|
|
| (321 intermediate revisions by 37 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{interwiki |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | de = 24-EDO |
| : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 19:04:27 UTC</tt>.<br>
| | | en = 24edo |
| : The original revision id was <tt>621462007</tt>.<br>
| | | es = 24 EDO |
| : The revision comment was: <tt></tt><br>
| | | ja = 24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">[[toc]]
| | {{ED intro}} |
| <span style="display: block; text-align: right;">[[xenharmonie/24edo|Deutsch]] - [[24平均律|日本語]]
| | {{Wikipedia|Quarter tone}} |
| </span>
| |
| =Basics=
| |
| The 24edo system divides the octave into 24 equal parts of exactly 50 cents each. It is also known as **quarter-tone tuning**, since it evenly divides the 12-tone equal tempered semitone in two. Quarter-tones are the most commonly used microtonal tuning due to its retention of the familiar 12 tones and since it is the smallest microtonal equal temperament that contains all the 12 notes, and also because of its use in theory and occasionally in practice in [[Arabic, Turkish, Persian|Arabic]] music. It is easy to jump into this tuning and make microtonal music right away using common 12 equal software and even instruments - [[DIY Quartertone Composition with 12 equal tools|see this page]].
| |
|
| |
|
| =24edo as a temperament=
| | 24edo is also known as '''quarter-tone tuning''', since it evenly divides the 12-tone equal tempered semitone in two. Quarter-tones are the most commonly used microtonal tuning due to its retention of the familiar 12 tones, since it is the smallest microtonal equal temperament that contains all the 12 notes, and also because of its use in theory and occasionally in practice in [[Arabic, Turkish, Persian music|Arabic music]]. |
| The [[Harmonic Limit|5-limit]] approximations in 24-tone equal temperament are the same as those in 12-tone equal temperament, therefore 24-tone equal temperament offers nothing new as far as approximating the 5-limit is concerned. The 7th harmonic-based intervals (7:4, 7:5 and 7:6) are almost as bad in 24-tET as in 12-tET. To achieve a satisfactory level of approximation while maintaining the 12 notes of 12-tET requires high-degree tunings like 36-tET, 72-tET, 84-tET or 156-tET.
| |
|
| |
|
| The tunings supplied by 72 cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24 subgroup]] 2.3.125.35.11.325.17 [[just intonation subgroup]], making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11 and 17. Another approach would be to treat 24-EDO as a 2.3.11.17.19 subgroup temperament, on which it is quite accurate.
| | It is easy to jump into this tuning and make [[microtonal music]] right away using common 12 equal software and even instruments as illustrated in ''[[DIY Quartertone Composition with 12 equal tools]]''. |
|
| |
|
| ||= Degree ||= Cents ||= Approximate Ratios* ||||||= [[Ups and Downs Notation|ups and downs notation]] ||
| | == Theory == |
| ||= 0 ||= 0 ||= 1/1 ||= P1 ||= unison ||= C ||
| | 24edo/24-TET, also known as the quarter-tone system, is the double of [[12edo|12edo/12-TET]], so it contains all of the notes of 12edo. It adds to 12edo another circle of it spaced a quarter tone apart, which contains unfamiliar intervals not found in 12edo, such as neutral seconds and thirds. Since it contains 12edo, it is very desirable for microtonalists who want new intervals while still having access to familiar ones. |
| ||= 1 ||= 50 ||= 33/32, 34/33 ||= ^P1, vm2 ||= up-unison, downminor 2nd ||= C^, Dbv ||
| |
| ||= 2 ||= 100 ||= 17/16, 18/17 ||= A1, m2 ||= aug unison, minor 2nd ||= C#, Db ||
| |
| ||= 3 ||= 150 ||= 12/11 ||= ~2 ||= mid 2nd ||= Dv ||
| |
| ||= 4 ||= 200 ||= 9/8 ||= M2 ||= major 2nd ||= D ||
| |
| ||= 5 ||= 250 ||= 22/19 ||= ^M2, vm3 ||= upmajor 2nd, downminor 3rd ||= D^, Ebv ||
| |
| ||= 6 ||= 300 ||= 19/16 ||= m3 ||= minor 3rd ||= Eb ||
| |
| ||= 7 ||= 350 ||= 11/9 ||= ~3 ||= mid 3rd ||= Ev ||
| |
| ||= 8 ||= 400 ||= 24/19 ||= M3 ||= major 3rd ||= E ||
| |
| ||= 9 ||= 450 ||= 22/17 ||= ^M3, vP4 ||= upmajor 3rd, down-fourth ||= E^, Fv ||
| |
| ||= 10 ||= 500 ||= 4/3 ||= P4 ||= fourth ||= F || | |
| ||= 11 ||= 550 ||= 11/8 ||= ^P4 ||= up-fourth ||= F^ ||
| |
| ||= 12 ||= 600 ||= 17/12 ||= A4, d5 ||= aug 4th, dim 5th ||= F#, Gb ||
| |
| ||= 13 ||= 650 ||= 16/11 ||= vP5 ||= down-fifth ||= Gv ||
| |
| ||= 14 ||= 700 ||= 3/2 ||= P5 ||= fifth ||= G ||
| |
| ||= 15 ||= 750 ||= 17/11 ||= ^P5, vm6 ||= up-fifth, downminor 6th ||= G^, Abv ||
| |
| ||= 16 ||= 800 ||= 19/12 ||= m6 ||= minor 6th ||= Ab ||
| |
| ||= 17 ||= 850 ||= 18/11 ||= ~6 ||= mid 6th ||= Av ||
| |
| ||= 18 ||= 900 ||= 32/19 ||= M6 ||= major 6th ||= A ||
| |
| ||= 19 ||= 950 ||= 19/11 ||= ^M6, vm7 ||= upmajor 6th, downminor 7th ||= A^, Bbv ||
| |
| ||= 20 ||= 1000 ||= 16/9 ||= m7 ||= minor 7th ||= Bb ||
| |
| ||= 21 ||= 1050 ||= 11/6 ||= ~7 ||= mid 7th ||= Bv ||
| |
| ||= 22 ||= 1100 ||= 17/9, 32/17 ||= M7 ||= major 7th ||= B ||
| |
| ||= 23 ||= 1150 ||= 33/17, 64/33 ||= ^M7, vP8 ||= upmajor 7th, down-8ve ||= B^, Cv ||
| |
| ||= 24 ||= 1200 ||= 2/1 ||= P8 ||= perfect 8ve ||= C ||
| |
| *based on treating 24-EDO as a 2.3.11.17.19 subgroup; other approaches are possible.
| |
|
| |
|
| Combining ups and downs notation with [[Kite's color notation|color notation]], qualities can be loosely associated with colors:
| | The [[5-limit]] approximations in 24edo are the same as those in 12edo, tempering out [[81/80]], [[128/125]], [[648/625]], and [[531441/524288]], so 24edo offers nothing new as far as approximating the 5-limit is concerned. However, it maps the [[7/1|7th harmonic]] differently from 12edo, with [[7/4]] mapped to 950{{c}} rather than 1000{{c}} in 12edo, being 18.8{{c}} flat of just rather than 31.2{{c}} sharp in 12edo. Most intervals of 7 are still approximated quite poorly for its size, though chords like [[6:7:9]] are nonetheless closer to just than in 12edo. Still, if one wishes to approximate intervals of 7 while still having access to the notes of 12edo, it is best to use finer divisions like [[36edo]], [[48edo]], [[72edo]], or [[84edo]]. |
| ||~ quality ||~ color ||~ monzo format ||~ examples ||
| |
| ||= downminor ||= blue ||= {a, b, 0, 1} ||= 7/6, 7/4 ||
| |
| ||= minor ||= fourthward white ||= {a, b}, b < -1 ||= 32/27, 16/9 ||
| |
| ||= " ||= green ||= {a, b, -1} ||= 6/5, 9/5 ||
| |
| ||= mid ||= jade ||= {a, b, 0, 0, 1} ||= 11/9, 11/6 ||
| |
| ||= " ||= amber ||= {a, b, 0, 0, -1} ||= 12/11, 18/11 ||
| |
| ||= major ||= yellow ||= {a, b, 1} ||= 5/4, 5/3 ||
| |
| ||= " ||= fifthward white ||= {a, b}, b > 1 ||= 9/8, 27/16 ||
| |
| ||= upmajor ||= red ||= {a, b, 0, -1} ||= 9/7, 12/7 ||
| |
|
| |
|
| The 11th harmonic, and most intervals derived from it, (11:10, 11:9, 11:8, 11:6, 12:11, 15:11, 16:11, 18:11, 20:11) are very well approximated in 24-tone equal temperament. The 24-tone interval of 550 cents is 1.3 cents flatter than 11:8 and is almost indistinguishable from it. In addition, the interval approximating 11:9 is 7 steps which is exactly half the perfect fifth. Some good chords in 24-tET are (the numbers are edosteps, e.g. 4 is a major second, 8 is a major third):
| | However, 24edo approximates the [[11/1|11th harmonic]] very accurately at 550{{c}}, only 1.3{{c}} flat of just. Most intervals of 11, such as [[11/8]], [[11/6]], [[11/10]], and [[11/9]], are approximated accurately as well. It is thus usable as an [[2.3.11 subgroup|2.3.11-]] or [[2.3.5.11 subgroup|2.3.5.11-]][[subgroup]] system, notably tempering out [[121/120]], splitting [[6/5]] into two neutral seconds of {{nowrap|[[11/10]][[~]][[12/11]]}}, and [[243/242]], splitting [[3/2]] into two 11/9 neutral thirds. It also has a decent approximation of the [[13/1|13th harmonic]] at 850{{c}}, being 9.5{{c}} sharp of just. Intervals of 13 are thus represented decently, with [[13/10]], [[15/13]], and their [[octave complement]]s being especially close to just due to the cancellation of the sharpness of harmonics 5 and 13. It is thus a good tuning for the 2.3.5.11.13 and 2.3.11.13/5 subgroups, tempering out [[144/143]] in the former, so that [[11/9]] and [[16/13]] are equated, and [[676/675]] in both subgroups, so two 15/13's add up to [[4/3]]. Finally, 24edo shares its tunings of harmonics [[17/1|17]] and [[19/1|19]] with 12edo, meaning that 7 and to an extent 5 are the only low primes 24edo tunes particularly poorly. Nonetheless, it is not the best system for approximating JI if one wishes to use prime 7, with other equal temperaments like [[22edo]], [[27edo]], and especially [[31edo]] being more accurate. |
|
| |
|
| 0-4-8-11-14 ("major" chord with a 9:8 and a 11:8 above the root)
| | Aside from harmony, it also preserves the melodic resources of 12edo, containing minor and major seconds and thirds. However, it adds several new intervals, including neutral seconds and thirds, so new melodies can be written in 24edo that aren't possible in 12edo. This also means 24edo contains new scales, most notably the "neutral diatonic" [[3L 4s]] [[MOS]] with step pattern LssLsLs, where ''L'' is a major second and ''s'' is a neutral second. These scales also contain chords unfamiliar to 12edo, such as the [[neutral tetrad]]. |
| Its inversion, 0-3-6-10-14 ("minor")
| |
| 0-7-14 ("neutral")
| |
| 0-5-10 (another kind of "neutral", splitting the fourth in two. The 0-5-10 can be extended into a pentatonic scale, 0-5-10-14-19-24 ([[godzilla]]), that is close to equi-pentatonic and also close to several Indonesian slêndros. In a similar way 0-7-14 extends to 0-4-7-11-14-18-21-24 ([[mohajira]]), a heptatonic scale close to several Arabic scales.)
| |
|
| |
|
| ===Commas===
| | While the 7th harmonic is poorly tuned, the intervals 24edo has do serve as reasonable substitutes to 7-limit intervals melodically, though it equates [[7/6]] with [[8/7]] due to vanishing of [[49/48]], leading to [[semaphore]]. Nonetheless, scales of semaphore are quite interesting, especially the 9-note [[5L 4s]] MOS. A supermajor chord is available as [0 9 14], and a subminor chord as [0 5 14]; however, they are better described as ultramajor and inframinor, being interpreted much more accurately as [[10:13:15]] and [[26:30:39|1/(10:13:15)]] respectively, the corresponding temperament being [[barbados]], the 2.3.13/5 temperament tempering out 676/675. These chords are relatively simple and may serve as alternatives to the regular [[4:5:6]] and [[10:12:15|1/(4:5:6)]] triads as bases for harmony; see [[Extraclassical tonality]]. |
| 24 EDO tempers out the following commas. (Note: This assumes val < 24 38 56 67 83 89 |.)
| |
| ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
| |
| ||= 531441/524288 ||= | -19 12 > ||= 23.46 ||= Pythagorean Comma ||= ||= ||
| |
| ||= 648/625 ||= | 3 4 -4 > ||= 62.57 ||= Major Diesis ||= Diminished Comma ||= ||
| |
| ||= 128/125 ||= | 7 0 -3 > ||= 41.06 ||= Diesis ||= Augmented Comma ||= ||
| |
| ||= 81/80 ||= | -4 4 -1 > ||= 21.51 ||= Syntonic Comma ||= Didymos Comma ||= Meantone Comma ||
| |
| ||= 2048/2025 ||= | 11 -4 -2 > ||= 19.55 ||= Diaschisma ||= ||= ||
| |
| ||= 5201701/5149091 ||= | 26 -12 -3 > ||= 17.60 ||= Misty Comma ||= ||= ||
| |
| ||= 32805/32768 ||= | -15 8 1 > ||= 1.95 ||= Schisma ||= ||= ||
| |
| ||= 1465155/1465142 ||= | 161 -84 -12 > ||= 0.02 ||= Atom ||= ||= ||
| |
| ||= 49/48 ||= | -4 -1 0 2 > ||= 35.70 ||= Slendro Diesis ||= ||= ||
| |
| ||= 245/243 ||= | 0 -5 1 2 > ||= 14.19 ||= Sensamagic ||= ||= ||
| |
| ||= 19683/19600 ||= | -4 9 -2 -2 > ||= 7.32 ||= Cataharry ||= ||= ||
| |
| ||= 6144/6125 ||= | 11 1 -3 -2 > ||= 5.36 ||= Porwell ||= ||= ||
| |
| ||= 121/120 ||= | -3 -1 -1 0 2 > ||= 14.37 ||= Biyatisma ||= ||= ||
| |
| ||= 176/175 ||= | 4 0 -2 -1 1 > ||= 9.86 ||= Valinorsma ||= ||= ||
| |
| ||= 896/891 ||= | 7 -4 0 1 -1 > ||= 9.69 ||= Pentacircle ||= ||= ||
| |
| ||= 243/242 ||= | -1 5 0 0 -2 > ||= 7.14 ||= Rastma ||= ||= ||
| |
| ||= 385/384 ||= | -7 -1 1 1 1 > ||= 4.50 ||= Keenanisma ||= ||= ||
| |
| ||= 9801/9800 ||= | -3 4 -2 -2 2 > ||= 0.18 ||= Kalisma ||= Gauss' Comma ||= ||
| |
| ||= 91/90 ||= | -1 -2 -1 1 0 1 > ||= 19.13 ||= Superleap ||= ||= ||
| |
| ||= 676/675 ||= | 2 -3 -2 0 0 2 > ||= 2.56 ||= Parizeksma ||= ||= ||
| |
| =Intervals=
| |
|
| |
|
| 24 EDO breaks intervals into two sets of five cartegories. Infra - Minor - Neutral - Major - Ultra for seconds, thirds, sixths, and sevenths; and diminished - narrow - perfect - wide - augmented for fourths, fifths, unison, and octave. For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth.
| | A notable superset of 24edo is [[72edo]], which has good approximations up to the [[19-limit]], and especially the [[11-limit]]. The tunings supplied by [[72edo]] cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24 subgroup]] 2.3.125.35.11.325.17.19, making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11, 17, and 19. One will find that 24edo is consistent in the no-7s 19-odd-limit, though the 2.3.11.17.19 [[subgroup]] is where it is the most accurate. |
|
| |
|
| These are the intervals of 24 EDO that do not exist in 12 EDO: 2
| | === Prime harmonics === |
| [[24 EDO Interval names and Harmonies|See full article on 24 Edo intervals.]]
| | {{Harmonics in equal|24|prec=2}} |
| ||||~ The twelve new intervals in 24edo ||||||~ some nearby JI intervals ||
| |
| ||~ cents ||~ common names ||~ frequency ratio ||~ cents ||~ common name ||
| |
| ||= 50 ||= quartertone
| |
| infra second, wide unison ||= [[36_35|36/35]]
| |
| [[35_34|35/34]]
| |
| [[34_33|34/33]]
| |
| [[33_32|33/32]] ||= 48.770
| |
| 50.184
| |
| 51.682
| |
| 53.273 ||= large septimal quarter-tone (Archytas)
| |
| large 17-limit quartertone
| |
| small 17-limit quartertone
| |
| 33rd harmonic ||
| |
| ||= 150 ||= neutral second ||= [[12_11|12/11]] ||= 150.637 ||= large undecimal neutral second ||
| |
| ||= 250 ||= ultra second | |
| <span style="line-height: 1.5;">infra third</span> ||= [[144_125|144/125]]
| |
| [[15_13|15/13]]
| |
| [[52_45|52/45]] ||= 244.969
| |
| 247.741
| |
| 250.304 ||= diminished third (6/5 x 24/25)
| |
| ..
| |
| .. ||
| |
| ||= 350 ||= neutral third ||= [[11_9|11/9]]
| |
| [[27_22|27/22]]
| |
| [[16_13|16/13]] ||= 347.408
| |
| 354.547
| |
| 359.472 ||= undecimal neutral third
| |
| ..
| |
| tridecimal neutral third ||
| |
| ||= 450 ||= minor fourth, ultra third, narrow fourth ||= [[22_17|22/17]]
| |
| [[35_27|35/27]]
| |
| [[13_10|13/10]] ||= 446.363
| |
| 449.275
| |
| 454.214 ||= 17-limit supermajor third
| |
| ..
| |
| tridecimal subfourth ||
| |
| ||= 550 ||= wide fourth ||= [[11_8|11/8]] ||= 551.318 ||= undecimal superfourth, harmonic 11th ||
| |
| ||= 650 ||= narrow fifth ||= [[16_11|16/11]] ||= 648.682 ||= undecimal subfifth, 11th subharmonic ||
| |
| ||= 750 ||= wide fifth, infra sixth ||= [[20_13|20/13]]
| |
| [[54_35|54/35]]
| |
| [[17_11|17/11]] ||= 745.786
| |
| 750.725
| |
| 753.637 ||= tridecimal superfifth
| |
| ..
| |
| 17-limit subminor sixth ||
| |
| ||= 850 ||= neutral sixth ||= [[13_8|13/8]]
| |
| [[44_27|44/27]]
| |
| [[18_11|18/11]] ||= 840.528
| |
| 845.453
| |
| 852.592 ||= overtone sixth, 13th harmonic
| |
| ..
| |
| undecimal neutral sixth ||
| |
| ||= 950 ||= ultra sixth , infra seventh ||= [[45_26|45/26]]
| |
| [[26_15|26/15]]
| |
| [[125_72|125/72]] ||= 949.696
| |
| 952.259
| |
| 955.031 ||= ..
| |
| ..
| |
| .. ||
| |
| ||= 1050 ||= neutral seventh ||= [[11_6|11/6]] ||= 1049.363 ||= undecimal neutral seventh ||
| |
| ||= 1150 ||= ultra seventh, narrow octave ||= [[31_16|31/16]]
| |
| [[33_17|33/17]]
| |
| [[35_18|35/18]] ||= 1145.036
| |
| 1148.318
| |
| 1151.230 ||= 31st harmonic
| |
| ..
| |
| .. ||
| |
|
| |
|
| =Notation= | | === Subsets and supersets === |
| There have been disputes about disadvantages of various systems for notating quarter tones. Here are some of the few systems along with pros and cons.
| | 24edo is the 6th [[highly composite edo]]. Its nontrivial divisors are {{EDOs| 2, 3, 4, 6, 8, and 12 }}. Some of its supersets, most notably [[72edo]] and [[96edo]], have been used by a variety of composers. |
|
| |
|
| ==Mainstream Quartertone Notation== | | === Miscellaneous properties === |
| [[image:http://www.wfg.woodwind.org/n/s14_blue.gif]] or ^ = quarter-tone sharp or "Jump" or "up"
| | Its step, at 50{{c}}, is notable for being generally seen as one of the most dissonant intervals possible (in fact, typical harmonic entropy models show a peak around this point). Intervals less than 40{{c}} tend to be perceived as being closer to a unison, and thus, more consonant as a result, while intervals larger than approximately 60{{c}} are often perceived as having less "tension", and thus are also considered to be more consonant. |
| [[image:http://www.wfg.woodwind.org/n/s34_blue.gif]] or #^ or ^# = three-quarter-tone sharp or "Jump-Sharp" or "upsharp"
| |
| [[image:http://www.wfg.woodwind.org/n/f14_blue.gif]] or v = quarter-tone flat or "Drop" or "down"
| |
| [[image:http://www.wfg.woodwind.org/n/f34_blue.gif]] or bv or vb = three-quarter-tone flat or "Drop-Flat" or "downflat"
| |
|
| |
|
| Pros: Familiar, fairly easy to learn
| | == Intervals == |
| Cons: Clutters a score easily, can get confusing when sight read at faster paces
| | {| class="wikitable center-all left-3" |
| | |- |
| | ! Degree |
| | ! Cents |
| | ! Approximate ratios<ref group="note">{{sg|limit=2.3.5.11.13.17.19-[[subgroup]] (no-sevens 19-limit)}}</ref> |
| | ! colspan="3" | [[Ups and downs notation]] ([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and d2) |
| | ! colspan="3" | [[SKULO interval names|SKULO notation]] {{nowrap|(U or S {{=}} 1)}} |
| | ! [[24edo solfege|Solfege]] |
| | |- |
| | | 0 |
| | | 0 |
| | | [[1/1]] |
| | | P1 |
| | | unison |
| | | D |
| | | unison |
| | | P1 |
| | | D |
| | | Do |
| | |- |
| | | 1 |
| | | 50 |
| | | [[33/32]], [[34/33]] |
| | | ^P1, vm2 |
| | | up-unison, downminor 2nd |
| | | ^D, vEb |
| | | super unison, uber unison |
| | | S1, U1 |
| | | SD, UD |
| | | Da/Ru |
| | |- |
| | | 2 |
| | | 100 |
| | | [[16/15]], [[17/16]], [[18/17]], [[19/18]] |
| | | A1, m2 |
| | | aug unison, minor 2nd |
| | | D#, Eb |
| | | aug unison, minor 2nd |
| | | A1, m2 |
| | | D#, Eb |
| | | Ro |
| | |- |
| | | 3 |
| | | 150 |
| | | [[13/12]], [[12/11]], [[11/10]] |
| | | ~2 |
| | | mid 2nd |
| | | vE |
| | | neutral 2nd |
| | | N2 |
| | | UEb, uE |
| | | Ra |
| | |- |
| | | 4 |
| | | 200 |
| | | [[9/8]], [[10/9]] |
| | | M2 |
| | | major 2nd |
| | | E |
| | | major 2nd |
| | | M2 |
| | | E |
| | | Re |
| | |- |
| | | 5 |
| | | 250 |
| | | [[15/13]], [[22/19]] |
| | | ^M2, vm3 |
| | | upmajor 2nd, downminor 3rd |
| | | ^E, vF |
| | | supermajor 2nd, subminor 3rd |
| | | SM2, sm3 |
| | | SE, sF |
| | | Ri/Mu |
| | |- |
| | | 6 |
| | | 300 |
| | | [[6/5]], [[13/11]], [[19/16]] |
| | | m3 |
| | | minor 3rd |
| | | F |
| | | minor 3rd |
| | | m3 |
| | | F |
| | | Mo |
| | |- |
| | | 7 |
| | | 350 |
| | | [[11/9]], [[16/13]], [[27/22]], [[39/32]] |
| | | ~3 |
| | | mid 3rd |
| | | vF# |
| | | neutral 3rd |
| | | N3 |
| | | UF, uF# |
| | | Ma |
| | |- |
| | | 8 |
| | | 400 |
| | | [[5/4]], [[24/19]] |
| | | M3 |
| | | major 3rd |
| | | F# |
| | | major 3rd |
| | | M3 |
| | | F# |
| | | Me |
| | |- |
| | | 9 |
| | | 450 |
| | | [[13/10]], [[17/13]], [[22/17]] |
| | | ^M3, v4 |
| | | upmajor 3rd, down-4th |
| | | ^F#, vG |
| | | supermajor 3rd, sub 4th |
| | | SM3, s4 |
| | | SF#, sG |
| | | Mi/Fu |
| | |- |
| | | 10 |
| | | 500 |
| | | [[4/3]] |
| | | P4 |
| | | fourth |
| | | G |
| | | perfect 4th |
| | | P4 |
| | | G |
| | | Fo |
| | |- |
| | | 11 |
| | | 550 |
| | | [[11/8]], [[15/11]] |
| | | ^4, ~4 |
| | | up-4th, mid-4th |
| | | ^G |
| | | uber 4th/neutral 4th |
| | | U4/N4 |
| | | UG |
| | | Fa/Su |
| | |- |
| | | 12 |
| | | 600 |
| | | [[17/12]], [[24/17]], [[45/32]], [[64/45]] |
| | | A4, d5 |
| | | aug 4th, dim 5th |
| | | G#, Ab |
| | | aug 4th, dim 5th |
| | | A4, d5 |
| | | G#/Ab |
| | | Fe/So |
| | |- |
| | | 13 |
| | | 650 |
| | | [[16/11]], [[22/15]] |
| | | v5, ~5 |
| | | down-5th, mid-5th |
| | | vA |
| | | unter 5th/neutral 5th |
| | | u5/N5 |
| | | uA |
| | | Fi/Sa |
| | |- |
| | | 14 |
| | | 700 |
| | | [[3/2]] |
| | | P5 |
| | | fifth |
| | | A |
| | | perfect 5th |
| | | P5 |
| | | A |
| | | Se |
| | |- |
| | | 15 |
| | | 750 |
| | | [[17/11]], [[20/13]] |
| | | ^5, vm6 |
| | | up-fifth, downminor 6th |
| | | ^A, vBb |
| | | super 5th, subminor 6th |
| | | S5, sm6 |
| | | SA, sBb |
| | | Si/Lu |
| | |- |
| | | 16 |
| | | 800 |
| | | [[8/5]], [[19/12]] |
| | | m6 |
| | | minor 6th |
| | | Bb |
| | | minor 6th |
| | | m6 |
| | | Bb |
| | | Lo |
| | |- |
| | | 17 |
| | | 850 |
| | | [[13/8]], [[18/11]], [[44/27]], [[64/39]] |
| | | ~6 |
| | | mid 6th |
| | | vB |
| | | neutral 6th |
| | | N6 |
| | | UBb, uB |
| | | La |
| | |- |
| | | 18 |
| | | 900 |
| | | [[5/3]], [[22/13]], [[32/19]] |
| | | M6 |
| | | major 6th |
| | | B |
| | | major 6th |
| | | M6 |
| | | B |
| | | Le |
| | |- |
| | | 19 |
| | | 950 |
| | | [[19/11]], [[26/15]] |
| | | ^M6, vm7 |
| | | upmajor 6th, downminor 7th |
| | | ^B, vC |
| | | supermajor 6th, subminor 7th |
| | | SM6, sm7 |
| | | SB, sC |
| | | Li/Tu |
| | |- |
| | | 20 |
| | | 1000 |
| | | [[9/5]], [[16/9]] |
| | | m7 |
| | | minor 7th |
| | | C |
| | | minor 7th |
| | | m7 |
| | | C |
| | | To |
| | |- |
| | | 21 |
| | | 1050 |
| | | [[11/6]], [[20/11]] |
| | | ~7 |
| | | mid 7th |
| | | vC# |
| | | neutral 7th |
| | | N7 |
| | | UC, uC# |
| | | Ta |
| | |- |
| | | 22 |
| | | 1100 |
| | | [[15/8]], [[17/9]], [[32/17]] |
| | | M7 |
| | | major 7th |
| | | C# |
| | | major 7th |
| | | M7 |
| | | C# |
| | | Te |
| | |- |
| | | 23 |
| | | 1150 |
| | | [[33/17]], [[64/33]] |
| | | ^M7, vP8 |
| | | upmajor 7th, down-8ve |
| | | ^C#, vD |
| | | sub 8ve, unter 8ve |
| | | s8, u8 |
| | | C#, uD |
| | | Ti/Du |
| | |- |
| | | 24 |
| | | 1200 |
| | | [[2/1]] |
| | | P8 |
| | | perfect 8ve |
| | | D |
| | | perfect 8ve |
| | | P8 |
| | | D |
| | | Do |
| | |} |
| | <references group="note" /> |
|
| |
|
| ==Alternate Quartertone Accidentals==
| | In many other edos, 5/4 is downmajor and 11/9 is mid. To agree with this, the term mid is generally preferred over down or downmajor. |
| [[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] = quarter-tone sharp or Jump
| |
| ††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp or Jump-Sharp
| |
| [[image:http://www.dolmetsch.com/onequarterflat.gif]] = quarter-tone flat or Drop
| |
| [[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png]] = three quarter-tones flat or drop-flat
| |
| For example, the scale 0-5-10-15-20 is written as C-D[[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] (or E[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png]]) F G[[image:http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif]] (or A[[image:http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png]]) Bb.
| |
|
| |
|
| Pros: Very easy to distinguish accidentals from one another
| | == Notation == |
| Cons: Not practical, tends to clutter a score
| | === Ups and downs notation === |
| | Ups and downs are spoken as up, sharp, upsharp, etc. Note that up can be respelled as downsharp. |
| | {{Ups and downs sharpness}} |
|
| |
|
| ==<span style="line-height: 1.5;">And in Persian music</span>== | | === Stein–Zimmermann accidentals === |
| [[image:http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png width="12" height="25"]]Koron ([[http://en.wikipedia.org/wiki/Koron_%28music%29|en]] | [[http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86|fa]]) = quarter-tone flat or Jump
| | {{Sharpness-sharp2|24}} |
| [[image:http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png width="15" height="25"]]Sori ([[http://fa.wikipedia.org/wiki/%D8%B3%D8%B1%DB%8C_%28%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C%29|fa]]) = quarter-tone sharp or Drop
| |
|
| |
|
| Pros: Easy to read
| | {| class="wikitable center-1" |
| Cons: Hard to write on a computer, doesn't fit with standard notation well
| | |- |
| | | style="width: 40px;" | [[File:HeQu1.svg|21px|center]] |
| | | A "semisharp" or "half-sharp" accidental comprising one half of a regular musical sharp symbol. |
| | |- |
| | | style="width: 40px;" | [[File:HeQu3.svg|32px|center]] |
| | | A "sharp and a half" or "sesquisharp" accidental, comprising the above half-sharp symbol connected to the right side of a normal sharp. |
| | |- |
| | | style="width: 40px;" | [[File:HeQd1.svg|22px|center]] |
| | | A "semiflat" or "half-flat" accidental, comprising a flat symbol mirrored horizontally so that the lobe is facing left. |
| | |- |
| | | style="width: 40px;" | [[File:HeQd3.svg|40px|center]] |
| | | A "flat and a half" or "sesquiflat" accidental, comprising a half-flat symbol and a regular flat symbol placed back to back. |
| | |} |
|
| |
|
| ==Sagittal Notation==
| | '''Pros:''' familiar, intuitive, and fairly easy to learn. |
| [[Sagittal notation]] works extremely well for 24 Edo notation as well as other systems.
| |
| It's easy on the eyes, easy to recognize the various symbols and keeps a score looking tidy and neat.
| |
| A possibility for the best approach would be to not use traditional sharps and flats altogether and replace them
| |
| with Sagittal signs for sharp and flat.
| |
|
| |
|
| [[image:sagittal 24.PNG]]
| | '''Cons:''' can clutter a score easily (especially when used in microtonal key signatures), can get confusing when sight read at faster paces. |
|
| |
|
| =Interval Alterations= | | === Persian quartertone accidentals === |
| The special alterations of the intervals and chords of 12 equal can be notated like this:
| | {{Wikipedia|Koron (music)|Sori (music)}} |
|
| |
|
| Supermajor or "**Tendo**" is a major interval raised a quarter tone
| | {| class="wikitable" |
| Subminor or "**Arto**" is a minor interval lowered a quarter tone
| | |- |
| Neutral are intervals that exist between the major and minor version of an interval
| | | style="width: 40px;" | [[File:Koron_sign.svg|39px|center]] |
| The prefix **under** indicates a perfect interval lowered by one quarter tone
| | | '''Koron''' = quarter-tone flat |
| The prefix **over** indicates a perfect interval raised by a quarter tone
| | |- |
| | | style="width: 40px;" | [[File:Sori_sign.svg|39px|center]] |
| | | '''Sori''' = quarter-tone sharp |
| | |} |
|
| |
|
| The Latin words "tendo" (meaning "expand") and "arto" (meaning "contract") can be used to replace the words "supermajor" and "subminor" in order to shorten the names of the intervals.
| | '''Pros:''' easy to read. |
|
| |
|
| =Chord Structures=
| | '''Cons:''' hard to write on a computer, does not fit with standard notation well. |
| 24edo features a rich variety on not only new chords, but also alterations that can be used with regular 12 Edo chords. For example, an approximation of the ninth, eleventh, and thirteenth harmonic can be added to a major triad to create a sort of super-extended chord structure of a major chord: 4:5:6:9:11:13.
| |
|
| |
|
| As for entirely new chords, 24edo features many possibilities for chords. The most obvious is the neutral or mid triad 0-7-14 however there are other options such as
| | === Sagittal notation === |
| 0-9-14 (Ultra Triad or upmajor triad) and 0-5-14 (Infra Triad or downminor triad), the chord names being based on what kind of third is in the chord.
| | This notation uses the same sagittal sequence as edos [[17edo #Sagittal notation|17]], [[31edo #Sagittal notation|31]], and [[38edo #Sagittal notation|38]], is a subset of the notations for edos [[48edo #Sagittal notation|48]] and [[72edo #Sagittal notation|72]], and is a superset of the notations for edos [[12edo #Sagittal notation|12]], [[8edo #Sagittal notation|8]], and [[6edo #Sagittal notation|6]]. |
| These chords though tend to lack the forcefulness to sound like resolved, tonal sonorities but can be resolved of that issue by using tetrads in place of triads.
| |
| For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad. 0-14-21-35 [[William Lynch]] considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality. 24 edo also is very good at 15 limit and does 13 quite well allowing barbodos 10:13:15 and barbodos minor triad 26:30:39 to be used as an entirely new harmonic system.
| |
|
| |
|
| William Lynch considers these as some possible good tetrads:
| | ==== Evo flavor ==== |
| | <imagemap> |
| | File:24-EDO_Evo_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 447 0 607 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 130 106 [[33/32]] |
| | default [[File:24-EDO_Evo_Sagittal.svg]] |
| | </imagemap> |
| | |
| | ==== Revo flavor ==== |
| | <imagemap> |
| | File:24-EDO_Revo_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 463 0 623 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 130 106 [[33/32]] |
| | default [[File:24-EDO_Revo_Sagittal.svg]] |
| | </imagemap> |
| | |
| | ==== Evo-SZ flavor ==== |
| | <imagemap> |
| | File:24-EDO_Evo-SZ_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 407 0 567 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 130 106 [[33/32]] |
| | default [[File:24-EDO_Evo-SZ_Sagittal.svg]] |
| | </imagemap> |
| | |
| | Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is identical to [[#Stein.E2.80.93Zimmermann_accidentals|Stein–Zimmerman notation]]. |
| | |
| | ==== Pros and cons ==== |
| | Revo [[Sagittal notation]] works extremely well for 24edo notation as well as other systems. It is easy on the eyes, easy to recognize the various symbols and keeps a score looking tidy and neat. A possibility for the best approach would be to not use traditional sharps and flats altogether and replace them with Sagittal signs for sharp and flat. |
|
| |
|
| [[image:Three chords.PNG]] | | [[File:sagittal_24.PNG|alt=sagittal 24.PNG|sagittal 24.PNG]] |
|
| |
|
| ||~ Chord name ||~ Degrees of 24edo ||~ Chord spelling ||~ Audio example ||
| | '''Pros:''' easy to read, and less likely to clutter the score. |
| || neutral || 0 7 14 21 || 1 v3 5 v7 || [[media type="file" key="Neutral Tetrad on C.mp3" width="200" height="30"]] ||
| |
| || arto || 0 5 14 20 || 1 bv3 5 b7 || [[media type="file" key="arto tetrad on C.mp3" width="200" height="30"]] ||
| |
| || tendo || 0 9 14 19 || 1 ^3 5 bv7 || ... ||
| |
|
| |
|
| Due to convenience, the names Arto and tendo have been changed to Ultra and Infra.
| | '''Cons:''' not as familiar as traditional notation, and thus not immediately accessible to many traditional musicians who are just starting out with microtonality. |
|
| |
|
| =Naming Chords in 24edo=
| | We also have, from the appendix to [[The Sagittal Songbook]] by [[Jacob Barton|Jacob A. Barton]], a diagram of how to notate 24edo in the Revo flavor of Sagittal: |
| Naming chords in 24edo can be achieved by adding a few things to the already [[#|existing]] set of terms that are used to name 12edo chords.
| |
| They are:
| |
| Super + perfect interval such as "perfect fifth" means to raise it by a quarter tone
| |
| Sub + perfect interval means to lower a quarter tone
| |
| Sharp is to raise by one half tone
| |
| Flat is to raise by a half tone
| |
| Neutral, arto and tendo refer to triads or tetrads
| |
| Neutral, arto, or tendo + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively
| |
|
| |
|
| Examples:
| | [[File:24edo Sagittal.png|800px]] |
| Neutral Super Eleventh or neut^11 = C neutral 7th chord with a super 11th thrown on top
| |
| Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11
| |
|
| |
|
| Alternatively, [[ups and downs notation]] can be used. Here are the blue, green, jade, yellow and red triads:
| | == Interval and chord naming == |
| ||~ color of the 3rd ||~ JI chord ||~ notes as edosteps ||~ notes of C chord ||~ written name ||~ spoken name ||
| | ==== Combining ups and downs with color notation ==== |
| ||= blue ||= 6:7:9 ||= 0-5-14 ||= C Ebv G ||= C.vm ||= C downminor ||
| | Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors: |
| ||= green ||= 10:12:15 ||= 0-6-14 ||= C Eb G ||= Cm ||= C minor ||
| |
| ||= jade ||= 18:22:27 ||= 0-7-14 ||= C Ev G ||= C~ ||= C mid ||
| |
| ||= yellow ||= 4:5:6 ||= 0-8-14 ||= C E G ||= C ||= C major or C ||
| |
| ||= red ||= 14:18:27 ||= 0-9-14 ||= C E^ G ||= C.^ ||= C upmajor or C dot up ||
| |
| For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]].
| |
|
| |
|
| =Rank two temperaments= | | {| class="wikitable center-all" |
| [[List of 24et rank two temperaments by badness]] | | |- |
| [[List of edo-distinct 24et rank two temperaments]]
| | ! Quality |
| | ! [[Color name]] |
| | ! Monzo format |
| | ! Examples |
| | |- |
| | | downminor |
| | | zo |
| | | {{nowrap|(a, b, 0, 1)}} |
| | | 7/6, 7/4 |
| | |- |
| | | rowspan="2" | minor |
| | | fourthward wa |
| | | {{nowrap|(a, b)}}; {{nowrap|b < −1}} |
| | | 32/27, 16/9 |
| | |- |
| | | gu |
| | | {{nowrap|(a, b, −1)}} |
| | | 6/5, 9/5 |
| | |- |
| | | rowspan="2" | mid |
| | | ilo |
| | | {{nowrap|(a, b, 0, 0, 1)}} |
| | | 11/9, 11/6 |
| | |- |
| | | lu |
| | | {{nowrap|(a, b, 0, 0, −1)}} |
| | | 12/11, 18/11 |
| | |- |
| | | rowspan="2" | major |
| | | yo |
| | | {{nowrap|(a, b, 1)}} |
| | | 5/4, 5/3 |
| | |- |
| | | fifthward wa |
| | | {{nowrap|(a, b)}}; {{nowrap|b > 1}} |
| | | 9/8, 27/16 |
| | |- |
| | | upmajor |
| | | ru |
| | | {{nowrap|(a, b, 0, −1)}} |
| | | 9/7, 12/7 |
| | |} |
|
| |
|
| ||~ Periods per octave ||~ Generator ||~ Name ||
| | Ups and downs notation can be used to name chords. See [[24edo Chord Names]] and [[Ups and downs notation #Chords and chord progressions]]. |
| || 1 || 1\24 || ||
| |
| || 1 || 5\24 || [[Semaphore and Godzilla|Semaphore/godzilla]] / [[Chromatic pairs#Bridgetown|Bridgetown]] ||
| |
| || 1 || 7\24 || [[Mohajira]] (or [[maqamic]] with 24d val) ||
| |
| || 1 || 11\24 || ||
| |
| || 2 || 1\24 || [[Shrutar]] ||
| |
| || 2 || 5\24 || Similar to [[decimal]] ||
| |
| || 3 || 1\24 || [[Semiaug]] ||
| |
| || 3 || 3\24 || [[Triforce]] ||
| |
| || 4 || 1\24 || ||
| |
| || 6 || 1\24 || ||
| |
| || 8 || 1\24 || ||
| |
| || 12 || 1\24 || [[Catler]] ||
| |
|
| |
|
| =Scales / Modes= | | === William Lynch's interval and chord names === |
| | 24edo breaks intervals into two sets of five categories. {{dash|Infra, Minor, Neutral, Major, Ultra|space|med}} for seconds, thirds, sixths, and sevenths; and {{dash|diminished, narrow, perfect, wide, augmented|space|med}} for fourths, fifths, unison, and octave. |
|
| |
|
| |||| ====Pentatonic:==== ||
| | For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth. |
| || {{**2 8 3 6 5**}} || Anchihoye: Ethiopia ||
| |
| || {{**5 5 4 5 5**}} || Quasi-equal Pentatonic - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] ||
| |
| || {{**5 5 5 5 4**}} || Hába's Pentatonic - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] ||
| |
|
| |
|
| |||| ====Hexatonic:==== ||
| | These are the intervals of 24edo that do not exist in 12edo: |
| || {{**1 1 8 4 2 8**}} || Spondeiakos ||
| |
|
| |
|
| |||| ====Heptatonic:==== || | | {| class="wikitable center-all right-6" |
| || {{**1 1 8 1 1 8 4**}} || Enharmonic Mixolydian ||
| | |- |
| || {{**1 8 1 1 8 4 1**}} || Enharmonic Lydian ||
| | ! [[Cent]]s |
| || {{**8 1 1 8 4 1 1**}} || Enharmonic Phrygian ||
| | ! Names |
| || {{**1 1 8 4 1 1 8**}} || Enharmonic Dorian ||
| | |- |
| || {{**1 8 4 1 1 8 1**}} || Enharmonic Hypolydian ||
| | | 50 |
| || {{**8 4 1 1 8 1 1**}} || Enharmonic Hypophrygian ||
| | | Quarter tone, infra second, wide unison |
| || {{**4 1 1 8 1 1 8**}} || Enharmonic Hypodorian ||
| | |- |
| || {{**2 3 5 2 3 5 4**}} || Soft Diatonic Mixolydian ||
| | | 150 |
| || {{**3 5 2 3 5 4 2**}} || Soft Diatonic Lydian ||
| | | Neutral second |
| || {{**5 2 3 5 4 2 3**}} || Soft Diatonic Phrygian ||
| | |- |
| || {{**2 3 5 4 2 3 5**}} || Soft Diatonic Dorian ||
| | | 250 |
| || {{**3 5 4 2 3 5 2**}} || Soft Diatonic Hypolydian ||
| | | Ultra second, infra third |
| || {{**5 4 2 3 5 2 3**}} || Soft Diatonic Hypophrygian ||
| | |- |
| || {{**4 2 3 5 2 3 5**}} || Soft Diatonic Hypodorian ||
| | | 350 |
| || {{**3 3 4 3 3 4 4**}} || Maqam Ouchairan-Hussaini, Bayatan, Neutral Diatonic Mixolydian - [[MODMOS Scales|MODMOS]] of type [[3L 4s|3L 4s (mosh)]] ||
| | | Neutral third |
| || {{**3 4 3 3 4 4 3**}} || Dastgah-e Sehgah, Neutral Diatonic Lydian - [[xenharmonic/MODMOS Scales|MODMOS]] of type [[3L 4s|3L 4s (mosh)]] || | | |- |
| || {{**4 3 3 4 4 3 3**}} || Arabic Diatonic, Maqam Rast, Quasi-equal Heptatonic, Neutral Diatonic Phrygian - [[xenharmonic/MODMOS Scales|MODMOS]] of type [[3L 4s|3L 4s (mosh)]] ||
| | | 450 |
| || {{**3 3 4 4 3 3 4**}} || Maqam Hussaini, Ushaq, Neutral Diatonic Dorian - [[xenharmonic/MODMOS Scales|MODMOS]] of type [[3L 4s|3L 4s (mosh)]] ||
| | | Minor fourth, ultra third, narrow fourth |
| || {{**3 4 4 3 3 4 3**}} || Maqam Sikah (Segah), Neutral Diatonic Hypolydian - [[xenharmonic/MODMOS Scales|MODMOS]] of type [[3L 4s|3L 4s (mosh)]] || | | |- |
| || {{**4 4 3 3 4 3 3**}} || Neutral Diatonic Hypophrygian - [[xenharmonic/MODMOS Scales|MODMOS]] of type [[3L 4s|3L 4s (mosh)]] || | | | 550 |
| || {{**4 3 3 4 3 3 4**}} || Miha'il Musaqa's mode: Egypt, Neutral Diatonic Hypodorian, Dastgah-e Sehgah, Maqam Nairuz - [[xenharmonic/MODMOS Scales|MODMOS]] of type [[3L 4s|3L 4s (mosh)]] || | | | Wide fourth |
| || {{**1 5 4 1 5 4 4**}} || Diatonic + Enharmonic Diesis Mixolydian || | | |- |
| || {{**5 4 1 5 4 4 1**}} || Diatonic + Enharmonic Diesis Lydian || | | | 650 |
| || {{**4 1 5 4 4 1 5**}} || Diatonic + Enharmonic Diesis Phrygian || | | | Narrow fifth |
| || {{**1 5 4 4 1 5 4**}} || Diatonic + Enharmonic Diesis Dorian || | | |- |
| || {{**5 4 4 1 5 4 1**}} || Diatonic + Enharmonic Diesis Hypolydian || | | | 750 |
| || {{**4 4 1 5 4 1 5**}} || Diatonic + Enharmonic Diesis Hypophrygian || | | | Wide fifth, infra sixth |
| || {{**4 1 5 4 1 5 4**}} || Diatonic + Enharmonic Diesis Hypodorian || | | |- |
| || {{**1 3 6 1 3 6 4**}} || Chromatic/Enharmonic Mixolydian ||
| | | 850 |
| || {{**3 6 1 3 6 4 1**}} || Chromatic/Enharmonic Lydian ||
| | | Neutral sixth |
| || {{**6 1 3 6 4 1 3**}} || Chromatic/Enharmonic Phrygian ||
| | |- |
| || {{**1 3 6 4 1 3 6**}} || Chromatic/Enharmonic Dorian ||
| | | 950 |
| || {{**3 6 4 1 3 6 1**}} || Chromatic/Enharmonic Hypolydian ||
| | | Ultra sixth, infra seventh |
| || {{**6 4 1 3 6 1 3**}} || Chromatic/Enharmonic Hypophrygian || | | |- |
| || {{**4 1 3 6 1 3 6**}} || Chromatic/Enharmonic Hypodorian ||
| | | 1050 |
| || {{**3 4 3 3 4 3 4**}} || Neutral Mixolydian - [[MOSScales|MOS]] of type [[3L 4s|3L 4s (mosh)]] ||
| | | Neutral seventh |
| || {{**4 3 3 4 3 4 3**}} || Neutral Lydian - [[MOSScales|MOS]] of type [[3L 4s|3L 4s (mosh)]] || | | |- |
| || {{**3 3 4 3 4 3 4**}} || Neutral Phrygian - [[MOSScales|MOS]] of type [[3L 4s|3L 4s (mosh)]] || | | | 1150 |
| || {{**3 4 3 4 3 4 3**}} || Neutral Dorian, Misaelides 2nd Byzantine mode, Maqam Sikah Baladi - [[MOSScales|MOS]] of type [[3L 4s|3L 4s (mosh)]] || | | | Ultra seventh, narrow octave |
| || {{**4 3 4 3 4 3 3**}} || Neutral Hypolydian - [[MOSScales|MOS]] of type [[3L 4s|3L 4s (mosh)]] || | | |} |
| || {{**3 4 3 4 3 3 4**}} || Neutral Hypophrygian - [[MOSScales|MOS]] of type [[3L 4s|3L 4s (mosh)]] || | |
| || {{**4 3 4 3 3 4 3**}} || Neutral Hypodorian - [[MOSScales|MOS]] of type [[3L 4s|3L 4s (mosh)]] || | |
| || {{**3 5 2 4 3 5 2**}} || Athanasopoulos' Byzantine Liturgical Chromatic, Dastgah-e Chahargah || | |
| || {{**4 2 4 4 3 3 4**}} || Dastgah-e Nava, Maqam Ushaq Masri || | |
| || {{**2 7 1 4 2 7 1**}} || Second plagal Byzantine Liturgical mode || | |
| || {{**3 3 4 4 2 4 4**}} || Maqam 'Ushshaq Turki, Urfa, Isfahan, Dastgah-e Shur || | |
| || {{**3 3 4 4 4 2 4**}} || Maqam Nahfat || | |
| || {{**3 3 2 6 2 4 4**}} || Maqam Saba || | |
| || {{**3 3 2 6 2 6 2**}} || Maqam Sabr Jadid || | |
| || {{**4 3 3 4 2 6 2**}} || Maqam Suznak (Soznak) || | |
| || {{**4 3 3 4 4 4 2**}} || Maqam Mahur || | |
| || {{**3 3 4 2 6 2 4**}} || Maqam Qarjighar, Bayati Shuri || | |
| || {{**3 4 2 6 2 4 3**}} || Maqam Hizam (Huzam, El Houzam), Rahat al Arouah ||
| |
| || {{**2 4 4 4 3 3 4**}} || Maqam Nawa ||
| |
| || {{**2 5 3 4 2 5 3**}} || Maqam Higaz-kar || | |
| || {{**3 4 4 2 4 4 3**}} || Maqam Su'ar, Naghmeh Abuata, Naghmeh Afshari || | |
| || {{**4 4 2 4 4 3 3**}} || Maqam Jahargah (Jiharkah), Naghmeh Bayat-e Tork, Naghmeh Dashti || | |
| || {{**3 5 2 4 2 4 4**}} || Dastgah-e Homayun || | |
| || {{**4 2 4 4 3 5 2**}} || Naghmeh Esfahan || | |
| || {{**3 6 1 5 2 6 1**}} || Maqam 'Awg 'ara (Aug-ara) || | |
| || {{**4 1 5 4 2 6 2**}} || Maqam Buselik || | |
| || {{**4 2 6 2 2 5 3**}} || Maqam Neuter || | |
| || {{**4 3 3 4 4 2 4**}} || Dance scale of Yi people: China || | |
| || {{**4 4 2 3 1 4 6**}} || Daniel-mode of Spanish-Arab Jews ||
| |
|
| |
|
| |||| ====Octatonic:==== ||
| | ==== Interval alterations ==== |
| || {{**3 3 3 3 3 3 3 3**}} || 8-equal, Wyschnegradsky's octatonic ||
| | The special alterations of the intervals and chords of 12edo can be notated like this: |
| || {{**3 3 4 4 2 1 3 4**}} || Maqam Bayati ||
| |
| || {{**3 3 2 6 2 4 2 2**}} || Maqam Saba ||
| |
| || {{**4 3 1 2 4 4 2 4**}} || Maqam Suzidil 'ara ||
| |
| || {{**3 3 2 2 4 3 3 4**}} || Maqam Mansuri ||
| |
| || {{**4 3 3 4 4 2 1 3**}} || Maqam Rast, Dilkashidah, Dilnishin ||
| |
| || {{**3 4 2 6 2 4 2 1**}} || Maqam Rahat al-Arwah ||
| |
| || {{**3 4 3 3 4 4 2 1**}} || Maqam Iraq ||
| |
| || {{**2 6 2 4 2 1 3 4**}} || Maqam Hijaz ||
| |
| || {{**3 4 4 2 1 3 4 3**}} || Maqam Musta'ar ||
| |
| || {{**3 4 4 4 2 4 2 1**}} || Maqam Farahnak ||
| |
| || {{**3 4 3 3 2 6 2 1**}} || Maqam Bastanikar, Tarz Nuin ||
| |
| || {{**4 2 6 2 4 2 1 3**}} || Maqam Farah Faza, Maqam Nakriz ||
| |
| || {{**3 1 2 4 4 2 4 4**}} || Maqam Jabburi ||
| |
| || {{**1 4 4 2 4 4 4 1**}} || Giancarlo Dalmonte's new quarter-tone scale (see [[http://www.ottavanota.info/|http://www.ottavanota.info]]) ||
| |
|
| |
|
| |||| ====Enneatonic:==== ||
| | * Supermajor or "'''Tendo'''" is a major interval raised a quarter tone |
| || {{**1 2 3 4 4 1 2 3 4**}} || Progressive Enneatonic ||
| | * Subminor or "'''Arto'''" is a minor interval lowered a quarter tone |
| || {{**4 1 4 1 4 1 4 1 4**}} || de Vries 9-tone - [[MOSScales|MOS]] of type [[5L 4s|5L 4s (unfair bug)]] ||
| | * Neutral are intervals that exist between the major and minor version of an interval |
| || {{**3 4 2 2 2 2 2 4 3**}} || Maqam Huzam ||
| | * The prefix '''under''' indicates a perfect interval lowered by one quarter tone |
| || {{**4 4 2 1 3 2 2 4 2**}} || Maqam Shawq Afza ||
| | * The prefix '''over''' indicates a perfect interval raised by a quarter tone |
| | * The Latin words "tendo" (meaning "expand") and "arto" (meaning "contract") can be used to replace the words "supermajor" and "subminor" in order to shorten the names of the intervals. |
|
| |
|
| |||| ====Decatonic:==== ||
| | ==== Chord names ==== |
| || {{**3 1 3 3 3 1 3 3 1 3**}} || Breed Decatonic - [[MOSScales|MOS]] of type [[7L 3s|7L 3s (unfair mosh)]] ||
| | Naming chords in 24edo can be achieved by adding a few things to the already [[#|existing]] set of terms that are used to name 12edo chords. |
| || {{**2 3 2 2 3 2 3 2 2 3**}} || Oljare Decatonic - [[MOSScales|MOS]] of type [[4L 6s|4L 6s (fair bicycle)]] ||
| |
| || {{**2 1 3 2 2 4 2 4 2 2**}} || Maqam Shawq Tarab ||
| |
| || {{**4 2 1 3 2 2 4 2 1 3**}} || Maqam Basandida ||
| |
| || {{**4 3 1 2 1 3 4 2 1 3**}} || Maqam Yakah ||
| |
|
| |
|
| |||| ====Hendecatonic:==== ||
| | They are: |
| || {{**4 2 1 3 2 2 2 2 3 1 2**}} || Maqam Hayyan ||
| |
|
| |
|
| |||| ====Tridecatonic:==== ||
| | * Super + perfect interval such as "perfect fifth" means to raise it by a quarter tone |
| || {{**1 2 2 2 2 2 2 1 2 2 2 2 2**}} || de Vries 13-tone - [[MOSScales|MOS]] of type [[11L 2s]] ||
| | * Sub + perfect interval means to lower a quarter tone |
| || {{**2 2 2 2 2 1 2 2 2 2 2 2 1**}} || Agmon Diatonic DS5, Ivan Wyschnegradsky's diatonicized chromatic scale - [[MOSScales|MOS]] of type [[11L 2s]] ||
| | * Sharp is to raise by one half tone |
| | * Flat is to raise by a half tone |
| | * Neutral, arto and tendo refer to triads or tetrads |
| | * Neutral, arto, or tendo + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively |
|
| |
|
| |||| ====Tetradecatonic:==== ||
| | Examples: |
| || **<span style="font-family: monospace;">2 2 1 2 2 2 1 2 2 1 2 2 2 1</span>** || Young Half-Octave Diatonic - [[MOSScales|MOS]] of type [[10L 4s]] ||
| |
|
| |
|
| =Instruments[[#instruments]]= | | * Neutral Super Eleventh or neut^11 = C neutral 7th chord with a super 11th thrown on top |
| The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This [[Microtonal Keyboards#twelvenoteoctavescales|"12 note octave scales"]] approach is used in a wide part of the existing literature - see below.
| | * Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11 |
| [[image:http://www.swordguitars.com/Sword_quartertone_stratsm.jpg width="406" height="195"]]24-tone "1/4-tone" Guitar by Ron Sword / Sword guitars
| |
|
| |
|
| Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called [[Iceface Tuning|Iceface tuning]].
| | === Further discussion of interval and chord naming === |
| | {{main|{{PAGENAME}}/Interval names and harmonies }} |
|
| |
|
| =Compositions=
| | * [[24edo Chord Names]] |
| ==Music==
| | * [[Ups and downs notation#Chords and Chord Progressions]]. |
| <span class="ymp-btn-page-play ymp-media-eb56a917c62000140296c2e1a6d89911">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex3.mp3|Microhex3]]</span> <span class="ymp-btn-page-play ymp-media-750620955011dabb8bc98c7c8830cbb8">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex4.mp3|Microhex4]]</span> and <span class="ymp-btn-page-play ymp-media-4aeb7c299c23983ba8081a591562e704">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex5.mp3|Microhex5]]</span> by [[http://www.96edo.com/About_me.html|Shaahin Mohajeri]]
| |
| <span class="ymp-btn-page-play ymp-media-30832be5610668b4b42451c8ce82dc80">[[http://micro.soonlabel.com/24et/quarterpicnic.mp3|Quarterpicnic]]</span> by [[Chris Vaisvil]]
| |
| [[http://micro.soonlabel.com/gene_ward_smith/Others/BeDell/Quarter%20Tone%20Prelude%20for%20two%20Harps.mp3|Quarter Tone Prelude For Two Harps]] by [[http://soundcloud.com/cerbeus-1/quarter-tone-prelude-for-two|Nathan BeDell]]
| |
| <span class="ymp-btn-page-play ymp-media-2738730931ba168a7364a84b5417488d">[[http://micro.soonlabel.com/24et/daily20111021-fretless-1.mp3|Fretless Chrome 1]]</span> and <span class="ymp-btn-page-play ymp-media-d35cb71128e927701930058ebd16b778">[[http://micro.soonlabel.com/24et/daily20111021-fretless-2.mp3|Fretless Chrome 2]]</span> by [[@http://chrisvaisvil.com/?p=1477|Chris Vaisvil]]
| |
| [[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lament.mp3|Lament]] by [[http://soundcloud.com/jdfreivald/lament|Jake Freivald]]. In the [[freivaldneutral24]] scale.
| |
| [[https://soundcloud.com/jdfreivald/mo-happy-happy|Mo - Happy - Happy]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3|play]] by Jake Freivald in Neuter[7] (2.3.11 mohajira), 24et tuning
| |
| [[http://www.youtube.com/watch?v=q1Lp8AtKK9o|Autumn Winds]], [[http://www.youtube.com/watch?v=Igxe3DwbFJ4&feature=c4-overview&list=UUvq5bg-LvOS6adpB5efPTyQ|Easter Time at Nine]], [[http://www.youtube.com/watch?v=z_3uhA9Cq08&list=UUvq5bg-LvOS6adpB5efPTyQ|Waters of Persia]] by William Lynch in mohajira, 24et tuning.
| |
| [[https://soundcloud.com/mason-l-green/serena|Serena]], by Mason Green (intro and coda in 24edo, the rest is in 12edo)
| |
| [[https://www.youtube.com/watch?v=yzvXEMYgHCY|Autumn Girl]], by Mason Green
| |
|
| |
|
| ==About== | | == Approximation to JI == |
| "Prométhée enchaîné" by [[http://en.wikipedia.org/wiki/Fromental_Hal%C3%A9vy|Fromental Halévy]] (considered the first mainstream western orchestral composition to use quarter tones.)
| | [[File:24ed2.svg|250px|thumb|right|none|alt=alt : Your browser has no SVG support.|Selected 19-limit intervals approximated in 24edo]] |
| "3 Hommages" by [[http://en.wikipedia.org/wiki/Georg_Friedrich_Haas|Georg Friedrich Haas]]
| |
| [[http://en.wikipedia.org/wiki/List_of_quarter_tone_pieces|List of quartertone pieces on Wikipedia]]
| |
|
| |
|
| =Practical Theory / Books= | | === Interval mappings === |
| | {{Q-odd-limit intervals|24}} |
|
| |
|
| [[image:http://ronsword.com/images/24_tet_Coversm.jpg width="179" height="236"]]**"Icosakaiteraphonic Scales for Guitar"** - A Book for Twenty-Four Equal Divisions of the Octave on guitar, or 'Quarter-tones'. Features a practical approach to understanding the tuning, and over 550 Scale Examples on Nine-String finger board charts, which allows for both symmetrical tuning visualization and standard guitar tuning- helpful for bassists and large range guitarists as well. Includes MOS, DE, and *all* the Scales / Modes from the list above. | | == 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]] (%) |
| | |- |
| | | 2.3.5.11 |
| | | 81/80, 121/120, 128/125 |
| | | {{mapping| 24 38 56 83 }} |
| | | −1.08 |
| | | 2.82 |
| | | 5.63 |
| | |- |
| | | 2.3.5.11.13 |
| | | 66/65, 81/80, 128/125, 144/143 |
| | | {{mapping| 24 38 56 83 89 }} |
| | | −1.37 |
| | | 2.59 |
| | | 5.19 |
| | |- |
| | | 2.3.5.11.13.17 |
| | | 51/50, 66/65, 81/80, 128/125, 144/143 |
| | | {{mapping| 24 38 56 83 89 98 }} |
| | | −0.94 |
| | | 2.55 |
| | | 5.11 |
| | |- |
| | | 2.3.5.11.13.17.19 |
| | | 51/50, 66/65, 76/75, 81/80, 128/125, 144/143 |
| | | {{mapping| 24 38 56 83 89 98 102 }} |
| | | −0.89 |
| | | 2.37 |
| | | 4.74 |
| | |} |
|
| |
|
| =External links= | | === Uniform maps === |
| [[http://tonalsoft.com/enc/q/quarter-tone.aspx|quarter-tone / 24-edo - Encyclopedia of Microtonal Music Theory]] [[http://www.webcitation.org/5xeFMH6cd|Permalink]]
| | {{Uniform map|edo=24}} |
| [[http://www.96edo.com/24_EDO.html|About 24-EDO]] by Shaahin Mohajeri [[http://www.webcitation.org/5xeFBNdQW|Permalink]]
| |
| [[https://docs.google.com/file/d/0Bzrl-iLY6DeEVkl1VjBGdEJlOTg/edit|Notation and Chord Names for 24-EDO]] by William Lynch
| |
| [[http://sonic-arts.org/darreg/contents.htm|The place of QUARTERTONES in Today's Xenharmonics]] by [[Ivor Darreg]] [[http://sonic-arts.org/darreg/dar8.htm|Permalink]]</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>24edo</title></head><body><!-- ws:start:WikiTextTocRule:60:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><div style="margin-left: 1em;"><a href="#Basics">Basics</a></div>
| |
| <!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><div style="margin-left: 1em;"><a href="#x24edo as a temperament">24edo as a temperament</a></div>
| |
| <!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><div style="margin-left: 3em;"><a href="#x24edo as a temperament--Commas">Commas</a></div>
| |
| <!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div>
| |
| <!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><div style="margin-left: 1em;"><a href="#Notation">Notation</a></div>
| |
| <!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><div style="margin-left: 2em;"><a href="#Notation-Mainstream Quartertone Notation">Mainstream Quartertone Notation</a></div>
| |
| <!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><div style="margin-left: 2em;"><a href="#Notation-Alternate Quartertone Accidentals">Alternate Quartertone Accidentals</a></div>
| |
| <!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><div style="margin-left: 2em;"><a href="#Notation-And in Persian music">And in Persian music</a></div>
| |
| <!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><div style="margin-left: 2em;"><a href="#Notation-Sagittal Notation">Sagittal Notation</a></div>
| |
| <!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><div style="margin-left: 1em;"><a href="#Interval Alterations">Interval Alterations</a></div>
| |
| <!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><div style="margin-left: 1em;"><a href="#Chord Structures">Chord Structures</a></div>
| |
| <!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><div style="margin-left: 1em;"><a href="#Naming Chords in 24edo">Naming Chords in 24edo</a></div>
| |
| <!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><div style="margin-left: 1em;"><a href="#Rank two temperaments">Rank two temperaments</a></div>
| |
| <!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><div style="margin-left: 1em;"><a href="#Scales / Modes">Scales / Modes</a></div>
| |
| <!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Pentatonic:">Pentatonic:</a></div>
| |
| <!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Hexatonic:">Hexatonic:</a></div>
| |
| <!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Heptatonic:">Heptatonic:</a></div>
| |
| <!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Octatonic:">Octatonic:</a></div>
| |
| <!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Enneatonic:">Enneatonic:</a></div>
| |
| <!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Decatonic:">Decatonic:</a></div>
| |
| <!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Hendecatonic:">Hendecatonic:</a></div>
| |
| <!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Tridecatonic:">Tridecatonic:</a></div>
| |
| <!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><div style="margin-left: 4em;"><a href="#Scales / Modes---Tetradecatonic:">Tetradecatonic:</a></div>
| |
| <!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><div style="margin-left: 1em;"><a href="#Instruments">Instruments</a></div>
| |
| <!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><div style="margin-left: 1em;"><a href="#Compositions">Compositions</a></div>
| |
| <!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><div style="margin-left: 2em;"><a href="#Compositions-Music">Music</a></div>
| |
| <!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><div style="margin-left: 2em;"><a href="#Compositions-About">About</a></div>
| |
| <!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><div style="margin-left: 1em;"><a href="#Practical Theory / Books">Practical Theory / Books</a></div>
| |
| <!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><div style="margin-left: 1em;"><a href="#External links">External links</a></div>
| |
| <!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --></div>
| |
| <!-- ws:end:WikiTextTocRule:90 --><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/24edo">Deutsch</a> - <a class="wiki_link" href="/24%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br />
| |
| </span><br />
| |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="Basics"></a><!-- ws:end:WikiTextHeadingRule:2 -->Basics</h1>
| |
| The 24edo system divides the octave into 24 equal parts of exactly 50 cents each. It is also known as <strong>quarter-tone tuning</strong>, since it evenly divides the 12-tone equal tempered semitone in two. Quarter-tones are the most commonly used microtonal tuning due to its retention of the familiar 12 tones and since it is the smallest microtonal equal temperament that contains all the 12 notes, and also because of its use in theory and occasionally in practice in <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic</a> music. It is easy to jump into this tuning and make microtonal music right away using common 12 equal software and even instruments - <a class="wiki_link" href="/DIY%20Quartertone%20Composition%20with%2012%20equal%20tools">see this page</a>.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc1"><a name="x24edo as a temperament"></a><!-- ws:end:WikiTextHeadingRule:4 -->24edo as a temperament</h1>
| |
| The <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> approximations in 24-tone equal temperament are the same as those in 12-tone equal temperament, therefore 24-tone equal temperament offers nothing new as far as approximating the 5-limit is concerned. The 7th harmonic-based intervals (7:4, 7:5 and 7:6) are almost as bad in 24-tET as in 12-tET. To achieve a satisfactory level of approximation while maintaining the 12 notes of 12-tET requires high-degree tunings like 36-tET, 72-tET, 84-tET or 156-tET.<br />
| |
| <br />
| |
| The tunings supplied by 72 cannot be used for all low-limit just intervals, but they can be used on the 17-limit <a class="wiki_link" href="/k%2AN%20subgroups">3*24 subgroup</a> 2.3.125.35.11.325.17 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>, making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11 and 17. Another approach would be to treat 24-EDO as a 2.3.11.17.19 subgroup temperament, on which it is quite accurate.<br />
| |
| <br />
| |
|
| |
|
| | === Commas === |
| | This is a partial list of the [[commas]] that 24edo [[tempering out|tempers out]] with its patent [[val]], {{val| 24 38 56 67 83 89 }}. |
|
| |
|
| <table class="wiki_table">
| | {| class="commatable wikitable center-1 center-2 right-4 center-5" |
| <tr>
| | |- |
| <td style="text-align: center;">Degree<br />
| | ! [[Harmonic limit|Prime<br>limit]] |
| </td>
| | ! [[Ratio]]<ref group="note">{{rd}}</ref> |
| <td style="text-align: center;">Cents<br />
| | ! [[Monzo]] |
| </td>
| | ! [[Cent]]s |
| <td style="text-align: center;">Approximate Ratios*<br />
| | ! [[Color name]] |
| </td>
| | ! Name(s) |
| <td colspan="3" style="text-align: center;"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs notation</a><br />
| | |- |
| </td>
| | | 3 |
| </tr>
| | | <abbr title="531441/524288">(12 digits)</abbr> |
| <tr>
| | | {{monzo| -19 12 }} |
| <td style="text-align: center;">0<br />
| | | 23.46 |
| </td>
| | | Lalawa |
| <td style="text-align: center;">0<br />
| | | [[Pythagorean comma]] |
| </td>
| | |- |
| <td style="text-align: center;">1/1<br />
| | | 5 |
| </td>
| | | [[648/625]] |
| <td style="text-align: center;">P1<br />
| | | {{monzo| 3 4 -4 }} |
| </td>
| | | 62.57 |
| <td style="text-align: center;">unison<br />
| | | Quadgu |
| </td>
| | | Diminished comma, greater diesis |
| <td style="text-align: center;">C<br />
| | |- |
| </td>
| | | 5 |
| </tr>
| | | <abbr title="262144/253125">(12 digits)</abbr> |
| <tr>
| | | {{monzo| 18 -4 -5 }} |
| <td style="text-align: center;">1<br />
| | | 60.61 |
| </td>
| | | Saquingu |
| <td style="text-align: center;">50<br />
| | | [[Passion comma]] |
| </td>
| | |- |
| <td style="text-align: center;">33/32, 34/33<br />
| | | 5 |
| </td>
| | | [[128/125]] |
| <td style="text-align: center;">^P1, vm2<br />
| | | {{monzo| 7 0 -3 }} |
| </td>
| | | 41.06 |
| <td style="text-align: center;">up-unison, downminor 2nd<br />
| | | Trigu |
| </td>
| | | Augmented comma, lesser diesis |
| <td style="text-align: center;">C^, Dbv<br />
| | |- |
| </td>
| | | 5 |
| </tr>
| | | [[81/80]] |
| <tr>
| | | {{monzo| -4 4 -1 }} |
| <td style="text-align: center;">2<br />
| | | 21.51 |
| </td>
| | | Gu |
| <td style="text-align: center;">100<br />
| | | Syntonic comma, Didymus' comma, meantone comma |
| </td>
| | |- |
| <td style="text-align: center;">17/16, 18/17<br />
| | | 5 |
| </td>
| | | [[2048/2025]] |
| <td style="text-align: center;">A1, m2<br />
| | | {{monzo| 11 -4 -2 }} |
| </td>
| | | 19.55 |
| <td style="text-align: center;">aug unison, minor 2nd<br />
| | | Sagugu |
| </td>
| | | Diaschisma |
| <td style="text-align: center;">C#, Db<br />
| | |- |
| </td>
| | | 5 |
| </tr>
| | | [[67108864/66430125| (16 digits)]] |
| <tr>
| | | {{monzo| 26 -12 -3 }} |
| <td style="text-align: center;">3<br />
| | | 17.60 |
| </td>
| | | Sasa-trigu |
| <td style="text-align: center;">150<br />
| | | [[Misty comma]] |
| </td>
| | |- |
| <td style="text-align: center;">12/11<br />
| | | 5 |
| </td>
| | | [[32805/32768]] |
| <td style="text-align: center;">~2<br />
| | | {{monzo| -15 8 1 }} |
| </td>
| | | 1.95 |
| <td style="text-align: center;">mid 2nd<br />
| | | Layo |
| </td>
| | | Schisma |
| <td style="text-align: center;">Dv<br />
| | |- |
| </td>
| | | 5 |
| </tr>
| | | <abbr title="2923003274661805836407369665432566039311865085952/2922977339492680612451840826835216578535400390625">(98 digits)</abbr> |
| <tr>
| | | {{monzo| 161 -84 -12 }} |
| <td style="text-align: center;">4<br />
| | | 0.02 |
| </td>
| | | Sepbisa-quadbigu |
| <td style="text-align: center;">200<br />
| | | [[Kirnberger's atom]] |
| </td>
| | |- |
| <td style="text-align: center;">9/8<br />
| | | 7 |
| </td>
| | | [[1323/1280]] |
| <td style="text-align: center;">M2<br />
| | | {{monzo| -8 3 -1 2 }} |
| </td>
| | | 57.20 |
| <td style="text-align: center;">major 2nd<br />
| | | Lazozogu |
| </td>
| | | Septimal two-seventh tone |
| <td style="text-align: center;">D<br />
| | |- |
| </td>
| | | 7 |
| </tr>
| | | [[49/48]] |
| <tr>
| | | {{monzo| -4 -1 0 2 }} |
| <td style="text-align: center;">5<br />
| | | 35.70 |
| </td>
| | | Zozo |
| <td style="text-align: center;">250<br />
| | | Semaphoresma, slendro diesis |
| </td>
| | |- |
| <td style="text-align: center;">22/19<br />
| | | 7 |
| </td>
| | | [[245/243]] |
| <td style="text-align: center;">^M2, vm3<br />
| | | {{monzo| 0 -5 1 2 }} |
| </td>
| | | 14.19 |
| <td style="text-align: center;">upmajor 2nd, downminor 3rd<br />
| | | Zozoyo |
| </td>
| | | Sensamagic comma |
| <td style="text-align: center;">D^, Ebv<br />
| | |- |
| </td>
| | | 7 |
| </tr>
| | | [[19683/19600]] |
| <tr>
| | | {{monzo| -4 9 -2 -2 }} |
| <td style="text-align: center;">6<br />
| | | 7.32 |
| </td>
| | | Labirugu |
| <td style="text-align: center;">300<br />
| | | Cataharry comma |
| </td>
| | |- |
| <td style="text-align: center;">19/16<br />
| | | 7 |
| </td>
| | | [[6144/6125]] |
| <td style="text-align: center;">m3<br />
| | | {{monzo| 11 1 -3 -2 }} |
| </td>
| | | 5.36 |
| <td style="text-align: center;">minor 3rd<br />
| | | Sarurutrigu |
| </td>
| | | Porwell comma |
| <td style="text-align: center;">Eb<br />
| | |- |
| </td>
| | | 11 |
| </tr>
| | | [[56/55]] |
| <tr>
| | | {{monzo| 3 0 -1 1 -1 }} |
| <td style="text-align: center;">7<br />
| | | 31.19 |
| </td>
| | | Luzogu |
| <td style="text-align: center;">350<br />
| | | Undecimal tritonic comma |
| </td>
| | |- |
| <td style="text-align: center;">11/9<br />
| | | 11 |
| </td>
| | | [[245/242]] |
| <td style="text-align: center;">~3<br />
| | | {{monzo| -1 0 1 2 -2 }} |
| </td>
| | | 21.33 |
| <td style="text-align: center;">mid 3rd<br />
| | | Luluzozoyo |
| </td>
| | | Frostma |
| <td style="text-align: center;">Ev<br />
| | |- |
| </td>
| | | 11 |
| </tr>
| | | [[121/120]] |
| <tr>
| | | {{monzo| -3 -1 -1 0 2 }} |
| <td style="text-align: center;">8<br />
| | | 14.37 |
| </td>
| | | Lologu |
| <td style="text-align: center;">400<br />
| | | Biyatisma |
| </td>
| | |- |
| <td style="text-align: center;">24/19<br />
| | | 11 |
| </td>
| | | [[176/175]] |
| <td style="text-align: center;">M3<br />
| | | {{monzo| 4 0 -2 -1 1 }} |
| </td>
| | | 9.86 |
| <td style="text-align: center;">major 3rd<br />
| | | Lorugugu |
| </td>
| | | Valinorsma |
| <td style="text-align: center;">E<br />
| | |- |
| </td>
| | | 11 |
| </tr>
| | | [[896/891]] |
| <tr>
| | | {{monzo| 7 -4 0 1 -1 }} |
| <td style="text-align: center;">9<br />
| | | 9.69 |
| </td>
| | | Saluzo |
| <td style="text-align: center;">450<br />
| | | Pentacircle comma |
| </td>
| | |- |
| <td style="text-align: center;">22/17<br />
| | | 11 |
| </td>
| | | [[243/242]] |
| <td style="text-align: center;">^M3, vP4<br />
| | | {{monzo| -1 5 0 0 -2 }} |
| </td>
| | | 7.14 |
| <td style="text-align: center;">upmajor 3rd, down-fourth<br />
| | | Lulu |
| </td>
| | | Rastma |
| <td style="text-align: center;">E^, Fv<br />
| | |- |
| </td>
| | | 11 |
| </tr>
| | | <abbr title="214990848/214358881">(18 digits)</abbr> |
| <tr>
| | | {{monzo| 15 8 0 0 -8 }} |
| <td style="text-align: center;">10<br />
| | | 5.10 |
| </td>
| | | Quadbilu |
| <td style="text-align: center;">500<br />
| | | [[Octatonic comma]] |
| </td>
| | |- |
| <td style="text-align: center;">4/3<br />
| | | 11 |
| </td>
| | | [[385/384]] |
| <td style="text-align: center;">P4<br />
| | | {{monzo| -7 -1 1 1 1 }} |
| </td>
| | | 4.50 |
| <td style="text-align: center;">fourth<br />
| | | Lozoyo |
| </td>
| | | Keenanisma |
| <td style="text-align: center;">F<br />
| | |- |
| </td>
| | | 11 |
| </tr>
| | | <abbr title="117440512/117406179">(18 digits)</abbr> |
| <tr>
| | | {{monzo| 24 -6 0 1 -5 }} |
| <td style="text-align: center;">11<br />
| | | 0.51 |
| </td>
| | | Saquinlu-azo |
| <td style="text-align: center;">550<br />
| | | [[Quartisma]] |
| </td>
| | |- |
| <td style="text-align: center;">11/8<br />
| | | 11 |
| </td>
| | | [[9801/9800]] |
| <td style="text-align: center;">^P4<br />
| | | {{monzo| -3 4 -2 -2 2 }} |
| </td>
| | | 0.18 |
| <td style="text-align: center;">up-fourth<br />
| | | Bilorugu |
| </td>
| | | Kalisma, Gauss' comma |
| <td style="text-align: center;">F^<br />
| | |- |
| </td>
| | | 11 |
| </tr>
| | | <abbr title="1771561/1771470">(14 digits)</abbr> |
| <tr>
| | | {{monzo| -1 -11 -1 0 6 }} |
| <td style="text-align: center;">12<br />
| | | 0.089 |
| </td>
| | | Satribilo-agu |
| <td style="text-align: center;">600<br />
| | | [[Parimo]] |
| </td>
| | |- |
| <td style="text-align: center;">17/12<br />
| | | 13 |
| </td>
| | | [[66/65]] |
| <td style="text-align: center;">A4, d5<br />
| | | {{monzo| 1 1 -1 0 1 -1 }} |
| </td>
| | | 26.43 |
| <td style="text-align: center;">aug 4th, dim 5th<br />
| | | Thulogu |
| </td>
| | | Winmeanma |
| <td style="text-align: center;">F#, Gb<br />
| | |- |
| </td>
| | | 13 |
| </tr>
| | | [[91/90]] |
| <tr>
| | | {{monzo| -1 -2 -1 1 0 1 }} |
| <td style="text-align: center;">13<br />
| | | 19.13 |
| </td>
| | | Thozogu |
| <td style="text-align: center;">650<br />
| | | Superleap comma, biome comma |
| </td>
| | |- |
| <td style="text-align: center;">16/11<br />
| | | 13 |
| </td>
| | | [[512/507]] |
| <td style="text-align: center;">vP5<br />
| | | {{monzo| 9 -1 0 0 0 -2 }} |
| </td>
| | | 16.99 |
| <td style="text-align: center;">down-fifth<br />
| | | Thuthu |
| </td>
| | | Tridecimal neutral thirds comma |
| <td style="text-align: center;">Gv<br />
| | |- |
| </td>
| | | 13 |
| </tr>
| | | [[105/104]] |
| <tr>
| | | {{monzo| -3 1 1 1 0 -1 }} |
| <td style="text-align: center;">14<br />
| | | 16.57 |
| </td>
| | | Thuzoyo |
| <td style="text-align: center;">700<br />
| | | Animist comma |
| </td>
| | |- |
| <td style="text-align: center;">3/2<br />
| | | 13 |
| </td>
| | | [[144/143]] |
| <td style="text-align: center;">P5<br />
| | | {{monzo| 4 2 0 0 -1 -1 }} |
| </td>
| | | 12.06 |
| <td style="text-align: center;">fifth<br />
| | | Thulu |
| </td>
| | | Grossma |
| <td style="text-align: center;">G<br />
| | |- |
| </td>
| | | 13 |
| </tr>
| | | [[351/350]] |
| <tr>
| | | {{Monzo| -1 3 -2 -1 0 1 }} |
| <td style="text-align: center;">15<br />
| | | 4.94 |
| </td>
| | | Thorugugu |
| <td style="text-align: center;">750<br />
| | | Ratwolfsma |
| </td>
| | |- |
| <td style="text-align: center;">17/11<br />
| | | 13 |
| </td>
| | | [[352/351]] |
| <td style="text-align: center;">^P5, vm6<br />
| | | {{monzo| 5 -3 0 0 1 -1 }} |
| </td>
| | | 4.93 |
| <td style="text-align: center;">up-fifth, downminor 6th<br />
| | | Thulo |
| </td>
| | | Minor minthma |
| <td style="text-align: center;">G^, Abv<br />
| | |- |
| </td>
| | | 13 |
| </tr>
| | | [[676/675]] |
| <tr>
| | | {{monzo| 2 -3 -2 0 0 2 }} |
| <td style="text-align: center;">16<br />
| | | 2.56 |
| </td>
| | | Bithogu |
| <td style="text-align: center;">800<br />
| | | Island comma, parizeksma |
| </td>
| | |- |
| <td style="text-align: center;">19/12<br />
| | | 13 |
| </td>
| | | [[4096/4095]] |
| <td style="text-align: center;">m6<br />
| | | {{monzo| 12 -2 -1 -1 0 -1 }} |
| </td>
| | | 0.42 |
| <td style="text-align: center;">minor 6th<br />
| | | Sathurugu |
| </td>
| | | Minisma |
| <td style="text-align: center;">Ab<br />
| | |- |
| </td>
| | | 17 |
| </tr>
| | | [[51/50]] |
| <tr>
| | | {{monzo| -1 1 -2 0 0 0 1 }} |
| <td style="text-align: center;">17<br />
| | | 34.28 |
| </td>
| | | Sogugu |
| <td style="text-align: center;">850<br />
| | | Large septendecimal sixth tone |
| </td>
| | |- |
| <td style="text-align: center;">18/11<br />
| | | 17 |
| </td>
| | | [[136/135]] |
| <td style="text-align: center;">~6<br />
| | | {{monzo| 3 -3 -1 0 0 0 1 }} |
| </td>
| | | 12.78 |
| <td style="text-align: center;">mid 6th<br />
| | | Sogu |
| </td>
| | | Diatisma, fiventeen comma |
| <td style="text-align: center;">Av<br />
| | |- |
| </td>
| | | 17 |
| </tr>
| | | [[170/169]] |
| <tr>
| | | {{monzo| 1 0 1 0 0 -2 1 }} |
| <td style="text-align: center;">18<br />
| | | 10.21 |
| </td>
| | | Sothuthuyo |
| <td style="text-align: center;">900<br />
| | | Major naiadma |
| </td>
| | |- |
| <td style="text-align: center;">32/19<br />
| | | 17 |
| </td>
| | | [[221/220]] |
| <td style="text-align: center;">M6<br />
| | | {{monzo| -2 0 -1 0 -1 1 1 }} |
| </td>
| | | 7.85 |
| <td style="text-align: center;">major 6th<br />
| | | Sotholugu |
| </td>
| | | Minor naiadma |
| <td style="text-align: center;">A<br />
| | |- |
| </td>
| | | 17 |
| </tr>
| | | [[256/255]] |
| <tr>
| | | {{monzo| 8 -1 -1 0 0 0 -1 }} |
| <td style="text-align: center;">19<br />
| | | 6.78 |
| </td>
| | | Sugu |
| <td style="text-align: center;">950<br />
| | | Charisma, septendecimal kleisma |
| </td>
| | |- |
| <td style="text-align: center;">19/11<br />
| | | 17 |
| </td>
| | | [[289/288]] |
| <td style="text-align: center;">^M6, vm7<br />
| | | {{monzo| -5 -2 0 0 0 0 2 }} |
| </td>
| | | 6.00 |
| <td style="text-align: center;">upmajor 6th, downminor 7th<br />
| | | Soso |
| </td>
| | | Semitonisma |
| <td style="text-align: center;">A^, Bbv<br />
| | |- |
| </td>
| | | 17 |
| </tr>
| | | [[1225/1224]] |
| <tr>
| | | {{monzo| -3 -2 2 2 0 0 -1 }} |
| <td style="text-align: center;">20<br />
| | | 1.41 |
| </td>
| | | Subizoyo |
| <td style="text-align: center;">1000<br />
| | | Noellisma |
| </td>
| | |- |
| <td style="text-align: center;">16/9<br />
| | | 19 |
| </td>
| | | [[76/75]] |
| <td style="text-align: center;">m7<br />
| | | {{monzo| 2 -1 -2 0 0 0 0 1 }} |
| </td>
| | | 22.93 |
| <td style="text-align: center;">minor 7th<br />
| | | Nogugu |
| </td>
| | | Large undevicesimal ninth tone |
| <td style="text-align: center;">Bb<br />
| | |- |
| </td>
| | | 19 |
| </tr>
| | | [[77/76]] |
| <tr>
| | | {{monzo| -2 0 0 1 1 0 0 -1 }} |
| <td style="text-align: center;">21<br />
| | | 22.63 |
| </td>
| | | Nulozo |
| <td style="text-align: center;">1050<br />
| | | Small undevicesimal ninth tone |
| </td>
| | |- |
| <td style="text-align: center;">11/6<br />
| | | 19 |
| </td>
| | | [[96/95]] |
| <td style="text-align: center;">~7<br />
| | | {{monzo| 5 1 -1 0 0 0 0 -1 }} |
| </td>
| | | 18.13 |
| <td style="text-align: center;">mid 7th<br />
| | | Nugu |
| </td>
| | | 19th-partial chroma |
| <td style="text-align: center;">Bv<br />
| | |- |
| </td>
| | | 19 |
| </tr>
| | | [[133/132]] |
| <tr>
| | | {{monzo| -2 -1 0 1 -1 0 0 1 }} |
| <td style="text-align: center;">22<br />
| | | 13.07 |
| </td>
| | | Noluzo |
| <td style="text-align: center;">1100<br />
| | | Minithirdma |
| </td>
| | |- |
| <td style="text-align: center;">17/9, 32/17<br />
| | | 19 |
| </td>
| | | [[153/152]] |
| <td style="text-align: center;">M7<br />
| | | {{monzo| -3 2 0 0 0 0 1 -1}} |
| </td>
| | | 11.35 |
| <td style="text-align: center;">major 7th<br />
| | | Nuso |
| </td>
| | | Ganassisma |
| <td style="text-align: center;">B<br />
| | |- |
| </td>
| | | 19 |
| </tr>
| | | [[171/170]] |
| <tr>
| | | {{monzo| -1 2 -1 0 0 0 -1 1 }} |
| <td style="text-align: center;">23<br />
| | | 10.15 |
| </td>
| | | Nosugu |
| <td style="text-align: center;">1150<br />
| | | Malcolmisma |
| </td>
| | |- |
| <td style="text-align: center;">33/17, 64/33<br />
| | | 19 |
| </td>
| | | [[209/208]] |
| <td style="text-align: center;">^M7, vP8<br />
| | | {{monzo| -4 0 0 0 1 -1 0 1 }} |
| </td>
| | | 8.30 |
| <td style="text-align: center;">upmajor 7th, down-8ve<br />
| | | Nothulo |
| </td>
| | | Yama comma |
| <td style="text-align: center;">B^, Cv<br />
| | |- |
| </td>
| | | 19 |
| </tr>
| | | [[324/323]] |
| <tr>
| | | {{monzo| 2 4 0 0 0 0 -1 -1 }} |
| <td style="text-align: center;">24<br />
| | | 5.35 |
| </td>
| | | Nusu |
| <td style="text-align: center;">1200<br />
| | | Photisma |
| </td>
| | |- |
| <td style="text-align: center;">2/1<br />
| | | 19 |
| </td>
| | | [[361/360]] |
| <td style="text-align: center;">P8<br />
| | | {{monzo| -3 -2 -1 0 0 0 0 2 }} |
| </td>
| | | 4.80 |
| <td style="text-align: center;">perfect 8ve<br />
| | | Nonogu |
| </td>
| | | Go comma |
| <td style="text-align: center;">C<br />
| | |- |
| </td>
| | | 19 |
| </tr>
| | | [[5776/5775]] |
| </table>
| | | {{monzo| 4 -1 -2 -1 -1 0 0 2 }} |
| | | 0.30 |
| | | Nonolurugugu |
| | | Neovish comma |
| | |} |
| | <references group="note" /> |
|
| |
|
| *based on treating 24-EDO as a 2.3.11.17.19 subgroup; other approaches are possible.<br />
| | === Rank-2 temperaments === |
| <br />
| | * [[List of 24et rank two temperaments by badness]] |
| Combining ups and downs notation with <a class="wiki_link" href="/Kite%27s%20color%20notation">color notation</a>, qualities can be loosely associated with colors:<br />
| | * [[List of edo-distinct 24et rank two temperaments]] |
|
| |
|
| | {| class="wikitable center-1 center-2" |
| | |- |
| | ! Periods<br>per 8ve |
| | ! Generator |
| | ! Name |
| | |- |
| | | 1 |
| | | 1\24 |
| | | [[Hemiripple]] (24) |
| | |- |
| | | 1 |
| | | 5\24 |
| | | [[Godzilla]] (24) / [[baragon]] (24) / [[semaphoresmic clan #Varan|varan]] (24) |
| | |- |
| | | 1 |
| | | 7\24 |
| | | [[Mohajira]] (24) / [[neutrominant]] (24d) / [[migration]] (24d) |
| | |- |
| | | 1 |
| | | 11\24 |
| | | [[Cohemiripple]] (24), [[freivald]] (24) |
| | |- |
| | | 2 |
| | | 1\24 |
| | | [[Shrutar]] (24) |
| | |- |
| | | 2 |
| | | 5\24 |
| | | [[Sruti]] (24), [[anguirus]] (24), [[decimal]] (24c) |
| | |- |
| | | 3 |
| | | 1\24 |
| | | [[Hemiaug]] (24) |
| | |- |
| | | 3 |
| | | 3\24 |
| | | [[Triforce]] (24) |
| | |- |
| | | 4 |
| | | 1\24 |
| | | [[Hemidim]] (24) |
| | |- |
| | | 6 |
| | | 1\24 |
| | | [[Hemisemiaug]] (24) |
| | |- |
| | | 8 |
| | | 1\24 |
| | | [[Semidim]] (24) |
| | |- |
| | | 12 |
| | | 1\24 |
| | | [[Catler]] |
| | |} |
|
| |
|
| <table class="wiki_table">
| | Important MOSes include: |
| <tr>
| | * Semaphore 4L 1s 55455 (generator: 5\24) |
| <th>quality<br />
| | * Semaphore 5L 4s 414141414 (generator: 5\24) |
| </th>
| | * Mohajira 3L 4s 3434343 (generator: 7\24) |
| <th>color<br />
| | * Mohajira 7L 3s 3313313313 (generator: 7\24) |
| </th>
| |
| <th>monzo format<br />
| |
| </th>
| |
| <th>examples<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">downminor<br />
| |
| </td>
| |
| <td style="text-align: center;">blue<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b, 0, 1}<br />
| |
| </td>
| |
| <td style="text-align: center;">7/6, 7/4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">minor<br />
| |
| </td>
| |
| <td style="text-align: center;">fourthward white<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b}, b &lt; -1<br />
| |
| </td>
| |
| <td style="text-align: center;">32/27, 16/9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">&quot;<br />
| |
| </td>
| |
| <td style="text-align: center;">green<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b, -1}<br />
| |
| </td>
| |
| <td style="text-align: center;">6/5, 9/5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">mid<br />
| |
| </td>
| |
| <td style="text-align: center;">jade<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b, 0, 0, 1}<br />
| |
| </td>
| |
| <td style="text-align: center;">11/9, 11/6<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">&quot;<br />
| |
| </td>
| |
| <td style="text-align: center;">amber<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b, 0, 0, -1}<br />
| |
| </td>
| |
| <td style="text-align: center;">12/11, 18/11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">major<br />
| |
| </td>
| |
| <td style="text-align: center;">yellow<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b, 1}<br />
| |
| </td>
| |
| <td style="text-align: center;">5/4, 5/3<br />
| |
| </td> | |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">&quot;<br />
| |
| </td>
| |
| <td style="text-align: center;">fifthward white<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b}, b &gt; 1<br />
| |
| </td> | |
| <td style="text-align: center;">9/8, 27/16<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">upmajor<br />
| |
| </td>
| |
| <td style="text-align: center;">red<br />
| |
| </td>
| |
| <td style="text-align: center;">{a, b, 0, -1}<br />
| |
| </td>
| |
| <td style="text-align: center;">9/7, 12/7<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | == Octave stretch or compression == |
| The 11th harmonic, and most intervals derived from it, (11:10, 11:9, 11:8, 11:6, 12:11, 15:11, 16:11, 18:11, 20:11) are very well approximated in 24-tone equal temperament. The 24-tone interval of 550 cents is 1.3 cents flatter than 11:8 and is almost indistinguishable from it. In addition, the interval approximating 11:9 is 7 steps which is exactly half the perfect fifth. Some good chords in 24-tET are (the numbers are edosteps, e.g. 4 is a major second, 8 is a major third):<br />
| | If one wishes to use 24edo as a full 19-or-lower-limit tuning, then it benefits from slight [[octave stretching]], mostly to improve its [[prime]] 7. If one wishes to use 24edo as a no-7s 19-or-lower-limit tuning, then it benefits from slight [[octave shrinking]], mostly to improve its primes 5 and 13. |
| <br />
| | * Stretched-octave tunings (least to most stretch): [[ed12|86ed12]], [[ed6|62ed6]], [[38edt]] |
| 0-4-8-11-14 (&quot;major&quot; chord with a 9:8 and a 11:8 above the root)<br />
| | * Compressed-octave tunings (least to most compression): [[zpi|90zpi]], [[equal tuning|80ed10]], [[ed5|56ed5]] |
| Its inversion, 0-3-6-10-14 (&quot;minor&quot;)<br />
| |
| 0-7-14 (&quot;neutral&quot;)<br />
| |
| 0-5-10 (another kind of &quot;neutral&quot;, splitting the fourth in two. The 0-5-10 can be extended into a pentatonic scale, 0-5-10-14-19-24 (<a class="wiki_link" href="/godzilla">godzilla</a>), that is close to equi-pentatonic and also close to several Indonesian slêndros. In a similar way 0-7-14 extends to 0-4-7-11-14-18-21-24 (<a class="wiki_link" href="/mohajira">mohajira</a>), a heptatonic scale close to several Arabic scales.)<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc2"><a name="x24edo as a temperament--Commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->Commas</h3>
| |
| 24 EDO tempers out the following commas. (Note: This assumes val &lt; 24 38 56 67 83 89 |.)<br />
| |
|
| |
|
| | == Scales and modes == |
| | ''See: [[24edo scales]] and [[List of MOS scales in 24edo]].'' |
|
| |
|
| <table class="wiki_table">
| | == Tetrachords == |
| <tr>
| | ''See [[24edo tetrachords]]''. |
| <th>Comma<br />
| |
| </th>
| |
| <th>Monzo<br />
| |
| </th>
| |
| <th>Value (Cents)<br />
| |
| </th>
| |
| <th>Name 1<br />
| |
| </th>
| |
| <th>Name 2<br />
| |
| </th>
| |
| <th>Name 3<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">531441/524288<br />
| |
| </td>
| |
| <td style="text-align: center;">| -19 12 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">23.46<br />
| |
| </td>
| |
| <td style="text-align: center;">Pythagorean Comma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">648/625<br />
| |
| </td>
| |
| <td style="text-align: center;">| 3 4 -4 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">62.57<br />
| |
| </td>
| |
| <td style="text-align: center;">Major Diesis<br />
| |
| </td>
| |
| <td style="text-align: center;">Diminished Comma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">128/125<br />
| |
| </td>
| |
| <td style="text-align: center;">| 7 0 -3 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">41.06<br />
| |
| </td>
| |
| <td style="text-align: center;">Diesis<br />
| |
| </td>
| |
| <td style="text-align: center;">Augmented Comma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">81/80<br />
| |
| </td>
| |
| <td style="text-align: center;">| -4 4 -1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">21.51<br />
| |
| </td>
| |
| <td style="text-align: center;">Syntonic Comma<br />
| |
| </td>
| |
| <td style="text-align: center;">Didymos Comma<br />
| |
| </td>
| |
| <td style="text-align: center;">Meantone Comma<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">2048/2025<br />
| |
| </td>
| |
| <td style="text-align: center;">| 11 -4 -2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">19.55<br />
| |
| </td>
| |
| <td style="text-align: center;">Diaschisma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">5201701/5149091<br />
| |
| </td>
| |
| <td style="text-align: center;">| 26 -12 -3 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">17.60<br />
| |
| </td>
| |
| <td style="text-align: center;">Misty Comma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">32805/32768<br />
| |
| </td>
| |
| <td style="text-align: center;">| -15 8 1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">1.95<br />
| |
| </td>
| |
| <td style="text-align: center;">Schisma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">1465155/1465142<br />
| |
| </td>
| |
| <td style="text-align: center;">| 161 -84 -12 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">0.02<br />
| |
| </td>
| |
| <td style="text-align: center;">Atom<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">49/48<br />
| |
| </td>
| |
| <td style="text-align: center;">| -4 -1 0 2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">35.70<br />
| |
| </td>
| |
| <td style="text-align: center;">Slendro Diesis<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">245/243<br />
| |
| </td>
| |
| <td style="text-align: center;">| 0 -5 1 2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">14.19<br />
| |
| </td>
| |
| <td style="text-align: center;">Sensamagic<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">19683/19600<br />
| |
| </td>
| |
| <td style="text-align: center;">| -4 9 -2 -2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">7.32<br />
| |
| </td>
| |
| <td style="text-align: center;">Cataharry<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">6144/6125<br />
| |
| </td>
| |
| <td style="text-align: center;">| 11 1 -3 -2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">5.36<br />
| |
| </td>
| |
| <td style="text-align: center;">Porwell<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">121/120<br />
| |
| </td>
| |
| <td style="text-align: center;">| -3 -1 -1 0 2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">14.37<br />
| |
| </td>
| |
| <td style="text-align: center;">Biyatisma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">176/175<br />
| |
| </td>
| |
| <td style="text-align: center;">| 4 0 -2 -1 1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">9.86<br />
| |
| </td>
| |
| <td style="text-align: center;">Valinorsma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">896/891<br />
| |
| </td>
| |
| <td style="text-align: center;">| 7 -4 0 1 -1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">9.69<br />
| |
| </td>
| |
| <td style="text-align: center;">Pentacircle<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">243/242<br />
| |
| </td>
| |
| <td style="text-align: center;">| -1 5 0 0 -2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">7.14<br />
| |
| </td>
| |
| <td style="text-align: center;">Rastma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">385/384<br />
| |
| </td>
| |
| <td style="text-align: center;">| -7 -1 1 1 1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">4.50<br />
| |
| </td>
| |
| <td style="text-align: center;">Keenanisma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">9801/9800<br />
| |
| </td>
| |
| <td style="text-align: center;">| -3 4 -2 -2 2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">0.18<br />
| |
| </td>
| |
| <td style="text-align: center;">Kalisma<br />
| |
| </td>
| |
| <td style="text-align: center;">Gauss' Comma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">91/90<br />
| |
| </td>
| |
| <td style="text-align: center;">| -1 -2 -1 1 0 1 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">19.13<br />
| |
| </td>
| |
| <td style="text-align: center;">Superleap<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">676/675<br />
| |
| </td>
| |
| <td style="text-align: center;">| 2 -3 -2 0 0 2 &gt;<br />
| |
| </td>
| |
| <td style="text-align: center;">2.56<br />
| |
| </td>
| |
| <td style="text-align: center;">Parizeksma<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc3"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:8 -->Intervals</h1>
| | == Chord types == |
| <br />
| | 24edo features a rich variety of not only new chords, but also alterations that can be used with regular 12edo chords. For example, an approximation of the ninth, eleventh, and thirteenth harmonic can be added to a major triad to create 4:5:6:9:11:13, a sort of super-extended major chord. |
| 24 EDO breaks intervals into two sets of five cartegories. Infra - Minor - Neutral - Major - Ultra for seconds, thirds, sixths, and sevenths; and diminished - narrow - perfect - wide - augmented for fourths, fifths, unison, and octave. For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth.<br />
| |
| <br />
| |
| These are the intervals of 24 EDO that do not exist in 12 EDO: 2<br />
| |
| <a class="wiki_link" href="/24%20EDO%20Interval%20names%20and%20Harmonies">See full article on 24 Edo intervals.</a><br />
| |
|
| |
|
| | As for entirely new chords, there are three new fundamental options, giving five basic triads over 12edo's two: |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable center-all" |
| <tr>
| | |+ style="white-space: nowrap; font-size: 105%;" | Fundamental triads of 24edo |
| <th colspan="2">The twelve new intervals in 24edo<br />
| | |- |
| </th>
| | ! JI Chord |
| <th colspan="3">some nearby JI intervals<br />
| | ! Edosteps |
| </th>
| | ! Notes of C Chord |
| </tr>
| | ! Written name |
| <tr>
| | ! Spoken name |
| <th>cents<br />
| | |- |
| </th>
| | | 6:7:9, 26:30:39 |
| <th>common names<br />
| | | {{dash|0, 5, 14|hair}} |
| </th>
| | | {{dash|C, E{{sesquiflat2}}, G|hair}} |
| <th>frequency ratio<br />
| | | Cvm<br>Cm({{demiflat2}}3), Cmin({{demiflat2}}3) |
| </th>
| | | C inframinor<br>C minor semiflat-three |
| <th>cents<br />
| | |- |
| </th>
| | | 10:12:15 |
| <th>common name<br />
| | | {{dash|0, 6, 14|hair}} |
| </th>
| | | {{dash|C, E♭, G|hair}} |
| </tr>
| | | Cm, Cmin |
| <tr>
| | | C minor |
| <td style="text-align: center;">50<br />
| | |- |
| </td>
| | | 18:22:27, 22:27:33 |
| <td style="text-align: center;">quartertone<br />
| | | 0-7-14 |
| infra second, wide unison<br />
| | | {{dash|C, E{{demiflat2}}, G|hair}} |
| </td>
| | | C~, Cneu |
| <td style="text-align: center;"><a class="wiki_link" href="/36_35">36/35</a><br />
| | | C neutral |
| <a class="wiki_link" href="/35_34">35/34</a><br />
| | |- |
| <a class="wiki_link" href="/34_33">34/33</a><br />
| | | 4:5:6 |
| <a class="wiki_link" href="/33_32">33/32</a><br />
| | | {{dash|0, 8, 14|hair}} |
| </td>
| | | {{dash|C, E, G|hair}} |
| <td style="text-align: center;">48.770<br />
| | | C, Cmaj |
| 50.184<br />
| | | C, C major |
| 51.682<br />
| | |- |
| 53.273<br />
| | | 14:18:21, 10:13:15 |
| </td>
| | | {{dash|0, 9, 14|hair}} |
| <td style="text-align: center;">large septimal quarter-tone (Archytas)<br />
| | | {{dash|C, E{{demisharp2}}, G|hair}} |
| large 17-limit quartertone<br />
| | | C^<br>C({{demisharp2}}3), Cmaj({{demisharp2}}3) |
| small 17-limit quartertone<br />
| | | C ultramajor<br>C major semisharp-three |
| 33rd harmonic<br />
| | |} |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">150<br />
| |
| </td>
| |
| <td style="text-align: center;">neutral second<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/12_11">12/11</a><br />
| |
| </td>
| |
| <td style="text-align: center;">150.637<br />
| |
| </td>
| |
| <td style="text-align: center;">large undecimal neutral second<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">250<br />
| |
| </td>
| |
| <td style="text-align: center;">ultra second<br />
| |
| <span style="line-height: 1.5;">infra third</span><br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/144_125">144/125</a><br />
| |
| <a class="wiki_link" href="/15_13">15/13</a><br />
| |
| <a class="wiki_link" href="/52_45">52/45</a><br />
| |
| </td>
| |
| <td style="text-align: center;">244.969<br />
| |
| 247.741<br />
| |
| 250.304<br />
| |
| </td>
| |
| <td style="text-align: center;">diminished third (6/5 x 24/25)<br />
| |
| ..<br />
| |
| ..<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">350<br />
| |
| </td>
| |
| <td style="text-align: center;">neutral third<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/11_9">11/9</a><br />
| |
| <a class="wiki_link" href="/27_22">27/22</a><br />
| |
| <a class="wiki_link" href="/16_13">16/13</a><br />
| |
| </td>
| |
| <td style="text-align: center;">347.408<br />
| |
| 354.547<br />
| |
| 359.472<br />
| |
| </td>
| |
| <td style="text-align: center;">undecimal neutral third<br />
| |
| ..<br />
| |
| tridecimal neutral third<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">450<br />
| |
| </td>
| |
| <td style="text-align: center;">minor fourth, ultra third, narrow fourth<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/22_17">22/17</a><br />
| |
| <a class="wiki_link" href="/35_27">35/27</a><br />
| |
| <a class="wiki_link" href="/13_10">13/10</a><br />
| |
| </td>
| |
| <td style="text-align: center;">446.363<br />
| |
| 449.275<br />
| |
| 454.214<br />
| |
| </td>
| |
| <td style="text-align: center;">17-limit supermajor third<br />
| |
| ..<br />
| |
| tridecimal subfourth<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">550<br />
| |
| </td>
| |
| <td style="text-align: center;">wide fourth<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/11_8">11/8</a><br />
| |
| </td>
| |
| <td style="text-align: center;">551.318<br />
| |
| </td>
| |
| <td style="text-align: center;">undecimal superfourth, harmonic 11th<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">650<br />
| |
| </td>
| |
| <td style="text-align: center;">narrow fifth<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/16_11">16/11</a><br />
| |
| </td>
| |
| <td style="text-align: center;">648.682<br />
| |
| </td>
| |
| <td style="text-align: center;">undecimal subfifth, 11th subharmonic<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">750<br />
| |
| </td>
| |
| <td style="text-align: center;">wide fifth, infra sixth<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/20_13">20/13</a><br />
| |
| <a class="wiki_link" href="/54_35">54/35</a><br />
| |
| <a class="wiki_link" href="/17_11">17/11</a><br />
| |
| </td>
| |
| <td style="text-align: center;">745.786<br />
| |
| 750.725<br />
| |
| 753.637<br />
| |
| </td>
| |
| <td style="text-align: center;">tridecimal superfifth<br />
| |
| ..<br />
| |
| 17-limit subminor sixth<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">850<br />
| |
| </td>
| |
| <td style="text-align: center;">neutral sixth<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/13_8">13/8</a><br />
| |
| <a class="wiki_link" href="/44_27">44/27</a><br />
| |
| <a class="wiki_link" href="/18_11">18/11</a><br />
| |
| </td>
| |
| <td style="text-align: center;">840.528<br />
| |
| 845.453<br />
| |
| 852.592<br />
| |
| </td>
| |
| <td style="text-align: center;">overtone sixth, 13th harmonic<br />
| |
| ..<br />
| |
| undecimal neutral sixth<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">950<br />
| |
| </td>
| |
| <td style="text-align: center;">ultra sixth , infra seventh<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/45_26">45/26</a><br />
| |
| <a class="wiki_link" href="/26_15">26/15</a><br />
| |
| <a class="wiki_link" href="/125_72">125/72</a><br />
| |
| </td>
| |
| <td style="text-align: center;">949.696<br />
| |
| 952.259<br />
| |
| 955.031<br />
| |
| </td>
| |
| <td style="text-align: center;">..<br />
| |
| ..<br />
| |
| ..<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">1050<br />
| |
| </td>
| |
| <td style="text-align: center;">neutral seventh<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/11_6">11/6</a><br />
| |
| </td>
| |
| <td style="text-align: center;">1049.363<br />
| |
| </td>
| |
| <td style="text-align: center;">undecimal neutral seventh<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">1150<br />
| |
| </td>
| |
| <td style="text-align: center;">ultra seventh, narrow octave<br />
| |
| </td>
| |
| <td style="text-align: center;"><a class="wiki_link" href="/31_16">31/16</a><br />
| |
| <a class="wiki_link" href="/33_17">33/17</a><br />
| |
| <a class="wiki_link" href="/35_18">35/18</a><br />
| |
| </td>
| |
| <td style="text-align: center;">1145.036<br />
| |
| 1148.318<br />
| |
| 1151.230<br />
| |
| </td>
| |
| <td style="text-align: center;">31st harmonic<br />
| |
| ..<br />
| |
| ..<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | These chords tend to lack the forcefulness to sound like resolved, tonal sonorities, but can be resolved of that issue by using tetrads in place of triads. For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: {{dash|0, 7, 14, 21|hair}}. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad: {{dash|0, 14, 21, 35|hair}} [[William Lynch]] considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality. |
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc4"><a name="Notation"></a><!-- ws:end:WikiTextHeadingRule:10 -->Notation</h1>
| |
| There have been disputes about disadvantages of various systems for notating quarter tones. Here are some of the few systems along with pros and cons.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc5"><a name="Notation-Mainstream Quartertone Notation"></a><!-- ws:end:WikiTextHeadingRule:12 -->Mainstream Quartertone Notation</h2>
| |
| <!-- ws:start:WikiTextRemoteImageRule:1872:&lt;img src=&quot;http://www.wfg.woodwind.org/n/s14_blue.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.wfg.woodwind.org/n/s14_blue.gif" alt="external image s14_blue.gif" title="external image s14_blue.gif" /><!-- ws:end:WikiTextRemoteImageRule:1872 --> or ^ = quarter-tone sharp or &quot;Jump&quot; or &quot;up&quot;<br />
| |
| <!-- ws:start:WikiTextRemoteImageRule:1873:&lt;img src=&quot;http://www.wfg.woodwind.org/n/s34_blue.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.wfg.woodwind.org/n/s34_blue.gif" alt="external image s34_blue.gif" title="external image s34_blue.gif" /><!-- ws:end:WikiTextRemoteImageRule:1873 --> or #^ or ^# = three-quarter-tone sharp or &quot;Jump-Sharp&quot; or &quot;upsharp&quot;<br />
| |
| <!-- ws:start:WikiTextRemoteImageRule:1874:&lt;img src=&quot;http://www.wfg.woodwind.org/n/f14_blue.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.wfg.woodwind.org/n/f14_blue.gif" alt="external image f14_blue.gif" title="external image f14_blue.gif" /><!-- ws:end:WikiTextRemoteImageRule:1874 --> or v = quarter-tone flat or &quot;Drop&quot; or &quot;down&quot;<br />
| |
| <!-- ws:start:WikiTextRemoteImageRule:1875:&lt;img src=&quot;http://www.wfg.woodwind.org/n/f34_blue.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.wfg.woodwind.org/n/f34_blue.gif" alt="external image f34_blue.gif" title="external image f34_blue.gif" /><!-- ws:end:WikiTextRemoteImageRule:1875 --> or bv or vb = three-quarter-tone flat or &quot;Drop-Flat&quot; or &quot;downflat&quot;<br />
| |
| <br />
| |
| Pros: Familiar, fairly easy to learn<br />
| |
| Cons: Clutters a score easily, can get confusing when sight read at faster paces<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6"><a name="Notation-Alternate Quartertone Accidentals"></a><!-- ws:end:WikiTextHeadingRule:14 -->Alternate Quartertone Accidentals</h2>
| |
| <!-- ws:start:WikiTextRemoteImageRule:1876:&lt;img src=&quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /><!-- ws:end:WikiTextRemoteImageRule:1876 --> = quarter-tone sharp or Jump<br />
| |
| ††† (the horizontal line should connect all three vertical lines) = three quarter-tones sharp or Jump-Sharp<br />
| |
| <!-- ws:start:WikiTextRemoteImageRule:1877:&lt;img src=&quot;http://www.dolmetsch.com/onequarterflat.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://www.dolmetsch.com/onequarterflat.gif" alt="external image onequarterflat.gif" title="external image onequarterflat.gif" /><!-- ws:end:WikiTextRemoteImageRule:1877 --> = quarter-tone flat or Drop<br />
| |
| <!-- ws:start:WikiTextRemoteImageRule:1878:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /><!-- ws:end:WikiTextRemoteImageRule:1878 --> = three quarter-tones flat or drop-flat<br />
| |
| For example, the scale 0-5-10-15-20 is written as C-D<!-- ws:start:WikiTextRemoteImageRule:1879:&lt;img src=&quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /><!-- ws:end:WikiTextRemoteImageRule:1879 --> (or E<!-- ws:start:WikiTextRemoteImageRule:1880:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /><!-- ws:end:WikiTextRemoteImageRule:1880 -->) F G<!-- ws:start:WikiTextRemoteImageRule:1881:&lt;img src=&quot;http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://faculty.mansfield.edu/jmurphy/oldsite/quartertonesharp.gif" alt="external image quartertonesharp.gif" title="external image quartertonesharp.gif" /><!-- ws:end:WikiTextRemoteImageRule:1881 --> (or A<!-- ws:start:WikiTextRemoteImageRule:1882:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Arabic_music_notation_half_flat.svg/9px-Arabic_music_notation_half_flat.svg.png" alt="external image 9px-Arabic_music_notation_half_flat.svg.png" title="external image 9px-Arabic_music_notation_half_flat.svg.png" /><!-- ws:end:WikiTextRemoteImageRule:1882 -->) Bb.<br />
| |
| <br />
| |
| Pros: Very easy to distinguish accidentals from one another<br />
| |
| Cons: Not practical, tends to clutter a score<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc7"><a name="Notation-And in Persian music"></a><!-- ws:end:WikiTextHeadingRule:16 --><span style="line-height: 1.5;">And in Persian music</span></h2>
| |
| <!-- ws:start:WikiTextRemoteImageRule:1883:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 25px; width: 12px;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Koron_sign.svg/200px-Koron_sign.svg.png" alt="external image 200px-Koron_sign.svg.png" title="external image 200px-Koron_sign.svg.png" style="height: 25px; width: 12px;" /><!-- ws:end:WikiTextRemoteImageRule:1883 -->Koron (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Koron_%28music%29" rel="nofollow">en</a> | <a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%DA%A9%D8%B1%D9%86" rel="nofollow">fa</a>) = quarter-tone flat or Jump<br />
| |
| <!-- ws:start:WikiTextRemoteImageRule:1884:&lt;img src=&quot;http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 25px; width: 15px;&quot; /&gt; --><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Sori_sign.svg/200px-Sori_sign.svg.png" alt="external image 200px-Sori_sign.svg.png" title="external image 200px-Sori_sign.svg.png" style="height: 25px; width: 15px;" /><!-- ws:end:WikiTextRemoteImageRule:1884 -->Sori (<a class="wiki_link_ext" href="http://fa.wikipedia.org/wiki/%D8%B3%D8%B1%DB%8C_%28%D9%85%D9%88%D8%B3%DB%8C%D9%82%DB%8C%29" rel="nofollow">fa</a>) = quarter-tone sharp or Drop<br />
| |
| <br />
| |
| Pros: Easy to read<br />
| |
| Cons: Hard to write on a computer, doesn't fit with standard notation well<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc8"><a name="Notation-Sagittal Notation"></a><!-- ws:end:WikiTextHeadingRule:18 -->Sagittal Notation</h2>
| |
| <a class="wiki_link" href="/Sagittal%20notation">Sagittal notation</a> works extremely well for 24 Edo notation as well as other systems.<br />
| |
| It's easy on the eyes, easy to recognize the various symbols and keeps a score looking tidy and neat.<br />
| |
| A possibility for the best approach would be to not use traditional sharps and flats altogether and replace them<br />
| |
| with Sagittal signs for sharp and flat.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:1870:&lt;img src=&quot;/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/sagittal%2024.PNG/500168246/sagittal%2024.PNG" alt="sagittal 24.PNG" title="sagittal 24.PNG" /><!-- ws:end:WikiTextLocalImageRule:1870 --><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc9"><a name="Interval Alterations"></a><!-- ws:end:WikiTextHeadingRule:20 -->Interval Alterations</h1>
| |
| The special alterations of the intervals and chords of 12 equal can be notated like this:<br />
| |
| <br />
| |
| Supermajor or &quot;<strong>Tendo</strong>&quot; is a major interval raised a quarter tone<br />
| |
| Subminor or &quot;<strong>Arto</strong>&quot; is a minor interval lowered a quarter tone<br />
| |
| Neutral are intervals that exist between the major and minor version of an interval<br />
| |
| The prefix <strong>under</strong> indicates a perfect interval lowered by one quarter tone<br />
| |
| The prefix <strong>over</strong> indicates a perfect interval raised by a quarter tone<br />
| |
| <br />
| |
| The Latin words &quot;tendo&quot; (meaning &quot;expand&quot;) and &quot;arto&quot; (meaning &quot;contract&quot;) can be used to replace the words &quot;supermajor&quot; and &quot;subminor&quot; in order to shorten the names of the intervals.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc10"><a name="Chord Structures"></a><!-- ws:end:WikiTextHeadingRule:22 -->Chord Structures</h1>
| |
| 24edo features a rich variety on not only new chords, but also alterations that can be used with regular 12 Edo chords. For example, an approximation of the ninth, eleventh, and thirteenth harmonic can be added to a major triad to create a sort of super-extended chord structure of a major chord: 4:5:6:9:11:13.<br />
| |
| <br />
| |
| As for entirely new chords, 24edo features many possibilities for chords. The most obvious is the neutral or mid triad 0-7-14 however there are other options such as<br />
| |
| 0-9-14 (Ultra Triad or upmajor triad) and 0-5-14 (Infra Triad or downminor triad), the chord names being based on what kind of third is in the chord.<br />
| |
| These chords though tend to lack the forcefulness to sound like resolved, tonal sonorities but can be resolved of that issue by using tetrads in place of triads.<br /> | |
| For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad. 0-14-21-35 <a class="wiki_link" href="/William%20Lynch">William Lynch</a> considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality. 24 edo also is very good at 15 limit and does 13 quite well allowing barbodos 10:13:15 and barbodos minor triad 26:30:39 to be used as an entirely new harmonic system.<br /> | |
| <br />
| |
| William Lynch considers these as some possible good tetrads:<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextLocalImageRule:1871:&lt;img src=&quot;/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/Three%20chords.PNG/489521008/Three%20chords.PNG" alt="Three chords.PNG" title="Three chords.PNG" /><!-- ws:end:WikiTextLocalImageRule:1871 --><br />
| |
| <br />
| |
|
| |
|
| | 24edo also is very good at 15 limit and does 13 quite well allowing barbados major (10:13:15) and barbodos minor (26:30:39) triads to be used as an entirely new harmonic system. |
|
| |
|
| <table class="wiki_table">
| | More good chords in 24edo: |
| <tr>
| |
| <th>Chord name<br />
| |
| </th>
| |
| <th>Degrees of 24edo<br />
| |
| </th>
| |
| <th>Chord spelling<br />
| |
| </th>
| |
| <th>Audio example<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>neutral<br />
| |
| </td>
| |
| <td>0 7 14 21<br />
| |
| </td>
| |
| <td>1 v3 5 v7<br />
| |
| </td>
| |
| <td><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/Neutral%20Tetrad%20on%20C.mp3?h=30&amp;w=200&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;Neutral Tetrad on C.mp3&amp;quot; width=&amp;quot;200&amp;quot; height=&amp;quot;30&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;30&quot; width=&quot;200&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="200" height="30" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FNeutral%252BTetrad%252Bon%252BC.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=200&height=30"></embed><!-- ws:end:WikiTextMediaRule:0 --><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>arto<br />
| |
| </td>
| |
| <td>0 5 14 20<br />
| |
| </td>
| |
| <td>1 bv3 5 b7<br />
| |
| </td>
| |
| <td><!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/arto%20tetrad%20on%20C.mp3?h=30&amp;w=200&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;arto tetrad on C.mp3&amp;quot; width=&amp;quot;200&amp;quot; height=&amp;quot;30&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;30&quot; width=&quot;200&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="200" height="30" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Farto%252Btetrad%252Bon%252BC.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=200&height=30"></embed><!-- ws:end:WikiTextMediaRule:1 --><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>tendo<br />
| |
| </td>
| |
| <td>0 9 14 19<br />
| |
| </td>
| |
| <td>1 ^3 5 bv7<br />
| |
| </td>
| |
| <td>...<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | * {{dash|0, 4, 8, 11, 14|hair}} ("major" chord with a 9:8 and a 11:8 above the root) |
| Due to convenience, the names Arto and tendo have been changed to Ultra and Infra.<br />
| | * Its inversion, {{dash|0, 3, 6, 10, 14|hair}} ("minor") |
| <br />
| | * 0-5-10 (another kind of "neutral", splitting the fourth in two. The {{dash|0, 5, 10|hair}} can be extended into a ([[Godzilla]]) pentatonic scale ({{dash|0, 5, 10, 14, 19, 24|hair}}), that is close to equi-pentatonic and also close to several Indonesian slendro scales. In a similar way {{dash|0, 7, 14|hair}} extends to {{dash|0, 4, 7, 11, 14, 18, 21, 24|hair}} ([[mohajira]]), a heptatonic scale close to several Arabic scales.) |
| <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc11"><a name="Naming Chords in 24edo"></a><!-- ws:end:WikiTextHeadingRule:24 -->Naming Chords in 24edo</h1>
| |
| Naming chords in 24edo can be achieved by adding a few things to the already [[#|existing]] set of terms that are used to name 12edo chords.<br />
| |
| They are:<br />
| |
| Super + perfect interval such as &quot;perfect fifth&quot; means to raise it by a quarter tone<br />
| |
| Sub + perfect interval means to lower a quarter tone<br />
| |
| Sharp is to raise by one half tone<br />
| |
| Flat is to raise by a half tone<br />
| |
| Neutral, arto and tendo refer to triads or tetrads<br />
| |
| Neutral, arto, or tendo + interval name of 2nd, 3rd, 6th, or 7th is to alter respectively<br />
| |
| <br />
| |
| Examples:<br />
| |
| Neutral Super Eleventh or neut^11 = C neutral 7th chord with a super 11th thrown on top<br />
| |
| Arto Sub Seventh Tendo Thirteenth or artsub7^13 = Arto tetrad with an arto seventh and a tendo thirteenth on top Minor Seventh Flat Five Arto Ninth Super Eleventh or m7b5^9^11<br />
| |
| <br />
| |
| Alternatively, <a class="wiki_link" href="/ups%20and%20downs%20notation">ups and downs notation</a> can be used. Here are the blue, green, jade, yellow and red triads:<br />
| |
|
| |
|
| | William Lynch considers these as some possible good tetrads: |
|
| |
|
| <table class="wiki_table">
| | [[File:Three_chords.PNG|alt=Three chords.PNG|Three chords.PNG]] |
| <tr>
| |
| <th>color of the 3rd<br />
| |
| </th>
| |
| <th>JI chord<br />
| |
| </th>
| |
| <th>notes as edosteps<br />
| |
| </th>
| |
| <th>notes of C chord<br />
| |
| </th>
| |
| <th>written name<br />
| |
| </th>
| |
| <th>spoken name<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">blue<br />
| |
| </td>
| |
| <td style="text-align: center;">6:7:9<br />
| |
| </td>
| |
| <td style="text-align: center;">0-5-14<br />
| |
| </td>
| |
| <td style="text-align: center;">C Ebv G<br />
| |
| </td>
| |
| <td style="text-align: center;">C.vm<br />
| |
| </td>
| |
| <td style="text-align: center;">C downminor<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">green<br />
| |
| </td>
| |
| <td style="text-align: center;">10:12:15<br />
| |
| </td>
| |
| <td style="text-align: center;">0-6-14<br />
| |
| </td>
| |
| <td style="text-align: center;">C Eb G<br />
| |
| </td>
| |
| <td style="text-align: center;">Cm<br />
| |
| </td>
| |
| <td style="text-align: center;">C minor<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">jade<br />
| |
| </td>
| |
| <td style="text-align: center;">18:22:27<br />
| |
| </td>
| |
| <td style="text-align: center;">0-7-14<br />
| |
| </td>
| |
| <td style="text-align: center;">C Ev G<br />
| |
| </td>
| |
| <td style="text-align: center;">C~<br />
| |
| </td>
| |
| <td style="text-align: center;">C mid<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">yellow<br />
| |
| </td>
| |
| <td style="text-align: center;">4:5:6<br />
| |
| </td>
| |
| <td style="text-align: center;">0-8-14<br />
| |
| </td>
| |
| <td style="text-align: center;">C E G<br />
| |
| </td>
| |
| <td style="text-align: center;">C<br />
| |
| </td>
| |
| <td style="text-align: center;">C major or C<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">red<br />
| |
| </td>
| |
| <td style="text-align: center;">14:18:27<br />
| |
| </td>
| |
| <td style="text-align: center;">0-9-14<br />
| |
| </td>
| |
| <td style="text-align: center;">C E^ G<br />
| |
| </td>
| |
| <td style="text-align: center;">C.^<br />
| |
| </td>
| |
| <td style="text-align: center;">C upmajor or C dot up<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| For a more complete list, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>.<br />
| | {| class="wikitable center-all" |
| <br />
| | |+ style="white-space: nowrap; font-size: 105%;" | Fundamental tetrads of 24edo |
| <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc12"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:26 -->Rank two temperaments</h1>
| | |- |
| <a class="wiki_link" href="/List%20of%2024et%20rank%20two%20temperaments%20by%20badness">List of 24et rank two temperaments by badness</a><br />
| | ! Degrees of 24edo |
| <a class="wiki_link" href="/List%20of%20edo-distinct%2024et%20rank%20two%20temperaments">List of edo-distinct 24et rank two temperaments</a><br />
| | ! Chord spelling |
| <br />
| | ! Notes of C chord |
| | ! Written name |
| | ! Spoken name |
| | ! Audio example |
| | |- |
| | | {{dash|0, 5, 14, 19|hair}} |
| | | {{dash|1, vb3, 5, vb7|hair}} |
| | | {{dash|C, E{{sesquiflat2}}, G, B{{sesquiflat2}}|hair}} |
| | | smin7<br>min7({{demiflat2}}3, {{demiflat2}}7) |
| | | Inframinor seven<br>Minor seven semiflat-three semiflat-seven |
| | |- |
| | | {{dash|0, 6, 14, 20|hair}} |
| | | {{dash|1, b3, 5, b7|hair}} |
| | | {{dash|C, E♭, G, B♭|hair}} |
| | | m7, min7 |
| | | Minor seven |
| | |- |
| | | {{dash|0, 7, 14, 21|hair}} |
| | | {{dash|1, v3, 5, v7|hair}} |
| | | {{dash|C, E{{demiflat2}}, G, B{{demiflat2}}|hair}} |
| | | n7, neu7 |
| | | Neutral seven |
| | | [[File:Neutral Tetrad on C.mp3]] |
| | |- |
| | | {{dash|0, 8, 14, 22|hair}} |
| | | {{dash|1, b3, 5, b7|hair}} |
| | | {{dash|C, E, G, B|hair}} |
| | | maj7 |
| | | Major seven |
| | |- |
| | | {{dash|0, 8, 14, 22|hair}} |
| | | {{dash|1, b3, 5, b7|hair}} |
| | | {{dash|C, E{{demisharp2}}, G, B{{demisharp2}}|hair}} |
| | | smaj7<br>maj7({{demisharp2}}3, {{demisharp2}}7) |
| | | Ultramajor seven<br>Major seven semisharp-three semisharp-seven |
| | |- |
| | | {{dash|0, 8, 14, 20|hair}} |
| | | {{dash|1, 3, 5, b7|hair}} |
| | | {{dash|C, E, G, B♭|hair}} |
| | | 7, dom7 |
| | | Dominant seven |
| | |- |
| | | {{dash|0, 8, 14, 19|hair}} |
| | | {{dash|1, 3, 5, vb7|hair}} |
| | | {{dash|C, E, G, B{{sesquiflat2}}|hair}} |
| | | h7<br>7({{demiflat2}}7) |
| | | Harmonic seven<br>Dominant 7 semiflat-seven |
| | |- |
| | | {{dash|0, 5, 14, 20|hair}} |
| | | {{dash|1, vb3, 5, b7|hair}} |
| | | {{dash|C, E{{sesquiflat2}}, G, B♭|hair}} |
| | | min7({{demiflat2}}3) |
| | | Arto<br>Minor seven semiflat-three |
| | | [[File:arto tetrad on C.mp3]] |
| | |- |
| | | {{dash|0, 9, 14, 19|hair}} |
| | | {{dash|1, ^3, 5, vb7|hair}} |
| | | {{dash|C, E{{demisharp2}}, G, B{{sesquiflat2}}|hair}} |
| | | h7({{demisharp2}}3)<br>7({{demisharp2}}3, {{demiflat2}}7) |
| | | Tendo<br>Harmonic seven semisharp-three<br>Dominant seven semisharp-three semiflat-seven |
| | | |
| | |} |
|
| |
|
| | The tendo chord can also be spelled {{nowrap|1 ^3 5 ^6}}. Due to convenience, the names Arto and tendo have been changed to Ultra and Infra. |
|
| |
|
| <table class="wiki_table">
| | == Counterpoint == |
| <tr>
| | 24edo is the first edo to have both a [[sqrt(25/24)]] distinct from [[25/24]] and a correct [[5-odd-limit]]. It is thus the first edo which allows to lead the two voices of a major third to a minor third by [[strict contrary motion]]. And vice versa. |
| <th>Periods per octave<br />
| |
| </th>
| |
| <th>Generator<br />
| |
| </th>
| |
| <th>Name<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>1\24<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>5\24<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Semaphore%20and%20Godzilla">Semaphore/godzilla</a> / <a class="wiki_link" href="/Chromatic%20pairs#Bridgetown">Bridgetown</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>7\24<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Mohajira">Mohajira</a> (or <a class="wiki_link" href="/maqamic">maqamic</a> with 24d val)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>11\24<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>1\24<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Shrutar">Shrutar</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>5\24<br />
| |
| </td>
| |
| <td>Similar to <a class="wiki_link" href="/decimal">decimal</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>1\24<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Semiaug">Semiaug</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>3\24<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Triforce">Triforce</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>1\24<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td>1\24<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
| |
| </td>
| |
| <td>1\24<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12<br />
| |
| </td>
| |
| <td>1\24<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/Catler">Catler</a><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | Furthermore, in the same fashion, every sequence of intervals available in 12edo are reachable by equal contrary motion in 24edo. |
| <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc13"><a name="Scales / Modes"></a><!-- ws:end:WikiTextHeadingRule:28 -->Scales / Modes</h1>
| | [[File:Strict-contrary-motion-24edo.png|left|frame|Every sequence of 12edo intervals are reachable by strict contrary motion in 24edo. [[File:24-EDO_Contrary_Motion.flac]]]] {{clear}} |
| <br />
| |
|
| |
|
| | == Instruments == |
| | The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This [[Microtonal_Keyboards#twelvenoteoctavescales|"12 note octave scales"]] approach is used in a wide part of the existing literature—see below. |
|
| |
|
| <table class="wiki_table">
| | === Guitar === |
| <tr>
| | Adam Hoey Xen ([https://www.youtube.com/@adamhoeyxen2199/videos on YouTube]) has used a "neutral thirds tuning" of F#-At-C#-Et-G#-Bt on a standard guitar to play in quartertones. |
| <td colspan="2"><!-- ws:start:WikiTextHeadingRule:30:&lt;h4&gt; --><h4 id="toc14"><a name="Scales / Modes---Pentatonic:"></a><!-- ws:end:WikiTextHeadingRule:30 -->Pentatonic:</h4>
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>2 8 3 6 5</strong></tt><br />
| |
| </td>
| |
| <td>Anchihoye: Ethiopia<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>5 5 4 5 5</strong></tt><br />
| |
| </td>
| |
| <td>Quasi-equal Pentatonic - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%201s">4L 1s (bug)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>5 5 5 5 4</strong></tt><br />
| |
| </td>
| |
| <td>Hába's Pentatonic - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%201s">4L 1s (bug)</a><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | Guitars with 24 frets per octave are also an option, although only [https://eastwoodguitars.com/products/hi-flier-edo-24-electric-microtonal-guitar Eastwood] offer this as a standard production model at the time of writing. Other luthiers you can commission custom microtonal instruments from, including 24edo ones, include [https://www.etsy.com/uk/listing/1154683769 JLJ instruments] and [https://meantoneguitar.com Meantone Guitar]. |
|
| |
|
| | [[File:24edo_guitar.jpg|500px]] |
|
| |
|
| <table class="wiki_table">
| | While these are playable, the extra frets can make playing chords and navigating the fretboard significantly more challenging for [[12edo]] chords and scales. |
| <tr>
| |
| <td colspan="2"><!-- ws:start:WikiTextHeadingRule:32:&lt;h4&gt; --><h4 id="toc15"><a name="Scales / Modes---Hexatonic:"></a><!-- ws:end:WikiTextHeadingRule:32 -->Hexatonic:</h4>
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>1 1 8 4 2 8</strong></tt><br />
| |
| </td>
| |
| <td>Spondeiakos<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br /> | | More common is the "Sazocaster" tuning popularised by Australian band [[King Gizzard & the Lizard Wizard]], which adds quarter tones between approximately half the regular frets. Multiple guitar makers, including [https://eastwoodguitars.com/products/sg2c-flying-banana-mt Eastwood] and [https://salamuzik.com/collections/guitar/products/professional-microtonal-electric-classical-guitar-with-equalizer-kg-5 Sala Muzik] have produced Sazocaster variations. |
|
| |
|
| | [[File:Eastwood-guitars-phase-4-mt-2307179.jpg|500px]] |
|
| |
|
| <table class="wiki_table">
| | It is also possible to create a guitar that has quartertones on all the lower frets, then switches to regular 12edo at some point on the neck to keep the upper notes easily acessible, as demonstrated by the band [[Angine de Poitrine]]. Guitars using this layout are available at [https://www.microtonalguitar.org/product-page/angine-de-poitrine-style-fixed-microtonal-electric-guitar-ap24 microtonalguitar.org] and doubleneck guitar/basses are available from [https://eastwoodguitars.com/products/eastwood-microtonal-doubleneck-electric-guitar-bass Eastwood]. |
| <tr>
| |
| <td colspan="2"><!-- ws:start:WikiTextHeadingRule:34:&lt;h4&gt; --><h4 id="toc16"><a name="Scales / Modes---Heptatonic:"></a><!-- ws:end:WikiTextHeadingRule:34 -->Heptatonic:</h4>
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>1 1 8 1 1 8 4</strong></tt><br />
| |
| </td>
| |
| <td>Enharmonic Mixolydian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>1 8 1 1 8 4 1</strong></tt><br />
| |
| </td>
| |
| <td>Enharmonic Lydian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>8 1 1 8 4 1 1</strong></tt><br />
| |
| </td>
| |
| <td>Enharmonic Phrygian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>1 1 8 4 1 1 8</strong></tt><br />
| |
| </td>
| |
| <td>Enharmonic Dorian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>1 8 4 1 1 8 1</strong></tt><br />
| |
| </td>
| |
| <td>Enharmonic Hypolydian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>8 4 1 1 8 1 1</strong></tt><br />
| |
| </td>
| |
| <td>Enharmonic Hypophrygian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 1 1 8 1 1 8</strong></tt><br />
| |
| </td>
| |
| <td>Enharmonic Hypodorian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>2 3 5 2 3 5 4</strong></tt><br />
| |
| </td>
| |
| <td>Soft Diatonic Mixolydian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 5 2 3 5 4 2</strong></tt><br />
| |
| </td>
| |
| <td>Soft Diatonic Lydian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>5 2 3 5 4 2 3</strong></tt><br />
| |
| </td>
| |
| <td>Soft Diatonic Phrygian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>2 3 5 4 2 3 5</strong></tt><br />
| |
| </td>
| |
| <td>Soft Diatonic Dorian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 5 4 2 3 5 2</strong></tt><br />
| |
| </td>
| |
| <td>Soft Diatonic Hypolydian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>5 4 2 3 5 2 3</strong></tt><br />
| |
| </td>
| |
| <td>Soft Diatonic Hypophrygian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 2 3 5 2 3 5</strong></tt><br />
| |
| </td>
| |
| <td>Soft Diatonic Hypodorian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 3 4 3 3 4 4</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Ouchairan-Hussaini, Bayatan, Neutral Diatonic Mixolydian - <a class="wiki_link" href="/MODMOS%20Scales">MODMOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 4 3 3 4 4 3</strong></tt><br />
| |
| </td>
| |
| <td>Dastgah-e Sehgah, Neutral Diatonic Lydian - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MODMOS%20Scales">MODMOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 3 3 4 4 3 3</strong></tt><br />
| |
| </td>
| |
| <td>Arabic Diatonic, Maqam Rast, Quasi-equal Heptatonic, Neutral Diatonic Phrygian - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MODMOS%20Scales">MODMOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 3 4 4 3 3 4</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Hussaini, Ushaq, Neutral Diatonic Dorian - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MODMOS%20Scales">MODMOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 4 4 3 3 4 3</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Sikah (Segah), Neutral Diatonic Hypolydian - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MODMOS%20Scales">MODMOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 4 3 3 4 3 3</strong></tt><br />
| |
| </td>
| |
| <td>Neutral Diatonic Hypophrygian - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MODMOS%20Scales">MODMOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 3 3 4 3 3 4</strong></tt><br />
| |
| </td>
| |
| <td>Miha'il Musaqa's mode: Egypt, Neutral Diatonic Hypodorian, Dastgah-e Sehgah, Maqam Nairuz - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MODMOS%20Scales">MODMOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>1 5 4 1 5 4 4</strong></tt><br />
| |
| </td>
| |
| <td>Diatonic + Enharmonic Diesis Mixolydian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>5 4 1 5 4 4 1</strong></tt><br />
| |
| </td>
| |
| <td>Diatonic + Enharmonic Diesis Lydian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 1 5 4 4 1 5</strong></tt><br />
| |
| </td>
| |
| <td>Diatonic + Enharmonic Diesis Phrygian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>1 5 4 4 1 5 4</strong></tt><br />
| |
| </td>
| |
| <td>Diatonic + Enharmonic Diesis Dorian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>5 4 4 1 5 4 1</strong></tt><br />
| |
| </td>
| |
| <td>Diatonic + Enharmonic Diesis Hypolydian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 4 1 5 4 1 5</strong></tt><br />
| |
| </td>
| |
| <td>Diatonic + Enharmonic Diesis Hypophrygian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 1 5 4 1 5 4</strong></tt><br />
| |
| </td>
| |
| <td>Diatonic + Enharmonic Diesis Hypodorian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>1 3 6 1 3 6 4</strong></tt><br />
| |
| </td>
| |
| <td>Chromatic/Enharmonic Mixolydian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 6 1 3 6 4 1</strong></tt><br />
| |
| </td>
| |
| <td>Chromatic/Enharmonic Lydian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>6 1 3 6 4 1 3</strong></tt><br />
| |
| </td>
| |
| <td>Chromatic/Enharmonic Phrygian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>1 3 6 4 1 3 6</strong></tt><br />
| |
| </td>
| |
| <td>Chromatic/Enharmonic Dorian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 6 4 1 3 6 1</strong></tt><br />
| |
| </td>
| |
| <td>Chromatic/Enharmonic Hypolydian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>6 4 1 3 6 1 3</strong></tt><br />
| |
| </td>
| |
| <td>Chromatic/Enharmonic Hypophrygian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 1 3 6 1 3 6</strong></tt><br />
| |
| </td>
| |
| <td>Chromatic/Enharmonic Hypodorian<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 4 3 3 4 3 4</strong></tt><br />
| |
| </td>
| |
| <td>Neutral Mixolydian - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 3 3 4 3 4 3</strong></tt><br />
| |
| </td>
| |
| <td>Neutral Lydian - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 3 4 3 4 3 4</strong></tt><br />
| |
| </td>
| |
| <td>Neutral Phrygian - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 4 3 4 3 4 3</strong></tt><br />
| |
| </td>
| |
| <td>Neutral Dorian, Misaelides 2nd Byzantine mode, Maqam Sikah Baladi - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 3 4 3 4 3 3</strong></tt><br />
| |
| </td>
| |
| <td>Neutral Hypolydian - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 4 3 4 3 3 4</strong></tt><br />
| |
| </td>
| |
| <td>Neutral Hypophrygian - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 3 4 3 3 4 3</strong></tt><br />
| |
| </td>
| |
| <td>Neutral Hypodorian - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%204s">3L 4s (mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 5 2 4 3 5 2</strong></tt><br />
| |
| </td>
| |
| <td>Athanasopoulos' Byzantine Liturgical Chromatic, Dastgah-e Chahargah<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 2 4 4 3 3 4</strong></tt><br />
| |
| </td>
| |
| <td>Dastgah-e Nava, Maqam Ushaq Masri<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>2 7 1 4 2 7 1</strong></tt><br />
| |
| </td>
| |
| <td>Second plagal Byzantine Liturgical mode<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 3 4 4 2 4 4</strong></tt><br />
| |
| </td>
| |
| <td>Maqam 'Ushshaq Turki, Urfa, Isfahan, Dastgah-e Shur<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 3 4 4 4 2 4</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Nahfat<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 3 2 6 2 4 4</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Saba<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 3 2 6 2 6 2</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Sabr Jadid<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 3 3 4 2 6 2</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Suznak (Soznak)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 3 3 4 4 4 2</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Mahur<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 3 4 2 6 2 4</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Qarjighar, Bayati Shuri<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 4 2 6 2 4 3</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Hizam (Huzam, El Houzam), Rahat al Arouah<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>2 4 4 4 3 3 4</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Nawa<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>2 5 3 4 2 5 3</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Higaz-kar<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 4 4 2 4 4 3</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Su'ar, Naghmeh Abuata, Naghmeh Afshari<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 4 2 4 4 3 3</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Jahargah (Jiharkah), Naghmeh Bayat-e Tork, Naghmeh Dashti<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 5 2 4 2 4 4</strong></tt><br />
| |
| </td>
| |
| <td>Dastgah-e Homayun<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 2 4 4 3 5 2</strong></tt><br />
| |
| </td>
| |
| <td>Naghmeh Esfahan<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 6 1 5 2 6 1</strong></tt><br />
| |
| </td>
| |
| <td>Maqam 'Awg 'ara (Aug-ara)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 1 5 4 2 6 2</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Buselik<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 2 6 2 2 5 3</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Neuter<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 3 3 4 4 2 4</strong></tt><br />
| |
| </td>
| |
| <td>Dance scale of Yi people: China<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 4 2 3 1 4 6</strong></tt><br />
| |
| </td>
| |
| <td>Daniel-mode of Spanish-Arab Jews<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | === Harp, Harpsichord, and Piano === |
|
| |
|
| | ==== Scordatura tuning of 12edo instruments ==== |
|
| |
|
| <table class="wiki_table">
| | Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called [[Iceface tuning]]. Iceface tuning is one type of scordatura piano (or other keyboard instrument) tuning. A simpler version of this (fewer notes retuned) is demonstrated in [https://www.youtube.com/watch?v=KS-mmj5kuxw ''when it blooms (24edo)''] (2021). A more complex type of [[Wikipedia:scordatura|scordatura]] tuning was required for a performance of Charles Ives' 4th Symphony which calls for a quarter-tone piano, but for which no quarter-tone piano was available, as described by Thomas Broadhead in [https://www.youtube.com/watch?v=T1G2XFVtnXU this video]. For this composition the gamut of notes needed would not be met using a simple transformation such as Iceface. |
| <tr>
| |
| <td colspan="2"><!-- ws:start:WikiTextHeadingRule:36:&lt;h4&gt; --><h4 id="toc17"><a name="Scales / Modes---Octatonic:"></a><!-- ws:end:WikiTextHeadingRule:36 -->Octatonic:</h4>
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 3 3 3 3 3 3 3</strong></tt><br />
| |
| </td>
| |
| <td>8-equal, Wyschnegradsky's octatonic<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 3 4 4 2 1 3 4</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Bayati<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 3 2 6 2 4 2 2</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Saba<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 3 1 2 4 4 2 4</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Suzidil 'ara<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 3 2 2 4 3 3 4</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Mansuri<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 3 3 4 4 2 1 3</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Rast, Dilkashidah, Dilnishin<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 4 2 6 2 4 2 1</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Rahat al-Arwah<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 4 3 3 4 4 2 1</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Iraq<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>2 6 2 4 2 1 3 4</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Hijaz<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 4 4 2 1 3 4 3</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Musta'ar<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 4 4 4 2 4 2 1</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Farahnak<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 4 3 3 2 6 2 1</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Bastanikar, Tarz Nuin<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 2 6 2 4 2 1 3</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Farah Faza, Maqam Nakriz<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 1 2 4 4 2 4 4</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Jabburi<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>1 4 4 2 4 4 4 1</strong></tt><br />
| |
| </td>
| |
| <td>Giancarlo Dalmonte's new quarter-tone scale (see <a class="wiki_link_ext" href="http://www.ottavanota.info/" rel="nofollow">http://www.ottavanota.info</a>)<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | Although no recording using the above tuning is currently legally freely available, [[Paweł Mykietyn]] has used a similar idea with harp and harpsichord. A score video of this is available as [https://www.youtube.com/watch?v=_7o0uwPrYas ''Klave for Microtonal Harpsichord and Chamber Orchestra (Score-Video)''] (2004, performed by Elżbieta Chojnacka with Marek Moś conducting the AUKSO chamber orchestra of the city of Tychy, uploaded by Quinone Bob with permission from Paweł Mykietyn); the video starts with slides explaining the scordatura tuning of each manual of the Revival harpsichord (with each manual having a different scordatura tuning), followed by the scordatura tuning of the harp. |
|
| |
|
| | ==== Quarter-tone instruments ==== |
|
| |
|
| <table class="wiki_table">
| | A very small number of quarter-tone pianos have been built — here are a couple of videos of these instruments being tested/played experimentally (to demonstrate their capabilities rather than to play specific compositions that would qualify for the 24edo Music section): |
| <tr>
| |
| <td colspan="2"><!-- ws:start:WikiTextHeadingRule:38:&lt;h4&gt; --><h4 id="toc18"><a name="Scales / Modes---Enneatonic:"></a><!-- ws:end:WikiTextHeadingRule:38 -->Enneatonic:</h4>
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>1 2 3 4 4 1 2 3 4</strong></tt><br />
| |
| </td>
| |
| <td>Progressive Enneatonic<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 1 4 1 4 1 4 1 4</strong></tt><br />
| |
| </td>
| |
| <td>de Vries 9-tone - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/5L%204s">5L 4s (unfair bug)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 4 2 2 2 2 2 4 3</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Huzam<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 4 2 1 3 2 2 4 2</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Shawq Afza<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | ; Quarter-tone grand piano, Czech Museum of Music (this piano is essentially two stacked grand pianos, and as such is massive, in order to avoid sacrificing strings per note) |
| | * [https://www.youtube.com/shorts/Ieqi54XE2lI Demonstration short video by Nahre Sol] (2024) |
|
| |
|
| | ; Quarter-tone upright piano, Academy of Music in Prague (Czech Republic) (this piano apparently sacrificed number of strings per note in order to be able to fit into a reasonable amount of space) |
| | * [https://www.youtube.com/watch?v=PdP4epQIUrU Demonstration video by Steve Cohn] (2011) |
|
| |
|
| <table class="wiki_table">
| | === Electronic Keyboards === |
| <tr>
| |
| <td colspan="2"><!-- ws:start:WikiTextHeadingRule:40:&lt;h4&gt; --><h4 id="toc19"><a name="Scales / Modes---Decatonic:"></a><!-- ws:end:WikiTextHeadingRule:40 -->Decatonic:</h4>
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>3 1 3 3 3 1 3 3 1 3</strong></tt><br />
| |
| </td>
| |
| <td>Breed Decatonic - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%203s">7L 3s (unfair mosh)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>2 3 2 2 3 2 3 2 2 3</strong></tt><br />
| |
| </td>
| |
| <td>Oljare Decatonic - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%206s">4L 6s (fair bicycle)</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>2 1 3 2 2 4 2 4 2 2</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Shawq Tarab<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 2 1 3 2 2 4 2 1 3</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Basandida<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 3 1 2 1 3 4 2 1 3</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Yakah<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | 24edo can also be played on the Lumatone, with better ergonomics than the quarter-tone pianos noted above: see [[Lumatone mapping for 24edo]] |
|
| |
|
| | === Flute === |
| | Likewise, some flutes have been built by Eva Kingma — here is a video exploring the capabilities of these, intermixed with regular 12edo playing: |
|
| |
|
| <table class="wiki_table">
| | ; Quarter-tone flute, made by Eva Kingma |
| <tr>
| | * [https://www.youtube.com/watch?v=F3GD0Omr4Z0 Visit to the workshop of Eva Kingma, followed by test by Manuel Luis Cochofel] (2010) (demonstration of fingering starts at 06:56) |
| <td colspan="2"><!-- ws:start:WikiTextHeadingRule:42:&lt;h4&gt; --><h4 id="toc20"><a name="Scales / Modes---Hendecatonic:"></a><!-- ws:end:WikiTextHeadingRule:42 -->Hendecatonic:</h4>
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>4 2 1 3 2 2 2 2 3 1 2</strong></tt><br />
| |
| </td>
| |
| <td>Maqam Hayyan<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br /> | | === Brass === |
| | Since the trombone is a free-pitched instrument, playing quartertones, or any other edo simply requires increased precision in moving the slide. If you want a brass instrument with fixed steps, [https://www.a-courtois.com/en/instruments/trompettes-2/t-o-m-a Courtois] and [https://www.vanlaartrumpets.nl/en/trumpets/quartertone Van Laar] both produce trumpets with an additional valve that enable you to easily play quartertones. In addition, {{W|Renold Schilke|Schilke Music Products Incorporated}} built quartertone trumpets (model B5), as shown in All Things Brass And Technology's [https://www.youtube.com/watch?v=1ip0lOlQ2Xo&list=WL&index=257 ''Schilke B5 Quartertone Trumpet from 1971''] (2023). |
|
| |
|
| | == Music == |
| | {{Wikipedia|List of quarter tone pieces}} |
| | {{Main|{{ROOTPAGENAME}}/Music}}{{clear}} |
|
| |
|
| <table class="wiki_table">
| | == Further reading == |
| <tr>
| | * Ellis, Don. ''[https://archive.org/details/don-ellis-quarter-tones/ Quarter Tones: A Text with Musical Examples, Exercises and Etudes]''. 1975. |
| <td colspan="2"><!-- ws:start:WikiTextHeadingRule:44:&lt;h4&gt; --><h4 id="toc21"><a name="Scales / Modes---Tridecatonic:"></a><!-- ws:end:WikiTextHeadingRule:44 -->Tridecatonic:</h4>
| | * [[Sword, Ron]]. ''[http://www.metatonalmusic.com/books.html Icosikaitetraphonic Scales for Guitar: Theory and Scales for Twenty-four Equal Divisions of the Octave]''. 2009. (Features a practical approach to understanding the tuning, and over 550 scale examples on nine-string finger board charts, which allows for both symmetrical tuning visualization and standard guitar tuning- helpful for bassists and large range guitarists as well. Includes MOS, DE, and *all* the scales/modes from the list above.) |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>1 2 2 2 2 2 2 1 2 2 2 2 2</strong></tt><br />
| |
| </td>
| |
| <td>de Vries 13-tone - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/11L%202s">11L 2s</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt><strong>2 2 2 2 2 1 2 2 2 2 2 2 1</strong></tt><br />
| |
| </td>
| |
| <td>Agmon Diatonic DS5, Ivan Wyschnegradsky's diatonicized chromatic scale - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/11L%202s">11L 2s</a><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | == See also == |
| | * [[Equal-step tuning|Equal multiplications]] of MIDI-resolution units |
| | ** [[48edo]] (2mu tuning) |
| | ** [[96edo]] (3mu tuning) |
| | ** [[192edo]] (4mu tuning) |
| | ** [[384edo]] (5mu tuning) |
| | ** [[768edo]] (6mu tuning) |
| | ** [[1536edo]] (7mu tuning) |
| | ** [[3072edo]] (8mu tuning) |
| | ** [[6144edo]] (9mu tuning) |
| | ** [[12288edo]] (10mu tuning) |
| | ** [[24576edo]] (11mu tuning) |
| | ** [[49152edo]] (12mu tuning) |
| | ** [[98304edo]] (13mu tuning) |
| | ** [[196608edo]] (14mu tuning) |
|
| |
|
| | == External links == |
| | * [http://tonalsoft.com/enc/q/quarter-tone.aspx quarter-tone / 24-edo / 24-ed2] [https://www.webcitation.org/5xeFMH6cd Permalink] on [[Tonalsoft Encyclopedia]] |
| | * [http://www.96edo.com/24_EDO.html About 24-EDO] [https://www.webcitation.org/5xeFBNdQW Permalink] by Shaahin Mohajeri |
| | * [https://docs.google.com/file/d/0Bzrl-iLY6DeEVkl1VjBGdEJlOTg/edit Notation and Chord Names for 24-EDO] by William Lynch |
| | * [http://www.tonalsoft.com/sonic-arts/darreg/dar8.htm The place of QUARTERTONES in Today's Xenharmonics] by [[Ivor Darreg]] |
| | * [http://tonalsoft.com/enc/q/quarter-tone.aspx Tonalsoft Encyclopedia | ''quarter-tone / 24-edo / 24-ed2''] |
|
| |
|
| <table class="wiki_table">
| | {{Todo| cleanup }} |
| <tr>
| |
| <td colspan="2"><!-- ws:start:WikiTextHeadingRule:46:&lt;h4&gt; --><h4 id="toc22"><a name="Scales / Modes---Tetradecatonic:"></a><!-- ws:end:WikiTextHeadingRule:46 -->Tetradecatonic:</h4>
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><strong><span style="font-family: monospace;">2 2 1 2 2 2 1 2 2 1 2 2 2 1</span></strong><br />
| |
| </td>
| |
| <td>Young Half-Octave Diatonic - <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/10L%204s">10L 4s</a><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | [[Category:Semaphore]] |
| <!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc23"><a name="Instruments"></a><!-- ws:end:WikiTextHeadingRule:48 -->Instruments<!-- ws:start:WikiTextAnchorRule:91:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@instruments&quot; title=&quot;Anchor: instruments&quot;/&gt; --><a name="instruments"></a><!-- ws:end:WikiTextAnchorRule:91 --></h1>
| | [[Category:Godzilla]] |
| The ever-arising question in microtonal music, how to play it on instruments designed for 12edo, has a relatively simple answer in the case of 24edo: use two standard instruments tuned a quartertone apart. This <a class="wiki_link" href="/Microtonal%20Keyboards#twelvenoteoctavescales">&quot;12 note octave scales&quot;</a> approach is used in a wide part of the existing literature - see below.<br />
| | [[Category:Meantone]] |
| <!-- ws:start:WikiTextRemoteImageRule:1885:&lt;img src=&quot;http://www.swordguitars.com/Sword_quartertone_stratsm.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 195px; width: 406px;&quot; /&gt; --><img src="http://www.swordguitars.com/Sword_quartertone_stratsm.jpg" alt="external image Sword_quartertone_stratsm.jpg" title="external image Sword_quartertone_stratsm.jpg" style="height: 195px; width: 406px;" /><!-- ws:end:WikiTextRemoteImageRule:1885 -->24-tone &quot;1/4-tone&quot; Guitar by Ron Sword / Sword guitars<br />
| | [[Category:Quartertone]] |
| <br />
| | [[Category:Quartismic]] |
| Hidekazu Wakabayashi tuned a piano and harp to where the normal sharps and flats are tuned 50 cents higher in which he called <a class="wiki_link" href="/Iceface%20Tuning">Iceface tuning</a>.<br />
| | [[Category:Subgroup temperaments]] |
| <br />
| | [[Category:Twentuning]] |
| <!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc24"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:50 -->Compositions</h1>
| |
| <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc25"><a name="Compositions-Music"></a><!-- ws:end:WikiTextHeadingRule:52 -->Music</h2>
| |
| <span class="ymp-btn-page-play ymp-media-eb56a917c62000140296c2e1a6d89911"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex3.mp3" rel="nofollow">Microhex3</a></span> <span class="ymp-btn-page-play ymp-media-750620955011dabb8bc98c7c8830cbb8"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex4.mp3" rel="nofollow">Microhex4</a></span> and <span class="ymp-btn-page-play ymp-media-4aeb7c299c23983ba8081a591562e704"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Microhex5.mp3" rel="nofollow">Microhex5</a></span> by <a class="wiki_link_ext" href="http://www.96edo.com/About_me.html" rel="nofollow">Shaahin Mohajeri</a><br />
| |
| <span class="ymp-btn-page-play ymp-media-30832be5610668b4b42451c8ce82dc80"><a class="wiki_link_ext" href="http://micro.soonlabel.com/24et/quarterpicnic.mp3" rel="nofollow">Quarterpicnic</a></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/BeDell/Quarter%20Tone%20Prelude%20for%20two%20Harps.mp3" rel="nofollow">Quarter Tone Prelude For Two Harps</a> by <a class="wiki_link_ext" href="http://soundcloud.com/cerbeus-1/quarter-tone-prelude-for-two" rel="nofollow">Nathan BeDell</a><br />
| |
| <span class="ymp-btn-page-play ymp-media-2738730931ba168a7364a84b5417488d"><a class="wiki_link_ext" href="http://micro.soonlabel.com/24et/daily20111021-fretless-1.mp3" rel="nofollow">Fretless Chrome 1</a></span> and <span class="ymp-btn-page-play ymp-media-d35cb71128e927701930058ebd16b778"><a class="wiki_link_ext" href="http://micro.soonlabel.com/24et/daily20111021-fretless-2.mp3" rel="nofollow">Fretless Chrome 2</a></span> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1477" rel="nofollow" target="_blank">Chris Vaisvil</a><br />
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lament.mp3" rel="nofollow">Lament</a> by <a class="wiki_link_ext" href="http://soundcloud.com/jdfreivald/lament" rel="nofollow">Jake Freivald</a>. In the <a class="wiki_link" href="/freivaldneutral24">freivaldneutral24</a> scale.<br />
| |
| <a class="wiki_link_ext" href="https://soundcloud.com/jdfreivald/mo-happy-happy" rel="nofollow">Mo - Happy - Happy</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3" rel="nofollow">play</a> by Jake Freivald in Neuter[7] (2.3.11 mohajira), 24et tuning<br />
| |
| <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=q1Lp8AtKK9o" rel="nofollow">Autumn Winds</a>, <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=Igxe3DwbFJ4&amp;feature=c4-overview&amp;list=UUvq5bg-LvOS6adpB5efPTyQ" rel="nofollow">Easter Time at Nine</a>, <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=z_3uhA9Cq08&amp;list=UUvq5bg-LvOS6adpB5efPTyQ" rel="nofollow">Waters of Persia</a> by William Lynch in mohajira, 24et tuning.<br />
| |
| <a class="wiki_link_ext" href="https://soundcloud.com/mason-l-green/serena" rel="nofollow">Serena</a>, by Mason Green (intro and coda in 24edo, the rest is in 12edo)<br />
| |
| <a class="wiki_link_ext" href="https://www.youtube.com/watch?v=yzvXEMYgHCY" rel="nofollow">Autumn Girl</a>, by Mason Green<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc26"><a name="Compositions-About"></a><!-- ws:end:WikiTextHeadingRule:54 -->About</h2>
| |
| &quot;Prométhée enchaîné&quot; by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Fromental_Hal%C3%A9vy" rel="nofollow">Fromental Halévy</a> (considered the first mainstream western orchestral composition to use quarter tones.)<br />
| |
| &quot;3 Hommages&quot; by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Georg_Friedrich_Haas" rel="nofollow">Georg Friedrich Haas</a><br />
| |
| <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/List_of_quarter_tone_pieces" rel="nofollow">List of quartertone pieces on Wikipedia</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:56:&lt;h1&gt; --><h1 id="toc27"><a name="Practical Theory / Books"></a><!-- ws:end:WikiTextHeadingRule:56 -->Practical Theory / Books</h1>
| |
| <br />
| |
| <!-- ws:start:WikiTextRemoteImageRule:1886:&lt;img src=&quot;http://ronsword.com/images/24_tet_Coversm.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 236px; width: 179px;&quot; /&gt; --><img src="http://ronsword.com/images/24_tet_Coversm.jpg" alt="external image 24_tet_Coversm.jpg" title="external image 24_tet_Coversm.jpg" style="height: 236px; width: 179px;" /><!-- ws:end:WikiTextRemoteImageRule:1886 --><strong>&quot;Icosakaiteraphonic Scales for Guitar&quot;</strong> - A Book for Twenty-Four Equal Divisions of the Octave on guitar, or 'Quarter-tones'. Features a practical approach to understanding the tuning, and over 550 Scale Examples on Nine-String finger board charts, which allows for both symmetrical tuning visualization and standard guitar tuning- helpful for bassists and large range guitarists as well. Includes MOS, DE, and *all* the Scales / Modes from the list above.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc28"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:58 -->External links</h1>
| |
| <a class="wiki_link_ext" href="http://tonalsoft.com/enc/q/quarter-tone.aspx" rel="nofollow">quarter-tone / 24-edo - Encyclopedia of Microtonal Music Theory</a> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeFMH6cd" rel="nofollow">Permalink</a><br />
| |
| <a class="wiki_link_ext" href="http://www.96edo.com/24_EDO.html" rel="nofollow">About 24-EDO</a> by Shaahin Mohajeri <a class="wiki_link_ext" href="http://www.webcitation.org/5xeFBNdQW" rel="nofollow">Permalink</a><br />
| |
| <a class="wiki_link_ext" href="https://docs.google.com/file/d/0Bzrl-iLY6DeEVkl1VjBGdEJlOTg/edit" rel="nofollow">Notation and Chord Names for 24-EDO</a> by William Lynch<br />
| |
| <a class="wiki_link_ext" href="http://sonic-arts.org/darreg/contents.htm" rel="nofollow">The place of QUARTERTONES in Today's Xenharmonics</a> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> <a class="wiki_link_ext" href="http://sonic-arts.org/darreg/dar8.htm" rel="nofollow">Permalink</a></body></html></pre></div>
| |