General theory: Difference between revisions

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{{interwiki
{{interwiki
| en = General theory
| de =  
| de =  
| en = General Theory
| es = Teoría Básica
| es = Teoría Básica
| ja =  
| ja = 一般理論
}}
}}
Here are some links to some of the key ideas underlying tuning:
Here are some links to some of the key ideas underlying tuning:


== Basics ==
== Basics ==
* Start here: [[Xen concepts for beginners]]
* [[Interval]]
* [[Interval]]
* [[Ratio]]
* [[Ratio]]
** [[Ratio math]]
** [[Ratio math]]
* [[Cent]]
* [[Cent]]
* [[Chords]]
* [[Chord]]
* [[Scale]]s
* [[Scale]]
* [[Mode]]
* [[Musical notation]]
* [[Musical notation]]
* Terminology
** [[Glossary]]
** [[Acronyms]]


== Core concepts ==
== Core concepts ==
* [[Just intonation]]
* [[Harmonic series]]
* [[Harmonic series]]
* [[Just intonation]]
** [[Chord of nature]]
* [[Equal division of the octave]]
* [[Equal division of the octave]]
* [[Equal division of the tritave]]
** [[Equal-step tuning]] ([[edt]], [[edf]], …)
* [[Equal-step tuning]]
** [[Well temperament]]
* [[Arithmetic tuning]]
* [[Regular temperaments]]
* [[Regular temperaments]]
* [[Periods and generators]]
** [[Diatonic, chromatic, enharmonic, subchromatic]]
* [[Periodic scale]]
* [[MOS scale]]
* [[MOS scale]]
* [[Well temperament]]
** [[Periods and generators]]
* [[Comma pump]]
* [[Hexany]]
* [[Hexany]]
* [[Delta-rational chord]]


== Online tools ==
== Online tools ==
{{Main| List of music software #Browser-based }}
{{Main| List of music software #Browser-based }}


* [https://www.yacavone.net/xen-calc/| xen-calc] – a nice online interval calculator tool.
* [https://scaleworkshop.plainsound.org/ Scale Workshop] – scale-creation site by [[Lumi Pakkanen]]. Allows playing via QWERTY computer keyboard. Can also export .scl and .kbm files.
* [[Xenpaper]] – text-based microtonal sequencer, like a notepad. Write down musical ideas and share the link around.
* [https://www.yacavone.net/xen-calc/ xen-calc] – interval calculator that translates to/from ratios, cents, FJS and color notation, much more too.


== Scales by size ==
== Common scales ==
* [[:Category: 5-tone scales]]
* [[:Category: 5-tone scales]]
* [[:Category: 6-tone scales]]
* [[:Category: 6-tone scales]]
Line 46: Line 52:
* [[:Category: 12-tone scales]]
* [[:Category: 12-tone scales]]


 
== Regular temperament theory (RTT) ==
'''Other sizes'''
* [[Monzo]]
{| class="wikitable center-all"
* [[Val]]
|+ style=white-space:nowrap | 0…99
* [[Mapping]]
| [[:Category:0-tone scales|0]]
* [[Patent val]]
| [[:Category:1-tone scales|1]]
* [[Tempering out]]
| [[:Category:2-tone scales|2]]
* [[Rank and codimension]]
| [[:Category:3-tone scales|3]]
* [[Keenan's explanation of vals]]
| [[:Category:4-tone scales|4]]
* [[Comma pump]]
| [[:Category:5-tone scales|5]]
* [[Comma basis]]
| [[:Category:6-tone scales|6]]
* [[Saturation, torsion, and contorsion]]
| [[:Category:7-tone scales|7]]
* [[Dyadic chord]]
| [[:Category:8-tone scales|8]]
* [[Essential tempering comma]]
| [[:Category:9-tone scales|9]]
* [[Graham complexity]]
|-
| [[:Category:10-tone scales|10]]
| [[:Category:11-tone scales|11]]
| [[:Category:12-tone scales|12]]
| [[:Category:13-tone scales|13]]
| [[:Category:14-tone scales|14]]
| [[:Category:15-tone scales|15]]
| [[:Category:16-tone scales|16]]
| [[:Category:17-tone scales|17]]
| [[:Category:18-tone scales|18]]
| [[:Category:19-tone scales|19]]
|-
| [[:Category:20-tone scales|20]]
| [[:Category:21-tone scales|21]]
| [[:Category:22-tone scales|22]]
| [[:Category:23-tone scales|23]]
| [[:Category:24-tone scales|24]]
| [[:Category:25-tone scales|25]]
| [[:Category:26-tone scales|26]]
| [[:Category:27-tone scales|27]]
| [[:Category:28-tone scales|28]]
| [[:Category:29-tone scales|29]]
|-
| [[:Category:30-tone scales|30]]
| [[:Category:31-tone scales|31]]
| [[:Category:32-tone scales|32]]
| [[:Category:33-tone scales|33]]
| [[:Category:34-tone scales|34]]
| [[:Category:35-tone scales|35]]
| [[:Category:36-tone scales|36]]
| [[:Category:37-tone scales|37]]
| [[:Category:38-tone scales|38]]
| [[:Category:39-tone scales|39]]
|-
| [[:Category:40-tone scales|40]]
| [[:Category:41-tone scales|41]]
| [[:Category:42-tone scales|42]]
| [[:Category:43-tone scales|43]]
| [[:Category:44-tone scales|44]]
| [[:Category:45-tone scales|45]]
| [[:Category:46-tone scales|46]]
| [[:Category:47-tone scales|47]]
| [[:Category:48-tone scales|48]]
| [[:Category:49-tone scales|49]]
|-
| [[:Category:50-tone scales|50]]
| [[:Category:51-tone scales|51]]
| [[:Category:52-tone scales|52]]
| [[:Category:53-tone scales|53]]
| [[:Category:54-tone scales|54]]
| [[:Category:55-tone scales|55]]
| [[:Category:56-tone scales|56]]
| [[:Category:57-tone scales|57]]
| [[:Category:58-tone scales|58]]
| [[:Category:59-tone scales|59]]
|-
| [[:Category:60-tone scales|60]]
| [[:Category:61-tone scales|61]]
| [[:Category:62-tone scales|62]]
| [[:Category:63-tone scales|63]]
| [[:Category:64-tone scales|64]]
| [[:Category:65-tone scales|65]]
| [[:Category:66-tone scales|66]]
| [[:Category:67-tone scales|67]]
| [[:Category:68-tone scales|68]]
| [[:Category:69-tone scales|69]]
|-
| [[:Category:70-tone scales|70]]
| [[:Category:71-tone scales|71]]
| [[:Category:72-tone scales|72]]
| [[:Category:73-tone scales|73]]
| [[:Category:74-tone scales|74]]
| [[:Category:75-tone scales|75]]
| [[:Category:76-tone scales|76]]
| [[:Category:77-tone scales|77]]
| [[:Category:78-tone scales|78]]
| [[:Category:79-tone scales|79]]
|-
| [[:Category:80-tone scales|80]]
| [[:Category:81-tone scales|81]]
| [[:Category:82-tone scales|82]]
| [[:Category:83-tone scales|83]]
| [[:Category:84-tone scales|84]]
| [[:Category:85-tone scales|85]]
| [[:Category:86-tone scales|86]]
| [[:Category:87-tone scales|87]]
| [[:Category:88-tone scales|88]]
| [[:Category:89-tone scales|89]]
|-
| [[:Category:90-tone scales|90]]
| [[:Category:91-tone scales|91]]
| [[:Category:92-tone scales|92]]
| [[:Category:93-tone scales|93]]
| [[:Category:94-tone scales|94]]
| [[:Category:95-tone scales|95]]
| [[:Category:96-tone scales|96]]
| [[:Category:97-tone scales|97]]
| [[:Category:98-tone scales|98]]
| [[:Category:99-tone scales|99]]
|}
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style=white-space:nowrap | 100…199
| [[:Category:100-tone scales|100]]
| [[:Category:101-tone scales|101]]
| [[:Category:102-tone scales|102]]
| [[:Category:103-tone scales|103]]
| [[:Category:104-tone scales|104]]
| [[:Category:105-tone scales|105]]
| [[:Category:106-tone scales|106]]
| [[:Category:107-tone scales|107]]
| [[:Category:108-tone scales|108]]
| [[:Category:109-tone scales|109]]
|-
| [[:Category:110-tone scales|110]]
| [[:Category:111-tone scales|111]]
| [[:Category:112-tone scales|112]]
| [[:Category:113-tone scales|113]]
| [[:Category:114-tone scales|114]]
| [[:Category:115-tone scales|115]]
| [[:Category:116-tone scales|116]]
| [[:Category:117-tone scales|117]]
| [[:Category:118-tone scales|118]]
| [[:Category:119-tone scales|119]]
|-
| [[:Category:120-tone scales|120]]
| [[:Category:121-tone scales|121]]
| [[:Category:122-tone scales|122]]
| [[:Category:123-tone scales|123]]
| [[:Category:124-tone scales|124]]
| [[:Category:125-tone scales|125]]
| [[:Category:126-tone scales|126]]
| [[:Category:127-tone scales|127]]
| [[:Category:128-tone scales|128]]
| [[:Category:129-tone scales|129]]
|-
| [[:Category:130-tone scales|130]]
| [[:Category:131-tone scales|131]]
| [[:Category:132-tone scales|132]]
| [[:Category:133-tone scales|133]]
| [[:Category:134-tone scales|134]]
| [[:Category:135-tone scales|135]]
| [[:Category:136-tone scales|136]]
| [[:Category:137-tone scales|137]]
| [[:Category:138-tone scales|138]]
| [[:Category:139-tone scales|139]]
|-
| [[:Category:140-tone scales|140]]
| [[:Category:141-tone scales|141]]
| [[:Category:142-tone scales|142]]
| [[:Category:143-tone scales|143]]
| [[:Category:144-tone scales|144]]
| [[:Category:145-tone scales|145]]
| [[:Category:146-tone scales|146]]
| [[:Category:147-tone scales|147]]
| [[:Category:148-tone scales|148]]
| [[:Category:149-tone scales|149]]
|-
| [[:Category:150-tone scales|150]]
| [[:Category:151-tone scales|151]]
| [[:Category:152-tone scales|152]]
| [[:Category:153-tone scales|153]]
| [[:Category:154-tone scales|154]]
| [[:Category:155-tone scales|155]]
| [[:Category:156-tone scales|156]]
| [[:Category:157-tone scales|157]]
| [[:Category:158-tone scales|158]]
| [[:Category:159-tone scales|159]]
|-
| [[:Category:160-tone scales|160]]
| [[:Category:161-tone scales|161]]
| [[:Category:162-tone scales|162]]
| [[:Category:163-tone scales|163]]
| [[:Category:164-tone scales|164]]
| [[:Category:165-tone scales|165]]
| [[:Category:166-tone scales|166]]
| [[:Category:167-tone scales|167]]
| [[:Category:168-tone scales|168]]
| [[:Category:169-tone scales|169]]
|-
| [[:Category:170-tone scales|170]]
| [[:Category:171-tone scales|171]]
| [[:Category:172-tone scales|172]]
| [[:Category:173-tone scales|173]]
| [[:Category:174-tone scales|174]]
| [[:Category:175-tone scales|175]]
| [[:Category:176-tone scales|176]]
| [[:Category:177-tone scales|177]]
| [[:Category:178-tone scales|178]]
| [[:Category:179-tone scales|179]]
|-
| [[:Category:180-tone scales|180]]
| [[:Category:181-tone scales|181]]
| [[:Category:182-tone scales|182]]
| [[:Category:183-tone scales|183]]
| [[:Category:184-tone scales|184]]
| [[:Category:185-tone scales|185]]
| [[:Category:186-tone scales|186]]
| [[:Category:187-tone scales|187]]
| [[:Category:188-tone scales|188]]
| [[:Category:189-tone scales|189]]
|-
| [[:Category:190-tone scales|190]]
| [[:Category:191-tone scales|191]]
| [[:Category:192-tone scales|192]]
| [[:Category:193-tone scales|193]]
| [[:Category:194-tone scales|194]]
| [[:Category:195-tone scales|195]]
| [[:Category:196-tone scales|196]]
| [[:Category:197-tone scales|197]]
| [[:Category:198-tone scales|198]]
| [[:Category:199-tone scales|199]]
|}


== Advanced theory ==
== Advanced theory ==
{{Main| Mathematical Theory }}
{{Main| Mathematical theory }}
 
* [[Chord of nature]]
* [[Cluster temperament]]
* [[Consonant class scale]]
* [[Diatonic, Chromatic, Enharmonic, Subchromatic]]
* [[Distributional evenness]]
* [[Essential tempering commas]]
* [[Fokker block]]
* [[Graham complexity]]
* [[Lumma stability]]
* [[Maximum variety]]
* [[Modal UDP Notation]]


[[Category:Theory]]
[[Category:Theory]]
[[Category:Todo:review]]
[[Category:Todo:review]]

Latest revision as of 04:54, 2 December 2025

Here are some links to some of the key ideas underlying tuning:

Basics

Core concepts

Online tools

Main article: List of music software § Browser-based
  • Scale Workshop – scale-creation site by Lumi Pakkanen. Allows playing via QWERTY computer keyboard. Can also export .scl and .kbm files.
  • Xenpaper – text-based microtonal sequencer, like a notepad. Write down musical ideas and share the link around.
  • xen-calc – interval calculator that translates to/from ratios, cents, FJS and color notation, much more too.

Common scales

Regular temperament theory (RTT)

Advanced theory

Main article: Mathematical theory
Retrieved from "https://en.xen.wiki/index.php?title=General_theory&oldid=218410"