User:BudjarnLambeth/13 levels of xenharmony

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This is a light-hearted page inspired by Adam Neely's "7 levels of jazz harmony". It lists tunings based on "how xenharmonic" they are.

This list does not list any non-Western tunings because framing those as "xen" as opposed to the Western "normal" is inaccurate. (Such tunings can still be discussed elsewhere on the wiki though, of course!)

"More xenharmonic" is not a value judgement. Subtle level 1 xenharmony is just as worthy of study and appreciation as bold level 10 xenharmony and everything in between. There is much beauty in subtlety, and much beauty in boldness, too.

Please feel free to add any tunings you like to these lists, and to move them from one level to another if you think they ought to be.

Level 0 xenharmony

Indistinguishable from 12edo.

• 12edo
• Slightly deviates from 12edo by accident
• Pianos using slightly stretched octaves
• 12edo with <4 ¢ stretch/compression (eg 34zpi)

Level 1 xenharmony

Built around 12edo or something nearly identical, but with small deliberate departures or deviations.

• Barbershop singing
• Classic blues (makes use of neutral thirds and just 7/5 & 10/7)
• Schismic[12]
• Pythagorean tuning
• Srutal[12]
• 12edo with >4 ¢ stretch/compression (eg 40ed10)
• A very equal neji of 12edo

Level 2 xenharmony

Still feels familiar to a listener raised with 12edo, but audibly differs a substantial degree.

• Augmented[12]
• Much of 5-limit just intonation
• Meantone[12]
• The well temperaments of Kirnberger, Neidhart, Vallotti, Weckmeister & Young
• A fairly equal neji of 12edo

Level 3 xenharmony

Melodies feel familiar to 12edo but the harmonies are starting to sound quite novel.

• Diminished[12]
• Flattone[12]
• Passion[13-]
• Ripple[12]
• A fairly unequal neji of 12edo

Level 4 xenharmony

Melodies feel familiar to 12edo but the harmonies feel dramatically different.

• Flattertone[12]
• Oceanfront[12]
• Superpyth[12]
• A very unequal neji of 12edo
• Many of the scales listed on gallery of 12-tone tempered scales & gallery of 12-tone just intonation scales

Level 5 xenharmony

Most melodies and harmonies from 12edo are still present, but lots of very different melodies and harmonies are both also available.

• Augmented[16+]
• Catler[24+]
• Compton[24+]
• Diminished[16+]
• Flattone[19+]
• Flattertone[19+]
• Helmholtz[17+]
• Meantone[19+]
• Oceanfront[17+]
• Passion[25+]
• Ripple[23+]
• Srutal[22+]
• Superpyth[17+]
• 17edo
• 19edo
• 22edo
• 24edo

Level 6 xenharmony

Familiar melodic shapes from 12edo are mostly gone. Many of the intervals in the harmony sound familiar, while many others sound completely unfamiliar.

• Amity temperament
• Hanson temperament
• Mohajira temperament
• Orwell temperament
• Sensi temperament
• Würschmidt temperament
• Harry Partch Genesis scale
• Full 7-limit or 11-limit just scales
• Many combination product sets

Level 7 xenharmony

Like level 6, but more unfamiliar still, forcing heavier use of the more unfamiliar melodies and harmonies and less of the familiar ones. But still preserves octaves and perfect fifths well.

• Blackwood temperament
• Magic temperament
• Negri temperament
• No-5s subgroups of just intonation
• Porcupine temperament
• Slendric temperament
• Tetracot temperament
• 5edo
• 7edo
• 10edo
• 14edo
• 15edo
• 20edo
• 21edo

Level 8 xenharmony

Perfect fifths or octaves start to behave weirdly; depending on the tuning fifths or octaves might need to be avoided unless using a tailored inharmonic timbre.

• Carlos Beta
• Carlos Gamma
• Mavila temperament
• Timbral tunings for very inharmonic timbres
• Xenharmonic series
• 9edo
• 16edo
• 18edo
• 23edo
• 25edo
• 6ed7/3

Level 9 xenharmony

Perfect fifths are entirely absent, or octaves are very weak, or both. Either way this forces the use of higher primes, even in inharmonic timbres.

• Didacus temperament
• Insect temperament
• No-3s subgroups of just intonation
• 8edo
• 11edo
• 13edo

Level 10 xenharmony

There are no octaves, so the most fundamental assumption of 12edo is completely absent. Forces the use of either no-2s subgroups or 4.n subgroups.

• Bohlen-Pierce scale/13edt
• BPS temperament
• Carlos Alpha
• Canopus temperament
• Deneb temperament
• Freivaldthree scale
• Meanquad temperament
• No-2s subgroups of just intonation
• Nonoctave zeta peak indexes
• Tetrahanson temperament
• 17edt
• 39edt
• Most scales from the gallery of nonoctave scales

Level 11 xenharmony

Tunings with no octaves, no double octaves (4/1), and no tritaves (twelfths) either. Any last remnant of 12edo music theory ceases to make sense at this level. But there are still consonances to be found (as in, intervals close to simple JI ratios).

• Antipyth temperament
• Halftone temperament
• Semiwolf temperament
• Auk temperament
• Doubleton temperament
• Hyperion temperament
• Juggernaut temperament
• 24ed5
• 33ed5

Level 13 xenharmony

Scales which cannot be approached using conventional harmonic-series-based harmony at all. Forcing the abandonment of every single concept present from 12edo. Timbre, instruments, harmony and melody must all be completely rebuilt from the ground up.

• 1ed230c
• 1ed330c
• 1ed370c/12ed13