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5 March 2026

  • 22:2322:23, 5 March 2026 Father (hist | edit) [2,601 bytes] Vector (talk | contribs) (Created page with "'''Father''' is the temperament (a very inaccurate exotemperament) that makes 3:4:5 equidistant, in other words equating 5/4 and 4/3 to a single "fourth-third" interval (which the name 'father' originates from). As a result, it serves as a simplification of 3:4:5-based (naiadic) harmony, in much the same way that dicot simplifies tertian harmony or semaphore simplifies chthonic harmony. Due to tempering out such a large and simple interv...") Tag: Visual edit

4 March 2026

  • 14:4814:48, 4 March 2026 40edo (hist | edit) [22,956 bytes] Lériendil (talk | contribs) (Created page with "'''40edo''', or 40 equal divisions of the octave (sometimes called '''40-TET''' or '''40-tone equal temperament'''), is the equal tuning featuring steps of (1200/40) ~= 30 cents, 40 of which stack to the perfect octave 2/1. 40edo is a straddle-3, or dual-3, system, as it has both the 5edo fifth of 720{{c}}, and a very flat diatonic fifth at 690{{c}}, being the smallest 5n EDO to have a diatonic perfect fifth. == General theory == === JI approxi...")

1 March 2026

  • 18:0018:00, 1 March 2026 Orwell (hist | edit) [6,909 bytes] Lériendil (talk | contribs) (Created page with "'''Orwell''' is a rank-2 temperament generated by a sharpened subminor third, representing 7/6. Three of these form 8/5, efficiently connecting to prime 5, and the result is then tuned such that it reaches 9/7 (an octave up) when stacked twice, so that seven generators in all form 3/1, a perfect twelfth. The equivalences that it makes are given by the commas 1728/1715 (the difference between 8/5 and (7/6)<sup>3</sup>), and 225/224 (the difference...")

28 February 2026

  • 01:2101:21, 28 February 2026 List of locking intervals (hist | edit) [1,605 bytes] Vector (talk | contribs) (Created page with "The following is a list of just intervals that are considered to "lock", according to the performer MidnightBlue. It serves as a useful reference for the actual extent of JI's effect on interval perception. 72edo is the smallest edo to make all the necessary categorical distinctions, and 94edo approximates all of these to within a kleisma. ''Italic'' intervals are those that only lock in a higher octave. {| class="wikitable" |+ !Interval !Cents !Notes |- |1/1 |0.00 | |-...") Tag: Visual edit

27 February 2026

  • 10:4710:47, 27 February 2026 Neutral temperaments (hist | edit) [7,519 bytes] 2^67-1 (talk | contribs) (Created page with "'''Dichotic''' is an exotemperament that can be defined to temper out 25/24, the dicot comma, 45/44, and 64/63. As a result it also tempers out 55/54. == Interval chart == This interval chart uses Partch's 11-limit tonality diamond and maps it onto 7edo and 10edo. This also gives an idea of what intervals are possible in dichotic temperament. '''Intervals in bold''' are in the 7-note MOS (symmetric mode) and ''intervals in italics'' are in the 1...") originally created as "Dichotic"

24 February 2026

  • 23:2923:29, 24 February 2026 Ammonite (hist | edit) [1,012 bytes] Inthar (talk | contribs) (Created page with "'''Ammonite''', 2.3.5.7.11.13[27 & 37], is a temperament generated by an accurate 13/10, such that * 2 generators = 22/13 * 3 generators = 10/9~11/10~12/11 (hence Ammonite is a weak extension of Porcupine) * 4 generators = 10/7 * 9 generators = 4/3 The generator generates a very soft oneirotonic (5L3s) MOS with L ~= 11/10 and s ~= 14/13. It is most accurate as its 2.7/5.11/5.13/5 restriction, which is technically called "Tridec". {{navbox regtemp}} {{cat|tem...")
  • 22:0322:03, 24 February 2026 Miracle (hist | edit) [498 bytes] Inthar (talk | contribs) (Created page with "'''Miracle''' is an 11-limit temperament that splits 3/2 into six equal parts, each representing both 16/15 and 15/14. Thus: *2 gens = 8/7 *3 gens = 11/9 *4 gens = 21/16 *5 gens = 7/5 *6 gens = 3/2 It has edo join 31 & 41. {{Navbox regtemp}} {{Cat|temperaments}}")
  • 21:5721:57, 24 February 2026 Porcupine (hist | edit) [2,838 bytes] Inthar (talk | contribs) (Created page with "'''Porcupine''' is a 2.3.5.11 temperament that splits 4/3 into three submajor seconds (approximately 11/10), representing 10/9~11/10~12/11. In the 5-limit, it equates 81/80 with 25/24. {{Navbox regtemp}} {{Cat|temperaments}}")
  • 21:3121:31, 24 February 2026 Tetracot (temperament) (hist | edit) [3,080 bytes] Inthar (talk | contribs) (Created page with "'''Tetracot''' is a 2.3.5 temperament that splits 3/2 into four flattened 10/9's. Its 5-limit edo join is 27 & 34. Tetracot has a number of extensions, but most of them are problematic in some way. {{Navbox regtemp}} {{Cat|temperaments}}") originally created as "Tetracot"
  • 21:2421:24, 24 February 2026 Buzzard (hist | edit) [1,704 bytes] Inthar (talk | contribs) (Created page with "{{Infobox regtemp | Title = Buzzard | Subgroups = 2.3.7, 2.3.5.7, 2.3.5.7.11.13 | Comma basis = 65536/64827 (2.3.7); <br>1728/1715, 5120/5103 (7-limit);<br>176/175, 351/350, 540/539, 676/675<br>(13-limit) | Edo join 1 = 53 | Edo join 2 = 58 | Mapping = 1; 4 21 -3 39 27 | Generators = 21/16 | Generators tuning = 475.7 | Optimization method = CWE | MOS scales = 3L 2s | Ploidacot = alpha-tetracot | Pergen = | Color name = | Odd limit 1 = 2.3.7...")
  • 20:5620:56, 24 February 2026 Magic (hist | edit) [2,609 bytes] Inthar (talk | contribs) (Created page with "{{Infobox regtemp | Title = Magic | Subgroups = 2.3.5, 2.3.5.7 | Comma basis = 3125/3072 (5-limit); <br>225/224, 245/243 (7-limit) | Edo join 1 = 19 | Edo join 2 = 22 | Mapping = 1; 5 1 12 | Generators = 5/4 | Generators tuning = 380.5 | Optimization method = CWE | MOS scales = 3L 4s, 3L 7s, …, 3L 16s, 19L 3s | Odd limit 1 = 5 | Mistuning 1 = 5.9 | Complexity 1 = 7 | Odd limit 2 = 9 | Mistuning 2 = 5.9 | Complexity 2 = 13 }}")
  • 20:4920:49, 24 February 2026 Kleismic (hist | edit) [2,333 bytes] Inthar (talk | contribs) (Created page with "{{Infobox regtemp | Title = Kleismic | Subgroups = 2.3.5, 2.3.5.13 | Comma basis = 15625/15552 (2.3.5); <br>325/324, 625/624 (2.3.5.13) | Edo join 1 = 15 | Edo join 2 = 19 | Mapping = 1; 6 5 14 | Generators = 6/5 | Generators tuning = 317.1 | Optimization method = CWE | MOS scales = 3L 1s, 4L 3s, 4L 7s, 4L 11s, 15L 4s | Pergen = (P8, P12/6) | Color name = Tribiyoti | Odd limit 1 = 5 | Mistuning 1 = 1.35 | Complexity 1 = 7 | Odd limit 2 = 2...")
  • 20:3420:34, 24 February 2026 Comma pump (hist | edit) [2,257 bytes] Inthar (talk | contribs) (Created page with "A '''comma pump''' is a chord progression whose starting and ending points differ by a comma in JI. The I-vi-ii-V-I progression is a Meantone or 81/80 comma pump: CEG -> ACEA -> DFA -> GDGB -> CEGC In non-Meantone tunings, attempting this comma pump results in the end point flatter by 81/80 relative to the starting point. There is some ambiguity in this term depending on whether the comma in question is tempered out or not. If the comma is tempered out the chord...")

23 February 2026

  • 04:2104:21, 23 February 2026 18edo (hist | edit) [7,626 bytes] Inthar (talk | contribs) (Created page with "{{problematic}} '''18edo''', or 18 equal divisions of the octave, is the equal tuning featuring steps of (1200/18) ~= 66.7 cents, 18 of which stack to the octave 2/1. With the sharp fifth 733.3c and the flat fifth 666.7c, 18edo is often considered the quintessential straddle-3 edo and the straddle-3 version of 12edo. {{Cat|Edos}}")

22 February 2026

  • 07:1007:10, 22 February 2026 Solfege (hist | edit) [4,465 bytes] Vector (talk | contribs) (Created page with "Solfege refers to any way of labelling notes with syllables to be sung, and conventionally one that utilizes syllables similar to the conventional ''do-re-mi-fa-so-la-ti'' system for labeling the notes of a heptatonic scale. Fixed solfege for note names is discouraged for xenharmony (the existing body of work generally prefers alphabetic notation); this page primarily discusses movable solfege. == Standard solfege == {| class="wikitable" |+ !Degree (1-indexed) !Solfege...") Tag: Visual edit
  • 04:0204:02, 22 February 2026 Bohlen-Pierce (hist | edit) [2,785 bytes] Vector (talk | contribs) (Created page with "The '''Bohlen-Pierce''' system is a non-octave tuning system of (exact or well-tempered) '''13 equal divisions of the perfect twelfth''' (or tritave). In the Bohlen-Pierce system, the tritave is generally seen as the interval of equivalence, and harmony emphasizes the odd harmonics (such as the chord 3:5:7:9). It is the smallest EDT that has a tuning of lambda, the 9-note scale of the sensamagic temperament (which serves an analogous role to meantone...") Tag: Visual edit

21 February 2026

19 February 2026

  • 17:5817:58, 19 February 2026 L'Antica Musica (hist | edit) [22,064 bytes] Unque (talk | contribs) (Created page with "{{Wip}} '''L'Antica Musica''' was a treatise published in 1555 by Nicola Vicentino, which explores how Renaissance-era advancements in musical tuning could be used to adapt the lost traditions of Ancient Greek musicians in such a way that blends them with the sensibilities of the 16th century. It is perhaps most revered in xenharmonic communities for its attestation and argument for 31 equal divisions of the octave<sup>†</sup>, a tuning for which Vicentino...") Tag: Visual edit

18 February 2026

  • 19:2319:23, 18 February 2026 7edo (hist | edit) [2,257 bytes] Lériendil (talk | contribs) (Created page with " == 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 === ===== Edostep interpretations ===== 7edo's edostep has the following interpretations in the 2.3.5 subgroup: * 9/8 (the diatonic major second) * 10/9 (the interval separating 9/8 and 5/4) * 16/15 (the interval separating 5/4 and 4/3) ===== JI approximation ===== 7edo is, very crudely, a 2.3.5 system, and streng...")
  • 19:2319:23, 18 February 2026 5edo (hist | edit) [2,514 bytes] Lériendil (talk | contribs) (Created page with "== 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 === ===== Edostep interpretations ===== 5edo's edostep has the following interpretations in the 2.3.7 subgroup: * 7/6 * 8/7 * 9/8 ===== JI approximation ===== 5edo is most obviously a 2.3.7 system (and this property carries to 5-form systems as a whole). although its 3 is audibly sharper than a just 3/2. There is no...")
  • 16:5916:59, 18 February 2026 Neutral interval (hist | edit) [420 bytes] Inthar (talk | contribs) (Created page with "A '''neutral interval''' is an interval halfway between two sizes of a diatonic ordinal (aka interval class). The following are diatonic neutral intervals: * Neutral second * Neutral third * Neutral/semiaugmented fourth * Neutral/semidiminished fifth * Neutral sixth * Neutral seventh The interval that separates neutral intervals from the corresponding large/small intervals is the ''semichroma'', (L-s)/2.")
  • 03:1403:14, 18 February 2026 10-form (hist | edit) [12,619 bytes] Inthar (talk | contribs) (Created page with "== Blackdye == == Pentawood == == Diaschismic[10] == == Taric ==") originally created as "10-form harmony"

14 February 2026

  • 20:4120:41, 14 February 2026 Chthonic harmony (hist | edit) [12,458 bytes] Unque (talk | contribs) (Created page with "'''Chthonic harmony''', sometimes called '''semiquartal''' or '''bilateral harmony''', is a type of chord structure useful in many styles of xenharmonic music. It serves as an analog for tertian harmony that splits the perfect fourth rather than the fifth. == Chthonic Intervals == The term "chthonic" is derived from the name of an interordinal interval which splits the perfect fourth into two roughly-equal parts. When this division is not equ...") Tag: Visual edit

13 February 2026

8 February 2026

  • 02:0302:03, 8 February 2026 Sensamagic (hist | edit) [1,704 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) [5,871 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) [5,695 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) [2,789 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) [6,759 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) [778 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) [3,621 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) [2,640 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) [477 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) [11,952 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) [9,396 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) [3,594 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
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