2L 2s: Difference between revisions

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-This tetrad has the special property that it is the smallest collection of notes which can create the feeling of "completely representing<span style="line-height: 1.5;">" a particular regular temperament in a "standard" way. However, it only works in even-numbered edxs, for it contains sqrt(x), and it becomes a very weakly "complete" representation of a regular temperament as L:s grows large.</span>
+{{Infobox MOS}}
-Golden bi-equal tetrad: major 0-phi-phi+1-2*phi+1, minor 0-1-phi+1-phi+2/(2*phi+2)edx
+{{MOS intro}}
-in edo: major 0-370.82-600-970.82 cents, minor 0-229.18-600-829.18 cents
+This scale is the parent of all half-octave-repeating MOS scales.
-Natural logarithm bi-equal tetrad: major 0-e-e+1-2e+1, minor 0-1-e+1-e+2/(2e+2)edx
+== Names ==
+[[TAMNAMS]] uses the name '''biwood''', based on the n-wood series.
-in edo: major 0-438.635.82-600-1038.635 cents, minor 0-162.365-600-762.365 cents
+== Modes ==
+{{MOS mode degrees}}
-Bi-equal wheel tetrad: major 0-pi-pi+1-tau+1, minor 0-1-pi+1-pi+2/(2*tau+2)edx
+== Intervals ==
+{{MOS intervals}}
-in edo: major 0-455.128-600-1055.128 cents, <span style="line-height: 1.5;">minor 0-144.872-600-744.872 cents</span>
+== Scale tree ==
+Generator ranges:
+* Chroma-positive generator: 300 cents (1\4) to 600 cents (1\2)
+* Chroma-negative generator: 0 cents (0\2) to 300 cents (1\4)
+{| class="wikitable center-all"
+! colspan="6" | Generator
+! Cents
+! L
+! s
+! L/s
+! Comments
+|-
+| 1\4 || || || || || || 300.000 || 1 || 1 || 1.000 ||
+|-
+| || || || || || 6\22 || 327.273 || 6 || 5 || 1.200 ||
+|-
+| || || || || 5\18 || || 333.333 || 5 || 4 || 1.250 ||
+|-
+| || || || || || 9\32 || 337.500 || 9 || 7 || 1.286 ||
+|-
+| || || || 4\14 || || || 342.857 || 4 || 3 || 1.333 ||
+|-
+| || || || || || 11\38 || 347.368 || 11 || 8 || 1.375 ||
+|-
+| || || || || 7\24 || || 350.000 || 7 || 5 || 1.400 ||
+|-
+| || || || || || 10\34 || 352.941 || 10 || 7 || 1.429 ||
+|-
+| || || 3\10 || || || || 360.000 || 3 || 2 || 1.500 ||
+|-
+| || || || || || 11\36 || 366.667 || 11 || 7 || 1.571 || [[Baladic]]
+|-
+| || || || || 8\26 || || 369.231 || 8 || 5 || 1.600 ||
+|-
+| || || || || || 13\42 || 371.429 || 13 || 8 || 1.625 || Golden [[Lemba]] (370.8204¢)
+|-
+| || || || 5\16 || || || 375.000 || 5 || 3 || 1.667 ||
+|-
+| || || || || || 12\38 || 378.947 || 12 || 7 || 1.714 ||
+|-
+| || || || || 7\22 || || 381.818 || 7 || 4 || 1.750 ||
+|-
+| || || || || || 9\28 || 385.714 || 9 || 5 || 1.800 ||
+|-
+| || 2\6 || || || || || 400.000 || 2 || 1 || 2.000 || Basic 2L 2s
+|-
+| || || || || || 9\26 || 415.385 || 9 || 4 || 2.250 || [[Unidec]] is around here
+|-
+| || || || || 7\20 || || 420.000 || 7 || 3 || 2.333 ||
+|-
+| || || || || || 12\34 || 423.529 || 12 || 5 || 2.400 ||
+|-
+| || || || 5\14 || || || 428.571 || 5 || 2 || 2.500 ||
+|-
+| || || || || || 13\36 || 433.333 || 13 || 5 || 2.600 || Golden [[Hedgehog]]-[[supers]] (434.1641¢)
+|-
+| || || || || 8\22 || || 436.364 || 8 || 3 || 2.667 ||
+|-
+| || || || || || 11\30 || 440.000 || 11 || 4 || 2.750 ||
+|-
+| || || 3\8 || || || || 450.000 || 3 || 1 || 3.000 ||
+|-
+| || || || || || 10\26 || 461.538 || 10 || 3 || 3.333 || [[Fifive]]
+|-
+| || || || || 7\18 || || 466.667 || 7 || 2 || 3.500 ||
+|-
+| || || || || || 11\28 || 471.429 || 11 || 3 || 3.667 ||
+|-
+| || || || 4\10 || || || 480.000 || 4 || 1 || 4.000 ||
+|-
+| || || || || || 9\22 || 490.909 || 9 || 2 || 4.500 || [[Diaschismic]] / [[Pajara]]
+|-
+| || || || || 5\12 || || 500.000 || 5 || 1 || 5.000 || [[Injera]] is around here
+|-
+| || || || || || 6\14 || 514.286 || 6 || 1 || 6.000 || [[Vishnu]]↓
+|-
+| 1\2 || || || || || || 600.000 || 1 || 0 || → inf ||
+|}
+{{todo|expand}}
+[[Category:Tetrad]]
+[[Category:4-tone scales]]