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 Polytempo?   What is tempo? First of all, we must understand what tempo is. So I will explore this topic as deliberately, naively, and as guilelessly as I possibly can, to ask the most basic questions without the pomp, rhetoric, and expectations of my doctorate, telling both me that I damn well know what tempo is, when in fact, do I? Jean-Baptiste Lully thought he knew what tempo was when he accidentally crushed his toe with his staff, pounding the tempo onto the floor while conducting Te Deum . Lully was 'tempoed' to death. There is no more concrete example of tempo than this. Now imagine three more Lullys pounding the floor at different rates of speed with their staffs. This is polytempo, and hopefully not the accidental polydeaths of the three additional Lullys.  Today's version of this would not be so much the conductor, but perhaps a drummer? Or more precisely, the click-track pounds the tempo into the ears of hapless musicians via headphones for them to p...

 "Irrational" Time Signatures What Is a Whole Note? Technically, it is assumed that a whole note lasts four beats. The whole note, lasting four beats, has been a law of music since mensuration was gradually developed and codified throughout the Middle Ages, up to the present day. We simply accept that the value of a whole note is equal to four counts, with one single beat lasting those four counts. This, then, becomes the entirety of the measure (bar) and is called Common Time , or 4/4 time . But the truth is that a whole note really does not mean anything at all. One could argue that a whole note lasts a full measure. But what does that mean? If we stipulate that a whole note, at 100 BPM, is the set tempo, then how do we really quantify the whole note? Each 1/100th part of this whole note lasts approximately .6 seconds.  Theoretically, the whole note could last forever. Ostensibly, a time signature is needed to give a quantifiable value to the whole note. Therefore, the wh...

 More on the Divisions of the Whole Note, in a Cowellian Sense " Decimal Rhythms " While in Champaign back in 2007, I was given a notebook. Since I had nothing but time on my hands, I began ruminating about the divisions of the whole note. Borrowing (as the best of us do) from Cowell , I wrote out a schema for a 'newer' approach to non-duple-based rhythms . I wrote this:           Figure 1. A figuration of Decimal Rhythms Figure 1 is a common-time bar of decimal rhythms: one third-note , at 33.3% of a whole note; one twelfth-note , at 1/3 of a third note of 11.1%; an eleventh-note , at 1/11th of a whole note, at 9%; a seventh-note , at 14.3%; and three tenth notes , obviously at 10% x 3 = 30% of a whole note. These add up to approximately. 97.7% of a whole note, or the 4/4 measure, is indicated. An outline of the Figure 1 decimal rhythmic measure is shown below in Figure 2.     Figure 2. An outline of the decimal measure is hidden   ...

More on Contrapuntal Tempi...  Polytempo as Static vs. Dynamic and Fluid Tempo has throughout Western musical history been thought of as a single-formed containment system for music, perhaps except the isorhythms of the Middle Ages, which actually had nothing to do with tempo, but marked the beginning of the awareness of the potential of several strands of musical thought working simultaneously, as in color and talea , that could conceivably be a thought-form precursor to polytempo . Additionally, and unrelatedly, many motets were written with differing text languages, also not related directly to polytempo, but actually more to polymicrotonality ; the different languages presented in polytextual works offered different vowels, phones, phonemes, and glottals--imperceptible at the time, but today would actually count as polymicrotonal by closer examination. It is here that I must declare that, for me, polytempic polymicrotonality is really nothing more than an attitude; an aesth...