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15edo/Interval names: Difference between revisions

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<noinclude>{{breadcrumb}}
<span style="font-size: 115%;">If you haven't made an interval naming system yet, make one and add a column when you finish your notation system!</span></noinclude>
{| class="wikitable"
{| class="wikitable"
!Degree
!Cents
!Aaron's Answer
![[Extra-Diatonic Intervals|Igs' Input]]
!Kite's Correction
!Keenan Category
!Margo's Method
![[User:PiotrGrochowski/Extra-Diatonic Intervals|Piotr Grochowski]]
!SagiSpeak
!Ups and a-downs
!Gareth's Go
!Represented Ratios
|-
|-
|0
! Steps
|0
! Cents
|P1
! Vector's interval names
|Unison
! [http://musictheory.zentral.zone/huntsystem4.html Aaron's Answer]
|Unison
! [[Extra-Diatonic Intervals|Igs' Input]]
|P1
! [http://dkeenan.com/Music/EdoIntervalNames.pdf Keenan Category]
|Unison
! [http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt Margo's Method]
|unison
! [[User:PiotrGrochowski/Extra-Diatonic Intervals|Piotr Grochowski]]
|P1
! [http://forum.sagittal.org/viewforum.php?f=9 SagiSpeak]
|P1, m2
! [[Ups and downs notation|Ups and Downs]]
|P1
! [[SKULO interval names|Lilly's List]]
|1/1
! Ordway's Order
! Ratios
|-
|-
|1
| 0
|80
| 0
|m2
| unison
|Subminor 2nd
| P1
|Subminor 2nd
| Unison
|m2
| P1
|Minor 2nd
| Unison
|augmented unison
| unison
|pai-P1
| P1
|^1, ^m2
| P1, m2
|m2
| P1
|25/24, 21/20, 16/15
| P1
| [[1/1]]
|-
|-
|2
| 1
|160
| 80
|NM2 (Narrow M2)
| semitone
|Neutral 2nd
| m2
|Neutral 2nd
| Subminor 2nd
|M2
| mi2
|Large Neutral 2nd
| Minor 2nd
|greater neutral second
| augmented unison
|pao-M2
| pai-P1
|vM2
| ^1, ^m2
|M2
| K1
|11/10, 12/11, 10/9
| m2
| [[25/24]], [[21/20]], [[16/15]], [[22/21]]
|-
|-
|3
| 2
|240
| 160
|LM2
| minor tone
|Supermajor 2nd
| NM2 (Narrow M2)
|Supermajor 2nd
| Neutral 2nd
|A2/d3
| Mi2
|Large Major 2nd
| Large Neutral 2nd
|M2
| high neutral second
|M2, m3
| pao-M2
|Serd*
| vM2
|8/7, 7/6, 9/8
| kM2
| M2
| [[11/10]], [[12/11]], [[10/9]]
|-
|-
|4
| 3
|320
| 240
|Lm3
| major tone, wolf third
|Minor 3rd
| LM2
|Minor 3rd
| Supermajor 2nd
|m3
| Ai2/di3
|Large Minor 3rd
| Large Major 2nd
|pai-m3
| second–third
|^m3
| M2
|m3
| M2, m3
|6/5, 11/9
| SM2/sm3
| S2/s3
| [[8/7]], [[7/6]], [[9/8]]
|-
|-
|5
| 4
|400
| 320
|M3
| minor third
|Major 3rd
| Lm3
|Major 3rd
| Minor 3rd
|M3
| mi3
|Major 3rd
| Large Minor 3rd
|pao-M3
| minor third
|vM3
| pai-m3
|M3
| ^m3
|5/4, 14/11
| Km3
| m3
| [[6/5]], [[11/9]]
|-
|-
|6
| 5
|480
| 400
|S4 (Small 4)
| major third
|Sub 4th
| M3
|Sub 4th
| Major 3rd
|P4
| Mi3
|Small Perfect 4th
| Major 3rd
|P4
| major third
|M3, P4, d5
| pao-M3
|P4
| vM3
|4/3, 9/7, 21/16
| kM3
| M3
| [[5/4]], [[14/11]]
|-
|-
|7
| 6
|560
| 480
|Na4/Sd5
| perfect fourth
|Narrow Tritone
| S4 (Small 4)
|Super 4th
| Sub 4th
|A4
| P4
|Small Tritone
| Small Perfect 4th
|pai-P4
| low fourth
|^4, ^d5
| P4
|A4
| M3, P4, d5
|11/8, 7/5
| SM3/s4
| P4
| [[4/3]], [[9/7]], [[21/16]]
|-
|-
|8
| 7
|640
| 560
|La4/Wd5
| wolf fourth, diminished fifth, narrow tritone
|Wide Tritone
| Na4/Sd5
|Sub 5th
| Narrow Tritone
|d5
| Ai4
|Large Tritone
| Small Tritone
|pao-P5
| low augmented fourth
|vA4, v5
| pai-P4
|d5
| ^4, ^d5
|16/11, 10/7
| K4
| m4
| [[11/8]], [[7/5]]
|-
|-
|9
| 8
|720
| 640
|L5
| wolf fifth, augmented fourth, wide tritone
|Super 5th
| La4/Wd5
|Super 5th
| Wide Tritone
|P5
| di5
|Large Perfect 5th
| Large Tritone
|P5
| high diminished fifth
|A4, P5, m6
| pao-P5
|P5
| vA4, v5
|3/2, 14/9, 32/21
| k5
| M5
| [[16/11]], [[10/7]]
|-
|-
|10
| 9
|800
| 720
|m6
| perfect fifth
|Minor 6th
| L5
|Minor 6th
| Super 5th
|m6
| P5
|Minor 6th
| Large Perfect 5th
|pai-m6
| high fifth
|^5, ^m6
| P5
|m6
| A4, P5, m6
|8/5, 11/7
| S5/sm6
| P5
| [[3/2]], [[14/9]], [[32/21]]
|-
|-
|11
| 10
|880
| 800
|SM6
| minor sixth
|Major 6th
| m6
|Major 6th
| Minor 6th
|M6
| mi6
|Small Major 6th
| Minor 6th
|pao-M6
| minor sixth
|vA5, vM6
| pai-m6
|M6
| ^5, ^m6
|5/3, 18/11
| Km6
| m6
| [[8/5]], [[11/7]]
|-
|-
|12
| 11
|960
| 880
|SM7
| major sixth
|Subminor 7th
| SM6
|Subminor 7th
| Major 6th
|A6/d7
| Mi6
|Small Minor 7th
| Small Major 6th
|m7
| major sixth
|M6, m7
| pao-M6
|Sinth*
| vA5, vM6
|7/4, 12/7, 16/9
| kM6
| M6
| [[5/3]], [[18/11]]
|-
|-
|13
| 12
|1040
| 960
|Wm7
| harmonic seventh, wolf sixth
|Neutral 7th
| SM7
|Neutral 7th
| Subminor 7th
|m7
| Ai6/di7
|Small Neutral 7th
| Small Minor 7th
|pai-m7
| sixth–seventh
|^m7
| m7
|m7
| M6, m7
|20/11, 11/6, 9/5
| SM6/sm7
| S6/s7
| [[7/4]], [[12/7]], [[16/9]]
|-
|-
|14
| 13
|1120
| 1040
|M7
| minor seventh
|Supermajor 7th
| Wm7
|Supermajor 7th
| Neutral 7th
|M7
| mi7
|Major 7th
| Small Neutral 7th
|pao-P8
| low neutral seventh
|vM7, v8
| pai-m7
|M7
| ^m7
|48/25, 40/21, 15/8
| Km7
| m7
| [[20/11]], [[11/6]], [[9/5]]
|-
|-
|15
| 14
|1200
| 1120
|P8
| major seventh
|Octave
| M7
|Octave
| Supermajor 7th
|P8
| Mi7
|Octave
| Major 7th
|P8
| diminished octave
|M7, P8
| pao-P8
|P8
| vM7, v8
|2/1
| kM7
| M7
| [[48/25]], [[40/21]], [[15/8]], [[21/11]]
|-
| 15
| 1200
| octave
| P8
| Octave
| P8
| Octave
| octave
| P8
| M7, P8
| P8
| P8
| [[2/1]]
<includeonly>
{{Navbar table|cols=12|15edo-interval_names}}
</includeonly>
|}
|}
<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.
<noinclude>
 
[[Category:15edo]]
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. 
[[Category:Tables]]
 
[[Category:Interval naming]]
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.
</noinclude>
 
I've done this for [[72edo-interval names|72edo]] as well.
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