Xen concepts for beginners: Difference between revisions
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== Edos == | == Edos == | ||
* 5edo: Equalized pentatonic ("Equipentatonic"). | * [[5edo]]: Equalized pentatonic ("Equipentatonic"). | ||
* 7edo: Equalized diatonic ("Equiheptatonic"). | * [[7edo]]: Equalized diatonic ("Equiheptatonic"). | ||
* 9edo: The simplest edo with a | * [[9edo]]: The simplest edo with a [[2L5]]s MOS (sssLssL). | ||
* 11edo: Stretched 12edo, has 4L3s MOS (LLsLsLs) which is a stretched diatonic. | * [[11edo]]: Stretched 12edo, has [[4L3s]] MOS (LLsLsLs) which is a stretched diatonic. | ||
* 13edo: Compressed 12edo having the 5L3s MOS (LLsLLsLs) which is a compressed version of the diatonic scale. | * [[13edo]]: Compressed 12edo having the [[5L3s]] MOS (LLsLLsLs) which is a compressed version of the diatonic scale. | ||
* 15edo: The smallest edo with a 5L5s MOS (LsLsLsLsLs) commonly called the Blackwood scale. | * [[15edo]]: The smallest edo with a [[5L5s]] MOS (LsLsLsLsLs) commonly called the Blackwood scale. | ||
* 16edo: Has 2L5s (sssLssL) and 7L2s (LLLsLLLLs). | * [[16edo]]: Has 2L5s (sssLssL) and [[7L2s]] (LLLsLLLLs). | ||
* 17edo: The smallest edo after 12edo with a diatonic scale, which can be harmonically very different from 12edo diatonic depending on how you use it. First neutral diatonic edo (providing neutral seconds, thirds, sixths, and sevenths). | * [[17edo]]: The smallest edo after 12edo with a diatonic scale, which can be harmonically very different from 12edo diatonic depending on how you use it. First neutral diatonic edo (providing neutral seconds, thirds, sixths, and sevenths). | ||
* 18edo: Has two fifths, 733c and 667c, that are nearly equally off from 3/2. | * [[18edo]]: Has two fifths, 733c and 667c, that are nearly equally off from [[3/2]]. | ||
* 19edo: The smallest edo after 12edo which supports [[Meantone]]. Just major and minor thirds are better approximated than in 12edo. First [[interordinal]] diatonic edo (interordinals are semifourths, semisixths, semitenths, and semitwelfths). | * [[19edo]]: The smallest edo after 12edo which supports [[Meantone]]. Just major and minor thirds are better approximated than in 12edo. First [[interordinal]] diatonic edo (interordinals are semifourths, semisixths, semitenths, and semitwelfths). | ||
* 22edo: Diatonic MOS with a fifth so sharp that it has supermajor and subminor thirds for its major and minor thirds. "Minor sevenths" such as A–G and C–B♭ are approximately 7/4 instead of 16/9 or 9/5. Has a 5-limit major third (approximate 5/4) which *cannot* be reached by stacking four fifths. Supports [[Superpyth]] like 27edo. | * [[22edo]]: Diatonic MOS with a fifth so sharp that it has supermajor and subminor thirds for its major and minor thirds. "Minor sevenths" such as A–G and C–B♭ are approximately 7/4 instead of 16/9 or 9/5. Has a 5-limit major third (approximate 5/4) which *cannot* be reached by stacking four fifths. Supports [[Superpyth]] like 27edo. | ||
* 23edo: The largest edo without a diatonic, 5edo, or 7edo fifth. | * [[23edo]]: The largest edo without a diatonic, 5edo, or 7edo fifth. | ||
* 24edo: Has both neutral thirds ( | * [[24edo]]: Has both neutral thirds (and other neutral intervals) and semifourths (and other interordinals), each of these lending itself to different harmony. Has 12edo MOS scales as well as new ones. | ||
* 29edo: Weird flat neogothic edo. | * [[29edo]]: Weird flat neogothic edo. | ||
* 31edo: Often considered the best Meantone edo. Close to historical [[quarter-comma meantone]]. Not only is its major third close to just 5/4, it also matches the harmonic seventh 7/4 well, also approximating other JI ratios like 6/5 (just minor third), 7/6 (septimal subminor third), and 25/16 (classical augmented fifth). | * [[31edo]]: Often considered the best Meantone edo. Close to historical [[quarter-comma meantone]]. Not only is its major third close to just 5/4, it also matches the harmonic seventh 7/4 well, also approximating other JI ratios like 6/5 (just minor third), 7/6 (septimal subminor third), and 25/16 (classical augmented fifth). | ||
* 34edo: Good for the 5-limit (2.3.5), as it doesn't temper out 81/80 and has a good 5/4. | * [[34edo]]: Good for the 5-limit (2.3.5), as it doesn't temper out 81/80 and has a good 5/4. | ||
* 36edo: Good for primes 3 and 7. | * [[36edo]]: Good for primes 3 and 7. | ||
* 37edo: Good for primes 5, 7, 11 and 13, in return for a sharp 3/2. | * [[37edo]]: Good for primes 5, 7, 11 and 13, in return for a sharp 3/2. | ||
* 41edo: Good 3; flat 5 and 7; sharp 11 and 13. Known for the [[Kite guitar]]. | * [[41edo]]: Good 3; flat 5 and 7; sharp 11 and 13. Known for the [[Kite guitar]]. | ||
* 46edo: Neogothic 3; sharp 5; flat 7, 11, and 13; good 17. Supports [[Parapyth]]. Some favor it over 41edo. | * [[46edo]]: Neogothic 3; sharp 5; flat 7, 11, and 13; good 17. Supports [[Parapyth]]. Some favor it over 41edo. | ||
* 53edo: Is a stack of near-just 3/2's which also approximates primes 5, 7, 13, and 19. | * [[53edo]]: Is a stack of near-just 3/2's which also approximates primes 5, 7, 13, and 19. | ||