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13 February 2026

8 February 2026

  • 02:0302:03, 8 February 2026 Sensamagic (hist | edit) [1,028 bytes] Vector (talk | contribs) (Created page with "'''Sensamagic''', sometimes known in a tritave-equivalent context as '''Bohlen-Pierce-Stearns''', is the temperament in the 3.5.7 subgroup equating a stack of two 9/7<nowiki/>s with 5/3; this means that the comma 245/243 is tempered out. 9/7 is tuned sharp (about 440 cents) and 5/3 is flattened (about 880 cents). It functions as a tritave analog of meantone, relating the two simplest prime harmonics after the equave with a medium accuracy. Sensamagic ca...") Tag: Visual edit

7 February 2026

  • 23:4823:48, 7 February 2026 34edo (hist | edit) [4,783 bytes] Vector (talk | contribs) (Created page with "thumb|377x377px|The structure of 34edo, visualized. 34edo is the equal tuning system which splits the octave into 34 equal steps, of about (1200/34) ~= 35.3 cents each. It is a 5-limit and 2.3.5.13 system with a number of melodically intuitive structures. == Derivation == === From doubling 17edo === One can observe that 17edo's step is a nearly perfectly tuned 25/24, and also that 5/4 and 6/5 are almost exactly halfway in-between notes of 17edo...") Tag: Visual edit
  • 00:3900:39, 7 February 2026 Vector's temperament accuracy metric (hist | edit) [6,924 bytes] Vector (talk | contribs) (Created page with "{{Technical}} To determine rank-2 temperament accuracy, one approach is to examine each tuning of the temperament where one prime (other than the equave) is tuned just (in this article, we will refer to this interval as the ''eigenmonzo'' - for example, 5 is the eigenmonzo for quarter-comma meantone because that tuning tunes 5 just by setting the generator to 5^(1/4)), and observe how it detunes the rest of the intervals. == The formula == <math>\frac{\operatorname{abs...") Tag: Visual edit

4 February 2026

  • 01:4301:43, 4 February 2026 Canonical extension (hist | edit) [5,619 bytes] Inthar (talk | contribs) (Created page with "{{Problematic}} {{Technical}} Let ''T'' be a regular temperament on JI group ''G''. A strong extension ''U'' of ''T'', on a JI group ''H'' of one rank higher than ''G'' is '''natural''' if the commas tempered out by ''T'' induces the presence of the added basis element of ''H''. A strong extension is merely '''canonical''' if it is agreed that it is an efficient (accurate and low-complexity) extension.") originally created as "Naturality and canonicality"

3 February 2026

  • 17:4517:45, 3 February 2026 14edo (hist | edit) [942 bytes] Calvera (talk | contribs) (Created page with "'''14edo''', or 14 equal divisions of the octave, is the equal tuning featuring steps of (1200/14) ~≃ 85.714 cents, 14 of which stack to the perfect octave 2/1. While it approximates the 5:7:9:11:17:19 harmony relatively well for its size, it lacks a convincing realization of other low-complexity just intervals. Consequently, Delta-rational chord-based approaches may be more practically useful. As a superset of the popular 7edo scale, it offers recognizable tri...")

31 January 2026

  • 23:4323:43, 31 January 2026 Ground's intro to tuning diversity (hist | edit) [8,392 bytes] Ground (talk | contribs) (Created page with "{{problematic}} NOTE: This article is incomplete. Audio examples and images are coming soon. If you've been a musician for long, you should be familiar with the 12 notes: A A#/Bb B C C#/Db D D#/Eb E F F#/Gb G G#/Ab (A) If you're anything like me, you took them for granted for years. After all, why wouldn't you? No one has told you how these were chosen, that's just how music is. But the truth is, these notes are a centuries-long compromise based on lots of math and s...")

30 January 2026

  • 00:5100:51, 30 January 2026 Xenpill (hist | edit) [337 bytes] Ground (talk | contribs) (Created page with "{{problematic}} The '''xenpill''' (verb: '''xenpilling''') is the process of getting a non-xen person to be interested in listening to or composing xenharmonic music. This is usually done by showing them music that is approachable, but contains some moments of obvious xenharmony. === Methods === TBD === Playlists === TBD")

27 January 2026

  • 12:0512:05, 27 January 2026 10edo (hist | edit) [3,854 bytes] Ground (talk | contribs) (Created page with "{{problematic}} '''10edo''', or 10 equal divisions of the octave, is the equal tuning featuring steps of (1200/10) = 120 cents, 10 of which stack to the perfect octave 2/1. It is notable for its good approximation of the 2.7.13 subgroup and for being possibly the smallest edo in the same class as 12edo. == Theory == ==== Chords ==== See also: Oneirotonic#Chords_of_oneirotonic ==== Detempers ==== Due to its small size and unique melodic character, it is ve...") Tag: Visual edit: Switched

26 January 2026

  • 00:1500:15, 26 January 2026 17edo (hist | edit) [1,775 bytes] Inthar (talk | contribs) (Created page with "'''17edo''', or 17 equal divisions of the octave, is the equal tuning featuring steps of (1200/17) ~= 70.6 cents, 17 of which stack to the octave 2/1. {{cat|Edos}}")

24 January 2026

  • 19:0919:09, 24 January 2026 3/1 (hist | edit) [660 bytes] Vector (talk | contribs) (Created page with "3/1, the '''tritave''' or '''perfect twelfth''', is the second most common equave after 2/1. In octave-equivalent systems, it is a fifth plus an octave, and can thus be seen as one of the two generators of Pythagorean tuning. It can be seen as the most consonant interval after the octave, which is the reason for its usage as an equave in systems such as Bohlen-Pierce tuning. Tritave-equivalent systems tend to avoid prime 2, only involving ratios between odd numb...") Tag: Visual edit

22 January 2026

  • 23:0423:04, 22 January 2026 21edo (hist | edit) [3,547 bytes] Inthar (talk | contribs) (Created page with "'''21edo''' is an equal division of the octave into 21 steps of 1200c/21 ~= 57.1c each. == Basic theory == === Intervals and notation === === Prime harmonic approximations === {{Harmonics in ED|21|31|0}} {{Cat|Edos}} ==== Edostep interpretations ==== 21edo's edostep has the following interpretations in the 2.3.5.7.23.29.31 subgroup: * 32/31 * 31/30 * 30/29 * 29/28 * 49/48 * 64/63")
  • 21:0521:05, 22 January 2026 19edo (hist | edit) [2,612 bytes] Inthar (talk | contribs) (Created page with "'''19edo''' is an equal division of 2/1 into 19 steps of 1200c/19 -= 63.2c each. It is very close to 1/3-comma Meantone. It has interordinals and also support semiquartal. {{Cat|Edos}}")

21 January 2026

17 January 2026

  • 07:0107:01, 17 January 2026 Octave (hist | edit) [436 bytes] Vector (talk | contribs) (Created page with "{{Infobox interval|2/1|Name=octave}} The '''octave''' is the most consonant interval, with a ratio of 2/1 and a size of 1200 cents by definition. It is the most common interval of equivalence, as patterns of consonance often roughly repeat at octaves up or down. Additionally, most scales repeat at an octave or a logarithmic fraction thereof. The octave is also useful as a measure of logarithmic size of intervals.") Tag: Visual edit

13 January 2026

  • 23:1223:12, 13 January 2026 Historical modes (hist | edit) [8,101 bytes] Hkm (talk | contribs) (Created page with "The following list details how historical theorists within the Western tradition categorized the scales (also known as modes) in use in their time. === Lucian of Samosata === The smallest mode system that Zarlino mentions was the four-mode system written by Lucian of Samosata:<blockquote>exalted Phrygian, joyous Lydian, majestic Dorian, voluptuous Ionic — all these I have mastered with your assistance.</blockquote>No elaboration is given by Lucian as to the nature of...") Tag: Visual edit

12 January 2026

  • 22:3522:35, 12 January 2026 29edo (hist | edit) [10,313 bytes] Unque (talk | contribs) (Created page with "'''29 equal divisions of the octave''', or '''29edo''', is the tuning system which divides the 2/1 ratio into 29 equal parts of approximately 41.3 cents each. It is notable for its extremely accurate tuning of prime 3, and for unique melodic properties that proponents of the system consider particularly desirable. == Tuning Theory == === JI Approximation === While 29edo excels at prime 3, the rest of the primes up to 31 are relatively lacking. However, primes 5 t...") Tag: Visual edit
  • 07:3907:39, 12 January 2026 List of interval regions (hist | edit) [3,395 bytes] Vector (talk | contribs) (Created page with "This is a list of interval regions within the octave according to an altered version of Margo Schulter's categorization scheme. [WIP] {| class="wikitable" |+ ! colspan="2" |Region name !Range !Important just intervals !Temperaments !MOSes |- | colspan="2" |Unison |0c (singleton) |1/1 | - | - |- | colspan="2" |Comma | | | | |- | colspan="2" |Diesis | | | | |- | rowspan="3" |Minor second |Subminor | | | | |- |Farminor | | | | |- |Nearminor | | | | |- | rowspan="3" |Neutra...") Tag: Visual edit

11 January 2026

  • 16:3516:35, 11 January 2026 Oneirotonic (hist | edit) [9,014 bytes] Inthar (talk | contribs) (Created page with " {| class="wikitable" |- ! Mode name !! Pattern !! 2nd !! 3rd !! 4th !! 5th !! 6th !! 7th |- | Locrian || sLLsLLL || style="background-color:#d66"|m || style="background-color:#d66"|m || style="background-color:#d66"|P || style="background-color:#d66"|d || style="background-color:#d66"|m || style="background-color:#d66"|m |- | Phrygian || sLLLsLL || style="background-color:#d66"|m || style="background-color:#d66"|m || style="background-color:#d66"|P || style="background-...")

10 January 2026

  • 23:0223:02, 10 January 2026 16edo (hist | edit) [7,345 bytes] Vector (talk | contribs) (Created page with "'''16edo''' is the tuning which divides the octave into 16 equal parts of 75 cents each. It is notable for its antidiatonic scale. == Tuning theory == === Edostep interpretations === In the 2.5.7.13.19 subgroup, 16edo's edostep, the '''eka''', represents the following intervals: * 20/19, the difference between 19/16 and 5/4 * 133/128, the difference between 8/7 and 19/16 * 26/25, the difference between 5/4 and 13/10 * 169/160, the difference between 13/10 and 16/13 *...") Tag: Visual edit

9 January 2026

6 January 2026

  • 03:0803:08, 6 January 2026 Just intonation (hist | edit) [2,759 bytes] Vector (talk | contribs) (Created page with "'''Just intonation''' is the set of intervals corresponding to frequency ratios between whole numbers, and the approach to musical tuning which utilizes exclusively such intervals. Just intonation can be described in terms of the harmonic series (which is the set of tones at integer multiples of a fundamental frequency), where all just intervals can be found between notes in the harmonic series. Particularly low-complexity just intervals tend to be perceived as consonant...") Tag: Visual edit

4 January 2026

3 January 2026

1 January 2026

31 December 2025

25 December 2025

  • 23:4323:43, 25 December 2025 31edo (hist | edit) [5,170 bytes] Tristanbay (talk | contribs) (Began page for 31edo)
  • 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)<br> (Only...") Tag: Visual edit

24 December 2025

  • 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...")

23 December 2025

  • 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...")

22 December 2025

21 December 2025

  • 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.")

20 December 2025

  • 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

18 December 2025

  • 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...")

17 December 2025

  • 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

16 December 2025

  • 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,...")

15 December 2025

  • 13:3113:31, 15 December 2025 Glossary (hist | edit) [24,279 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 ([...")
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