Fifteen limit tetrads: Difference between revisions
Jump to navigation
Jump to search
m Added links (as requested by the to:do notice) |
m Recategorize; +todo |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
=5-9-13-15= | =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- | 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= | =9-11-13-15= | ||
These two tetrads are the otonal, 1-15/13- | 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:15-odd-limit]] | ||
[[Category: | [[Category:Tetrads]] | ||
{{Todo| cleanup | discuss title }} | |||
Latest revision as of 12:01, 23 May 2023
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 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.
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.