Twice-All-Interval Pentachord by: Tristin Bailey [Atonal 11edo, with 11edo set-class list in desc.]
4This is my first 11edo piece, my first quintet, and my first rondo.
I finished this months ago, but delayed uploading to ask some string players for opinions on notation. 11edo upsets string players.
I wanted to get a feel for each interval within the 11edo system, which resulted in this atonal mess. I do use some tonal gestures, but they are not very prominent throughout the piece.
This is an 11 part rondo, with the pitch content focused around the sc(01247) twice-all-interval pentachord (TAIP) and its complement, the sc(012457) thrice-all-interval hexachord (TAIH).
The A section has the TAIP in the Violin I part, and the TAIH in the Cello II part. The Violin II, Viola, and Cello I parts then fill in each of the TAIPs which can exist with the present [3,7] dyad being sustained in the Violin I and Cello II parts.
From there the B to F sections focus on ic1 to 5 respectively. Granted, the F section also heavily features each ic, especially with the melodies which use one of each pi ranging from 1 to 11. Each of these sections starts off with one of the symmetric trichords; (012), (024), (036), (037), and (016), being sounded in the higher Violins and Viola. For the most part I wanted to have a pitch center of p1 (the C# + 9 cents), and the huge amount of symmetric subsets that exist in sc(01247) made this a bit easier, but I didn't consciously adhere too heavily to the pitch center.
Most of the rhythmic material is derived from the A section, however each new section does get one or two characteristic ostinati or rhythmic cells.
While I didn't really go into writing this piece with specific goals in mind beyond "give each interval a section", it did develop into the piece slowly devolving from more consonant gestures (especially with the use of upi7), to absolute atonal chaos.
Like my other xenharmonic pieces, I labeled each pitch-class underneath
the parts to allow for visual relations as well as audible ones. (A = 10)
Now, since I have a TON of extra space in this description, here's the full list of set-classes in 11edo that I made. I'm sure others exist, and I could refine this one, but I think anyone who really wants to make 11edo atonal music will probably be fine taking my draft as a starting point for their own personal use.
Note: Since 11edo is an asymmetric system, transpositional symmetry doesn't really exist. Despite this, I've included the redundant value for formatting sake. The list is based off A. Forte's 12edo set-class list.
Dyads Nonachords
01 [10000] 1,1 012345678 [87777] Minor Second
02 [01000] 1,1 012345679 [78777] Major Second
03 [00100] 1,1 012345689 [77877] Minor Third
04 [00010] 1,1 012345789 [77787] Supermajor Third
05 [00001] 1,1 012346789 [77778] Major Fourth
Trichords Octachords 10
012 [21000] 1,1 01234567 [76555] Chromatic Cluster
013 [11100] 1,0 01234568 [66655]
014 [10110] 1,0 01234578 [65665]
015 [10011] 1,0 01234678 [65566]
016 [10002] 1,1 01235678 [65557] M4 Stack
024 [02010] 1,1 01234579 [57565] M2 Stack
025 [01101] 1,0 01234679 [56656]
026 [01011] 1,0 01235679 [56566]
036 [00201] 1,1 01235689 [55756] m3 Stack/Consonant Triad
037 [00120] 1,1 01245689 [55675] M3 Stack
Tetrachords Septachords 20
0123 [32100] 1,1 0123456 [65433] Chromatic Cluster
0124 [22110] 1,0 0123457 [55443]
0125 [21111] 1,0 0123467 [54444]
0126 [21012] 1,0 0123567 [54345]
0134 [21210] 1,1 0123458 [54543]
0135 [12111] 1,0 0123468 [45444]
0136 [11202] 1,0 0123568 [44535]
0137 [11121] 1,0 0124568 [44454]
0145 [20121] 1,1 0123478 [53454]
0146 [11112] 1,0 0123578 [44445]
0147 [10221] 1,0 0124578 [53554]
0156 [20013] 1,1 0123678 [53346] M4 Stack
0157 [11022] 1,1 0124678 [44355]
0235 [12201] 1,1 0123469 [45534]
0236 [11211] 1,0 0123569 [44544]
0246 [03021] 1,1 0123579 [36354] M2 Stack
0247 [02121] 1,0 0124579 [35454]
0257 [02112] 1,1 0124679 [35445]
0258 [01302] 1,1 0134679 [34635] m3 Stack/Dominant
0347 [10230] 1,1 0134578 [43563] M3 Stack
Pentachords Hexachords 26
01234 [43210] 1,1 012345 [54321] Chromatic Cluster
01235 [33211] 1,0 012346 [44322]
01236 [32212] 1,0 012356 [43323]
01237 [32122] 1,1 012456 [43233]
01245 [32221] 1,0 012347 [43332]
01246 [23122] 1,0 012357 [34233]
01247 [22222] 1,0 012457 [33333] Double All-Interval
01256 [31123] 1,0 012367 [42234]
01257 [22123] 1,0 012467 [33234]
01258 [21322] 1,1 013467 [32433]
01267 [31024] 1,1 012567 [32135] M4 Stack
01346 [22312] 1,0 012358 [33423]
01347 [21331] 1,0 012458 [32443]
01356 [22213] 1,1 012368 [33324]
01357 [13132] 1,0 012468 [24243]
01358 [12322] 1,0 013568 [23433]
01367 [21223] 1,0 012568 [32334]
01368 [12313] 1,0 013568 [23424]
01457 [21232] 1,0 012478 [32343]
01458 [20341] 1,1 013478 [31452] M3 Stack
01468 [12232] 1,1 013578 [23343]
02346 [23221] 1,1 012359 [34332]
02347 [22231] 1,0 012459 [33342]
02357 [13222] 1,0 012469 [24333]
02358 [21403] 1,1 013469 [32514] m3 Stack
02468 [04132] 1,1 013579 [15243] M2 Stack