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26 July 2026

  • 05:2005:20, 26 July 2026 Straddle cluster temperaments (hist | edit) [4,966 bytes] Ground (talk | contribs) (Created page with "{{proposed}} '''Paddle''', short for "Passion straddle", is a 2.-3.+3.5.7 straddle version of Passion. It is especially useful for generating the aberration scale '''trackdye''' (5L2m8s), along with a straddle variant of Undecimation. It may be extended with Pentagoth. {| class="wikitable" |+Tuning range from 2\25 to 1\12, edos under 100 ! rowspan="2" | ! !<nowiki>¦|</nowiki> !¦ !<nowiki>¦|</nowiki> !<nowiki>|</nowiki> !<nowiki>¦|</nowiki> !...") Tag: Visual edit: Switched originally created as "Paddle"

25 July 2026

  • 16:1916:19, 25 July 2026 Monarch (hist | edit) [8,203 bytes] Ground (talk | contribs) (Created page with "'''Archtone''' is a rank-3 Straddle primes temperament tempering out 64/63[+3] and 81/80[-3] in the 2.-3.+3.5.7 subgroup. The name comes from Archy and Meantone, the two temperaments combined to make Archtone. They are linearly independent, but extensions and erac tunings make use of combining the two tunings of 3. The name may also be read with the arch- prefix, implying that this is a tonality of greater scope or importance. {{UserTag|g_|Ground|7766ff|110edo is ap...") originally created as "Archtone"

24 July 2026

  • 04:4504:45, 24 July 2026 9edo (hist | edit) [3,717 bytes] CompactStar (talk | contribs) (Created page with "{{stub}} UNDER CONSTRUCTION '''Xedo''', or X equal divisions of the octave (sometimes called '''X-TET''' or '''X-tone equal temperament'''), is the equal tuning featuring steps of (1200/X) = Y cents exactly, X of which stack to the perfect octave 2/1. [Overview of tuning properties for key intervals] == General theory == === Derivation === [Derivation by equal division of various key intervals or of interval qualities] === JI app...") Tag: Visual edit: Switched

19 July 2026

  • 06:4606:46, 19 July 2026 Xenharmonic Reference:EDO page skeleton (hist | edit) [2,946 bytes] Vector (talk | contribs) (Created page with "This page is to be used as a template for making EDO pages. '''Xedo''', or X equal divisions of the octave (sometimes called '''X-TET''' or '''X-tone equal temperament'''), is the equal tuning featuring steps of (1200/X) = Y cents exactly, X of which stack to the perfect octave 2/1. [Overview of tuning properties for key intervals] == General theory == === Derivation === [Derivation by equal division of various key intervals or of...") Tag: Visual edit originally created as "EDO page skeleton"

12 July 2026

  • 00:2800:28, 12 July 2026 Intergan (hist | edit) [8,619 bytes] Ground (talk | contribs) (Created page with "'''Intergan''' is a set of temperaments related to 24edo semiquartal. The term is short for "interseptimal Ganassi, after 12edo's 2.3.17.19 Ganassi temperament. It seeks to cover all of the notable concordances generated by a meantone-range semifourth. * The most basic version is 2.3.11.13/5.17.19 5&24. 22/17 is equated to 13/10 and 22/19 is equated to 15/13. It contains the 16:19:22 sub-diminished triad. * Tempering out 81/80 is somewhat obvious, resulting in 2.3.5.11....") Tag: Visual edit: Switched

8 July 2026

  • 00:4700:47, 8 July 2026 Hedgehog (hist | edit) [1,089 bytes] Ground (talk | contribs) (Created page with "Conventionally, '''Hedgehog''' tempers out Jubilisma 50/49, splitting the octave in half into a tritone representing both 7/5 and 10/7, and the Sensamagic comma 245/243, equating a stack of two 9/7s with 5/3. If the subgroup is reduced to just 2.3.7, it tempers out the Stearnsma 118098/117649, resulting in a much more accurate temperament that can be extended in other ways. {{UserTag|g_|Ground|7766ff|The 2.3.7 temperament is extremely useful in virtually any even ed...")

7 July 2026

  • 02:3702:37, 7 July 2026 Hibernal (hist | edit) [2,752 bytes] Ground (talk | contribs) (Created page with "'''Hibernal''' is a set of temperaments based on stacking a 25/21 minor third and 19/15 major third. 25 and 15 are both divisible by 5, resulting in 63:75:95, which is also delta-rational +3+5. The name is the adjective form of "winter" after the 32edo song that uses it extensively, Winter's Mortal Hope. {{UserTag|g_|Ground|7766ff|I used Hibernal in 32edo for a while because I loved the melodic properties of its blackdye, without knowing why it sounded more concordant t...") Tag: Visual edit: Switched

5 July 2026

3 July 2026

  • 23:2823:28, 3 July 2026 Ground's composition theory (hist | edit) [21,960 bytes] Ground (talk | contribs) (Created page with "{{problematic}} I'm User:Ground. This document is going to be very long. Obviously it isn't done. I have more content to add and a need to revise the existing content. Don't expect it to make the most sense yet. My music has had a distinctively shifting key center since about 2018. Even in 12edo, my simultaneous regard and disregard for tonality may be confusing. This article is an attempt to explain how it works, with an emphasis on my other theories, Aberrisma|...")

16 June 2026

14 June 2026

  • 23:2523:25, 14 June 2026 Tcherepnin (hist | edit) [8,305 bytes] Unque (talk | contribs) (Created page with "The '''Tcherepnin''' scale, or ''3L 6s'', is a common structural scale which repeats at one third of the octave; as such, it is often associated with the augmented temperament which splits the octave into three major thirds. The scale is named after the music theorist Alexander Tcherepnin, who utilized its 12edo tuning to create a double-tonal sound with two different types of thirds; the pattern was also noted by Olivier Messiaen, who listed...") Tag: Visual edit

6 June 2026

  • 22:4222:42, 6 June 2026 Pentagoth (hist | edit) [10,792 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
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