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== Theory ==
== Theory ==
80edo is the first edo that represents the [[19-odd-limit]] [[tonality diamond]] [[consistent]]ly, though it barely manages to do so. Despite this, a large number of intervals in higher odd limits in the [[29-limit|29-prime-limit]] are consistent, and its [[patent val]] generally does well at approximating (29-prime-limited) [[harmonic series]] segments, such as modes 16 through 30 but especially modes 8 through 15. It achieves this much consistency because all primes in the 29-limit except 13 are sharp of just, with inconsistencies usually arising through not cancelling the over-sharpness of compound harmonics 21, 27, 35, 45, and 49 (and their octave-equivalents), which may be seen as an interesting limitation. This means it can be used as a general-purpose approximate 29-prime-limit system with a relatively manageable number of tones, with some care taken around inconsistency. It can also model larger primes if one is willing to accept their sharpness and for this purpose it does well for its size at the no-31's [[41-limit]], or even the [[43-limit]] if you are fine with [[43/32]] being slightly flat causing more inconsistencies. In fact, except for [[26/25]], it is consistent in the no-21's no-27's no-31's no-35's [[41-odd-limit]]! If one wants higher precision as one goes to higher primes to try to convey the subtle harmonic qualities of those primes, 80et arguably fails in general, although many specific cases may be convincing. A promising alternative is using 80et as a model in which to fit higher-limit JI by way of approximating as much of the harmonic series as possible, for which it can model the 125-odd-limit quite well (corresponding to the 113-prime-limit), leading to an excellent [[Ringer scale]] described in the [[#Ringer 80|Ringer 80 section of this article]].
80edo is the first edo that represents the [[19-odd-limit]] [[tonality diamond]] [[consistent]]ly, though it barely manages to do so. Despite this, a large number of intervals in higher odd limits are consistent, and its [[patent val]] generally does well at approximating the [[29-limit|29-prime-limited]] [[harmonic series]] segments, such as modes 16 through 30 but especially modes 8 through 15. It achieves this much consistency with all primes in the 29-limit except 13 being sharp of just; the inconsistencies usually arise through not cancelling the over-sharpness of compound harmonics [[21/1|21]], [[27/1|27]], [[35/1|35]], [[45/1|45]], [[49/1|49]], and their octave-equivalents, which may be seen as an interesting limitation. This means it can be used as a general-purpose approximate 29-limit system with a relatively manageable number of tones, with some care taken around inconsistency. In fact, it is almost consistent to the no-21 no-27 [[29-odd-limit]], with the exception of [[25/13]] and its octave complement. Possible additions to this include [[33/1|33]], [[37/1|37]], [[39/1|39]], and [[41/1|41]]. Thus, it can also model larger primes if one is willing to accept their sharpness, and for this purpose, it does well for its size at the no-31's [[41-limit]], or even the [[43-limit]] if you are fine with [[43/32]] being slightly flat causing more inconsistencies.  


=== Significance of echidna ===
If one wants higher precision as one goes to higher primes to try to convey the subtle harmonic qualities of those primes, 80et arguably fails in general, although many specific cases may be convincing. A promising alternative is using 80et as a model in which to fit higher-limit JI by way of approximating as much of the harmonic series as possible, for which it can model the 125-odd-limit quite well (corresponding to the 113-prime-limit), leading to an excellent [[Ringer scale]] described in the [[#Ringer 80|Ringer 80 section of this article]].
As an equal temperament, it is well-tuned for the important 11-limit and 17-limit half-octave-period temperament [[echidna]] (the {{nowrap|22 & 58}} temperament), which affords great freedom in a 36-note MOS and still many choices in a 22-note MOS, offering a high-accuracy rank 2 detemper of [[22edo]], which in comparison conflates many important distinctions of the 11-limit. This is not insignificant as many abundant intervals of echidna, such as (especially) [[11/10]], [[9/7]] and [[17/16]], are tuned so accurately that they [[#Consistent circles|form 80-note consistent circles]]. Echidna supports [[srutal archagall]], which is also tuned near-optimally for [[fiventeen]] — specifically, for the characteristic fiventeen pentad, 30:34:40:45:51:60, consisting of steps of [[20/17]] and [[9/8]]~[[17/15]], and is the smallest edo to improve on the tuning of srutal archagall + fiventeen after [[34edo]]. In its representation of echidna, the least accurate tuning is that of [[7/4]], which is (relatively) very sharp in 80edo, for which [[58edo]] does better as a tuning of echidna (though much worse as a tuning for srutal archagall/diaschismic and especially fiventeen); one can reason this makes the 80edo tuning of echidna feel more like a detemper of 22edo (especially given the smaller step size between adjacent notes equated in 22edo).


=== Potential for a general-purpose system ===
=== As a tuning of other temperaments ===
Though a strange tuning* in lower prime limits, 80edo offers a very unique composite structure that can aid with familiarization/conceptualization by way of its subset edos of (2, 4, 5,) 8, 10, 16 and 20. Initially this doesn't seem very useful unless one is interested in learning those edos, but 80edo supports a plethora of multiperiod temperaments with accurate JI interval interpretations based on these edos; to see a fairly comprehensive list of these temperaments and of their most accurate JI interpretations w.r.t. (integer multiples of) their period, see [[#Consistent circles|the section on consistent circles]]. These represent a large number of practically completely unexplored and novel high-limit temperaments with varying musical potential.
80et [[tempering out|tempers out]] [[2048/2025]] in the 5-limit; [[1728/1715]], [[3136/3125]], [[4000/3969]], and [[4375/4374]] in the [[7-limit]]; [[176/175]], [[540/539]] and [[4000/3993]] in the [[11-limit]]; [[169/168]], [[325/324]], [[351/350]], [[352/351]], [[364/363]] and [[1001/1000]] in the [[13-limit]]; [[136/135]], [[221/220]], [[256/255]], [[289/288]], [[561/560]], [[595/594]], [[715/714]], [[936/935]] and [[1275/1274]] in the [[17-limit]]; [[190/189]], [[286/285]], [[361/360]], [[400/399]], [[456/455]], [[476/475]], [[969/968]], [[1331/1330]], [[1445/1444]], [[1521/1520]], [[1540/1539]] and [[1729/1728]] in the [[19-limit]]; [[208/207]], [[253/252]], [[323/322]] and [[460/459]] in the [[23-limit]]; and 320/319 in the [[29-limit]]. The last comma is notable as it equates a sharp [[29/16]] with a near-perfect [[20/11]], although this equivalence begins to make more sense when you consider the error cancellations with other sharp harmonics and as a way to give more reasonable interpretations to otherwise questionably mapped intervals. It provides the [[optimal patent val]] for 5-limit [[diaschismic]], for 13-limit [[srutal]], and for 7-, 11- and 13-limit [[bidia]]. It is a good tuning for various temperaments in [[canou family]], especially in higher limits.  


<nowiki />* The strangeness of its tuning can largely be explained by the addition of vals [[80edo]] = [[53edo]] + [[27edo]], where [[27edo]] exaggerates the idiosyncratic mapping of the 2.3.5.7.13 subgroup, as while 53edo tempers {[[625/624|S25]], [[676/675|S26]], [[729/728|S27]]} (supporting [[catakleismic]]) and {[[1728/1715|S6/S7]], [[5120/5103|S8/S9]]} (supporting [[buzzard]]), 27edo tempers {[[1728/1715|S6/S7]], [[64/63|S8]], [[325/324|S25*S26]], [[351/350|S26*S27]]} [[Square superparticular|implying]] {[[4375/4374|S25/S27]], [[169/168|S13]]} but maps S25~S27 positively and S26 negatively, which 80et thus inherits though with less damage. This is not insignificant, because this plays a special role (as we'll see in the next section on subsets).
As an equal temperament, it is well-tuned for the important 11-limit and 17-limit half-octave-period temperament [[echidna]], the {{nowrap| 22 & 58 }} temperament, which affords great freedom in a 36-note mos and still many choices in a 22-note mos, offering a high-accuracy rank-2 detemper of [[22edo]], which in comparison conflates many important distinctions of the 11-limit. This is not insignificant as many abundant intervals of echidna, such as [[11/10]], [[9/7]] and [[17/16]], are tuned so accurately that they form 80-note [[#Consistent circles|consistent circles]]. Echidna extends [[srutal archagall]], which is also tuned near-optimally for [[fiventeen]] – specifically, for the characteristic fiventeen pentad, 30:34:40:45:51:60, consisting of steps of [[20/17]] and [[9/8]]~[[17/15]], and is the smallest edo to improve on the tuning of srutal archagall plus fiventeen after [[34edo]]. In its representation of echidna, the least accurate tuning is that of [[7/4]], which is (relatively) very sharp in 80edo, for which [[58edo]] does better as a tuning of echidna, though much worse as a tuning for srutal archagall and especially fiventeen; one can reason this makes the 80edo tuning of echidna feel more like a detemper of 22edo, especially given the smaller step size between adjacent notes equated in 22edo.


==== Based on subsets ====
=== Potential for a general-purpose system ===
As a composite edo, the main subsets it lacks are subsets of [[3edo|3]] and [[9edo|9]], but 9\80 = 135{{cent}} offers a good approximation to 1\9 = 133.33..{{cent}}, and one could argue that 1\3 = 400{{cent}} is the most difficult small edo interval to interpret (assuming interpreting it as [[5/4]] is not convincing or pleasing enough) in that its interpretations tend to be a large variety of high-complexity intervals, though if one wants a similar sound there is 27\80 = 405{{cent}} as ~[[24/19]]~[[19/15]] (though 24/19 is more accurate), thus serving a similar function to the [[nestoria]] major third. As a result, 80edo is in some sense uniquely tasked with approximating small edos because it will often share subsets that can help make the approximation feel more regular and consistent by interpreting it as a near-equal multiperiod MOS. This has the benefit of offering a relatively unexplored strategy of "tempered [[detempering]]", a sort of middle path between complete detempering to JI (which lacks the simplifications and unique comma pumping and structural opportunities of tempering) and not detempering the small edo at all (which can lead to challenging interpretation of harmony if one's goal is approximation to JI).
Though a strange tuning in lower prime limits, 80edo offers a very unique composite structure that can aid with familiarization/conceptualization by way of its subset edos of 2, 4, 5, 8, 10, 16 and 20. 80edo supports a plethora of multiperiod temperaments with accurate JI interval interpretations based on these edos; to see a fairly comprehensive list of these temperaments and of their most accurate JI interpretations with respect to integer multiples of their period, see [[#Consistent circles]]. These represent a large number of practically completely unexplored and novel high-limit temperaments with varying musical potential.
 
Even if one finds this reasoning about not having subsets of 3 and 9 unconvincing, there is the fact that the idiosyncracies in the tuning profile of 80edo is intimately related to those of 27edo, so that it shares a deep logic with it through the 13-limit {{nowrap|27e &amp; 53}} temperament [[quartonic]].. Even the [[#Significance of echidna|aforementioned]] sharp 7 is explained by 27edo being a sharp [[superpyth]] system. More mysterious is that the approximation of 1\9 at 9\80 = 135{{cent}}, when taken as a generator, is related to the shared [[41-limit]] structure between 80edo and the ultimate general purpose system, [[311edo]], through the {{nowrap|80 &amp; 231}} temperament [[superlimmal]], where it represents [[27/25]]~[[40/37]], implying a slightly sharp tuning for 27/25, which is characteristic.
 
=== Commas ===
80et [[Tempering out|tempers out]] [[2048/2025]] in the 5-limit; [[1728/1715]], [[3136/3125]], [[4000/3969]], and [[4375/4374]] in the [[7-limit]]; [[176/175]], [[540/539]] and [[4000/3993]] in the [[11-limit]]; [[169/168]], [[325/324]], [[351/350]], [[352/351]], [[364/363]] and [[1001/1000]] in the [[13-limit]]; [[136/135]], [[221/220]], [[256/255]], [[289/288]], [[561/560]], [[595/594]], [[715/714]], [[936/935]] and [[1275/1274]] in the [[17-limit]]; [[190/189]], [[286/285]], [[361/360]], [[400/399]], [[456/455]], [[476/475]], [[969/968]], [[1331/1330]], [[1445/1444]], [[1521/1520]], [[1540/1539]] and [[1729/1728]] in the [[19-limit]]; [[208/207]], [[253/252]], [[323/322]] and [[460/459]] in the [[23-limit]]; and 320/319 in the [[29-limit]]. The last comma is notable as it equates a sharp [[29/16]] with a near-perfect [[20/11]], although this equivalence begins to make more sense when you consider the error cancellations with other sharp harmonics and as a way to give more reasonable interpretations to otherwise questionably mapped intervals. It provides the [[optimal patent val]] for 5-limit [[diaschismic]], for 13-limit [[srutal]], and for 7-, 11- and 13-limit [[bidia]]. It is a good tuning for various temperaments in [[canou family]], especially in higher limits.  


=== Prime harmonics ===
=== Prime harmonics ===
Line 25: Line 19:


=== Subsets and supersets ===
=== Subsets and supersets ===
Since 80 factors into {{factorization|80}}, 80edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 16, 20, and 40 }}.
Since 80 factors into primes as 2<sup>4</sup> × 5, 80edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 16, 20, and 40 }}.


80edo is notable in not only it is consistent in the 19-odd-limit, but a large number of its supersets are also consistent in at least 19-odd-limit, if not larger. These are {{EDOs|320, 400, 1600, 1920, 2000, 2320, 3920, 4320}}. Temperament mergers of these produce various [[80th-octave temperaments]].
As a composite edo, the main subsets it lacks are subsets of [[3edo|3]] and [[9edo|9]], but 9\80 = 135{{cent}} offers a good approximation to 1\9 = 133.33…{{c}}, and instead of 1\3 = 400{{cent}}, it has 27\80 = 405{{cent}} as [[19/15]]~[[24/19]], thus serving a similar function to the [[nestoria]] major third. As a result, 80edo is in some sense uniquely tasked with approximating small edos because it will often share subsets that can help make the approximation feel more regular and consistent by interpreting it as a near-equal multiperiod mos. This has the benefit of offering a relatively unexplored strategy of "tempered [[detempering]]", a sort of middle path between complete detempering to JI (which lacks the simplifications and unique comma pumping and structural opportunities of tempering) and not detempering the small edo at all (which can lead to challenging interpretation of harmony if one's goal is approximation to JI).
 
80edo is notable in not only it is consistent in the 19-odd-limit, but a large number of its supersets are also consistent in at least 19-odd-limit, if not larger. These are {{EDOs| 320, 400, 1600, 1920, 2000, 2320, 3920, 4320 }}. Temperament mergers of these produce various [[80th-octave temperaments]].


== Intervals ==
== Intervals ==
Line 673: Line 669:
| 17/13
| 17/13
| [[Semisept]]
| [[Semisept]]
|-
| 1
| 33\80
| 495
| 3/2
| [[Leapfrog]] / [[leapday]]
|-
|-
| 1
| 1
Line 744: Line 746:
Mode 63 of the harmonic series (corresponding to 125-odd-limit) with added odds from mode 63 × 2 = 126 in square brackets:
Mode 63 of the harmonic series (corresponding to 125-odd-limit) with added odds from mode 63 × 2 = 126 in square brackets:


: 63:64:[129]:65:[131]:66:[133]:67:68:[137]:69:[139]:70:71:[143]:72:[145]:73:74:[149]
<pre>
: 75:76:[153]:77:78:[157]:79:80:[161]:81:82:83:[167]:84:85:86:[173]:87:88:89
63:64:[129]:65:[131]:66:[133]:67:68:[137]:69:[139]:70:71:[143]:72:[145]:73:74:[149]
: [179]:90:91:92:[185]:93:94:95:96:97:[195]:98:99:100:101:102:103:104:[209]:105
75:76:[153]:77:78:[157]:79:80:[161]:81:82:83:[167]:84:85:86:[173]:87:88:89
: 106:107:108:109:110:111:112:113:114:115:116:117:118:119:120:121:122:123:124:125(:126)
[179]:90:91:92:[185]:93:94:95:96:97:[195]:98:99:100:101:102:103:104:[209]:105
106:107:108:109:110:111:112:113:114:115:116:117:118:119:120:121:122:123:124:125(:126)
</pre>


The above is split into 20 harmonics per line a.k.a. ~300¢ worth of harmonic content per line.
The above is split into 20 harmonics per line a.k.a. ~300¢ worth of harmonic content per line.
Line 753: Line 757:
In lowest terms as a /105 scale corresponding to a [[primodal]] /53 scale, among other possible interpretations:
In lowest terms as a /105 scale corresponding to a [[primodal]] /53 scale, among other possible interpretations:


: 105:106:107:108:109:110:111:112:113:114:115:116:117:118:119:120:121:122:123:124:125:126:128:129:130:131:132:133:134:136:137:138:139:140:142:143:144:145:146:148:149:150:152:153:154:156:157:158:160:161:162:164:166:167:168:170:172:173:174:176:178:179:180:182:184:185:186:188:190:192:194:195:196:198:200:202:204:206:208:209:210
<pre>
105:106:107:108:109:110:111:112:113:114:115:116:117:118:119:120:121:122:123:124:125:126:128:129:130:131:132:133:134:136:137:138:139:140:142:143:144:145:146:148:149:150:152:153:154:156:157:158:160:161:162:164:166:167:168:170:172:173:174:176:178:179:180:182:184:185:186:188:190:192:194:195:196:198:200:202:204:206:208:209:210
</pre>


This form is useful for copy-pasting into tools that accept colon-separated harmonic series chord enumerations as scales.
This form is useful for copy-pasting into tools that accept colon-separated harmonic series chord enumerations as scales.
Line 759: Line 765:
As reduced, rooted intervals (16 intervals per line):
As reduced, rooted intervals (16 intervals per line):


: 129/128, 65/64, 131/128, 33/32, 133/128, 67/64, 17/16, 137/128, 69/64, 139/128, 35/32, 71/64, 143/128, 9/8, 145/128, 73/64,
<pre>
: 37/32, 75/64, 19/16, 153/128, 77/64, 39/32, 157/128, 79/64, 5/4, 161/128, 81/64, 41/32, 83/64, 167/128, 21/16, 85/64,
129/128, 65/64, 131/128, 33/32, 133/128, 67/64, 17/16, 137/128, 69/64, 139/128, 35/32, 71/64, 143/128, 9/8, 145/128, 73/64,
: 43/32, 173/128, 87/64, 11/8, 89/64, 179/128, 45/32, 91/64, 23/16, 185/128, 93/64, 47/32, 95/64, 3/2, 97/64, 195/128,
37/32, 75/64, 19/16, 153/128, 77/64, 39/32, 157/128, 79/64, 5/4, 161/128, 81/64, 41/32, 83/64, 167/128, 21/16, 85/64,
: 49/32, 99/64, 25/16, 101/64, 51/32, 103/64, 13/8, 209/128, 105/64, 53/32, 107/64, 27/16, 109/64, 55/32, 111/64, 7/4,
43/32, 173/128, 87/64, 11/8, 89/64, 179/128, 45/32, 91/64, 23/16, 185/128, 93/64, 47/32, 95/64, 3/2, 97/64, 195/128,
: 113/64, 57/32, 115/64, 29/16, 117/64, 59/32, 119/64, 15/8, 121/64, 61/32, 123/64, 31/16, 125/64, 63/32, 2/1
49/32, 99/64, 25/16, 101/64, 51/32, 103/64, 13/8, 209/128, 105/64, 53/32, 107/64, 27/16, 109/64, 55/32, 111/64, 7/4,
113/64, 57/32, 115/64, 29/16, 117/64, 59/32, 119/64, 15/8, 121/64, 61/32, 123/64, 31/16, 125/64, 63/32, 2/1
</pre>


== Scales ==
== Scales ==
; [[MOS scale]]s
; [[MOS scale]]s
* [[Deca]][30]: 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3
* [[Bidia]][20]: 6 1 6 1 6 6 1 6 1 6 6 1 6 1 6 6 1 6 1 6
* Bidia[32]: 1 5 1 5 1 1 5 1 1 5 1 5 1 1 5 1 1 5 1 5 1 1 5 1 1 5 1 5 1 1 5 1
* [[Deca]][20]: 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3
* Deca[30]: 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3
* [[Echidna]][22]: 4 3 4 4 3 3 3 4 4 3 4 4 3 4 4 3 4 3 4 4 3 4
* [[Echidna]][22]: 4 3 4 4 3 3 3 4 4 3 4 4 3 4 4 3 4 3 4 4 3 4
* [[Parakleismic]][19]: 4 4 5 4 4 4 4 5 4 4 4 5 4 4 4 4 5 4 4
* Echidna[36]: 3 1 3 1 3 3 1 3 3 1 3 1 3 3 1 3 1 3 3 1 3 1 3 3 1 3 3 1 3 1 3 3 1 3 1 3
* [[Semisept]][31]: 3 2 3 2 3 2 3 2 2 3 2 3 3 2 3 2 3 2 3 3 2 3 2 3 3 2 3 2 3 2 3
* [[Leapday]][46] ^: 1 3 1 1 3 1 3 1 1 3 1 1 3 1 3 1 1 3 1 1 3 1 1 3 1 3 1 1 3 1 1 3 1 3 1 1 3 1 1 3 1 3 1 1 3 1
* [[Leapfrog]][12]: 5 9 5 9 5 5 9 5 9 5 9 5
* Leapfrog[17]: 5 4 5 5 5 4 5 5 4 5 5 4 5 5 5 4 5
* Leapfrog[29]: 4 1 4 1 4 4 1 4 1 4 1 4 4 1 4 1 4 4 1 4 1 4 1 4 4 1 4 1 4
* [[Octopus]][40]: 1 1 6 1 1 1 1 6 1 1 1 1 6 1 1 1 1 6 1 1 1 1 6 1 1 1 1 6 1 1 1 1 6 1 1 1 1 6 1 1
* [[Parakleismic]][23]: 4 4 1 4 4 4 4 4 1 4 4 4 4 4 1 4 4 4 4 4 1 4 4
* Parakleismic[42]: 1 3 1 3 1 3 1 3 1 3 1 1 3 1 3 1 3 1 3 1 1 3 1 3 1 3 1 3 1 3 1 1
* [[Semisept]][18]: 5 3 5 5 5 3 5 5 3 5 5 5 3 5 5 5 3 5
* Semisept[31]: 3 2 3 2 3 2 3 2 2 3 2 3 3 2 3 2 3 2 3 3 2 3 2 3 3 2 3 2 3 2 3
* [[Srutal]][22]: 5 2 5 2 5 2 5 2 5 2 5 5 2 5 2 5 2 5 2 5 2 5
* [[Srutal]][22]: 5 2 5 2 5 2 5 2 5 2 5 5 2 5 2 5 2 5 2 5 2 5
* Srutal[34]: 2 3 2 2 3 2 2 3 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2 3 2 2 3 2 2 3 2
* [[Trisedodge]][15]: 5 6 5 5 6 5 5 6 5 5 6 5 5 6 5
* [[Trisedodge]][15]: 5 6 5 5 6 5 5 6 5 5 6 5 5 6 5
* Trisedodge[20]: 5 1 5 5 5 1 5 5 5 1 5 5 5 1 5 5 5 1 5 5
* Trisedodge[35]: 1 4 1 4 1 4 1 1 4 1 4 1 4 1 1 4 1 4 1 4 1 1 4 1 4 1 4 1 1 4 1 4 1 4 1
^ ''Leapday and leapfrog map to the same scale, but leapday has higher complexity (ie requires more notes to reach all its most important intervals).''




Line 789: Line 812:
11-tone CPS ''(1-of-1,3,5,9,11,15,19,25,27,29,33)''
11-tone CPS ''(1-of-1,3,5,9,11,15,19,25,27,29,33)''
* 5 9 8 4 7 4 10 6 6 11 10
* 5 9 8 4 7 4 10 6 6 11 10
''Some of its interesting subsets:''
* 5 21 7 14 12 11 10 (''closely resembles [[14edo#scales|fennec scale]]{{idio}} from [[14edo]]'')
* 14 12 11 10 12 11 10 (''loosely resembles porcupine[7] or [[7edo]]'')
* 22 11 4 10 23 10 (''loosely resembles minor blues scale'')
* 22 11 14 12 11 10 (''loosely resembles [[porcupine]][6] or [[6afdo]]'')
* 26 7 14 6 27 (''sounds regal but brooding'')
* 26 7 14 12 21 (''sounds sparkly and delicate'')
* 22 11 14 23 10  (''closely resembles [[6afdo#scales|geode]]{{idio}} subset of [[6afdo]]'')




Line 801: Line 832:
12-tone CPS ''(11-of-3,5,9,11,15,19,25,27,29,33,37,41)''
12-tone CPS ''(11-of-3,5,9,11,15,19,25,27,29,33,37,41)''
* 10 11 4 8 9 5 10 8 3 6 3 3
* 10 11 4 8 9 5 10 8 3 6 3 3
15-tone CPS ''(1-of-1,3,5,9,11,15,19,25,27,29,33,37,41,55,57)''
* 5 9 2 4 2 4 7 4 10 3 3 6 3 8 10
15-tone CPS ''(14-of-1,3,5,9,11,15,19,25,27,29,33,37,41,55,57)''
* 10 8 3 6 3 3 10 4 7 4 2 4 2 9 5
13-tone degen. [[eikosany]] ''(1,3,5,9,15,25)''
* 5 2 5 9 5 7 14 7 5 9 5 2 5
14-tone degen. eikosany ''(3,5,9,15,25,27)''
* 9 3 2 7 5 7 2 3 9 7 5 9 5 7
16-tone degen. eikosany ''(1,3,5,9,11,15)''
* 4 7 3 2 5 2 3 7 4 7 3 11 1 11 3 7
18-tone degen. eikosany ''(3,5,9,11,15,19)''
* 4 2 4 6 5 6 3 3 3 6 5 6 4 2 4 6 5 6




; Other scales
; Other scales
* [[Equipentatonic]]: 16 16 16 16 16
* [[Equipentatonic]] (exactly [[5edo]]): 16 16 16 16 16
* [[Equiheptatonic]] (approximate): 11 12 11 12 11 12 11


== Music ==
== Music ==
[[Bryan Deister]]
=== Modern renditions ===
; {{w|Frédéric Chopin}}
* [https://www.youtube.com/watch?v=ng1UyvhHcrQ Prelude Op. 28, No. 4 in E minor « Suffocation »] (1839), arranged for harpsichord, tuned into 80-edo – rendered by [[Claudi Meneghin]] (2025)
 
=== 21st century ===
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/H6DlCHKii-o ''microtonal improvisation in 80edo''] (2025)
* [https://www.youtube.com/shorts/H6DlCHKii-o ''microtonal improvisation in 80edo''] (2025)


; [[Francium]]
; [[Francium]]
* [https://www.youtube.com/watch?v=-MRhrpzRSC8 ''Itself''] (2024) – semisept in 80edo
* [https://www.youtube.com/watch?v=-MRhrpzRSC8 ''Itself''] (2024) – in semisept, 80edo tuning
* [https://www.youtube.com/watch?v=QuRHzoIozwo ''the circular one''] (2024)
* [https://www.youtube.com/watch?v=QuRHzoIozwo ''the circular one''] (2024)


Line 817: Line 878:
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* [https://luphoria.com/xenpaper/#%23_licensed_under_CC-BY-4.0%2C_by_User%3AGodtone_(en.xen.wiki)%0A(osc%3Asawtooth12)%7B80edo%7D%7Br253Hz%7D%0A(bpm%3A96)(env%3A3085)%0A%5B0%2C47%5D-%5B0%2C14%2C47%5D-%5B0%2C14%2C26%2C47%5D-%0A%5B0%2C33%2C47%5D-%5B0%2C47%5D-%5B0%5D-%0A%5B0%2C47%5D-%5B0%2C14%2C47%5D-%5B0%2C14%2C26%2C47%5D-%0A%5B0%2C33%2C47%5D-%5B0%2C47%5D-%5B0%2C14%5D-%0A%5B%6061%2C14%2C28%5D-%5B14%2C28%2C61%5D-%5B1%2C40%2C61%5D-%0A%5B%6075%2C14%2C47%2C61%5D-%5B14%2C61%2C74%5D%5B14%5D--%0A%5B%6061%2C14%2C28%5D-%5B14%2C28%2C61%5D-%5B14%2C40%2C61%5D-%0A%5B%6075%2C14%2C47%2C61%5D--%5B%6066%2C14%2C33%2C80%5D--%0A%0A(bpm%3A128)(env%3A1282)%0A%5B0%5D-%5B0%2C6%5D._%5B0%2C18%5D-%5B0%2C6%2C47%5D.%0A%5B0%2C6%2C40%5D-%5B7%2C40%2C66%5D.%0A%5B0%2C7%2C26%2C59%5D-%5B7%2C26%2C59%2C80%5D.%0A%5B0%2C21%2C47%2C80%5D-%5B7%5D._%5B0%2C21%5D-%5B7%2C21%2C47%5D.%0A%5B0%2C7%2C40%5D-%5B0%2C7%2C40%2C66%5D._%5B0%2C7%2C26%2C61%5D-%5B7%2C26%2C61%2C80%5D.%0A%7Br%6061%7D%5B26%2C47%2C80%2C95%2C108%5D-%5B0%2C7%5D.%0A%5B0%2C20%5D-%5B%6047%2C0%2C20%2C47%5D._%5B%6040%2C%6066%2C7%2C40%5D-%5B7%2C40%2C66%5D._%5B%6060%2C6%2C27%2C60%5D-%5B27%2C60%2C80%5D.%0A%5B0%2C26%2C47%2C80%5D-%5B0%2C7%5D.%0A%5B0%2C20%5D-%5B%6047%2C0%2C20%2C47%5D._%5B%6040%2C%6066%2C7%2C40%5D-%5B7%2C40%2C66%5D._%5B%6060%2C6%2C27%2C60%5D-%5B27%2C60%2C80%5D.%0A%5B7%2C27%2C60%2C88%5D--%5B7%2C27%5D%5B27%2C60%2C88%5D---..%0A%7Br21%7D%5B0%2C26%2C47%5D-%7Br%6059%7D%5B0%2C26%2C47%5D-%7Br21%7D%5B0%2C26%2C47%5D-%0A%7Br%6059%7D%5B7%2C27%2C60%2C88%5D--%5B7%2C27%2C60%5D%5B27%2C60%2C88%5D---..%0A%7Br21%7D%5B0%2C26%2C47%5D-%7Br%6059%7D%5B0%2C26%2C47%2C80%5D-%7Br21%7D%5B0%2C26%2C47%5D-%0A%5B7%2C27%2C60%2C88%5D--%5B7%2C27%5D%5B27%2C60%2C88%5D---..%0A%7Br21%7D%5B0%2C26%2C47%5D-%7Br%6059%7D%5B0%2C26%2C47%5D-%7Br21%7D%5B0%2C26%2C47%5D-%0A%7Br%6059%7D%5B0%2C27%2C47%2C80%5D-%5B%6047%2C0%2C28%2C47%5D-%7Br%6040%7D%5B0%2C26%2C47%2C65%5D-%5B47%2C65%2C80%2C106%5D-%0A%7Br20%7D%5B0%2C27%2C47%2C80%5D-%5B%6047%2C0%2C28%2C47%5D-%7Br%6040%7D%5B0%2C26%2C47%2C65%5D-%5B47%2C65%2C80%2C106%5D-%0A%7Br20%7D%5B0%2C27%2C47%2C80%5D-%5B%6047%2C0%2C28%2C47%5D-%7Br%6040%7D%5B0%2C26%2C47%2C65%5D-%5B47%2C65%2C80%2C106%5D-%0A%7Br20%7D%5B0%2C27%2C47%2C80%5D-%5B%6047%2C0%2C28%2C47%5D-%7Br%6040%7D%5B0%2C26%2C47%2C65%5D-%5B47%2C65%2C80%2C106%5D-%0A%7Br20%7D%5B0%2C26%2C47%2C80%5D- unnamed xenpaper sketch] licensed under [https://creativecommons.org/licenses/by/4.0/ CC-BY-4.0]
* [https://luphoria.com/xenpaper/#%23_PLEASE_play_this_80_EDO_xenpaper_piece_out_loud%0A%23_PREFERABLY_on_mediocre_laptop_speakers%2C%0A%23_as_it_sounds_BETTER_acoustically!%0A%23_licensed_under_CC-BY-4.0%2C_by_User%3AGodtone_(en.xen.wiki)%0A(osc%3Asawtooth24)(bpm%3A161)%0A%7B80edo%7D_%23_inspiration%3A%0A%23_%7B44_%3A_54_%3A_56_%3A___58_%3A_60_%3A__69__%3A__74__%3A_82_%3A_85%7D%0A%23_%7B0%5C1_24%5C80_28%5C80_32%5C80_36%5C80_52%5C80_60%5C80_72%5C80_76%5C80%7D%0A%5B0_24_32_60%5D---%0A%5B0_23_36_52%5D---%0A%5B%6078_24_45_60%5D---%0A%5B%6075_24_46_61%5D---%0A%5B%6072_11_24_46_70%5D-------%0A%5B%6046_%6072_11_24_46%5D-------%0A%5B%6040_%6072_11_26_60%5D----%0A%5B%6040_%6072_11_26_52%5D--%0A%5B%6060_%6072_11_24_60%5D---%0A%5B%6055_%6072_11_24_62%5D---%0A%5B%6050_%6072_11_24_70%5D-------%0A%5B%6024_%6050_%6072_11_24_46%5D-------%0A%7Br20%7D%0A%5B%6024_%6050_%6072_11_24_46%5D-------%0A%6024_%6050_%6072_11_24_46%0A%5B%6024_%6055_%6072_11_24%5D-%0A%5B%6011_%6045_%6072_11_24_45%5D-------%0A%6011_%6045_%6072_11_24_45%0A%5B%6024_%6050_%6072_11_24_46%5D---------%0A%6024_%6050_%6072_11_24_46%0A%5B%6024_%6055_%6072_11_24%5D-%0A%5B%6011_%6045_%6072_11_24_45%5D---------%0A%6011_%6045_%6072_11_24_45%0A%5B%6024_%6050_%6072_11_24_46%5D-------%0A%5B%6024_%6055_%6072_11_24%5D---%0A%5B%6055_%6072_11_24_62%5D---%0A%5B%6040_%6074_25_44_59%5D%0A%5B%6040_%6072_25_44_59%5D-----%0A%5B%6042_%6072_25_42%5D%0A%5B%6060_%6072_25_36%5D------%0A%5B%6042_%6072_25_42%5D%0A%7Br%6060%7D%0A%5B%6055_%6072_11_24_62%5D%0A%5B%6050_%6072_11_24_70%5D----%0A%5B%6024_%6050_%6072_11_24_46%5D-%0A%5B%6072_11_24_46_70%5D-------%0A%5B%6050_%6072_11_24_70%5D-------%0A%5B%6072_11_24_46_70%5D-------%0A%5B%6040_%6072_11_26_52%5D-------%0A%5B%6060_%6072_11_24_60%5D----%0A%5B%6055_%6072_11_24_62%5D--%0A%5B%6050_%6072_11_24_62%5D%0A%5B%6050_%6072_11_24_70%5D----%0A%5B%6024_%6050_%6072_11_24_46%5D-%0A%5B%6072_11_24_46_70%5D------- unnamed piece] licensed under [https://creativecommons.org/licenses/by/4.0/ CC-BY-4.0]
* [https://luphoria.com/xenpaper/#%23_PLEASE_play_this_80_EDO_xenpaper_piece_out_loud%0A%23_PREFERABLY_on_mediocre_laptop_speakers%2C%0A%23_as_it_sounds_BETTER_acoustically!%0A%23_licensed_under_CC-BY-4.0%2C_by_User%3AGodtone_(en.xen.wiki)%0A(osc%3Asawtooth24)(bpm%3A161)%0A%7B80edo%7D_%23_inspiration%3A%0A%23_%7B44_%3A_54_%3A_56_%3A___58_%3A_60_%3A__69__%3A__74__%3A_82_%3A_85%7D%0A%23_%7B0%5C1_24%5C80_28%5C80_32%5C80_36%5C80_52%5C80_60%5C80_72%5C80_76%5C80%7D%0A%5B0_24_32_60%5D---%0A%5B0_23_36_52%5D---%0A%5B%6078_24_45_60%5D---%0A%5B%6075_24_46_61%5D---%0A%5B%6072_11_24_46_70%5D-------%0A%5B%6046_%6072_11_24_46%5D-------%0A%5B%6040_%6072_11_26_60%5D----%0A%5B%6040_%6072_11_26_52%5D--%0A%5B%6060_%6072_11_24_60%5D---%0A%5B%6055_%6072_11_24_62%5D---%0A%5B%6050_%6072_11_24_70%5D-------%0A%5B%6024_%6050_%6072_11_24_46%5D-------%0A%7Br20%7D%0A%5B%6024_%6050_%6072_11_24_46%5D-------%0A%6024_%6050_%6072_11_24_46%0A%5B%6024_%6055_%6072_11_24%5D-%0A%5B%6011_%6045_%6072_11_24_45%5D-------%0A%6011_%6045_%6072_11_24_45%0A%5B%6024_%6050_%6072_11_24_46%5D---------%0A%6024_%6050_%6072_11_24_46%0A%5B%6024_%6055_%6072_11_24%5D-%0A%5B%6011_%6045_%6072_11_24_45%5D---------%0A%6011_%6045_%6072_11_24_45%0A%5B%6024_%6050_%6072_11_24_46%5D-------%0A%5B%6024_%6055_%6072_11_24%5D---%0A%5B%6055_%6072_11_24_62%5D---%0A%5B%6040_%6074_25_44_59%5D%0A%5B%6040_%6072_25_44_59%5D-----%0A%5B%6042_%6072_25_42%5D%0A%5B%6060_%6072_25_36%5D------%0A%5B%6042_%6072_25_42%5D%0A%7Br%6060%7D%0A%5B%6055_%6072_11_24_62%5D%0A%5B%6050_%6072_11_24_70%5D----%0A%5B%6024_%6050_%6072_11_24_46%5D-%0A%5B%6072_11_24_46_70%5D-------%0A%5B%6050_%6072_11_24_70%5D-------%0A%5B%6072_11_24_46_70%5D-------%0A%5B%6040_%6072_11_26_52%5D-------%0A%5B%6060_%6072_11_24_60%5D----%0A%5B%6055_%6072_11_24_62%5D--%0A%5B%6050_%6072_11_24_62%5D%0A%5B%6050_%6072_11_24_70%5D----%0A%5B%6024_%6050_%6072_11_24_46%5D-%0A%5B%6072_11_24_46_70%5D------- unnamed piece] licensed under [https://creativecommons.org/licenses/by/4.0/ CC-BY-4.0]
[[User:Tristanbay|'''Tristan Bay''']]


* ''Subtract Hominem'' (2025) [https://tristanbay.bandcamp.com/track/subtract-hominem Bandcamp] | [https://youtu.be/JhGvrJ86jLU YouTube]
; [[Budjarn Lambeth]]
* [https://youtu.be/6N_8QM2UK5I ''Improvisation in compressed 80edo'' (435zpi)] (2025)
 
; [[Tristan Bay]]
* ''Subtract Hominem'' (2025) – [https://tristanbay.bandcamp.com/track/subtract-hominem Bandcamp] | [https://youtu.be/JhGvrJ86jLU YouTube]
 
; [[Xotla]]
; [[Xotla]]
* "Mollusc Merchant" from ''Jazzbeetle'' (2023) [https://xotla.bandcamp.com/track/mollusc-merchant-80edo Bandcamp] | [https://www.youtube.com/watch?v=5cb0WHAwVuM YouTube]
* "Mollusc Merchant" from ''Jazzbeetle'' (2023) [https://xotla.bandcamp.com/track/mollusc-merchant-80edo Bandcamp] | [https://www.youtube.com/watch?v=5cb0WHAwVuM YouTube]
Retrieved from "https://en.xen.wiki/w/80edo"