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Interseptimal interval: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
|+The pentatonic framework
|+ style="font-size: 105%;" | The pentatonic framework
! colspan="2" | names
|-
! quality
! colspan="2" | Names
! boundaries
! Quality
! colspan="2" | heptatonic equivalent
! Boundaries
! colspan="2" | Heptatonic equivalent
|-
|-
| rowspan="3" | 1sn
| rowspan="3" | 1sn
| rowspan="3" | unison
| rowspan="3" | Unison
| perfect
| Perfect
| 1/1 to 64/63
| 1/1 to 64/63
| perfect
| Perfect
| 1sn
| 1sn
|-
|-
| half-augmented
| Half-augmented
| (interseptimal)
| (Interseptimal)
! colspan="2" |
! colspan="2" |  
|-
|-
| augmented
| Augmented
| 28/27 to 16/15
| 28/27 to 16/15
| minor
| Minor
| rowspan="3" |2nd
| rowspan="3" | 2nd
|-
|-
! colspan="3" |
! colspan="3" |  
| (interpental)
| (Interpental)
| neutral
| Neutral
|-
|-
| rowspan="3" | penta-2nd
| rowspan="3" | Penta-2nd
| rowspan="3" | subthird
| rowspan="3" | Subthird
| minor
| Minor
| 10/9 to 8/7
| 10/9 to 8/7
| major
| Major
|-
|-
| neutral
| Neutral
| (interseptimal)
| (Interseptimal)
! colspan="2" |
! colspan="2" |  
|-
|-
| major
| Major
| 7/6 to 6/5
| 7/6 to 6/5
| minor
| Minor
| rowspan="3" | 3rd
| rowspan="3" | 3rd
|-
|-
! colspan="3" |
! colspan="3" |  
| (interpental)
| (Interpental)
| neutral
| Neutral
|-
|-
| rowspan="5" | penta-3rd
| rowspan="5" | Penta-3rd
| rowspan="5" | fourthoid
| rowspan="5" | Fourthoid
| diminished
| Diminished
| 5/4 to 9/7
| 5/4 to 9/7
| major
| Major
|-
|-
| half-diminished
| Half-diminished
| (interseptimal)
| (Interseptimal)
! colspan="2" |
! colspan="2" |  
|-
|-
| perfect
| Perfect
| 21/16 to 27/20
| 21/16 to 27/20
| perfect
| perfect
| rowspan="3" | 4th
| rowspan="3" | 4th
|-
|-
| half-augmented
| Half-augmented
| (interpental)
| (Interpental)
| half-augmented
| Half-augmented
|-
|-
| augmented
| Augmented
| rowspan="2" |7/5 to 10/7
| rowspan="2" | 7/5 to 10/7
| augmented
| Augmented
|-
|-
| rowspan="5" | penta-4th
| rowspan="5" | Penta-4th
| rowspan="5" | fifthoid
| rowspan="5" | Fifthoid
| diminished
| Diminished
| diminished
| Diminished
| rowspan="3" | 5th
| rowspan="3" | 5th
|-
|-
| half-diminished
| Half-diminished
| (interpental)
| (Interpental)
| half-diminished
| Half-diminished
|-
|-
| perfect
| Perfect
| 40/27 to 32/21
| 40/27 to 32/21
| perfect
| Perfect
|-
|-
| half-augmented
| Half-augmented
| (interseptimal)
| (Interseptimal)
! colspan="2" |
! colspan="2" |  
|-
|-
| augmented
| Augmented
| 14/9 to 8/5
| 14/9 to 8/5
| minor
| Minor
| rowspan="3" | 6th
| rowspan="3" | 6th
|-
|-
! colspan="3" |
! colspan="3" |  
| (interpental)
| (Interpental)
| neutral
| Neutral
|-
|-
| rowspan="3" |penta-5th
| rowspan="3" | Penta-5th
| rowspan="3" |subseventh
| rowspan="3" | Subseventh
| minor
| Minor
| 5/3 to 12/7
| 5/3 to 12/7
| major
| Major
|-
|-
| neutral
| Neutral
| (interseptimal)
| (Interseptimal)
! colspan="2" |
! colspan="2" |  
|-
|-
| major
| Major
| 7/4 to 9/5
| 7/4 to 9/5
| minor
| Minor
| rowspan="3" |7th
| rowspan="3" | 7th
|-
|-
! colspan="3" |
! colspan="3" |  
| (interpental)
| (Interpental)
| neutral
| Neutral
|-
|-
| rowspan="3" | hexave
| rowspan="3" | Hexave
| rowspan="3" | octoid
| rowspan="3" | Octoid
| diminished
| Diminished
| 15/8 to 27/14
| 15/8 to 27/14
| major
| Major
|-
|-
| half-diminished
| Half-diminished
| (interseptimal)
| (Interseptimal)
! colspan="2" |
! colspan="2" |  
|-
|-
| perfect
| Perfect
| 63/32 to 2/1
| 63/32 to 2/1
| perfect
| Perfect
| 8ve
| 8ve
|}
|}
Note the two additional interseptimal regions. The boundary ratios are mostly either 81/80 or 64/63 away from a 3-limit interval. The exceptions are 7/5 and 10/7, which are only a [[5120/5103|Saruyo]] comma away from the 3-limit diminished 5th and augmented 4th respectively.  
Note the two additional interseptimal regions. The boundary ratios are mostly either 81/80 or 64/63 away from a 3-limit interval. The exceptions are 7/5 and 10/7, which are only a [[5120/5103|Saruyo]] comma away from the 3-limit diminished 5th and augmented 4th respectively.  


Line 210: Line 212:


=== Maj2–min3 (semifourth/chthonic) ===
=== Maj2–min3 (semifourth/chthonic) ===
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
! Interval
! Interval
! Cents Value
! Cents Value
Line 222: Line 224:
| 1\[[5edo|5]]
| 1\[[5edo|5]]
| 240.000
| 240.000
| -
| —
|-
|-
| 54/47
| 54/47
Line 250: Line 252:
| 6\[[29edo|29]]
| 6\[[29edo|29]]
| 248.276
| 248.276
| -
| —
|-
|-
| 5\[[24edo|24]]
| 5\[[24edo|24]]
| 250.000
| 250.000
| -
| —
|-
|-
| [[52/45]]
| [[52/45]]
Line 270: Line 272:
| 4\[[19edo|19]]
| 4\[[19edo|19]]
| 252.632
| 252.632
| -
| —
|-
|-
| [[22/19]]
| [[22/19]]
Line 282: Line 284:
| 3\[[14edo|14]]
| 3\[[14edo|14]]
| 257.143
| 257.143
| -
| —
|-
|-
| 297/256
| 297/256
Line 294: Line 296:
| 5\[[23edo|23]]
| 5\[[23edo|23]]
| 260.870
| 260.870
| -
| —
|}
|}


=== Maj3–4 (semisixth/naiadic) ===
=== Maj3–4 (semisixth/naiadic) ===
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
! Interval
! Interval
! Cents Value
! Cents Value
Line 306: Line 308:
| 5\[[88cET]] or 11\[[30edo|30]]
| 5\[[88cET]] or 11\[[30edo|30]]
| 440.000
| 440.000
| -
| —
|-
|-
| [[40/31]]
| [[40/31]]
Line 314: Line 316:
| 7\[[19edo|19]]
| 7\[[19edo|19]]
| 442.015
| 442.015
| -
| —
|-
|-
| [[31/24]]
| [[31/24]]
Line 322: Line 324:
| 10\[[27edo|27]]
| 10\[[27edo|27]]
| 444.444
| 444.444
| -
| —
|-
|-
| [[22/17]]
| [[22/17]]
Line 334: Line 336:
| 3\[[8edo|8]]
| 3\[[8edo|8]]
| 450.000
| 450.000
| -
| —
|-
|-
| 48/37
| 48/37
Line 346: Line 348:
| 11\[[29edo|29]]
| 11\[[29edo|29]]
| 455.172
| 455.172
| -
| —
|-
|-
| [[125/96]]
| [[125/96]]
Line 354: Line 356:
| 8\[[21edo|21]]
| 8\[[21edo|21]]
| 457.143
| 457.143
| -
| —
|-
|-
| 56/43
| 56/43
Line 370: Line 372:
| 5\[[13edo|13]]
| 5\[[13edo|13]]
| 461.538
| 461.538
| -
| —
|-
|-
| 47/36
| 47/36
Line 390: Line 392:
| 12\[[31edo|31]]
| 12\[[31edo|31]]
| 464.516
| 464.516
| -
| —
|-
|-
| 7\[[18edo|18]]
| 7\[[18edo|18]]
| 466.667
| 466.667
| -
| —
|-
|-
| [[38/29]]
| [[38/29]]
Line 402: Line 404:


=== 5–min6 (semitenth/cocytic) ===
=== 5–min6 (semitenth/cocytic) ===
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
! Interval
! Interval
! Cents Value
! Cents Value
Line 410: Line 412:
| 5\[[Bohlen-Pierce]]
| 5\[[Bohlen-Pierce]]
| 731.521
| 731.521
| -
| —
|-
|-
| [[29/19]]
| [[29/19]]
Line 418: Line 420:
| 11\[[18edo|18]]
| 11\[[18edo|18]]
| 733.333
| 733.333
| -
| —
|-
|-
| 19\[[31edo|31]]
| 19\[[31edo|31]]
| 735.484
| 735.484
| -
| —
|-
|-
| [[26/17]]
| [[26/17]]
Line 454: Line 456:
| 13\[[21edo|21]]
| 13\[[21edo|21]]
| 742.857
| 742.857
| -
| —
|-
|-
| [[182/125]]
| [[182/125]]
Line 462: Line 464:
| 18\[[29edo|29]]
| 18\[[29edo|29]]
| 744.828
| 744.828
| -
| —
|-
|-
| [[20/13]]
| [[20/13]]
Line 474: Line 476:
| 5\[[8edo|8]]
| 5\[[8edo|8]]
| 750.000
| 750.000
| -
| —
|-
|-
| [[54/35]]
| [[54/35]]
Line 486: Line 488:
| 17\[[27edo|27]]
| 17\[[27edo|27]]
| 755.556
| 755.556
| -
| —
|-
|-
| [[48/31]]
| [[48/31]]
Line 494: Line 496:
| 12\[[19edo|19]]
| 12\[[19edo|19]]
| 757.895
| 757.895
| -
| —
|-
|-
| [[31/20]]
| [[31/20]]
Line 502: Line 504:
| 19\[[30edo|30]]
| 19\[[30edo|30]]
| 760.000
| 760.000
| -
| —
|}
|}


=== Maj6–min7 (semitwelfth/ouranic) ===
=== Maj6–min7 (semitwelfth/ouranic) ===
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
! Interval
! Interval
! Cents Value
! Cents Value
Line 514: Line 516:
| 18\[[23edo|23]]
| 18\[[23edo|23]]
| 939.130
| 939.130
| -
| —
|-
|-
| [[31/18]]
| [[31/18]]
Line 526: Line 528:
| 11\[[14edo|14]]
| 11\[[14edo|14]]
| 942.857
| 942.857
| -
| —
|-
|-
| [[50/29]]
| [[50/29]]
Line 542: Line 544:
| 15\[[19edo|19]]
| 15\[[19edo|19]]
| 947.368
| 947.368
| -
| —
|-
|-
| 64/37
| 64/37
Line 554: Line 556:
| 19\[[24edo|24]]
| 19\[[24edo|24]]
| 950.000
| 950.000
| -
| —
|-
|-
| 23\[[29edo|29]]
| 23\[[29edo|29]]
| 951.724
| 951.724
| -
| —
|-
|-
| [[26/15]]
| [[26/15]]
Line 586: Line 588:
| 4\[[5edo|5]]
| 4\[[5edo|5]]
| 960.000
| 960.000
| -
| —
|-
|-
| 256/147
| 256/147
Retrieved from "https://en.xen.wiki/w/Interseptimal_interval"