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{{Interwiki
{{Infobox interval|Monzo= -702 400 0 -99 100|debug=1}}
| en = Main Page
The difference between 100 [[896/891]]'s and [[7/4]]
| de = Hauptseite
{{Clear}}
| es = Bienvenidos
== Rank-3 tuning spectrum ==
| ja = メインページ
9-odd-limit: 1/1, 10/9, 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, and complements
| ro = Pagina Principală
| zh = 主页
}}__NOTOC__
== Welcome to the Xenharmonic Wiki! ==
The Xenharmonic Wiki is an open resource dedicated to musical [[tuning system]]s, focusing on [[xenharmonic music]] while also documenting [[historical tunings]] and tuning practices from [[world musical traditions|world traditions]]. It covers the [[theory]] and [[practice|practical applications]] of these systems.


For a lengthier introduction, see [[Xenharmonic Wiki: Introduction]].
Single tunings fully defined by eigenmonzos (+ the octave):


[[File:Pts-2-3-5-e2-twtop-tlin.jpg|thumb|right]]
{10/9, 9/8, 6/5, 5/4, 4/3}, {10/9, 8/7}, {10/9, 7/6}, {10/9, 9/7, 7/5}, {9/8, 8/7, 7/6, 9/7, 4/3}, {9/8, 4/3, 7/5}, {8/7, 6/5}, {8/7, 5/4, 7/5}, {7/6, 6/5, 7/5}, {7/6, 5/4}, {6/5, 9/7}, {5/4, 9/7}
== If you are new to musical tuning ==
* [[Why use alternative tunings?]]
* [[Microtonal music|What are microtonal and xenharmonic music]]?
* [[Listen]] to alternatively tuned music, in case you're wondering what it all sounds like.
* [[List of approaches to musical tuning|Discover approaches to musical tuning]]
* [[Links|Explore links]] to xenharmonic websites
* [[The Library|Browse the library]] of published works about microtonal/xenharmonic music
* Learn about the [[Xenharmonic Alliance]], a social group of xenharmonic musicians


== Popular topics ==
=== Marvel ===
* [[Just intonation]]
* [[EDO]]s and other [[equal-step tuning]]s
* [[MOS scale|Moment of Symmetry (MOS) scales]]
* [[Regular temperaments]]
* [[Historical temperaments]]


== Practical xenharmonics ==
{10/9, 9/8, 6/5, 5/4, 4/3}:
* [[List of music software]]
* [[List of microtonal software plugins]]
* [[Instruments]]
* [[Guides]]


== Contributing to the Xenharmonic Wiki ==
~3/2: 701.955{{C}}, ~5/4: 386.314{{C}}
This wiki is created by volunteers. It is a perpetual work in progress, depending on members of the community to help us develop it. We welcome relevant new content and constructive updates to existing pages, so please feel free to [[Help: How to get your Xenharmonic Wiki account|sign up and contribute]]!
 
{10/9, 8/7}:
 
~3/2: 700.670{{C}}, ~5/4: 383.743{{C}}
 
{10/9, 7/6}:
 
~3/2: 700.413{{C}}, ~5/4: 383.229 {{C}}
 
{10/9, 9/7, 7/5}:
 
~3/2: 700.027{{C}}, ~5/4: 382.458{{C}}
 
{9/8, 8/7, 7/6, 9/7, 4/3}:
 
~3/2: 701.955{{C}}, ~5/4: 382.458{{C}}
 
{9/8, 4/3, 7/5}:
 
~3/2: 701.955{{C}}, ~5/4: 378.602{{C}}
 
{8/7, 6/5}:
 
~3/2: 700.027{{C}}, ~5/4: 384.386{{C}}
 
{8/7, 5/4, 7/5}:
 
~3/2: 698.099{{C}}, ~5/4: 386.314{{C}}
 
{7/6, 6/5, 7/5}:
 
~3/2: 699.384{{C}}, ~5/4: 383.743{{C}}
 
{7/6, 5/4}:
 
~3/2: 694.243{{C}}, ~5/4: 386.314{{C}}
 
{6/5, 9/7}:
 
~3/2: 698.099{{C}}, ~5/4: 382.458{{C}}
 
<s>{5/4, 9/7}</s> (impossible)
 
Additional eigenmonzo tunings up to 21-odd-limit (new intervals: 21/20, 16/15, 15/14, 21/16)
 
{21/20, 16/15}
 
{21/20, 5/4}
 
{21/20, 9/7}
 
<s>{16/15, 8/7}</s> (impossible)
 
{16/15, 7/6}
 
{16/15, 9/7}
 
{16/15, 7/5}
 
{15/14, ''Incomplete''
 
{| class="wikitable center-all"
! Gene-<br>rator
! colspan=17 | ~3/2
|-
! rowspan=17 | ~5/4
! colspan=3 | EDO tuning
! rowspan=3 |
|
| [[19edo|11\19]]
| [[31edo|18\31]]
|
|
| [[12edo|7\12]]
|
|
|
| [[53edo|31\53]]
|
| [[41edo|24\41]]
| [[22edo|1\22]]
|-
! rowspan=2 | (↓↓↓)
! colspan=2 | Eigenmonzo
| 112/75
|
|
| 25/14
| 25/21
|
| 63/50
| 189/100
| 567/400
|
| 3/2
|
|
|-
! (↓↓↓)
! Size (¢)
| 694.243
| 694.737
| 696.774
| 698.099
| 699.384
| 700.000
| 700.027
| 700.413
| 700.670
| 701.887
| 701.955
| 702.439
| 709.091
|-
! colspan=3 |
! style="height: 5px;" |
! colspan=13 |
|-
|
| 56/45
| 378.692
! rowspan=13 |
|
|
|
|
|
|
|
|
|
|
| {3/2, 7/5}
|
|
|-
| [[19edo|6\19]]
|
| 378.947
|
| [[19edo]]
|
|
|
|
|
|
|
|
|
|
|
|-
| [[41edo|13\41]]
|
| 380.488
|
|
|
|
|
|
|
|
|
|
|
| [[41edo]]
|
|-
| [[22edo|7\22]]
|
| 381.818
|
|
|
|
|
|
|
|
|
|
|
|
| [[22edo]]
|-
|
| 9/7
| 382.458
|
|
|
| {5/3, 9/7}
|
|
| {7/5, 9/5}
|
|
|
| {3/2, 7/4}
|
|
|-
|
| 245/162
| 383.229
|
|
|
|
|
|
|
| {7/6, 9/5}
|
|
|
|
|
|-
| [[72edo|23\72]]
|
| 383.333
|
|
|
|
|
| [[72edo]]
|
|
|
|
|
|
|
|-
|
| 36/35
| 383.743
|
|
|
|
| {5/3, 7/6}
|
|
|
| {7/4, 9/5}
|
|
|
|
|-
|
| 175/144
| 384.386
|
|
|
|
|
|
| {5/3, 7/4}
|
|
|
|
|
|
|-
| [[53edo|17\53]]
|
| 384.906
|
|
|
|
|
|
|
|
|
| [[53edo]]
|
|
|
|-
|
| 5/4
| 386.314
| {5/4, 7/6}
|
|
| {5/4, 7/4}
|
|
|
|
|
|
| {3/2, 5/4}
|
|
|-
| [[31edo|10\31]]
|
| 387.097
|
|
| [[31edo]]
|
|
|
|
|
|
|
|
|
|
|-
| [[12edo|4\12]]
|
| 400.000
|
|
|
|
|
| [[12edo]]
|
|
|
|
|
|
|
|}
 
11-odd-limit adds 12/11, 11/10, 11/9, 14/11, 11/8
 
15-odd-limit: 16/15, 15/14, 15/11
 
21-odd-limit: 22/21, 21/20, 21/16
 
== Stuff ==
=== Orwell as 9-form ===
(Note that 13/10 and 20/13 are mapped via tridecimal orwell)
 
{| class="wikitable center-all"
! Degree
! 0-step
! 1-step
! 2-step
! 3-step
! 4-step
! 5-step
! 6-step
! 7-step
! 8-step
! 9-step
|-
! Cents
| 43
| 200
| 314
| 471
| 586
| 743
| 857
| 1014
| 1129
|
|-
! Ratios
| style="background-color: white;" | 36/35~33/32
| style="background-color: white;" | 9/8
| style="background-color: white;" | 6/5
| style="background-color: white;" | 21/16
| style="background-color: white;" | 7/5
| style="background-color: white;" | (20/13)
| style="background-color: white;" | 18/11
| style="background-color: white;" | 9/5
| style="background-color: white;" | 27/14~48/25
| style="background-color: white;" |
|-
! Cents
| 0
| 157
| 271
| 429
| 543
| 700
| 814
| 971
| 1086
|
|-
! Ratios
| style="background-color: white;" | 1/1
| style="background-color: white;" | 11/10~12/11
| style="background-color: white;" | 7/6
| style="background-color: white;" | 9/7~14/11
| style="background-color: white;" | 11/8~15/11
| style="background-color: white;" | 3/2
| style="background-color: white;" | 8/5
| style="background-color: white;" | 7/4
| style="background-color: white;" | 15/8~28/15
| style="background-color: white;" |
|-
! Cents
|
| 114
| 229
| 386
| 500
| 657
| 771
| 929
| 1043
| 1200
|-
! Ratios
| style="background-color: white;" |
| style="background-color: white;" | 15/14~16/15
| style="background-color: white;" | 8/7
| style="background-color: white;" | 5/4
| style="background-color: white;" | 4/3
| style="background-color: white;" | 16/11~22/15
| style="background-color: white;" | 11/7~14/9
| style="background-color: white;" | 12/7
| style="background-color: white;" | 11/6~20/11
| style="background-color: white;" | 2/1
|-
! Cents
|
| 71
| 186
| 343
| 457
| 614
| 729
| 886
| 1000
| 1157
|-
! Ratios
| style="background-color: white;" |
| style="background-color: white;" | 25/24~28/27
| style="background-color: white;" | 10/9
| style="background-color: white;" | 11/9
| style="background-color: white;" | (13/10)
| style="background-color: white;" | 10/7
| style="background-color: white;" | 32/21
| style="background-color: white;" | 5/3
| style="background-color: white;" | 16/9
| style="background-color: white;" | 35/18~64/33
|}
Retrieved from "https://en.xen.wiki/w/User:Overthink/Sandbox"