana.


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## Torkelburger (Jan 14, 2014)

Synthetic Scales
A synthetic scale is a scale in which the whole step-half step pattern of the scale does not follow any major or minor scale pattern or modal pattern, but is usually made up by the composer. An example of a synthetic scale might be half-whole-whole-whole-whole-whole-half, or C-Db-Eb-F-G-A-B-C.

This post will focus on one synthetic scale called the octatonic scale, which is the most popular synthetic scale used in the modern era. It was made popular by Bartok and Stravinsky. It's pattern is simple, it is alternating half and whole steps. Half-whole-half-whole-half-whole-and so on. Or you can start it on the whole step-half-whole, etc. Due to note repetitions, there are only three possible octatonic scales/modes.

The first two examples are simple. One is Bartok's Harvest Song #33 from 44 Duos for Violin. The entire piece is based on the octatonic scale.





The second Bartok example is Mikrokosmos Vol IV No. 101 (entire piece)





Stravinsky used the scale probably more than anyone else. His first example comes from his Octet, the second movement starting at 4:02.

Rehearsal #27 and it's repeats use two octatonic scales together one after the other in the bassoons. (Bb-A-G-F#-E and E-D-C#-B-Bb).





The next Stravinsky example comes from his Symphony in Three Movements first movement at 0:47 and its repeat.





Lastly, the first movement from his Symphony of Psalms, with a few minor interruptions of the Phrygian mode, is otherwise entirely octatonic.


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## Torkelburger (Jan 14, 2014)

Ostinato
An ostinato is a well-defined melodic fragment repeated over and over again. It usually has a simultaneously repeating rhythm and repeating group of pitches. The ostinato can actually be quite versatile. Their tonal simplicity can clarify a polytonal texture. They build rhythmic momentum and can be melodically obstinate, obtrusive, serve as a ground bass or accompaniment, or when a couple are used at the same time, can create harmonic tension.

A good example of one (occurs throughout entire piece):





One from the first movement of _Excursions_ by Samuel Barber, in the left hand of the piano:





Finally, we return to the masterpiece, _Symphony of Psalms_ by Igor Stravinsky where the first movement is full of ostinatos. Not just at the obvious 0:18 but throughout the entire movement they are used rather brilliantly.





Does anyone have any more examples of ostinatos to share?


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## tdc (Jan 17, 2011)

Torkelburger said:


> Ostinato
> An ostinato is a well-defined melodic fragment repeated over and over again. It usually has a simultaneously repeating rhythm and repeating group of pitches. The ostinato can actually be quite versatile. Their tonal simplicity can clarify a polytonal texture. They build rhythmic momentum and can be melodically obstinate, obtrusive, serve as a ground bass or accompaniment, or when a couple are used at the same time, can create harmonic tension.
> 
> Does anyone have any more examples of ostinatos to share?


Some good examples there, thank you. I would assume ostinatos would be used heavily in minimalism? How about Reich's _Music for 18 Musicians_?


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## Torkelburger (Jan 14, 2014)

Yes, of course! Good catch! I had overlooked that. And the Reich piece is one of my favorite minimalist pieces. Really good example of ostinatos.


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## Woodduck (Mar 17, 2014)

Ostinato wasn't a modern invention, of course. Monteverdi and other Baroque composers used repeated figuration as a "ground" beneath a piece's melody lines, Beethoven used it a number of times in his symphonies (notably in #6 and #7, to create a sense of relaxed expansiveness in the former and gathering tension in the latter), and Sibelius reveled in it, often to hypnotic effect.


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## Tikoo Tuba (Oct 15, 2018)

There are the pivot points , at which the music must absolutely change direction or end . Re: a whallop and whang bang in conclusion will not do .


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## Torkelburger (Jan 14, 2014)

Mirror writing is an important technique used in modern times. Mirror writing is basically contrary motion in two voices, except the intervals in which they mirror one another are usually exact (when one voice goes up a whole step, the other voice goes down exactly a whole step and so on). The rhythms of the two voices are concerted (usually the same) and can sometimes be in imitation.

Two examples from Bartok's _Mikrokosmos_:









Another example from Bartok's _Concerto for Orchestra_ bars 7-9, 11 (except for the g); again in bars 17-19.






In the first movement of Samuel Jones' _Symphony No. 3_, the main Canyon Theme in the brass from 2:07 through 2:55 is written using mirror technique. It is to musically depict the outward rising of canyon walls from the ground. It starts with just three notes in mirror and builds to a much longer phrase.






Mirror technique is not limited to melodic writing but can also be utilized harmonically. An example of a mirror chord would be D (as the pivotal note), then up to the Eb, F, and Bb, say all in the horns. Then (using the D as the pivotal note), down to C#, B, and F#, say in the trombones. When all played together as a single chord, you have a mirror chord.

The following piece utilizes mirror chords in the tuttis and is apart of the composer's signature sound.


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## millionrainbows (Jun 23, 2012)

When ostinato was mentioned, I thought of Webern's Passacaglia Op. 1, which is a similar idea, but refers more to root movement than a melodic figuration. I love to listen to his variations on this, and once you have memorized the pattern, it is even more fun to listen to.


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## millionrainbows (Jun 23, 2012)

Torkelburger said:


> Secundal Harmony and Clusters
> 
> Chords built on the interval of the second is called secundal harmony. A secundal chord may have open spacing in the voicing and defined inner voice movement between chords. An example of a secundal chord would be B,C, (up a fifth to the…) G,A.


It's worth noting that the Bulgarian Women's Choir's distinctive harmonic quality uses secundal harmony, and is called "diaphonic singing." 
See Wik: https://en.wikipedia.org/wiki/Parallel_harmony






I think "parallel harmony" is a concept worth pondering, because Western "tertial" harmony is all thirds, but minor and major. Quartal harmony would yield fifths as well as fourths, by inversion. Debussy moved triads in parallel, which on the surface was recognizable because they're triads, but moved in parallel "without function" in the normal harmonic (diatonic) sense.

What's left after thirds, seconds, and fifths (fourths)? Just the minor second and the tritone. 
When you think of intervals in terms of inversions, there are only six: m2, M2, m3, M3, 4th, and tritone. The fourth, inverted, is a fifth, so it's not included, just as sixths and sevenths are not, because they are inversions, and redundant. The tritone, when inverted, becomes itself again, so it's really not subject to inversion in the same sense.


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## Torkelburger (Jan 14, 2014)

> I think "parallel harmony" is a concept worth pondering, because Western "tertial" harmony is all thirds, but minor and major. Quartal harmony would yield fifths as well as fourths, by inversion. Debussy moved triads in parallel, which on the surface was recognizable because they're triads, but moved in parallel "without function" in the normal harmonic (diatonic) sense.


Yes! Thanks for mentioning that! I like that technique as well. Another example of moving triads in parallel without function is from Holst's _The Planets_ starting with the "B theme" at 1:28


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## Torkelburger (Jan 14, 2014)

Microtonal technique is when the composer is asking for the chromatic scale to be divided into smaller steps than half steps, sometimes called quarter-tones. This type of technique is still very popular today.

The first example is from Bela Bartok's _Violin Concerto No. 2_. The example is at 12:04 here:






The second example is from Penderecki's _St. Luke Passion_. The notation for the quarter-tones is explained at the 0:02 mark. The microtonal passages start at 12:28.


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## Torkelburger (Jan 14, 2014)

This post about 12-tone technique is very brief. I don't believe there is any need to explain it or even post a link to an explanation. Most people here probably know what it is. I will, however, post a very nice and accessible, easy to digest, 12-tone piece as an example of it.

The piece is brief, only a few minutes long, and is for one instrument only, a solo cello. It is by Ernst Krenek. It is very easy to listen to, occurring only one note at a time (except for a few double stops). I think Krenek does a good job getting melodic material out of the row, especially in the second movement. I hope you take the time to give it a really good listen.


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## Phil loves classical (Feb 8, 2017)

Bumping this thread up, which I think is the best thread on modern music.

The Canon form was utilized for both chromaticism and atonalism.


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## Manxfeeder (Oct 19, 2010)

Is the pitch continuum still a thing? My old theory teacher talked about Varese's use of sirens as an exploration of the pitch continuum. Also, do Gloria Coates' glissandi relate to the pitch continuum concept also?


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## Guest (Jan 15, 2019)

Manxfeeder said:


> Is the pitch continuum still a thing? My old theory teacher talked about Varese's use of sirens as an exploration of the pitch continuum. Also, do Gloria Coates' glissandi relate to the pitch continuum concept also?


I'd be interested in an answer to this question too...........

In the meantime, something that I'm interested in is not so based on harmony and pitch, but form.

Moment form, specifically, was something that was first discussed by Stockhausen in the late 50s with regard to his composition _Kontakte_. Characteristics of this form is the avoidance of creating clear beginnings and endings to the composition, phrase by phrase-or more accurately, moment by moment-there is a strong sense of being in the _present_. The composition process tends to avoid an overall goal or climactic point followed by a resolution. Stockhausen wrote:



Stockhausen said:


> ...these forms are immediately intense and seek to maintain the level of continued "main points", which are constantly equally present, right up until they stop. In these forms a minimum or a maximum may be expected in every moment, and no developmental direction can be predicted with certainty from the present one; they have always already commenced, and could continue forever; in them either everything present counts, or nothing at all; and each and every Now is not unremittingly regarded as the mere consequence of the one which preceded it and as the upbeat to the coming one-in which one puts one's hope-but rather as something personal, independent and centred, capable of existing on its own. They are forms in which an instant does not have to be just a bit of a temporal line, nor a moment just a particle of a measured duration, but rather in which concentration on the Now-on every Now-makes vertical slices, as it were, that cut through a horizontal temporal conception to a timelessness I call eternity: an eternity that does not begin at the end of time but is attainable in every moment. I am speaking of musical forms in which apparently nothing less is being attempted than to explode (even to overthrow) the temporal concept-or, put more accurately: the concept of duration. . . .
> In works of this kind the start and stop are open and yet they cease after a certain duration.


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## Woodduck (Mar 17, 2014)

shirime said:


> I'd be interested in an answer to this question too...........
> 
> In the meantime, something that I'm interested in is not so based on harmony and pitch, but form.
> 
> Moment form, specifically, was something that was first discussed by Stockhausen in the late 50s with regard to his composition _Kontakte_. Characteristics of this form is the avoidance of creating clear beginnings and endings to the composition, phrase by phrase-or more accurately, moment by moment-there is a strong sense of being in the _present_. The composition process tends to avoid an overall goal or climactic point followed by a resolution. Stockhausen wrote:


Could you post some examples of this?


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## Guest (Jan 15, 2019)

Woodduck said:


> Could you post some examples of this?


Sure, to get a good sense of it one would probably be best to listen all the way through to some of his pieces (which are admittedly rather long in some cases). I really love _Freude_ from _Klang_:






Here's _Kontakte_, which to me sounds like much more deliberate act of Stockhausen personally rebelling against linear forms:


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## Manxfeeder (Oct 19, 2010)

shirime said:


> In the meantime, something that I'm interested in is not so based on harmony and pitch, but form.
> 
> Moment form . . .


Reading the Stockhausen quote, I think you explained it better in two words.


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## Torkelburger (Jan 14, 2014)

Pandiatonicism is writing freely, but diatonically, in a given key, but avoiding any "conventional" chords, melodies, and counterpoint. In the key of D Major, for example, instead of writing a triad of D-F#-A, you might write D-E-G. And instead of a melody ending in the cadential tones of B-C#-D, you might write something more angular and unorthodox like C#-G-D. And instead of parallel thirds or sixths, you might write parallel sevenths or seconds, or even clusters. You are free to do anything you wish, as long as it is diatonic.

The second movement (Epilogue 1) at 3:00 utilizes pandiatonic writing. The first part adds two accidentals to the "key" (f natural and c#), while the second part at 3:54 starting at the ¾ bar just uses the key signature alone.






Stravinsky's Sonata for Two Pianos has pandiatonic passages throughout the first two movements.






Other examples:


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## millionrainbows (Jun 23, 2012)

Here's an interesting idea: complimentary scales. The C Major scale is a 7-note scale, so the "left-over" black notes are its "compliment". Together, they make all 12 notes.

Note that any 7-note scale will have a 5-note compliment scale.

In the case of C major, the five notes left over are the most _harmonically distant_ from C major. If you really want to create a clash, play F# major pentatonic over a C major chord or harmony. You could also consider the complimentary scale to be a D# _minor_ pentatonic as well.


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## Bwv 1080 (Dec 31, 2018)

The first movement of Brian Ferneyhough's guitar piece Kurze Shatten II is an example of what he calls 'interference form'. If you look at the score there are three staves (unusual for guitar music which usually has a single staff). The first two staves are long held notes and harmonics with the action in the bottom stave. There are 4 different types of material in this stave - the snap pizzicato passages, the chordal pieces, the irregular rhythmic passages market expressivo or similarly, etc. BF then juxtaposes this material together so that instead of four separate sections, there are multiple gestures consisting of a composite of multiple types of material


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## Tikoo Tuba (Oct 15, 2018)

There are several ways to make 1-11 chromatic smash more digestible . It need not be rude .


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## Torkelburger (Jan 14, 2014)

millionrainbows said:


> Here's an interesting idea: complimentary scales. The C Major scale is a 7-note scale, so the "left-over" black notes are its "compliment". Together, they make all 12 notes.
> 
> Note that any 7-note scale will have a 5-note compliment scale.
> 
> In the case of C major, the five notes left over are the most _harmonically distant_ from C major. If you really want to create a clash, play F# major pentatonic over a C major chord or harmony. You could also consider the complimentary scale to be a D# _minor_ pentatonic as well.


Yes, I think the piano especially lends itself to composing with complimentary scales, as you can have one hand play white keys while the other hand plays black keys. I think Milhaud wrote a piece doing that? Ligeti exploited something similar in _Atmospheres_ where he sounded all 12 notes of the chromatic scale as a long-held chord, then it morphed into a long-held chord of all "white" notes, then that morphed into a long-held chord of all "black" notes, etc.


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## BrahmsWasAGreatMelodist (Jan 13, 2019)

Torkelburger said:


> Yes, I think the piano especially lends itself to composing with complimentary scales, as you can have one hand play white keys while the other hand plays black keys. I think Milhaud wrote a piece doing that? Ligeti exploited something similar in _Atmospheres_ where he sounded all 12 notes of the chromatic scale as a long-held chord, then it morphed into a long-held chord of all "white" notes, then that morphed into a long-held chord of all "black" notes, etc.


There's no b natural explicitly played in the left hand, but Bartok sorta does this at the beginning of this piece:


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## flamencosketches (Jan 4, 2019)

I'm no theorist but I am interested in Arvo Pärt's minimal composition technique of tintinabuli which is inspired by the sounds of bells from what I understand. It basically involves one voice playing the notes of a triad (for example A minor, A, C, and E) and the other playing the notes of a corresponding scale (the A minor scale, A, B, C, D, E, F, G) to create unusual harmonies. It naturally results in very minimal composition, but it can have beautiful results. The composer himself goes into it to an extent here:






and this canon is a good example of it in an orchestral setting:






another piano piece:


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## BabyGiraffe (Feb 24, 2017)

Manxfeeder said:


> Is the pitch continuum still a thing? My old theory teacher talked about Varese's use of sirens as an exploration of the pitch continuum. Also, do Gloria Coates' glissandi relate to the pitch continuum concept also?


There is no accessible pitch continuum on the piano or fretted string instruments...

Music theory is not really based on continuous functions (this is one of the reasons why electronic music sucks - the real theory of rhythm and tempo is way more complex than what is implemented in the drum machines/software).

One of the first posts was about quartal/quintal sonorities, but they are hardly anything modern and predate major and minor chords (see Medieval music: http://www.medieval.org/emfaq/harmony/pyth.html http://www.medieval.org/emfaq/harmony/13c.html I guess Greek and Romans were maybe using them too to sing in harmony, because of the way of construction of many of their scales)... alot of Eastern Asian music also features them.

This forum thread will probably be better suited for the music theory subforum (which is less crowded and won't be "lost" as easily).


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## Bwv 1080 (Dec 31, 2018)

BabyGiraffe said:


> There is no accessible pitch continuum on the piano or fretted string instruments...
> 
> Music theory is not really based on continuous functions (this is one of the reasons why electronic music sucks - the real theory of rhythm and tempo is way more complex than what is implemented in the drum machines/software).


? What continuous functions are applicable to music theory (as opposed to acoustics)?


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## Torkelburger (Jan 14, 2014)

> This forum thread will probably be better suited for the music theory subforum (which is less crowded and won't be "lost" as easily).


I understand what you mean. It's just I had originally posted this in the main Classical Music Forum with the hopes that it would be a modern music appreciation type thread with posts of contributors displaying some of their favorite modern music examples, with the added bonus of it explaining a modern musical technique. And because this was where other threads about modern music discussions were posted. So while it would have some theory, it wasn't completely designed for theoretical purposes (the theory was just one aspect of it).

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Here are some pieces that I think many will enjoy. They illustrate the technique of Added-Note Harmony, which is taking a structure, such as a triad or quartal chord, and adding a note to it that is one note either up or down from one of the chord tones. This added note can appear either in close voicing to the actual chord, or as a bass note. An example would be taking the triad G-B-D and adding one of the following notes that are one step away from a chord tone: E/Eb, C/C#, Bb/A/Ab, F/F#.

The first piece is Eric Whitacre's _Sleep_ which uses Added-Note Chords as its signature sound throughout. It takes a triad and adds the half step above the third (i.e. C-G-E-F).






Aaron Copland's _Sonata for Violin_ also uses both the close voicing added note chord (scored for both the violin with the piano) and also where the added note is in the bass with a triad on top (as in the beginning with the piano solo). Interestingly, many of the chords are similar to the Whitacre chord, but just voiced with the chord in the bass (i.e. C-E-G in the treble, F in bass).






The last example comes from Charles Ives' 4th Violin Sonata first movement which uses Added-Note Chords as its signature sound throughout. But as you'll see, the effect is quite different than the previous two pieces. It has the most variety of all the examples. (F-A-C-D; Bb-D-F-E, etc.).


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## Tikoo Tuba (Oct 15, 2018)

I would like to hear an acoustic instrument that would produce our chromatic interval as a unified set of micro-tones . Hmm ... I suppose many of my piano keys could present sets of 6-tone . I imagine 16 tones would be more pleasant .


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## BabyGiraffe (Feb 24, 2017)

Tikoo Tuba said:


> I would like to hear an acoustic instrument that would produce our chromatic interval as a unified set of micro-tones . Hmm ... I suppose many of my piano keys could present sets of 6-tone . I imagine 16 tones would be more pleasant .


Our chromatic system is great not only because it's good for transposing the diatonic scale, but also because of the efficiency of scale size (easier to build, learn and play without pressing the wrong keys) and how well it represents intervals found between the partials of the overtone series of the idealised vibrating string... Dividing the tones has nothing to do with the efficiency of the whole gamut or having accuracy for the harmonics. If you are interested in equal tunings, the best after 12 are 19 and 31 steps per octave (you generally don't want anything bigger than 31, despite how harmonically accurate it is, because there is often a cluster of very small intervals and many common progressions or harmonies don't even exist without modulating through enharmonic steps that are tempered in 12, 19 or 31. This is a nightmare not only for composing, but also for performing). For non equal tunings (similar to these used by Bach for the well tempered clavier) or a pattern (generated scale) from a much bigger system with variety of well-tuned intervals, I wouldn't suggest more than 17 or 19 steps.

Schoenberg mentioned in one of his music theory books that in the future we may move to unequal or bigger system... While it was not practical in his time, now we can do it with the electronic software or harware, plus it's not that hard to modify a cheap midi keyboard by replacing white and black keys.


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## BrahmsWasAGreatMelodist (Jan 13, 2019)

Yeah, I'm surprised no one has talked about microtones and alternative temperaments. There was a group of Germans in the 20th century who were convinced about the superiority of 19-TET, haha. Anyway, Wendy Carlos also used some weird scales:

https://en.wikipedia.org/wiki/Alpha_scale

Although most tuning systems preserve the octave, this one doesn't, which creates a very interesting dynamic for the composer to explore.

Re the "best" temperament: There really is none (just as with anything else in music), although if you are looking for consonance, 12, 19, 24 (quarter tones), and 31 are probably most useful as BabyGiraffe stated. Although the biggest issue with composing for alternate tuning systems is of course performability, I'm still surprised more composers haven't explored them.


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## Tikoo Tuba (Oct 15, 2018)

BabyGiraffe said:


> Our chromatic system is great ...


That's all fine . I am rather imagining a utterly undivided spectrum unit (such as octave) divided into 7 tonal clusters . And I hope the instrument that may produce this sound is not electronic ; perhaps a wind instrument .


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## Torkelburger (Jan 14, 2014)

BrahmsWasAGreatMelodist, microtonal technique was posted about in post #23.

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Indeterminacy technique can be read about here:

https://en.wikipedia.org/wiki/Indeterminacy_(music)

"Indeterminate or chance music can be divided into three groups: (1) the use of random procedures to produce a determinate, fixed score, (2) mobile form, and (3) indeterminate notation, including graphic notation and texts."

A good example of this is John Cage's Concert for Piano and Orchestra which can be read about here:

https://johncage.org/pp/John-Cage-Work-Detail.cfm?work_ID=48


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## BrahmsWasAGreatMelodist (Jan 13, 2019)

Sorry, I must've skipped over it. Thanks and good examples, but to be fair your post did focus solely on quarter tones. Also, indeterminacy was around long before the 20th century:

http://sunsite.univie.ac.at/Mozart/dice/#about

(only half joking)


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## tortkis (Jul 13, 2013)

To play microtones on piano, either piano is tuned in non-12ET tuning (12 tones per octave) like Young, Riley, Michael Harrison, or multiple pianos are tuned quarter/sixth/etc. tone apart (over 12 tones per octave) like Wyschnegradsky, Haas. Are there contemporary compositions for enharmonic keyboard like Vicentino's archicembalo (e.g. C-sharp and D-flat are assigned to different keys)?

There is an interesting recording of Ives' Concord Sonata by Gabriel Zucker and Erica Dohi, played on two pianos tuned differently to comprise extended Pythagorian scale.
piano 1: C C# D D# E F F# G G# A A# B
piano 2: B# Db Cx Eb Fb E# Gb Fx Ab Gx Bb Cb
Ives composed a quarter tone piece for 2 pianos (Three Quarter-Tone Pieces), but I didn't know that Ives might have intended microtones for Concord Sonata. He insisted to keep the notation of enharmonic notes in the score. (for example, C# should not be replaced with Db.)
https://johnnyreinhard.bandcamp.com...r-erica-dohi-pianists-in-extended-pythagorean









Kyle Gann's massive keyboard work Hyperchromatica uses 3 Disklaviers tuned in the 13-limit just intonation. 33 pitches per octave are assigned to 12 keys per octave x 3 pianos (there are duplications.) Weird and melodic, worth repeated listening.
https://www.kylegann.com/Hyperchromatica.html


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## SuperTonic (Jun 3, 2010)

BrahmsWasAGreatMelodist said:


> Yeah, I'm surprised no one has talked about microtones and alternative temperaments. There was a group of Germans in the 20th century who were convinced about the superiority of 19-TET, haha. Anyway, Wendy Carlos also used some weird scales:
> 
> https://en.wikipedia.org/wiki/Alpha_scale


Does anyone know which of Carlos' pieces use the alpha scale? I'm curious to hear what it is like in use.


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## BabyGiraffe (Feb 24, 2017)

SuperTonic said:


> Does anyone know which of Carlos' pieces use the alpha scale? I'm curious to hear what it is like in use.


"Beauty In The Beast"


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