Chromium: Difference between revisions

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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 ===

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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.

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

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.

[[Category:Chromium| ]]

[[Category:~~Temperaments~~]]

[[Category:Rank-2 temperaments]]

[[Category:Landscape microtemperaments]]

@@ Line 7: / Line 7: @@
 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 ===
@@ Line 14: / Line 19: @@
 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.
-=== 250/243 as the porcupine comma ===
-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.
 [[Category:Chromium| ]] <!-- main article -->
-[[Category:Temperaments]]
+[[Category:Rank-2 temperaments]]
 [[Category:Landscape microtemperaments]]