Techniques of Polytempic Polymicrotonal Composition

  Microtonal Intervals and Harmony Figures 1-3. J. Murray Barbour 's Superparticular Ratios   from octave to schisma (added by me.) fig. 2 fig. 3 I am deliberately using an old textbook ( Tuning and Temperament: A Historical Survey , by J. Murray Barbour) list of superparticular ratios converted into cents values for a semi-comprehensive list of intervals for the effect of tabula rasa vis-à-vis the wealth of tuning and microtonal information available today.  Between Ellis-Helmholtz's On the Sensations of Tone , 1875, and today, a good deal of literature exists concerning tuning and microtones by hundreds of writers on the subject. This rather simple list of Barbour's helps me gain perspective on what I am attempting to convey about pitch relations and intervals without the extra baggage of thoughts, opinions, and tuning inventions since 1953, when this book was published.  What I have found myself doing in my own music is that I have made a mental separation bet...

  Why is this Philosophical Question Relevant?  CHOICE AND INTENT During post-war music composition , the chaotic and hapless state of the geopolitical arena had caused ontological shock to people around the planet. People feel out of control, as they are starting to again, today. One way to deal with feeling helpless is to immerse oneself in some kind of system of control. Schönberg had created his system after the Great War, in the 1920s. Arnold, in fact, served in that war. One interesting outcome of Schönberg's system was the abnegation of personal choice; systems became paramount. This led to total serialism , and Cage's chance operations similarly showed another aspect of the dethroning of one's own personal choice. As though the composer's personal druthers were to be removed at once.  Polytempic Polymicrotonality , a non-system system, encourages choice and intention. Out of 5000 Scala microtonal scales, one MUST choose. Out of unlimited tempi, one MUST choos...

  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...

  5000 Microtonal Scales Myriad intervals from a plethora of microtonal scales . Considering the wealth of information about this on the internet, this will oddly be my shortest blog entry. As I write these, I am trying not to recreate my own book, Polytempic Polymicrotonal Music , or start another survey of sorts. I would rather just get down to it, but I have to consider whether things are extraneous or redundant.  Ultimately, we are still at the precipice of the eternal argument between Pythagoras and Aristoxenus . Will we use rational unequal tunings , or equal divisions with or without octave equivalence into infinity? Answer: BOTH. I prefer to forget the position of either/or in consideration of a stance that embraces both of these paradigms. So, with precision and concision, I will adroitly say this:  There are choices to be made in polymicrotonal composition (you may use dice for this decision). If we consider the historical, theoretical, and cultural microton...

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 ...

  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...