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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{interwiki |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | de = |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-04 10:23:51 UTC</tt>.<br>
| | | en = 14edo |
| : The original revision id was <tt>601330454</tt>.<br>
| | | es = |
| : The revision comment was: <tt></tt><br>
| | | ja = 14平均律 |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | }} |
| <h4>Original Wikitext content:</h4>
| | {{Infobox ET}} |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html"><span style="display: block; text-align: right;">[[14平均律|日本語]]
| | {{ED intro}} |
| </span>
| |
| [[toc|flat]]
| |
| =**Intervals**=
| |
| || **DEGREE** ||||= [[xenharmonic/Ups and Downs Notation|up/down]] | |
| [[xenharmonic/Ups and Downs Notation| notation]] || **CENTS (coarse/fine)**
| |
| **<span style="background-color: #ffffff;">DMS</span>** ||= **Approximate**
| |
| **Ratios 1``*``** ||= **Approximate**
| |
| **Ratios 2** **``**``** ||= Nearest
| |
| Harmonic || Interval Type ||
| |
| || 0 ||= C ||= unison || 0 ||= 1/1 ||= 1/1 ||= 1 || Unison ||
| |
| || 1 ||= C^, Dv ||= up-unison,
| |
| down-2nd || 85.714, 102.857
| |
| 25°42'51" ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 || Narrow Minor 2nd ||
| |
| || 2 ||= D ||= 2nd || 171.429, 205.714
| |
| <span style="background-color: #ffffff;">51°25'43"</span> ||= 11/10, 10/9,
| |
| 19/17 ||= 9/8, 10/9,
| |
| 11/10, 12/11 ||= 71 || Neutral 2nd, or
| |
| Narrow Major 2nd ||
| |
| || 3· ||= D^, Ev ||= up-2nd,
| |
| down-3rd || 257.143, 308.571
| |
| 77°8'34" ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 || Subminor 3rd ||
| |
| || 4 ||= E ||= 3rd || 342.857, 411.429
| |
| <span style="background-color: #ffffff;">102°51'26"</span> ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 || Neutral 3rd ||
| |
| || 5· ||= E^, Fv ||= up-3rd,
| |
| down-4th || 428.571, 514.286
| |
| <span style="line-height: 15.6000003814697px;">128°34'17"</span> ||= 9/7, 14/11,
| |
| 22/17 ||= 9/7, 14/11 ||= 41 || Supermajor 3rd ||
| |
| || 6 ||= F ||= 4th || 51<span style="line-height: 1.5;">4.286, 617.143</span>
| |
| <span style="background-color: #ffffff;">154°17'9"</span> ||= 19/14 ||= 4/3, 11/8 ||= 43 || Wide 4th ||
| |
| || 7· ||= F^, Gv ||= up-4th,
| |
| down-5th || 600, 720
| |
| 180° ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || Tritone ||
| |
| || 8 ||= G ||= 5th || 685.714, 823.857
| |
| <span style="background-color: #ffffff;">205°42'51"</span> ||= 28/19 ||= 3/2, 16/11 ||= 95 || Narrow 5th ||
| |
| || 9· ||= G^, Av ||= up-5th,
| |
| down-6th || 771.429, 925.714
| |
| 231°25'43" ||= 14/9, 11/7,
| |
| 17/11 ||= ||= 25 || Subminor 6th ||
| |
| || 10 ||= A ||= 6th || 857.143, 1028.571
| |
| <span style="background-color: #ffffff;">257°8'34"</span> ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || Neutral 6th ||
| |
| || 11· ||= A^, Bv ||= up-6th,
| |
| down-7th || 942.857, 1131.429
| |
| 282°51'26" ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 || Supermajor 6th ||
| |
| || 12 ||= B ||= 7th || 1028.571, 1234.286
| |
| <span style="background-color: #ffffff;">308°34'17"</span> ||= 20/11, 9/5,
| |
| 34/19 ||= 16/9, 9/5,
| |
| 20/11, 11/6 ||= 29 || Neutral 7th, or
| |
| Wide Minor 7th ||
| |
| || 13 ||= B^, Cv ||= up-7th,
| |
| down-8ve || 1114.286, 1337.143
| |
| 334°17'9" ||= 19/10, 36/19,
| |
| 17/9 ||= 21/11, 27/14, 40/21 ||= 61 || Wide Major 7th ||
| |
| || 14··(or 0) ||= C ||= 8ve || 1200, 1440
| |
| 360° ||= 2/1 ||= 2/1 ||= 2 || Octave ||
| |
| ``*``based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible.
| |
| <span style="display: block; text-align: center;">``**``</span>
| |
| based on treating 14edo as an 11-limit temperament
| |
| [[media type="custom" key="24802838"]]
| |
|
| |
|
| [[file:14ed2-001.svg]] | | == Theory == |
| | 14edo is the double of [[7edo]], and thus contains its flat 686{{C}} fifth, while adding new intervals halfway between each 7edo step. The intervals of 14edo not found in 7edo are [[Backslash notation|1\14]] = 86{{C}}, 3\14 = 257{{C}}, 5\14 = 429{{C}}, 7\14 = 600{{C}}, and their [[octave complement]]s. The 1\14 interval is a small semitone, and its inversion a major seventh, which is suitable for a {{w|leading tone}}. The 3\14 interval can be considered a small [[subminor third]] (or inframinor third), thus bringing a new, distinct flavor from the [[neutral third]] of 7edo, which is 4 steps of 14edo. The 5\14 interval is the [[fifth complement]] of 3\14, and can be considered a [[supermajor third]], so that stacking 3\14 and 5\14 gives the triad 0–3–8 steps (0–257–686{{C}}). Finally, the 7\14 interval is the familiar [[tritone]] found in [[12edo]], as well as every even-numbered [[edo]]. |
|
| |
|
| =Rank two temperaments=
| | In terms of [[just intonation]], 14edo contains the approximation of [[3/2]] from 7edo. 14edo does not do well in the [[5-limit]], with [[5/4]] being close to halfway between its steps, so that 14edo does not approximate the [[4:5:6]] major triad or the [[10:12:15|1/(6:5:4)]] minor triad accurately. The closest approximation of [[7/4]] is very flat at 11\14 (943{{C}}), so that two of them stack to [[3/1]], meaning that [[49/48]] is [[tempering out|tempered out]], so that 14edo [[support]]s the [[semaphore]] temperament. However, since the 3rd harmonic is flat, the [[7/6]] and [[9/7]] intervals are approximated much more accurately, so that the 0–3–8 steps triad is a usable approximation of [[6:7:9]], and the 0–5–8 steps (0–429–686{{C}}) triad approximates [[14:18:21|1/(9:7:6)]]. The semaphore temperament notably generates the [[mos scale]] with pattern [[5L 4s]] (named ''semiquartal''), which contains many [[~]]6:7:9 and ~1/(9:7:6) triads. In the [[11-limit]], the [[11/8]] interval is tuned very flat and equated with [[4/3]]. However, [[11/9]] is tuned rather accurately, being represented with the 4\14 interval (343{{C}}), so that the [[Neutral (interval quality)|neutral]] triad formed by dividing the perfect fifth in two can be interpreted as a stack of two [[11/9]]'s, thus tempering out [[243/242]]. The neutral third can also be stacked on the supermajor third to get a ~[[7:9:11]] chord. |
| [[xenharmonic/List of 14edo rank two temperaments by badness|List of 14edo rank two temperaments by badness]] | |
|
| |
|
| =Harmony=
| | While prime [[5/1|5]] is poorly approximated, the [[7/5]] and [[11/10]] intervals are approximated fairly well. If we accept these approximations in addition to the ones described earlier, then we end up with a low-complexity, high-damage full [[11-limit]] temperament where many rather large [[comma]]s are tempered out. This leads to some of the bizarre equivalences described in the second "Approximate ratios" column in the table. This mapping uses the (barely) second-best mapping of prime 5, so it is notated with [[wart notation]] as "14c", where c is the 3rd letter of the alphabet, and 5 is the 3rd prime number. While not very accurate as a temperament, this mapping can be used to classify 11-limit intervals, which conveniently tempers out the [[square superparticular]]s of odds 5, 7, 9, and 11, and is the unique mapping to do so. |
| The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11:17:19 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs). However, the ratios 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage 11-limit temperament where the commas listed at the bottom of this page are tempered out. This leads to some of the bizarre equivalences described in the second "Approximate Ratios" column in the table above.
| |
|
| |
|
| 14-EDO has quite a bit of xenharmonic appeal, in a similar way to 17-EDO, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12-TET. Since 14-EDO also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of 5L4s, wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad.
| | 14et has quite a bit of [[xenharmonic]] appeal, in a similar way to [[17edo|17et]], on account of having three types of 3rd and three types of 6th, rather than the usual two of [[12et]]. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. The 5L 4s mos scale is rich in triads, wherein 7 of 9 notes are [[tonic]] to a subminor, supermajor, and/or neutral triad. |
|
| |
|
| ===Titanium[9]===
| | 14edo also contains an [[omnidiatonic]] scale that can replace the standard diatonic scale, allowing for recognizable triadic harmony using the chords [[6:7:9]] and [[14:18:21]], as well as a neutral chord which can be seen as [[2:sqrt(6):3]]. |
|
| |
|
| 14edo is also the largest edo whose patent val supports [[titanium]] temperament, tempering out the chromatic semitone (21:20), and falling toward the "brittle" (fifths wider than in 9edo) end of that spectrum. Titanium is one of the simplest 7-limit temperaments, although rather inaccurate (the 7:5 is mapped onto 6\14, over 70 cents flat). Its otonal/major and utonal/minor tetrads are inversions of one another, which allows a greater variety of chord progressions (since different inversions of the same chord may have very different expressive qualities). Despite being so heavily tempered, the tetrads are still recognizable and aren't unpleasant-sounding as long as one uses the right timbres ("bell-like" or opaque-sounding ones probably work best). Titanium forms enneatonic modes which are melodically strong and are very similar to diatonic modes, only with two mediants and submediants instead of one. Titanium[9] has similarities to mavila, slendro, and pelog scales as well.
| | === Prime harmonics === |
| | {{Harmonics in equal|14}} |
|
| |
|
| Using titanium[9], we could name the intervals of 14edo as follows. The 3, 5, 6, 8, 9, and 11-step intervals are all consonant, while 1, 2, 4, 7, 10, 12, and 13 steps are dissonant. There is no distinction between "perfect" (modulatory) and "imperfect" (major/minor) consonances here; there are enough chords here that root motion may occur by //any// consonant interval, and thus //all// six consonances are "perfect" intervals, rather than just two of them as in the diatonic system. As in the diatonic scale, the perfect intervals come in pairs separated by a major second, and with a characteristic dissonance between them; in titanium[9] there are three such pairs rather than just one.
| | === Subsets and supersets === |
| | Since 14 factors into primes as 2 × 7, 14edo contains [[2edo]] and [[7edo]] as subsets. |
|
| |
|
| 1\14: Minor 2nd<span style="vertical-align: sub;">9</span>: functions similarly to the diatonic minor second, but is more incisive. | | == Notation == |
| 2\14: Major 2nd<span style="vertical-align: sub;">9</span>: functions similarly to the diatonic major second, but is narrower and has a rather different quality. | | === Ups and downs notation === |
| 3\14: Perfect 3rd<span style="vertical-align: sub;">9</span>: the generator, standing in for 8:7, 7:6, //and// 6:5, but closest to 7:6.
| | {| class="wikitable center-all right-3" |
| 4\14: Augmented 3rd<span style="vertical-align: sub;">9</span>/diminished 4th<span style="vertical-align: sub;">9</span>: A dissonance, falling in between two perfect consonances and hence analogous to the tritone. | | |- |
| 5\14: Perfect 4th<span style="vertical-align: sub;">9</span>: technically represents 5:4 but is quite a bit wider. | | ! Steps |
| 6\14: Perfect 5th<span style="vertical-align: sub;">9</span>: represents 4:3 and 7:5, much closer to the former. | | ! Cents |
| 7\14: Augmented 5th<span style="vertical-align: sub;">9</span>/diminished 6th<span style="vertical-align: sub;">9</span>: The so-called "tritone" (but no longer made up of three whole tones). Like 4\14 and 10\14, this is a characteristic dissonance separating a pair of perfect consonances. | | ! Approximate<br>[[Harmonic]]s |
| 8\14: Perfect 6th<span style="vertical-align: sub;">9</span>: represents 10:7 and 3:2, much closer to the latter. | | ! Approximate<br>Ratios 1 <ref group="note">{{sg|limit=2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]}}</ref> |
| 9\14: Perfect 7th<span style="vertical-align: sub;">9</span>: technically represents 5:8 but noticeably narrower. | | ! Approximate<br>Ratios 2 <ref group="note">Based on treating 14edo as an 11-limit temperament of {{val| 14 22 32 39 48}} (14c).</ref> |
| 10\14: Augmented 7th<span style="vertical-align: sub;">9</span>/diminished 8th<span style="vertical-align: sub;">9</span>: The third and final characteristic dissonance, analogous to the tritone. | | ! Approximate<br>Ratios 3 <ref group="note">Nearest 15-odd-limit intervals by [[direct approximation]].</ref> |
| 11\14: Perfect 8th<span style="vertical-align: sub;">9</span>: Represents 5:3, 12:7 and 7:4. | | ! colspan="3" | [[Ups and downs notation]] |
| 12\14: Minor 9th<span style="vertical-align: sub;">9</span>: Analogous to the diatonic minor seventh, but sharper than usual. | | ! Interval Type |
| 13\14: Major 9th<span style="vertical-align: sub;">9</span>: A high, incisive leading tone. | | ! Audio |
| 14\14: The 10th<span style="vertical-align: sub;">9 </span>or "enneatonic decave", (i. e., the octave, 2:1). | | |- |
| | | 0 |
| | | 0.000 |
| | | 1 |
| | | 1/1 |
| | | 1/1 |
| | | 1/1 |
| | | unison |
| | | 1 |
| | | D |
| | | Unison |
| | | [[File:piano_0_1edo.mp3]] |
| | |- |
| | | 1 |
| | | 85.714 |
| | | 67 |
| | | 20/19, 19/18, 18/17 |
| | | 28/27, 22/21, 21/20 |
| | | |
| | | up-unison,<br>down-2nd |
| | | ^1, v2 |
| | | ^D, vE |
| | | Narrow Minor 2nd |
| | | [[File:piano_1_14edo.mp3]] |
| | |- |
| | | 2 |
| | | 171.429 |
| | | 71 |
| | | 11/10, 10/9, 19/17 |
| | | 12/11, 11/10, 10/9, 9/8 |
| | | 11/10, 10/9 |
| | | 2nd |
| | | 2 |
| | | E |
| | | Neutral 2nd |
| | | [[File:piano_1_7edo.mp3]] |
| | |- |
| | | 3 |
| | | 257.143 |
| | | 37 |
| | | 22/19, 20/17 |
| | | 8/7, 7/6 |
| | | 15/13, 7/6 |
| | | up-2nd,<br>down-3rd |
| | | ^2, v3 |
| | | ^E, vF |
| | | Subminor 3rd |
| | | [[File:piano_3_14edo.mp3]] |
| | |- |
| | | 4 |
| | | 342.857 |
| | | 39 |
| | | 17/14, 11/9 |
| | | 6/5, 11/9, 5/4 |
| | | 11/9 |
| | | 3rd |
| | | 3 |
| | | F |
| | | Neutral 3rd |
| | | [[File:piano_2_7edo.mp3]] |
| | |- |
| | | 5 |
| | | 428.571 |
| | | 41 |
| | | 22/17, 14/11, 9/7 |
| | | 14/11, 9/7 |
| | | 14/11, 9/7 |
| | | up-3rd,<br>down-4th |
| | | ^3, v4 |
| | | ^F, vG |
| | | Supermajor 3rd |
| | | [[File:piano_5_14edo.mp3]] |
| | |- |
| | | 6 |
| | | 514.286 |
| | | 43 |
| | | 19/14 |
| | | 4/3, 15/11, 11/8 |
| | | 4/3 |
| | | 4th |
| | | 4 |
| | | G |
| | | Wide 4th |
| | | [[File:piano_3_7edo.mp3]] |
| | |- |
| | | 7 |
| | | 600.000 |
| | | 91 |
| | | 7/5, 10/7 |
| | | 7/5, 10/7 |
| | | 7/5, 10/7 |
| | | up-4th,<br>down-5th |
| | | ^4, v5 |
| | | ^G, vA |
| | | Tritone |
| | | [[File:piano_1_2edo.mp3]] |
| | |- |
| | | 8 |
| | | 685.714 |
| | | 95 |
| | | 28/19 |
| | | 16/11, 22/15, 3/2 |
| | | 3/2 |
| | | 5th |
| | | 5 |
| | | A |
| | | Narrow 5th |
| | | [[File:piano_4_7edo.mp3]] |
| | |- |
| | | 9 |
| | | 771.429 |
| | | 25 |
| | | 14/9, 11/7, 17/11 |
| | | 14/9, 11/7 |
| | | 14/9, 11/7 |
| | | up-5th,<br>down-6th |
| | | ^5, v6 |
| | | ^A, vB |
| | | Subminor 6th |
| | | [[File:piano_9_14edo.mp3]] |
| | |- |
| | | 10 |
| | | 857.143 |
| | | 105 |
| | | 18/11, 28/17 |
| | | 8/5, 18/11, 5/3 |
| | | 18/11 |
| | | 6th |
| | | 6 |
| | | B |
| | | Neutral 6th |
| | | [[File:piano_5_7edo.mp3]] |
| | |- |
| | | 11 |
| | | 942.857 |
| | | 55 |
| | | 17/10, 19/11 |
| | | 12/7, 7/4 |
| | | 12/7, 26/15 |
| | | up-6th,<br>down-7th |
| | | ^6, v7 |
| | | ^B, vC |
| | | Supermajor 6th |
| | | [[File:piano_11_14edo.mp3]] |
| | |- |
| | | 12 |
| | | 1028.571 |
| | | 29 |
| | | 19/34, 9/5, 20/11 |
| | | 16/9, 9/5, 20/11, 11/6 |
| | | 9/5, 20/11 |
| | | 7th |
| | | 7 |
| | | C |
| | | Neutral 7th |
| | | [[File:piano_6_7edo.mp3]] |
| | |- |
| | | 13 |
| | | 1114.286 |
| | | 61 |
| | | 17/9, 36/19, 19/10 |
| | | 40/21, 21/11, 27/14 |
| | | |
| | | up-7th,<br />down-8ve |
| | | ^7, v8 |
| | | ^C, vD |
| | | Wide Major 7th |
| | | [[File:piano_13_14edo.mp3]] |
| | |- |
| | | 14 |
| | | 1200.000 |
| | | 2 |
| | | 2/1 |
| | | 2/1 |
| | | 2/1 |
| | | 8ve |
| | | 8 |
| | | D |
| | | Octave |
| | | [[File:piano_1_1edo.mp3]] |
| | |} |
| | <references group="note" /> |
|
| |
|
| =Notation= | | === Sagittal notation === |
| [[Ivor Darreg]] wrote in [[http://sonic-arts.org/darreg/dar15.htm|this article]]: | | This notation uses the same sagittal sequence as [[9edo#Sagittal notation|9-EDO]], is a subset of the notations for EDOs [[28edo#Sagittal notation|28]] and [[42edo#Second-best fifth notation|42b]], and is a superset of the notation for [[7edo#Sagittal notation|7-EDO]]. |
|
| |
|
| //The 14-tone scale presents a new situation: while one might use ordinary sharps and flats in addition to conventional naturals for the notes of the 7-tone-equal temperament, it would be misleading and confusing to do so, because there is a 7-tone circle of fifths (admittedly quite distorted) already notatable and nameable as F C G D A E B in the usual manner. But there is no 14-tone circle of fifths. There is simply a second set of 7 fifths in a circle which does not intersect the with the first set. Thus is we think of B-flat and B, or B-natural and F-sharp, the 14-tone-system interval would NOT be a fifth of that system and would not sound like one, since B F would be the very same kind of distorted fifth that C G or A E happens to be in 7 or 14. Our suggestion is to call the new notes of 14, the second set of 7, F* C* G* D* A* E* B*, and use asterisks or arrows or whatever you please on the staff. Or just number the tones as for 13.// | | {{Sagittal chart|}} |
| | |
| | === Ivor Darreg's notation === |
| | [[Ivor Darreg]] wrote in [http://www.tonalsoft.com/sonic-arts/darreg/dar15.htm this article]: |
| | |
| | ''The 14-tone scale presents a new situation: while one might use ordinary sharps and flats in addition to conventional naturals for the notes of the 7-tone-equal temperament, it would be misleading and confusing to do so, because there is a 7-tone circle of fifths (admittedly quite distorted) already notatable and nameable as F C G D A E B in the usual manner. But there is no 14-tone circle of fifths. There is simply a second set of 7 fifths in a circle which does not intersect the with the first set. Thus is we think of B-flat and B, or B-natural and F-sharp, the 14-tone-system interval would NOT be a fifth of that system and would not sound like one, since B F would be the very same kind of distorted fifth that C G or A E happens to be in 7 or 14. Our suggestion is to call the new notes of 14, the second set of 7, F* C* G* D* A* E* B*, and use asterisks or arrows or whatever you please on the staff. Or just number the tones as for 13.'' |
|
| |
|
| The following chart (made by [[Tútim Dennsuul Wafiil|TDW]]) shows this recommendation as "standard notation" as well as a proposed alternative. | | The following chart (made by [[Tútim Dennsuul Wafiil|TDW]]) shows this recommendation as "standard notation" as well as a proposed alternative. |
|
| |
|
| [[image:Ciclo_Tetradecafonía.png width="456" height="468" caption="Intervallic Cycle of 14 steps Equal per Octave"]] | | {| class="wikitable" |
| | |- |
| | | [[File:Ciclo_Tetradecafonía.png|alt=Ciclo_Tetradecafonía.png|456x468px|Ciclo_Tetradecafonía.png]] |
| | |- |
| | | Intervallic Cycle of 14 steps Equal per Octave |
| | |} |
| | |
| | == Chord names == |
| | Ups and downs can be used to name 14edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used. Alterations are always enclosed in parentheses, additions never are. An up or down immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). |
| | |
| | 0-4-8 = C E G = C = C or C perfect<br> |
| | 0-3-8 = C vE G = Cv = C down<br> |
| | 0-5-8 = C ^E G = C^ = C up<br> |
| | 0-4-7 = C E vG = C(v5) = C down-five<br> |
| | 0-5-9 = C ^E ^G = C^(^5) = C up up-five<br> |
| | 0-4-8-12 = C E G B = C7 = C seven<br> |
| | 0-4-8-11 = C E G vB = C,v7 = C add down-seven<br> |
| | 0-3-8-12 = C vE G B = Cv,7 = C down add seven<br> |
| | 0-3-8-11 = C vE G vB = Cv7 = C down-seven |
| | |
| | For a more complete list, see [[Ups and downs notation #Chords and Chord Progressions]]. |
| | |
| | == Approximation to JI == |
| | === Selected just intervals by error === |
| | ==== Selected 13-limit intervals ==== |
| | [[File:14ed2-001.svg|alt=alt : Your browser has no SVG support.]] |
| | === Interval mappings === |
| | {{Q-odd-limit intervals|14}} |
| | {{Q-odd-limit intervals|13.95|apx=val|header=none|tag=none|title=15-odd-limit intervals by 14c val mapping}} |
| | |
| | == Regular temperament properties == |
| | {| class="wikitable center-4 center-5 center-6" |
| | |- |
| | ! rowspan="2" | [[Subgroup]] |
| | ! rowspan="2" | [[Comma list]] |
| | ! rowspan="2" | [[Mapping]] |
| | ! rowspan="2" | Optimal<br>8ve stretch (¢) |
| | ! colspan="2" | Tuning error |
| | |- |
| | ! [[TE error|Absolute]] (¢) |
| | ! [[TE simple badness|Relative]] (%) |
| | |- |
| | | 2.3.7 |
| | | 49/48, 2187/2048 |
| | | {{mapping| 14 22 39 }} |
| | | +6.52 |
| | | 4.64 |
| | | 5.38 |
| | |- |
| | | 2.3.7.11 |
| | | 33/32, 49/48, 243/242 |
| | | {{mapping| 14 22 39 48 }} |
| | | +7.58 |
| | | 4.42 |
| | | 5.12 |
| | |} |
| | |
| | === Uniform maps === |
| | {{Uniform map|edo=14}} |
| | |
| | === Rank-2 temperaments === |
| | * [[List of 14edo rank two temperaments by badness]] |
| | |
| | === Commas === |
| | 14et [[tempering out|tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 14 22 33 39 48 52 }}. |
| | |
| | {| class="commatable wikitable center-all left-3 right-4 left-6" |
| | |- |
| | ! [[Harmonic limit|Prime<br>limit]] |
| | ! [[Ratio]]<ref group="note">{{rd}}</ref> |
| | ! [[Monzo]] |
| | ! [[Cent]]s |
| | ! [[Color name]] |
| | ! Name |
| | |- |
| | | 3 |
| | | [[2187/2048]] |
| | | {{monzo| -11 7 }} |
| | | 113.69 |
| | | Lawa |
| | | Whitewood comma, apotome |
| | |- |
| | | 5 |
| | | [[27/25]] |
| | | {{monzo| 0 -3 2 }} |
| | | 133.24 |
| | | Gugu |
| | | Bug comma, large limma |
| | |- |
| | | 5 |
| | | [[2048/2025]] |
| | | {{monzo| 11 -4 -2 }} |
| | | 19.55 |
| | | Sagugu |
| | | Diaschisma |
| | |- |
| | |7 |
| | |[[21/20]] |
| | |[-2 1 -1 1⟩ |
| | |84.47 |
| | |Zogu |
| | |Chroma |
| | |- |
| | | 7 |
| | | [[36/35]] |
| | | {{monzo| 2 2 -1 -1 }} |
| | | 48.77 |
| | | Rugu |
| | | Mint comma, septimal quartertone |
| | |- |
| | | 7 |
| | | [[49/48]] |
| | | {{monzo| -4 -1 0 2 }} |
| | | 35.70 |
| | | Zozo |
| | | Sempahoresma, slendro diesis |
| | |- |
| | | 7 |
| | | [[1728/1715]] |
| | | {{monzo| 6 3 -1 -3 }} |
| | | 13.07 |
| | | Triru-agu |
| | | Orwellisma |
| | |- |
| | | 7 |
| | | [[10976/10935]] |
| | | {{monzo| 5 -7 -1 3 }} |
| | | 6.48 |
| | | Satrizo-agu |
| | | Hemimage comma |
| | |- |
| | | 7 |
| | | <abbr title="140737488355328/140710042265625">(30 digits)</abbr> |
| | | {{monzo| 47 -7 -7 -7 }} |
| | | 0.34 |
| | | Trisa-seprugu |
| | | [[Akjaysma]] |
| | |- |
| | | 11 |
| | | [[99/98]] |
| | | {{monzo| -1 2 0 -2 1 }} |
| | | 17.58 |
| | | Loruru |
| | | Mothwellsma |
| | |- |
| | | 11 |
| | | [[243/242]] |
| | | {{monzo| -1 5 0 0 -2 }} |
| | | 7.14 |
| | | Lulu |
| | | Rastma |
| | |- |
| | | 11 |
| | | [[385/384]] |
| | | {{monzo| -7 -1 1 1 1 }} |
| | | 4.50 |
| | | Lozoyo |
| | | Keenanisma |
| | |- |
| | | 13 |
| | | [[91/90]] |
| | | {{monzo| -1 -2 -1 1 0 1 }} |
| | | 19.13 |
| | | Thozogu |
| | | Superleap comma, biome comma |
| | |- |
| | | 13 |
| | | [[676/675]] |
| | | {{monzo| 2 -3 -2 0 0 2 }} |
| | | 2.56 |
| | | Bithogu |
| | | Island comma |
| | |} |
| | <references group="note" /> |
| | |
| | == Octave stretch or compression == |
| | 14edo benefits from [[octave stretch]] as harmonics 3, 7, and 11 are all tuned flat. [[22edt]], [[ed6|36ed6]] and [[42zpi]] are among the possible choices. |
| | |
| | == Scales == |
| | === MOS scales === |
| | {{Main|List of MOS scales in {{PAGENAME}}}} |
| | |
| | Here are the modes that create MOS scales in 14edo shown on horagrams from Scala, skipping multiples of 14: |
| | [[File:Screen Shot 2020-04-23 at 11.47.09 PM.png|none|thumb|877x877px|3\14 MOS using 1L 1s, 1L 2s, 1L 3s, 4L 1s, 5L 4s]] |
| | [[File:Screen Shot 2020-04-23 at 11.47.30 PM.png|none|thumb|870x870px|5\14 MOS using 1L 1s, 2L 1s, 3L 2s, 3L 5s, 3L 8s]] |
|
| |
|
| =Images= | | ==== Beep[9] ==== |
| | 14edo is also the largest edo whose patent val [[support]]s [[beep]] temperament, tempering out the chromatic semitone (21:20), and falling toward the "brittle" (fifths wider than in 9edo) end of that spectrum. beep is one of the simplest 7-limit temperaments, although rather inaccurate (the 7:5 is mapped onto 6\14, over 70 cents flat). Its otonal/major and utonal/minor tetrads are inversions of one another, which allows a greater variety of chord progressions (since different inversions of the same chord may have very different expressive qualities). Despite being so heavily tempered, the tetrads are still recognizable and aren't unpleasant-sounding as long as one uses the right timbres ("bell-like" or opaque-sounding ones probably work best). beep forms enneatonic modes which are melodically strong and are very similar to diatonic modes, only with two mediants and submediants instead of one. Beep[9] has similarities to mavila, slendro, and pelog scales as well. |
|
| |
|
| [[image:14edo wheel.png width="343" height="343"]] | | Using beep[9], we could name the intervals of 14edo as follows. The 3, 5, 6, 8, 9, and 11-step intervals are all consonant, while 1, 2, 4, 7, 10, 12, and 13 steps are dissonant. There is no distinction between "perfect" (modulatory) and "imperfect" (major/minor) consonances here; there are enough chords here that root motion may occur by ''any'' consonant interval, and thus ''all'' six consonances are "perfect" intervals, rather than just two of them as in the diatonic system. As in the diatonic scale, the perfect intervals come in pairs separated by a major second, and with a characteristic dissonance between them; in beep[9] there are three such pairs rather than just one. |
|
| |
|
| =Commas=
| | * 1\14: Minor 2nd<sub>9</sub>: functions similarly to the diatonic minor second, but is more incisive. |
| 14 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the val < 14 22 33 39 48 52/1 |.) | | * 2\14: Major 2nd<sub>9</sub>: functions similarly to the diatonic major second, but is narrower and has a rather different quality. |
| ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||
| | * 3\14: Perfect 3rd<sub>9</sub>: the generator, standing in for 8:7, 7:6, ''and'' 6:5, but closest to 7:6. |
| ||= 2187/2048 ||< | -11 7 > ||> 113.69 ||= Apotome ||= ||
| | * 4\14: Augmented 3rd<sub>9</sub>, diminished 4th<sub>9</sub>: A dissonance, falling in between two perfect consonances and hence analogous to the tritone. |
| ||= 2048/2025 ||< | 11 -4 -2 > ||> 19.55 ||= Diaschisma ||= ||
| | * 5\14: Perfect 4th<sub>9</sub>: technically represents 5:4 but is quite a bit wider. |
| ||= 36/35 ||< | 2 2 -1 -1 > ||> 48.77 ||= Septimal Quarter Tone ||= ||
| | * 6\14: Perfect 5th<sub>9</sub>: represents 4:3 and 7:5, much closer to the former. |
| ||= 49/48 ||< | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||= ||
| | * 7\14: Augmented 5th<sub>9</sub>, diminished 6th<sub>9</sub>: The so-called "tritone" (but no longer made up of three whole tones). Like 4\14 and 10\14, this is a characteristic dissonance separating a pair of perfect consonances. |
| ||= 1728/1715 ||< | 6 3 -1 -3 > ||> 13.07 ||= Orwellisma ||= Orwell Comma ||
| | * 8\14: Perfect 6th<sub>9</sub>: represents 10:7 and 3:2, much closer to the latter. |
| ||= 10976/10935 ||< | 5 -7 -1 3 > ||> 6.48 ||= Hemimage ||= ||
| | * 9\14: Perfect 7th<sub>9</sub>: technically represents 8:5 but noticeably narrower. |
| ||= ||< | 47 -7 -7 -7 > ||> 0.34 ||= Akjaysma ||= 5\7 Octave Comma ||
| | * 10\14: Augmented 7th<sub>9</sub>, diminished 8th<sub>9</sub>: The third and final characteristic dissonance, analogous to the tritone. |
| ||= 99/98 ||< | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||= ||
| | * 11\14: Perfect 8th<sub>9</sub>: Represents 5:3, 12:7 and 7:4. |
| ||= 243/242 ||< | -1 5 0 0 -2 > ||> 7.14 ||= Rastma ||= ||
| | * 12\14: Minor 9th<sub>9</sub>: Analogous to the diatonic minor seventh, but sharper than usual. |
| ||= 385/384 ||< | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||= ||
| | * 13\14: Major 9th<sub>9</sub>: A high, incisive leading tone. |
| ||= 91/90 ||< | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= ||
| | * 14\14: The 10th<sub>9</sub> or "enneatonic decave" (i. e. the octave, 2:1). |
| ||= 676/675 ||< | 2 -3 -2 0 0 2 > ||> 2.56 ||= Parizeksma ||= ||
| |
|
| |
|
| =**[[modes|Modes]]**= | | === Others === |
| 5 5 4 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[2L1s]]</span>
| | * 2 2 2 2 2 2 2 - [[Equiheptatonic]] (exactly [[7edo]]) |
| 5 4 5 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[2L1s]]</span>
| | * 2 2 2 2 1 4 1 - Fennec{{idiosyncratic}} (original/default tuning) |
| | * 1 4 1 2 2 2 2 - Inverse fennec{{idiosyncratic}} (original/default tuning) |
| | * 3 1 4 1 4 1 - Pseudo-[[augmented]] |
| | * 1 4 1 2 1 4 1 - Pseudo-double harmonic minor |
|
| |
|
| 4 1 4 4 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[3L2s]]
| | == Diagrams == |
| 4 1 4 1 4 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[3L2s]]</span>
| | [[File:14edo_wheel.png|alt=14edo wheel.png|343x343px|14edo wheel.png]] |
| 3 3 3 3 2 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[4L1s]]
| |
| 3 2 3 3 3 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[4L1s]]</span>
| |
| 3 2 2 2 2 3 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[2L4s]]
| |
| 2 2 3 2 2 3 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[2L4s]]</span>
| |
| **3 3 1 3 3 1 -** <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[4L2s]]
| |
| 3 1 3 3 1 3 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[4L2s]]</span>
| |
| 3 1 3 1 3 3 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[4L2s]]</span>
| |
| 2 2 1 2 2 2 2 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[6L2s]]
| |
| 2 2 2 1 2 2 2 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[6L2s]]</span>
| |
| **2 2 2 2 1 2 2 1 -** <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[6L2s]]</span>
| |
| 2 1 2 2 1 2 2 2 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[6L2s]]</span>
| |
| 2 1 2 1 2 1 2 1 2 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[5L4s]]
| |
| 2 1 2 1 2 1 2 2 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[5L4s]]</span>
| |
| 2 1 2 1 2 2 1 2 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[5L4s]]</span>
| |
| 2 1 1 2 1 2 1 1 2 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[4L6s]]
| |
| 2 1 1 1 2 1 1 2 1 1 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[3L8s]]
| |
| **1 1 2 1 1 1 2 1 1 1 2** - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[3L8s]]</span>
| |
|
| |
|
| | == Software support == |
|
| |
|
| =Books=
| | [[File:SA14 for Mus2.zip]] |
| [[image:Libro_Tetradecafónico.PNG]] | |
| //Sword, Ron. "Tetradecaphonic Scales for Guitar" IAAA Press. First Ed: June 2009.//
| |
|
| |
|
| =**Compositions**=
| | [[File:14edo_mus2.jpg|thumb]] |
| [[http://split-notes.com/004/|NANA WODORI]] by knowsur | |
| [[http://micro.soonlabel.com/0-praxis/audio/August/august_03_thereminnards.mp3|Thereminnards]] by Ralph Lewis
| |
| Pendula (for amplified trombone) by Philip Schuessler
| |
| [[http://www.freewebs.com/ralphjarzombek/|Music]] by Ralph Jarzombek
| |
| [[http://home.snafu.de/djwolf/IvorDarregInEagleRock.pdf|Ivor Darreg in Eagle Rock]] by [[Daniel Wolf]]
| |
| <span class="ymp-btn-page-play ymp-media-4c2dab90062954a92dc59831018d92d9">[[http://micro.soonlabel.com/14-et/daily20110610-sax-Riding_The_L.mp3|Riding the L]]</span> by [[@http://chrisvaisvil.com/?p=943|Chris Vaisvil]]
| |
| <span class="ymp-btn-page-play ymp-media-579db51554bd270599a9397e8446cdb9">[[http://clones.soonlabel.com/public/micro/jon-lyle-smith/Thorium%20Road.mp3|Thorium Road]]</span> by [[Jon Lyle Smith]]
| |
| [[http://archive.org/download/tranSentient/tranSentient.mp3|tranSentient]] by [[Jon Lyle Smith]]
| |
| [[http://archive.org/download/TheSpectrumOfDesire/the_spectrum_of_desire.mp3|the spectrum of desire]] by [[Jon Lyle Smith]]
| |
| [[https://sites.google.com/site/teamouse/home|This Way to the Egress]] <span class="ymp-btn-page-play ymp-media-0135aaddbe40aa681d77552715064991">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/egress-gpo.mp3|play]]</span> by [[http://www.io.com/%7Ehmiller/music/index.html|Herman Miller]]
| |
| [[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=145852&songID=3680443|Hyperimprovisation 'Tasty']] <span class="ymp-btn-page-play ymp-media-882819e185058b65278d03572ba40da1">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Hyperimprovisation%20Tasty.mp3|play]]</span> by [[Jacob Barton]]
| |
| <span class="ymp-btn-page-play ymp-media-285313eab060867d8d5d941dea1d4152">[[http://www.h-pi.com/mp3/14ETPrelude.mp3|14ETPrelude]]</span> by [[Aaron Andrew Hunt]]
| |
| [[http://youtu.be/mHyaW1fVWsg|Medicine Wheel]] by Mark Allan Barnes
| |
| [[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Fourteen_EDO_CBobro_r8b.mp3|Fourteen EDO]] by [[Cameron Bobro]]</pre></div>
| |
| <h4>Original HTML content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>14edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/14%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br />
| |
| </span><br />
| |
| <!-- ws:start:WikiTextTocRule:25:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Rank two temperaments">Rank two temperaments</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Harmony">Harmony</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Notation">Notation</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Images">Images</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Modes">Modes</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --> | <a href="#Books">Books</a><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: -->
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| <!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc0"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:5 --><strong>Intervals</strong></h1>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | == Instruments == |
| <tr>
| | [[Lumatone mapping for 14edo|Lumatone mappings for 14edo]] are available. |
| <td><strong>DEGREE</strong><br />
| |
| </td>
| |
| <td colspan="2" style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">up/down</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"> notation</a><br />
| |
| </td>
| |
| <td><strong>CENTS (coarse/fine)</strong><br />
| |
| <strong><span style="background-color: #ffffff;">DMS</span></strong><br />
| |
| </td>
| |
| <td style="text-align: center;"><strong>Approximate</strong><br />
| |
| <strong>Ratios 1<!-- ws:start:WikiTextRawRule:00:``*`` -->*<!-- ws:end:WikiTextRawRule:00 --></strong><br />
| |
| </td>
| |
| <td style="text-align: center;"><strong>Approximate</strong><br />
| |
| <strong>Ratios 2</strong> <strong><!-- ws:start:WikiTextRawRule:01:``**`` -->**<!-- ws:end:WikiTextRawRule:01 --></strong><br />
| |
| </td>
| |
| <td style="text-align: center;">Nearest<br />
| |
| Harmonic<br />
| |
| </td>
| |
| <td>Interval Type<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>0<br />
| |
| </td>
| |
| <td style="text-align: center;">C<br />
| |
| </td>
| |
| <td style="text-align: center;">unison<br />
| |
| </td>
| |
| <td>0<br />
| |
| </td>
| |
| <td style="text-align: center;">1/1<br />
| |
| </td>
| |
| <td style="text-align: center;">1/1<br />
| |
| </td>
| |
| <td style="text-align: center;">1<br />
| |
| </td>
| |
| <td>Unison<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td style="text-align: center;">C^, Dv<br />
| |
| </td>
| |
| <td style="text-align: center;">up-unison,<br />
| |
| down-2nd<br />
| |
| </td>
| |
| <td>85.714, 102.857<br />
| |
| 25°42'51&quot;<br />
| |
| </td>
| |
| <td style="text-align: center;">20/19, 19/18, 18/17<br />
| |
| </td>
| |
| <td style="text-align: center;">22/21, 28/27, 21/20<br />
| |
| </td>
| |
| <td style="text-align: center;">67<br />
| |
| </td>
| |
| <td>Narrow Minor 2nd<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td style="text-align: center;">D<br />
| |
| </td>
| |
| <td style="text-align: center;">2nd<br />
| |
| </td>
| |
| <td>171.429, 205.714<br />
| |
| <span style="background-color: #ffffff;">51°25'43&quot;</span><br />
| |
| </td>
| |
| <td style="text-align: center;">11/10, 10/9,<br />
| |
| 19/17<br />
| |
| </td>
| |
| <td style="text-align: center;">9/8, 10/9,<br />
| |
| 11/10, 12/11<br />
| |
| </td>
| |
| <td style="text-align: center;">71<br />
| |
| </td>
| |
| <td>Neutral 2nd, or<br />
| |
| Narrow Major 2nd<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3·<br />
| |
| </td>
| |
| <td style="text-align: center;">D^, Ev<br />
| |
| </td>
| |
| <td style="text-align: center;">up-2nd,<br />
| |
| down-3rd<br />
| |
| </td>
| |
| <td>257.143, 308.571<br />
| |
| 77°8'34&quot;<br />
| |
| </td>
| |
| <td style="text-align: center;">22/19, 20/17<br />
| |
| </td>
| |
| <td style="text-align: center;">7/6, 8/7<br />
| |
| </td>
| |
| <td style="text-align: center;">37<br />
| |
| </td>
| |
| <td>Subminor 3rd<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td style="text-align: center;">E<br />
| |
| </td>
| |
| <td style="text-align: center;">3rd<br />
| |
| </td>
| |
| <td>342.857, 411.429<br />
| |
| <span style="background-color: #ffffff;">102°51'26&quot;</span><br />
| |
| </td>
| |
| <td style="text-align: center;">11/9, 17/14<br />
| |
| </td>
| |
| <td style="text-align: center;">11/9, 5/4, 6/5<br />
| |
| </td>
| |
| <td style="text-align: center;">39<br />
| |
| </td>
| |
| <td>Neutral 3rd<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5·<br />
| |
| </td>
| |
| <td style="text-align: center;">E^, Fv<br />
| |
| </td>
| |
| <td style="text-align: center;">up-3rd,<br />
| |
| down-4th<br />
| |
| </td>
| |
| <td>428.571, 514.286<br />
| |
| <span style="line-height: 15.6000003814697px;">128°34'17&quot;</span><br />
| |
| </td>
| |
| <td style="text-align: center;">9/7, 14/11,<br />
| |
| 22/17<br />
| |
| </td>
| |
| <td style="text-align: center;">9/7, 14/11<br />
| |
| </td>
| |
| <td style="text-align: center;">41<br />
| |
| </td>
| |
| <td>Supermajor 3rd<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td style="text-align: center;">F<br />
| |
| </td>
| |
| <td style="text-align: center;">4th<br />
| |
| </td>
| |
| <td>51<span style="line-height: 1.5;">4.286, 617.143</span><br />
| |
| <span style="background-color: #ffffff;">154°17'9&quot;</span><br />
| |
| </td>
| |
| <td style="text-align: center;">19/14<br />
| |
| </td>
| |
| <td style="text-align: center;">4/3, 11/8<br />
| |
| </td>
| |
| <td style="text-align: center;">43<br />
| |
| </td>
| |
| <td>Wide 4th<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7·<br />
| |
| </td>
| |
| <td style="text-align: center;">F^, Gv<br />
| |
| </td>
| |
| <td style="text-align: center;">up-4th,<br />
| |
| down-5th<br />
| |
| </td>
| |
| <td>600, 720<br />
| |
| 180°<br />
| |
| </td>
| |
| <td style="text-align: center;">7/5, 10/7<br />
| |
| </td>
| |
| <td style="text-align: center;">7/5, 10/7<br />
| |
| </td>
| |
| <td style="text-align: center;">91<br />
| |
| </td>
| |
| <td>Tritone<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
| |
| </td>
| |
| <td style="text-align: center;">G<br />
| |
| </td>
| |
| <td style="text-align: center;">5th<br />
| |
| </td>
| |
| <td>685.714, 823.857<br />
| |
| <span style="background-color: #ffffff;">205°42'51&quot;</span><br />
| |
| </td>
| |
| <td style="text-align: center;">28/19<br />
| |
| </td>
| |
| <td style="text-align: center;">3/2, 16/11<br />
| |
| </td>
| |
| <td style="text-align: center;">95<br />
| |
| </td>
| |
| <td>Narrow 5th<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9·<br />
| |
| </td>
| |
| <td style="text-align: center;">G^, Av<br />
| |
| </td>
| |
| <td style="text-align: center;">up-5th,<br />
| |
| down-6th<br />
| |
| </td>
| |
| <td>771.429, 925.714<br />
| |
| 231°25'43&quot;<br />
| |
| </td>
| |
| <td style="text-align: center;">14/9, 11/7,<br />
| |
| 17/11<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">25<br />
| |
| </td>
| |
| <td>Subminor 6th<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10<br />
| |
| </td>
| |
| <td style="text-align: center;">A<br />
| |
| </td>
| |
| <td style="text-align: center;">6th<br />
| |
| </td>
| |
| <td>857.143, 1028.571<br />
| |
| <span style="background-color: #ffffff;">257°8'34&quot;</span><br />
| |
| </td>
| |
| <td style="text-align: center;">18/11<br />
| |
| </td>
| |
| <td style="text-align: center;">18/11, 8/5, 5/3<br />
| |
| </td>
| |
| <td style="text-align: center;">105<br />
| |
| </td>
| |
| <td>Neutral 6th<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11·<br />
| |
| </td>
| |
| <td style="text-align: center;">A^, Bv<br />
| |
| </td>
| |
| <td style="text-align: center;">up-6th,<br />
| |
| down-7th<br />
| |
| </td>
| |
| <td>942.857, 1131.429<br />
| |
| 282°51'26&quot;<br />
| |
| </td>
| |
| <td style="text-align: center;">19/11, 17/10<br />
| |
| </td>
| |
| <td style="text-align: center;">12/7, 7/4<br />
| |
| </td>
| |
| <td style="text-align: center;">55<br />
| |
| </td>
| |
| <td>Supermajor 6th<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12<br />
| |
| </td>
| |
| <td style="text-align: center;">B<br />
| |
| </td>
| |
| <td style="text-align: center;">7th<br />
| |
| </td>
| |
| <td>1028.571, 1234.286<br />
| |
| <span style="background-color: #ffffff;">308°34'17&quot;</span><br />
| |
| </td>
| |
| <td style="text-align: center;">20/11, 9/5,<br />
| |
| 34/19<br />
| |
| </td>
| |
| <td style="text-align: center;">16/9, 9/5,<br />
| |
| 20/11, 11/6<br />
| |
| </td>
| |
| <td style="text-align: center;">29<br />
| |
| </td>
| |
| <td>Neutral 7th, or<br />
| |
| Wide Minor 7th<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13<br />
| |
| </td>
| |
| <td style="text-align: center;">B^, Cv<br />
| |
| </td>
| |
| <td style="text-align: center;">up-7th,<br />
| |
| down-8ve<br />
| |
| </td>
| |
| <td>1114.286, 1337.143<br />
| |
| 334°17'9&quot;<br />
| |
| </td>
| |
| <td style="text-align: center;">19/10, 36/19,<br />
| |
| 17/9<br />
| |
| </td>
| |
| <td style="text-align: center;">21/11, 27/14, 40/21<br />
| |
| </td>
| |
| <td style="text-align: center;">61<br />
| |
| </td>
| |
| <td>Wide Major 7th<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14··(or 0)<br />
| |
| </td>
| |
| <td style="text-align: center;">C<br />
| |
| </td>
| |
| <td style="text-align: center;">8ve<br />
| |
| </td>
| |
| <td>1200, 1440<br />
| |
| 360°<br />
| |
| </td>
| |
| <td style="text-align: center;">2/1<br />
| |
| </td>
| |
| <td style="text-align: center;">2/1<br />
| |
| </td>
| |
| <td style="text-align: center;">2<br />
| |
| </td>
| |
| <td>Octave<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextRawRule:02:``*`` -->*<!-- ws:end:WikiTextRawRule:02 -->based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 <a class="wiki_link" href="/subgroup">subgroup</a>; other approaches are possible.<br />
| | == Music == |
| <span style="display: block; text-align: center;"><!-- ws:start:WikiTextRawRule:03:``**`` -->**<!-- ws:end:WikiTextRawRule:03 --></span><br />
| | {{Main|14edo/Music}} |
| based on treating 14edo as an 11-limit temperament<br />
| | {{Catrel|14edo tracks}} |
| <!-- ws:start:WikiTextMediaRule:4:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/24802838?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;24802838&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/14ed2-001.svg">alt : Your browser has no SVG support.</object><!-- ws:end:WikiTextMediaRule:4 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextFileRule:486:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/14ed2-001.svg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@14ed2-001.svg&quot; title=&quot;File: 14ed2-001.svg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/14ed2-001.svg/480713166/14ed2-001.svg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="14ed2-001.svg" /></a><div><a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/14ed2-001.svg/480713166/14ed2-001.svg');" class="filename" title="14ed2-001.svg">14ed2-001.svg</a><br /><ul><li><a href="/file/detail/14ed2-001.svg">Details</a></li><li><a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg">Download</a></li><li style="color: #666">15 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:486 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc1"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:7 -->Rank two temperaments</h1>
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/List%20of%2014edo%20rank%20two%20temperaments%20by%20badness">List of 14edo rank two temperaments by badness</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc2"><a name="Harmony"></a><!-- ws:end:WikiTextHeadingRule:9 -->Harmony</h1>
| |
| The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11:17:19 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs). However, the ratios 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage 11-limit temperament where the commas listed at the bottom of this page are tempered out. This leads to some of the bizarre equivalences described in the second &quot;Approximate Ratios&quot; column in the table above.<br />
| |
| <br />
| |
| 14-EDO has quite a bit of xenharmonic appeal, in a similar way to 17-EDO, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12-TET. Since 14-EDO also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of 5L4s, wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:11:&lt;h3&gt; --><h3 id="toc3"><a name="Harmony--Titanium[9]"></a><!-- ws:end:WikiTextHeadingRule:11 -->Titanium[9]</h3>
| |
| <br />
| |
| 14edo is also the largest edo whose patent val supports <a class="wiki_link" href="/titanium">titanium</a> temperament, tempering out the chromatic semitone (21:20), and falling toward the &quot;brittle&quot; (fifths wider than in 9edo) end of that spectrum. Titanium is one of the simplest 7-limit temperaments, although rather inaccurate (the 7:5 is mapped onto 6\14, over 70 cents flat). Its otonal/major and utonal/minor tetrads are inversions of one another, which allows a greater variety of chord progressions (since different inversions of the same chord may have very different expressive qualities). Despite being so heavily tempered, the tetrads are still recognizable and aren't unpleasant-sounding as long as one uses the right timbres (&quot;bell-like&quot; or opaque-sounding ones probably work best). Titanium forms enneatonic modes which are melodically strong and are very similar to diatonic modes, only with two mediants and submediants instead of one. Titanium[9] has similarities to mavila, slendro, and pelog scales as well.<br />
| |
| <br />
| |
| Using titanium[9], we could name the intervals of 14edo as follows. The 3, 5, 6, 8, 9, and 11-step intervals are all consonant, while 1, 2, 4, 7, 10, 12, and 13 steps are dissonant. There is no distinction between &quot;perfect&quot; (modulatory) and &quot;imperfect&quot; (major/minor) consonances here; there are enough chords here that root motion may occur by <em>any</em> consonant interval, and thus <em>all</em> six consonances are &quot;perfect&quot; intervals, rather than just two of them as in the diatonic system. As in the diatonic scale, the perfect intervals come in pairs separated by a major second, and with a characteristic dissonance between them; in titanium[9] there are three such pairs rather than just one.<br />
| |
| <br />
| |
| 1\14: Minor 2nd<span style="vertical-align: sub;">9</span>: functions similarly to the diatonic minor second, but is more incisive.<br />
| |
| 2\14: Major 2nd<span style="vertical-align: sub;">9</span>: functions similarly to the diatonic major second, but is narrower and has a rather different quality.<br />
| |
| 3\14: Perfect 3rd<span style="vertical-align: sub;">9</span>: the generator, standing in for 8:7, 7:6, <em>and</em> 6:5, but closest to 7:6.<br />
| |
| 4\14: Augmented 3rd<span style="vertical-align: sub;">9</span>/diminished 4th<span style="vertical-align: sub;">9</span>: A dissonance, falling in between two perfect consonances and hence analogous to the tritone.<br />
| |
| 5\14: Perfect 4th<span style="vertical-align: sub;">9</span>: technically represents 5:4 but is quite a bit wider.<br />
| |
| 6\14: Perfect 5th<span style="vertical-align: sub;">9</span>: represents 4:3 and 7:5, much closer to the former.<br />
| |
| 7\14: Augmented 5th<span style="vertical-align: sub;">9</span>/diminished 6th<span style="vertical-align: sub;">9</span>: The so-called &quot;tritone&quot; (but no longer made up of three whole tones). Like 4\14 and 10\14, this is a characteristic dissonance separating a pair of perfect consonances.<br />
| |
| 8\14: Perfect 6th<span style="vertical-align: sub;">9</span>: represents 10:7 and 3:2, much closer to the latter.<br />
| |
| 9\14: Perfect 7th<span style="vertical-align: sub;">9</span>: technically represents 5:8 but noticeably narrower.<br />
| |
| 10\14: Augmented 7th<span style="vertical-align: sub;">9</span>/diminished 8th<span style="vertical-align: sub;">9</span>: The third and final characteristic dissonance, analogous to the tritone.<br />
| |
| 11\14: Perfect 8th<span style="vertical-align: sub;">9</span>: Represents 5:3, 12:7 and 7:4.<br />
| |
| 12\14: Minor 9th<span style="vertical-align: sub;">9</span>: Analogous to the diatonic minor seventh, but sharper than usual.<br />
| |
| 13\14: Major 9th<span style="vertical-align: sub;">9</span>: A high, incisive leading tone.<br />
| |
| 14\14: The 10th<span style="vertical-align: sub;">9 </span>or &quot;enneatonic decave&quot;, (i. e., the octave, 2:1).<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc4"><a name="Notation"></a><!-- ws:end:WikiTextHeadingRule:13 -->Notation</h1>
| |
| <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> wrote in <a class="wiki_link_ext" href="http://sonic-arts.org/darreg/dar15.htm" rel="nofollow">this article</a>:<br />
| |
| <br />
| |
| <em>The 14-tone scale presents a new situation: while one might use ordinary sharps and flats in addition to conventional naturals for the notes of the 7-tone-equal temperament, it would be misleading and confusing to do so, because there is a 7-tone circle of fifths (admittedly quite distorted) already notatable and nameable as F C G D A E B in the usual manner. But there is no 14-tone circle of fifths. There is simply a second set of 7 fifths in a circle which does not intersect the with the first set. Thus is we think of B-flat and B, or B-natural and F-sharp, the 14-tone-system interval would NOT be a fifth of that system and would not sound like one, since B F would be the very same kind of distorted fifth that C G or A E happens to be in 7 or 14. Our suggestion is to call the new notes of 14, the second set of 7, F* C* G* D* A* E* B*, and use asterisks or arrows or whatever you please on the staff. Or just number the tones as for 13.</em><br />
| |
| <br />
| |
| The following chart (made by <a class="wiki_link" href="/T%C3%BAtim%20Dennsuul%20Wafiil">TDW</a>) shows this recommendation as &quot;standard notation&quot; as well as a proposed alternative.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:483:&lt;img src=&quot;/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png&quot; alt=&quot;Intervallic Cycle of 14 steps Equal per Octave&quot; title=&quot;Intervallic Cycle of 14 steps Equal per Octave&quot; style=&quot;height: 468px; width: 456px;&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png" alt="Ciclo_Tetradecafonía.png" title="Ciclo_Tetradecafonía.png" style="height: 468px; width: 456px;" /></td></tr><tr><td class="imageCaption">Intervallic Cycle of 14 steps Equal per Octave</td></tr></table><!-- ws:end:WikiTextLocalImageRule:483 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc5"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:15 -->Images</h1>
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:484:&lt;img src=&quot;/file/view/14edo%20wheel.png/516971016/343x343/14edo%20wheel.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 343px; width: 343px;&quot; /&gt; --><img src="/file/view/14edo%20wheel.png/516971016/343x343/14edo%20wheel.png" alt="14edo wheel.png" title="14edo wheel.png" style="height: 343px; width: 343px;" /><!-- ws:end:WikiTextLocalImageRule:484 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc6"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:17 -->Commas</h1>
| |
| 14 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the val &lt; 14 22 33 39 48 52/1 |.)<br />
| |
|
| |
|
| | == See also == |
| | * [[MisterShafXen’s take on 14edo harmony]] |
|
| |
|
| <table class="wiki_table">
| | == Further reading == |
| <tr>
| | [[File:Libro_Tetradecafónico.PNG|alt=Libro_Tetradecafónico.PNG|Libro_Tetradecafónico.PNG|thumb|''Tetradecaphonic Scales for Guitar'' cover art.]] |
| <th>Comma<br />
| | * [[Sword, Ron]]. ''[http://www.metatonalmusic.com/books.html Tetradecaphonic Scales for Guitar: Scales, Chord-Scales, Notation, and Theory for Fourteen Equal Divisions of the Octave]''. 2009. |
| </th>
| |
| <th>Monzo<br />
| |
| </th>
| |
| <th>Value (Cents)<br />
| |
| </th>
| |
| <th>Name 1<br />
| |
| </th>
| |
| <th>Name 2<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">2187/2048<br />
| |
| </td>
| |
| <td style="text-align: left;">| -11 7 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">113.69<br />
| |
| </td>
| |
| <td style="text-align: center;">Apotome<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">2048/2025<br />
| |
| </td>
| |
| <td style="text-align: left;">| 11 -4 -2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">19.55<br />
| |
| </td>
| |
| <td style="text-align: center;">Diaschisma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">36/35<br />
| |
| </td>
| |
| <td style="text-align: left;">| 2 2 -1 -1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">48.77<br />
| |
| </td>
| |
| <td style="text-align: center;">Septimal Quarter Tone<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">49/48<br />
| |
| </td>
| |
| <td style="text-align: left;">| -4 -1 0 2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">35.70<br />
| |
| </td>
| |
| <td style="text-align: center;">Slendro Diesis<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">1728/1715<br />
| |
| </td>
| |
| <td style="text-align: left;">| 6 3 -1 -3 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">13.07<br />
| |
| </td>
| |
| <td style="text-align: center;">Orwellisma<br />
| |
| </td>
| |
| <td style="text-align: center;">Orwell Comma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">10976/10935<br />
| |
| </td>
| |
| <td style="text-align: left;">| 5 -7 -1 3 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">6.48<br />
| |
| </td>
| |
| <td style="text-align: center;">Hemimage<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: left;">| 47 -7 -7 -7 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">0.34<br />
| |
| </td>
| |
| <td style="text-align: center;">Akjaysma<br />
| |
| </td>
| |
| <td style="text-align: center;">5\7 Octave Comma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">99/98<br />
| |
| </td>
| |
| <td style="text-align: left;">| -1 2 0 -2 1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">17.58<br />
| |
| </td>
| |
| <td style="text-align: center;">Mothwellsma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">243/242<br />
| |
| </td>
| |
| <td style="text-align: left;">| -1 5 0 0 -2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">7.14<br />
| |
| </td>
| |
| <td style="text-align: center;">Rastma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">385/384<br />
| |
| </td>
| |
| <td style="text-align: left;">| -7 -1 1 1 1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">4.50<br />
| |
| </td>
| |
| <td style="text-align: center;">Keenanisma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">91/90<br />
| |
| </td>
| |
| <td style="text-align: left;">| -1 -2 -1 1 0 1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">19.13<br />
| |
| </td>
| |
| <td style="text-align: center;">Superleap<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">676/675<br />
| |
| </td>
| |
| <td style="text-align: left;">| 2 -3 -2 0 0 2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: right;">2.56<br />
| |
| </td>
| |
| <td style="text-align: center;">Parizeksma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | [[Category:14edo| ]] <!-- main article --> |
| <!-- ws:start:WikiTextHeadingRule:19:&lt;h1&gt; --><h1 id="toc7"><a name="Modes"></a><!-- ws:end:WikiTextHeadingRule:19 --><strong><a class="wiki_link" href="/modes">Modes</a></strong></h1>
| | [[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> |
| 5 5 4 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/2L1s">2L1s</a></span><br />
| | [[Category:Modes]] |
| 5 4 5 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/2L1s">2L1s</a></span><br />
| | [[Category:Teentuning]] |
| <br />
| |
| 4 1 4 4 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/3L2s">3L2s</a><br />
| |
| 4 1 4 1 4 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/3L2s">3L2s</a></span><br />
| |
| 3 3 3 3 2 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/4L1s">4L1s</a><br />
| |
| 3 2 3 3 3 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/4L1s">4L1s</a></span><br />
| |
| 3 2 2 2 2 3 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/2L4s">2L4s</a><br />
| |
| 2 2 3 2 2 3 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/2L4s">2L4s</a></span><br />
| |
| <strong>3 3 1 3 3 1 -</strong> <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/4L2s">4L2s</a><br />
| |
| 3 1 3 3 1 3 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/4L2s">4L2s</a></span><br />
| |
| 3 1 3 1 3 3 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/4L2s">4L2s</a></span><br />
| |
| 2 2 1 2 2 2 2 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/6L2s">6L2s</a><br />
| |
| 2 2 2 1 2 2 2 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/6L2s">6L2s</a></span><br />
| |
| <strong>2 2 2 2 1 2 2 1 -</strong> <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/6L2s">6L2s</a></span><br />
| |
| 2 1 2 2 1 2 2 2 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/6L2s">6L2s</a></span><br />
| |
| 2 1 2 1 2 1 2 1 2 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/5L4s">5L4s</a><br />
| |
| 2 1 2 1 2 1 2 2 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/5L4s">5L4s</a></span><br />
| |
| 2 1 2 1 2 2 1 2 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/5L4s">5L4s</a></span><br />
| |
| 2 1 1 2 1 2 1 1 2 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/4L6s">4L6s</a><br />
| |
| 2 1 1 1 2 1 1 2 1 1 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/3L8s">3L8s</a><br />
| |
| <strong>1 1 2 1 1 1 2 1 1 1 2</strong> - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/3L8s">3L8s</a></span><br />
| |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:21:&lt;h1&gt; --><h1 id="toc8"><a name="Books"></a><!-- ws:end:WikiTextHeadingRule:21 -->Books</h1>
| |
| <!-- ws:start:WikiTextLocalImageRule:485:&lt;img src=&quot;/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/Libro_Tetradecaf%C3%B3nico.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/Libro_Tetradecaf%C3%B3nico.PNG" alt="Libro_Tetradecafónico.PNG" title="Libro_Tetradecafónico.PNG" /><!-- ws:end:WikiTextLocalImageRule:485 --><br />
| |
| <em>Sword, Ron. &quot;Tetradecaphonic Scales for Guitar&quot; IAAA Press. First Ed: June 2009.</em><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:23:&lt;h1&gt; --><h1 id="toc9"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:23 --><strong>Compositions</strong></h1>
| |
| <a class="wiki_link_ext" href="http://split-notes.com/004/" rel="nofollow">NANA WODORI</a> by knowsur<br />
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/0-praxis/audio/August/august_03_thereminnards.mp3" rel="nofollow">Thereminnards</a> by Ralph Lewis<br />
| |
| Pendula (for amplified trombone) by Philip Schuessler<br />
| |
| <a class="wiki_link_ext" href="http://www.freewebs.com/ralphjarzombek/" rel="nofollow">Music</a> by Ralph Jarzombek<br />
| |
| <a class="wiki_link_ext" href="http://home.snafu.de/djwolf/IvorDarregInEagleRock.pdf" rel="nofollow">Ivor Darreg in Eagle Rock</a> by <a class="wiki_link" href="/Daniel%20Wolf">Daniel Wolf</a><br />
| |
| <span class="ymp-btn-page-play ymp-media-4c2dab90062954a92dc59831018d92d9"><a class="wiki_link_ext" href="http://micro.soonlabel.com/14-et/daily20110610-sax-Riding_The_L.mp3" rel="nofollow">Riding the L</a></span> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=943" rel="nofollow" target="_blank">Chris Vaisvil</a><br />
| |
| <span class="ymp-btn-page-play ymp-media-579db51554bd270599a9397e8446cdb9"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/jon-lyle-smith/Thorium%20Road.mp3" rel="nofollow">Thorium Road</a></span> by <a class="wiki_link" href="/Jon%20Lyle%20Smith">Jon Lyle Smith</a><br />
| |
| <a class="wiki_link_ext" href="http://archive.org/download/tranSentient/tranSentient.mp3" rel="nofollow">tranSentient</a> by <a class="wiki_link" href="/Jon%20Lyle%20Smith">Jon Lyle Smith</a><br />
| |
| <a class="wiki_link_ext" href="http://archive.org/download/TheSpectrumOfDesire/the_spectrum_of_desire.mp3" rel="nofollow">the spectrum of desire</a> by <a class="wiki_link" href="/Jon%20Lyle%20Smith">Jon Lyle Smith</a><br />
| |
| <a class="wiki_link_ext" href="https://sites.google.com/site/teamouse/home" rel="nofollow">This Way to the Egress</a> <span class="ymp-btn-page-play ymp-media-0135aaddbe40aa681d77552715064991"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/egress-gpo.mp3" rel="nofollow">play</a></span> by <a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/music/index.html" rel="nofollow">Herman Miller</a><br />
| |
| <a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=145852&amp;songID=3680443" rel="nofollow">Hyperimprovisation 'Tasty'</a> <span class="ymp-btn-page-play ymp-media-882819e185058b65278d03572ba40da1"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Hyperimprovisation%20Tasty.mp3" rel="nofollow">play</a></span> by <a class="wiki_link" href="/Jacob%20Barton">Jacob Barton</a><br />
| |
| <span class="ymp-btn-page-play ymp-media-285313eab060867d8d5d941dea1d4152"><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/14ETPrelude.mp3" rel="nofollow">14ETPrelude</a></span> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br />
| |
| <a class="wiki_link_ext" href="http://youtu.be/mHyaW1fVWsg" rel="nofollow">Medicine Wheel</a> by Mark Allan Barnes<br />
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Fourteen_EDO_CBobro_r8b.mp3" rel="nofollow">Fourteen EDO</a> by <a class="wiki_link" href="/Cameron%20Bobro">Cameron Bobro</a></body></html></pre></div>
| |