TAMNAMS/Appendix: Difference between revisions
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==== Machinoid (5L 1s)==== | ==== Machinoid (5L 1s)==== | ||
[[Machine]] is the 5&6 temperament in the 2.9.7.11 subgroup with a comma list of 64/63 and 99/98. | [[Machine]] is the {{nowrap|5 & 6}} temperament in the 2.9.7.11 subgroup with a comma list of 64/63 and 99/98. | ||
This temperament is supported by {{Optimal ET sequence| 5, 6, 11, 12, 16, 17, 22, 23, 27, 28 and 33 }} equal divisions, many of which correspond to both simple tunings ({{nowrap|L:s {{=}} 2:1}}, 3:1, 3:2, etc) and degenerate tunings ({{nowrap|L:s {{=}} 1:1}} or 1:0) for 5L 1s. Non-patent val tunings include {{nowrap|5 + 5 {{=}} 10e|5 + 10e + 12 {{=}} 21be|and 5 + 5 + 5 + 5 + 6 {{=}} 26qe}}; these are mentioned here for demonstrating virtual completeness of the tuning range, as is 33edo to show 11edo's strength as a tuning. | This temperament is supported by {{Optimal ET sequence| 5, 6, 11, 12, 16, 17, 22, 23, 27, 28 and 33 }} equal divisions, many of which correspond to both simple tunings ({{nowrap|L:s {{=}} 2:1}}, 3:1, 3:2, etc) and degenerate tunings ({{nowrap|L:s {{=}} 1:1}} or 1:0) for 5L 1s. Non-patent val tunings include {{nowrap|5 + 5 {{=}} 10e|5 + 10e + 12 {{=}} 21be|and 5 + 5 + 5 + 5 + 6 {{=}} 26qe}}; these are mentioned here for demonstrating virtual completeness of the tuning range, as is 33edo to show 11edo's strength as a tuning. | ||
==== Sephiroid (3L 7s) ==== | ==== Sephiroid (3L 7s) ==== | ||
[[Sephiroth]] is the 3&10 temperament in the 2.5.11.13.17.21 subgroup with commas including 65/64, 85/84, 105/104, 169/168, 170/169, 221/220, 273/272, 275/273. | [[Sephiroth]] is the {{nowrap|3 & 10}} temperament in the 2.5.11.13.17.21 subgroup with commas including 65/64, 85/84, 105/104, 169/168, 170/169, 221/220, 273/272, 275/273. | ||
This temperament is supported by {{Optimal ET sequence| 3, 10, 13, 16, 23, and 26 }} equal divisions, with non-patent val tunings including 6eg, 7e, 19eg, 20e, 29g, 32egq, 33ce, 36c. Like with that of 5L 1s, these represent both simple and degenerate tunings for 3L 7s. Extreme tunings, such as 7e, may lie outside the mos's step ratio spectrum, although such tunings are generally not considered good tunings. | This temperament is supported by {{Optimal ET sequence| 3, 10, 13, 16, 23, and 26 }} equal divisions, with non-patent val tunings including 6eg, 7e, 19eg, 20e, 29g, 32egq, 33ce, 36c. Like with that of 5L 1s, these represent both simple and degenerate tunings for 3L 7s. Extreme tunings, such as 7e, may lie outside the mos's step ratio spectrum, although such tunings are generally not considered good tunings. | ||
==== Dicoid (7L 3s) ==== | ==== Dicoid (7L 3s) ==== | ||
[[Dicot family#Dichotic|Dichotic]] is the 7&10 temperament in the 11-limit with commas including 25/24, 45/44, 55/54, 56/55, 64/63. This is an extension of the 5-limit exotemperament [[dicot]] which tempers 25/24, equating 5/4 and 6/5 into a neutral third sized interval, which is the generator. | [[Dicot family#Dichotic|Dichotic]] is the {{nowrap|7 & 10}} temperament in the 11-limit with commas including 25/24, 45/44, 55/54, 56/55, 64/63. This is an extension of the 5-limit exotemperament [[dicot]] which tempers 25/24, equating 5/4 and 6/5 into a neutral third sized interval, which is the generator. | ||
This temperament is supported by {{Optimal ET sequence| 7, 10, and 17 }} equal divisions, with non-patent val tunings including (but not limited to) {{nowrap|7 + 7 {{=}} 14cd|10 + 10 {{=}} 20e|17 + 7 {{=}} 24cd|and 17 + 10 {{=}} 27ce}}. | This temperament is supported by {{Optimal ET sequence| 7, 10, and 17 }} equal divisions, with non-patent val tunings including (but not limited to) {{nowrap|7 + 7 {{=}} 14cd|10 + 10 {{=}} 20e|17 + 7 {{=}} 24cd|and 17 + 10 {{=}} 27ce}}. | ||