Schismatic family: Difference between revisions

The arithmetic formula is basically of little value compared to an intro to notation
Correction (pontiac's 7-limit normal comma isn't the nanisma)
Line 36: Line 36:
* [[#Grackle]] adds {{monzo| -44 26 0 1 }},  
* [[#Grackle]] adds {{monzo| -44 26 0 1 }},  
* [[#Schism]] adds [[64/63|{{monzo| 6 -2 0 -1 }}]],  
* [[#Schism]] adds [[64/63|{{monzo| 6 -2 0 -1 }}]],  
* [[#Pontiac]] adds [[nanisma|{{monzo| -59 39 0 -1 }}]].  
* [[#Pontiac]] adds {{monzo| -59 39 0 -1 }}.  
Those all have a fifth as generator.  
Those all have a fifth as generator.  


Line 516: Line 516:
{{Main| Pontiac }}
{{Main| Pontiac }}


Pontiac tempers out the [[nanisma]], rendering a very accurate 7-limit microtemperament. The 7/4 is found at +39 fifths, represented by the quintuple augmented third (C-Exx#), or triple-up major sixth (C-^<sup>3</sup>A).  
Pontiac tempers out the [[ragisma]], rendering a very accurate 7-limit microtemperament. The 7/4 is found at +39 fifths, represented by the quintuple augmented third (C-Exx#), or triple-up major sixth (C-^<sup>3</sup>A).  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 546: Line 546:


=== Helenoid ===
=== Helenoid ===
The helenoid temperament (53 &amp; 118) is closely related to the helenus temperament, but with the [[4375/4374|ragisma]] rather than the [[225/224|marvel comma]] tempered out.
The helenoid temperament (53 &amp; 118) is closely related to the helenus temperament, but with the ragisma rather than the [[225/224|marvel comma]] tempered out.


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11