Chromium: Difference between revisions

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~~#REDIRECT [[Landscape microtemperaments #Chromium]]~~

[[Category:Temperaments]]

[[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.

== 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 [[Highly composite equal division#Largely composite numbers|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.

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-#REDIRECT [[Landscape microtemperaments #Chromium]]
 [[Category:Temperaments]]
 [[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.
+== 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 [[Highly composite equal division#Largely composite numbers|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.