Techniques of Polytempic Polymicrotonal Composition

 More about Meter Poetic Meter , for me, is essentially music. Song. The art of songwriting . Although different, the art of poetic meter has a built-in logic that suits musical construction. Most of the time, songwriters, or composers of Lieder , or Art Songs , simply use the rhythms of the composition itself. Or the words of the poem may dictate the rhythms to the composer in a type of durch-komponiert style of writing, like Wagner or Schubert have done. As a matter of fact, prosody is a poetic analysis, much akin to musical analysis. Yet, there is a compositional system dormant and employable in this analytical system. Much like atonal analysis using set theory , or intervallic cell analysis , these types of techniques can also lend themselves to creation by working backwards. I have frequently composed music backwards, or even started in the middle of a piece.  Figure 1. As said earlier in this blog, poetic forms themselves are just as numerous and organic as musical...

  Compression of Harmon y in Polymicrotonality One technique regarding the gradual compression of micro-intervallic structures in the microchromatic line is shown below, in Figure 3, from my String Quartet 12 , Big Bad Mother Fucker From Outer Space, 2019.  Figure 1. Tuning Legend from String Quartet #12 String Quartet 12 is explicitly polymicrotonal , with microtonal systems in full, except for the last one. We start with 20tet at 60 cents, 22tet at 54.5 cents, quartertones at 50 cents, and lastly, 18 of the 26tet gamut , at 46.15 cents. Since a starting pitch needs to be chosen for further divisions of the octave of a pitch class set , and inclusive of all other pitch classes within that octave, and for all microtonal systems within the given octaves of each system, I chose C as "1/1" as indicating the "untouched," pure beginning pitch. In this case, the pitch C is from 12tet and is 261.6 Hz. Any pitch class can be used, including a starting pitch up the over...

  What is JND? Just Noticeable Difference , which has nothing to do with just intonation , btw, is a psychoacoustic metric associated with the smallest interval detectable by the human ear . There is no point in making microtonal scales that can not be heard at their smallest division. Or is it?  The Greek schisma is a 2-cent interval created by subtracting the Syntonic Comma at 22 cents from the Pythagorean Comma , at 24 cents ( Ditonic Comma ). Ben Johnston used this 2-cent interval in his music. To truly hear a 2-cent interval, one would have to count the beats in between this narrow structure. I believe it was Marin Mersenne who discovered counting beats for intervals back in the 1600s, and this technique was discussed in Ellis-Helmholtz . Nevertheless, if Johnston used the schisma, then what stops the rest of us from using the cent itself?  Ellis-Helmholtz suggested the ten-cent threshold, while David Whaley , in his 1975 dissertation on the  microtonal ca...

Examples of Polytempic Polymicrotonal Music are found in my archive . Please explore my Internet Archive.  So, rather than take snapshots of sections out of context and paste them in each blog, I thought that the interested reader would rather look through my work to see how I have used Polytempic Polymicrotonality , polymeter , and polyrhythms and microtones in general.  List of Works in Score Thoegersen freely distributes his scores via the   Internet Archive . Scores for all the works below are available there. Dates indicate composition. Drumset 3:4:5:7, for Solo drumset #1 1995 Solo for Drumset #2 2022 Solo for Drumset #3 2022 Solo for Drumset #4 2022 Solo for Drumset #5 2022 Solo for Drumset VI 2022 STSOMA Drumsolo #7 2022 solo for drumset #8 2022 Solo for Drumset #9 2022 Solo for Drumset X: polymixtures 2022 Drumset solo #11 2022 Vocals and other instruments Always Sleeping 2006 Facebook Song Cycle: What's on your mind, 2017 Solo works Dreams Like Little Movies,...

  What is a Whole Tone, and Why Divide It? Anaximander Anaximander believed in a concept called " unity ," wherein infinite divisions were possible, and apparently, this philosophy included divisions of musical intervals, such as the tone. Aristoxenus was also an advocate of this philosophical standpoint. "All and innumerable worlds are infinite in possible harmonies."  Conventional wisdom states that a whole tone is composed of two semitones that range from ratios 11:10, at 165 cents, all the way through 8:7, at 234 cents. Generally, the ratio 9/8 is the most accepted version at 204 cents. If we are not speaking about rational tunings or string lengths from the monochord , then we are referring to 12tet, where the whole tone is simply 200 cents.  Although I went through a bit of the history of tuning in my thesis, Polytempic Polymicrotonal Music: the road less traveled, 2012, I just want to discuss my personal thoughts on pitch.  I am not a tuning/temperament ...

  The Idea of Fuxian Counterpoint of Tempos In looking over what music I have composed over the years, I have noticed a desire to independently vary the tempi of all constituent parts, not unlike Nancarrow did in his Tempo Canons .  I think that the amount of freedom Nancarrow had in making huge punch-rolls for the player piano , gave him a sense of total control over his materials. Although it must have been enormously painstaking, I am sure that after mastering his approach to this, he had way more freedom to calculate tempic relations to which even our modern-day sequencers and notation programs can not even compare. Not being a computer language programmer, I have to hassle with Finale or Dorico , down to the minutest detail, just to get a bit of cooperation from these programs to compose polytempic music , only to then obtain a halfway decent playback.  Elliott Carter also had huge pre-compositional notes and scores pasted on his walls for the calculation of large...

  A Quasi Syllabus for this Blog Blog Ideas Contrapuntal Tempos, or a Counterpoint of Tempos  Divisions of the Whole Note  Divisions of the Whole Tone  Contour Creation/ Analysis of Polymicrotonal Lines Myriad New Intervallic Structures Harmony Resulting from Vertical "Cadence" Points- vertical structures Intervallic Compression of Polymicrotonal Systems Centricity Simultaneities Panmicrotonal Harmony: tonal vs atonal, or tonal sublation What is a Polymicrotonal Chord? Counterpoint of Microtonal Systems Pitch Organization   Pitch Cells vs Gamut Tetrachords Serial Techniques?  "Just Noticeable Difference" and Microtonal Hearing Composer Intent Nancarrow-Ives-Cowell-Marie-Xenakis Alternate Staves? Fatter spaces and lines for microtones?  Human Performance Strategies Manifold Electronic Realizations In many regards, these topics have already been broached in other blogs and may not require their own section...

Preliminary Considerations Dividing the Whole Note into Non-standard Parts Many ideas under consideration for a compositional system for Polytempic Polymicrotonal music are not wholly new. I have been influenced by many composers, theorists, and authors of works that are common fodder in the more arcane areas of music theory. Henry Cowell comes to mind. Amazingly, much of Cowell's work still remains unused and unexplored. Something as simple as fifth notes , or pentuplets , up to today, 2025 -26, really should be standard rhythmic practice, just as triplets are. But, they are not. Nevertheless, the division of the whole note into parts other than the binary divisor 2 should be in common use now. Anyone should be able to play pentuplets, septuplets , and nonuplets , as nonuplets are essentially a nested rhythm of three sets of triplets...So, not quite complex nested rhythms, but not merely duple rhythms based on the number 2. Human limitations, of course, limit tempo and speed f...

Although I have heretofore written two textbooks on this subject, I have yet to issue forth a methodology on writing Polytempic Polymicrotonal music . Up until now, my approach to composing polytempic polymicrotonality has largely been intuitive. The impetus for this enterprise came from my drumming background, playing four meters at once on the drumset . This gave birth to later ideas as a composer for myriad ways to synchronize four-part writing in a deliberately syncopated way that would preclude predictable alignment of harmony. The words " verticalities " and "simultaneities" come to mind.  The non-pitched inharmonically tuned drums have always been " microtonal "; the extension of this idea, for me, was to assemble an array of pitches that at first glance would have nothing in common, yet could be heard as an infinite set of tom-toms that could be represented by hundreds of microtonal pitches , other than the mere designation of high, medium, and l...