User:BudjarnLambeth: Difference between revisions

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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''', the wiki contributor and amateur music theorist.


==Personal information==
Not to be confused with ''[[lambeth chords]]'' nor ''[[1573/1568]] (the lambeth comma)''. Those are unrelated to me.
 
== Personal information ==
* Location: New South Wales, Australia
* Location: New South Wales, Australia
* Born: 1999
* Born: 1999
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<br><br>
<br><br>


==Music==
== Music ==
My favourite tracks I have made:)
My favourite tracks I have made :)
# [https://m.youtube.com/watch?v=scCuGXnj5IY 33edo track Feb 2024] (bright, lush, mellow and colourful synthwave)
# [https://m.youtube.com/watch?v=scCuGXnj5IY 33edo track Feb 2024] (bright, lush, mellow and colourful synthwave)
# [https://www.youtube.com/watch?v=_NepcrTf9ng Recording in my "Rocket temperament"] (melancholic, wistful dungeon synth; loosely inspired by [[Greystar]])
# [https://www.youtube.com/watch?v=_NepcrTf9ng Recording in my "Rocket temperament"] (melancholic, wistful dungeon synth; loosely inspired by [[Greystar]])
# [https://www.youtube.com/watch?v=iZI9x2Fto-A 60afdo track Dec 2024] (bright, spacious, slightly hypnotic dungeon synth; loosely inspired by Greystar)
# [https://www.youtube.com/watch?v=6N_8QM2UK5I Compressed 8ve 80edo track Aug 2025] (contemporary classical improv on synthesizer)
# [https://www.youtube.com/watch?v=KsB9T9_6cGk 43edo track Nov 2024] (dark dungeon synth; loosely inspired by Indonesian [[gamelan]] music)
# [https://www.youtube.com/watch?v=tIwfO1lZWAc 21edo track May 2025] (dark dungeon synth; loosely inspired by Indonesian [[gamelan]] and Japanese music)
# [https://m.youtube.com/watch?v=CN4cLOyaVGE 29edo track Jan 2024] (somber, slow, minimalist chiptune)
# [https://www.youtube.com/watch?v=iZI9x2Fto-A 60afdo track Dec 2024] (bright, spacious, tropical dungeon synth; loosely inspired by Greystar)




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====Invented approaches to constructing tunings ====
====Invented approaches to constructing tunings ====
These are the same category of thing as “equal temperaments”.
These are the same category of thing as “equal temperaments”.
''Procedural approaches'':
* [[Basal subgroup]]s
* [[Basal subgroup]]s
* [[Half-prime subgroup|Half-basis, third-basis, quarter-basis, etc. subgroups]]
* [[Half-prime subgroup|Half-basis, third-basis, quarter-basis, etc. subgroups]]
* [[Equalizer subgroup]]s
* [[Equalizer subgroup]]s
* [[Sin(x) tuning#Generalizations|Function(x) tuning]]s
* [[Polytriadic]] tunings
* [[Substitute harmonic]]s
* [[Substitute harmonic]]s
* [[Tritavesque]] intervals
* [[Tritavesque]] intervals
* The [[breuddwyd scale]]s
* [[Sin(x) tuning#Generalizations|Waveform(x) tuning]]s
* The [[breuddwyd scale|sonhar scale]]s
* The [[sooty fox scale]]s
* The [[breuddwyd scale|wijzerplaat scale⁠]]s
* [[Ed255/128|Equal divisions of 255/128]]
* [[Ed255/128|Equal divisions of 255/128]]
* [[Ed257/128|Equal divisions of 257/128]]
* [[Ed257/128|Equal divisions of 257/128]]
* The [[Gallery of arithmetic pitch sequences|APS#farab scales]]
 
* The [[Gallery of arithmetic pitch sequences|APS#gene scales]]
''Sculptural approaches'':
* The [[Gallery of arithmetic pitch sequences|APS#hekt scales]]
* [[Breuddwyd scale]]s
* The [[Gallery of arithmetic pitch sequences|APS#jot scales]]
* [[Breuddwyd scale|Sonhar tuning]]s
* The [[Gallery of arithmetic pitch sequences|APS#méride scales]]
* [[Sooty fox scale]]s
* The [[Gallery of arithmetic pitch sequences|APS#tina scales]]
* [[Breuddwyd scale|Wijzerplaat scale⁠]]s
* [[Gallery of arithmetic pitch sequences|APS#farab scales]]
* [[Gallery of arithmetic pitch sequences|APS#gene scales]]
* [[Gallery of arithmetic pitch sequences|APS#hekt scales]]
* [[Gallery of arithmetic pitch sequences|APS#jot scales]]
* [[Gallery of arithmetic pitch sequences|APS#méride scales]]
* [[Gallery of arithmetic pitch sequences|APS#tina scales]]


====Invented approaches to classifying tunings ====
====Invented approaches to classifying tunings ====
These are the same category of thing as “pentatonic scales”.
These are the same category of thing as “pentatonic scales”.
* [[The Riemann Zeta Function and Tuning#Non-record edos|Anti-zeta EDOs]]
* [[the Riemann zeta function and tuning#Non-record edos|Anti-zeta EDOs]]
* [[The Riemann Zeta Function and Tuning#Non-record edos|Indecisive EDOs]]
* [[the Riemann zeta function and tuning#Non-record edos|Indecisive EDOs]]
* [[The Riemann Zeta Function and Tuning#Non-record edos|Local zeta EDOs]]
* [[the Riemann zeta function and tuning#Non-record edos|Local zeta EDOs]]
* [[The Riemann Zeta Function and Tuning#''k''-ary peak EDOs|Parker EDOs]]
* [[the Riemann zeta function and tuning#''k''-ary peak EDOs|Parker EDOs]]
* [[Human EDO size categorization]] (HUECAT)
* [[Human EDO size categorization]] (HUECAT)
*[[Metascale]]s
* [[Metascale]]s
* [[Runoff]] scales
* [[Structural beating]]


====Invented tunings (scales)====
====Invented tunings (scales)====
These are the same category of thing as “the chromatic scale”.
These are the same category of thing as “the chromatic scale”.
* The [[Shoal17#Scales|algal bloom]] scale
* The [[25edo#Scales|amulet]] scale
* The [[anisopteran scale]]
* The [[anisopteran scale]]
* The [[antipental blues]] scale
* The [[antipental blues]] scale
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* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|candycorn]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|candycorn]] scale
* The [[30edo#Scales|carousel]] scale
* The [[30edo#Scales|carousel]] scale
* The [[9edf#Scales|cloudscape]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|cola]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|cola]] scale
* The [[9edf#Scales|corrugated]] scale
* The [[32afdo#Scales|cosmic]] scale
* The [[32afdo#Scales|cosmic]] scale
* The [[dalmatian scale]]
* The [[dalmatian scale]]
** The Dante, Da Vinci, Dawkins, Deepak, Deja Vu, Delgado, Dolly, Dylan, Fergus & Hansel [[101afdo#Scales|scales]]
** The Dante, Da Vinci, Dawkins, Deepak, Deja Vu, Delgado, Dolly, Dylan, Fergus & Hansel [[101afdo#Scales|scales]]
* The [[30edo#Scales|dewdrops]] scale
* The [[30edo#Scales|dewdrops]] scale
* The [[Shoal17#Scales|diffractive scale]]
* The [[Shoal17#Scales|diffractive tetrad]]
* The [[27edo#Scales|direct sunlight]] scale
* The [[27edo#Scales|direct sunlight]] scale
* The [[Shoal17#Scales|driftwood]] scale
* The [[Peppermint-24#Salt and pepper scale and its subsets|evacuated planet]] scale
* The [[firedance]] scale
* The [[firedance]] scale
* The [[5- to 10-tone scales in 60edo|fossa tetratonic]] scale
* The [[5- to 10-tone scales in 60edo|fossa tetratonic]] scale
* The [[5- to 10-tone scales in 60edo|fossa pentatonic]] scale
* The [[5- to 10-tone scales in 60edo|fossa pentatonic]] scale
* The [[56edo#Scales|frankincense]] scale
* The [[goldfish]] scale
* The [[goldfish]] scale
* The [[27edo#Scales|hypersakura]] scale
* The [[27edo#Scales|hypersakura]] scale
* The [[Peppermint-24#Ketchup and mustard scale and its subsets|ketchup and mustard]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|lemonade]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|lemonade]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|liquorice]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|liquorice]] scale
* The [[9edf#Scales|livewire]] scale
* The [[lost spirit]] scale
* The [[lost spirit]] scale
* The [[magnetosphere scale]]
* The [[magnetosphere scale]]
* The [[16afdo#Scales|mechanical]] scale
* The [[16afdo#Scales|mechanical]] scale
* The [[9edf#Scales|molten pelog]] scale
* The [[9edf#Scales|molten slendro]] scale
* The [[5- to 10-tone scales in 47zpi|monsoon]] scale
* The [[5- to 10-tone scales in 47zpi|monsoon]] scale
* The [[16afdo#Scales|moonbeam]] scale
* The [[16afdo#Scales|moonbeam]] scale
* The [[30edo#Scales|nightdrive]] scale
* The [[30edo#Scales|nightdrive]] scale
* The [[oclock]] scale
* The [[User:BudjarnLambeth/Over the Hedge|Over the Hedge]] scale
* The [[User:BudjarnLambeth/Over the Hedge|Over the Hedge]] scale
** The H.ammy, H.eather, O.zzie, R.J, S.tella, T.iger & V.erne [[User:BudjarnLambeth/Over the Hedge|scales]]
** The H.ammy, H.eather, O.zzie, R.J, S.tella, T.iger & V.erne [[User:BudjarnLambeth/Over the Hedge|scales]]
* The [[29edo#Scales|palace]] scale
* The [[29edo#Scales|palace]] scale
* The [[30edo#Scales|pelagic]] scale
* The [[30edo#Scales|pelagic]] scale
* The [[Peppermint-24#Salt_and_pepper_scale_and_its_subsets|pepperbass]] scale
* The [[9edf#Scales|purgatory]] scale
* The [[9edf#Scales|pylon]] scale
* The [[47edo#Scales|quasi-equiheptatonic minor pentatonic]] scale
* The [[9edf#Scales|quest]] scale
* The [[Shoal17#Scales|refractive scale]]
* The [[Shoal17#Scales|refractive tetrad]]
* The [[5- to 10-tone scales in 47zpi|rockpool]] scale
* The [[5- to 10-tone scales in 47zpi|rockpool]] scale
* The [[47edo#Scales|sabertooth hexatonic]] scale
* The [[47edo#Scales|sabertooth neutral]] scale
* The [[47edo#Scales|sabertooth pentatonic]] scale
* The [[Peppermint-24#Salt and pepper scale and its subsets|salt and pepper]] scale
* The [[Shoal17#Scales|shoal17 over-9 tetrad]]
* The [[breuddwyd6|snow braid]] scale
* The [[breuddwyd6|snow braid]] scale
* The [[9edf#Scales|snowcone]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|sourgummy]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|sourgummy]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|spearmint]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|spearmint]] scale
* The [[spectral blues]] scale
* The [[spectral blues]] scale
* The [[9edf#Scales|swan]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|trailmix]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|trailmix]] scale
* The [[Batch 89 temperaments#Example inflected MOS scale: UFO scale|UFO scale]]
* The [[Batch 89 temperaments#Example inflected MOS scale: UFO scale|UFO scale]]
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* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|whitechocolate]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|whitechocolate]] scale
* The [[26ed5#13ed5plus|13ed5plus]] scale
* The [[26ed5#13ed5plus|13ed5plus]] scale
* The [[80edo#Scales|16-tone 5&16edo scale]]
* The [[80edo#Scales|12-tone 5&16edo scale]]
* The [[80edo#Scales|14-tone 8&10edo scale]]
* The [[80edo#Scales|12-tone 8&10edo scale]]
* The [[80edo#Scales|14-tone 8&20edo scale]]
* The [[80edo#Scales|12-tone 8&20edo scale]]
* [[1ed148.5c|APS148.5¢]]
* [[1ed148.5c|APS148.5¢]]
* [[1ed237.8c|APS237.8¢]]
* [[1ed237.8c|APS237.8¢]]
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* [[1ed28.7c|APS720jot]]
* [[1ed28.7c|APS720jot]]
* [[Gallery of arithmetic pitch sequences#APS of mérides|APS4/5méride]]
* [[Gallery of arithmetic pitch sequences#APS of mérides|APS4/5méride]]
* [[Gallery of arithmetic pitch sequences#APS of mérides|APS5/8méride]]
* [[Gallery of arithmetic pitch sequences#APS of mérides|APS7/12méride]]
* [[Gallery of arithmetic pitch sequences#APS of tinas|APS70tina]]
* [[Gallery of arithmetic pitch sequences#APS of tinas|APS70tina]]


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* [[Substitute harmonic#Sahara|Sahara]] temperament
* [[Substitute harmonic#Sahara|Sahara]] temperament
* [[Substitute harmonic#Narrowed compton|Satcom]] temperament
* [[Substitute harmonic#Narrowed compton|Satcom]] temperament
* [[Equalizer subgroup|Semiamulet]] temperament
* [[Equalizer subgroup|Semihaunt]] temperament
* [[Equalizer subgroup|Shadecimal]] temperament
* [[Equalizer subgroup|Shadecimal]] temperament
* [[Equalizer subgroup|Shrutarnatural]] temperament
* [[Equalizer subgroup|Shrutarnatural]] temperament
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===Improvements===
===Improvements===
====Significant page creations====
====Significant page creations====
* Authored dozens of wanted pages about [[:Category:Composers|composers]]
* Authored several extensive [[:Category:Lists of scales|lists of scales]]
* Authored the [[survey of efficient temperaments by subgroup]] to help people navigate quickly to their favourite temperament pages
* 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 [[scale]]s
* Authored the [[Gallery of arithmetic pitch sequences]] & [[Gallery of combination product sets]] pages to help people find musical [[scale]]s
* 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
* 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:
* Authored pages answering the [[FAQ]] questions:
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** “[[I'm a new editor, what is everything I can do to help?]]”
** “[[I'm a new editor, what is everything I can do to help?]]”
** “[[Systematic comma names explained|How do I decode those strange looking comma names?]]”
** “[[Systematic comma names explained|How do I decode those strange looking comma names?]]”
* Authored dozens of wanted pages about [[:Category:Composers|composers]]
* Authored several extensive [[:Category:Lists of scales|lists of scales]]


====Bulk page improvements====
====Bulk page improvements====
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* Heavily added to the 2-, 3- and 4-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]]
* Added dozens of sources and inline citations to the [[historical temperaments]] page
* Added dozens of sources and inline citations to the [[historical temperaments]] page
* Added [[Template:Temp gallery]] to all '[[User:BudjarnLambeth/Prominent temperament gallery pages|very highly prominent temperament gallery pages]]'
* Added [[Template:Temp gallery]] to all '[[User:BudjarnLambeth/Prominent temperament gallery pages|highly prominent temperament gallery pages]]'
* Added [[Template:Temp gallery]] to all '[[User:BudjarnLambeth/Prominent temperament gallery pages|moderately prominent temperament gallery pages]]'
* Added [[Template:Temp gallery]] to all '[[User:BudjarnLambeth/Prominent temperament gallery pages|less prominent temperament]] families and clans'
* Merged “useful tools” & “software” into [[Software|one unified page]]
* Added infobox, intro, intervals, modes, subheadings & todo categories to dozens of previously close-to-empty [[MOS scale]] pages
* Added infobox, intro, intervals, modes, subheadings & todo categories to dozens of previously close-to-empty [[MOS scale]] pages
* Merged “useful tools” & “software” into [[Software|one unified page]]
* 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 intro, intervals table and harmonics table to several hundred [[equal-step tuning]] pages (which used to just be blank pages with a single infobox)


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* Added categories & formatting tags to several hundred [[:Category:Pages with Scala files|pages with Scala files]]
* Added categories & formatting tags to several hundred [[:Category:Pages with Scala files|pages with Scala files]]
* Added links around the wiki to over 150 previously [[Special:LonelyPages|orphaned pages]], bringing the number down from above 250 to below 70 (as of 4 Dec 2024)
* Added links around the wiki to over 150 previously [[Special:LonelyPages|orphaned pages]], bringing the number down from above 250 to below 70 (as of 4 Dec 2024)
* Created [[Template:Lumatone mapping navigation]] with very extensive help from [[User:ArrowHead294]]
* 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]]
** 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
* 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=====
===== • List and table creations=====
* Constructed [[User:BudjarnLambeth/List of taxicab-2 intervals]]
Constructed:
* Constructed [[User:BudjarnLambeth/Table of n-comma meantone generators]]
* [[List of taxicab-2 intervals]]
* Constructed [[Table of zeta-stretched edos]]
* [[User:BudjarnLambeth/Table of n-comma meantone generators]]
* [[Harmonic entropy of just intervals]]
* [[Table of zeta-stretched edos]]


===== • Comma documentation and organisation=====
===== • Comma documentation and organisation=====
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====Name changes I was involved in====
====Name changes I was involved in====
* 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 “'''[[7th-octave temperaments#Austinpowers|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 “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 “'''[[7th-octave temperaments#Austinpowers|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 “catcall temperament”. When I discovered the name, I disliked it because it was creepy. I decided I wanted to change it. Many people on [[Discord]] and on the wiki talk page agreed. I coined the new name “'''[[catnip|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 “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|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 “decades temperament”. Some people on the XA Discord said that they disliked it due to its convoluted etymology. I coined the new name “'''[[gamelstearn|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 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 sectarian 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 “'''[[969/968|the kingfisher comma]]'''” was the clear favourite, so I renamed the comma to the kingfisher comma.
* 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|ammon temperament]]” for the first, and I coined “'''[[octonion|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 “'''[[1682/1681|the shaftesburisma]]'''” which has now replaced it.
* 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 “'''[[1682/1681|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 - “'''[[nokotan|the nokotan]]'''” - for use cases where a shorter name is needed.
* 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 - “'''[[nokotan|the nokotan]]'''” - for use cases where a shorter name is needed.
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==== Construct diagrams or lists ====
==== Construct diagrams or lists ====
* Make manual, curated tables of [[interval]]s for:
* 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 [[interval]]s for:<small>
** [[8ed5/4]] to 9ed5/4
** [[8ed5/4]] to 9ed5/4
** [[4ed4/3]] to 8ed4/3
** [[4ed4/3]] to 8ed4/3
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** [[8ed4]] to 15ed4
** [[8ed4]] to 15ed4
** [[3ed5]] to 5ed5
** [[3ed5]] to 5ed5
** [[4ed6]]
** [[4ed6]]</small>
* Construct a [[:Category:Tables|table]] of how relatively well each odd [[harmonic]] up to [[23/1|23]] is approximated in each [[EDO]] up to [[100edo]]
* Make all the wanted mappings listed in [[:Category:Todo:add lumatone mapping]]
* 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 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
* Construct a [[tonality diamond]] or something like one for each “[[equalizer subgroup]]” and document them on the equalizer subgroup page
* 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 mappings listed in [[:Category:Todo:add lumatone mapping]]
* Make all the wanted tables listed in [[:Category:Todo:add rank 2 temperaments table]]


==== Repair mistakes ====
==== 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 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 72edo]], change the scales to be in the more compact format that is used on edo pages instead of a ‘Scala-like’ format
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==== Explore, discover, document ====
==== Explore, discover, document ====
* Create a 15 to 25 tone [[complexity]] 2.3.7.13 [[temperament]] and document it on [[No-fives subgroup temperaments]]
* Create a 15 to 25 tone complexity 2.5.11 & 2.5.11.13 temperament and document it on [[No-threes subgroup temperaments]]
* Find nice 5 to 7 tone subsets of [[Shaka10]], [[Starling12]], [[Thrush12]] and document them under a “subsets” heading on those scales’ pages
* 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 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]]
* Add subsets to all 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 tone scales pages
* Find 4 to 7 tone subsets for every 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 or 19-tone scale page
* Test the following [[arithmetic pitch sequence]]s and add any especially useful or interesting ones to the [[Gallery of arithmetic pitch sequences]]:
**APS1/2méride
**APS1/3méride
**APS2/3méride
**APS1/4méride
**APS3/4méride
**APS1/5méride
**APS2/5méride
**APS3/5méride
**APS1/6méride
**APS5/6méride
**APS1/7méride
**APS2/7méride
**APS3/7méride
**APS4/7méride
**APS5/7méride
**APS6/7méride
**APS1/8méride
**APS3/8méride
**APS5/8méride
**APS7/8méride
**APS1/9méride
**APS2/9méride
**APS4/9méride
**APS5/9méride
**APS7/9méride
**APS8/9méride
**APS1/10méride
**APS3/10méride
**APS7/10méride
**APS1/11méride
**APS2/11méride
**APS3/11méride
**APS4/11méride
**APS5/11méride
**APS6/11méride
**APS7/11méride
**APS8/11méride
**APS9/11méride
**APS10/11méride
**APS1/12méride
**APS5/12méride
**APS7/12méride
**APS11/12méride
**APS1/13méride
**APS2/13méride
**APS3/13méride
**APS4/13méride
**APS5/13méride
**APS6/13méride
**APS7/13méride
**APS8/13méride
**APS9/13méride
**APS10/13méride
**APS11/13méride
**APS12/13méride
**APS1/14méride
**APS3/14méride
**APS5/14méride
**APS9/14méride
**APS11/14méride
**APS13/14méride
**APS1/15méride
**APS2/15méride
**APS4/15méride
**APS7/15méride
**APS8/15méride
**APS11/15méride
**APS13/15méride
**APS14/15méride
**APS1/16méride
**APS3/16méride
**APS5/16méride
**APS7/16méride
**APS9/16méride
**APS11/16méride
**APS13/16méride
**APS15/16méride
**APS1/17méride
**APS2/17méride
**APS3/17méride
**APS4/17méride
**APS5/17méride
**APS6/17méride
**APS7/17méride
**APS8/17méride
**APS9/17méride
**APS10/17méride
**APS11/17méride
**APS12/17méride
**APS13/17méride
**APS14/17méride
**APS15/17méride
**APS16/17méride
**APS1/18méride
**APS5/18méride
**APS7/18méride
**APS11/18méride
**APS13/18méride
**APS17/18méride
**APS1/19méride
**APS2/19méride
**APS3/19méride
**APS4/19méride
**APS5/19méride
**APS6/19méride
**APS7/19méride
**APS8/19méride
**APS9/19méride
**APS10/19méride
**APS11/19méride
**APS12/19méride
**APS13/19méride
**APS14/19méride
**APS15/19méride
**APS16/19méride
**APS17/19méride
**APS18/19méride
**APS1/20méride
**APS3/20méride
**APS7/20méride
**APS9/20méride
**APS11/20méride
**APS13/20méride
**APS17/20méride
**APS19/20méride


==== Approximate x in y ====
==== Approximate x in y ====
Line 680: Line 611:


==Random stuff I’d like to share==
==Random stuff I’d like to share==
===List of equal divisions including novelties===
* [[User:BudjarnLambeth/List of equal divisions including novelties]]
<br>


===Hot takes===
===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 🎉
* '''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 [[:Category:Novelties|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.)
* '''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 [[:Category:Novelties|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 [[Temperament naming|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 [[damage|accurate]] and [[badness|technically better]] - a bland name can kill a temperament’s appeal, a fun name can create appeal out of nothing.
* '''Importance of common names:''' I would prefer to use a temperament [[Temperament naming|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 [[damage|accurate]] and [[badness|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 index]]es 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:  
* '''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:  


Line 691: Line 633:


::: [[User:BudjarnLambeth/Brainstorming mostly bad ideas to solve the comma naming debate]]
::: [[User:BudjarnLambeth/Brainstorming mostly bad ideas to solve the comma naming debate]]
* '''My preferred EDO subgroups:''' A list of subgroup interpretations for the first 50 and a bit EDOs. Also includes a description of [[12edo]] as a 2.3.5.17.19 subgroup [[temperament]] with a list of [[chord]]s and [[interval]]s viewed from that lens:
<br><br>
 
===Approximations of gamelan scales in edos up to 60===
* [[User:BudjarnLambeth/Edo approximations of gamelan scales]]
<br><br>
 
===Eagle JI subsets===
* [[User:BudjarnLambeth/Eagle JI subsets]]
<br><br>
 
===12edo interpreted as a 2.3.5.17.19 subgroup temperament===
* [[User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning]]
<br><br>
 
===Tunings for each subgroup===
* [[User:BudjarnLambeth/Tunings for each subgroup]]
<br><br>


::: [[User:BudjarnLambeth/How I choose a subgroup for an EDO]]
===Gallery of xenharmonic word painting (you can contribute!)===
* [[User:BudjarnLambeth/Gallery of xenharmonic word painting]]
<br><br>
<br><br>
===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.
<br><br><br>


===Ratios as planets===
===Ratios as planets===
Line 711: Line 678:
* '''[[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.
* '''[[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.
<br><br>
<br><br>
===Integer commas===
All commas with numerator less than 5 digits, and prime limit 97 or lower, which are  within 0.01 cents of a round-number cents value from 1 to 210:
UNNOTICEABLE
* 2888/2883 = 31lim 3c
SMALL
* 1040/1037 = 61lim 5c
* '''289/288 = 17lim 6c'''
* '''248/247 = 31lim 7c'''
* '''217/216 = 31lim 8c'''
* 1350/1343 = 79lim 9c
* 1275/1264 = 79lim 15c
* 290/287 = 41lim 18c
* '''396/391 = 23lim 22c'''
* '''279/275 = 31lim 25c'''
* 323/318 = 53lim 27c
* '''187/184 = 23lim 28c'''
* 301/296 = 43lim 29c
MEDIUM
* 169/166 = 83lim 31c
* 1296/1273 = 67lim 31c
* 273/268 = 67lim 32c
* 1430/1403 = 61lim 33c
* 1449/1420 = 71lim 35c
* '''243/238 = 17lim 36c'''
* 1007/948 = 53lim 40c
* 470/459 = 47lim 41c
* 292/285 = 73lim 42c
* 6300/6149 = 43lim 42c
* '''693/676 = 13lim 43c'''
* 6889/6720 = 83lim 43c
* '''279/272 = 31lim 44c'''
* 267/260 = 89lim 46c
* 20213/19683 = 41lim 46c
* 256/249 = 83lim 48c
* 215/209 = 43lim 49c
* 6358/6177 = 71lim 50c
* 310/301 = 43lim 51c
* 999/970 = 97lim 51c
* 169/164 = 41lim 52c
* 377/365 = 73lim 56c
* 2482/2403 = 89lim 56c
* 14110/13653 = 83lim 57c
* 388/375 = 97lim 59c
* 675/649 = 59lim 68c
* 224/215 = 43lim 71c
* 2862/2747 = 67lim 71c
* 270/259 = 37lim 72c
* 1769/1694 = 61lim 75c
* 155/148 = 37lim 80c
* 1247/1190 = 43lim 81c
* 235/224 = 47lim 83c
* 815/775 = 37lim 85c
* 533/506 = 41lim 90c
* 1520/1443 = 37lim 90c
* 332/315 = 83lim 91c
* 1140/1081 = 47lim 92c
* 8723/8262 = 61lim 94c
* 2135/2021 = 61lim 95c
* 312/295 = 59lim 97c
* 2231/2107 = 97lim 99c
* 196/185 = 37lim 100c
LARGE
* 847/799 = 47lim 101c
* '''343/323 = 19lim 104c'''
* 666/625 = 37lim 110c
* '''364/341 = 31lim 113c'''
* 1435/1342 = 61lim 116c
* 658/615 = 47lim 117c
* 3071/2867 = 83lim 119c
* '''224/209 = 19lim 120c'''
* 237/221 = 79lim 121c
* '''338/315 = 13lim 122c'''
* 1984/1849 = 43lim 122c
* 1079/1005 = 83lim 123c
* '''2610/2431 = 29lim 123c'''
* 5125/4757 = 71lim 129c
* 9317/8643 = 67lim 130c
* 1825/1692 = 73lim 131c
* 725/671 = 61lim 134c
* '''225/208 = 13lim 136c'''
* 1681/1554 = 41lim 136c
* '''92/85 = 23lim 137c'''
* '''605/558 = 31lim 140c'''
* 800/737 = 67lim 142c
* '''391/360 = 23lim 143c'''
* 555/511 = 73lim 143c
* 946/871 = 67lim 143c
* 213/196 = 71lim 144c
* 915/841 = 61lim 146c
* '''476/437 = 23lim 148c'''
* 2626/2409 = 73lim 148c
* 1736/1591 = 43lim 151c
* 345/316 = 79lim 152c
* '''441/403 = 31lim 156c'''
* 259/236 = 59lim 161c
* 12826/11687 = 53lim 161c
* '''343/312 = 13lim 164c'''
* '''11/10 = 11lim 165c'''
* 175/159 = 53lim 166c
* 1739/1580 = 79lim 166c
* 87/79 = 79lim 167c
* 1157/1050 = 89lim 168c
* 645/584 = 73lim 172c
* 1020/923 = 71lim 173c
* 7000/6327 = 37lim 175c
* 1769/1598 = 61lim 176c
* 50344/45425 = 79lim 178c
* '''621/590 = 23lim 179c'''
* 319/287 = 41lim 183c
* 648/583 = 53lim 183c
* 148/133 = 37lim 185c
* 481/432 = 37lim 186c
* '''589/529 = 31lim 186c'''
* 826/741 = 59lim 188c
* '''279/250 = 31lim 190c'''
* 455/407 = 37lim 193c
* 2613/2336 = 73lim 194c
* 291/260 = 97lim 195c
* 3692/3293 = 89lim 198c
* 7215/6413 = 53lim 204c
* 517/459 = 47lim 206c
* '''5491/4875 = 19lim 206c'''
* 630/559 = 43lim 207c
* 53/47 = 53lim 208c
* 534/473 = 89lim 210c


== Useful links for my own convenience ==
== Useful links for my own convenience ==
<br>
<br>
<big>[[User:BudjarnLambeth/Sandbox]]
<big>[[User:BudjarnLambeth/Sandbox]]
<br>
<br>
[[User:BudjarnLambeth/Sandbox2]]
<br>
<br>
[[Gallery of just intervals]]
<br>
<br>
[[Harmonic entropy of just intervals]]
<br>
<br>
[[User:Userminusone/Constructing a comma list using the Averiant]]
<br>
<br>
<br>
<br>
[[User:Ganaram inukshuk/Catalog of MOS Scales]]
[[User:Ganaram inukshuk/Catalog of MOS Scales]]
</big>
</big>

Latest revision as of 09:06, 21 August 2025

This is the user page of Budjarn Lambeth, the wiki contributor and amateur music theorist.

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

Personal information



Music

My favourite tracks I have made :)

  1. 33edo track Feb 2024 (bright, lush, mellow and colourful synthwave)
  2. Recording in my "Rocket temperament" (melancholic, wistful dungeon synth; loosely inspired by Greystar)
  3. Compressed 8ve 80edo track Aug 2025 (contemporary classical improv on synthesizer)
  4. 21edo track May 2025 (dark dungeon synth; loosely inspired by Indonesian gamelan and Japanese music)
  5. 60afdo track Dec 2024 (bright, spacious, tropical dungeon synth; loosely inspired by Greystar)


YouTube discography:

https://youtube.com/playlist?list=PLVHnByvMeRTohfmDPkc0EfOByWaX4xXAF


Bandcamp discography:

https://budjarnlambeth.bandcamp.com/


Most tracks on Bandcamp have not yet been uploaded to YouTube and vice versa.



My favourite microtonal composers




Wiki contributions

Discoveries

Invented approaches to constructing tunings

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

Procedural approaches:

Sculptural approaches:

Invented approaches to classifying tunings

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

Invented tunings (scales)

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

Invented tunings (regular temperaments)

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



Improvements

Significant page creations

Bulk page improvements

Structural wiki improvements

• List and table creations

Constructed:

• Comma documentation and organisation

Name changes I was involved in

  • 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 “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 “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 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 sectarian 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.
  • 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”.



Full list of contributions



(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 :)

Structural wiki improvements

Construct diagrams or lists

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

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.
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.
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:



Random stuff I’d like to share

List of equal divisions including novelties


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



Approximations of gamelan scales in edos up to 60



Eagle JI subsets



12edo interpreted as a 2.3.5.17.19 subgroup temperament



Tunings for each subgroup



Gallery of xenharmonic word painting (you can contribute!)



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.


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.



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