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Combined display of all available logs of Xenharmonic Reference. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).

• 09:28, 13 December 2025 Vector talk contribs created page Notation (Created page with "There are many different forms of '''musical notation''' in xenharmony. This page will serve as an introduction to some of the concepts found in xenharmonic notation, and some of the more common types. Note that this does not cover interval naming systems with no notational counterpart. Notation systems are usually designed for consistent tuning systems such as regular temperaments, or approximately consistent tuning systems....") Tag: Visual edit
• 07:30, 13 December 2025 Vector talk contribs created page Diatonic notation (Created page with "'''Diatonic notation''' or '''chain-of-fifths notation''' is the standard notation system in Western music, which notates systems that are octave-periodic and generated by a (just or tempered) perfect fifth. Many tuning systems may be notated this way. EDOs can be notated using unmodified diatonic notation if they contain a single chain of fifths that generates a diatonic scale. For example, 23edo cannot be notated with standard diatonic notation because it d...") Tag: Visual edit
• 06:55, 13 December 2025 Vector talk contribs created page User:Vector/primes.css (Template page for prime background colors class)
• 03:03, 13 December 2025 Vector talk contribs created page User talk:Calvera (Hi: new section)
• 02:46, 13 December 2025 Vector talk contribs created page Temperament archetype (Created page with "A '''temperament archetype''' is a way of expressing the structure of a regular temperament. It is notated by a '''ploidacot signature.''' ''TODO: Provide a description of ploidacot notation''") Tag: Visual edit
• 02:29, 13 December 2025 Vector talk contribs created page Irregular temperament (Created page with "An '''irregular temperament''' is a temperament that is not a regular temperament. Specifically, an irregular temperament either does not allow free transposition, or its JI interpretation is otherwise not consistent (for example, a temperament where stacking 3/2 twice does not result in 9/8). Any temperament with a finite set of notes is an irregular temperament, and other than the equal temperaments, any temperament with a finite set of notes ''within the octav...") Tag: Visual edit
• 01:48, 13 December 2025 Vector talk contribs created page Vector's just notation (Created page with " Vector's just notation is a way of writing intervals based on the pyth-spine and combining syllables for commatic alterations, somewhat similarly to [https://en.xen.wiki/w/Color_notation color notation]. It uses Vector's ordinal anchors, which are equal to neutral Pythagorean intervals. === 3-limit alterations === The 3-limit follows standard diatonic notation. This table is for seconds, thirds, sixths, and sevenths. Note that the nominals are the C major scale, so C-...") Tag: Visual edit
• 00:33, 13 December 2025 Vector talk contribs created page Equipentatonic (Created page with "An '''equipentatonic scale''' is a scale with 5 approximately equally spaced notes within the octave. A tuning system that generates an equipentatonic scale may be conceptualized with the '''5-form'''. == 5edo == 5edo is the basic equipentatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/5) = 240 cents. === Theory === ===== JI approximation ===== 5edo is most obviously a 2.3.7 system (and this property carries to 5-form systems as...") Tag: Visual edit
• 23:49, 12 December 2025 Vector talk contribs created page Diatonic major second (Created page with "The '''diatonic major second''' ('''M2'''), represented by the frequency ratio '''9/8''', is the larger of the two seconds (1-step intervals) in the diatonic scale. It is generated by stacking 2 fifths and octave-reducing. In Pythagorean tuning (and thus purely-tuned just intonation), it is approximately 203.9 cents in size, but as an interval in the abstract diatonic scale it may range from 171 to 240 cents, depending on the tuning. It functions as the large st...") Tag: Visual edit
• 23:40, 12 December 2025 Vector talk contribs created page 9/8 (Redirected page to Diatonic major second) Tags: New redirect Visual edit
• 23:15, 12 December 2025 Vector talk contribs created page Template:First 12 edo intervals (Created page with "{{#expr: 1200/{{{edo|31}}} round 1}}, {{#expr: 2*1200/{{{edo|31}}} round 1}}, {{#expr: 3*1200/{{{edo|31}}} round 1}}, {{#expr: 4*1200/{{{edo|31}}} round 1}}, {{#expr: 5*1200/{{{edo|31}}} round 1}}, {{#expr: 6*1200/{{{edo|31}}} round 1}}, {{#expr: 7*1200/{{{edo|31}}} round 1}}, {{#expr: 8*1200/{{{edo|31}}} round 1}}, {{#expr: 9*1200/{{{edo|31}}} round 1}}, {{#expr: 10*1200/{{{edo|31}}} round 1}}, {{#expr: 11*1200/{{{edo|31}}} round 1}}, {{#expr: 12*1200/{{{edo|31}}} round...")
• 07:37, 12 December 2025 Vector talk contribs created page Interval space (Created page with "An '''interval space''' is a multi-dimensional space in which intervals in just intonation or a regular temperament exist. The ''dimensionality'' or ''rank'' of an interval space is the minimum number of different "step sizes" you need to stack to all the intervals in the space. An equal (rank-1) temperament has a 1D interval space, because any interval can be represented by one integer (the number of steps). A temperament such as meantone...") Tag: Visual edit
• 06:52, 12 December 2025 Vector talk contribs moved page Color Scheme E to Color schemes
• 06:52, 12 December 2025 Vector talk contribs created page Color Scheme E (Created page with "thumb|342x342px|Color Scheme E '''Color Scheme E''' is a tentative color scheme to use for prime harmonics and potentially other intervals on the wiki. It aligns with various strong consensi about the colors associated with primes (most notably, "7 is blue"). It is based on Hojo Minori's color scheme, in that it defines a gradient to be used throughout the octave and pulls colors from that. The "neutral" colo...") Tag: Visual edit
• 06:38, 12 December 2025 Vector talk contribs created page File:Color Scheme E, neutral and standard version.png
• 06:38, 12 December 2025 Vector talk contribs uploaded File:Color Scheme E, neutral and standard version.png
• 04:41, 12 December 2025 Vector talk contribs created page Vector's interval naming scheme (Created page with "Each interval name consists of a ''quality'' and an ''ordinal.'' Note that this is not the same as VJN, which names intervals based on commatic alterations, or ADIN, which names intervals based on their position in edos. == Process == To name an interval: === 1. Octave-reduce and determine closest ordinal. === The ordinals are as follows: {| class="wikitable" |+ !Ordinal !Neutral location !Cents |- |Unison |sqrt(2048/2187) | -57 |- |Seco...") Tag: Visual edit
• 10:27, 11 December 2025 Vector talk contribs created page Pythagorean tuning (Created page with "'''Pythagorean tuning''' is the tuning system in which only '''3-limit''' just intonation intervals are used - that is, intervals generated by stacking perfect fifths of 3/2 and octaves of 2/1 up and down. Pythagorean tuning is a rank-2 system that does not include any tempering, and is thus useful as a basis for notation. When accounting for octave equivalence, Pythagorean tuning mirrors the structure of the chain of fifths. Simple Pytha...") Tag: Visual edit
• 10:01, 11 December 2025 Vector talk contribs created page Equal temperament (Created page with "An '''equal temperament''' is the regular temperament interpretation of an EDO (or more generally, any equal tuning). As such, it contains not only a set of notes but a way to translate JI intervals into numbers of steps in a consistent manner. == Vals == An equal temperament is notated by a '''val''', a sequence of numbers that specifies how many steps each prime is mapped to in the ET. The val consisting of the edo's best direct approximations of each prime i...") Tag: Visual edit
• 09:16, 11 December 2025 Vector talk contribs created page Xenharmonic Reference talk:Guidelines (What to use for the cutoff for referring to just intervals by name?: new section)
• 08:49, 11 December 2025 Vector talk contribs created page Mode (Created page with "The term '''mode''', in modern music theory, is usually used to refer to the rotations of a periodic scale, that is, versions of the scale starting on each of its notes. An abstract scale pattern is usually mode-agnostic, without a specified root note, although one is usually chosen as the 'default' for notational purposes (e.g. LLsLLLs - each L represents a large step and each s represents a small step). For example, modes of LssLs include sLssL, LsLss, and the specific...") Tag: Visual edit
• 08:42, 11 December 2025 Vector talk contribs created page User:Vector/Official prime color scheme (Created page with "{| class="wikitable" | style="background-color:#666" |2 || Light Gray |- | style="background-color:#bb6" |3|| Yellow |- | style="background-color:#b66" |5|| Red |- | style="background-color:#67b" |7|| Dark Blue |- | style="background-color:#86b" |11|| Violet |- | style="background-color:#b86" |13|| Orange |- | style="background-color:#6b6" |17|| Green |- | style="background-color:#444" |19|| Dark Gray |- | style="background-color:#69b" |23|| Sky Blue |- | style="backgrou...") Tag: Visual edit: Switched
• 08:21, 11 December 2025 Vector talk contribs created page Golden sequences and tuning (Created page with "Golden sequences (the generalization of the Fibonacci sequence to have any two starting values) have a number of interesting properties relating to the tuning of MOS scales, and potentially can be used to determine a way to "naturally" tune a MOS (and thus generate a line of daughter MOSes). == Theory == Say that we want to tune a moment-of-symmetry scale, such as diatonic, such that continuing the chain of generators never results in extremely close Diesi...") Tag: Visual edit
• 08:18, 11 December 2025 Vector talk contribs created page Template:C (Created page with "¢")
• 08:03, 11 December 2025 Vector talk contribs created page Diesis (Created page with "Diesis is a word with a number of different meanings. A diesis is the difference between two enharmonic notes in a tuning system, or any small difference between two notes in a scale. A diesis is usually understood to ''not'' be tempered out, as opposed to a comma, which is tempered out. More specifically, a diesis may be: - The difference between a small step and a chromatic semitone in a scale, such as the Pythagorean comma in the diatonic scale. - The int...") Tag: Visual edit
• 06:37, 11 December 2025 Vector talk contribs created page Collection of chords (Created page with "This page covers chords with fewer than 5 pitch classes. At 5 pitch classes or above, the "chord" becomes more treatable as a scale, and may be found at Collection of scales. == Triads == A '''triad''' is a chord containing 3 pitch classes. That is, C-E-G is a triad, but C-E-C is not a triad because even though the Cs may be separated by an octave, they are the same pitch class. Some theorists restrict the word 'triad' to exclusively refer to stacks of two thirds....") Tag: Visual edit
• 06:04, 11 December 2025 Vector talk contribs created page Harmonic tetrad (Redirected page to Collection of chords) Tags: New redirect Visual edit
• 05:36, 11 December 2025 Vector talk contribs created page 12edo (Created page with "'''12edo''' is the equal tuning featuring steps of (1200/12) = 100 cents, by definition, as 12 steps stack to the octave 2/1. It is the dominant tuning system in the world, and as such is covered by Xenbase for completeness as it is not 'xenharmonic'. == Theory == ==== JI approximation ==== 12edo is conventionally seen as a 2.3.5 edo, though perhaps more salient to conventional Western musical practice is the fact that it contains the basic diat...") Tag: Visual edit: Switched
• 04:45, 11 December 2025 Vector talk contribs created page Module:Sequence (Created page with "local p = {} local getArgs = require('Module:Arguments').getArgs function p.contains(seq, n) if n > seq[#seq] then return nil end for i = 1, #seq do if seq[i] == n then return true end end return false end function p.get_term(frame) local args = getArgs(frame) return p._get_term(args[1], tonumber (args[2])) end function p._get_term(seq, n) local sequences = { ["odd_limit_diff"] = p.odd_limit_diff, ["zeta_peak"] = p.zeta_peak, ["zeta_integral"]...")
• 04:43, 11 December 2025 Vector talk contribs created page Module:Template input utils (Created page with "-- This module follows User:Ganaram inukshuk/Provisional style guide for Lua local p = {} -- TODO: move tip functions here? See Module:Template input parse -- TODO: -- Add param name normalization: params close enough to snake_case are normal- -- ized to snake_case -- Library module for common operations with handling template input. -- - Numbered <anything> to table extract args and places them into a table. -- Extracts numbered args (from frame.args) and st...")
• 04:43, 11 December 2025 Vector talk contribs created page Module:Navbar (Created page with "local p = {} -- Main function called by navigation box templates function p._navbar(name, mode, text, namespace) mode = mode or "" text = (text == nil and "" or text .. " ") namespace = namespace or "Template" local p_name = string.format("%s:%s", namespace, name) local p_talk_name = string.format("%s talk:%s", namespace, name) local p_edit_name = "Special:EditPage/" .. p_name local s = " • " local links = (mode == mini and {"V", "T", "E"} or {"View", "Ta...")
• 04:42, 11 December 2025 Vector talk contribs created page Module:Arguments (Created page with "-- This module provides easy processing of arguments passed to Scribunto from -- #invoke. It is intended for use by other Lua modules, and should not be -- called from #invoke directly. local libraryUtil = require("libraryUtil") local checkType = libraryUtil.checkType local arguments = {} -- Generate four different tidyVal functions, so that we don't have to check the -- options every time we call it. local function tidyValDefault(key, val) if type(val) == "string"...")
• 04:41, 11 December 2025 Vector talk contribs created page Module:Rational (Created page with "local p = {} local seq = require("Module:Sequence") local utils = require("Module:Utils") -- enter a numerator n and denominator m -- returns a table of prime factors -- similar to a monzo, but the indices are prime numbers. function p.new(n, m) m = m or 1 if n == 0 and m == 0 then return { nan = true } elseif n == 0 then return { zero = true, sign = utils.signum(m) } elseif m == 0 then return { inf = true, sign = utils.signum(n) } end local sign = utils.s...")
• 04:41, 11 December 2025 Vector talk contribs created page Module:Yesno (Created page with "-- Function allowing for consistent treatment of boolean-like wikitext input. return function(val, default) -- If your wiki uses non-ascii characters for any of "yes", "no", etc., you -- should replace "val:lower()" with "mw.ustring.lower(val)" in the -- following line. val = (type(val) == "string" and mw.ustring.lower(val) or val) if val == nil then return nil elseif val == true or val == "yes" or val == "y" or val == "true" or val == "t" or val == "...")
• 04:37, 11 December 2025 Vector talk contribs created page Module:Utils (Created page with "local p = {} local get_args = require("Module:Arguments").getArgs local yesno = require("Module:Yesno") -- TODO??? Enforce rule for prefixing module-callable functions with an -- underscore, regardless of whether a wrapper is needed or can be made???? -- Trim a string (remove leading and trailing, but not interior, whitespace) function p.trim(s) return s:match("^%s*(.-)%s*$") end -- Wrapper function for template access to Module:Yesno function p._yesno(frame)...")
• 04:35, 11 December 2025 Vector talk contribs created page Module:Infobox (Created page with "-- This module follows User:Ganaram inukshuk/Provisional style guide for Lua local getArgs = require("Module:Arguments").getArgs local navbar = require("Module:Navbar")._navbar local tiu = require("Module:Template input utils") local yesno = require("Module:Yesno") local p = {} -- TODO (medium priority): -- - Use templatestyles -------------------------------------------------------------------------------- -------------------------------- MAIN FUNCTIONS --...")
• 04:33, 11 December 2025 Vector talk contribs created page Module:Infobox interval region (Created page with " local p = {} local u = require("Module:Utils") local infobox = require("Module:Infobox") local rat = require("Module:Rational") local yesno = require("Module:Yesno") function p.concatenate_tables(t1, t2)     for i=1, #t2 do         t1[#t1 + 1] = t2[i]     end end function p.infobox_IR(frame)     local name = frame.args["regionname"]     local complement = frame.args["complement"]     local centslower = frame.args["centsLowerWide"]     lo...") Tag: Visual edit
• 04:32, 11 December 2025 Vector talk contribs created page Template:Infobox interval region (Created page with "{{#invoke: Infobox_interval_region | infobox_IR | regionname={{{Name|{{PAGENAME}}}}} | complement={{{Complement|}}} | centsLowerWide={{{Cents lower wide|}}} | centsLower={{{Cents lower|}}} | centsUpperWide={{{Cents upper wide|}}} | centsUpper={{{Cents upper|}}} | equave={{{Equave|}}} | ji3={{{3-limit intervals|}}} | ji5={{{5-limit intervals|}}} | ji7={{{7-limit intervals|}}} | ji11={{{11-limit intervals|}}} | ji13={{{13-limit intervals|}}} | jiHigh={{{Other JI intervals|...")
• 04:23, 11 December 2025 Vector talk contribs created page Template:Diatonic interval category (Created page with "As a diatonic interval category, a {{#ifeq: {{{ordinal}}} | 0 | unison |}} {{#ifeq: {{{ordinal}}} | 1 | second |}} is an interval that spans {{#ifeq: yes | yes | Hooray...! | Darn...! }}")
• 04:15, 11 December 2025 Vector talk contribs created page Rotation (Redirected page to Mode) Tags: New redirect Visual edit
• 04:12, 11 December 2025 Vector talk contribs created page MOS (Created page with "A MOS (or mos, or moment of symmetry scale) is a scale where every step is either small or large (with no in-between), and the same is true with any interval formed by two adjacent steps (a "2-step"), etc. Any multiple of the period (which is usually an octave or a fraction thereof) has only one size. MOS scales are often referred to as MOSes, thus MOS can be used as either an adjective or a noun. == Examples == The most widely used MOS scale is the MOS form of the dia...") Tag: Visual edit
• 04:03, 11 December 2025 Vector talk contribs created page Collection of scales (Created page with "This page serves as a collection of less notable scales. == JI lattices == thumb|218x218px|The lattice for the Chair of Mr. Bob === Kee'ra (Chair of Mr. Bob) === This scale consists of the intervals 21/20, 35/32, 6/5, 21/16, 7/5, 3/2, 8/5, 105/64, and 7/4 within the octave 2/1. When it is loaded in Scale Workshop, the lattice resembles a chair. The name "Chair of Mr. Bob" was given by dotuXil. The name "Kee'ra" was given by Vector Gr...") Tag: Visual edit
• 03:58, 11 December 2025 Vector talk contribs created page File:Mr bob.png
• 03:58, 11 December 2025 Vector talk contribs uploaded File:Mr bob.png
• 03:24, 11 December 2025 Vector talk contribs created page User:Vector/Edo template (Created page with "(ED), or (equal divisions), is the equal tuning featuring steps of (equave/N) ~= # cents, N of which stack to the (equave). (Additional notes) == Theory == ==== JI approximation ==== - Basic prime limit or subgroup - Diatonic scale - Additional notes ===== Subsection: Interval accuracy table - style guide ===== {| class="wikitable" |+Approximation of prime harmonics in example edo ! colspan="2" |Harmonic ! style="background-color:#666" |2 ! style="background-color:#...") Tag: Visual edit: Switched
• 03:02, 11 December 2025 Vector talk contribs created page 22edo (Created page with "'''22edo''', or 22 equal divisions of the octave, is the equal tuning featuring steps of (1200/22) ~= 54.5 cents, 22 of which stack to the perfect octave 2/1. It is not a meantone system, but it is a functional 11-limit system, with 3 at ~709 cents, 5 at ~382 cents, 7 at ~982 cents, and 11 at ~545 cents. == Theory == 22edo is comparable in accuracy in the 7-limit to 12edo in the 5-limit. Because it is not a meantone system, the best diatonic to use for 5-limit harm...")
• 02:04, 11 December 2025 Vector talk contribs created page Regular temperament (Created page with "A '''regular temperament''' is a temperament (an approximation of just intonation) that is consistent. That is, the (logarithmic) sum of two tempered intervals must always be the tempered version of the sum of the JI intervals. For example, in a regular temperament, if you stack the tempered version of 9/8, it must always produce the tempered versions of 81/64, 729/512, 6561/4096, etc. It follows from this that unlimited free modulation must be possible - any...")
• 01:24, 11 December 2025 Vector talk contribs created page Mabilic (Created page with "'''Mabilic''' is a rank-2 regular temperament based around the antidiatonic scale structure. 5/2 is split into three generators which are somewhat sharper than a fourth (~520-530 cents), five of which stack (octave-reduced) to make 8/7. Mabilic in its basic form is a 2.5.7 subgroup temperament, because 3 cannot be added without a high complexity or a significant loss of accuracy. Extensions of mabilic include * trismegistus (best tuned aro...")
• 00:43, 11 December 2025 Vector talk contribs created page Diatonic (Created page with "'''Diatonic''' is a kind of scale characterized by the division of the octave into 5 large steps (''L'') and 2 small steps (''s'') in an ''LLsLLLs'' pattern, or any rotation thereof. The most widespread diatonic is the MOS form, ''5L 2s'', where the large steps are equally sized and the small steps are also equally sized. However, other similar scales may be called diatonic as well. == MOS diatonic == The MOS diatonic scale is ''5L 2s'', tuned most simply i...")
• 00:13, 10 December 2025 User account Vector talk contribs was created