The title of this post is incorrect. It should be "My New Composition Methods and Tuning Methods".I want professionals and/or experts to thoroughly test and scrutinise my new composition methods and tuning methods.
Twelve-Tone Matrices: Most Consonant and Most Dissonant
The specific purpose of the experiment below is to test the limits of dodecaphony in terms of consonance and dissonance.
Most Consonant Twelve-Tone Matrix
1. Start with any note on the circle of fifths and include it on a tone row.2. Proceed in a clockwise or anticlockwise direction around the circle of fifths.3. Add each consecutive note on the tone row until all twelve tones have been included without being repeated.For example, if C was chosen in step 1, the original tone row would be as follows by proceeding clockwise around the circle of fifths:C G D A E B F# C# Ab Eb Bb F
7 7 7 7 7 7 7 7 7 7 7 (Number of half-steps needed to get to next note)
4. Create a matrix by calculating all prime, inversion, retrograde and retrograde inversion forms of the original tone row.Visit this website to create a matrix automatically: https://www.musictheory.net/calculators/matrix5. Conform to the two fundamental rules of twelve-tone technique:• Pitch classes should be played in order.• Once a pitch class has been played, it should not be repeated until the next tone row is played.The most consonant symmetrical 12-note chord (Symmetrical pure 12-tone quintal chord) can be produced by superimposing 11 perfect fifths.
Most Dissonant Twelve-Tone Matrix
1. Start with any note on the chromatic scale and include it on a tone row.2. Proceed upwards above or downwards below the note chosen in step 1.3. Add each consecutive note that is separated by a semitone to the tone row until all twelve tones have been included without being repeated.For example, if C was chosen in step 1, the original tone row would be as follows by proceeding upwards above C:C C# D D# E F F# G G# A A# B
1 1 1 1 1 1 1 1 1 1 1
4. Create a matrix by calculating all prime, inversion, retrograde and retrograde inversion forms of the original tone row.Visit this website to create a matrix automatically: https://www.musictheory.net/calculators/matrix5. Conform to the two fundamental rules of twelve-tone technique:• Pitch classes should be played in order.• Once a pitch class has been played, it should not be repeated until the next tone row is played.The most dissonant symmetrical 12-note chord (Symmetrical pure 12-tone secundal chord/Prototypical 12-tone cluster) can be produced by superimposing 11 semitones.
12-Tone Chords: Combining Consonance and Dissonance
My Theories and Methods
A sound that is consonant is not dissonant and a sound that is dissonant is not consonant. This creates a dichotomy between consonance and dissonance. The only way to solve this dichotomy is by combining both. Symmetrical 12-note chords with minimum tension are simultaneously consonant and dissonant so they solve the dichotomy between consonance and dissonance. All symmetrical 12-note chords can be considered static because each of their notes is equidistant with respect to another, relative to their midpoint, which means all the consonances and dissonances that are present within them have been frozen. This is because the harmony of all symmetrical 12-note chords will gravitate towards their midpoint which means their midpoint can be considered their centre of musical gravity. This means they can be considered stable.It is possible to create atonal polyphonic compositions based solely on 12-note chords because all 12 tones of each of these chords can be considered simultaneous lines of independent melody. It is possible to use the tone rows of multiple 12-tone matrices. Examples: roshankakiya123's 12-Note Chord Composition 1 and roshankakiya123's 12-Note Chord Composition 2 below.Furthermore, two different 12-tone matrices can be superimposed by playing the same 12-note chord (first matrix) 12 times in the order of all 12 parallel tone rows of a different 12-tone matrix (second matrix) [Treat each note of the initial 12-note chord as the starting point of each parallel tone row in the second matrix]. This is valid because all 12 parallel tone rows within the second matrix can be played separately and simultaneously in the same direction (upwards, downwards, rightwards or leftwards). This will cause all 12 tones to be played only once within, and in the correct order of, each parallel tone row in the second matrix. Compositions based on this method will be completely atonal because all 12 pitch classes will be played in order and none of the 12 pitch classes will be repeated within any tone row (both of these fundamental rules of 12-tone technique will be strictly followed within the first and the second matrix by using this method). Example: roshankakiya123's 12-Note Chord Composition 3 below. Moreover, the same 12-note chord can also be played 12 times in the order of its own notes. This is valid because all 12 pitch classes can be played in order and only once within each tone row. This is also valid because overlapping tone rows (Prime with Retrograde Inversion, Inversion with Retrograde, Retrograde with Inversion and Retrograde Inversion with Prime) can be merged to form a single aggregate if symmetrical 12-note chords are used. Examples: roshankakiya123's 12-Note Chord Composition 4, roshankakiya123's 12-Note Chord Composition 5 and roshankakiya123's 12-Note Chord Composition 6 below.Interestingly, it is impossible to break the fundamental rules of 12-tone technique within the matrix that is produced by a 12-note chord if only 12-note chords are used within a composition. This is because all 12 pitch classes will be played in the correct order of any tone row and none of the 12 pitch classes will be repeated within any tone row within the matrix that is produced by a 12-note chord [Treat each 12-note chord as the original tone row of a 12-tone matrix].Ideally, the chords and compositions below should be played on instruments using the 12-tone equal temperament tuning system. This is a completely symmetrical form of tuning so it is mathematically perfect for symmetrical 12-note chords. All my theories will fall apart if well temperament and just intonation are used because they are not completely symmetrical. Tuning systems that are not completely symmetrical will destroy the symmetry of symmetrical 12-note chords. However, experimenting with different tuning systems is desirable. The results of these experiments are more important than my theories.All my methods above unlock new ways of composing atonal music. It is important to note that I have tried to rigorously adhere to the fundamental rules of 12-tone technique throughout this post and construct compositions based solely on symmetrical 12-note chords with minimum tension, with the exception of roshankakiya123's 12-Note Chord 4 which is one of the most tense symmetrical 12-note chords. However, this is only one way of composing. There are numerous possibilities waiting to be discovered with regard to 12-note chords. Therefore, it is now time to start a new musical trend in the 21st century: composing music based solely on 12-note chords.My Symmetrical 12-Tone Chords
I have superimposed major thirds, minor thirds and perfect fifths to create a 12-note chord. I will call this chord "roshankakiya123's 12-Note Chord 1" (Symmetrical 12-tone tertian and quintal chord):
C G D F# A C# E Ab B Eb Bb F
7 7 4 3 4 3 4 3 4 7 7 (Number of half-steps needed to get to next note)
https://onlinesequencer.net/695480 I have also superimposed major and minor thirds to create another 12-note chord. I will call this chord "roshankakiya123's 12-Note Chord 2" (Symmetrical pure 12-tone tertian chord):
C E Ab B Eb G Bb D F# A C# F
4 4 3 4 4 3 4 4 3 4 4
https://onlinesequencer.net/695482 I have also superimposed major and minor thirds again to create another 12-note chord. I will call this chord "roshankakiya123's 12-Note Chord 3" (Symmetrical pure 12-tone tertian chord):
C Eb F# A C# E G Bb D F Ab B
3 3 3 4 3 3 3 4 3 3 3
https://onlinesequencer.net/718849 I have also superimposed two whole tone scales to create another 12-note chord. I will call this chord "roshankakiya123's 12-Note Chord 4" (Symmetrical pure 12-tone secundal chord) [I have broken my own rules by creating this chord because it is one of the most tense symmetrical 12-note chords. The most tense symmetrical 12-note chord is the prototypical 12-tone cluster which contains 11 semitones]:
C D E F# Ab Bb B C# Eb F G A
2 2 2 2 2 1 2 2 2 2 2
https://onlinesequencer.net/740733 I have also extended Scriabin's Mystic Chord to create two more 12-note chords. I will call the first chord "roshankakiya123's Extended Mystic Chord Arrangement 1" (Symmetrical 12-tone tertian and quartal chord) and the second chord "roshankakiya123's Extended Mystic Chord Arrangement 2" (Symmetrical pure 12-tone quartal chord):
Arrangement 1: C Eb F# Bb E A D G C# F Ab B
3 3 4 6 5 5 5 6 4 3 3
https://onlinesequencer.net/702362 Arrangement 2: Ab C F# Bb E A D G C# F B Eb
4 6 4 6 5 5 5 6 4 6 4
https://onlinesequencer.net/702363 Method and Rationale: 1. Start with Scriabin's Mystic Chord: C F# Bb E A D
6 4 6 5 5
2. Calculate the mirror image of the half-steps: the mirror image of 6 4 6 5 is 5 6 4 6
3. Assemble a 10-note chord by using the mirror image of the half-steps: C F# Bb E A D G C# F B
6 4 6 5 5 5 6 4 6
4. Add the remaining notes Ab and Eb to the chord.
Arrangement 1: I have placed the Eb between C and F# and the Ab between F and B. This is
because the Eb and the Ab cannot be placed anywhere else within the first and last note of the
10-note chord above without creating a chord that contains major and/or minor seconds.
Arrangement 2: I have placed the Ab to the left of C and the Eb to the right of B. This
arrangement ensures Scriabin's quartal harmony is maintained because it only contains
diminished fourths (such as B-Eb), perfect fourths (such as A-D) and augmented fourths (such
as C-F#) and no other intervals between each adjacent note.
Finally, I have superimposed the Tristan Chord and the Mystic Chord to create another 12-note chord. I will call this chord "roshankakiya123's Tristan-Mystic Chord" (Symmetrical pure 12-tone quartal chord):
D G C# F B Eb Ab C F# Bb E A
5 6 4 6 4 5 4 6 4 6 5
https://onlinesequencer.net/798603
My 12-Note Chord CompositionsHere are two of my atonal polyphonic compositions based on roshankakiya123's 12-Note Chord 1 (C G D F# A C# E Ab B Eb Bb F), roshankakiya123's 12-Note Chord 2 (C E Ab B Eb G Bb D F# A C# F) and roshankakiya123's Extended Mystic Chord Arrangement 1 (C Eb F# Bb E A D G C# F Ab B). By doing this, I have used tone rows from three different 12-tone matrices:
roshankakiya123's 12-Note Chord Composition 1:
https://onlinesequencer.net/697399 roshankakiya123's 12-Note Chord Composition 2:
https://onlinesequencer.net/697400 Here is my atonal polyphonic composition that contains two superimposed 12-tone matrices. I have played roshankakiya123's 12-Note Chord 1 (C G D F# A C# E Ab B Eb Bb F) 12 times in the order of the notes of roshankakiya123's Extended Mystic Chord Arrangement 2 (Ab C F# Bb E A D G C# F B Eb) from left to right. By doing this, I have superimposed the 12-tone matrices that both of these 12-note chords produce:
roshankakiya123's 12-Note Chord Composition 3:
https://onlinesequencer.net/702367 Here are three of my atonal polyphonic compositions that have been constructed by playing the same 12-note chord in the order of its own notes from left to right. By doing this, I have merged each of the 12 parallel prime rows with its overlapping retrograde inversion row which has led to the creation of 12 aggregates. roshankakiya123's 12-Note Chord Composition 4 is based on roshankakiya123's 12-Note Chord 2 (C E Ab B Eb G Bb D F# A C# F), roshankakiya123's 12-Note Chord Composition 5 is based on roshankakiya123's 12-Note Chord 3 (C Eb F# A C# E G Bb D F Ab B) and roshankakiya123's 12-Note Chord Composition 6 is based on roshankakiya123's 12-Note Chord 4 (C D E F# Ab Bb B C# Eb F G A):
roshankakiya123's 12-Note Chord Composition 4:
https://onlinesequencer.net/702082 roshankakiya123's 12-Note Chord Composition 5:
https://onlinesequencer.net/718871 roshankakiya123's 12-Note Chord Composition 6:
https://onlinesequencer.net/740731Conclusion I think it is possible to emancipate 12-tone technique by creating compositions that are solely based on 12-tone chords. I think it is possible to do this because the rules of 12-tone technique can be enshrined in 12-tone chords which means it is impossible to break them if compositions are solely based on 12-tone chords.