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| '''Neutral seconds''' are intervals with a size in between a whole tone and a semitone. They are one of the most distinctive-sounding yet versatile xenharmonic intervals, which makes them highly valuable.
| | #REDIRECT [[Second]] |
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| ==Function==
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| The large step of armotonic is always some sort of neutral second, which functions similar to both a whole tone and semitone.
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| A step of 13ed3 is a middle neutral second. It is notable for having an unusually good approximation of LCJI for a system generated by neutral seconds.
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| '''Porcupine neutral seconds''' are larger neutral seconds most commonly between 2\15 and 3\22 which, consistent with Porcupine temperament, split a sharp 6/5 in half and a flat 4/3 into thirds. This functionally makes them a very flat minor whole tone (T10/9), and are thus an easy way to make otherwise uninteresting progressions sound xenharmonic.
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| In larger edos, it's possible to have a similar tuning of intervals, but without Porcupine tempering. In the 100b val, the T10/9 is a slightly larger 168¢ in exchange for making the T81/80 48¢, a much more usable aberrisma than Porcupine typically offers.
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| ==Categorization==
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| Neutral seconds are generally considered to be between 1\9 and 1\7, being half of some sort of minor third. If semifourths are included, they can be as narrow as 1\10.
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| ===Proposal: Ground's Neutral Second Categorization System===
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| Import splitting table here.
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| {| class="wikitable"
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| |+ Names Based on Interval Splitting (with Nearby Edo Intervals)
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| ! ¢ !! Definition !! Name (accepted names are bold) !! Edo !! ¢ !! Error ¢
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| | 109.050 || 7/6 / √(6/5) || Sepsemipental Semitone || 1\11 || 109.091 || 0.041
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| | 111.731 || '''16/15''' || '''Pental Semitone''' || 3\32 || 112.500 || 0.769
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| | 119.443 || '''15/14''' || '''Septimal Major Semitone''' || 1\10 || 120.000 || 0.557
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| | 121.243 || 7/6 / <sup>4</sup>√(7/5) || Quadranseptimal Supraminor Second || 1\10 || 120.000 || -1.243
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| | 124.511 || <sup>4</sup>√(4/3) || Quadranpyth Supraminor Second || 3\29 || 124.138 || -0.373
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| | 128.298 || '''14/13''' || '''Tridecimal Supraminor Second''' || 3\28 || 128.571 || 0.273
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| | 133.435 || √(7/6) || Semiseptal Neutral Second || 1\9 || 133.333 || -0.102
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| | 138.573 || '''13/12''' || '''Tridecimal Neutral Second''' || 3\26 || 138.462 || -0.111
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| | 140.391 || <sup>5</sup>√(3/2) || Quintanpyth Neutral Second || 2\17 || 141.176 || 0.785
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| | 145.628 || <sup>4</sup>√(7/5) || Quadranseptimal Neutral Second || 4\33 || 145.455 || -0.174
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| | 150.637 || '''12/11''' || '''Undecimal Neutral Second''' || 1\8 || 150.000 || -0.637
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| | 157.821 || √(6/5) || Semipental Neutral Second || 5\38 || 157.895 || 0.074
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| | 165.004 || '''11/10''' || '''Undecimal Submajor Second''' || 4\29 || 165.517 || 0.513
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| | 166.015 || <sup>3</sup>√(4/3) || Trienpyth Submajor Second || 4\29 || 165.517 || -0.498
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| | 170.013 || 6/5 / <sup>4</sup>√(7/5) || Quadranseptimal Submajor Second || 1\7 || 171.429 || 1.415
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| | 175.489 || <sup>4</sup>√(3/2) || Quadranpyth Major Second || 6\41 || 175.610 || 0.121
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| | 182.206 || 6/5 / √(7/6) || Pensemiseptal Major Second || 5\33 || 181.818 || -0.388
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| | 182.404 || '''10/9''' || '''Minor Whole Tone''' || 5\33 || 181.818 || -0.586
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| |}
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