49/45: Difference between revisions

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Discourage this name, which invokes the 11-limit for a 7-limit interval. + how to conceptualize it in the 7-limit
 
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{{Infobox Interval
{{Infobox Interval
| Name = swetismic neutral second
| Name =  
| Color name = zzg3, zozogu 3rd
| Color name = zzg3, zozogu 3rd
}}
}}
'''49/45''' is a [[7-limit]] interval. It appears as the interval between [[15/14]] and [[7/6]] as well as [[9/7]] and [[7/5]], and their [[octave complement|inversions]]. It therefore functions as a diminished third, flat of the [[65536/59049|Pythagorean diminished third]] by a [[septimal comma]] and an [[aberschisma]]. Alternatively, if viewed as a second, it is flat of the [[9/8|whole tone]] by 405/392, the [[greenwoodma]].


'''49/45''', the '''swetismic neutral second''', is [[540/539]] (3.2 cents) flatter than [[12/11]], and appears in [[7-limit]] scales as the interval between [[15/14]] and [[7/6]] as well as [[9/7]] and [[7/5]], and their inversions. It therefore represents one of the ways approximate [[11-limit]] harmony appears in 7-limit scales.
== Terminology ==
This interval has been called the ''swetismic neutral second'', viewed as being fudged from [[12/11]] by [[540/539]] (3.21 cents), which  represents one of the ways approximate [[11-limit]] harmony appears in 7-limit scales.  


[[Category:Second]]
[[Category:Second]]
[[Category:Neutral second]]
[[Category:Neutral second]]
[[Category:Swetismic]]
[[Category:Third]]
[[Category:Diminished third]]

Latest revision as of 10:09, 20 July 2026

Interval information
Ratio 49/45
Factorization 3-2 × 5-1 × 72
Monzo [0 -2 -1 2
Size in cents 147.4281¢
Name(s) missing ? 
Color name zzg3, zozogu 3rd
FJS name [math]\displaystyle{ \text{d3}^{7,7}_{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 11.1066
Weil norm (log2 max(n, d)) 11.2294
Wilson norm (sopfr(nd)) 25
Open this interval in xen-calc

49/45 is a 7-limit interval. It appears as the interval between 15/14 and 7/6 as well as 9/7 and 7/5, and their inversions. It therefore functions as a diminished third, flat of the Pythagorean diminished third by a septimal comma and an aberschisma. Alternatively, if viewed as a second, it is flat of the whole tone by 405/392, the greenwoodma.

Terminology

This interval has been called the swetismic neutral second, viewed as being fudged from 12/11 by 540/539 (3.21 cents), which represents one of the ways approximate 11-limit harmony appears in 7-limit scales.