1053/1024: Difference between revisions

'''1053/1024''', the '''tridecimal quartertone''', '''tridecimal comma''' or '''Hunt minor submediant comma''', is a [[13-limit]] interval of about 48.3 [[cent]]s. It is the interval between the Pythagorean major third of [[81/64]] and the tridecimal neutral third of [[16/13]]. It can be considered a type of quartertone. It is [[4096/4095]] smaller than [[36/35]], and [[352/351]] smaller than [[33/32]].  

In the [[Sagittal]] system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal | /|) }} and is called the '''13 medium diesis''', or '''13M''' for short, because the simplest interval it notates is 13/1 (equiv. 13/8), as for example in A-F{{nbhsp}}{{sagittal | /|) }}. The primary role of {{ sagittal | /|) }} is [[36/35#Sagittal notation | 36/35]] (35M up). The downward version is called '''1/13M''' or '''13M down''' and is represented (in a secondary role) by {{sagittal| \!) }}.

1053/1024 is significant in [[Functional Just System]] as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to [[64/63]] and [[33/32]] for septimal and undecimal, respectively. However, in [[Helmholtz-Ellis notation]], that role is taken by [[27/26]].