24576/24565: Difference between revisions

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'''24576/24565''', the '''mavka comma''', is an unnoticeable 17-limit comma that represents the difference between two adjacent square superparticulars – [[289/288]] and [[256/255]]. In addition, it is the amount by which a stack of three instances of [[17/16]] falls short of a [[6/5]] minor third, and, the amount by which a stack of two instances of [[128/85]] octave-reduced exceeds [[17/15]].
'''24576/24565''', the '''mavka comma''', is an unnoticeable 17-limit comma that represents the difference between two adjacent [[square superparticular]]s – [[289/288]] and [[256/255]], [[Square superparticular#Sk/S(k + 1) (ultraparticulars)|therefore]], it is the amount by which a stack of three [[17/16]]'s fall short of a [[6/5]] minor third. It is also the amount by which a stack of two [[128/85]]'s octave-reduced exceeds [[17/15]].


It can be factored into [[4096/4095]] × [[4914/4913]].  
It can be factored into [[4096/4095]] × [[4914/4913]].  

Revision as of 04:51, 12 August 2022

Interval information
Ratio 24576/24565
Factorization 213 × 3 × 5-1 × 17-3
Monzo [13 1 -1 0 0 0 -3
Size in cents 0.7750585¢
Name mavka comma
Color name trisu-agu negative 2nd
FJS name [math]\displaystyle{ \text{d}{-2}_{5,17,17,17} }[/math]
Special properties reduced
Tenney norm (log2 nd) 29.1693
Weil norm (log2 max(n, d)) 29.1699
Wilson norm (sopfr(nd)) 85
Open this interval in xen-calc

24576/24565, the mavka comma, is an unnoticeable 17-limit comma that represents the difference between two adjacent square superparticulars289/288 and 256/255, therefore, it is the amount by which a stack of three 17/16's fall short of a 6/5 minor third. It is also the amount by which a stack of two 128/85's octave-reduced exceeds 17/15.

It can be factored into 4096/4095 × 4914/4913.

Temperaments

By tempering it out, the rank-6 mavka temperament is defined.

Subgroup: 2.3.5.7.11.13.17

Mapping:

[ ⟨ 1 0 1 0 0 0 4 ]

⟨ 0 1 1 0 0 0 0 ]

⟨ 0 0 3 0 0 0 -1 ]

⟨ 0 0 0 1 0 0 0 ]

⟨ 0 0 0 0 1 0 0 ]

⟨ 0 0 0 0 0 1 0 ] ⟩

Template:Val list.