99/98: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = mothwellsma
| Ratio = 99/98
| Color name = 1orr-2, loruru negative<br>2nd, Loruru comma
| Monzo = -1 2 0 -2 1
| Comma = yes
| Cents = 17.57613
| Name = Mothwellsma
| Color name = 1orr-2, loruru comma
| FJS name = m-2<sup>11</sup><sub>49</sub>  
| Sound =  
}}
}}
'''99/98''', or the '''Mothwellsma''' (17.576 [[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 14/11 - ''but closer to 7/6'' - is befitting of Orwell.
'''99/98''', or the '''mothwellsma''', is a [[small comma|small]] [[11-limit]] [[comma]] of 17.6 [[cent]]s in size. It 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 = (7/6)<sup>2</sup>(99/98) 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.
 
== Etymology ==
This comma's name comes from a contraction of ''mothra'' and ''orwell'', two of the rank-2 temperaments that temper out the comma.  


== See also ==
== See also ==
 
* [[99/49]] – the same interval but one octave higher
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
* [[Comma]]
[[Category:11-limit]]
[[Category:Small comma]]
[[Category:Interval ratio]]
[[Category:Superparticular]]


[[Category:Todo:expand]]
[[Category:Mothwellsmic]]
[[Category:Commas named by combining multiple temperament names]]

Latest revision as of 14:56, 29 April 2025

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, is a small 11-limit comma of 17.6 cents in size. It 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 = (7/6)2(99/98) 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.

Etymology

This comma's name comes from a contraction of mothra and orwell, two of the rank-2 temperaments that temper out the comma.

See also

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