User:2^67-1/Sandbox II: Difference between revisions

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


* 0 1# 2 3# 4 5 6# 7 8# 9 0: Taliesin
* 0 1# 2 3# 4 5 6# 7 8# 9 0: Atlantic
* 0 1# 2 3 4 5 6# 7 8 9 0: Lumian
* 0 1# 2 3 4 5 6# 7 8 9 0: Lumian
* 0 1 2 3 4 5 6 7 8 9 0: Pacific
* 0 1 2 3 4 5 6 7 8 9 0: Pacific
* 0 1 2 3 4b 5 6 7 8 9b 0: Atlantic
* 0 1 2 3 4b 5 6 7 8 9b 0: Taliesin
* 0 1 2b 3 4b 5 6 7b 8 9b 0: Dresden
* 0 1 2b 3 4b 5 6 7b 8 9b 0: Dresden



Revision as of 12:38, 14 March 2025

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 block. This block has five modes.

  • 0 1# 2 3# 4 5 6# 7 8# 9 0: Atlantic
  • 0 1# 2 3 4 5 6# 7 8 9 0: Lumian
  • 0 1 2 3 4 5 6 7 8 9 0: Pacific
  • 0 1 2 3 4b 5 6 7 8 9b 0: Taliesin
  • 0 1 2b 3 4b 5 6 7b 8 9b 0: 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