46032edo: Difference between revisions
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'''46032EDO''' is the [[EDO|equal division of the octave]] into 46032 parts of | '''46032EDO''' is the [[EDO|equal division of the octave]] into 46032 parts of approximately 0.02606882 cents each. This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is precisely 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations. | ||
In the 5-limit the 46032 division tempers out [[Kirnberger's atom]], {{monzo| 161 -84 -12 }} as well as {{monzo| 454 427 -487 }}. It maps the syntonic comma, 81/80, to 825 FLUs, and the Pythagorean comma, 531441/524228, to 900 FLUs. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 FLUs, which is the measure in FLUs of the schisma, 32805/32768. | In the 5-limit the 46032 division tempers out [[Kirnberger's atom]], {{monzo| 161 -84 -12 }} as well as {{monzo| 454 427 -487 }}. It maps the syntonic comma, 81/80, to 825 FLUs, and the Pythagorean comma, 531441/524228, to 900 FLUs. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 FLUs, which is the measure in FLUs of the schisma, 32805/32768. | ||
Revision as of 18:19, 22 March 2024
| ← 46031edo | 46032edo | 46033edo → |
46032EDO is the equal division of the octave into 46032 parts of approximately 0.02606882 cents each. This creates the unit known as the FLU (five-limit unit), in terms of which the cent is precisely 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.
In the 5-limit the 46032 division tempers out Kirnberger's atom, [161 -84 -12⟩ as well as [454 427 -487⟩. It maps the syntonic comma, 81/80, to 825 FLUs, and the Pythagorean comma, 531441/524228, to 900 FLUs. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 FLUs, which is the measure in FLUs of the schisma, 32805/32768.
46032edo marks the optimal patent val for atomic in the 5-limit. The size of the atom, however, does exceed half of the edostep's size.