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However, while 159edo is [[consistent]] up to the 17-odd-limit, it proves to be inconsistent in the 19-odd-limit, with the ~[[19/17]] mapped to the second closest step, and this despite 53edo's approximation of [[19/16]] being inherited from 53edo.  In addition, the [[direct mapping]] and the more complicated traditional mapping for intervals such as [[49/32]], [[35/32]], and [[169/128]] do not match, and as a result, 159edo can be thought of as having a perfunctory [[7-limit]] that mainly serves to bridge to the [[11-limit]] and divide the nearly just 3/2 into three, as well as a similarly perfunctory [[13-limit]] that mainly serves to bridge to the 17-limit and to absorb complex combinations of 3 and 5.
However, while 159edo is [[consistent]] up to the 17-odd-limit, it proves to be inconsistent in the 19-odd-limit, with the ~[[19/17]] mapped to the second closest step, and this despite 53edo's approximation of [[19/16]] being inherited from 53edo.  In addition, the [[direct mapping]] and the more complicated traditional mapping for intervals such as [[49/32]], [[35/32]], and [[169/128]] do not match, and as a result, 159edo can be thought of as having a perfunctory [[7-limit]] that mainly serves to bridge to the [[11-limit]] and divide the nearly just 3/2 into three, as well as a similarly perfunctory [[13-limit]] that mainly serves to bridge to the 17-limit and to absorb complex combinations of 3 and 5.
Notably, 159edo provides the [[optimal patent val]] for 11-limit guiron, 13-limit tritikleismic, the 13-limit rank-3 temperament [[Gamelismic family #Portending|portending]], as well as the 17-limit rank-6 temperament tempering out 273/272. In addition to this, it also supports both forms of the yarman temperament, with a generator of 2\159 which can be taken as an approximate 105/104. Both have a [[MOS]] of 79 or 80 notes to the octave, and have their optimal patent vals supplied by 159edo in 7-limit, 11-limit, 13-limit, 17-limit and even 19-limit forms.


=== Prime harmonics ===
=== Prime harmonics ===
Line 1,690: Line 1,692:
|  
|  
| Ursulisma
| Ursulisma
|-
| 17
| [[595/594]]
| {{monzo| -1 -3 1 1 -1 0 1 }}
| 2.9121
|
| Dakotisma
|-
| 17
| [[715/714]]
| {{monzo| -1 -1 1 -1 1 1 -1 }}
| 2.4230
|
| September comma
|-
| 17
| [[833/832]]
| {{monzo| -6 0 0 2 0 -1 1 }}
| 2.0796
| Sothuzozo
| Horizon comma
|-
| 17
| [[936/935]]
| {{monzo| 3 2 -1 0 -1 1 -1 }}
| 1.8506
|
| Ainos comma
|-
|-
| 17
| 17
Line 1,695: Line 1,725:
| {{monzo| 0 4 2 -1 0 0 -2 }}
| {{monzo| 0 4 2 -1 0 0 -2 }}
| 1.7107
| 1.7107
|
| Fidesma
|-
| 17
| [[1089/1088]]
| {{monzo| -6 2 0 0 2 0 -1 }}
| 1.5905
|
| Twosquare comma
|-
| 17
| [[1701/1700]]
| {{monzo| -2 5 -2 1 0 0 -1 }}
| 1.0181
|
| Palingenetic comma
|-
| 17
| 24576/24565
| {{monzo| 13 1 -1 0 0 0 -3 }}
| 0.7751
|
| [[24576/24565|Archagallisma]]
|-
| 17
| [[2431/2430]]
| {{monzo| -1 -5 -1 0 1 1 1 }}
| 0.7123
|
|
|-
| 17
| <abbr title="248897/248832">(12 digits)</abbr>
| {{monzo| -10 -5 0 0 4 0 1 }}
| 0.44522
|  
|  
|  
|  
|-
| 17
| 12376/12375
| {{monzo| 3 -2 -3 1 -1 1 1 }}
| 0.1399
|
| [[Flashma]]
|-
| 17
| 14400/14399
| {{monzo| 6 2 2 -1 -2 0 -1 }}
| 0.1202
| Sululuruyoyo
| [[Sparkisma]]
|-
|-
|}
|}
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* In the 23-limit, with the 19-limit skipped, this system is known to temper out 392/391, 460/459, 507/506, 529/528, 897/896, 1105/1104, 1288/1287, 2024/2023, 2025/2024, and 2646/2645 among others.
* In the 23-limit, with the 19-limit skipped, this system is known to temper out 392/391, 460/459, 507/506, 529/528, 897/896, 1105/1104, 1288/1287, 2024/2023, 2025/2024, and 2646/2645 among others.
Notably, 159edo provides the [[optimal patent val]] for 11-limit guiron, 13-limit tritikleismic, the 13-limit rank-3 temperament [[Gamelismic family #Portending|portending]], as well as the 17-limit rank-6 temperament tempering out 273/272. In addition to this, it also supports both forms of the yarman temperament, with a generator of 2\159 which can be taken as an approximate 105/104. Both have a [[MOS]] of 79 or 80 notes to the octave, and have their optimal patent vals supplied by 159edo in 7-limit, 11-limit, 13-limit, 17-limit and even 19-limit forms.


As a result of tempering out some of the commas, it allows [[essentially tempered chord]]s including [[marveltwin chords]], [[gentle chords]], [[keenanismic chords]], [[werckismic chords]], and [[sinbadmic chords]] in the 13-odd-limit, in addition to [[island chords]] and [[nicolic chords]] in the 15-odd-limit.
As a result of tempering out some of the commas, it allows [[essentially tempered chord]]s including [[marveltwin chords]], [[gentle chords]], [[keenanismic chords]], [[werckismic chords]], and [[sinbadmic chords]] in the 13-odd-limit, in addition to [[island chords]] and [[nicolic chords]] in the 15-odd-limit.
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