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23:2423:24, 25 December 2025 Isomorphic (hist | edit) [1,199 bytes] Vector (talk | contribs) (Created page with "An '''isomorphic''' table of notes is one where every instance of the same offset represents the same interval, every step in the same direction is the same size of interval, and the same chord always has the same shape, even when moved to different notes. When used as a note entry device, it is called an '''isomorphic keyboard''', and the Lumatone is an example. The standard keyboard layout is not isomorphic, because a C major chord and an A minor chord have the sam...") Tag: Visual edit
21:4321:43, 25 December 2025 Penslen (hist | edit) [2,001 bytes] Ground (talk | contribs) (Created page with "'''Penslen''' is an aberrismic ternary scale with structure 5L5m6s. It is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024. Tuning shown is just 2.3.5, Slendric 7, tempered 11/8 offset. 7 ≈ 2^((10-log2(3))/3) {| class="wikitable" |+Mode A3 (msLsmLsmLsmsLmsL) Just-2.3.5 Tuning | |0 |1 |- |3 |702.0 |51.6 |- |2 |468.0 |1017.6 |- |1 |234.0 |783.6 |- |0 |0.0 |549.6 |- | -1 |966.0 |315.6 |- | -2 |732.0 |81.7 |- | -3 |498.0 |1047...") Tag: Visual edit: Switched
17:2817:28, 25 December 2025 24edo (hist | edit) [2,340 bytes] Aura (talk | contribs) (Might as well get this started...) Tag: Visual edit: Switched
17:0017:00, 25 December 2025 Souvenirs of the Affliction (hist | edit) [4,703 bytes] Ground (talk | contribs) (Created page with "'''Souvenirs of the Affliction''' is the first full microtonal album by GroundFault Corporation. It is sometimes referred to as '''The Gralbum''' '''2'''. The songs were primarily written from 2023 to 2025, although Nocturne Paranoia was started in 2020. Infobox links [https://groundfco.bandcamp.com/album/souvenirs-of-the-affliction Bandcamp] [https://youtu.be/rrjuGmmodn0 YouTube] == Lyrics == === 1. The Life Unreachable === (Give me another reason to die) (Only...") Tag: Visual edit

21:5621:56, 24 December 2025 37edo (hist | edit) [10,679 bytes] Ground (talk | contribs) (Created page with "{{problematic}} Note from User:ground: hey sorry this was copied from my notes so I'm gradually making my way through the formatting 37edo is the tuning that I use the largest number of distinct scales in. Here are the ones I could think of: * 5:2:1 trackdye 5L2m8s ** Step tunings: (227¢) : 162¢ : 97¢ : 62¢ ** This is the quintessential Aberration scale. There are seven possible structures depending on which diatonic mode you choose to aberrate. It's basic...")
20:5020:50, 24 December 2025 Straddle primes (hist | edit) [301 bytes] Ground (talk | contribs) (Created page with "{{problematic}} '''Straddle primes''' are functional primes in a temperament that straddle their respective just interval by having at least one flat and one sharp approximation available. Dual-fifth systems are usually straddle-3. Eracs were designed to be a notation for straddle prime systems.")
05:2405:24, 24 December 2025 Equiheptatonic (hist | edit) [4,640 bytes] Vector (talk | contribs) (Created page with "An equiheptatonic scale is a scale with 7 approximately equally spaced notes within the octave. A tuning system that generates an equiheptatonic scale may be conceptualized with the '''7-form'''. Below are several examples of equiheptatonic scales. == 7edo == 7edo is the basic equiheptatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/7) ~= 171.4 cents. === Theory === ===== JI approximation ===== 7edo is, very crudely, a 2.3.5 syst...") Tag: Visual edit
03:0703:07, 24 December 2025 Optimizing MOS scales for DR (hist | edit) [1,985 bytes] Inthar (talk | contribs) (Created page with "{{expert}} == Optimizing a MOS for one DR chord == TODO: reword A MOS can tune exactly one DR chord with two non-free deltas can be tuned exactly. === Example === We start by choosing the MOS scale and equave, and the DR chord. For example with 5L 2s ⟨2/1⟩, the usual diatonic scale, and we want to approximate 4:5:6, the just major chord, with a delta-rational MOS chord. Identify the mappings of each of the deltas. The deltas are 5/4, 6/5, 7/6. For a Meanto...")

05:4705:47, 23 December 2025 Combination product set (hist | edit) [2,574 bytes] Inthar (talk | contribs) (Created page with "{{Expert}} A '''combination product set''' (CPS) is a scale generated by the following means: # A set S of n intervals is the starting point. # All the combinations of k elements of the set are obtained, and their products taken. # These are combined into a set, and then all of the elements of that set are divided by one of them (which one is arbitrary; if a canonical choice is required, the smallest element could be used). # The resulting elements are octave-reduced an...")

23:3423:34, 22 December 2025 Cross-set (hist | edit) [5,666 bytes] Inthar (talk | contribs) (Created page with "A '''cross-set''' of two or more chords is a scale formed by taking every element of the Cartesian product of these chords and stacking all the intervals listed in the element (and reducing by the equave if necessary). On this wiki, a cross-set of two chords is denoted as chord1 × chord2 {{adv|(though this is abuse of Cartesian product notation)}}. Category:Scale construction")

06:5006:50, 21 December 2025 Generator sequence (hist | edit) [1,253 bytes] Inthar (talk | contribs) (Created page with "A '''generator sequence''' (GS) is a cyclically repeating sequence of stacked intervals. A GS can be denoted: GS(interval1, interval2, interval3, ..., intervaln), which means: stack interval2 on top of interval1, interval3 on top of interval2, etc. up to intervaln, then stack interval1 again and repeat.")

04:3704:37, 20 December 2025 Xenverse/Earth 22 (hist | edit) [8,068 bytes] Vector (talk | contribs) (Created page with "< Xenverse {{Worldbuilding}} This page discusses the 22EDO music theory used in Earth#22. Earth#22 treats 22edo as a 2.3.7.5 system, with the basic chord being 4:6:7 and 5 being included optionally. == Greek music theory == === Trichords === A ''trichord'' is a set of three notes spanning a perfect fourth. For example, C-D-F is a trichord. They are analogous to real-world tetrachords, but with only one movable tone, rather than two. A trichord may be joined with...") Tag: Visual edit

21:5521:55, 18 December 2025 Operations on intervals (hist | edit) [7,417 bytes] Inthar (talk | contribs) (Created page with "The following are common '''arithmetic operations on musical intervals'''. == Stacking and unstacking == Stacking two intervals feels perceptually like we are adding two distances, though it corresponds to multiplying two frequency ratios. The logarithm function is the bridge between frequency space and pitch space: <math>\log_2 (ab) = \log_2 a + \log_2 b</math> for any two frequency ratios ''a'' and ''b''. The above equation tells us that the sum of the size (in octa...")

10:0810:08, 17 December 2025 Chromatic semitone (hist | edit) [1,925 bytes] Vector (talk | contribs) (Created page with "{{Infobox interval|2187/2048|names=Chromatic semitone, augmented unison|name=Chromatic semitone, augmented unison|Name=Chromatic semitone, augmented unison}} The 3-limit '''chromatic semitone''', also called the '''augmented unison''' ('''A1''') and represented by the ratio '''2187/2048,''' is the difference between the large and small steps of the MOS diatonic scale. It is generated by stacking 7 fifths and octave-reducing. In Pythagorean tuni...") Tag: Visual edit

19:1319:13, 16 December 2025 Taylor series (hist | edit) [4,827 bytes] Lériendil (talk | contribs) (Created page with "''This is an advanced page dealing with detailed mathematical topics, and should not be referred to for guidance on aspects of xenharmony mentioned here that can be described more simply.'' A '''Taylor series''' is a method of approximating a function within a certain range by means of adding successive powers of a small parameter, such that each approximation is increasingly precise by a factor of that parameter. While these can be defined for essentially any function,...")

13:3113:31, 15 December 2025 Glossary (hist | edit) [24,301 bytes] Lériendil (talk | contribs) (Created page with "This page lists various terms conventionally used in xenharmony (or in some cases, general music theory as it applies to xen) that can be briefly described. == Cent == A '''cent''' (abbreviated to c or ¢) is the conventional measurement unit of the logarithmic distance between frequencies; in other words, the size of the interval between them. A cent is defined as a frequency ratio of 2^(1/1200), or a factor of about 1.0005778, such that the octave ([...")
09:3409:34, 15 December 2025 Just-noticeable difference (hist | edit) [1,215 bytes] Vector (talk | contribs) (Created page with "The '''just-noticeable difference,''' about 3.5 cents, is an estimation of the minimum difference in pitch that can be distinguished by the average listener. However, this number actually varies widely, from up to 20 cents in some cases (certain casual listeners) to a fraction of a cent in others (especially with harmonic intervals). The conventional just-noticeable difference also defines an interval region of "'''unnoticeable commas'''" around the unison,...") Tag: Visual edit
05:1905:19, 15 December 2025 41edo (hist | edit) [3,772 bytes] Tristanbay (talk | contribs) (Created page for 41edo) Tag: Visual edit: Switched
00:3000:30, 15 December 2025 Perfect fifth (hist | edit) [5,324 bytes] Vector (talk | contribs) (Created page with "The '''perfect fifth (P5)''', represented by the frequency ratio '''3/2''', is a generator of the MOS diatonic scale and of Pythagorean tuning. It is also the most consonant octave-reduced interval after the octave itself. The note a perfect fifth above the root serves as an important structural anchor for scales, similarly to the perfect fourth. Nearly all musical cultures use the perfect fifth. The perfect fifth contrasts with the diato...") Tag: Visual edit
00:1300:13, 15 December 2025 15edo (hist | edit) [17,844 bytes] Vector (talk | contribs) (Created page with "'''15edo''', or 15 equal divisions of the octave, is the equal tuning featuring steps of (1200/15) ~= 80 cents, 15 of which stack to the perfect octave 2/1. It is notable for its acceptable but rather distant approximation of the 11-limit featuring a near-isoharmonic 4:5:6, and for its contorted mappings. == Theory == ==== JI approximation ==== 15edo has roughly 10-20% error on harmonics 3 through 11, which is a deviation from just intonation significant enough to...") Tag: Visual edit

03:5503:55, 14 December 2025 List of just intonation intervals (hist | edit) [23,053 bytes] Vector (talk | contribs) (Created page with " This is a list of just ratios, similar to the list of EDOs and the list of regular temperaments. It exists to compile information on a number of just ratios. '''Commas should not redirect here!''' They should instead redirect to their corresponding entry on the temperament page, or if present, a page for the temperament itself. {{Adv|The formula for "good edos" is the edos that satisfy, for interval x in cents and edo n: abs(round(xn/1200)-xn/1200)*...") Tag: Visual edit originally created as "List of just ratios"

09:2809:28, 13 December 2025 Notation (hist | edit) [5,350 bytes] Vector (talk | contribs) (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
07:3007:30, 13 December 2025 Diatonic notation (hist | edit) [4,577 bytes] Vector (talk | contribs) (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
02:4602:46, 13 December 2025 Temperament archetype (hist | edit) [198 bytes] Vector (talk | contribs) (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
02:2902:29, 13 December 2025 Irregular temperament (hist | edit) [2,431 bytes] Vector (talk | contribs) (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
02:2002:20, 13 December 2025 Temperament (hist | edit) [2,042 bytes] Calvera (talk | contribs) (stub for temperament article)
01:4801:48, 13 December 2025 Vector's just notation (hist | edit) [3,088 bytes] Vector (talk | contribs) (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
00:5100:51, 13 December 2025 Comma (hist | edit) [2,893 bytes] Calvera (talk | contribs) (stub of a comma article)
00:3300:33, 13 December 2025 Equipentatonic (hist | edit) [4,933 bytes] Vector (talk | contribs) (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

07:3707:37, 12 December 2025 Interval space (hist | edit) [2,196 bytes] Vector (talk | contribs) (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
06:5206:52, 12 December 2025 Xenharmonic Reference:Color schemes (hist | edit) [8,847 bytes] Vector (talk | contribs) (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 originally created as "Color Scheme E"
04:4104:41, 12 December 2025 User:Vector/Vector's interval naming scheme (hist | edit) [3,983 bytes] Vector (talk | contribs) (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 originally created as "Vector's interval naming scheme"

18:0518:05, 11 December 2025 Interseptimal (hist | edit) [229 bytes] Inthar (talk | contribs) (Redirected page to Interordinal) Tag: New redirect
17:4217:42, 11 December 2025 Interordinal (hist | edit) [3,739 bytes] Inthar (talk | contribs) (Created page with "'''Interordinals''' are interval categories halfway between adjacent interval classes of some MOS (usually diatonic). For example, 250c is an interordinal because it falls between 200c (the 12edo major second) and 300c (the 12edo minor third). 19edo and 24edo are notable edos with interordinals. Notable JI interordinals include 15/13 (a semifourth) and 13/10 (a semisixth). The following table shows various ways to name interordinals: {| class="wikitable" |+ Interordina...")
10:2710:27, 11 December 2025 Pythagorean tuning (hist | edit) [7,349 bytes] Vector (talk | contribs) (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
10:0110:01, 11 December 2025 Equal temperament (hist | edit) [4,126 bytes] Vector (talk | contribs) (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
08:4908:49, 11 December 2025 Mode (hist | edit) [2,371 bytes] Vector (talk | contribs) (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
08:2108:21, 11 December 2025 Golden sequences and tuning (hist | edit) [8,707 bytes] Vector (talk | contribs) (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
08:0308:03, 11 December 2025 Diesis (hist | edit) [749 bytes] Vector (talk | contribs) (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
06:3706:37, 11 December 2025 Collection of chords (hist | edit) [7,998 bytes] Vector (talk | contribs) (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
05:3605:36, 11 December 2025 12edo (hist | edit) [3,620 bytes] Vector (talk | contribs) (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
04:1204:12, 11 December 2025 MOS (hist | edit) [11,764 bytes] Vector (talk | contribs) (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
04:0304:03, 11 December 2025 Collection of scales (hist | edit) [626 bytes] Vector (talk | contribs) (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
03:5803:58, 11 December 2025 Software (hist | edit) [2,520 bytes] ArcusRays (talk | contribs) (daws)
03:0203:02, 11 December 2025 22edo (hist | edit) [28,731 bytes] Vector (talk | contribs) (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...")
02:0402:04, 11 December 2025 Regular temperament (hist | edit) [4,332 bytes] Vector (talk | contribs) (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...")
01:2401:24, 11 December 2025 Mabilic (hist | edit) [2,758 bytes] Vector (talk | contribs) (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...")
00:4300:43, 11 December 2025 Diatonic (hist | edit) [5,302 bytes] Vector (talk | contribs) (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...")

05:3905:39, 7 December 2025 DR error measures (hist | edit) [14,517 bytes] Inthar (talk | contribs) (Created page with "<adv>{{adv|Least-squares linear error (here ''linear'' means "in frequency space, not pitch space") is the most naive error measure for approximations to delta-rational chords. Like any other numerical measure of concordance, you should take it with a grain of salt. The idea motivating least-squares error on a chord as an approximation to a given delta signature is the following: Say we want the error of a chord 1:''r''1:''r''2:...:''r''''...") originally created as "Least-squares linear error"

07:1307:13, 2 December 2025 MOS substitution (hist | edit) [5,684 bytes] Inthar (talk | contribs) (Created page with "MOS substitution is a procedure for obtaining a ternary (3 step sizes) scale from two MOS patterns. It consists of taking one MOS pattern (called the template MOS), choosing a step size, and overwriting all instances of that step size using the step pattern of another MOS pattern (called the filling MOS). Unlike MV3 scales, a MOS substitution scale may have any combination of step sizes.")

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