499edo: Difference between revisions

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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
Line 43: Line 34:
| 0.1345
| 0.1345
| 5.59
| 5.59
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br />per 8ve
! Generator*
! Cents*
! Associated<br />ratio*
! Temperaments
|-
|-
| 1
| 1
Line 77: Line 62:
| 2800/2187
| 2800/2187
| [[Osiris]]
| [[Osiris]]
|}
{{rank-2 end}}
{{orf}}
{{orf}}


== Music ==
== Music ==
; [[Francium]]
; [[Francium]]
* "still not desperate enough" from ''hope in dark times'' (2024) &ndash; [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]
* "Still not desperate enough" from ''hope in dark times'' (2024) &ndash; [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]


[[Category:Listen]]
[[Category:Listen]]

Revision as of 01:51, 16 November 2024

← 498edo 499edo 500edo →
Prime factorization 499 (prime)
Step size 2.40481 ¢ 
Fifth 292\499 (702.204 ¢)
Semitones (A1:m2) 48:37 (115.4 ¢ : 88.98 ¢)
Consistency limit 9
Distinct consistency limit 9

Template:EDO intro

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

Approximation of prime harmonics in 499edo
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

Template:Comma basis begin |- | 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 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 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 Template:Rank-2 end Template:Orf

Music

Francium