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{{Interwiki
| de =
| en = Dyadic chord
| es = Relación diádica
| ja =
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{{Distinguish| Dyad }}
{{Distinguish| Dyad }}


A '''dyadic chord''' is a [[chord]] each of whose [[interval]]s belongs to a specified set of intervals considered to be [[Consonance and dissonance|consonant]]; it is therefore relative to the set of intervals in question. Such a chord may also be described as ''dyadically'' or ''pairwise consonant''.  
A '''dyadic chord''', also described as a ''dyadically consonant chord'' or ''pairwise consonant chord'', is a [[chord]] each of whose [[interval]]s belongs to a specified set of intervals considered to be [[consonance and dissonance|consonant]]; it is therefore relative to the set of intervals in question.  


For example, the [[tetrad]]
For example, the [[tetrad]]
* 1-6/5-7/5-8/5
* 1 – 6/5 – 7/5 – 8/5


is a dyadic chord in the [[7-odd-limit]] since every interval involved in it is an element of the 7-odd-limit [[tonality diamond]]. Now if we replace 7/5 with 10/7:  
is a dyadic chord in the [[7-odd-limit]] since every interval involved in it is an element of the 7-odd-limit [[tonality diamond]]. Now if we replace 7/5 with 10/7:  
* 1-6/5-10/7-8/5
* 1 – 6/5 – 10/7 – 8/5


is ''not'' a dyadic chord in the 7-odd-limit. Although each note is 7-odd-limit over the bass, the interval between 10/7 and 6/5 is 25/21, and that between 10/7 and 8/5 is 28/25 – these are not 7-odd-limit.  
is ''not'' a dyadic chord in the 7-odd-limit. Although each note is 7-odd-limit over the bass, the interval between 10/7 and 6/5 is 25/21, and that between 10/7 and 8/5 is 28/25 – these are not 7-odd-limit.  
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== Essentially tempered dyadic chord ==
== Essentially tempered dyadic chord ==
In [[regular temperament theory]], we may speak of a just or tempered dyadic chord. By a ''just'' dyadic chord is meant a chord in rational intonation which is dyadic, so that each of its notes in relation to the lowest note is a rational number belonging to the set of consonances, and moreover each interval between the notes belongs to the set of consonances. By an ''essentially just'' dyadic chord is meant a chord which is considered to be an approximation of a just dyadic chord, such that each of its intervals is considered to be an approximation of the corresponding interval in the just dyadic chord. So, for instance, [[Ratios|1-5/4-3/2]] is a just dyadic chord when the consonance set is the [[5-odd-limit]] diamond with [[octave equivalence]], and 0-10-18 in 31edo with consonance set {8, 10, 13, 18, 21, 23, 31} modulo 31 is an essentially just dyadic chord approximating 1-5/4-3/2.
In [[regular temperament theory]], we may speak of a just or tempered dyadic chord. By a ''just'' dyadic chord is meant a chord in just intonation which is dyadic, so that each of its notes in relation to the lowest note is a rational number belonging to the set of consonances, and moreover each interval between the notes belongs to the set of consonances. An ''essentially just'' dyadic chord is a chord which is considered to be an approximation of a just dyadic chord, such that each of its intervals is considered to be an approximation of the corresponding interval in the just dyadic chord. So, for instance, [[4:5:6|1 – 5/4 – 3/2]] is a just dyadic chord when the consonance set is the [[5-odd-limit]] diamond with [[octave equivalence]], and 0 – 10 – 18 in 31edo with consonance set {8, 10, 13, 18, 21, 23, 31} modulo 31 is an essentially just dyadic chord approximating 1 – 5/4 – 3/2.


[[File:Essentially tempered chord.png|400px|thumb|right|A more in-depth work-through of the starling 1-6/5-10/7 essentially tempered chord example]]
[[File:Essentially tempered chord.png|400px|thumb|right|A more in-depth work-through of the starling 1-6/5-10/7 essentially tempered chord example]]


By an '''essentially tempered dyadic chord''' is meant a chord defined in an [[abstract regular temperament]] such that each interval belongs to a consonance set, but there is no corresponding just dyadic chord. This means there is no just chord such that each interval, when mapped by the abstract regular temperament, belongs to the consonance set. For example, the chord 1-6/5-10/7, when mapped by starling temperament, which makes [[126/125]] [[vanish]], has each of its intervals in the set of [[7-odd-limit]] consonances which is the tempering of the 7-odd-limit diamond by 126/125 (this is because 10/7 is off from 36/25 by 126/125, and therefore 10/7 and 36/25 are tempered together in starling temperament, and since 36/25 = (6/5)², the interval from 6/5 to 10/7 in starling may be heard as a second move by 6/5). However, (10/7)/(6/5) = 25/21 is [[25-odd-limit]], and there is no other 7-odd-limit just dyadic chord which can be used instead to give the result, so it is an essentially tempered dyadic chord. Essentially tempered dyadic chords are a related notion to [[comma pump]]s, and can be used as a basis for creating pumps. Using essentially tempered chords in chord progressions breaks the harmony out of exclusively just chord relations, and serves as a sort of harmonic lubricant imparting fluidity and dynamism to the harmony, at the cost fairly often of some blurring of the sense of tonality.
An '''essentially tempered dyadic chord''', often simply written as '''essentially tempered chord''', or '''dyadically essentially tempered chord''' ('''DET chord'''){{idio}}, is a chord defined in a [[regular temperament]] and relative to a set of consonances such that each interval is within that consonance set, but there is no corresponding just dyadic chord. This means there is no just chord such that each interval, when mapped by the abstract regular temperament, belongs to the consonance set. For example, the chord 1 – 6/5 – 10/7, when mapped by starling temperament, which makes [[126/125]] [[vanish]], has each of its intervals in the set of [[7-odd-limit]] consonances which is the tempering of the 7-odd-limit diamond by 126/125 (this is because 10/7 is off from 36/25 by 126/125, and therefore 10/7 and 36/25 are tempered together in starling temperament, and since 36/25 = (6/5)², the interval from 6/5 to 10/7 in starling may be heard as a second move by 6/5). However, (10/7)/(6/5) = 25/21 is [[25-odd-limit]], and there is no other 7-odd-limit just dyadic chord which can be used instead to give the result, so it is an essentially tempered dyadic chord.  
 
Essentially tempered dyadic chords are a related notion to [[comma pump]]s, and can be used as a basis for creating pumps. Using essentially tempered chords in chord progressions breaks the harmony out of exclusively just chord relations, and serves as a sort of harmonic lubricant imparting fluidity and dynamism to the harmony, at the cost fairly often of some blurring of the sense of tonality.


== Innate comma chord ==
== Innate comma chord ==
An '''innate comma chord''', proposed by [[Kite Giedraitis]], is the type of chord that cannot be mapped to just intonation in a given prime limit and odd limit, hence a chord that will not "ring". This is broader than the essentially tempered chord because it includes the possibility that the chord is not tempered at all, and contains a wolf interval. For example, the augmented triad in 5-limit JI is an innate comma chord, because it is impossible to tune all three major 3rds to 5/4. The innate comma here is 128/125 = 41¢. In practice, it might be sung or played justly, but with a large odd limit and hence a wolf interval, as 1/1 - 5/4 - 25/16 or 1/1 - 5/4 - 8/5. Or it might be tempered, e.g. in 12-edo as 0¢ - 400¢ - 800¢ - 1200¢. In 7-limit JI, one of the 3rds can be tuned to 9/7. The innate comma is reduced to 225/224, only 8¢. This comma can be distributed among the three 3rds, resulting in tempering each only a few cents, which may be close enough to be acceptable. In 11-limit JI, this chord isn't an innate comma chord, because it can be tuned justly as 7:9:11, a low enough odd limit to "ring". However, it's debatable that this chord qualifies as an augmented triad, because the upper 3rd hardly sounds major.
An '''innate comma chord''', proposed by [[Kite Giedraitis]], is the type of chord that cannot be mapped to just intonation in a given prime limit and odd limit. However, instead of specifying the targeted JI ratios as in an [[#Essentially tempered dyadic chord|essentially tempered chord]], an innate comma chord describes only the general chord shape: the [[mapped interval]] representations or the [[interval span|sizes]] of its constituent intervals.  
 
For example, the [[augmented triad]] in 5-limit JI is an innate comma chord below the 25-odd-limit, because it is impossible to tune all three major thirds (in the four-note chord doubling the root up an octave) to [[5/4]] or any other 5-limit interval with odd limit below 25: the innate comma here is 128/125 (41¢). In practice, it might be sung or played justly but with a large odd limit (containing [[wolf interval]]s): for example, 1–5/4–8/5–2, or 1–5/4–25/16–2 (or even 1–5/4–25/16–125/64). Or it might be tempered, e.g. in 12edo as 0¢–400¢–800¢–1200¢. In 7-limit JI, one of the major thirds can be tuned to 9/7, reducing the innate comma to 225/224 (only 8¢). This comma can be distributed among the three thirds, tempering each by only a few cents, which is usually close enough to be acceptable. In 11-limit JI, the augmented chord is not an innate comma chord, because it can be tuned justly as 7:9:11:14, a low enough odd limit to "ring". (However, it is debatable whether this chord qualifies as an augmented triad, because the middle [[11/9]] interval is a neutral third rather than a major third.)


== Anomalous saturated suspension ==
== Anomalous saturated suspension ==
An '''anomalous saturated suspension''' ('''ASS'''), introduced by [[Graham Breed]]<ref>[http://www.webcitation.org/60VBgPSUS]{{dead link}}</ref>, is a ''q''-odd-limit just dyadic chord to which no pitch ''q''-odd-limit pitch class can be added while keeping it in the ''q''-odd-limit, and which is neither an otonal or a utonal chord; that is, it is not contained as a subchord of either the 1:3:5:…:''q'' chord or the 1:1/3:1/5:…:1/q chord. The existence of such chords was discovered by [[Paul Erlich]]<ref>[http://www.webcitation.org/60VCUHe6d]{{dead link}}</ref>. Below are listed two 9-odd-limit ASSes of special interest, as they avoid intervals smaller than a minor whole tone.
An '''anomalous saturated suspension''' ('''ASS'''), introduced by [[Graham Breed]]<ref>[https://www.webcitation.org/60VBgPSUS ''Anomalous Saturated Suspensions'']</ref>, is a ''q''-odd-limit just dyadic chord to which no pitch ''q''-odd-limit pitch class can be added while keeping it in the ''q''-odd-limit, and which is neither an otonal or a utonal chord; that is, it is not contained as a subchord of either the 1:3:5:…:''q'' chord or the 1:1/3:1/5:…:1/''q'' chord. The existence of such chords was discovered by [[Paul Erlich]]<ref>[https://www.webcitation.org/60VCUHe6d ''Anomalous Saturated Suspensions -- Paul Erlich's post'']</ref>. Below are listed two 9-odd-limit ASSes of special interest, as they avoid intervals smaller than a minor whole tone.


* [[Just added sixth chord]]
* [[12:15:18:20]]
* [[Swiss tetrad]]
* [[12:14:18:21]]


For a complete list of ASS chords through the 23-odd-limit see [[List of anomalous saturated suspensions]].
For a complete list of ASS chords through the 23-odd-limit see [[List of anomalous saturated suspensions]].
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== List of essentially tempered dyadic chords ==
== List of essentially tempered dyadic chords ==
Here are some pages on certain essentially tempered dyadic chords, sorted by odd limit. See [[Dyadic chord/Pattern of essentially tempered chords]] for some notable abstract chord patterns.  
Here are some pages on certain essentially tempered dyadic chords, sorted by the lowest odd limit in which they are available (<span style="background-color:#D4D4D4">shaded rows</span> mark [[octave-splitting comma]] chords, which are induced by octave-splitting commas). See [[Dyadic chord/Pattern of essentially tempered chords]] for some notable abstract chord patterns.  
 
=== 5-odd-limit ===
{| class="wikitable"
|-
! Chords !! Associated Temperament !! Associated Commas
|-
| bgcolor="#D4D4D4" | [[Augmented triad]] || bgcolor="#D4D4D4" | [[Augmented (temperament)|Augmented]] || bgcolor="#D4D4D4" | [[128/125]]
|}


=== 7-odd-limit ===
=== 7-odd-limit ===
{| class="wikitable"
{| class="wikitable"
|-
|-
! Chords !! Associated Temperament !! Associated Commas
! Chords !! Associated temperament !! Associated commas
|-
| bgcolor="#D4D4D4" | [[Jubilismic chords]] || bgcolor="#D4D4D4" | [[Jubilismic]] || bgcolor="#D4D4D4" | [[50/49]]
|-
|-
| [[Archytas chords]] || [[Archytas]] || [[64/63]]
| [[Archytas chords]] || [[Archytas]] || [[64/63]]
|-
|-
| [[Starling chords]] || [[Starling]] || [[126/125]]
| [[Starling chords]] || [[Starling]] || [[126/125]]
|-
| bgcolor="#D4D4D4" | [[5edo|Blackwood pentad]] || bgcolor="#D4D4D4" | [[Blackwood]] || bgcolor="#D4D4D4" | [[28/27]], [[49/48]]
|-
| bgcolor="#D4D4D4" | [[Diminished seventh chord]] || bgcolor="#D4D4D4" | [[Diminished (temperament)|Diminished]] || bgcolor="#D4D4D4" | [[36/35]], [[50/49]]
|}
|}


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{| class="wikitable"
{| class="wikitable"
|-
|-
! Chords !! Associated Temperament !! Associated Commas
! Chords !! Associated temperament !! Associated commas
|-
|-
| [[Didymic chords]] || [[Meantone]] || [[81/80]]
| [[Didymic chords]] || [[Meantone]] || [[81/80]]
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{| class="wikitable"
{| class="wikitable"
|-
|-
! Chords !! Associated Temperament !! Associated Commas
! Chords !! Associated temperament !! Associated commas
|-
|-
| [[Mothwellsmic chords]] || [[Mothwellsmic]] || [[99/98]]
| [[Mothwellsmic chords]] || [[Mothwellsmic]] || [[99/98]]
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|-
|-
| [[Rastmic chords]] || [[Rastmic]] || [[243/242]]
| [[Rastmic chords]] || [[Rastmic]] || [[243/242]]
|-
| [[Frostmic chords]] || [[Frostmic]] || [[245/242]]
|-
|-
| [[Keenanismic chords]] || [[Keenanismic]] || [[385/384]]
| [[Keenanismic chords]] || [[Keenanismic]] || [[385/384]]
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|-
|-
| [[Pentacircle chords]] || [[Pentacircle]] || [[896/891]]
| [[Pentacircle chords]] || [[Pentacircle]] || [[896/891]]
|-
| bgcolor="#D4D4D4" | [[Jubilismic chords|Undecimal jubilismic chords]] || bgcolor="#D4D4D4" | [[Jubilismic family|Undecimal jubilismic]] || bgcolor="#D4D4D4" | [[50/49]], [[99/98]]
|-
|-
| [[Undecimal marvel chords]] || [[Marvel]] || 225/224, 385/384
| [[Undecimal marvel chords]] || [[Marvel]] || 225/224, 385/384
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| [[Magic chords]] || [[Magic]] || 100/99, 225/224, 245/243
| [[Magic chords]] || [[Magic]] || 100/99, 225/224, 245/243
|-
|-
| [[Magical seventh chord]] || [[Supermagic]] || 100/99, 385/384
| [[Keemic chords]] || [[Keemic]] || 100/99, 385/384
|-
| [[Orwell tetrad]] || [[Orwellian]] || 99/98, 385/384
|-
| [[Tutonic hexad|Tutonic hexads]] || [[Meantone]] || 81/80, 99/98, 126/125
|-
|-
| [[Orwell tetrad]] || [[Guanyin]] || 176/175, 540/539
| [[Baldanders chords|Baldanders hexads]] || [[Andromeda]] || 100/99, 225/224, 245/242
|-
|-
| [[Tutonic hexad]] || [[Meantone]] || 81/80, 99/98, 126/125
| [[Porcupine heptad]] || [[Porkypine]] || 55/54, 100/99
|}
|}


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{| class="wikitable"
{| class="wikitable"
|-
|-
! Chords !! Associated Temperament !! Associated Commas
! Chords !! Associated temperament !! Associated commas
|-
|-
| [[Buzurgismic chords]] || [[Buzurgismic]] || [[169/168]]
| [[Buzurgismic chords]] || [[Buzurgismic]] || [[169/168]]
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| [[Marveltwin chords]] || [[Marveltwin]] || [[325/324]]
| [[Marveltwin chords]] || [[Marveltwin]] || [[325/324]]
|-
|-
| [[Ratwolf triad]] || [[Ratwolfsmic]] || [[351/350]]
| [[Sooty fox chords]] || [[Sooty fox]] || [[343/338]]
|-
|-
| [[Minthmic chords]] || [[Minthmic]] || [[352/351]]
| [[Ratwolfsmic chords]] || [[Ratwolfsmic]] || [[351/350]]
|-
|-
| [[Gentle chords]] || [[Gentle]] || [[364/363]]
| [[Major minthmic chords]] || [[Major minthmic]] || [[352/351]]
|-
| [[Minor minthmic chords]] || [[Minor minthmic]] || [[364/363]]
|-
|-
| [[Huntmic chords]] || [[Huntmic]] || [[640/637]]
| [[Huntmic chords]] || [[Huntmic]] || [[640/637]]
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|-
|-
| [[Kestrel chords]] || [[Kestrel]] || [[1188/1183]]
| [[Kestrel chords]] || [[Kestrel]] || [[1188/1183]]
|-
| [[Catadictmic chords]] || [[Catadictmic]] || [[1287/1280]]
|-
|-
| [[Lambeth chords]] || [[Lambeth]] || [[1573/1568]]
| [[Lambeth chords]] || [[Lambeth]] || [[1573/1568]]
|-
|-
| [[Petrmic chords]] || [[Petrmic]] || [[2200/2197]]
| [[Petrmic chords]] || [[Petrmic]] || [[2200/2197]]
|-
| [[Rastmic chords #Rastgross heptad|Rastgross heptad]] || [[Namo]] || 144/143, 243/242
|-
| [[Parapyth chords]] || [[Parapyth]], [[gentle]] || 352/351, 364/363
|-
|-
| [[Hecate hexad]] || [[Hecate]] || 225/224, 325/324, 385/384
| [[Hecate hexad]] || [[Hecate]] || 225/224, 325/324, 385/384
|-
|-
| [[Woodpecker octad]] || [[Woodpecker]] || 66/65, 121/120, 126/125
| [[Woodpecker octad]] || [[Woodpecker]] || 66/65, 121/120, 126/125
|-
| [[Miraculous decad]] || [[Miraculous]], [[Revelation]] || 105/104, 196/195, 512/507
|}
|}


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{| class="wikitable"
{| class="wikitable"
|-
|-
! Chords !! Associated Temperament !! Associated Commas
! Chords !! Associated temperament !! Associated commas
|-
|-
| [[Island chords]] || [[Island]] || [[676/675]]
| [[Island chords]] || [[The Archipelago|Island]] || [[676/675]]
|-
|-
| [[Nicolic chords]] || [[Nicolic]] || [[1575/1573]]
| [[Nicolic chords]] || [[Nicolic]] || [[1575/1573]]
|-
|-
| [[Myhemiwell chords]] || [[Myhemiwell]] || [[3388/3375]]
| [[Myhemiwell chords]] || [[Myhemiwell]] || [[3388/3375]]
|-
| [[Battaglia chord]] || [[Marvel]] || 225/224
|-
| [[Tetracot chords]] || [[Tetracot]] || 100/99, 243/242
|-
|-
| [[Orwell tetrad|Orwell ennead]] || [[Guanyin]] || 176/175, 540/539
| [[Orwell tetrad|Orwell ennead]] || [[Guanyin]] || 176/175, 540/539
|-
| [[Battaglia chord]] || [[Marvel]] || 225/224
|}
|}


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{| class="wikitable"
{| class="wikitable"
|-
|-
! Chords !! Associated Temperament !! Associated Commas
! Chords !! Associated temperament !! Associated commas
|-
| [[Augustmic chords]] || [[Augustmic]] || [[154/153]]
|-
|-
| [[Augustmic chords|Augustmic tetrad]] || [[Augustmic]] || [[154/153]]
| [[Charismic chords]] || [[Charismic]] || [[256/255]]
|-
|-
| [[Diasemismic chords]] || [[Diasemismic]] || [[256/255]]
| [[Prototannismic chords]] || [[Prototannismic]] || [[273/272]]
|-
|-
| [[Ursulismic chords]] || [[Ursulismic]] || [[375/374]]
| [[Ursulismic chords]] || [[Ursulismic]] || [[375/374]]
|-
|-
| [[Seminaiadmic chords]] || [[Seminaiadmic]] || [[442/441]]
| [[Seminaiadmic chords]] || [[Seminaiadmic]] || [[442/441]]
|-
| [[Monardismic chords]] || [[Monardismic]] || [[561/560]]
|-
| [[Dakotismic chords]] || [[Dakotismic]] || [[595/594]]
|-
|-
| [[September chords]] || [[September]] || [[715/714]]
| [[September chords]] || [[September]] || [[715/714]]
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| [[Horizmic chords]] || [[Horizmic]] || [[833/832]]
| [[Horizmic chords]] || [[Horizmic]] || [[833/832]]
|-
|-
| [[Ainic chords]] || [[Ainic]] || [[936/935]]
| [[Ainismic chords]] || [[Ainismic]] || [[936/935]]
|-
| [[Twosquare chords]] || [[Twosquare]] || [[1089/1088]]
|-
| [[Quadrantonismic chords]] || [[Quadrantonismic]] || [[1156/1155]]
|-
| [[Cimbrismic chords]] || [[Cimbrismic]] || [[1275/1274]]
|-
|-
| [[Fidesmic chords]] || [[Fidesmic]] || [[2025/2023]]
| [[Fidesmic chords]] || [[Fidesmic]] || [[2025/2023]]
|-
| [[Heptacircle chords]] || [[Heptacircle]] || [[2431/2430]]
|-
|-
| [[Sextantonismic chords]] || [[Sextantonismic]] || [[2601/2600]]
| [[Sextantonismic chords]] || [[Sextantonismic]] || [[2601/2600]]
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{| class="wikitable"
{| class="wikitable"
|-
|-
! Chords !! Associated Temperament !! Associated Commas
! Chords !! Associated temperament !! Associated commas
|-
| [[Photismic chords]] || [[Photismic]] || [[324/323]]
|-
|-
| [[Nutrismic chords]] || [[Nutrismic]] || [[343/342]]
| [[Nutrismic chords]] || [[Nutrismic]] || [[343/342]]
|-
| [[Dudon chords]] || [[Dudon]] || [[361/360]]
|-
|-
| [[Devichromic chords]] || [[Devichromic]] || [[400/399]]
| [[Devichromic chords]] || [[Devichromic]] || [[400/399]]
|-
| [[Abnobismic chords]] || [[Abnobismic]] || [[456/455]]
|-
| [[Hedwigmic chords]] || [[Hedwigmic]] || [[476/475]]
|-
| [[Eulalismic chords]] || [[Eulalismic]] || [[495/494]]
|-
|-
| [[Boethius chords]] || [[Boethius]] || [[513/512]]
| [[Boethius chords]] || [[Boethius]] || [[513/512]]
|-
| [[Kingfisher chords]] || [[Kingfisher]] || [[969/968]]
|-
| [[Bihendrixmic chords]] || [[Bihendrixmic]] || [[1083/1078]]
|-
|-
| [[Eratosthenes chords]] || [[Eratosthenes]] || [[1216/1215]]
| [[Eratosthenes chords]] || [[Eratosthenes]] || [[1216/1215]]
|-
| [[Solvejgsmic chords]] || [[Solvejgsmic]] || [[1331/1330]]
|-
|-
| [[Aureusmic chords]] || [[Aureusmic]] || [[1445/1444]]
| [[Aureusmic chords]] || [[Aureusmic]] || [[1445/1444]]
|-
| [[Pinkanberry chords]] || [[Pinkanberry]] || [[1521/1520]]
|-
| [[Kevolismic chords]] || [[Kevolismic]] || [[1540/1539]]
|-
|-
| [[Ramanujanismic chords]] || [[Ramanujanismic]] || [[1729/1728]]
| [[Ramanujanismic chords]] || [[Ramanujanismic]] || [[1729/1728]]
|-
| [[Blumeyer chords]] || [[Blumeyer]] || [[2432/2431]]
|-
| [[Neovulturismic chords]] || [[Neovulturismic]] || [[2926/2925]]
|-
| [[Neomirkwaismic chords]] || [[Neomirkwaismic]] || [[3136/3135]]
|-
| [[Neosatanismic chords]] || [[Neosatanismic]] || [[4200/4199]]
|-
| [[Langwismic chords]] || [[Langwismic]] || [[6144/6137]]
|}
|}


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{| class="wikitable"
{| class="wikitable"
|-
|-
! Chords !! Associated Temperament !! Associated Commas
! Chords !! Associated temperament !! Associated commas
|-
| [[Dakotismic chords]] || [[Dakotismic]] || [[595/594]]
|-
|-
| [[Slendric pentad]] || [[Gamelismic]] || [[1029/1024]]
| [[Slendric pentad]] || [[Gamelismic]] || [[1029/1024]]
|-
| [[Quadrantonismic chords]] || [[Quadrantonismic]] || [[1156/1155]]
|-
|-
| [[Palingenetic chords]] || [[Palingenetic]] || [[1701/1700]]
| [[Palingenetic chords]] || [[Palingenetic]] || [[1701/1700]]
|-
|-
| [[Xenismic chords]] || [[Xenismic]] || [[2058/2057]]
| [[Xenismic chords]] || [[Xenismic]] || [[2058/2057]]
|-
| [[Ibnsinmic chords]] || [[Ibnsinmic]] || [[2080/2079]]
|-
|-
| [[Heartlandismic chords]] || [[Heartlandismic]] || [[3971/3969]]
| [[Heartlandismic chords]] || [[Heartlandismic]] || [[3971/3969]]
|-
| [[Minismic chords]] || [[Minismic]] || [[4096/4095]]
|-
| [[Baladismic chords]] || [[Baladismic]] || [[4914/4913]]
|-
| [[Neogrendelismic chords]] || [[Neogrendelismic]] || [[5985/5984]]
|-
| [[Heartland #Chords|Heartland chords]] || [[Heartland]] || 243/242, 1083/1078
|}
=== 23-odd-limit ===
{| class="wikitable"
|-
! Chords !! Associated temperament !! Associated commas
|-
| [[Scanismic chords]] || [[Scanismic]] || [[460/459]]
|-
| [[Pittsburghismic chords]] || [[Pittsburghismic]] || [[484/483]]
|-
| [[Laodicismic chords]] || [[Laodicismic]] || [[507/506]]
|-
| [[Preziosismic chords]] || [[Preziosismic]] || [[529/528]]
|-
| [[Worcester chords]] || [[Worcester]] || [[576/575]]
|-
| [[Harvardismic chords]] || [[Harvardismic]] || [[736/735]]
|-
| [[Squadronismic chords]] || [[Squadronismic]] || [[760/759]]
|-
| [[Lysistratismic chords]] || [[Lysistratismic]] || [[897/896]]
|-
| [[Fragarismic chords]] || [[Fragarismic]] || [[1105/1104]]
|-
| [[Rodessismic chords]] || [[Rodessismic]] || [[1197/1196]]
|-
| [[Triaphonismic chords]] || [[Triaphonismic]] || [[1288/1287]]
|-
| [[Turkismic chords]] || [[Turkismic]] || [[1496/1495]]
|-
| [[Antinousismic chords]] || [[Antinousismic]] || [[1863/1862]]
|-
| [[Artifismic chords]] || [[Artifismic]] || [[2024/2023]]
|-
| [[Cupcake chords]] || [[Cupcake]] || [[2025/2024]]
|-
| [[Guangdongismic chords]] || [[Guangdongismic]] || [[2185/2184]]
|-
| [[Travellismic chords]] || [[Travellismic]] || [[2300/2299]]
|-
| [[Biyativice chords]] || [[Biyativice]] || [[2646/2645]]
|-
| [[Kotkismic chords]] || [[Kotkismic]] || [[2737/2736]]
|-
| [[Vicious chords]] || [[Vicious]] || [[3060/3059]]
|-
| [[Mikkolismic chords]] || [[Mikkolismic]] || [[3381/3380]]
|-
| [[Vicedim chords]] || [[Vicedim]] || [[3520/3519]]
|-
| [[Shoalmic chords]] || [[Shoalmic]] || [[3888/3887]]
|-
| [[Viceaug chords]] || [[Viceaug]] || [[4693/4692]]
|-
| [[Demiquartervice chords]] || [[Demiquartervice]] || [[4761/4760]]
|-
| [[Broadviewsmic chords]] || [[Broadviewsmic]] || [[5083/5082]]
|-
| [[Vicetertismic chords]] || [[Vicetertismic]] || [[Vicetertisma|12168/12167]]
|}
|}


Line 223: Line 377:
{| class="wikitable"
{| class="wikitable"
|-
|-
! Chords !! Associated Temperament !! Associated Commas
! Chords !! Associated temperament !! Associated commas
|-
| [[Tunbarsmic chords]] || [[Tunbarsmic]] || [[625/624]]
|-
| [[Nymphismic chords]] || [[Nymphismic]] || [[875/874]]
|-
| [[Noellismic chords]] || [[Noellismic]] || [[1225/1224]]
|-
| [[Trichthonismic chords]] || [[Trichthonismic]] || [[2376/2375]]
|-
|-
| [[Sperasmic chords]] || [[Sperasmic]] || [[2500/2499]]
| [[Sperasmic chords]] || [[Sperasmic]] || [[2500/2499]]
|-
|-
| [[Lehmerismic chords]] || [[Lehmerismic temperaments|Lehmerismic]] || [[3025/3024]]
| [[Lehmerismic chords]] || [[Lehmerismic temperaments|Lehmerismic]] || [[3025/3024]]
|-
| [[Martebismic chords]] || [[Martebismic]] || [[3250/3249]]
|-
| [[Leprechaun chords]] || [[Leprechaun]] || [[4225/4224]]
|-
| [[Neovishmic chords]] || [[Neovishmic]] || [[5776/5775]]
|-
| [[Neonewtismic chords]] || [[Neonewtismic]] || [[6175/6174]]
|}
|}


Line 233: Line 403:
{| class="wikitable"
{| class="wikitable"
|-
|-
! Chords !! Associated Temperament !! Associated Commas
! Chords !! Associated temperament !! Associated commas
|-
| [[Ragismic chords]] || [[Ragismic]] || [[4375/4374]]
|-
| [[Hagendorfismic chords]] || [[Hagendorfismic]] || [[8075/8073]]
|}
 
=== 29-odd-limit ===
{| class="wikitable"
|-
! Chords !! Associated temperament !! Associated commas
|-
| [[Vinecute chords]] || [[Vinecute]] || [[4641/4640]]
|-
| [[Large grapevine chords]] || [[Large grapevine]] || [[4901/4900]]
|-
| [[Small grapevine chords]] || [[Small grapevine]] || [[7425/7424]]
|-
| [[Vinous chords]] || [[Vinous]] || [[8671/8670]]
|}
 
=== 31-odd-limit ===
{| class="wikitable"
|-
! Chords !! Associated temperament !! Associated commas
|-
| [[Kibismic chords]] || [[Kibismic]] || [[1024/1023]]
|-
| [[Acronymismic chords]] || [[Acronymismic]] || [[Acronymisma|17577/17576]]
|-
|-
| [[Ragismic chords]] || [[Ragismic microtemperaments|Ragismic]] || [[4375/4374]]
| [[Tricecubismic chords]] || [[Tricecubismic]] || [[Tricecubisma|29792/29791]]
|}
|}


Line 241: Line 439:
{| class="wikitable"
{| class="wikitable"
|-
|-
! Chords !! Associated Temperament !! Associated Commas
! Chords !! Associated temperament !! Associated commas
|-
|-
| [[Wizardharry chords]] || [[Wizardharry]] || [[4000/3993]]
| [[Wizardharry chords]] || [[Wizardharry]] || [[4000/3993]]
|-
|-
| [[Flashmic chords]] || [[Flashmic]] || [[12376/12375]]
| [[Flashmic chords]] || [[The Flashmob|Flashmic]] || [[12376/12375]]
|}
 
=== 35-odd-limit ===
{| class="wikitable"
|-
! Chords !! Associated temperament !! Associated commas
|-
| [[Lummic chords]] || [[Lummic]] || [[1716/1715]]
|}
 
=== 37-odd-limit ===
{| class="wikitable"
|-
! Chords !! Associated temperament !! Associated commas
|-
| [[Bullionismic chords]] || [[Bullionismic]] || [[5292/5291]]
|}
 
=== 39-odd-limit ===
{| class="wikitable"
|-
! Chords !! Associated temperament !! Associated commas
|-
| [[Harmonismic chords]] || [[Harmonismic]] || [[10648/10647]]
|}
|}


Line 251: Line 473:
{| class="wikitable"
{| class="wikitable"
|-
|-
! Chords !! Associated Temperament !! Associated Commas
! Chords !! Associated temperament !! Associated commas
|-
|-
| [[Jacobin chords]] || [[Jacobin]] || [[6656/6655]]
| [[Jacobin chords]] || [[The Jacobins|Jacobin]] || [[6656/6655]]
|}
|}


Line 265: Line 487:
|-
|-
| [[Hendrix chord]]
| [[Hendrix chord]]
| 8:10:14:19 ~ 12:15:21:28
| <font style="font-size:0.85em">8:10:14:19 ~ 12:15:21:28</font>
| [[57/56]]
| [[57/56]]
|-
|-
Line 279: Line 501:
| 10:12:15 ~ 16:19:24
| 10:12:15 ~ 16:19:24
| [[96/95]]
| [[96/95]]
|-
| [[Lynchismic chords|Lynchismic plurichords]]
| <font style="font-size:0.85em">12:14:17:20 ~ 1/(20:17:14:12) <br>6:7:8:10 ~ 1/(20:17:15:12)</font>
| [[120/119]]
|-
| [[Augustmic chords|Augustmic plurichords]]
| <font style="font-size:0.85em">14:17:18:22 ~ 1/(22:18:17:14)</font>
| [[154/153]]
|}
|}


Line 290: Line 520:
[[Category:Dyadic chords| ]] <!-- main article -->
[[Category:Dyadic chords| ]] <!-- main article -->
[[Category:Lists of chords]]
[[Category:Lists of chords]]
<references />
Retrieved from "https://en.xen.wiki/w/Dyadic_chord"