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The '''14 equal divisions of the octave''' ('''14edo'''), or the '''14(-tone) equal temperament''' ('''14tet''', '''14et''') when viewed from a [[regular temperament]] perspective, is the tuning that divides the [[octave]] into fourteen equal steps of about 86 [[cent]]s. 14edo contains [[7edo]], doubling its number of tones.
== 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]].


== Theory ==
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.
The character of 14edo 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 below.
 
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.
 
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.


14et has quite a bit of xenharmonic appeal, in a similar way to 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. It possesses a triad-rich 9-note MOS scale of [[5L 4s]], wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad.
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]].


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|14}}
{{Harmonics in equal|14}}


== Intervals ==
=== Subsets and supersets ===
{| class="wikitable center-all right-3 left-5 left-6"
Since 14 factors into primes as 2 × 7, 14edo contains [[2edo]] and [[7edo]] as subsets.
 
== Notation ==
=== Ups and downs notation ===
{| class="wikitable center-all right-3"
|-
|-
! Steps
! Steps
! Cents
! Cents
! Approximate<br>[[Harmonic]]s
! Approximate<br>[[Harmonic]]s
! Approximate<br>Ratios 1 <ref>based on treating 14edo as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible.</ref>
! Approximate<br>Ratios 1 <ref group="note">{{sg|limit=2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]}}</ref>
! Approximate<br>Ratios 2 <ref>based on treating 14edo as an 11-limit temperament of {{val| 14 22 32 39 48}} (14c)</ref>
! 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>
! colspan="3" | [[Ups and Downs Notation]]
! Approximate<br>Ratios 3 <ref group="note">Nearest 15-odd-limit intervals by [[direct approximation]].</ref>
! colspan="3" | [[Ups and downs notation]]
! Interval Type
! Interval Type
! Audio
|-
|-
| 0
| 0
| 0.000
| 0.000
| 1
| 1
| 1/1
| 1/1
| 1/1
| 1/1
| 1/1
Line 37: Line 49:
| D
| D
| Unison
| Unison
| [[File:piano_0_1edo.mp3]]
|-
|-
| 1
| 1
Line 42: Line 55:
| 67
| 67
| 20/19, 19/18, 18/17
| 20/19, 19/18, 18/17
| 22/21, 28/27, 21/20
| 28/27, 22/21, 21/20
|
| up-unison,<br>down-2nd
| up-unison,<br>down-2nd
| ^1, v2
| ^1, v2
| ^D, vE
| ^D, vE
| Narrow Minor 2nd
| Narrow Minor 2nd
| [[File:piano_1_14edo.mp3]]
|-
|-
| 2
| 2
Line 52: Line 67:
| 71
| 71
| 11/10, 10/9, 19/17
| 11/10, 10/9, 19/17
| 9/8, 10/9, 11/10, 12/11
| 12/11, 11/10, 10/9, 9/8
| 11/10, 10/9
| 2nd
| 2nd
| 2
| 2
| E
| E
| Neutral 2nd
| Neutral 2nd
| [[File:piano_1_7edo.mp3]]
|-
|-
| 3
| 3
Line 62: Line 79:
| 37
| 37
| 22/19, 20/17
| 22/19, 20/17
| 7/6, 8/7
| 8/7, 7/6
| 15/13, 7/6
| up-2nd,<br>down-3rd
| up-2nd,<br>down-3rd
| ^2, v3
| ^2, v3
| ^E, vF
| ^E, vF
| Subminor 3rd
| Subminor 3rd
| [[File:piano_3_14edo.mp3]]
|-
|-
| 4
| 4
| 342.857
| 342.857
| 39
| 39
| 11/9, 17/14
| 17/14, 11/9
| 11/9, 5/4, 6/5
| 6/5, 11/9, 5/4
| 11/9
| 3rd
| 3rd
| 3
| 3
| F
| F
| Neutral 3rd
| Neutral 3rd
| [[File:piano_2_7edo.mp3]]
|-
|-
| 5
| 5
| 428.571
| 428.571
| 41
| 41
| 9/7, 14/11, 22/17
| 22/17, 14/11, 9/7
| 9/7, 14/11
| 14/11, 9/7
| 14/11, 9/7
| up-3rd,<br>down-4th
| up-3rd,<br>down-4th
| ^3, v4
| ^3, v4
| ^F, vG
| ^F, vG
| Supermajor 3rd
| Supermajor 3rd
| [[File:piano_5_14edo.mp3]]
|-
|-
| 6
| 6
Line 93: Line 116:
| 19/14
| 19/14
| 4/3, 15/11, 11/8
| 4/3, 15/11, 11/8
| 4/3
| 4th
| 4th
| 4
| 4
| G
| G
| Wide 4th
| Wide 4th
| [[File:piano_3_7edo.mp3]]
|-
|-
| 7
| 7
| 600.000
| 600.000
| 91
| 91
| 7/5, 10/7
| 7/5, 10/7
| 7/5, 10/7
| 7/5, 10/7
| 7/5, 10/7
Line 107: Line 133:
| ^G, vA
| ^G, vA
| Tritone
| Tritone
| [[File:piano_1_2edo.mp3]]
|-
|-
| 8
| 8
Line 112: Line 139:
| 95
| 95
| 28/19
| 28/19
| 3/2, 22/15, 16/11
| 16/11, 22/15, 3/2
| 3/2
| 5th
| 5th
| 5
| 5
| A
| A
| Narrow 5th
| Narrow 5th
| [[File:piano_4_7edo.mp3]]
|-
|-
| 9
| 9
Line 122: Line 151:
| 25
| 25
| 14/9, 11/7, 17/11
| 14/9, 11/7, 17/11
| 14/9, 11/7
| 14/9, 11/7
| 14/9, 11/7
| up-5th,<br>down-6th
| up-5th,<br>down-6th
Line 127: Line 157:
| ^A, vB
| ^A, vB
| Subminor 6th
| Subminor 6th
| [[File:piano_9_14edo.mp3]]
|-
|-
| 10
| 10
| 857.143
| 857.143
| 105
| 105
| 18/11, 28/17
| 8/5, 18/11, 5/3
| 18/11
| 18/11
| 18/11, 8/5, 5/3
| 6th
| 6th
| 6
| 6
| B
| B
| Neutral 6th
| Neutral 6th
| [[File:piano_5_7edo.mp3]]
|-
|-
| 11
| 11
| 942.857
| 942.857
| 55
| 55
| 19/11, 17/10
| 17/10, 19/11
| 12/7, 7/4
| 12/7, 7/4
| 12/7, 26/15
| up-6th,<br>down-7th
| up-6th,<br>down-7th
| ^6, v7
| ^6, v7
| ^B, vC
| ^B, vC
| Supermajor 6th
| Supermajor 6th
| [[File:piano_11_14edo.mp3]]
|-
|-
| 12
| 12
| 1028.571
| 1028.571
| 29
| 29
| 20/11, 9/5, 34/19
| 19/34, 9/5, 20/11
| 16/9, 9/5, 20/11, 11/6
| 16/9, 9/5, 20/11, 11/6
| 9/5, 20/11
| 7th
| 7th
| 7
| 7
| C
| C
| Neutral 7th
| Neutral 7th
| [[File:piano_6_7edo.mp3]]
|-
|-
| 13
| 13
| 1114.286
| 1114.286
| 61
| 61
| 19/10, 36/19, 17/9
| 17/9, 36/19, 19/10
| 21/11, 27/14, 40/21
| 40/21, 21/11, 27/14
|
| up-7th,<br />down-8ve
| up-7th,<br />down-8ve
| ^7, v8
| ^7, v8
| ^C, vD
| ^C, vD
| Wide Major 7th
| Wide Major 7th
| [[File:piano_13_14edo.mp3]]
|-
|-
| 14
| 14
| 1200.000
| 1200.000
| 2
| 2
| 2/1
| 2/1
| 2/1
| 2/1
| 2/1
Line 177: Line 217:
| D
| D
| Octave
| Octave
| [[File:piano_1_1edo.mp3]]
|}
|}
<references group="note" />
=== Sagittal notation ===
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]].


<references />
{{Sagittal chart|}}


=== Ivor Darreg's notation ===
[[Ivor Darreg]] wrote in [http://www.tonalsoft.com/sonic-arts/darreg/dar15.htm this article]:
[[Ivor Darreg]] wrote in [http://www.tonalsoft.com/sonic-arts/darreg/dar15.htm this article]:


Line 194: Line 240:
|}
|}


=== Chord names ===
== 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).
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).


Line 207: Line 253:
0-3-8-11 = C vE G vB = Cv7 = C down-seven
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]].
For a more complete list, see [[Ups and downs notation #Chords and Chord Progressions]].


== JI approximation ==
== Approximation to JI ==
=== Selected just intervals by error ===
=== Selected just intervals by error ===
==== Selected 13-limit intervals ====
==== Selected 13-limit intervals ====
[[File:14ed2-001.svg|alt=alt : Your browser has no SVG support.]]
[[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 ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
Line 227: Line 277:
| 2.3.7
| 2.3.7
| 49/48, 2187/2048
| 49/48, 2187/2048
| [{{val| 14 22 39 }}]
| {{mapping| 14 22 39 }}
| +6.52
| +6.52
| 4.64
| 4.64
Line 234: Line 284:
| 2.3.7.11
| 2.3.7.11
| 33/32, 49/48, 243/242
| 33/32, 49/48, 243/242
| [{{val| 14 22 39 48 }}]
| {{mapping| 14 22 39 48 }}
| +7.58
| +7.58
| 4.42
| 4.42
| 5.12
| 5.12
|}
|}
=== Uniform maps ===
{{Uniform map|edo=14}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
Line 244: Line 297:


=== Commas ===
=== Commas ===
14edo [[tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 14 22 33 39 48 52 }}.  
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"
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
|-
! [[Harmonic limit|Prime<br>Limit]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Monzo]]
! [[Cent]]s
! [[Cent]]s
Line 260: Line 313:
| 113.69
| 113.69
| Lawa
| Lawa
| Apotome
| Whitewood comma, apotome
|-
| 5
| [[27/25]]
| {{monzo| 0 -3 2 }}
| 133.24
| Gugu
| Bug comma, large limma
|-
|-
| 5
| 5
Line 268: Line 328:
| Sagugu
| Sagugu
| Diaschisma
| Diaschisma
|-
|7
|[[21/20]]
|[-2 1 -1 1⟩
|84.47
|Zogu
|Chroma
|-
|-
| 7
| 7
Line 274: Line 341:
| 48.77
| 48.77
| Rugu
| Rugu
| Septimal quartertone
| Mint comma, septimal quartertone
|-
|-
| 7
| 7
Line 281: Line 348:
| 35.70
| 35.70
| Zozo
| Zozo
| Slendro diesis
| Sempahoresma, slendro diesis
|-
|-
| 7
| 7
Line 295: Line 362:
| 6.48
| 6.48
| Satrizo-agu
| Satrizo-agu
| Hemimage
| Hemimage comma
|-
|-
| 7
| 7
Line 330: Line 397:
| 19.13
| 19.13
| Thozogu
| Thozogu
| Superleap
| Superleap comma, biome comma
|-
|-
| 13
| 13
Line 339: Line 406:
| Island comma
| Island comma
|}
|}
<references/>
<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 ==
== Scales ==
* 5 4 5 - [[MOS]] of [[2L 1s]]
=== MOS scales ===
* 4 1 4 1 4 - [[MOS]] of [[3L 2s]]
{{Main|List of MOS scales in {{PAGENAME}}}}
* 3 3 2 3 3 - [[MOS]] of [[4L 1s]]
* 3 1 3 3 1 3 - [[MOS]] of [[4L 2s]]
* 3 2 2 2 2 3 - [[MODMOS]] of [[2L 4s]]
* 3 1 3 1 3 3 - [[MODMOS]] of [[4L 2s]]
* 2 2 1 2 2 2 1 2 - [[MOS]] of [[6L 2s]]
* 2 1 2 2 2 2 1 2 - [[MODMOS]] of [[6L 2s]]
* 2 1 2 1 2 1 2 1 2 - [[MOS]] of [[5L 4s]]
* 1 2 1 2 1 1 2 1 2 1 - [[MOS]] of [[4L 6s]]
* 1 2 1 1 1 2 1 1 1 2 1 - [[MOS]] of [[3L 8s]]
* 1 1 2 1 1 1 1 1 2 1 1 1 [[MOS]] of [[2L 10s]]
* 1 1 1 1 1 3 1 1 1 1 1 1 [[MOS]] of [[1L 11s]]
* 1 1 1 1 1 1 2 1 1 1 1 1 1 [[MOS]] of [[1L 12s]]


Here are the modes that create MOS scales in 14edo shown on horagrams from Scala, skipping multiples of 14:
Here are the modes that create MOS scales in 14edo shown on horagrams from Scala, skipping multiples of 14:
Line 361: Line 419:
[[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]]
[[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]]


=== Titanium[9] ===
==== Beep[9] ====
14edo is also the largest edo whose patent val [[support]]s [[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.
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.


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.
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.


* 1\14: Minor 2nd<sub>9</sub>: functions similarly to the diatonic minor second, but is more incisive.  
* 1\14: Minor 2nd<sub>9</sub>: functions similarly to the diatonic minor second, but is more incisive.  
Line 380: Line 438:
* 13\14: Major 9th<sub>9</sub>: A high, incisive leading tone.  
* 13\14: Major 9th<sub>9</sub>: A high, incisive leading tone.  
* 14\14: The 10th<sub>9</sub> or "enneatonic decave" (i. e. the octave, 2:1).
* 14\14: The 10th<sub>9</sub> or "enneatonic decave" (i. e. the octave, 2:1).
=== Others ===
* 2 2 2 2 2 2 2 - [[Equiheptatonic]] (exactly [[7edo]])
* 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


== Diagrams ==
== Diagrams ==
[[File:14edo_wheel.png|alt=14edo wheel.png|343x343px|14edo wheel.png]]
[[File:14edo_wheel.png|alt=14edo wheel.png|343x343px|14edo wheel.png]]


== Books ==
== Software support ==
[[File:Libro_Tetradecafónico.PNG|alt=Libro_Tetradecafónico.PNG|Libro_Tetradecafónico.PNG]]


''Sword, Ron. "Tetradecaphonic Scales for Guitar" IAAA Press. First Ed: June 2009.''
[[File:SA14 for Mus2.zip]]


== Music ==
[[File:14edo_mus2.jpg|thumb]]
{{See also|:Category:14edo tracks}}


; [[Knowsur]]
== Instruments ==
* [http://split-notes.com/004/ ''NANA WODORI'']
[[Lumatone mapping for 14edo|Lumatone mappings for 14edo]] are available.


; [[Stephen Weigel]]
== Music ==
* [https://soundcloud.com/overtoneshock/our-pixel-perfect-telephone-discussion-14-edo ''Our Pixel Perfect Dial Tone of Voice'']
{{Main|14edo/Music}}
{{Catrel|14edo tracks}}


; [[Ralph Lewis]]
== See also ==
* [http://micro.soonlabel.com/0-praxis/audio/August/august_03_thereminnards.mp3 ''Thereminnards'']
* [[MisterShafXen’s take on 14edo harmony]]
 
; [[Philip Schuessler]]
* ''Pendula (for amplified trombone)''
 
; [[Ralph Jarzombek]] ([http://www.freewebs.com/ralphjarzombek/ site])
 
; [[Daniel Wolf]]
* [http://home.snafu.de/djwolf/IvorDarregInEagleRock.pdf ''Ivor Darreg in Eagle Rock''] (score)
 
; [[Chris Vaisvil]] [http://chrisvaisvil.com/?p=943 site]
* [http://micro.soonlabel.com/14-et/daily20110610-sax-Riding_The_L.mp3 ''Riding the L'']


; [[Jon Lyle Smith]]
== Further reading ==
* [http://clones.soonlabel.com/public/micro/jon-lyle-smith/Thorium%20Road.mp3 ''Thorium Road'']{{dead link}}
[[File:Libro_Tetradecafónico.PNG|alt=Libro_Tetradecafónico.PNG|Libro_Tetradecafónico.PNG|thumb|''Tetradecaphonic Scales for Guitar'' cover art.]]
* [http://archive.org/download/tranSentient/tranSentient.mp3 ''tranSentient'']{{dead link}}
* [[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.
* [http://archive.org/download/TheSpectrumOfDesire/the_spectrum_of_desire.mp3 ''the spectrum of desire'']{{dead link}}
 
; [[Herman Miller]]
* [https://sites.google.com/site/teamouse/home ''This Way to the Egress''] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/egress-gpo.mp3 play]{{dead link}}
 
; [[Jacob Barton]]
* [https://www.soundclick.com/music/songInfo.cfm?songID=3680443 Hyperimprovisation 'Tasty'] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Hyperimprovisation%20Tasty.mp3 play]{{dead link}}
 
; [[Aaron Andrew Hunt]]
* [http://www.h-pi.com/mp3/14ETPrelude.mp3 ''14ETPrelude'']{{dead link}}
 
; [[Mark Allan Barnes]]
* [https://youtu.be/mHyaW1fVWsg ''Medicine Wheel'']
 
; [[Cameron Bobro]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Fourteen_EDO_CBobro_r8b.mp3 ''Fourteen EDO'']{{dead link}}
 
; [[Yin Bell]]
* [https://soundcloud.com/yinbell/study-in-a-newly-discovered-scale ''Study in a newly discovered 14&#45;ET'']
 
== Software support ==
 
[[File:SA14 for Mus2.zip]]
 
[[File:14edo_mus2.jpg|frame|left]]
 
== See also ==
* [[Lumatone mapping for 14edo]]


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