601edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|601}} == Theory == 601edo is only consistent to the 3-odd-limit and the error of the harmonic 3 is very large. It can be used i..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|601}}
{{ED intro}}


== Theory ==
== Theory ==
601edo is only [[consistent]] to the [[3-odd-limit]] and the error of the [[harmonic]] [[3/1|3]] is very large. It can be used in the 2.9.7.11.13.19 [[subgroup]], [[tempering out]] [[41503/41472]], 104272/104247, [[10648/10647]], 388962/388531 and 10097379/10092544.
601edo is in[[consistent]] to the [[5-odd-limit]] and both [[harmonic]]s [[3/1|3]] and [[5/1|5]] are about halfway between its steps. It can be used in the 2.9.15.7.11.13.19 [[subgroup]], [[tempering out]] [[41503/41472]], 104272/104247, [[10648/10647]], 388962/388531 and 10097379/10092544.


=== Odd harmonics ===
=== Odd harmonics ===
Line 9: Line 9:


=== Subsets and supersets ===
=== Subsets and supersets ===
601edo is the 110th [[prime EDO]]. [[1202edo]], which doubles it, gives a good correction to the harmonics 3 and 5.
601edo is the 110th [[prime edo]]. [[1202edo]], which doubles it, gives a good correction to the harmonics 3 and 5.


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! 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]] (%)
|-
|-
|2.9
! rowspan="2" | [[Subgroup]]
|{{monzo|-1905 601}}
! rowspan="2" | [[Comma list]]
|{{mapping|601 1905}}
! rowspan="2" | [[Mapping]]
| 0.0393
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.9
| {{monzo| -1905 601 }}
| {{mapping| 601 1905 }}
| +0.0393
| 0.0393
| 0.0393
| 1.97
| 1.97
|-
|-
|2.9.5
| 2.9.5
|32805/32768, {{monzo|-105 -65 134}}
| 32805/32768, {{monzo| -105 -65 134 }}
|{{mapping|601 1905 1395}}
| {{mapping| 601 1905 1395 }}
| 0.1635
| +0.1635
| 0.1785
| 0.1785
| 8.94
| 8.94
|-
|-
|2.9.5.7
| 2.9.5.7
|32805/32768, 68359375/68024448, {{monzo|-16 -5 -2 13}}
| 32805/32768, 68359375/68024448, {{monzo| -16 -5 -2 13 }}
|{{mapping|601 1905 1395 1687}}
| {{mapping| 601 1905 1395 1687 }}
| 0.1618
| +0.1618
| 0.1546
| 0.1546
| 7.74
| 7.74
|-
|-
|2.9.5.7.11
| 2.9.5.7.11
|6250/6237, 41503/41472, 32805/32768, 3294225/3294172
| 6250/6237, 41503/41472, 32805/32768, 3294225/3294172
|{{mapping|601 1905 1395 1687 2079}}
| {{mapping| 601 1905 1395 1687 2079 }}
| 0.1431
| +0.1431
| 0.1432
| 0.1432
| 7.17
| 7.17
|-
|-
|2.9.5.7.11.13
| 2.9.5.7.11.13
|1575/1573, 6250/6237, 41503/41472, 32805/32768, 2200/2197
| 1575/1573, 6250/6237, 41503/41472, 32805/32768, 2200/2197
|{{mapping|601 1905 1395 1687 2079 2224}}
| {{mapping| 601 1905 1395 1687 2079 2224 }}
| 0.1160
| +0.1160
| 0.1441
| 0.1441
| 7.22
| 7.22
|}
|}
== Music ==
; [[Francium]]
* "younothingbluck" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/3DSwkkzzAmrwnjHacqXfxl Spotify] | [https://francium223.bandcamp.com/track/younothingbluck Bandcamp] | [https://www.youtube.com/watch?v=bWNHr2sIPng YouTube] – stacks[19] in 601edo tuning

Latest revision as of 13:04, 21 February 2025

← 600edo 601edo 602edo →
Prime factorization 601 (prime)
Step size 1.99667 ¢ 
Fifth 352\601 (702.829 ¢)
Semitones (A1:m2) 60:43 (119.8 ¢ : 85.86 ¢)
Dual sharp fifth 352\601 (702.829 ¢)
Dual flat fifth 351\601 (700.832 ¢)
Dual major 2nd 102\601 (203.661 ¢)
Consistency limit 3
Distinct consistency limit 3

601 equal divisions of the octave (abbreviated 601edo or 601ed2), also called 601-tone equal temperament (601tet) or 601 equal temperament (601et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 601 equal parts of about 2 ¢ each. Each step represents a frequency ratio of 21/601, or the 601st root of 2.

Theory

601edo is inconsistent to the 5-odd-limit and both harmonics 3 and 5 are about halfway between its steps. It can be used in the 2.9.15.7.11.13.19 subgroup, tempering out 41503/41472, 104272/104247, 10648/10647, 388962/388531 and 10097379/10092544.

Odd harmonics

Approximation of odd harmonics in 601edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.874 -0.956 -0.440 -0.249 -0.236 +0.071 -0.082 +0.868 -0.009 +0.434 +0.677
Relative (%) +43.8 -47.9 -22.0 -12.5 -11.8 +3.6 -4.1 +43.5 -0.4 +21.7 +33.9
Steps
(reduced) 		953
(352) 		1395
(193) 		1687
(485) 		1905
(102) 		2079
(276) 		2224
(421) 		2348
(545) 		2457
(53) 		2553
(149) 		2640
(236) 		2719
(315)

Subsets and supersets

601edo is the 110th prime edo. 1202edo, which doubles it, gives a good correction to the harmonics 3 and 5.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.9 [-1905 601⟩ [⟨601 1905]] +0.0393 0.0393 1.97
2.9.5 32805/32768, [-105 -65 134⟩ [⟨601 1905 1395]] +0.1635 0.1785 8.94
2.9.5.7 32805/32768, 68359375/68024448, [-16 -5 -2 13⟩ [⟨601 1905 1395 1687]] +0.1618 0.1546 7.74
2.9.5.7.11 6250/6237, 41503/41472, 32805/32768, 3294225/3294172 [⟨601 1905 1395 1687 2079]] +0.1431 0.1432 7.17
2.9.5.7.11.13 1575/1573, 6250/6237, 41503/41472, 32805/32768, 2200/2197 [⟨601 1905 1395 1687 2079 2224]] +0.1160 0.1441 7.22

Music

Francium
  • "younothingbluck" from albumwithoutspaces (2024) – Spotify | Bandcamp | YouTube – stacks[19] in 601edo tuning
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