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6 June 2026

  • 22:4222:42, 6 June 2026 Pentagoth (hist | edit) [8,707 bytes] Ground (talk | contribs) (Created page with "''This portion of the page was written from the perspective of User:Ground. This is a new format being tested and the article is incomplete.'' I've always been interested in the 2.5.7 subgroup and its extensions. Prime 3 is so central to how we tend to understand harmony that removing it is always interesting, and 5 and 7 are the next two simplest, thus the best alternatives to create a new harmonic system. Here's a list of some of the best temperaments with their...")

2 June 2026

30 May 2026

  • 19:5319:53, 30 May 2026 Tertian structure (hist | edit) [5,368 bytes] Vector (talk | contribs) (Created page with "'''Tertian structure''' is the relative spacing of the thirds in a tempered tuning system, such as an equal temperament. In general, it usually refers to the spacing of the 7-limit color-quality thirds 7/6, 6/5, 5/4, and 9/7, which can be expressed as the relative size of 25/24 and 36/35. Other thirds like 19/16, 19/15, or 11/9 may be invoked to describe more complex structures. Common rank-3 temperaments can be expressed as tertian structures. These are mint...") Tag: Visual edit

18 May 2026

  • 19:5719:57, 18 May 2026 Equal tuning accuracy functions (hist | edit) [4,152 bytes] Vector (talk | contribs) (Created page with "{{Technical}} There are a number of ways to quantify the tuning accuracy of equal temperaments. == Mu function == The mu function is defined as: $$ \mu \left( x, σ \right) = \sum_{k=1}^{\infty}f \left( x, k \right) $$ for a given edo x and weight σ, where <nowiki>$$ f \left( x, k \right) = \frac{\abs{\operatorname{mod} \left( 2g \left( k \right) x, 2 \right) - 1}}{k^{σ}} $$</nowiki> and $$ g \left( k \right) = \log_{2} \left( k \right) $$.") Tag: Visual edit
  • 17:0517:05, 18 May 2026 31edo/SCL files (hist | edit) [690 bytes] Vector (talk | contribs) (Created page with "== Tempered-octave skip-fretting == <pre> ! 127zpi-sfguitar.scl ! Tempered-octave tuning of 31et (zeta), skip-fretting {2,9\31} in upper register 47 ! 38.736691 77.473382 116.210073 154.946764 193.683455 232.420147 271.156838 309.893529 348.63022 387.366911 426.103602 464.840293 503.576984 542.313675 581.050366 619.787058 658.523749 697.26044 735.997131 774.733822 813.470513 852.207204 890.943895 929.680586 968.417277 1007.153968 1045.89066 1084.627351 1123.364042 1162.1...") Tag: Visual edit

17 May 2026

  • 08:2008:20, 17 May 2026 Perfect consonance (hist | edit) [1,153 bytes] Vector (talk | contribs) (Created page with "A '''perfect consonance''' is one of the most consonant intervals; they are usually extremely easy to sing and recognize by ear. The set of perfect consonances is equivalent in most systems of theory to the '''3-odd-limit''', which is the set of intervals wherein the highest allowable odd in the numerator and denominator is 3. It is the smallest odd-limit containing intervals of the 3-limit. == Table of 3-odd-limit intervals == Reduced to an octave, the intervals of the...") Tag: Visual edit

15 May 2026

  • 01:4801:48, 15 May 2026 22edo/Intervals (hist | edit) [30,259 bytes] Vector (talk | contribs) (Created page with "This page goes over each of the steps of 22edo in detail, as is done in the documentation for various other equal temperaments on various websites. The notation used is ups and downs notation. ''Function names are derived from Aura's function names. Standard super-/sub- terminology is restored; this section will not cover treble-down harmony.'' ==== 1\22 ==== Degree: b2 Interval: ^1, m2 Category: Dissonance Function: Supergradient (leads past tonic) This is the edo...") Tag: Visual edit

14 May 2026

  • 23:3323:33, 14 May 2026 Patent gap (hist | edit) [1,486 bytes] Vector (talk | contribs) (Created page with "A '''patent gap''' is a notable gap between patent tunings of an interval. This may be applied in the context of all edos, or in the context of those supporting a specific regular temperament, often containing a specific tuning optimum or structurally significant tuning. They usually represent mild exotemperings and occur often in temperaments with very few patent vals. They are one of the main motivations for using non-patent tunings. A notable general patent gap is th...") Tag: Visual edit
  • 22:2422:24, 14 May 2026 Chord (hist | edit) [12,035 bytes] Vector (talk | contribs) (Created page with "thumb|A G major chord played as a "block" chord and as an arpeggio. A '''chord''' is a set of multiple pitch classes. The use of the term 'chord' generally implies that the notes are sounded together, creating harmonic intervals, although chords can also be ''broken chords'', with the notes played separately in some sequence. An arpeggio is a broken chord wherein the notes are played in ascending or descending order. Therefore, the distinction between ch...") Tag: Visual edit
  • 00:3900:39, 14 May 2026 User:Kili/Scales (hist | edit) [1,184 bytes] Kili (talk | contribs) (Created page with "I am Kili and this is where I will put my Scales.") Tag: Visual edit originally created as "Kili:Scales"

11 May 2026

  • 00:2200:22, 11 May 2026 TAMNAMS (hist | edit) [1,936 bytes] Vector (talk | contribs) (Created page with "TAMNAMS, the Temperament-Agnostic Mos NAMing System, is a system of names for MOS scales alongside their intervals, degrees, and tunings. MOS names on the wiki generally follow TAMNAMS, and may be found at MOS. Note that while other scales such as 1L 6s may fall under some definitions of ''diatonic'', in TAMNAMS ''diatonic'' refers exclusively to 5L 2s; it is recommended to make this sense explicit by saying "MOS diatonic" or "mosdiatonic". == MOS tuning softness...") Tag: Visual edit

10 May 2026

6 May 2026

5 May 2026

  • 03:2903:29, 5 May 2026 WT13C (hist | edit) [803 bytes] Inthar (talk | contribs) (Created page with "The '''Well-Tempered Trisdekatonic Clavier (WT13C)''' is a collaborative Discord project to create 14 pieces in 13edo, not necessarily in a Baroque style. This project is currently on hiatus, but anyone is welcome to resurrect it. == Credits == Each item should have an mp3 and a score file. You may use any notation as long as you clearly specify the notation. The key centers on this page are in 26edo notation with C = 261.625... Hz. # C # Cx # D # Dx # E # Fb # F#...") originally created as "Well-Tempered Triskaidekatonic Clavier"

4 May 2026

30 April 2026

  • 07:0907:09, 30 April 2026 Notation/Generalizations of sharp and flat (hist | edit) [911 bytes] Vector (talk | contribs) (Created page with "In modern 12edo theory, the accidentals sharp (#) and flat (b) refer to alterations by a single edostep, formally a ''chromatic semitone''. Various generalizations of this exist, some compatible with the historical meaning which treated the chromatic semitone as a notable structural interval as it is functionally today. == Consensus == The consensus is that where the interval 2187/2048 is present and structurally relevant, the symbols # and b unambiguously refer to an a...") Tag: Visual edit

25 April 2026

  • 23:2623:26, 25 April 2026 22edo/V/Exposition (hist | edit) [32,018 bytes] Vector (talk | contribs) (Created page with "== Just intonation == In music, the basic concept behind most tuning systems is the harmonic series, or the series of pitches whose frequencies are a multiple of some frequency called the fundamental. These are the frequencies that make up the sounds of notes on most instruments, and we hear ''concordance'' when two notes share frequencies. Sets of notes that do this are themselves tuned so that the intervals between them can be found somewhere in the harmonic series. Th...") Tag: Visual edit

13 April 2026

  • 00:3600:36, 13 April 2026 5-odd-limit (hist | edit) [6,451 bytes] Vector (talk | contribs) (Created page with "The '''5-odd-limit''' is the set of intervals where the largest allowable odd factor in the numerator and denominator is 5. It is the smallest odd-limit containing intervals of the 5-limit. In general, the intervals of the 5-odd-limit are also those considered consonances in standard Western music theory, and include as a subset the intervals of the 3-limit, which are the perfect consonances. This is where the xenharmonic generalization of a set of interva...") Tag: Visual edit

12 April 2026

11 April 2026

9 April 2026

7 April 2026

  • 21:0321:03, 7 April 2026 Myna (hist | edit) [375 bytes] Inthar (talk | contribs) (Created page with "{{stub}} '''Myna''' is a rank-2 temperament that splits 6/1 (perfect fifth + 2 octaves) into ten 6/5 minor thirds. {{Navbox regtemp}} {{Cat|Temperaments}}")
  • 19:3519:35, 7 April 2026 Ennealimmal/Patent vals (hist | edit) [4,799 bytes] Inthar (talk | contribs) (Created page with "The following patent vals support Ennealimmal. Vals contorted in the 7-limit are not included. {| class="wikitable sortable" |- !|Edo||Generator||3/2 tuning||5/4 tuning||7/4 tuning |- ||45||346.666667||693.333333||373.333333||960.000000 |- ||72||350.000000||700.000000||383.333333||966.666667 |- ||315||350.476190||700.952381||384.761905||967.619048 |- ||243||350.617284||701.234568||385.185185||967.901235 |- ||414||350.724638||701.449275||385.507246||968.115942 |- ||58...")
  • 16:4516:45, 7 April 2026 Ennealimmal (hist | edit) [3,337 bytes] Inthar (talk | contribs) (Created page with "{{Stub}} '''Ennealimmal''' is a 7-limit rank-2 microtemperament that tempers out the two smallest 7-limit superparticulars: * 2401/2400 = S49, the difference between 49/40 neutral third and its 3/2-complement 60/49 * 4375/4374, the difference between (27/25)<sup>2</sup> and 7/6 This implies a period of 1\9 (representing 27/25) and a generator of 49/40. {{Navbox regtemp}} {{Cat|Temperaments}}")
  • 16:3716:37, 7 April 2026 Neogothic (hist | edit) [241 bytes] Inthar (talk | contribs) (Created page with "'''Neogothic''' may mean: * Intervals close to 13/11 (called a neominor third) and 14/11 (called a neomajor third), and their fifth transpositions and octave complements * Gentle tuning of diatonic {{Cat|Disambiguation pages$}}")
  • 15:5415:54, 7 April 2026 Ammonite/Patent vals (hist | edit) [1,093 bytes] Inthar (talk | contribs) (Created page with "The following patent vals support 2.7/5.11/5.13/5 Ammonite. {|class="wikitable sortable" |- !|Edo!!13-limit extension!!Generator |- ||8||29 & 37||450.000 |- ||61||||452.459 |- ||53||||452.830 |- ||98||||453.061 |- ||45||||453.333 |- ||127||||453.543 |- ||82||||453.659 |- ||119||||453.782 |- ||156||||453.846 |- ||37||29 & 37||454.054 |- ||214||||454.206 |- ||177||||454.237 |- ||140||||454.286 |- ||243||||454.321 |- ||103||||454.369 |- ||272||||454.412 |- ||169||||454.438...")
  • 14:5314:53, 7 April 2026 Parapyth/Patent vals (hist | edit) [2,643 bytes] Inthar (talk | contribs) (Created page with "The following patent vals support 2.3.7.11.13 Parapyth. Vals contorted in 2.3.7.11.13 are not included. {|class="wikitable sortable" |- !|Edo!!5 extension!!23 extension!!3/2 tuning!!28/27 tuning!!7/4 tuning!!11/8 tuning!!13/8 tuning |- ||24||||||700.000||50.000||950.000||550.000||850.000 |- ||65||||||701.538||55.385||960.000||553.846||849.231 |- ||41||41 & 46 & 58||17 & 41 & 46||702.439||58.537||965.854||556.098||848.780 |- ||128||41 & 46 & 58||||703.125||56.250||965...")
  • 14:2314:23, 7 April 2026 Marvel/Patent vals (hist | edit) [2,863 bytes] Inthar (talk | contribs) (Created page with " The following are patent vals that support 7-limit Marvel. Vals contorted in the 7-limit are not included. {|class="wikitable sortable" |- !|Edo!!Extension to 11!!3/2 tuning!!5/4 tuning!!7/4 tuning |- ||2||||600.000||600.000||1200.000 |- ||11||||654.545||436.364||981.818 |- ||9||19 & 22 & 31||666.667||400.000||933.333 |- ||21||||685.714||400.000||971.429 |- ||40||19 & 22 & 31||690.000||390.000||960.000 |- ||33||||690.909||400.000||981.818 |- ||52||||692.308||392.308||96...")
  • 05:4905:49, 7 April 2026 94edo (hist | edit) [3,591 bytes] Vector (talk | contribs) (Created page with "'''94edo''' is most notable for being the sum of 53 and 41, and thus serving as a tuning of garibaldi that lies in between the two. It is additionally one of the first EDOs where the distance between steps is below certain thresholds of intonational accuracy on free-pitch instruments; in other words, 94edo could be seen as approximately the most accurate resolution a free-pitch instrument player or vocalist can be expected to manage. It is also the first edo other t...") Tag: Visual edit

5 April 2026

  • 02:1002:10, 5 April 2026 Marvel (hist | edit) [2,628 bytes] Inthar (talk | contribs) (Created page with "'''Marvel''', 19 & 22 & 31, is a 7-limit rank-3 temperament tempering out 225/224, thereby equating 16/15 with 15/14 and equating 25/16 (= 5/4 * 5/4) with 14/9. On account of enlarging 16/15, Marvel favors somewhat flat tunings for 3 and 5. == Intervals == == Supporting temperaments == Many rank-2 temperaments in classical RTT support Marvel: * 19 & 31, Septimal Meantone * 19 & 22, Magic * 22 & 31, Orwell * 31 & 41, Miracle...")
  • 01:3901:39, 5 April 2026 Injera (hist | edit) [338 bytes] Inthar (talk | contribs) (Created page with "'''Injera''', 26 & 38, is a 7-limit weak extension of 5-limit Meantone that splits the octave into two tritones each representing 7/5~10/7. {{Navbox regtemp}} {{Cat|temperaments}}")

4 April 2026

  • 23:5823:58, 4 April 2026 Parapyth (hist | edit) [4,041 bytes] Inthar (talk | contribs) (Created page with "'''Parapyth''', 17 & 41 & 46, is generally viewed as a no-5 2.3.7.11.13 rank-3 regular temperament, sometimes called '''Parapythic'''. (In the strict sense, parapyth is Margo Schulter's rank-3 tuning construct inspired by medieval European and Middle Eastern music theory, where Schulter imposes commas that are to be ''observed'' as well as commas that are to be tempered out.{{citation needed}}) == Theory == The regular temperament Parapyth has two non-octave generators:...")
  • 14:4914:49, 4 April 2026 Blackwood (hist | edit) [4,280 bytes] Vector (talk | contribs) (Created page with "thumb|An example of Blackwood temperament in a song by Vector '''Blackwood''' is a regular temperament primarily supported by 15edo but in technicality by any EDO with 5edo's fifth (such as 25edo or 10edo) which takes 5edo as its 2.3.7, and treats 5 as an independent generator. Its 10-note scale (LsLsLsLsLs, '''pentawood''') is unique among scales of its complexity for making a perfect fifth available on every note of the scale, at the cost...") Tag: Visual edit
  • 12:2812:28, 4 April 2026 99edo (hist | edit) [13,125 bytes] Inthar (talk | contribs) (Created page with "'''99edo''' is an equal tuning with steps of size 12.12... cents. It is known for being very accurate in the 7-limit. {{Navbox edo}} {{Cat|edos}}")
  • 12:0312:03, 4 April 2026 46edo (hist | edit) [4,320 bytes] Inthar (talk | contribs) (Created page with "'''46edo''', or 46 equal divisions of the octave, is an equal tuning with a step size of approximately 26.1 cents. It is known for its relatively good approximation of 13-limit just intonation. == Theory == === JI approximation === 41edo is most accurately a 2.3.5.7.11.13.17.23 tuning. It has somewhat opposite tendencies to 41edo in the 2.3.5.7.11.13 subgroup, though it has 41edo's Rodan characteristic of sharp prime 3 and flat prime 7 (more extremely). Hence th...")
  • 06:0506:05, 4 April 2026 Tritone (hist | edit) [589 bytes] Vector (talk | contribs) (Created page with "A tritone is an interval close to 600 cents, or the size of three whole tones (hence the name). The interval of exactly 600 cents is the '''semioctave''', ''perfect median'', or ''perfect tritone'', and is the unique interval whose octave complement is itself == Properties of tritones in general == A tritone produces a neutral trine when played with the octave. Tritones tend to not be easily found in odd-numbered forms, but are structurally import...") Tag: Visual edit
  • 01:4801:48, 4 April 2026 Gentle tuning (hist | edit) [4,733 bytes] Vector (talk | contribs) (Created page with "'''Gentle tuning''' is the regular tuning of the perfect fifth somewhere between the tunings given by 29edo and 17edo, producing MOS diatonic scales with step size ratios between 5:2 and 3:1 (and consequently chromatic scales between 3:2 and 2:1, including the golden tuning of p-chromatic). As a result, the major third generated is between 413.8 and 423.5 cents, and approximates 14/11. It is so named because melodically it functions as a...") Tag: Visual edit

3 April 2026

  • 22:4122:41, 3 April 2026 Argent (hist | edit) [382 bytes] Inthar (talk | contribs) (Redirected page to Hemifamity) Tag: New redirect
  • 21:5421:54, 3 April 2026 Aberschismic (hist | edit) [5,421 bytes] Inthar (talk | contribs) (Created page with "'''Hemifamity''' or '''Aberschismic''', 2.3.5.7[41 & 46 & 53], is a 7-limit temperament that tempers out 5120/5103 (known as the hemifamiton or the aberschisma), which manifests in several different ways: # equates the 3-spine prime commas for 5 and 7, 81/80 and 64/63 # equates the limma 256/243 with 21/20 # equates the apotome 2187/2048 with 15/14 # equates the Pythagorean augmented fourth 729/512 with 10/7 {{navbox regtemp}} {{Cat|Temperaments}}") originally created as "Hemifamity"

2 April 2026

  • 02:5702:57, 2 April 2026 Misty (hist | edit) [3,475 bytes] Inthar (talk | contribs) (Created page with "'''Misty''' is a 7-limit temperament with generator 3/2 and period 1/3-octave which represents 63/50. It results from tempering out the following 2 commas: * 5120/5103, the aberschisma, which equates 64/63 and 81/80 * 3136/3125, the Didacus comma {{Navbox regtemp}} {{Cat|Temperaments}}")

1 April 2026

30 March 2026

  • 18:3318:33, 30 March 2026 Compositional theory (hist | edit) [2,956 bytes] Inthar (talk | contribs) (Created page with "A '''xen theory''' is a musical framework that governs the way tuning-related elements are used in music, analogous to Western 12edo functional harmony. All you can say about the use of tuning universally is * cent values; what chords, structures, and JI/DR (approximations or not) various tuning systems have * LCJI is a psychoacoustic effect * DR is a psychoacoustic effect These things ''don't tell you how to write music'' any more than the neurobiology of human color...") originally created as "Xen theories"

28 March 2026

  • 11:5511:55, 28 March 2026 159edo (hist | edit) [11,971 bytes] Aura (talk | contribs) (Created page with "'''159edo''', or 159 equal divisions of the octave, is the equal tuning featuring steps of (1200/159) ~= 7.55 cents, 159 of which stack to the perfect octave 2/1. Like 53edo, 159edo is an excellent approximation to Pythagorean tuning (stacking pure 3/2 fifths), but this time, you have access to near-just approximations of the 11th and 17th harmonics, and a slightly more accurate 7th harmonic, giving you consistency up to the 17-odd-limit. == Theory == 159edo wa...")
  • 04:3004:30, 28 March 2026 Diaschismic (hist | edit) [4,473 bytes] Inthar (talk | contribs) (Created page with "'''Diaschismic''', 2.3.5[10 & 12], is a 5-limit temperament equating 45/32 to the half-octave, thereby * equating a stack of two 5/4's and two 9/8's to the octave * equivalently, it equates stack of one 5/4 and two 16/15's to the half-octave. The generator of Diaschismic can be taken to be 16/15 or 3/2. Notable tunings of Diaschismic that are more accurate in the 5-limit are 34edo and 46edo. 22edo is another notable Diaschismic tuning. Diaschismic has an ...")
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