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43edo-interval names: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
!Degree
! Degree
!Cents
! Cents
!Aaron's Answer
! [[User:PiotrGrochowski/Extra-Diatonic Intervals|Piotr Grochowski]], [[Extended meantone notation]] (named)
![[Extra-Diatonic Intervals|Igs' Input]]
! [[Extra-Diatonic Intervals|Igs' Input]]
!Kite's Correction
! Kite's Correction
!Keenan Category
! Margo's Method
!Margo's Method
! Aaron's Answer
!SagiSpeak
! SagiSpeak
!Ups and a-downs
! Ups and downs
!Gareth's Go
! Gareth's Go
!Represented Ratios
! Keenan Category
! Represented Ratios
|-
|-
|0
| 0
|0
| 0
|P1
| colspan="4" | Unison
|Unison
| colspan="5" | P1
|Unison
| 1/1
|P1
|Unison
|P1
|P1, m2
|P1
|1/1
|-
|-
|1
| 1
|80
| 27.907
|m2
| high unison, diminished second
|Subminor 2nd
| colspan="3" | Comma
|Subminor 2nd
| L1/Nm2
|m2
| pai-P1, d2
|Minor 2nd
| ^1, d2
|pai-P1
| colspan="2" | d2
|^1, ^m2
| 64/63, 81/80
|m2
|25/24, 21/20, 16/15
|-
|-
|2
| 2
|160
| 55.814
|NM2 (Narrow M2)
| low augmented unison
|Neutral 2nd
| colspan="2" | Low Subminor 2nd
|Neutral 2nd
| Chromatic Minor 2nd
|M2
| Sm2 (Small M2)
|Large Neutral 2nd
| pao-A1, pai-m2
|pao-M2
| vA1, ^d2
|vM2
| *Unicond
|M2
| sA1, Sd2
|11/10, 12/11, 10/9
| 33/32
|-
|-
|3
| 3
|240
| 83.721
|LM2
| augmented unison
|Supermajor 2nd
| colspan="2" | High Subminor 2nd
|Supermajor 2nd
| Neutral Minor 2nd
|A2/d3
| m2
|Large Major 2nd
| A1, pao-m2
|M2
| A1, vm2
|M2, m3
| colspan="2" | A1
|Serd*
| 21/20
|8/7, 7/6, 9/8
|-
|-
|4
| 4
|320
| 111.628
|Lm3
| colspan="3" | Minor 2nd
|Minor 3rd
| Diatonic Minor 2nd
|Minor 3rd
| Lm2
|m3
| colspan="4" | m2
|Large Minor 3rd
| 17/16, 16/15, 15/14
|pai-m3
|^m3
|m3
|6/5, 11/9
|-
|-
|5
| 5
|400
| 139.535
|M3
| low neutral second
|Major 3rd
| colspan="2" | Superminor 2nd
|Major 3rd
| Small Neutral 2nd
|M3
| Wm2/NM2 (Narrow M2)
|Major 3rd
| pai-m2
|pao-M3
| ^m2
|vM3
| colspan="2" | Sm2
|M3
| 12/11, 13/12, 14/13
|5/4, 14/11
|-
|-
|6
| 6
|480
| 167.442
|S4 (Small 4)
| high neutral second
|Sub 4th
| colspan="2" | Submajor 2nd
|Sub 4th
| Large Neutral 2nd, Chromatic Major 2nd
|P4
| d.SM2
|Small Perfect 4th
| pao-M2
|P4
| vM2
|M3, P4, d5
| colspan="2" | sM2
|P4
| 11/10
|4/3, 9/7, 21/16
|-
|-
|7
| 7
|560
| 195.349
|Na4/Sd5
| colspan="3" | Major 2nd
|Narrow Tritone
| Low Neutral Major 2nd
|Super 4th
| (S)M2
|A4
| colspan="4" | M2
|Small Tritone
| 9/8, 10/9
|pai-P4
|^4, ^d5
|A4
|11/8, 7/5
|-
|-
|8
| 8
|640
| 223.256
|La4/Wd5
| high major second, diminished third
|Wide Tritone
| colspan="2" | Supermajor 2nd
|Sub 5th
| High Neutral Major 2nd
|d5
| LM2
|Large Tritone
| pai-M2, d3
|pao-P5
| ^M2, d3
|vA4, v5
| colspan="2" | SM2, d3
|d5
| 8/7
|16/11, 10/7
|-
|-
|9
| 9
|720
| 251.163
|L5
| low augmented second, high diminished third
|Super 5th
| colspan="2" | Super 2nd, Sub 3rd
|Super 5th
| Diatonic Major 2nd, Interseptimal 2nd-3rd
|P5
| A.LM2/d.Sm3
|Large Perfect 5th
| pao-A2, pai-d3
|P5
| vA2, ^d3
|A4, P5, m6
| Serd*
|P5
| sA2, Sd3
|3/2, 14/9, 32/21
| 15/13
|-
|-
|10
| 10
|800
| 279.07
|m6
| augmented second, low minor third
|Minor 6th
| colspan="2" | Subminor 3rd
|Minor 6th
| Small Minor 3rd
|m6
| Sm3
|Minor 6th
| A2, pao-m3
|pai-m6
| A2, vm3
|^5, ^m6
| colspan="2" | sm3. A2
|m6
| 7/6, 13/11
|8/5, 11/7
|-
|-
|11
| 11
|880
| 306.977
|SM6
| colspan="3" | Minor 3rd
|Major 6th
| Large Minor 3rd
|Major 6th
| (L)m3
|M6
| colspan="4" | m3
|Small Major 6th
| 6/5
|pao-M6
|vA5, vM6
|M6
|5/3, 18/11
|-
|-
|12
| 12
|960
| 334.884
|SM7
| low neutral third
|Subminor 7th
| colspan="2" | Superminor 3rd
|Subminor 7th
| Small Neutral 3rd
|A6/d7
| Wm3
|Small Minor 7th
| pai-m3
|m7
| ^m3
|M6, m7
| colspan="2" | Sm3
|Sinth*
| 17/14, 39/32
|7/4, 12/7, 16/9
|-
|-
|13
| 13
|1040
| 362.791
|Wm7
| high neutral third
|Neutral 7th
| colspan="2" | Submajor 3rd
|Neutral 7th
| Large Neutral 3rd
|m7
| NM3
|Small Neutral 7th
| pao-M3
|pai-m7
| vM3
|^m7
| colspan="2" | sM3
|m7
| 11/9, 16/13
|20/11, 11/6, 9/5
|-
|-
|14
| 14
|1120
| 390.698
|M7
| colspan="3" | Major 3rd
|Supermajor 7th
| Small Major 3rd
|Supermajor 7th
| (S)M3
|M7
| colspan="4" | M3
|Major 7th
| 5/4
|pao-P8
|vM7, v8
|M7
|48/25, 40/21, 15/8
|-
|-
|15
| 15
|1200
| 418.605
|P8
| diminished fourth, high major third
|Octave
| colspan="2" | Low Supermajor 3rd
|Octave
| Large Major 3rd
|P8
| M.M3/LM3
|Octave
| d4, pai-M3
|P8
| ^M3
|M7, P8
| colspan="2" | SM3, d4
|P8
| 9/7, 14/11
|2/1
|-
|-
|16
| 16
|0
| 446.512
|P1
| low augmented third, high diminished fourth
|Unison
| colspan="2" | High Supermajor 3rd
|Unison
| Interseptimal 3rd-4th
|P1
| rowspan="2" | S4 (Small 4)
|Unison
| pao-A3, pai-d4
|P1
| vA3, ^d4
|P1, m2
| *Thorth
|P1
| sA3, Sd4
|1/1
| 13/10
|-
|-
|17
| 17
|80
| 474.419
|m2
| augmented third, low fourth
|Subminor 2nd
| colspan="2" | Sub 4th
|Subminor 2nd
| Small Perfect 4th
|m2
| A3, pao-P4
|Minor 2nd
| A3, v4
|pai-P1
| colspan="2" | A3
|^1, ^m2
| 21/16
|m2
|25/24, 21/20, 16/15
|-
|-
|18
| 18
|160
| 502.326
|NM2 (Narrow M2)
| fourth
|Neutral 2nd
| colspan="2" | Perfect 4th
|Neutral 2nd
| Medium Perfect 4th
|M2
| P4/L4
|Large Neutral 2nd
| colspan="4" | P4
|pao-M2
| 4/3
|vM2
|M2
|11/10, 12/11, 10/9
|-
|-
|19
| 19
|240
| 530.233
|LM2
| high fourth
|Supermajor 2nd
| colspan="2" | Super 4th
|Supermajor 2nd
| Large Perfect 4th
|A2/d3
| A.L4
|Large Major 2nd
| pai-P4
|M2
| ^4
|M2, m3
| colspan="2" | S4
|Serd*
| 15/11
|8/7, 7/6, 9/8
|-
|-
|20
| 20
|320
| 558.139
|Lm3
| low augmented fourth
|Minor 3rd
| colspan="2" | Sub Tritone
|Minor 3rd
| Small Tritone
|m3
| NA4/Sd5
|Large Minor 3rd
| pao-A4
|pai-m3
| vA4
|^m3
| colspan="2" | sA4
|m3
| 11/8, 18/13
|6/5, 11/9
|-
|-
|21
| 21
|400
| 586.046
|M3
| augmented fourth
|Major 3rd
| colspan="2" | Narrow Tritone
|Major 3rd
| Narrow Medium Tritone
|M3
| d5
|Major 3rd
| pao-d5, A4
|pao-M3
| A4, vd5
|vM3
| colspan="2" | A4
|M3
| 7/5
|5/4, 14/11
|-
|-
|22
| 22
|480
| 613.953
|S4 (Small 4)
| diminished fifth
|Sub 4th
| colspan="2" | Wide Tritone
|Sub 4th
| Wide Medium Tritone
|P4
| A4
|Small Perfect 4th
| pai-A4, d5
|P4
| ^A4, d5
|M3, P4, d5
| colspan="2" | d5
|P4
| 10/7
|4/3, 9/7, 21/16
|-
|-
|23
| 23
|560
| 641.86
|Na4/Sd5
| high diminished fifth
|Narrow Tritone
| colspan="2" | Super Tritone
|Super 4th
| Large Tritone
|A4
| La4/Wd5
|Small Tritone
| pai-d5
|pai-P4
| ^d5
|^4, ^d5
| colspan="2" | Sd5
|A4
| 16/11, 13/9
|11/8, 7/5
|-
|-
|24
| 24
|640
| 669.767
|La4/Wd5
| low fifth
|Wide Tritone
| colspan="2" | Sub 5th
|Sub 5th
| Small Perfect 5th
|d5
| d.S5
|Large Tritone
| pao-P5
|pao-P5
| v5
|vA4, v5
| colspan="2" | s5
|d5
| 22/15
|16/11, 10/7
|-
|-
|25
| 25
|720
| 697.674
|L5
| fifth
|Super 5th
| colspan="2" | Perfect 5th
|Super 5th
| Medium Perfect 5th
|P5
| S5/P5
|Large Perfect 5th
| colspan="4" | P5
|P5
| 3/2
|A4, P5, m6
|P5
|3/2, 14/9, 32/21
|-
|-
|26
| 26
|800
| 725.581
|m6
| diminished sixth, high fifth
|Minor 6th
| colspan="2" | Super 5th
|Minor 6th
| Large Perfect 5th
|m6
| rowspan="2" | L5
|Minor 6th
| d6, pai-P5
|pai-m6
| ^5
|^5, ^m6
| colspan="2" | d6
|m6
| 32/21
|8/5, 11/7
|-
|-
|27
| 27
|880
| 753.488
|SM6
| low augmented fifth, high diminished sixth
|Major 6th
| colspan="2" | Low Subminor 6th
|Major 6th
| Interseptimal 5th-6th
|M6
| pao-A5, pai-d6
|Small Major 6th
| vA5, ^d6
|pao-M6
|  
|vA5, vM6
| sA5, Sd6
|M6
| 20/13
|5/3, 18/11
|-
|-
|28
| 28
|960
| 781.395
|SM7
| low minor sixth
|Subminor 7th
| colspan="2" | High Subminor 6th
|Subminor 7th
| Small Minor 6th
|A6/d7
| Sm6/m.m6
|Small Minor 7th
| A5, pao-m6
|m7
| vm6
|M6, m7
| colspan="2" | sm6, A5
|Sinth*
| 14/9, 11/7
|7/4, 12/7, 16/9
|-
|-
|29
| 29
|1040
| 809.302
|Wm7
| colspan="3" | Minor 6th
|Neutral 7th
| MediuenMinor 6th
|Neutral 7th
| (L)m6
|m7
| colspan="4" | m6
|Small Neutral 7th
| 8/5
|pai-m7
|^m7
|m7
|20/11, 11/6, 9/5
|-
|-
|30
| 30
|1120
| 837.209
|M7
| low neutral sixth
|Supermajor 7th
| colspan="2" | Superminor 6th
|Supermajor 7th
| Large Minor 6th
|M7
| Wm6
|Major 7th
| pai-m6
|pao-P8
| ^m6
|vM7, v8
| colspan="2" | Sm6
|M7
| 18/11, 13/8
|48/25, 40/21, 15/8
|-
|-
|31
| 31
|1200
| 865.116
|P8
| high neutral sixth
|Octave
| colspan="2" | Submajor 6th
|Octave
| Large Neutral 6th
|P8
| NM6
|Octave
| pao-M6
|P8
| vM6
|M7, P8
| colspan="2" | sM6
|P8
| 28\17, 64\39
|2/1
|-
|-
|32
| 32
|0
| 893.023
|P1
| colspan="3" | Major 6th
|Unison
| Small Major 6th
|Unison
| (S)M6
|P1
| colspan="4" | M6
|Unison
| 5/3
|P1
|P1, m2
|P1
|1/1
|-
|-
|33
| 33
|80
| 920.93
|m2
| high major sixth
|Subminor 2nd
| colspan="2" | Supermajor 6th
|Subminor 2nd
| Large Major 6th
|m2
| LM6
|Minor 2nd
| pai-M6, d7
|pai-P1
| ^M6
|^1, ^m2
| colspan="2" | SM6, d7
|m2
| 12/7
|25/24, 21/20, 16/15
|-
|-
|34
| 34
|160
| 948.837
|NM2 (Narrow M2)
| low augmented sixth, high diminished seventh
|Neutral 2nd
| colspan="2" | Super 6th, Sub 7th
|Neutral 2nd
| Diatonic Minor 7th, Interseptimal 6th-7th
|M2
| A.LM6/d.Sm7
|Large Neutral 2nd
| pao-A6, pai-d7
|pao-M2
| vA6, ^d7
|vM2
| Sinth*
|M2
| sA6, Sd7
|11/10, 12/11, 10/9
| 26/15
|-
|-
|35
| 35
|240
| 976.744
|LM2
| low minor seventh, augmented sixth
|Supermajor 2nd
| colspan="2" | Subminor 7th
|Supermajor 2nd
| Low Neutral Minor 7th
|A2/d3
| Sm7
|Large Major 2nd
| pao-m7, A6
|M2
| vm7
|M2, m3
| colspan="2" | sm7, A6
|Serd*
| 7/4
|8/7, 7/6, 9/8
|-
|-
|36
| 36
|320
| 1004.651
|Lm3
| colspan="3" | Minor 7th
|Minor 3rd
| High Neutral Minor 7th
|Minor 3rd
| (L)m7
|m3
| colspan="4" | m7
|Large Minor 3rd
| 16/9, 9/5
|pai-m3
|^m3
|m3
|6/5, 11/9
|-
|-
|37
| 37
|400
| 1032.558
|M3
| low neutral seventh
|Major 3rd
| colspan="2" | Superminor 7th
|Major 3rd
| Chromatic Minor 7th, Small Neutral 7th
|M3
| A.Lm7
|Major 3rd
| pai-m7
|pao-M3
| ^m7
|vM3
| colspan="2" | Sm7
|M3
| 20/11
|5/4, 14/11
|-
|-
|38
| 38
|480
| 1060.465
|S4 (Small 4)
| high neutral seventh
|Sub 4th
| colspan="2" | Submajor 7th
|Sub 4th
| Large Neutral 7th
|P4
| Wm7/NM7
|Small Perfect 4th
| pao-M7
|P4
| vM7
|M3, P4, d5
| colspan="2" | sM7
|P4
| 11/6, 24/13, 13/7
|4/3, 9/7, 21/16
|-
|-
|39
| 39
|560
| 1088.372
|Na4/Sd5
| colspan="3" | Major 7th
|Narrow Tritone
| Diatonic Major 7th
|Super 4th
| SM7
|A4
| colspan="4" | M7
|Small Tritone
| 15/8, 28/15
|pai-P4
|^4, ^d5
|A4
|11/8, 7/5
|-
|-
|40
| 40
|640
| 1116.279
|La4/Wd5
| diminished octave
|Wide Tritone
| colspan="2" | Low Supermajor 7th
|Sub 5th
| Neutral Major 7th
|d5
| M7
|Large Tritone
| d8, pai-M7
|pao-P5
| ^M7
|vA4, v5
| colspan="2" | SM7. d8
|d5
| 40/21
|16/11, 10/7
|-
|-
|41
| 41
|720
| 1144.186
|L5
| high diminished octave
|Super 5th
| colspan="2" | High Supermajor 7th
|Super 5th
| Chromatic Major 7th
|P5
| LM7
|Large Perfect 5th
| pai-d8, pao-A7
|P5
| vA7, ^d8
|A4, P5, m6
| *Septave
|P5
| sA7, Sd8
|3/2, 14/9, 32/21
| 64/33
|-
|-
|42
| 42
|800
| 1172.093
|m6
| low octave, augmented seventh
|Minor 6th
| colspan="3" | Ultramajor 7th
|Minor 6th
| S8/WM7
|m6
| pao-P8, A7
|Minor 6th
| A7, v8
|pai-m6
| colspan="2" | A7
|^5, ^m6
| 63/32, 160/81
|m6
|8/5, 11/7
|-
|-
|43
| 43
|880
| 1200
|SM6
| colspan="4" | Octave
|Major 6th
| colspan="5" | P8
|Major 6th
| 2/1
|M6
<includeonly>
|Small Major 6th
{{Navbar table|cols=12|43edo-interval_names}}
|pao-M6
</includeonly>
|vA5, vM6
|}<noinclude>
|M6
|5/3, 18/11
|}
<nowiki>*</nowiki>'Serd' and 'Sinth' are Portmanteaux of Second and Third; and Sixth and Seventh respectively. These intervals represent exact half Perfect 4ths and Perfect 5ths, and replace the "regular" interval name. I have put them in there to gain functionality at the cost of losing familiarity/introducing novelty in addition to 'HO', the half-octave. My (Gareth's) system at this stage is the same as Dave Keenan's but for the addition of these. I suppose they could just be optional additional names for those steps. I was led to this after not finding any reason to change Dave's system, but not liking that it led to A2/d3 for the 240c interval in 5n-edos, and A6/d7 for the 960c interval. Seems weird.


Sagi-Speak, Ups and Downs, and Colours are all great, but are completely new ideas that can be linked to on the pages. Sagi-Speak and Ups are directly linked to the two main options for notation.
<nowiki>*</nowiki> "Serd" and "Sinth" are Portmanteaux of Second and Third; and Sixth and Seventh respectively. These intervals represent exact half Perfect 4ths and Perfect 5ths, and replace the "regular" interval name. I have put them in there to gain functionality at the cost of losing familiarity/introducing novelty in addition to 'HO', the half-octave. My (Gareth's) system at this stage is the same as Dave Keenan's but for the addition of these. I suppose they could just be optional additional names for those steps. I was led to this after not finding any reason to change Dave's system, but not liking that it led to A2/d3 for the 240c interval in 5n-edos, and A6/d7 for the 960c interval. Seems weird.  


I like Igs' and Dave's systems the best I think. They are very different. Both are 'size' based rather than 'function', but the point of reference for Igs' is 12edo, which would be more familiar to new readers. Dave's uses JI / 72edo alterations two short chains of the edos best fifth - giving the perfect and neutral intervals, so is malleable in it's application to edos, and more able to reflect the 'function' of the intervals in an edo. I've added a few functional labels to it. Might be best to have those in brackets. At this stage I would like to see both on every edo page. Igs' has a point that his extra-diatonic names need not or perhaps should not be associated with ratios. Dave's on the other hand benifit from such an association. Perhaps an edo page could start with Igs' in the intervals section without ratios as he first edits, and in the temperament section Dave's names can be included.
Sagi-Speak, Ups and Downs, and Colours are all great, but are completely new ideas that can be linked to on the pages. Sagi-Speak and Ups are directly linked to the two main options for notation.
 
I like Igs' and Dave's systems the best I think. They are very different. Both are 'size' based rather than 'function', but the point of reference for Igs' is 12edo, which would be more familiar to new readers. Dave's uses JI / 72edo alterations two short chains of the edos best fifth - giving the perfect and neutral intervals, so is malleable in its application to edos, and more able to reflect the 'function' of the intervals in an edo. I've added a few functional labels to it. Might be best to have those in brackets. At this stage I would like to see both on every edo page. Igs' has a point that his extra-diatonic names need not or perhaps should not be associated with ratios. Dave's on the other hand benefit from such an association. Perhaps an edo page could start with Igs' in the intervals section without ratios as he first edits, and in the temperament section Dave's names can be included.


I've done this for [[72edo-interval names|72edo]] as well.
I've done this for [[72edo-interval names|72edo]] as well.
[[Category:43edo]]
[[Category:Tables]]
[[Category:Interval naming]]
</noinclude>
Retrieved from "https://en.xen.wiki/w/43edo-interval_names"