19-limit: Difference between revisions

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The 19-prime-limit can be modeled in a 7-dimensional lattice, with the primes 3, 5, 7, 11, 13, 17, and 19 represented by each dimension. The prime 2 does not appear in the typical 19-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, an eighth dimension is need.
The 19-prime-limit can be modeled in a 7-dimensional lattice, with the primes 3, 5, 7, 11, 13, 17, and 19 represented by each dimension. The prime 2 does not appear in the typical 19-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, an eighth dimension is need.


==19-odd limit Intervals of 19==
[[EDO]]s which provides an excellent tuning for 19-limit intervals are: 80, 94, 111, 121, 217, 270, 282, 311, 320, 364, 388, 400, 422, 436, 460, 525, 581, 597, 624, 643, 653, 692, 718, 742, 771, 860, 867, 882, 908, 925, 935, 954, and 997 among others.
 
{| class="wikitable"
|-
! | Ratio
! | Cents Value
! colspan="2" |[[Kite's color notation|Color name]]
! | Name
|-
| | [[20/19|20/19]]
| | 88.801
|19uy1
|nuyo 1sn
| | lesser undevicesimal semitone
|-
| | [[19/18|19/18]]
| | 93.603
|19o2
|ino 2nd
| | greater undevicesimal semitone
|-
| | [[19/17|19/17]]
| | 192.558
|19o17u2
|nosu 2nd
| | undevicesimal whole tone ("meantone")
|-
| | [[22/19|22/19]]
| | 253.805
|19u1o2
|nulo 2nd
| | enneadecimal second–third
|-
| | [[19/16|19/16]]
| | 297.513
|19o3
|ino 3rd
| | undevicesimal minor third
|-
| | [[24/19|24/19]]
| | 404.442
|19u3
|inu 3rd
| | lesser undevicesimal major third
|-
| | [[19/15|19/15]]
| | 409.244
|19og4
|nogu 4th
| | greater undevicesimal major third
|-
| | [[19/14|19/14]]
| | 528.687
|19or4
|noru 4th
| | undevicesimal acute fourth
|-
| | [[26/19|26/19]]
| | 543.015
|19u3o5
|nutho 5th
| | undevicesimal superfourth
|-
| | [[19/13|19/13]]
| | 656.985
|19o3u4
|nothu 4th
| | undevicesimal subfifth
|-
| | [[28/19|28/19]]
| | 671.313
|19uz5
|nuzo 5th
| | undevicesimal grave fifth
|-
| | [[30/19|30/19]]
| | 790.756
|19uy5
|nuyo 5th
| | lesser undevicesimal minor sixth
|-
| | [[19/12|19/12]]
| | 795.558
|19o6
|ino 6th
| | lesser undevicesimal minor sixth
|-
| | [[32/19|32/19]]
| | 902.487
|19u6
|inu 6th
| | undevicesimal major sixth
|-
| | [[19/11|19/11]]
| | 946.195
|19o1u7
|nolu 7th
| | enneadecimal sixth–seventh
|-
| | [[34/19|34/19]]
| | 1007.442
|19u17o7
|nuso 7th
| | undevicesimal minor seventh
|-
| | [[36/19|36/19]]
| | 1106.397
|19u7
|inu 7th
| | lesser undevicesimal major seventh
|-
| | [[19/10|19/10]]
| | 1111.199
|19og8
|nogu 8ve
| | greater undevicesimal major seventh
|}


see [[Harmonic_Limit|Harmonic Limit]]       
see [[Harmonic_Limit|Harmonic Limit]]       

Revision as of 02:33, 3 May 2019

In 19-limit Just Intonation, all ratios in the system will contain no primes higher than 19.

The 19-prime-limit can be modeled in a 7-dimensional lattice, with the primes 3, 5, 7, 11, 13, 17, and 19 represented by each dimension. The prime 2 does not appear in the typical 19-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, an eighth dimension is need.

EDOs which provides an excellent tuning for 19-limit intervals are: 80, 94, 111, 121, 217, 270, 282, 311, 320, 364, 388, 400, 422, 436, 460, 525, 581, 597, 624, 643, 653, 692, 718, 742, 771, 860, 867, 882, 908, 925, 935, 954, and 997 among others.

see Harmonic Limit

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