99/98: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
TallKite (talk | contribs)
autopatrolled, Sysops
3,990 edits
mNo edit summary
Rework for the temperaments section
Line 4: Line 4:
| Comma = yes
| Comma = yes
}}
}}
'''99/98''', or the '''mothwellsma''' (17.6 [[cent]]s in size), represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. If tempered, it leads to the [[Mothwellsmic triad]], and is related to 11-limit [[orwell]], as a generator between 7/6 and (11/8)<sup>1/2</sup> – is befitting of orwell.
'''99/98''', or the '''mothwellsma''' (17.6 [[cent]]s in size), represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that (11/8)<sup>1/2</sup> = (7/6)(99/98)<sup>1/2</sup> and that (7/6)99/98 = [[33/28]], which is the fifth complement of 14/11.


(Note that (11/8)<sup>1/2</sup> = 7/6 × (99/98)<sup>1/2</sup> and that 7/6 × 99/98 = [[33/28]], which is the fifth complement of 14/11.)
== Temperaments ==
Tempering out this comma alone in the 11-limit leads to the '''mothwellsmic temperament''' (→ [[Catalog of rank-4 temperaments #Mothwellsmic (99/98)]]) and enables [[mothwellsmic chords]]. It is related to 11-limit [[orwell]], as a generator between 7/6 and (11/8)<sup>1/2</sup> is befitting of orwell.


== See also ==
== See also ==

Revision as of 09:25, 12 October 2024

Interval information
Ratio 99/98
Factorization 2-1 × 32 × 7-2 × 11
Monzo [-1 2 0 -2 1⟩
Size in cents 17.57613¢
Name mothwellsma
Color name 1orr-2, loruru negative
2nd, Loruru comma
FJS name [math]\displaystyle{ \text{m}{-2}^{11}_{7,7} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 13.2441
Weil height (log2 max(n, d)) 13.2587
Wilson height (sopfr(nd)) 33
Comma size small
Open this interval in xen-calc

99/98, or the mothwellsma (17.6 cents in size), represents the difference between the 9/7 and 14/11 supermajor thirds, or the difference between two 7/6 subminor thirds and one 11/8 semi-augmented fourth. Note that (11/8)1/2 = (7/6)(99/98)1/2 and that (7/6)99/98 = 33/28, which is the fifth complement of 14/11.

Temperaments

Tempering out this comma alone in the 11-limit leads to the mothwellsmic temperament (→ Catalog of rank-4 temperaments #Mothwellsmic (99/98)) and enables mothwellsmic chords. It is related to 11-limit orwell, as a generator between 7/6 and (11/8)1/2 is befitting of orwell.

See also

Retrieved from "https://en.xen.wiki/index.php?title=99/98&oldid=159596"