169/168: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = Thothoru
| Name = buzurgisma, dhanvantarisma
| Color name = 3oor1, thothoru 1sn,<br>Thothoru comma
| Color name = 3oor1, thothoru 1sn,<br>Thothoru comma
}}
}}
'''169/168''', is a [[superparticular]] ratio measuring about 10.3 cents. It is the difference between [[13/12]] and [[14/13]] semitones, and also between [[224/169]] and [[4/3]] perfect fourths.  
'''169/168''', the '''buzurgisma''' or the '''dhanvantarisma''' is a [[superparticular]] ratio measuring about 10.3 [[cent]]s. It is the difference between [[13/12]] and [[14/13]] semitones, and also between [[224/169]] and [[4/3]] perfect fourths.  


== Theory ==
169/168 is tempered out in a 13-0-2-8 chord of [[19edo]], which is a symmetrical relative to itself - it is the same when inverted. Such a chord consists of a stack of [[16/13]] - [[13/12]] - [[16/13]], which also intertwines two 4/3s 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.
169/168 is tempered out in a 13-0-2-8 chord of [[19edo]], which is a symmetrical relative to itself - it is the same when inverted. Such a chord consists of a stack of [[16/13]] - [[13/12]] - [[16/13]], which also intertwines two 4/3s 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]]

Revision as of 07:33, 11 January 2023

Interval information
Ratio 169/168
Factorization 2-3 × 3-1 × 7-1 × 132
Monzo [-3 -1 0 -1 0 2
Size in cents 10.27442¢
Names buzurgisma,
dhanvantarisma
Color name 3oor1, thothoru 1sn,
Thothoru comma
FJS name [math]\displaystyle{ \text{d1}^{13,13}_{7} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 14.7932
Weil height (log2 max(n, d)) 14.8018
Wilson height (sopfr(nd)) 42
Open this interval in xen-calc

169/168, the buzurgisma or the dhanvantarisma is a superparticular ratio measuring about 10.3 cents. It is the difference between 13/12 and 14/13 semitones, and also between 224/169 and 4/3 perfect fourths.

169/168 is tempered out in a 13-0-2-8 chord of 19edo, which is a symmetrical relative to itself - it is the same when inverted. Such a chord consists of a stack of 16/13 - 13/12 - 16/13, which also intertwines two 4/3s 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.