169/168: Difference between revisions
13/12 and 14/13 are closer to neutral seconds than semitones. The other pair lacks representativeness, replaced with 21/13 and 13/8 |
The chord described in the page isn't specific to 19edo, so I'm not sure why that's mentioned. +temperaments |
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'''169/168''', the '''buzurgisma''' or the '''dhanvantarisma''' is a [[superparticular]] ratio measuring about 10.3 [[cent]]s. It is the difference between the neutral seconds of [[13/12]] and [[14/13]] as well as between the neutral sixths of [[21/13]] and [[13/8]]. | '''169/168''', the '''buzurgisma''' or the '''dhanvantarisma''' is a [[superparticular]] ratio measuring about 10.3 [[cent]]s. It is the difference between the neutral seconds of [[13/12]] and [[14/13]] as well as between the neutral sixths of [[21/13]] and [[13/8]]. | ||
== Temperaments == | |||
[[Tempering out]] this comma in the 13-limit gives the rank-5 '''buzurgismic''' or '''dhanvantarismic temperament'''. Tempering it out in the 2.3.7.13 [[subgroup]] gives the rank-3 '''buzurg''' or '''dhanvantari temperament'''. In such systems, 13/12 and 14/13 are equated, enabling [[buzurgismic chords|buzurgismic or dhanvantarismic chords]]. This is very comparable to tempering out of [[121/120]], which results in [[biyatismic]], in which [[11/10]] is equated with [[12/11]]. | |||
169/168 is tempered out in the 1-16/13-[[4/3]]-[[64/39]] chord, with the steps [[16/13]]-13/12-16/13-[[39/32]], which is symmetrical (it is the same when inverted). It intertwines two 4/3's between the 1st and 3rd, and 2nd and 4th notes. Tempering out 169/168 means that 14/13 can appear in this chord as well as 13/12. | |||
[[Category:Buzurgismic]] | [[Category:Buzurgismic]] | ||