46edo: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 238827225 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
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The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the [[octave]] into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 [[cent]]s, an interval close in size to [[66_65|66/65]], the interval from [[13_11|13/11]] to [[6_5|6/5]]. | The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the [[octave]] into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 [[cent]]s, an interval close in size to [[66_65|66/65]], the interval from [[13_11|13/11]] to [[6_5|6/5]]. | ||
46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. [[Rank two temperaments]] it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The [[11-limit]] [[Target tunings|minimax]] tuning for [[Starling family|valentine temperament]], (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the [[13-limit]], though others award that distinction to [[41edo]]. | 46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. [[Rank two temperaments]] it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The [[11-limit]] [[Target tunings|minimax]] tuning for [[Starling family|valentine temperament]], (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the [[13-limit]], though others award that distinction to [[41edo]]. In fact, while 41 is a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]] but not a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta gap edo]], 46 is zeta gap but not zeta integral. | ||
The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the [[just fifth]] and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad. | The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the [[just fifth]] and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad. | ||
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The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 <a class="wiki_link" href="/cent">cent</a>s, an interval close in size to <a class="wiki_link" href="/66_65">66/65</a>, the interval from <a class="wiki_link" href="/13_11">13/11</a> to <a class="wiki_link" href="/6_5">6/5</a>.<br /> | The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 <a class="wiki_link" href="/cent">cent</a>s, an interval close in size to <a class="wiki_link" href="/66_65">66/65</a>, the interval from <a class="wiki_link" href="/13_11">13/11</a> to <a class="wiki_link" href="/6_5">6/5</a>.<br /> | ||
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46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. <a class="wiki_link" href="/Rank%20two%20temperaments">Rank two temperaments</a> it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The <a class="wiki_link" href="/11-limit">11-limit</a> <a class="wiki_link" href="/Target%20tunings">minimax</a> tuning for <a class="wiki_link" href="/Starling%20family">valentine temperament</a>, (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the <a class="wiki_link" href="/13-limit">13-limit</a>, though others award that distinction to <a class="wiki_link" href="/41edo">41edo</a>.<br /> | 46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. <a class="wiki_link" href="/Rank%20two%20temperaments">Rank two temperaments</a> it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The <a class="wiki_link" href="/11-limit">11-limit</a> <a class="wiki_link" href="/Target%20tunings">minimax</a> tuning for <a class="wiki_link" href="/Starling%20family">valentine temperament</a>, (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the <a class="wiki_link" href="/13-limit">13-limit</a>, though others award that distinction to <a class="wiki_link" href="/41edo">41edo</a>. In fact, while 41 is a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta integral edo</a> but not a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta gap edo</a>, 46 is zeta gap but not zeta integral.<br /> | ||
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The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the <a class="wiki_link" href="/just%20fifth">just fifth</a> and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.<br /> | The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the <a class="wiki_link" href="/just%20fifth">just fifth</a> and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.<br /> | ||