Chromium: Difference between revisions

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

'''Chromium''' is a rank-2 temperament which has a period of 1/24th of the octave and a generator of [[10/7]] or [[7/5]]. It is named after the 24th chemical element.

[[Category:~~Temperaments~~]]

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 and also means that chromium temperament contains [[palingenetic chords]].

Chromium has mos scales of size 48, 72, and 120.

=== 250/243 as the porcupine comma ===

From a regular temperament theory perspective in the 5-limit, chromium is defined entirely by the {{monzo|-23 120 -72}} comma that closes a stack of 24 porcupine commas with the octave.

Chromium reaches [[10/9]] in just one generator step. 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 10/9's.

=== 120-tone mos ===

The 120-tone mos of chromium is notable because it has 3rd, 5th, 7th, and 11th harmonics within reach of 5 generator steps or less. In addition in higher limits, it also has [[17/13]] within the reach of two generator steps.

The brightest mode has the pattern (LLsLs)×24, and in addition it is a very hard tuning, which means it sounds nothing like [[120edo]].

A tuning where it is 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. This is realized via the 480fgg val in the 17-limit.

[[Category:Chromium| ]]

[[Category:Rank-2 temperaments]]

[[Category:Landscape microtemperaments]]

@@ Line 1: / Line 1: @@
-#REDIRECT [[Landscape microtemperaments #Chromium]]
+'''Chromium''' is a rank-2 temperament which has a period of 1/24th of the octave and a generator of [[10/7]] or [[7/5]]. It is named after the 24th chemical element.
-[[Category:Temperaments]]
+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 and also means that chromium temperament contains [[palingenetic chords]].
+Chromium has mos scales of size 48, 72, and 120.
+=== 250/243 as the porcupine comma ===
+From a regular temperament theory perspective in the 5-limit, chromium is defined entirely by the {{monzo|-23 120 -72}} comma that closes a stack of 24 porcupine commas with the octave.
+Chromium reaches [[10/9]] in just one generator step. 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 10/9's.
+=== 120-tone mos ===
+The 120-tone mos of chromium is notable because it has 3rd, 5th, 7th, and 11th harmonics within reach of 5 generator steps or less. In addition in higher limits, it also has [[17/13]] within the reach of two generator steps.
+The brightest mode has the pattern (LLsLs)×24, and in addition it is a very hard tuning, which means it sounds nothing like [[120edo]].
+A tuning where it is 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. This is realized via the 480fgg val in the 17-limit.
+[[Category:Chromium| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
 [[Category:Landscape microtemperaments]]