169/168: Difference between revisions

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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~~.

{{Infobox Interval

| Name = buzurgisma, dhanvantarisma

| Color name = 3oor1, thothoru 1sn,<br>Thothoru comma

| Comma = yes

}}

'''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]].

== ~~Theory~~ ==

== Temperaments ==

~~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 intertwine 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.~~

[[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 '''buzurgic''' or '''dhanvantaric 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]].

Besides tempering, the interval serves as a period in the 13-limit temperament [[oganesson]], where it is equated with 1/118th of the octave.

== Etymology ==

The buzurgisma was named by [[Margo Schulter]] in 2012. The name comes from the buzurg aka buzurk [[genus]] by [[Safi al-Din Urmavi]], which features a neutral second<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105622.html Yahoo! Tuning Group | ''13 limit comma names'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_78630.html Yahoo! Tuning Group | ''Correction to Buzurk'']</ref>.

The dhanvantarisma was presumably named by an unknown guest in 2011 since it seems this wiki was the place where it made its first appearance<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13493 Small comma (Revision as of 15:50, 13 September 2011 by Wikispaces>guest)]</ref>.

It looks as if it “dhavantarisma” might be named after Dhavantari, the Hindu god of Ayurvedic medicine, physician of the gods, and an avatar of Lord Vishnu. It is unclear whether 169/168 has anything to do with [[Indian]] music or with the [[Vishnu]] temperament.{{todo|research|add etymology|comment=figure out whether it does}}

Alternatively, it might be named after the word “dhavanta” from the Pali and Kannada languages. It has multiple meanings including “running away”, “hurrying, especially due to eagerness or anxiety”, “great or unreasoning affection or fondness (for a person or thing)”, or “fatigue, weariness”. {{todo|research|add etymology|comment=figure out whether the comma or its temperaments reflect any of those meanings in any way}}

== Notes ==

[[Category:Buzurgismic]]

[[Category:Commas named after musical traditions]]

[[Category:Commas named after mythology or literature]]

@@ Line 1: / Line 1: @@
-/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.
+{{Infobox Interval
+| Name = buzurgisma, dhanvantarisma
+| Color name = 3oor1, thothoru 1sn,<br>Thothoru comma
+| Comma = yes
+}}
+'''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]].
-== Theory ==
+== Temperaments ==
-/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 intertwine 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.
+[[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 '''buzurgic''' or '''dhanvantaric 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]].
+Besides tempering, the interval serves as a period in the 13-limit temperament [[oganesson]], where it is equated with 1/118th of the octave.
+== Etymology ==
+The buzurgisma was named by [[Margo Schulter]] in 2012. The name comes from the buzurg aka buzurk [[genus]] by [[Safi al-Din Urmavi]], which features a neutral second<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105622.html Yahoo! Tuning Group | ''13 limit comma names'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_78630.html Yahoo! Tuning Group | ''Correction to Buzurk'']</ref>.
+The dhanvantarisma was presumably named by an unknown guest in 2011 since it seems this wiki was the place where it made its first appearance<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13493 Small comma (Revision as of 15:50, 13 September 2011 by Wikispaces>guest)]</ref>.
+It looks as if it “dhavantarisma” might be named after Dhavantari, the Hindu god of Ayurvedic medicine, physician of the gods, and an avatar of Lord Vishnu. It is unclear whether 169/168 has anything to do with [[Indian]] music or with the [[Vishnu]] temperament.{{todo|research|add etymology|comment=figure out whether it does}}
+Alternatively, it might be named after the word “dhavanta” from the Pali and Kannada languages. It has multiple meanings including “running away”, “hurrying, especially due to eagerness or anxiety”, “great or unreasoning affection or fondness (for a person or thing)”, or “fatigue, weariness”. {{todo|research|add etymology|comment=figure out whether the comma or its temperaments reflect any of those meanings in any way}}
+== Notes ==
+[[Category:Buzurgismic]]
+[[Category:Commas named after musical traditions]]
+[[Category:Commas named after mythology or literature]]