Septimal ennealimma: Difference between revisions

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'''Septimal ennealimma''', '''no-five ennealimma''', or '''tritrizo comma''' is an unnoticeable 7-limit comma defined as 40353607/40310784 and measuring 1.838 cents. It arises as a stack between 9 [[7/6]]<nowiki/>s and 2 octaves.  
'''Septimal ennealimma''', '''no-five ennealimma''', or '''tritrizo comma''' is an unnoticeable 7-limit comma defined as 40353607/40310784 and measuring 1.838 cents. It arises as a stack between 9 [[7/6]]<nowiki/>s and 2 octaves.  


Tempering it out leads to the 7-limit version of the [[ennealimmal temperament]], which is a subset of the [[tritrizo clan]].
Tempering it out leads to the 7-limit version of the [[ennealimmal temperament]], which is a subset of the [[tritrizo clan]]. For EDOs up to circa 3000, it is tempered if and only if the EDO is divisible by 9.

Revision as of 18:53, 7 November 2021

Interval information
Ratio 40353607/40310784
Factorization 2-11 × 3-9 × 79
Monzo [-11 -9 0 9
Size in cents 1.83815¢
Names septimal ennealimma,
no-five ennealimma
Color name tritrizo comma
FJS name [math]\displaystyle{ \text{dddd5}^{7,7,7,7,7,7,7,7,7} }[/math]
Special properties reduced
Tenney height (log2 nd) 50.5309
Weil height (log2 max(n, d)) 50.5324
Wilson height (sopfr(nd)) 112
Open this interval in xen-calc

Septimal ennealimma, no-five ennealimma, or tritrizo comma is an unnoticeable 7-limit comma defined as 40353607/40310784 and measuring 1.838 cents. It arises as a stack between 9 7/6s and 2 octaves.

Tempering it out leads to the 7-limit version of the ennealimmal temperament, which is a subset of the tritrizo clan. For EDOs up to circa 3000, it is tempered if and only if the EDO is divisible by 9.