593edo: Difference between revisions

Akselai (talk | contribs)
m add links
Preserve the distinction between ET and edo. "Supporting speric" can be better worded as tempering out 2500/2499 in the 2.3.5.7.17 subgroup, same for garischismic and decovulture
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== Theory ==
== Theory ==
593et is [[consistent]] to the [[9-odd-limit]]. It tempers out [[4375/4374]], 52734375/52706752 and 3276800000/3268642167 in the 7-limit, [[support]]ing [[2500/2499#Temperaments|speric]], [[Garischismic clan|garischismic]], [[Olympic clan#Baffin|decovulture]], [[Vulture family#Septimal vulture|septimal vulture]] and [[squarschmidt]].  
593edo is [[consistent]] to the [[9-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[4375/4374]], [[33554432/33480783]], 52734375/52706752, and 67108864/66976875 in the 7-limit. It [[support]]s [[vulture]] and [[squarschmidt]]. It is also notable in the 2.3.5.7.17 [[subgroup]], tempering out [[2500/2499]].  


=== Prime harmonics ===
=== Prime harmonics ===
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== 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" | [[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
! colspan="2" | Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
| 2.3
|{{monzo|940 -593}}
| {{monzo| 940 -593 }}
|{{mapping|593 940}}
| {{mapping| 593 940 }}
| -0.0748
| -0.0748
| 0.0748
| 0.0748
| 3.70
| 3.70
|-
|-
|2.3.5
| 2.3.5
|{{monzo|24 -21 4}}, {{monzo|37 25 -33}}
| {{monzo| 24 -21 4 }}, {{monzo| 37 25 -33 }}
|{{mapping|593 940 1377}}
| {{mapping| 593 940 1377 }}
| -0.0780
| -0.0780
| 0.0613
| 0.0613
| 3.03
| 3.03
|-
|-
|2.3.5.7
| 2.3.5.7
|4375/4374, 52734375/52706752, 3276800000/3268642167
| 4375/4374, 33554432/33480783, 52734375/52706752
|{{mapping|593 940 1377 1665}}
| {{mapping| 593 940 1377 1665 }}
| -0.1015
| -0.1015
| 0.0669
| 0.0669
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! Temperaments
! Temperaments
|-
|-
|1
| 1
|196\593
| 196\593
|396.63
| 396.63
|98304/78125
| 98304/78125
|[[Squarschmidt]]
| [[Squarschmidt]]
|-
|-
|1
| 1
|215\593
| 215\593
|435.08
| 435.08
|9/7
| 9/7
|[[Supermajor]]
| [[Supermajor]]
|-
|-
|1
| 1
|235\593
| 235\593
|475.55
| 475.55
|320/243
| 320/243
|[[Vulture]]
| [[Vulture]]
|-
|-
|1
| 1
|277\593
| 277\593
|560.54
| 560.54
|864/625
| 864/625
|[[Whoosh]]
| [[Whoosh]]
|}
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct