Generator sequence: Difference between revisions
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== Series arising from well-formed generator sequences == | == Series arising from well-formed generator sequences == | ||
Only CS sizes at least 5 are listed. | Only CS sizes at least 5 are listed. Todo: check for larger CS sizes. | ||
* The Zarlino series, AGS(5/4, 6/5): 5, 7, 10, 17, 24, 41, 65 | * The Zarlino series, AGS(5/4, 6/5): 5, 7, 10, 17, 24, 41, 65 | ||
** Other scales with the same AGS structure of two thirds adding up to 3/2 share the same CS sizes, including undecimal Zarlino (AGS(11/9, 27/22)), and Neogothic Zarlino (AGS(14/11, 13/11) with [[364/363]] tempered), although the latter may break at higher sizes depending on how the intervals are tuned. | ** Other scales with the same AGS structure of two thirds adding up to 3/2 share the same CS sizes, including undecimal Zarlino (AGS(11/9, 27/22)), and Neogothic Zarlino (AGS(14/11, 13/11) with [[364/363]] tempered), although the latter may break at higher sizes depending on how the intervals are tuned. | ||
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* The Dwyn series: AGS(25/24 21/20 22/21 23/22 24/23 21/20 22/21 23/22 24/23): 15, 16, 31, 46 | * The Dwyn series: AGS(25/24 21/20 22/21 23/22 24/23 21/20 22/21 23/22 24/23): 15, 16, 31, 46 | ||
* AGS(13/11, 16/13, 77/64, 13/11, 16/13, 33/28): 7, 11, 15, 19 | * AGS(13/11, 16/13, 77/64, 13/11, 16/13, 33/28): 7, 11, 15, 19 | ||
* AGS(16/13, 5/4, 5/4, 31/25, 39/31): 7, 10, 13, 16, 19, 22, 41 | * AGS(16/13, 5/4, 5/4, 31/25, 39/31): 7, 10, 13, 16, 19, 22, 41 | ||
* AGS(7/5, 19/14, 80/57) | * AGS(7/5, 19/14, 80/57) | ||
* AGS(19/14, 51/38, 23/17, 63/46, 19/14, 51/38, 23/17, 896/621) | * AGS(19/14, 51/38, 23/17, 63/46, 19/14, 51/38, 23/17, 896/621) | ||