Notation

The notation used is decatonic. 0 1 2 3 4 5 6 7 8 9 0 is the Pacific mode of the Hemipyth[10] 4L 6s MOS. # and b after a number represent alterations of raising and lowering by sqrt(256/243) respectively. ^ and v before a number represent alterations of the greenland subchroma, sqrt(50/49)~sqrt(sqrt(25/24))~sqrt(49/48) respectively.

Chapter 1: Fokker blocks

Decatonic Fokker blocks

Since greenland is essentially an extension of hemipyth with extra subchromatic alterations, it follows that one should probably treat greenland in this way.

The quintessential Fokker block, though not rank-3 in nature, is the hemipyth[10] block. This block has five modes.

Notes Step pattern Name
0 1# 2 3# 4 5 6# 7 8# 9 LsLssLsLss Atlantic
0 1# 2 3 4 5 6# 7 8 9 LssLsLssLs Lumian
0 1 2 3 4 5 6 7 8 9 sLsLssLsLs Pacific
0 1 2 3 4b 5 6 7 8 9b sLssLsLssL Taliesin
0 1 2b 3 4b 5 6 7b 8 9b ssLsLssLsL Dresden

14-tone Fokker blocks

24-tone Fokker blocks

Larger Fokker blocks

Chapter 2: JI scales

Preliminary: The 7-odd-limit Tonality Diamond

The 15-odd-limit Tonality Diamond

JI detemperings of Fokker blocks