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{{Infobox Interval
{{Infobox Interval
| Name = la brea second
| Name = diptolemaic major second, supersharp comma
| Color name = sayoyo 2nd, syy2
| Color name = sayoyo 2nd, syy2
| Comma = yes
| 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 (sharper than 3\5).


== Etymology ==
== 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.
[[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.
 
== Notes ==
 
[[Category:Commas named for their regular temperament properties]]

Latest revision as of 06:36, 3 November 2024

Interval information
Ratio 800/729
Factorization 25 × 3-6 × 52
Monzo [5 -6 2
Size in cents 160.8974¢
Names diptolemaic major second,
supersharp comma
Color name sayoyo 2nd, syy2
FJS name [math]\displaystyle{ \text{M2}^{5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 19.1536
Weil norm (log2 max(n, d)) 19.2877
Wilson norm (sopfr(nd)) 38
Comma size large
Open this interval in xen-calc

The diptolemaic major second is a 5-limit interval measuring about 161 ¢. It is the difference between 27/20 and 40/27, as well as 9/8 lowered by two syntonic commas.

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 (sharper than 3\5).

Etymology

The name supersharp has been around no later than 2010[1], coming from the fact that a very sharp fifth is a generator for the temperament.

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.

Notes