Chromium: Difference between revisions
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[[Category:Landscape microtemperaments]] | [[Category:Landscape microtemperaments]] | ||
'''Chromium''' is a rank-2 temperament which has a period of 1/24th of the octave and a generator of [[10/7]] (dark) or [[7/5]] (bright). It is named after the 24th chemical element. | '''Chromium''' is a rank-2 temperament which has a period of 1/24th of the octave and a generator of [[10/7]] (dark) or [[7/5]] (bright). It is named after the 24th chemical element. | ||
For technical data see: [[Landscape microtemperaments#Chromium]] | |||
== Theory == | == Theory == | ||
Revision as of 02:34, 18 December 2022
Chromium is a rank-2 temperament which has a period of 1/24th of the octave and a generator of 10/7 (dark) or 7/5 (bright). It is named after the 24th chemical element.
For technical data see: Landscape microtemperaments#Chromium
Theory
In the 17-limit, chromium has a comma basis {936/935, 1701/1700, 1716/1715, 2025/2023, 11016/11011}. The period of chromium is mapped to 250/243, and in this paradigm it is referred to as chromium quartertone. In the 17-limit, the period is also represented by 35/34, which means that 1701/1700 is tempered out.
Chromium has MOS scales of size 48, 72, and 120.
120-tone MOS
The 120-tone MOS of chromium is notable because it has 3rd, 5th, 7th, and 11th harmonics within reach of 5 generators or less. In addition in higher limits, it also has 17/13 within the reach of two generators.
The brightest mode has the pattern (LLsLs)x24, and in addition it's a very hard tuning, which means it sounds nothing like 120edo.
A tuning where it's worth exploring chromium if one seeks large divisibility is 480edo, which is a largely composite EDO. In this instance, the L step of 120-tone scale becomes equal to one step of 80edo, and s step maps to one step of the 480edo itself. In regular temperament theory, this is realized via the 480fgg val in the 17-limit.
250/243 as the porcupine comma
Chromium reaches 10/9 in just one bright generator. As such, it reaches 100/81 in two, while simultaneously reaching 6/5 in two. Because every note is replicated 24 times around the octave, and 250/243 maps to the period, 6/5 occurs exactly one step of 24edo above two 10/9s.