Star and Nova: Difference between revisions
Wikispaces>genewardsmith **Imported revision 361726612 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 361817448 - 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> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-03 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-03 23:48:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>361817448</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Star is an eight-note tempered scale, with something of the sound of the [[octatonic scale]]; however it is less regular and closer to just intonation. Star can be reached from various starting points, one of which is a 5-limit [[Fokker blocks|Fokker block]] which serves as a [[transversal]] for star. The block in question is [[smithgw_star]], 25/24-6/5-5/4-36/25-3/2-5/3-9/5-2/1, which consists of a chain of minor thirds 5/3-1-6/5-36/35 and that chain translated by 5/4, and which has three major and three minor triads. | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Star is an eight-note tempered scale, with something of the sound of the [[octatonic scale]]; however it is less regular and closer to just intonation. Star can be reached from various starting points, one of which is a 5-limit [[Fokker blocks|Fokker block]] which serves as a [[transversal]] for star. The block in question is [[smithgw_star]], 25/24-6/5-5/4-36/25-3/2-5/3-9/5-2/1, which consists of a chain of minor thirds 5/3-1-6/5-36/35 and that chain translated by 5/4, and which has three major and three minor triads. | ||
By tempering out 126/125, leading to [[Starling family#x7-limit starling|7-limit starling temperament]] we add the 7-limit intervals 8/7, 7/6, 7/5 and their inversions to the mix, and by tempering by 385/384 also, leading to [[Starling family#x7-limit starling-11-limit|11-limit starling]], the 11/8 interval also. There is no significant tuning advantage to 11-limit starling, a planar temperament, over the linear temperament [[Starling temperaments#Valentine temperament-11-limit|valentine]], so we may consider star to be a scale of valentine. In valentine, with generator a tempered 21/20 of 78 cents, the notes of star are -4, 0, 1, 4, 5, 8, 9 and 13 generators. | By tempering out 126/125, leading to [[Starling family#x7-limit starling|7-limit starling temperament]] we add the 7-limit intervals 8/7, 7/6, 7/5 and their inversions to the mix, and by tempering by 385/384 also, leading to [[Starling family#x7-limit starling-11-limit|11-limit starling]], the 11/8 interval also. There is no significant tuning advantage to 11-limit starling, a planar temperament, over the linear temperament [[Starling temperaments#Valentine temperament-11-limit|valentine]], so we may consider star to be a scale of valentine. In valentine, with generator a tempered 21/20 of 78 cents, the notes of star are -4, 0, 1, 4, 5, 8, 9 and 13 generators; in the ordering of the scale itself, that's 0, 1, 4, 5, 8, 9, -4, 13, 0. | ||
Since there are a finite number of 11-limit 8-note [[lesfip scales]], we may consider the [[star-lesfip|lesfip version of star]], star-lesfip, to be canonical. It can be reached from a variety of starting points. Lesfipping the 5-limit transversal in the range 14 to 17 cents of tolerance leads to star; so does lesfipping the 46et version in the range from 9 to 17 cents or the 77et version in the range 6 to 16 cents.</pre></div> | Since there are a finite number of 11-limit 8-note [[lesfip scales]], we may consider the [[star-lesfip|lesfip version of star]], star-lesfip, to be canonical. It can be reached from a variety of starting points. Lesfipping the 5-limit transversal in the range 14 to 17 cents of tolerance leads to star; so does lesfipping the 46et version in the range from 9 to 17 cents or the 77et version in the range 6 to 16 cents. Another tuning for star, not very different, is [[star|star in 77et]]; 77 giving the optimal patent val for both 11-limit starling and valentine. | ||
Star has sixteen [[dyadic chords|dyadic tetrads]], of eleven different types, which are among those listed on the [[chords of valentine]] page. In terms of what's lsted on that page, star has one otonal tetrad, given in the form 1-8/7-10/7-12/7 but better known as 1-5/4-3/2-7/4; one 1-6/5-3/2-12/7 utonal tetrad; and one each of the [[keenanismic chords|keenanismic tetrads]] 1-8/7-11/8-12/7, 1-6/5-11/8-12/7, 1-5/4-10/7-12/7 and 1-5/4-3/2-12/7. It also has two each of the starling tetrad, the tradition diminished seventh chord of meantone; the ambitonal [[just added sixth chord]] 1-6/5-3/2-9/5; and the three 9-limit starling tetrads 1-6/5-10/7-9/5, 1-5/4-10/7-9/5 and 1-5/4-3/2-9/5. | |||
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<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Star and Nova</title></head><body>Star is an eight-note tempered scale, with something of the sound of the <a class="wiki_link" href="/octatonic%20scale">octatonic scale</a>; however it is less regular and closer to just intonation. Star can be reached from various starting points, one of which is a 5-limit <a class="wiki_link" href="/Fokker%20blocks">Fokker block</a> which serves as a <a class="wiki_link" href="/transversal">transversal</a> for star. The block in question is <a class="wiki_link" href="/smithgw_star">smithgw_star</a>, 25/24-6/5-5/4-36/25-3/2-5/3-9/5-2/1, which consists of a chain of minor thirds 5/3-1-6/5-36/35 and that chain translated by 5/4, and which has three major and three minor triads.<br /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Star and Nova</title></head><body>Star is an eight-note tempered scale, with something of the sound of the <a class="wiki_link" href="/octatonic%20scale">octatonic scale</a>; however it is less regular and closer to just intonation. Star can be reached from various starting points, one of which is a 5-limit <a class="wiki_link" href="/Fokker%20blocks">Fokker block</a> which serves as a <a class="wiki_link" href="/transversal">transversal</a> for star. The block in question is <a class="wiki_link" href="/smithgw_star">smithgw_star</a>, 25/24-6/5-5/4-36/25-3/2-5/3-9/5-2/1, which consists of a chain of minor thirds 5/3-1-6/5-36/35 and that chain translated by 5/4, and which has three major and three minor triads.<br /> | ||
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By tempering out 126/125, leading to <a class="wiki_link" href="/Starling%20family#x7-limit starling">7-limit starling temperament</a> we add the 7-limit intervals 8/7, 7/6, 7/5 and their inversions to the mix, and by tempering by 385/384 also, leading to <a class="wiki_link" href="/Starling%20family#x7-limit starling-11-limit">11-limit starling</a>, the 11/8 interval also. There is no significant tuning advantage to 11-limit starling, a planar temperament, over the linear temperament <a class="wiki_link" href="/Starling%20temperaments#Valentine temperament-11-limit">valentine</a>, so we may consider star to be a scale of valentine. In valentine, with generator a tempered 21/20 of 78 cents, the notes of star are -4, 0, 1, 4, 5, 8, 9 and 13 generators.<br /> | By tempering out 126/125, leading to <a class="wiki_link" href="/Starling%20family#x7-limit starling">7-limit starling temperament</a> we add the 7-limit intervals 8/7, 7/6, 7/5 and their inversions to the mix, and by tempering by 385/384 also, leading to <a class="wiki_link" href="/Starling%20family#x7-limit starling-11-limit">11-limit starling</a>, the 11/8 interval also. There is no significant tuning advantage to 11-limit starling, a planar temperament, over the linear temperament <a class="wiki_link" href="/Starling%20temperaments#Valentine temperament-11-limit">valentine</a>, so we may consider star to be a scale of valentine. In valentine, with generator a tempered 21/20 of 78 cents, the notes of star are -4, 0, 1, 4, 5, 8, 9 and 13 generators; in the ordering of the scale itself, that's 0, 1, 4, 5, 8, 9, -4, 13, 0.<br /> | ||
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Since there are a finite number of 11-limit 8-note <a class="wiki_link" href="/lesfip%20scales">lesfip scales</a>, we may consider the <a class="wiki_link" href="/star-lesfip">lesfip version of star</a>, star-lesfip, to be canonical. It can be reached from a variety of starting points. Lesfipping the 5-limit transversal in the range 14 to 17 cents of tolerance leads to star; so does lesfipping the 46et version in the range from 9 to 17 cents or the 77et version in the range 6 to 16 cents. Another tuning for star, not very different, is <a class="wiki_link" href="/star">star in 77et</a>; 77 giving the optimal patent val for both 11-limit starling and valentine.<br /> | |||
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Star has sixteen <a class="wiki_link" href="/dyadic%20chords">dyadic tetrads</a>, of eleven different types, which are among those listed on the <a class="wiki_link" href="/chords%20of%20valentine">chords of valentine</a> page. In terms of what's lsted on that page, star has one otonal tetrad, given in the form 1-8/7-10/7-12/7 but better known as 1-5/4-3/2-7/4; one 1-6/5-3/2-12/7 utonal tetrad; and one each of the <a class="wiki_link" href="/keenanismic%20chords">keenanismic tetrads</a> 1-8/7-11/8-12/7, 1-6/5-11/8-12/7, 1-5/4-10/7-12/7 and 1-5/4-3/2-12/7. It also has two each of the starling tetrad, the tradition diminished seventh chord of meantone; the ambitonal <a class="wiki_link" href="/just%20added%20sixth%20chord">just added sixth chord</a> 1-6/5-3/2-9/5; and the three 9-limit starling tetrads 1-6/5-10/7-9/5, 1-5/4-10/7-9/5 and 1-5/4-3/2-9/5.</body></html></pre></div> | |||