Name: Piano Collection #4a Microtonal (19tet) by pthoege
Duration: 8 min 8 s
Description: Piano Collection #4a, microtonal, is in 19tet, and was composed in 2016, and features a microtonal version of Piano Collection #4, in an ongoing series of collections mainly for 12tet piano.

With 12 pitch classes one has 144 2-note sequences or just 132 upon insisting on 2 distinct notes.  

Dividing these 132 sequences randomly into 3 "buckets" of about 44 sequences each one can seek out, for each bucket, all the 12-tone cycles that each bucket affords: so each adjacent pair of notes in each cycle must constitute a 2-note sequence in the affiliated bucket.

Now repeating this recipe millions of times, I eventually discover three instances where each bucket affords, in total, exactly 30 conforming cycles each.

Musically speaking, all the cycles associated to a particular bucket, seeing as how they got cobbled out of the same 2-note sequences, they all turn out to share a common feeling.   Moving from one bucket to the next that feeling changes.  Indeed I feel a distinct but subtle shift, akin, something to something like a key change or modulation and this occurs despite how composing with 12-tone cycles promotes consistent pitch saturation, and thus the classic "atonal" sound you will hear.

But honestly, even having composed the piece myself, and thus knowing in advance where to expect these quasi key changes, only after repeated hearings did I suddenly find these shifts, these reconfiguations, obvious.  

With three 30-30-30's, I had one to use to govern the pitch classes, but also one for durations, and one for orchestration.

Think of this as very unconventional 12-tone-music: the rows never get transposed or inverted or retrograded, but rather variety arises from employing multiple rows that happen, by design, to share common "DNA."  Rather than burying this "row technique" under some sort of subjective rhetoric, as traditional 12-tone composers feel they must, I organize all these materials for transparency, hoping for listeners to follow the goings on.  One usually views "complexity" and "minimalism" as opposite poles, but both attitudes inform every moment of this piece.

Fritillary, for small orchestra

Kondor: Piano Concerto 1st Mmt

Kondor: Piano Concerto 3d Mmt

Kondor: Piano Concerto 2d Mmt

Dedicated to Christopher Maher, who urged me to take a serious interest in Cuban timba, the band Klimax in particular, a type of music far removed from my usual listening habits, to say the least

Johann Wolfgang von Goethe said “Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.”

Composer that I am, I am also a mathematician and that is exactly what happened.

Harvesting Timba

méson kaí ákron

Lately I'm making pieces for a synthetic percussion orchestra with a virtually infinite number of instruments.

This is a proof of concept piece.

Perkodhuskurunbarggruauyagokgorlayorgromgremmitghundhurthrumathunaradidillifaititillibumullunukkunun

The most basic rhythmic transformation consists in subdividing a single unit of time into two equal halves.  Repeating this operation produces an infinitude of patterns of which this piece might be considered a partial catalog.  The tempo is chosen so that the beginning sounds like some sort of virtuoso drumming (but these are my own computer generated sounds, and no sampling was involved), yet gradually, as the patterns grow more complex, execution would require superhuman ability and the result verges on the biological.  The catalog has its own emergent shape, so there is rhythmic interest too on larger time scales.

Halve and Whole

Title:
Crackle

Dates:
28-Apr-2024 (inception), 01-May-2024 (finalised), 28-May-2025 (released)

Artists:
Music composed, performed, produced by Norman Freund
Artwork by Norman Freund
Photography by Zachary Freund
Astrophotography by John Holgate

BandCamp Purchase:
https://normanfreund.bandcamp.com/track/crackle
YouTube Video:
https://youtu.be/WeRj2nls07A

Description:

Midnight Run Through The Port Hills
	
Valley run,
Moon light night,
Tree shadows sweep by.

Forest behind,
Sweeping bends ahead.

Tension builds,
Revs increase,
Hill climb begins.
City lights flicker below.

Sky lights appear,
Ascending light beam,
Hatch silhouette,
Galaxy engulfs,
Silence,
Darkness.


Behind the scenes music notes:

The main motivation behind Crackle is the Just Intonation (JI) tuning used, taking all the harmonics from octaves 0 to 5, octave reduce, remove duplicates and re-order in ascending order. This resulted in a 29 frequency ratios (not including in the 2/1 octave). These 30 frequency ratios were then transposed by JI perfect fifths (3/2 ratio) to expand the scale in violin style ready for a four string violin. When applied to violin, this means there are 30 notes per string spanning one octave.

The scale outline (** full details see my social media and BandCamp **):
Scale Index(i), [string number], JI Equation, Cent
0[1], 1/1, 0c
1[1], 33/32, 53c
2[1], 17/16, 105c
3[1], 9/8, 204c
4[1], 37/32, 251c
5[1], 19/16, 298c
6[1], 39/32, 342c
7[1], 5/4, 386c
8[1], 41/32, 429c
9[1], 21/16, 471c
10[1], 43/32, 512c
11[1], 11/8, 551c
12[1], 23/16, 628c
13[1], 47/32, 666c
14[1], 3/2, 702c
15[1], 49/32, 738c
16[1], 25/16, 773c
17[1], 51/32, 807c
18[1], 13/8, 841c
19[1], 53/32, 874c
20[1], 27/16, 906c
21[1], 55/32, 938c
22[1], 7/4, 969c
23[1], 57/32, 999c
24[1], 29/16, 1030c
25[1], 59/32, 1059c
26[1], 15/8, 1088c
27[1], 61/32, 1117c
28[1], 31/16, 1145c
29[1], 2/1, 1200c
30[2], 3/2, 702c
31[2], 99/64, 755c
...
59[2], 3/1, 1902c
60[3], 9/4, 1404c
61[3], 297/128, 1457c
...
89[3], 9/2, 2604c
90[4], 27/8, 2106c
91[4], 891/256, 2159c
...
118[4], 837/128, 3251c
119[4], 27/4, 3306c


It was then time to start playing around with the scale. The reference note used for this scale was not as per a concert pitch violin, rather concert pitch middle C, then some differing octave transpositions for the various string tracks.

The string sections were played on a 64 note midi controller, the Ableton Push2, so only a subset of the full 120 notes could be played at once. Played "organ style", as chords, well beyond double stop capabilities of a single physical string instrument. These tracks provided the basic harmony and melodic concepts.

Next the Soma Pipe (hardware synthesiser, here accepting the human voice as input) was played to provide improvised lead and percussive parts. The lead parts used various Pipe algorithms (Filtera, Harcho, MadDelay and Synth), the tuning was not necessarily strictly as per the table above, but rather improvised live tuning, where I as the performer, used my ears and emotions to guide the tuning choices. Some of the Pipe parts used a digital amplitude modulation device (Max for Live, custom programmed, the NOF_AENV Release 06). This amplitude modulation tool, used two simultaneous sine wave modulations with JI frequency ratios.

A wave table synthesiser in Ableton Live was used for the string section and for one additional instrument.

** See BandCamp and Social Media links for video production notes. **

Artist Links:
Norman Freund; Social media: https://www.facebook.com/norman.freund.545; YouTube: https://youtube.com/@normanfreund; Music: https://soundcloud.com/norman-freund, https://normanfreund.bandcamp.com

John Holgate; Social media: https://www.facebook.com/blundering.fool.3; YouTube: https://www.youtube.com/@quedecree; Music: johnholgate.bandcamp.com

Zachary Freund, Social Media: https://www.facebook.com/zac.freund.9, Instagram: https://www.instagram.com/zac_freund

Crackle

There is a slender stream in my output, but extending back five decades now, of music based on scales repeating, not at the octave, but at the fifth (or fourth).  In particular, while the effect here is always "locally pentatonic," as the piece progresses it grows increasing pantonal.  By the end all the pitch classes get equal treatment.  

By a "hypercanon," I mean a canon whose theme is itself a canon, and perhaps, and so on.  

Here the  ultimate theme and patterns of canonic repetitions have been chosen very carefully so that music has an overall constant density.  Get the math wrong and the music will just grow muddy or thin out prematurely.

A pulse unifies the rhythmic surface, but it beats so fast, on the order of 50 clicks per second, that the audible rhythm will not imply it even the pulse arguably still informs the rhythm.  So just as the tonality here doesn't count as either diatonic or traditionally atonal, the rhythmic profile is neither entirely "free" nor based on a perceptible count.

Another quite different interpretation of the underlying structure is forthcoming.  Watch this space.

Sometimes the New Place to Go Sits In Between the Places You Know, for piano

Piano Collection #4a, microtonal, is in 19tet, and was composed in 2016, and features a microtonal version of Piano Collection #4, in an ongoing series of collections mainly for 12tet piano.

Piano Collection #4a Microtonal (19tet)

To all concerned: 
I am announcing publication of my new book, NOW AVAILABLE:
https://www.routledge.com/Maqam-Melodies-Pitches-Patterns-and-Developments-of-Music-in-the-Middle-East-and-other-Microtonal-Writings/Thoegersen/p/book/9789815129052
My book, Polytempic Polymicrotonal Music, is available on Amazon. 
https://www.routledge.com/Polytempic-Polymicrotonal-Music-The-Road-Less-Traveled/Thoegersen/p/book/9789814968294

I have a new album out through Magic&Unique Group Records on Spotify and other digital streaming platforms:
https://open.spotify.com/album/5qWHmcvyAemvVn2TJH1bio?si=OD5TmPptQ-ypr8WOI0EZKA&nd=1

https://whitecentipedenoise.com/products/peter-thoegersen-facebook-cantos-cdr-flea
My CD via Flea label has been out since April, 2021, featuring the wonderful Lore Lixenberg singing over my microtonal piano accompaniment
Hope you enjoy it!

https://www.newworldrecords.org/collections/vendors?q=Peter%20Thoegersen

From the liner notes on my CD now available on AMAZON and New World Records:
"The author of these notes has spent his life explaining radical music, and the music on this disc may be the most radical I've ever written about. Peter Thoegersen (b. 1967) is not yet a name known to the music world; not for any lack of connection to other famous musicians, but because he came to composition late, and because his artistic aims are so broad and complex that they have taken years to evolve. His aesthetic is well defined, and he is upfront about having a name for it: "Polytempic Polymicrotonal Music." That means he has musical layers simultaneously moving in different tempos, plus, even more radically, that he has different microtonal scales playing at the same time. Few composers have aimed at such fervent and heterogeneous multidimensionality. And yet, while Thoegersen's music can seem overwhelming at first, running through it is a level of charm and simplicity that belies the initial impression.

In total, these three pieces emphasize a particular side of Thoegersen's output. The image his music creates of ornately mathematical structures filled with intuitively friendly melodies maps on to the personality of the man himself: outspoken and acerbically ruthless in his musical opinions, Thoegersen is also marked by a jolly sense of humor and an inexhaustible love of cats and other animals that make him ultimately less imposing and more personable than he might seem at first. The same can be said for his music. And by going further than anyone else has gone in terms of this particularly American concept of fusing the polytempic with the polymicrotonal - extending and combining the conceptual worlds of Ives, Cowell, Nancarrow, Partch, Carter, even Frank Zappa and many others - he has created a special place for himself within American music."                                                             

-Kyle Gann (from the liner notes)

Piano Collection #4a Microtonal (19tet)

pthoege

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