Chromium: Difference between revisions
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'''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. | |||
'''Chromium''' is a rank-2 temperament which has a period of 1/24th of the octave and a generator of [[10/7]] | For technical data see [[Landscape microtemperaments #Chromium]]. | ||
== Theory == | == 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. | 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. | |||
The | === 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]] | |||
Latest revision as of 13:59, 28 April 2025
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.
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 [-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 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.