Xenharmonic Wiki

130edo: Difference between revisions

← Older edit
VisualWikitext
Eufalesio (talk | contribs)
autopatrolled
682 edits
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"
 
(5 intermediate revisions by one other user not shown)
Line 3: Line 3:


== Theory ==
== Theory ==
130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit|odd-prime-sum-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the [[rank-3 temperament]] [[jove]], tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[harry]].  
130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit|odd-prime-sum-limit]]. It is also almost consistent in the no-29 [[31-odd-limit]], missing [[19/11]] (50.5%), [[25/19]] (52.9%), [[17/11]] (64,4%), [[25/17]] (66.8%), and [[octave complement]]<nowiki/>s.
 
As an equal temperament, it [[tempering out|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the [[rank-3 temperament]] [[jove]], tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[harry]].  


=== Prime harmonics ===
=== Prime harmonics ===
Line 297: Line 299:
130edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation#Spartan single-shaft|Spartan extension]], with the apotome equal to 12 edosteps and the limma to 10 edosteps. Since the the [[243/242|rastma]] is tempered out, a SZ half-sharp and a half-flat may be used instead of pakai/pakao. Here is a simplified table:
130edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation#Spartan single-shaft|Spartan extension]], with the apotome equal to 12 edosteps and the limma to 10 edosteps. Since the the [[243/242|rastma]] is tempered out, a SZ half-sharp and a half-flat may be used instead of pakai/pakao. Here is a simplified table:
{| class="wikitable" data-darkreader-inline-color="" style="text-align: center;"
{| class="wikitable" data-darkreader-inline-color="" style="text-align: center;"
!Degree
! colspan="2" |Steps
|0
!0
| +1
! 1
| +2
! 2
| +3
! 3
| +4
! 4
| +5
! 5
| +6
! 6
| +7
! 7
| +8
! 8
| +9
! 9
| +10
! 10
| +11
! 11
| +12
! 12
|-
|-
! rowspan="3" |Symbol
!Evo+SZ
!Evo+SZ
| rowspan="3" |<big>{{sagittal||//|}}</big>
| rowspan="3" |<big>{{sagittal||//|}}</big>
Line 329: Line 332:
!Evo
!Evo
| rowspan="2" |<big>{{sagittal|/|\}}</big>
| rowspan="2" |<big>{{sagittal|/|\}}</big>
|<small>{{sagittal|#}}<big>{{sagittal|\!)}}</big></small>
|<small>{{sagittal|#}}</small><small><big>{{sagittal|\\!}}</big></small>
|<small>{{sagittal|#}}<big>{{sagittal|!)}}</big></small>
|<small>{{sagittal|#}}<big>{{sagittal|\!}}</big></small>
|<small>{{sagittal|#}}<big>{{sagittal|!(}}</big></small>
|<small>{{sagittal|#}}<big>{{sagittal|!(}}</big></small>
|<small>{{sagittal|#}}<big>{{sagittal|!/}}</big></small>
|<small>{{sagittal|#}}<big>{{sagittal|!)}}</big></small>
|<small>{{sagittal|#}}<big>{{sagittal|\\!}}</big></small>
|<small>{{sagittal|#}}<big>{{sagittal|\!)}}</big></small>
|-
|-
!Revo
!Revo
Line 344: Line 347:
|}
|}


*
Because it uses the entire Spartan extension, it allows no accidental enharmonic respellings.
 
See [[Sagittal notation#Revo|apotome complements]] for equivalent accidental pairs.


== Approximation to JI ==
== Approximation to JI ==
Line 505: Line 506:
| [[Bosonic]]
| [[Bosonic]]
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<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


== Scales ==
== Scales ==
Retrieved from "https://en.xen.wiki/w/130edo"