Star and Nova
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2012-09-03 16:33:46 UTC.
- The original revision id was 361726612.
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Original Wikitext content:
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. 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.
Original HTML content:
<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 /> <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.<br /> <br /> 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.</body></html>