Fifteen limit tetrads: Difference between revisions

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=5-9-13-15=

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.

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.

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:Tetrad]]

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 =5-9-13-15=
-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.
+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.
+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:Tetrad]]