499edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
499et tempers out [[33554432/33480783]], 359661568/358722675 and [[2401/2400]] in the 7-limit; 100663296/100656875, 2097152/2096325, [[536870912/535869675]], 151263/151250, 104857600/104825259, [[131072/130977]], [[200704/200475]], 17537553/17500000, [[19712/19683]], 1479016/1476225, [[3025/3024]], [[41503/41472]], [[532400/531441]] and 67110351/67108864 in the 11-limit. | 499et tempers out [[33554432/33480783]], 359661568/358722675 and [[2401/2400]] in the 7-limit; 100663296/100656875, 2097152/2096325, [[536870912/535869675]], 151263/151250, 104857600/104825259, [[131072/130977]], [[200704/200475]], 17537553/17500000, [[19712/19683]], 1479016/1476225, [[3025/3024]], [[41503/41472]], [[532400/531441]], and 67110351/67108864 in the 11-limit. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 26: | Line 26: | ||
| {{monzo|791 -499}} | | {{monzo|791 -499}} | ||
| {{val|499 791}} | | {{val|499 791}} | ||
| | | −0.0787 | ||
| 0.0787 | | 0.0787 | ||
| 3.27 | | 3.27 | ||
| Line 33: | Line 33: | ||
| {{monzo|32 -7 -9}}, {{monzo|1 36 -25}} | | {{monzo|32 -7 -9}}, {{monzo|1 36 -25}} | ||
| {{val|499 791 1159}} | | {{val|499 791 1159}} | ||
| | | −0.1760 | ||
| 0.1519 | | 0.1519 | ||
| 6.32 | | 6.32 | ||
| Line 40: | Line 40: | ||
| 2401/2400, 1959552/1953125, 26873856/26796875 | | 2401/2400, 1959552/1953125, 26873856/26796875 | ||
| {{val|499 791 1159 1401}} | | {{val|499 791 1159 1401}} | ||
| | | −0.1598 | ||
| 0.1345 | | 0.1345 | ||
| 5.59 | | 5.59 | ||
| Line 79: | Line 79: | ||
| [[Osiris]] | | [[Osiris]] | ||
|} | |} | ||
<nowiki />* [[Normal | <nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* " | * "still not desperate enough" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/4BkTyDG9JO2vRKrtta3iwz Spotify] | [https://francium223.bandcamp.com/track/still-not-desperate-enough Bandcamp] | [https://www.youtube.com/watch?v=nTYClZbsH4k YouTube] | ||
* "Dumping Thickness" from ''Check Us Out'' (2026) – [https://open.spotify.com/track/5ytxIITz1HVR81FPaxZF78 Spotify] | [https://francium223.bandcamp.com/track/dumping-thickness Bandcamp] | [https://www.youtube.com/watch?v=saRSyUZwEZ0 YouTube] | |||
[[Category:Listen]] | [[Category:Listen]] | ||
Latest revision as of 11:06, 30 April 2026
| ← 498edo | 499edo | 500edo → |
499 equal divisions of the octave (abbreviated 499edo or 499ed2), also called 499-tone equal temperament (499tet) or 499 equal temperament (499et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 499 equal parts of about 2.4 ¢ each. Each step represents a frequency ratio of 21/499, or the 499th root of 2.
Theory
499et tempers out 33554432/33480783, 359661568/358722675 and 2401/2400 in the 7-limit; 100663296/100656875, 2097152/2096325, 536870912/535869675, 151263/151250, 104857600/104825259, 131072/130977, 200704/200475, 17537553/17500000, 19712/19683, 1479016/1476225, 3025/3024, 41503/41472, 532400/531441, and 67110351/67108864 in the 11-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.25 | +0.86 | +0.31 | -0.62 | +1.16 | +0.86 | +0.68 | -0.62 | -0.32 | -0.35 |
| Relative (%) | +0.0 | +10.4 | +35.8 | +13.0 | -25.6 | +48.1 | +35.6 | +28.4 | -25.7 | -13.3 | -14.4 | |
| Steps (reduced) |
499 (0) |
791 (292) |
1159 (161) |
1401 (403) |
1726 (229) |
1847 (350) |
2040 (44) |
2120 (124) |
2257 (261) |
2424 (428) |
2472 (476) | |
Subsets and supersets
499edo is the 95th prime edo.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [791 -499⟩ | ⟨499 791] | −0.0787 | 0.0787 | 3.27 |
| 2.3.5 | [32 -7 -9⟩, [1 36 -25⟩ | ⟨499 791 1159] | −0.1760 | 0.1519 | 6.32 |
| 2.3.5.7 | 2401/2400, 1959552/1953125, 26873856/26796875 | ⟨499 791 1159 1401] | −0.1598 | 0.1345 | 5.59 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 23\499 | 55.311 | 16875/16384 | Escapade |
| 1 | 126\499 | 303.006 | 25/21 | Quinmite |
| 1 | 146\499 | 351.102 | 49/40 | Newt |
| 1 | 178\499 | 428.056 | 2800/2187 | Osiris |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct