800/729: Difference between revisions

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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 '''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]].


Tempering it out leads to rank-2 [[la brea]] temperament, which splits the octave into two ~27/20 intervals and generally tempers 3/2 bery 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 from 6/5 are tempered to one and a half octaves. Reasonable higher-limit extensions to this temperent probably exist.
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 from 6/5 are tempered to one and a half octaves. Reasonable higher-limit extensions to this temperent probably exist.


== Etymology ==
== Etymology ==


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.
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.

Revision as of 08:46, 11 August 2024

Interval information
Ratio 800/729
Factorization 25 × 3-6 × 52
Monzo [5 -6 2
Size in cents 160.8974¢
Name la brea second
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 la brea 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.

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 Zarlino generator sequence starting from 6/5 are tempered to one and a half octaves. Reasonable higher-limit extensions to this temperent probably exist.

Etymology

This interval was named by Tristan Bay in August 2024 in reference to the taric MOS scale pattern that can be formed from tempering it out.