User:BudjarnLambeth

Not to be confused with lambeth chords nor 1573/1568 (the lambeth comma). Those are unrelated to me.

This is the user page of Budjarn Lambeth, an amateur, hobbyist:

• wiki contributor
• scalesmith
• music theorist
• improviser-composer

Personal information

• Location: New South Wales, Australia
• Born: 1999
• Pronouns: he/she
• Contactable at: https://www.facebook.com/budjarnlambeth/ or on my talk page

Music I made

My original microtonal music is hosted on YouTube:

• Best pieces (playlist)
• All pieces (playlist) (some of these are not very good 👉👈)

Groups I belong to

I'm a contributor to:

• the Xenharmonic Wiki
  • Xenharmonic Wiki:WikiProject Just Intonation
• the Xenharmonic Alliance on both Discord and Facebook
  • the Monthly Tunings Facebook group
• the Xenrhythmic Alliance
  • Xenrhythm Zone Discord server
  • the Xenrhythmic Wiki
• the Microtonal Encyclopedia

My favourite microtonal composers

(alphabetical order)

• Benyamind
• Brendan Byrnes
• Tolgahan Çoğulu
• Greystar
• Maeve Gutierrez
• JUMBLE
• King Gizzard & the Lizard Wizard
• Merct
• Sevish

See also: my Apple Music playlists (mostly not microtonal, but some are): @budjarn Apple Music playlists.

Discoveries made

AI summary

I don't and won't ever use AI for contributions to wiki pages, I'm only using it this once to summarize my own user page (this page) because it is currently difficult to read. Also, I did not ask the AI to scrape the wiki, I used my own local copies of my pages from my computer to ask the AI about.

Theoretical frameworks

Lambeth has proposed several original theoretical frameworks for understanding and composing microtonal music.

Quasipelog theory

This is a framework for approaching 16edo (and other EDOs supporting the 2.3.5.11 mavila temperament, like EDOS 23, 30, 37, and 39). It is inspired by Indonesian Gamelan theory, the Armodue school, and Erv Wilson's MOS scales.

• Concept: It focuses on specific scales that mimic the feel of Pelog scales but within a 16-tone equal temperament context.
• Scales: The theory defines four essential scales derived from Mavila MOS modes:
  • Quasipelog Minor: Mode ssLsL of mavila[5].
  • Quasipelog Major: Mode LssLs of mavila[5].
  • Quasipelog Heptatonic: Mode ssLssLs of mavila[7].
  • Quasipelog Chromatic: A mavila[16] MOS scale (7 fifths up, 8 down).
• Timbre: A key part of the theory is the avoidance of harmonic timbres. Lambeth recommends "inharmonic" sounds such as metallophones, bells, or "thin/reedy" waveforms (like sine or woodwinds) to complement the tuning.

Structural beating

Lambeth hypothesized this property for equal-step tunings where the period of the scale differs from the interval of psychoacoustic equivalence (usually the octave, 2/1).

• Effect: Because the scale repeats at an interval different from the ear's point of equivalence, the scale creates a macro-scale "beating" or phasing effect as it ascends or descends.
• Goal: This is considered a desirable property that makes a periodic scale feel less repetitive, offering shifting colors and shapes ("something from nothing").
• Examples: Equal divisions of sevenths (e.g., ed7/4) or ninths (ed16/9) if the equivalence is the octave.

Polytriadicism

This concept involves tuning an ensemble (of 2 or more instruments/groups) so that each is tuned to a different triad or subset of a larger overarching scale.

• Application: It allows composers to approach complex temperaments (like those without consonant small MOS scales) or large just intonation sets by breaking them down into simpler, manageable triadic parts.
• Function: It can be used to "flag" different rhythmic elements harmonically or to create complex, interweaving voice lines that generate consonance from the aggregate of the instruments.
• Example: Shoal[17], a 17-tone MOS scale in the Shoal temperament (a 2.3.13.23 subgroup detemper of 17edo), is cited as a prime candidate for this approach.

Equalizer subgroups

A just intonation subgroup designed to balance specific types of harmonics to achieve a specific aesthetic.

• Criteria:
  • Structural Harmonics (2, 3, 4, 5): 2 or 3 present. They provide stability and "tonal gravity."
  • Assertive Harmonics (5–12): None present. These are excluded because they have "strong personalities" that define the scale's flavor too rigidly.
  • Ethereal Harmonics (13+): At least 3 present. These provide subtle, background influence.
• Goal: To allow subtle "ethereal" harmonics to shine by removing the "assertive" middle harmonics, akin to using an EQ to cut mids and boost highs/lows.
• Examples: Subgroups like (2.3.5.13.17.19) used in Lambeth's Fifigeist temperament.

Substitute harmonics

This theory involves replacing a simple, lower harmonic with a complex, higher harmonic that closely approximates it, thereby "fudging" the tuning into a different subgroup.

• Sharp Substitutes: Replacing a harmonic with a slightly sharper higher harmonic. Lambeth names these temperaments after weapons or with "com"-ending names (e.g., Daggerminished, Pajaraxe, Dotcom, Sitcom, Romcom).
• Flat Substitutes: Replacing with a flatter harmonic. Naming convention involves flat regions (e.g., Sahara).

Scalesmithing

Lambeth has invented numerous specific scales and temperaments.

• Batch 89 Temperaments: A set of temperaments first documented in 2023, honoring the characters from Guardians of the Galaxy Vol. 3. Each tempers 4 harmonics: the 2nd, the 89th (representing shared trauma), and two others derived from the character's name via A1Z26 cipher.
  • Floor: 2.3.11.89 (Neutral related).
  • Teefs: 2.5.11.89 (Bug related).
  • Rocket: 2.9+.9-.89 (Lu/Deutone related).
• Ed255/128 and Ed257/128: These are "Equal Divisions of Reduced Harmonics."
  • Ed255/128: Divides the interval 255/128 (slightly flatter than an octave). Useful for correcting EDOs where consonances are too sharp (e.g., used as an alternative to 5edo).
  • Ed257/128: Divides the interval 257/128 (slightly sharper than an octave). Useful for correcting EDOs where consonances are too flat (e.g., alternative to 7edo).
• Antipental Blues scale: A 6-tone scale subset of the Dwarf17marv scale. It mimics the melodic shape of the minor blues scale but uses exotic 2.3.7.11 intervals (7/6, 11/8, 7/4) instead of the standard 5-limit intervals.
• Moon Dust scale: A 16-tone just intonation scale with a period of 16/1 (four octaves). It features dynamic step sizes and a mix of familiar 3-limit harmonies with xenharmonic 19-limit (no-5, no-13) intervals.
• Firedance scale: A 5-tone subset of zeta-stretched 15edo (47zpi). It was designed by ear, starting from 5edo and adjusting steps by degrees of 15edo.

Tuning recommendations

Lambeth recommends the following tunings for Western musicians exploring world music traditions:

• For Gamelan scales (Pelog/Slendro): He recommends specific EDOs that approximate these scales well. His personal favorite is 44edo. Other good approximations include 21, 23, 35, 39, 40, 42, 54, and 60edo.
• For Japanese scales: He prefers Meantone temperaments in 55edo, 98edo, or 43edo (approx. 1/5-comma meantone). He generally dislikes 5-limit JI or Pythagorean tunings for these scales, finding the "wolf" intervals objectionable.

Wiki contributions

Improvements to the broader wiki

Significant page creations

• Authored the survey of efficient temperaments by subgroup to help people navigate quickly to their favourite temperament pages
• Authored the Gallery of arithmetic pitch sequences & Gallery of combination product sets pages to help people find musical scales
• Authored the pages about equipentatonic and equiheptatonic scales
• Created the Xenharmonic Wiki:Cross-platform dialogue page to aid collaboration between editors who are mostly active on Facebook and those who are mostly active on Discord
• Authored pages answering the FAQ questions:
  • “What are this wiki's strengths and weaknesses? (How does it compare to other resources?)”
  • “I'm a new editor, what is everything I can do to help?”
  • “How do I decode those strange looking comma names?”
• Authored dozens of wanted pages about composers
• Authored several extensive lists of scales

Bulk page improvements

• Added dozens of sources and inline citations to the historical temperaments page
• Added infobox, intro, intervals, modes, subheadings & todo categories to dozens of previously close-to-empty MOS scale pages
• Added intro, intervals table and harmonics table to several hundred equal-step tuning pages (which used to just be blank pages with a single infobox)
• Added Template:Temp gallery to all 'very highly prominent temperament gallery pages'
• Added Template:Temp gallery to all 'highly prominent temperament gallery pages'
• Added Template:Temp gallery to all 'moderately prominent temperament gallery pages'
• Added Template:Temp gallery to all 'less prominent temperament families and clans'
• Constructed the 5-, 6-, 7-, 8-, 9-, 10-, 11- and 12-period tables on the map of rank-2 temperaments
• Heavily added to the 2-, 3- and 4-period tables on the map of rank-2 temperaments
• Merged “useful tools” & “software” into one unified page
• Created circle diagrams for dozens of hexany pages using Nick Vuci's circle diagram maker

Structural wiki improvements

• Added categories & formatting tags to several hundred pages with Scala files
• Added links around the wiki to over 150 previously orphaned pages, bringing the number down from above 250 to below 70 (as of 4 Dec 2024)
• Created Template:Navbox Lumatone with very extensive help from User:ArrowHead294
  • With ArrowHead294’s extensive help, incorporated the template into over 50 pages for Category:Lumatone mappings
• Ran a survey of editors, created the Xenharmonic Wiki:Optional guidelines for interval page todo categories (XW:IntTodo) from the results, and ensured all interval pages were categorized in line with XW:IntTodo

(list and table creations)

Constructed:

• List of taxicab-2 intervals
• User:BudjarnLambeth/Table of n-comma meantone generators
• Harmonic entropy of just intervals
• Table of zeta-stretched edos

(comma documentation and organisation)

• Added all missing commas from “Category:Large commas” to the table on the page “Large commas”
• Added all missing commas from “Category:Medium commas” to the table on the page “Medium commas”
• Added all missing commas from “Category:Small commas” to the table on the page “Small comma”
• Added all missing commas from “Category:Unnoticeable commas” to the table on the page “Unnoticeable commas”
• Constructed “Category:Commas by name” and its many subcategories
• Categorised all 5, 7, 11, 13, 17, 19, 23 and >23 limit large commas into ’Commas by name’ subcategories
• Categorised all 5, 7, 11, 13, 17, 19, 23 and >23 limit medium commas into ’Commas by name’ subcategories
• Categorised all 5, 7, 11, 13, 17, 19, 23 and >23 limit small commas into ’Commas by name’ subcategories
• Categorised all 5, 7, 11, 13, 17, 19, 23 and >23 limit unnoticeable commas into ’Commas by name’ subcategories
• Conducted the User:BudjarnLambeth/Survey of named and unnamed commas

(name changes I was involved in)

Correcting confusing names

• There was an old temperament that pre-dated my participation in the wiki. Its old, original name was “septimal temperament”. When I discovered the name, I disliked it because of its potential for confusion with other uses of the term “septimal”. I decided I wanted to change it. Many people on Discord, the Wiki Workgroup on XA Facebook, and the wiki talk page agreed. I coined the new name “austinpowers temperament” which has now replaced it.
• There was an old temperament that pre-dated my participation in the wiki. Its old, original name was “decades temperament”. Some people on the XA Discord said that they disliked it due to its convoluted etymology. I coined the new name “gamelstearn temperament” based on its two defining commas. After a few days, not many people commented or reacted to the proposal, but all were in favour and none were against, so the name "gamelstearn" was adopted.
• There used to be two temperaments named “semidim temperament”. To resolve the confusion, after discussion on the XA Discord, myself and Lériendil came up with new names for each of the two temperaments. Lériendil coined “ammon temperament” for the first, and I coined “octonion temperament” for the second.
• There was an old comma that pre-dated my participation in the wiki. Its old, original name was “the erogluisma”. Its original namer posted on Discord that he no longer liked it, and would like someone to please rename it. I coined the new name “the shaftesburisma” which has now replaced it.
• Someone else described a new comma and named it “the shikanokonokonokokoshitantanma”. This name was kept, but it was too long for some use cases, so I invented an alternate short version - “the nokotan” - for use cases where a shorter name is needed.
• The comma “68630377364883 / 68630356164608” was too long to be referred to by its number alone, it needed a name instead. So I named it “the zudilisma”.

Correcting divisive or hurtful names

• There was an old temperament that pre-dated my participation in the wiki. Its old, original name was “catcall temperament”. When I discovered the name, I disliked it because it was demeaning to women. I decided I wanted to change it. Many people on Discord and on the wiki talk page agreed. I coined the new name “catnip temperament” which has now replaced it.
• There was an old temperament that pre-dated my participation in the wiki. Its old, original name was “catamite temperament”. When I discovered the name, I disliked it because it referenced a historical practice that often involved child abuse. I decided I wanted to change it. I suggested the change on the talk page where it received no replies, and the Discord where it received few reactions but those it did receive were in favour. I coined the new name “stalagmite temperament” which has now replaced it.
• There was an old comma that pre-dated my participation in the wiki. Its old, original name was “the Buddhisma”. There was nothing wrong with that name in and of itself, the problem is that it was explicitly stated to be named after the anti-Muslim group the 969 Movement, and the comma number was 969/968. I thought this was inappropriate, so I proposed a few replacement names on Discord. Of the names I coined “the kingfisher comma” was the clear favourite, so I renamed the comma to the kingfisher comma.

Full list of contributions

• Special:Contributions/BudjarnLambeth

Pages on my own discoveries

Invented approaches to constructing tunings

These are the same category of thing as “equal temperaments”.

Procedural approaches:

• Basal subgroups
• Half-basis, third-basis, quarter-basis, etc. subgroups
• Equalizer subgroups
• Function(x) tunings
• Polytriadic tunings
• Quasipelog theory
• Substitute harmonics
• Tritavesque intervals
• Waveform(x) tunings
• Equal divisions of 255/128
• Equal divisions of 257/128

Sculptural approaches:

• Breuddwyd scales
• Sonhar tunings
• Sooty fox scales
• Wijzerplaat scale⁠s
• APS#farab scales
• APS#gene scales
• APS#hekt scales
• APS#jot scales
• APS#méride scales
• APS#tina scales

Invented approaches to classifying tunings

These are the same category of thing as “pentatonic scales”.

• Indecisive EDOs
• Local zeta peak EDOs
• Local zeta valley EDOs
• Parker EDOs
• Human EDO size categorization (HUECAT)
• Metascales
• Runoff scales
• Structural beating

Invented tunings (scales)

These are the same category of thing as “the chromatic scale”.

(named after theory properties)

• The antechinus scale
• The breuddwyd inverse scale
• The breuddwyd-6 scale
• The fourfourths scale
• The hemisettled11 scale
• The hemisettled16 scale
• The hypersakura scale
• The molten pelog scale
• The molten slendro scale
• The nineteenplus scale
• The oclock scale
• The opalised ammonite scale
• The quasi-equiheptatonic minor pentatonic scale
• The secund chance scale
• The shoal17 over-9 tetrad
• The tame bison scale
• The tame possum scale
• The trippy warped hirajoshi scale (credit shared with Moonshine The Yellow Toaster)
• The undecimal quasi-equipentatonic scale
• The undecimal minor hexatonic scale
• The undecimal Mixolydian scale
• The vinyl braid scale
• The well-tempered 19-in-38 scale
• The will-o-wisps' scale
• The 13ed5plus scale
• The antipental blues scale and its expansions:
  • The antipental blues maj 6th scale
  • The antipental blues neutral 7th scale
  • The antipental blues maj 7th scale
  • The antipental blues harmonic scale
• (subsets of blackwood[20]):
  • The blackwood neutral nonatonic scale
  • The blackwood pseudo-Akebono neutral scale
  • The blackwood pseudo-Akebono supermajor scale
  • The blackwood pseudo-Hirajoshi scale
  • The blackwood pseudo-pelog scale
  • The blackwood-tempered 5afdo scale
  • The blackwood undecimal harmonic scale
• (expansions of Gutierrez's sunbreak scale):
  • The chromaticized sunbreak scale
  • The mirrored sunbreak scale
  • The negative harmony sunbreak scale
  • The fractalized sunbreak scale
• All the scales listed at: User:BudjarnLambeth/Quasipelog theory

(named after subjective feeling)

• The algal bloom scale
• The amulet scale
• The anisopteran scale
• The apex scale
• The bathypelagic scale
• The blackened skies scale
• The bubblegum scale
• The bustling docks scale
• The candycorn scale
• The canopy scale
• The carousel scale
• The cavernous scale
• The clear pond scale
• The cloudscape scale
• The cola scale
• The corrugated scale
• The cosmic scale
• The dalmatian scale
  • The Dante, Da Vinci, Dawkins, Deepak, Deja Vu, Delgado, Dolly, Dylan, Fergus & Hansel scales
• The dewdrops scale
• The diffractive scale
• The diffractive tetrad
• The direct sunlight scale
• The driftwood scale
• The enrichment scale
• The evacuated planet scale
• The firedance scale
• The fishcrackers scale
• The formicarium scale
• The fossa tetratonic scale
• The fossa pentatonic scale
• The frankincense scale
• The free range scales
• The goldfish scale
• The greyed skies scale
• The hall-of-mirrors scale
• The ibex scale
• The ketchup and mustard scale
• The lemonade scale
• The liquorice scale
• The livewire scale
• The lost spirit scale
• The magnetosphere scale
• The mechanical scale
• The meta-monsoon scale
  • The monsoon scale
  • The monsoon major scale
  • The monsoon otonal scale
• The moonbeam scale
• The moon dust scale
• The nightdrive scale
• The Over the Hedge scale
  • The H.ammy, H.eather, O.zzie, R.J, S.tella, T.iger & V.erne scales
• The palace scale
• The pelagic scale
• The pepperbass scale
• The purgatory scale
• The pylon scale
• The quest scale
• The refractive scale
• The refractive tetrad
• The rockpool scale
• The sabertooth scales
• The salt and pepper scale
• The sandcastle scale
• The snow braid scale
• The snowcone scale
• The sourgummy scale
• The spectral blues scale
• The swan scale
• The trailmix scale
• The tropicalpunch scale
• The UFO scale
• The understory scale
• The volcanic scale
• The whitechocolate scale
• The meta-tropolis scale and its subsets:
  • The city-at-dawn scale
  • The city-at-midday scale
  • The city-at-dusk scale
  • The city-at-midnight scale
  • The port-at-dawn scale
  • The port-at-midday scale
  • The port-at-dusk scale
  • The port-at-midnight scale

(polymicrotonal)

• The 8-tone 4&5edo scale
• The 10-tone 4&7edo scale
• The 10-tone 5&6edo scale
• The 12-tone 4&9edo scale
• The 12-tone 4&10edo scale
• The 12-tone 5&8edo scale
• The 12-tone 5&9edo scale
• The 12-tone 5&16edo scale
• The 12-tone 6&7edo scale
• The 12-tone 6&8edo scale
• The 12-tone 6&10edo scale
• The 12-tone 6&15edo scale
• The 12-tone 8&10edo scale
• The 12-tone 8&20edo scale
• The 12-tone 9&12edo scale
• The 12-tone 10&15edo scale
• The 12-tone 12&18edo scale
• The 13-tone 5&9edo scale
• The 14-tone 6&10edo scale
• The 14-tone 8&10edo scale
• The 14-tone 8&20edo scale
• The 16-tone 5&16edo scale
• The 12-tone 6&15edo scale
• The 18-tone 9&12edo scale
• The 18-tone 12&18edo scale
• The 20-tone blackwood&greenwood scale
• The 20-tone 10&15edo scale
• The 24-tone blackwood&greenwood scale

(arithmetic pitch sequence)

• APS148.5¢
• APS237.8¢
• APS3.21farab
• APS7hekt
• APS715jot
• APS720jot
• APS4/5méride
• APS5/8méride
• APS7/12méride
• APS70tina
• The Argentina scale

Invented tunings (regular temperaments)

These are the same category of thing as “quarter-comma meantone temperament”.

• Attic temperament
• Basement temperament
• Blacktetra temperament
• Canine temperament
• Daggerminished temperament
• Dotcom temperament
• Doubloon temperaments
• Dreamtone temperament
• Ectophotia temperament
• Fifigeist temperament
• Floor temperament
• Fomalhaut temperament
• Fourwar temperament
• Glycome temperament
• Hypnotone temperament
• Incisor temperament
• Income temperament
• Intercom temperament
• Kaboom temperament
• Lieerie temperament
• Lightyear temperament
• Lilac temperament
• Lilly pilly temperament
• Lily temperament
• Lipsett temperament
• Lylla temperament
• Minicom temperament
• Molar temperament
• Newcome temperament
• Nimona temperament
• Outcome temperament
• Oxidizer temperament
• Pajaraxe temperament
• Phantadecimal temperament
• Phantasrutal temperament
• Poltercompton temperament
• Rocket temperament
• Romcom temperament
• Sahara temperament
• Satcom temperament
• Semihaunt temperament
• Shadecimal temperament
• Shrutarnatural temperament
• Sitcom temperament
• Sixscared temperament
• Spectrephore temperament
• Tailwind temperament
• Teefs temperament
• Telecom temperament
• Tetramagic temperament
• Vacuum temperament
• Void temperament
• Vortex temperament
• Werecatler temperament

(To-do)

Things I plan to do on the wiki in the near future. Feel free to go ahead and do these any of these things first if you’re interested in doing so. I feel overwhelmed by the sheer amount of things I want to do and am very happy for any help I receive getting through it all :)

WikiProject Just Intonation

• Recruit more members (especially an expert on Harry Partch, an expert on Erv Wilson, or an expert on primodality).
• Examine the names of all Scala file pages and rename those with confusing or ambiguous names.
• Find all examples of multiple similar Scala file pages (eg "exampletone10", "exampletone15", "exampletone_major") and merge them into scale galleries.
• Record improvisations using JI scales that have no music examples, and post those as examples on the relevant scale pages.
• Add handmade tables of intervals to pages about JI scales that have a fixed tonic (are not rotatable).

Structural wiki improvements

• Fix the issues found in the User:BudjarnLambeth/Map of linear temperaments page health survey
• Improve scales sections of pages:
  • 21edo
  • 26edo
  • 32edo
  • 33edo
  • 34edo
  • 37edo
  • 39edo
  • 40edo
  • 46edo
  • 53edo
• Make “Undertone scales” page that exists in mutually supportive conversation with “IFDO” in a similar way how “Overtone scale” does with “AFDO”
• Add “Category:Temperaments” to all temperament redirects

Construct diagrams or lists

• Add every temperament from the 3 Middle Path table pages and every temperament from Survey of efficient temperaments by subgroup to the tables on Map of linear temperaments and Map of rank-2 temperaments
• For every temperament on the page Survey of efficient temperaments by subgroup, generate a Scala file of whichever of its MOS scales is closest to (2 x its graham complexity). List all the Scala files in a wiki page along the lines of “Scala files for efficient subgroup temperaments” or something like that and link it from the Survey page
• Make all the wanted tables listed in Category:Todo:add rank 2 temperaments table
• Make manual, curated tables of intervals for:
  • 8ed5/4 to 9ed5/4
  • 4ed4/3 to 8ed4/3
  • 4ed5/3 to 6ed5/3
  • 11ed5/3
  • 5ed7/4 to 12ed7/4
  • 5ed9/5 to 7ed9/5
  • 11ed9/4
  • 5ed7/3
  • 8ed7/3
  • 5ed5/2 to 6ed5/2
  • 8ed5/2
  • 12edt
  • 3ed4 to 6ed4
  • 8ed4 to 15ed4
  • 3ed5 to 5ed5
  • 4ed6
• Construct a table of the sharpness or flatness of every prime harmonic in every edo up to 53.
  • Each edo will be a row, and the columns will be from -60%, -55%, -50%… -5%, 0, +5%… +50%, +55%, +60%. And I will list each prime in whichever bin it is closest too (so if prime 7/1 had +23.9% error in Nedo, it goes in column +25% in that edo’s row).
  • Make a separate absolute error table in cents for EDOs 1 to 30, and relative error table for all EDOs 1 to 53 with the possibility of expanding both to higher edos later.
• Construct a version of an “odd limit” but for each “equalizer subgroup” and document them on the equalizer subgroup page
• Construct a tonality diamond or something like one for each “equalizer subgroup” and document them on the equalizer subgroup page

Improve pages I made

• On my page 5- to 10-tone scales in 60edo, change the scales to be in the more compact format that is used on edo pages instead of a ‘Scala-like’ format
• On my page 5- to 10-tone scales in 72edo, change the scales to be in the more compact format that is used on edo pages instead of a ‘Scala-like’ format
• On my page 5- to 10-tone scales in 84edo, change the scales to be in the more compact format that is used on edo pages instead of a ‘Scala-like’ format
• On my page 5- to 10-tone scales in 91edo, change the scales to be in the more compact format that is used on edo pages instead of a ‘Scala-like’ format
• On my page 5- to 10-tone scales in 96edo, change the scales to be in the more compact format that is used on edo pages instead of a ‘Scala-like’ format

Explore, discover, document

• Find nice 5 to 7 tone subsets of Shaka10, Starling12, Thrush12 and document them under a “subsets” heading on those scales’ pages
• Find more unique scales in Catnip[36] in 60edo that can’t be replicated in Compton[36] and document them on 5- to 10-tone scales in 60edo
• Find 4 to 7 tone subsets for every 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 or 19-tone scale page

Approximate x in y

• Approximate the following scales in modes 34 to 101 of the harmonic series and document the results in “5- to 10-tone scales from the modes of the harmonic series”:

Tobago6
101.53846
350.76923
600.
701.53846
950.76923
1200.

Zeus1
157.57576
387.87879
545.45455
703.03030
1042.42424
2/1

Oceanfront5
227.82
486.09
713.91
972.18
1200.

Oceanfront Ionian Pent.
455.64
486.09
713.91
1169.55
1200.

Oceanfront Minor Harmonic Pent.
258.27
486.09
713.91
1169.55
1200.

Oceanfront Mixolydian Pent.
455.64
486.09
713.91
972.18
1200.

Oceanfront Adrift Pent.
197.37
258.27
683.46
713.91
1200.

• Approximate the following scales in modes 102 to 200 of the harmonic series and document the results in “5- to 10-tone scales from the modes of the harmonic series”:

5edo
1\5
2\5
3\5
4\5
5\5

6edo
1\6
2\6
3\6
4\6
5\6
6\6

7edo
1\7
2\7
3\7
4\7
5\7
6\7

Slendric6
233.68421
467.36842
701.05263
934.73684
966.31579
1200.

Tobago6
101.53846
350.76923
600.
701.53846
950.76923
1200.

Zeus1
157.57576
387.87879
545.45455
703.03030
1042.42424
1200.

Oceanfront5
227.82
486.09
713.91
972.18
1200.

Oceanfront Ionian Pent.
455.64
486.09
713.91
1169.55
1200.

Oceanfront Minor Harmonic Pent.
258.27
486.09
713.91
1169.55
1200.

Oceanfront Mixolydian Pent.
455.64
486.09
713.91
972.18
1200.

Oceanfront Adrift Pent.
197.37
258.27
683.46
713.91
1200.

• Approximate the following scales in BOTH prime modes 75-100 of the harmonic series AND sqfr semiprm modes 75-100 and document the results in “5- to 10-tone scales from the modes of the harmonic series”:

Antipental Blues
7/6
4/3
11/8
3/2
7/4
2/1

Evened Minor Hexatonic
187.500
312.500
500.000
700.000
987.500
1200.000

Evened Phrygian Dominant Hexatonic
112.500
387.500
500.000
712.500
987.500
1200.000

Flattened Blues Aeolian Pentatonic
287.500
487.500
687.500
787.500
1200.000

Flattened Blues Minor Maj7
287.500
500.000
600.000
700.000
1100.000
1200.000

Roughened Blues Dorian Pentatonic
300.000
700.000
912.500
987.500
1200.000

Sharpened Blues Aeolian Pentatonic
312.500
712.500
800.000
1000.000
1200.000

Sharpened Blues Dorian Hexatonic
312.500
512.500
712.500
900.000
1012.500
1200.000

Sharpened Blues Harmonic Septatonic
312.500
512.500
612.500
712.500
812.500
1112.500
1200.000

Sharpened Dorian Harmonic
212.500
312.500
612.500
712.500
912.500
1012.500
1200.000

Sharpened Hirajoshi
200.000
312.500
700.000
812.500
1200.000

Sharpened Kokin-Joshi
200.000
312.500
700.000
900.000
1200.000

Sharpened Minor Pentatonic
312.500
500.000
700.000
1012.500
1200.000

Xenharmonify 12edo scales

Approximate 12edo subsets with these tunings, test them by noodling, and list all good-sounding ones in a big page:

• August in EDOs: ................. 21, 33, 45, 58, 69
• Augene in EDOs: ................. 15, 27, 39, 66
• Bidia in EDOs: ................. 56, 68, 80
• Diaschismic in EDOs: ................. 46, 58, 104
• Dimcomp in EDOs: ................. 44, 48, 56, 60, 68, 72
• Diminished in EDOs: ................. 20, 28, 32, 44
• Grackle in EDOs: ................. 53, 65, 77, 89
• Helenus/Photia in EDOs: ................. 41, 53, 65, 118
• Hexe in EDOs: ................. 30, 42
• Injera in EDOs: ................. 14, 26, 38, 40, 90, 102
• Misty in EDOs: ................. 39, 51, 63, 75, 87, 99
• Nickel in EDOs: ................. 16, 21, 28
• Pajara in EDOs: ................. 22, 34, 56
• Pajarous in EDOs: ................. 22, 32, 54, 76, 120
• Passion in EDOs: ................. 25, 37, 49, 61, 73, 110
• Ripple in EDOs: ................. 71, 83, 95, 107, 119
• Semimeantone in EDOs: ................. 38, 50, 62
• Srutal/Srutal archagall in EDOs: ................. 22, 34, 46, 80, 114, 126
• Wronecki in EDOs: ................. 66, 78, 90, 102, 114, 126

Reference lists and technical resources

List of equal divisions including novelties

• User:BudjarnLambeth/List of equal divisions including novelties

Tunings for each subgroup

• User:BudjarnLambeth/Tunings for each subgroup

12edo interpreted as a 2.3.5.17.19 subgroup temperament

• User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning

Scale recommendations

Neji scales I found while tinkering in Scale Workshop

• User:BudjarnLambeth/Neji scales I found while tinkering in Scale Workshop

Approximations of gamelan scales in edos up to 60 (in my opinion)

• User:BudjarnLambeth/Edo approximations of gamelan scales

Some good tunings of Japanese scales (in my opinion)

• User:BudjarnLambeth/Some tunings for Japanese scales

My favourite hexanies using at least one odd greater than 15

• User:BudjarnLambeth/My favourite hexanies using at least one odd greater than 15

Eagle JI subsets

• User:BudjarnLambeth/Eagle JI subsets

Community projects I started

Gallery of xenharmonic word painting (you can contribute!)

• User:BudjarnLambeth/Gallery of xenharmonic word painting

The 13 levels of xenharmony (you can contribute!)

• User:BudjarnLambeth/13 levels of xenharmony

WikiProject Just Intonation (you can contribute!)

• Xenharmonic Wiki:WikiProject Just Intonation

Stats and surveys about the wiki

• User:BudjarnLambeth/Survey of 100 random wiki pages
• User:BudjarnLambeth/Survey of todo categories
• User:BudjarnLambeth/Survey of named and unnamed commas
• Tuning regulars

Hot takes

Everything in this section is opinion, not facts!

Do not give any of it too much weight.

• Silliness: We should take ourselves less seriously: we should have more fun, we should be more silly 🎉
• Arbitrary numbers: It’s fine to explore the 2.3.5.101 subgroup if you want to. It doesn’t matter that it’s less concordant than 2.3.5.7. Explore it anyway and see what happens. Do some stuff with arbitrary numbers that don’t make logical sense and just see what comes of it. That’s where the fun is! (Though do keep a “2.3” or “3.5” in there just to smooth over the gnarliest edges, heehee.)
• Importance of common names: I would prefer to use a temperament named something fun like “waterslide” or “jinglebells” even if it has lots of error, over one named something dry and bland like “countertrihexakleismatic” even if it’s super accurate and technically better - a bland name can kill a temperament’s appeal, a fun name can create appeal out of nothing.
• My opinion on zeta peak indexes: My view on to what degree zeta peak indexes are useful or not.

User:BudjarnLambeth/My opinion on zeta peak indexes

• Misrepresentation of traditions: A cheeky little opinion piece I wrote criticising the negative and celebrating the positive ways Western tuning theory has borrowed from the world’s traditions:

User:BudjarnLambeth/Cultural appropriation-o-meter

• Comma naming debate brainstorm: A futile attempt I made to try to begin resolving one of the big behind the scenes debates among wiki editors:

User:BudjarnLambeth/Brainstorming mostly bad ideas to solve the comma naming debate

• Rating my wiki contributions

User:BudjarnLambeth/Rating my wiki contributions

Fun: Ratios as planets

The ratios of the octave as celestial bodies of the solar system:

• 2/1, the sun, defining the overall structure of the entire octave.
• 3/2, Jupiter, the biggest pull aside from the sun itself. Marks out a rough middle of the solar system.
• 4/3, Saturn, a kind of echo of Jupiter. Vast and mighty in its own right, similar to Jupiter, but colder and subtler.
• 5/3, Uranus, has a strong enough pull to be one of the big guys, but markedly smaller than Jupiter and Saturn. Has a gentle appearance.
• 5/4, Neptune, the last of the giant planets, with their huge gravitational pull. Has an energetic, lively surface with the fastest winds in the solar system. Defines the boundary of the Kuiper Belt (like the boundary of major and minor tonality).
• 6/5, Earth, a small planet that punches above its weight. It manages to hold an unreasonably large moon, given the small gravitational influence it has. It even developed life and sent probes to explore the other planets. It has far more influence than it seems like it should.
• 7/4, Venus, a kind of parallel version of Earth. Its diameter and gravitational pull are almost identical to Earth, but its character is completely different. Home to a completely different temperature, chemical composition and volcanic system.
• 7/5, Mars, appears barren and frozen upon first glance, but looking closer reveals a rich and storied history, and potential wonders and microcosms hidden in its underground caves.
• 8/5, Mercury. Caught in a region of the solar system so wild that much of its mass has been stripped away by the solar wind while it was still forming. Still, it holds firm, a foothold in difficult territory.
• 7/6, the moon. Caught in Earth’s orbit, it’s difficult to view separately from the Earth’s influence. If the Earth wasn’t there, it’d be a whole planet in its own right.
• 9/5, Ceres. It doesn’t pull much weight on its own, but in the context of the wider solar system, it demarcates an important in-between point for the other planets. If you want to travel between the different planets, Ceres makes the journey much more pleasant.
• 11/8, Pluto, often dismissed outright due to having such a tiny gravitational pull. But it is a whole other type of ‘planet’, the first of a whole new family. When approached on its own terms, it opens up a larger, more diverse solar system than we ever knew existed.

Fun: What I look for in a good xenharmonic piece

The tuning sounds consonant, all the combinations of intervals you used sound within the same range of consonant-ness as all the combinations available in 12edo. There are more dissonant and less dissonant sections, but none that sound more dissonant than the maximum limit of dissonance I'm willing to tolerate (ie, the maximum amount of dissonance achievable with 12edo). All that is a long winded way of saying nothing sounds "out of tune".

The timbre also sounds good. Despite being midi instruments, the samples used and whatever effects were applied to them (reverb, volume levels, etc.) all come together well into something that is more than the sum of its parts. The timbre works well with the tuning to create a kind of pleasant, warm glow.

The piece has enough dynamic range, sense of harmonic movement, and interaction between melody lines to hold my interest, to not sound bland, but instead sound captivating.

Useful links for my own convenience

User:BudjarnLambeth/Sandbox

User:BudjarnLambeth/Sandbox2

Gallery of just intervals

Harmonic entropy of just intervals

User:Userminusone/Constructing a comma list using the Averiant

User:Ganaram inukshuk/Catalog of MOS Scales