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List of superparticular intervals: Difference between revisions

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Split the superparticulars table into subsections based on prime limit.
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== List of superparticular intervals ==
== List of superparticular intervals ==
=== 2-limit ===
{| class="wikitable center-6"
{| class="wikitable center-6"
|-
|-
Line 12: Line 13:
! [[Monzo]]
! [[Monzo]]
! Name(s)
! Name(s)
! Meta<ref>Denoted by s-expressions, where s''k'' is defined as (''k''/(''k'' - 1))/((''k'' + 1)/''k''). See [[square superparticular]] for details.</ref>
! Meta<ref name="ssp">Denoted by S-expressions, where s''k'' is defined as (''k''/(''k'' - 1))/((''k'' + 1)/''k''). See [[square superparticular]] for details.</ref>
|-
! colspan="6" | 2-limit (complete)
|-
|-
| [[2/1]]
| [[2/1]]
Line 22: Line 21:
| Octave, duple; ''after [[octave reduction]]:'' (perfect) unison, unity, perfect prime, tonic
| Octave, duple; ''after [[octave reduction]]:'' (perfect) unison, unity, perfect prime, tonic
|
|
|-
|}
! colspan="6" | 3-limit (complete)
=== 3-limit ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[3/2]]
| [[3/2]]
Line 45: Line 51:
| (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, octave-reduced 9th harmonic or harmonic ninth
| (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, octave-reduced 9th harmonic or harmonic ninth
| S3
| S3
|-
|}
! colspan="6" | 5-limit (complete)
=== 5-limit ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[5/4]]
| [[5/4]]
Line 89: Line 102:
| Syntonic comma, Didymus comma
| Syntonic comma, Didymus comma
| S9
| S9
|-
|}
! colspan="6" | 7-limit (complete)
=== 7-limit ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[7/6]]
| [[7/6]]
Line 182: Line 202:
| Ragisma
| Ragisma
|
|
|-
|}
! colspan="6" | 11-limit (complete)
=== 11-limit ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[11/10]]
| [[11/10]]
Line 303: Line 330:
| Kalisma, Gauss comma
| Kalisma, Gauss comma
| S99
| S99
|-
|}
! colspan="6" | 13-limit (complete)
=== 13-limit ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[13/12]]
| [[13/12]]
Line 501: Line 535:
| Chalmersia
| Chalmersia
| S351
| S351
|-
|}
! colspan="6" | 17-limit (complete)
=== 17-limit ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[17/16]]
| [[17/16]]
Line 783: Line 824:
|  
|  
|
|
|-
|}
! colspan="6" | 19-limit (complete)
=== 19-limit ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[19/18]]
| [[19/18]]
Line 1,198: Line 1,246:
|  
|  
|
|
|-
|}
! colspan="6" | 23-limit (complete)
=== 23-limit ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[23/22]]
| [[23/22]]
Line 1,718: Line 1,773:
|  
|  
|  
|  
|-
|}
! colspan="6" | 29-limit (complete)
=== 29-limit ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[29/28]]
| [[29/28]]
Line 2,448: Line 2,510:
|
|
| S13311
| S13311
|-
|}
! colspan="6" | 31-limit (incomplete)
=== 31-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[31/30]]
| [[31/30]]
Line 2,520: Line 2,589:
| Yunzee comma
| Yunzee comma
| S63
| S63
|-
|}
! colspan="6" | 37-limit (incomplete)
=== 37-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[37/36]]
| [[37/36]]
Line 2,571: Line 2,647:
| Bullionisma
| Bullionisma
|  
|  
|-
|}
! colspan="6" | 41-limit (incomplete)
=== 41-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[41/40]]
| [[41/40]]
Line 2,615: Line 2,698:
| Shaftesburisma
| Shaftesburisma
|  
|  
|-
|}
! colspan="6" | 43-limit (incomplete)
=== 43-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[43/42]]
| [[43/42]]
Line 2,673: Line 2,763:
|
|
| S44
| S44
|-
|}
! colspan="6" | 47-limit (incomplete)
=== 47-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[47/46]]
| [[47/46]]
Line 2,724: Line 2,821:
|  
|  
| S48
| S48
|-
|}
! colspan="6" | 53-limit (incomplete)
=== 53-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[53/52]]
| [[53/52]]
Line 2,754: Line 2,858:
|
|
|
|
|-
|}
! colspan="6" | 59-limit (incomplete)
=== 59-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[59/58]]
| [[59/58]]
Line 2,777: Line 2,888:
|  
|  
| S59
| S59
|-
|}
! colspan="6" | 61-limit (incomplete)
=== 6-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[61/60]]
| [[61/60]]
Line 2,814: Line 2,932:
|  
|  
| S61
| S61
|-
|}
! colspan="6" | 67-limit (incomplete)
=== 67-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[67/66]]
| [[67/66]]
Line 2,830: Line 2,955:
|  
|  
|
|
|-
|}
! colspan="6" | 71-limit (incomplete)
=== 71-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[71/70]]
| [[71/70]]
Line 2,846: Line 2,978:
|  
|  
|
|
|-
|}
! colspan="6" | 73-limit (incomplete)
=== 73-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[73/72]]
| [[73/72]]
Line 2,862: Line 3,001:
|  
|  
|
|
|-
|}
! colspan="6" | 79-limit (incomplete)
=== 79-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[79/78]]
| [[79/78]]
Line 2,878: Line 3,024:
|  
|  
|
|
|-
|}
! colspan="6" | 83-limit (incomplete)
=== 83-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[83/82]]
| [[83/82]]
Line 2,894: Line 3,047:
|  
|  
|
|
|-
|}
! colspan="6" | 89-limit (incomplete)
=== 89-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[89/88]]
| [[89/88]]
Line 2,910: Line 3,070:
|  
|  
|
|
|-
|}
! colspan="6" | 97-limit (incomplete)
=== 97-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[97/96]]
| [[97/96]]
Line 2,926: Line 3,093:
|  
|  
|
|
|-
|}
! colspan="6" | 101-limit (incomplete)
=== 101-limit (incomplete) ===
{| class="wikitable center-6"
! [[Ratio]]
! [[Cent]]s
! Factorization
! [[Monzo]]
! Name(s)
! Meta<ref name="ssp"/>
|-
|-
| [[101/100]]
| [[101/100]]
Retrieved from "https://en.xen.wiki/w/List_of_superparticular_intervals"