800/729: Difference between revisions

Line 1:

{{Infobox Interval

| Name = ~~la brea~~ second

| Name = diptolemaic major second, supersharp comma

| Color name = sayoyo 2nd, syy2

| Comma = yes

}}

The '''~~la brea~~ second''' is a 5-limit interval measuring about 161~~[[Cent|¢]]~~. It is the difference between [[27/20]] and [[40/27]], as well as [[9/8]] lowered by two [[81/80|syntonic commas]].

The '''diptolemaic major second''' is a [[5-limit]] [[interval]] measuring about 161{{cent}}. It is the difference between [[27/20]] and [[40/27]], as well as [[9/8]] lowered by two [[81/80|syntonic commas]].

~~Tempering~~ it out leads to rank-2 [[~~la brea~~]] temperament, which splits the octave into two ~27/20 ~~intervals~~ and generally tempers 3/2 very sharp (by more than 20¢). This means that five generators from the [[generator sequence#JI scales obtained from guided generator sequences|Zarlino generator sequence]] starting with 6/5 are tempered to one and a half octaves. ~~Reasonable higher~~-limit ~~extensions~~ to ~~this temperent probably exist~~.

== Temperaments ==

If used as a [[comma]] to be tempered out, this interval may be called the '''supersharp comma''', and tempering it out leads to the rank-2 [[supersharp]] temperament, which splits the octave into two 27/20~40/27 semioctaves and generally tempers 3/2 very sharp (by more than 20¢). This means that five generators from the [[generator sequence #JI scales obtained from guided generator sequences|Zarlino generator sequence]] starting with 6/5 are tempered to one and a half octaves. The only reasonable 7-limit [[extension]] adds [[50/49]] to the comma list, taking advantage of the existing semioctave.

== Etymology ==

The name ''supersharp'' has been around no later than 2010<ref>[https://en.xen.wiki/index.php?title=Proposed_names_for_rank_2_temperaments&oldid=24809 Xenharmonic Wiki | Proposed names for rank 2 temperaments (Revision as of 22:54, 11 June 2010 by Wikispaces>Mizarian)]</ref>, coming from the fact that a very sharp fifth is a generator for the temperament.

~~This interval was named by~~ [[User:Tristanbay|Tristan Bay]] in August 2024 in reference to the ''taric'' [[~~MOS~~ scale]] pattern that can be formed from tempering it out.

== Notes ==

[[User:Tristanbay|Tristan Bay]] proposes the name ''la brea'' in August 2024 in reference to the ''taric'' [[mos scale]] pattern that can be formed from tempering it out.

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = la brea second
+| Name = diptolemaic major second, supersharp comma
 | Color name = sayoyo 2nd, syy2
 | Comma = yes
 }}
-The '''la brea second''' is a 5-limit interval measuring about 161[[Cent|¢]]. It is the difference between [[27/20]] and [[40/27]], as well as [[9/8]] lowered by two [[81/80|syntonic commas]].
+The '''diptolemaic major second''' is a [[5-limit]] [[interval]] measuring about 161{{cent}}. It is the difference between [[27/20]] and [[40/27]], as well as [[9/8]] lowered by two [[81/80|syntonic commas]].
-Tempering it out leads to rank-2 [[la brea]] temperament, which splits the octave into two ~27/20 intervals and generally tempers 3/2 very sharp (by more than 20¢). This means that five generators from the [[generator sequence#JI scales obtained from guided generator sequences|Zarlino generator sequence]] starting with 6/5 are tempered to one and a half octaves. Reasonable higher-limit extensions to this temperent probably exist.
+== Temperaments ==
+If used as a [[comma]] to be tempered out, this interval may be called the '''supersharp comma''', and tempering it out leads to the rank-2 [[supersharp]] temperament, which splits the octave into two 27/20~40/27 semioctaves and generally tempers 3/2 very sharp (by more than 20¢). This means that five generators from the [[generator sequence #JI scales obtained from guided generator sequences|Zarlino generator sequence]] starting with 6/5 are tempered to one and a half octaves. The only reasonable 7-limit [[extension]] adds [[50/49]] to the comma list, taking advantage of the existing semioctave.
 == Etymology ==
+The name ''supersharp'' has been around no later than 2010<ref>[https://en.xen.wiki/index.php?title=Proposed_names_for_rank_2_temperaments&oldid=24809 Xenharmonic Wiki | Proposed names for rank 2 temperaments (Revision as of 22:54, 11 June 2010 by Wikispaces>Mizarian)]</ref>, coming from the fact that a very sharp fifth is a generator for the temperament.
-This interval was named by [[User:Tristanbay|Tristan Bay]] in August 2024 in reference to the ''taric'' [[MOS scale]] pattern that can be formed from tempering it out.
+== Notes ==
+[[User:Tristanbay|Tristan Bay]] proposes the name ''la brea'' in August 2024 in reference to the ''taric'' [[mos scale]] pattern that can be formed from tempering it out.