Xen concepts for beginners: Difference between revisions
→Edos: the "7/4" is also a "16/9" according to Archy, and I don't hear 18\22 as an approximate 7/4 |
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* [[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 | * [[22edo]]: Diatonic MOS with a fifth so sharp that it has supermajor and subminor thirds (approximately [[9/7]] and [[7/6]]) for its major and minor thirds. 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 (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. | * [[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 [[3/2|3]] and [[7/4|7]]. | ||
* [[37edo]]: Good for primes 5, 7, 11 and 13, in return for a sharp 3/2. | * [[37edo]]: Good for primes [[5/4|5]], [[7/4|7]], [[11/8|11]] and [[13/8|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. | ||