Chromatisma: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Xenllium (talk | contribs)
Created page with "{{Infobox Interval | Icon = | Ratio = 640000000000000000 / 635585924776181463 | Monzo = 22 -32 16 -3 | Cents = 11.98167 | Name = chromatisma, <br>218EDO comma | Color name =..."
 
Xenllium (talk | contribs)
No edit summary
Line 10: Line 10:
}}
}}


The '''chromatisma''', {{monzo|22 -32 16 -3}} = (10/9)<sup>16</sup>/(7/4)<sup>3</sup> is a [[7-limit]] [[comma]] measuring about 12 cents. It is the difference between a stack of three [[7/4]]s and a stack of sixteen [[10/9]]s. It is also known as '''[[218edo|218EDO comma]]''', because 218EDO tempers it out in the 2.9.5.7 subgroup (''not'' in the full [[7-limit]] = 2.3.5.7 subgroup).
The '''chromatisma''', {{monzo|22 -32 16 -3}} = (10/9)<sup>16</sup>/(7/4)<sup>3</sup> is a [[7-limit]] [[comma]] measuring about 12 cents. It is the difference between a stack of three [[7/4]]s and a stack of sixteen [[10/9]]s. It is also known as '''[[218edo|218EDO comma]]''', because 218EDO tempers it out in the 2.9.5.7 subgroup (''not'' in the full [[7-limit]] = 2.3.5.7 subgroup). The name ''chromatisma'' was named after the [[Hemimage temperaments #Chromat|chromat]] temperament by [[User:Xenllium|Xenllium]].


== Temperaments ==
== Temperaments ==
Tempering out this comma leads a number of regular temperaments including [[Hemimage temperaments #Chromat|chromat]]. Chromatismic rank three temperament can be described as the 99&amp;159&amp;277 temperament, which has a generator tuned about 61 cents, three of which gives ~10/9 and sixteen gives ~7/4.
Tempering out this comma leads a number of regular temperaments including chromat. Chromatismic rank three temperament can be described as the 99&amp;159&amp;277 temperament, which has a generator tuned about 61 cents, three of which gives ~10/9 and sixteen gives ~7/4.


'''<font style="font-size: 1.15em">7-limit chromatismic (99&amp;159&amp;277)</font>'''<br>
'''<font style="font-size: 1.15em">7-limit chromatismic (99&amp;159&amp;277)</font>'''<br>

Revision as of 00:34, 5 May 2021

Interval information
Ratio 640000000000000000 / 635585924776181463
Factorization 222 × 3-32 × 516 × 7-3
Monzo [22 -32 16 -3
Size in cents 11.98167¢
Names chromatisma,
218EDO comma
FJS name [math]\displaystyle{ \text{5d}{-3}^{5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}_{7,7,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 118.292
Weil norm (log2 max(n, d)) 118.302
Wilson norm (sopfr(nd)) 241
Open this interval in xen-calc

The chromatisma, [22 -32 16 -3 = (10/9)16/(7/4)3 is a 7-limit comma measuring about 12 cents. It is the difference between a stack of three 7/4s and a stack of sixteen 10/9s. It is also known as 218EDO comma, because 218EDO tempers it out in the 2.9.5.7 subgroup (not in the full 7-limit = 2.3.5.7 subgroup). The name chromatisma was named after the chromat temperament by Xenllium.

Temperaments

Tempering out this comma leads a number of regular temperaments including chromat. Chromatismic rank three temperament can be described as the 99&159&277 temperament, which has a generator tuned about 61 cents, three of which gives ~10/9 and sixteen gives ~7/4.

7-limit chromatismic (99&159&277)
Comma: [22 -32 16 -3
Mapping: [1 0 -1 2], 0 1 2 0], 0 0 3 16]]
POTE generators: ~3/2 = 702.261, ~5/4 = 60.566
Vals: Template:Val list

See also