73edt: Difference between revisions
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{{Infobox ET}} | |||
'''[[Edt|Division of the third harmonic]] into 73 equal parts''' (73EDT) is related to [[46edo|46 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 1.5078 cents compressed and the step size is about 26.0542 cents. It is consistent to the [[17-odd-limit|18-integer-limit]]. In comparison, 46edo is only consistent up to the [[13-odd-limit|14-integer-limit]]. | '''[[Edt|Division of the third harmonic]] into 73 equal parts''' (73EDT) is related to [[46edo|46 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 1.5078 cents compressed and the step size is about 26.0542 cents. It is consistent to the [[17-odd-limit|18-integer-limit]]. In comparison, 46edo is only consistent up to the [[13-odd-limit|14-integer-limit]]. | ||
== | ==Harmonics== | ||
{{Harmonics in equal | |||
| steps = 73 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = integer | |||
}} | |||
{{Harmonics in equal | |||
| steps = 73 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = integer | |||
}} | |||
==Intervals== | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
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! | comments | ! | comments | ||
|- | |- | ||
! colspan="3" | 0 | |||
| | '''exact [[1/1]]''' | | | '''exact [[1/1]]''' | ||
| | | | | | ||
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|} | |} | ||
==Related regular | ==Related regular temperaments== | ||
73edt is also related to the microtemperament which tempers out |73 -153 73> in the 5-limit, which is supported by 46, 783, 829, 1612, 2395, 3128, and 4007 EDOs. | 73edt is also related to the microtemperament which tempers out |73 -153 73> in the 5-limit, which is supported by 46, 783, 829, 1612, 2395, 3128, and 4007 EDOs. | ||
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POTE generator: ~|21 -44 21> = 26.0543 | POTE generator: ~|21 -44 21> = 26.0543 | ||
Mapping: [<1 0 -1|, <0 73 153|] | |||
EDOs: 46, 737, 783, 829, 875, 1612, 2395, 2441, 3128, 4007, 5573, 6402 | EDOs: {{EDOs|46, 737, 783, 829, 875, 1612, 2395, 2441, 3128, 4007, 5573, 6402}} | ||
===7-limit 46&783=== | ===7-limit 46&783=== | ||
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POTE generator: ~335544320/330812181 = 26.0533 | POTE generator: ~335544320/330812181 = 26.0533 | ||
Mapping: [<1 0 -1 5|, <0 73 153 -101|] | |||
EDOs: 46, 691, 737, 783, 829, 1520, 1612 | EDOs: {{EDOs|46, 691, 737, 783, 829, 1520, 1612}} | ||
===11-limit 46&783=== | ===11-limit 46&783=== | ||
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POTE generator: ~3072/3025 = 26.0542 | POTE generator: ~3072/3025 = 26.0542 | ||
Mapping: [<1 0 -1 5 6|, <0 73 153 -101 -117|] | |||
EDOs: 46, 737, 783, 829, 875 | EDOs: {{EDOs|46, 737, 783, 829, 875}} | ||
[[ | == Music == | ||
[[ | ; [[Ray Perlner]] | ||
* [https://www.youtube.com/watch?v=N7inULohKQI ''Fugue for that other kind of string quartet in 73EDT BPS<nowiki>[</nowiki>9<nowiki>]</nowiki> (Sensi Extension) in LsLssLsLs "Moll I"''] (2024) | |||