Fifteen limit tetrads: Difference between revisions

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=5-9-13-15=

The two ''trinidad tetrads'' are 15-limit tetrads with no step size smaller than 10/9 and containing an interval of a fifth; these are the otonal trinidad tetrad, 1-13/10-3/2-9/5, with steps 13/10-15/13-6/5-10/9, and the utonal trinidad tetrad, 1-15/13-3/2-5/3, with steps 15/13-13/10-10/9-6/5. These are just intonation tetrads and do not require tempering in [[The_Archipelago#Subgroup temperaments|trinidad temperament]] or anything else, but they do belong to the same 2.3.5.13 subgroup on which trinidad is defined and are certainly characteristic of the temperament.

The two ''[[trinidad]] [[Tetrad|tetrads]]'' are [[15-limit tonality diamond|15-limit]] tetrads with no step size smaller than [[10/9]] and containing an interval of a fifth; these are the [[Otonality and utonality|otonal]] trinidad tetrad, 1-13/10-3/2-9/5, with steps 13/10-15/13-6/5-10/9, and the [[Otonality and utonality|utonal]] trinidad tetrad, 1-15/13-3/2-5/3, with steps 15/13-13/10-10/9-6/5. These are just intonation tetrads and do not require tempering in [[The_Archipelago#Subgroup temperaments|trinidad temperament]] or anything else, but they do belong to the same 2.3.5.13 [[Just intonation subgroup|subgroup]] on which trinidad is defined and are certainly characteristic of the temperament.

=9-11-13-15=

These two tetrads are the otonal, 1-15/13-15/11-5/3, with steps of 15/13-13/11-11/9-6/5, and the utonal, 1-11/9-13/9-5/3 with steps of 11/9-13/11-15/13-6/5.

[[Category:15-odd-limit]]

[[Category:~~Chords~~]]

[[Category:Tetrads]]

~~[[Category:Tetrad]]~~

~~[[Category:~~Todo~~:add links]]~~

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 =5-9-13-15=
-The two ''trinidad tetrads'' are 15-limit tetrads with no step size smaller than 10/9 and containing an interval of a fifth; these are the otonal trinidad tetrad, 1-13/10-3/2-9/5, with steps 13/10-15/13-6/5-10/9, and the utonal trinidad tetrad, 1-15/13-3/2-5/3, with steps 15/13-13/10-10/9-6/5. These are just intonation tetrads and do not require tempering in [[The_Archipelago#Subgroup temperaments|trinidad temperament]] or anything else, but they do belong to the same 2.3.5.13 subgroup on which trinidad is defined and are certainly characteristic of the temperament.
+The two ''[[trinidad]] [[Tetrad|tetrads]]'' are [[15-limit tonality diamond|15-limit]] tetrads with no step size smaller than [[10/9]] and containing an interval of a fifth; these are the [[Otonality and utonality|otonal]] trinidad tetrad, 1-13/10-3/2-9/5, with steps 13/10-15/13-6/5-10/9, and the [[Otonality and utonality|utonal]] trinidad tetrad, 1-15/13-3/2-5/3, with steps 15/13-13/10-10/9-6/5. These are just intonation tetrads and do not require tempering in [[The_Archipelago#Subgroup temperaments|trinidad temperament]] or anything else, but they do belong to the same 2.3.5.13 [[Just intonation subgroup|subgroup]] on which trinidad is defined and are certainly characteristic of the temperament.
 =9-11-13-15=
 These two tetrads are the otonal, 1-15/13-15/11-5/3, with steps of 15/13-13/11-11/9-6/5, and the utonal, 1-11/9-13/9-5/3 with steps of 11/9-13/11-15/13-6/5.
 [[Category:15-odd-limit]]
-[[Category:Chords]]
+[[Category:Tetrads]]
-[[Category:Tetrad]]
-[[Category:Todo:add links]]
+{{Todo| cleanup | discuss title }}