46edo: Difference between revisions
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= | =46 tone equal temperament= | ||
The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the [[Octave|octave]] into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 [[cent|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 <b>46-tET</b>, <b>46-EDO</b>, or <b>46-ET</b>, is the scale derived by dividing the [[Octave|octave]] into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 [[cent|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|Rank two temperaments]] it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The [[11-limit|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|13-limit]], though others award that distinction to [[41edo|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. | 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|Rank two temperaments]] it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The [[11-limit|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|13-limit]], though others award that distinction to [[41edo|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|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|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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=Music= | =Music= | ||
by [[Aaron_Krister_Johnson|Aaron Krister Johnson | [http://aaronkristerjohnson.bandcamp.com/track/satiesque Satiesque] by [[Aaron_Krister_Johnson|Aaron Krister Johnson.]] | ||
[http:// | [http://www.archive.org/details/Chromosounds Chromosounds] [http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3 play] by [[Gene_Ward_Smith|Gene Ward Smith.]] | ||
by [[Gene_Ward_Smith|Gene Ward Smith | [http://www.archive.org/details/MusicForYourEars Music For Your Ears] [http://www.archive.org/download/MusicForYourEars/musicfor.mp3 play] by [[Gene_Ward_Smith|Gene Ward Smith.]] The central portion is in [[27edo|27edo]], the rest is in 46edo. | ||
[http:// | [http://andrewheathwaite.bandcamp.com/track/rats Rats] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2001%20Rats.mp3 play] by [[Andrew_Heathwaite|Andrew Heathwaite]]. | ||
[http:// | [http://andrewheathwaite.bandcamp.com/track/tumbledown-stew Tumbledown Stew] | ||
[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2012%20Tumbledown%20Stew.mp3 play] by [[Andrew_Heathwaite|Andrew Heathwaite]]. | |||
[http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-1 Hypnocloudsmack 1] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2004%20Hypnocloudsmack%201.mp3 play] by [[Andrew_Heathwaite|Andrew Heathwaite]]. | |||
[http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-2 Hypnocloudsmack 2] | |||
[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2009%20Hypnocloudsmack%202.mp3 play] by [[Andrew_Heathwaite|Andrew Heathwaite]]. | |||
[http://andrewheathwaite.bandcamp.com/track/hypnocloudsmack-3 Hypnocloudsmack 3] | |||
[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2013%20Hypnocloudsmack%203.mp3 play] by [[Andrew_Heathwaite|Andrew Heathwaite]]. | |||
[http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Bach_BWV_1029_E46-Alto-Sax-+-Harpsichord.mp3 Bach BWV 1029 in 46 equal] Claudi Meneghin version | [http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Bach_BWV_1029_E46-Alto-Sax-+-Harpsichord.mp3 Bach BWV 1029 in 46 equal] Claudi Meneghin version | ||