46032edo: Difference between revisions
cents value can't be exact because 137 goes into 46032, but not 5 |
Adopt template: EDO intro; +prime error table; -redundant categories |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro}} This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is approximately 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. | ||
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46032edo marks the [[optimal patent val]] for [[Very high accuracy temperaments #Atomic|atomic]] in the 5-limit. The size of the atom, however, does exceed half of the edostep's size. | 46032edo marks the [[optimal patent val]] for [[Very high accuracy temperaments #Atomic|atomic]] in the 5-limit. The size of the atom, however, does exceed half of the edostep's size. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|46032}} | |||
[[Category:Atomic]] | [[Category:Atomic]] | ||
Revision as of 09:43, 24 March 2024
| ← 46031edo | 46032edo | 46033edo → |
Template:EDO intro This creates the unit known as the FLU (five-limit unit), in terms of which the cent is approximately 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.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0002 | +0.0002 | -0.0042 | +0.0116 | +0.0094 | -0.0023 | +0.0104 | +0.0103 | +0.0109 | +0.0114 |
| Relative (%) | +0.0 | +0.6 | +0.6 | -16.2 | +44.4 | +35.9 | -9.0 | +40.1 | +39.6 | +41.9 | +43.5 | |
| Steps (reduced) |
46032 (0) |
72959 (26927) |
106883 (14819) |
129228 (37164) |
159245 (21149) |
170339 (32243) |
188154 (4026) |
195541 (11413) |
208229 (24101) |
223623 (39495) |
228052 (43924) | |