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
|-
! Steps
! Cents
! Cents
! Aaron's Answer
! Vector's interval names
! [http://musictheory.zentral.zone/huntsystem4.html Aaron's Answer]
! [[Extra-Diatonic Intervals|Igs' Input]]
! [[Extra-Diatonic Intervals|Igs' Input]]
! Kite's Correction
! [http://dkeenan.com/Music/EdoIntervalNames.pdf Keenan Category]
! Keenan Category
! [http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt Margo's Method]
! [[User:Mike Battaglia|Marg]]o's Method
! [[User:PiotrGrochowski/Extra-Diatonic Intervals|Piotr Grochowski]]
! SagiSpeak
! [http://forum.sagittal.org/viewforum.php?f=9 SagiSpeak]
! Ups and downs
! [[Ups and downs notation|Ups and Downs]]
! Gareth's Go
! [[SKULO interval names|Lilly's List]]
!Extra-diatonic 2
! Ordway's Order
! Represented Ratios
! Ratios
|-
|-
| 0
| 0
| 0
| 0
| unison
| P1
| P1
| Unison
| Unison
| Unison
| P1
| P1
| Unison
| Unison
| unison
| P1
| P1
| P1, m2
| P1, m2
| P1
| P1
|P1
| P1
| [[1/1]]
| [[1/1]]
|-
|-
| 1
| 1
| 80
| 80
| semitone
| m2
| m2
| Subminor 2nd
| Subminor 2nd
| Subminor 2nd
| mi2
| m2
| Minor 2nd
| Minor 2nd
| augmented unison
| pai-P1
| pai-P1
| ^1, ^m2
| ^1, ^m2
| K1
| m2
| m2
|S1
| [[25/24]], [[21/20]], [[16/15]], [[22/21]]
| [[25/24]], [[21/20]], [[16/15]]
|-
|-
| 2
| 2
| 160
| 160
| minor tone
| NM2 (Narrow M2)
| NM2 (Narrow M2)
| Neutral 2nd
| Neutral 2nd
| Neutral 2nd
| Mi2
| M2
| Large Neutral 2nd
| Large Neutral 2nd
| high neutral second
| pao-M2
| pao-M2
| vM2
| vM2
| kM2
| M2
| M2
|sM2
| [[11/10]], [[12/11]], [[10/9]]
| [[11/10]], [[12/11]], [[10/9]]
|-
|-
| 3
| 3
| 240
| 240
| major tone, wolf third
| LM2
| LM2
| Supermajor 2nd
| Supermajor 2nd
| Supermajor 2nd
| Ai2/di3
| A2/d3
| Large Major 2nd
| Large Major 2nd
| second–third
| M2
| M2
| M2, m3
| M2, m3
| Serd*
| SM2/sm3
|M2, m3 (Serd)
| S2/s3
| [[8/7]], [[7/6]], [[9/8]]
| [[8/7]], [[7/6]], [[9/8]]
|-
|-
| 4
| 4
| 320
| 320
| minor third
| Lm3
| Lm3
| Minor 3rd
| Minor 3rd
| Minor 3rd
| mi3
| m3
| Large Minor 3rd
| Large Minor 3rd
| minor third
| pai-m3
| pai-m3
| ^m3
| ^m3
| Km3
| m3
| m3
|Sm3
| [[6/5]], [[11/9]]
| [[6/5]], [[11/9]]
|-
|-
| 5
| 5
| 400
| 400
| major third
| M3
| M3
| Major 3rd
| Major 3rd
| Mi3
| Major 3rd
| Major 3rd
| M3
| major third
| Major 3rd
| pao-M3
| pao-M3
| vM3
| vM3
| kM3
| M3
| M3
|sM3
| [[5/4]], [[14/11]]
| [[5/4]], [[14/11]]
|-
|-
| 6
| 6
| 480
| 480
| perfect fourth
| S4 (Small 4)
| S4 (Small 4)
| Sub 4th
| Sub 4th
| Sub 4th
| P4
| P4
| Small Perfect 4th
| Small Perfect 4th
| low fourth
| P4
| P4
| M3, P4, d5
| M3, P4, d5
| SM3/s4
| P4
| P4
|M3, P4 (Thourth)
| [[4/3]], [[9/7]], [[21/16]]
| [[4/3]], [[9/7]], [[21/16]]
|-
|-
| 7
| 7
| 560
| 560
| wolf fourth, diminished fifth, narrow tritone
| Na4/Sd5
| Na4/Sd5
| Narrow Tritone
| Narrow Tritone
| Super 4th
| Ai4
| A4
| Small Tritone
| Small Tritone
| low augmented fourth
| pai-P4
| pai-P4
| ^4, ^d5
| ^4, ^d5
| A4
| K4
|S4
| m4
| [[11/8]], [[7/5]]
| [[11/8]], [[7/5]]
|-
|-
| 8
| 8
| 640
| 640
| wolf fifth, augmented fourth, wide tritone
| La4/Wd5
| La4/Wd5
| Wide Tritone
| Wide Tritone
| Sub 5th
| di5
| d5
| Large Tritone
| Large Tritone
| high diminished fifth
| pao-P5
| pao-P5
| vA4, v5
| vA4, v5
| d5
| k5
|s5
| M5
| [[16/11]], [[10/7]]
| [[16/11]], [[10/7]]
|-
|-
| 9
| 9
| 720
| 720
| perfect fifth
| L5
| L5
| Super 5th
| Super 5th
| Super 5th
| P5
| P5
| Large Perfect 5th
| Large Perfect 5th
| high fifth
| P5
| P5
| A4, P5, m6
| A4, P5, m6
| S5/sm6
| P5
| P5
|P5, m6 (Fixth)
| [[3/2]], [[14/9]], [[32/21]]
| [[3/2]], [[14/9]], [[32/21]]
|-
|-
| 10
| 10
| 800
| 800
| minor sixth
| m6
| m6
| Minor 6th
| Minor 6th
| mi6
| Minor 6th
| Minor 6th
| m6
| minor sixth
| Minor 6th
| pai-m6
| pai-m6
| ^5, ^m6
| ^5, ^m6
| Km6
| m6
| m6
|Sm6
| [[8/5]], [[11/7]]
| [[8/5]], [[11/7]]
|-
|-
| 11
| 11
| 880
| 880
| major sixth
| SM6
| SM6
| Major 6th
| Major 6th
| Major 6th
| Mi6
| M6
| Small Major 6th
| Small Major 6th
| major sixth
| pao-M6
| pao-M6
| vA5, vM6
| vA5, vM6
| kM6
| M6
| M6
|sM6
| [[5/3]], [[18/11]]
| [[5/3]], [[18/11]]
|-
|-
| 12
| 12
| 960
| 960
| harmonic seventh, wolf sixth
| SM7
| SM7
| Subminor 7th
| Subminor 7th
| Subminor 7th
| Ai6/di7
| A6/d7
| Small Minor 7th
| Small Minor 7th
| sixth–seventh
| m7
| m7
| M6, m7
| M6, m7
| Sinth*
| SM6/sm7
|M6, m7 (Sinth)
| S6/s7
| [[7/4]], [[12/7]], [[16/9]]
| [[7/4]], [[12/7]], [[16/9]]
|-
|-
| 13
| 13
| 1040
| 1040
| minor seventh
| Wm7
| Wm7
| Neutral 7th
| Neutral 7th
| Neutral 7th
| mi7
| m7
| Small Neutral 7th
| Small Neutral 7th
| low neutral seventh
| pai-m7
| pai-m7
| ^m7
| ^m7
| Km7
| m7
| m7
|Sm7
| [[20/11]], [[11/6]], [[9/5]]
| [[20/11]], [[11/6]], [[9/5]]
|-
|-
| 14
| 14
| 1120
| 1120
| major seventh
| M7
| M7
| Supermajor 7th
| Supermajor 7th
| Supermajor 7th
| Mi7
| M7
| Major 7th
| Major 7th
| diminished octave
| pao-P8
| pao-P8
| vM7, v8
| vM7, v8
| kM7
| M7
| M7
|sM7
| [[48/25]], [[40/21]], [[15/8]], [[21/11]]
| [[48/25]], [[40/21]], [[15/8]]
|-
|-
| 15
| 15
| 1200
| 1200
| octave
| P8
| P8
| Octave
| Octave
| Octave
| P8
| P8
| Octave
| Octave
| octave
| P8
| P8
| M7, P8
| M7, P8
| P8
| P8
|P8
| P8
| [[2/1]]
| [[2/1]]
<includeonly>
{{Navbar table|cols=12|15edo-interval_names}}
</includeonly>
|}
|}
 
<noinclude>
<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.
[[Category:15edo]]
 
[[Category:Tables]]
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:Interval naming]]
 
</noinclude>
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.
 
I've done this for [[72edo-interval names|72edo]] as well.<sup> [author: Gareth.hearne ([[User_talk:Gareth.hearne|talk]])]</sup>
 
== See also ==
* [[User:PiotrGrochowski/Extra-Diatonic Intervals]]

Latest revision as of 01:07, 20 August 2025

< 15edo

If you haven't made an interval naming system yet, make one and add a column when you finish your notation system!

Steps Cents Vector's interval names Aaron's Answer Igs' Input Keenan Category Margo's Method Piotr Grochowski SagiSpeak Ups and Downs Lilly's List Ordway's Order Ratios
0 0 unison P1 Unison P1 Unison unison P1 P1, m2 P1 P1 1/1
1 80 semitone m2 Subminor 2nd mi2 Minor 2nd augmented unison pai-P1 ^1, ^m2 K1 m2 25/24, 21/20, 16/15, 22/21
2 160 minor tone NM2 (Narrow M2) Neutral 2nd Mi2 Large Neutral 2nd high neutral second pao-M2 vM2 kM2 M2 11/10, 12/11, 10/9
3 240 major tone, wolf third LM2 Supermajor 2nd Ai2/di3 Large Major 2nd second–third M2 M2, m3 SM2/sm3 S2/s3 8/7, 7/6, 9/8
4 320 minor third Lm3 Minor 3rd mi3 Large Minor 3rd minor third pai-m3 ^m3 Km3 m3 6/5, 11/9
5 400 major third M3 Major 3rd Mi3 Major 3rd major third pao-M3 vM3 kM3 M3 5/4, 14/11
6 480 perfect fourth S4 (Small 4) Sub 4th P4 Small Perfect 4th low fourth P4 M3, P4, d5 SM3/s4 P4 4/3, 9/7, 21/16
7 560 wolf fourth, diminished fifth, narrow tritone Na4/Sd5 Narrow Tritone Ai4 Small Tritone low augmented fourth pai-P4 ^4, ^d5 K4 m4 11/8, 7/5
8 640 wolf fifth, augmented fourth, wide tritone La4/Wd5 Wide Tritone di5 Large Tritone high diminished fifth pao-P5 vA4, v5 k5 M5 16/11, 10/7
9 720 perfect fifth L5 Super 5th P5 Large Perfect 5th high fifth P5 A4, P5, m6 S5/sm6 P5 3/2, 14/9, 32/21
10 800 minor sixth m6 Minor 6th mi6 Minor 6th minor sixth pai-m6 ^5, ^m6 Km6 m6 8/5, 11/7
11 880 major sixth SM6 Major 6th Mi6 Small Major 6th major sixth pao-M6 vA5, vM6 kM6 M6 5/3, 18/11
12 960 harmonic seventh, wolf sixth SM7 Subminor 7th Ai6/di7 Small Minor 7th sixth–seventh m7 M6, m7 SM6/sm7 S6/s7 7/4, 12/7, 16/9
13 1040 minor seventh Wm7 Neutral 7th mi7 Small Neutral 7th low neutral seventh pai-m7 ^m7 Km7 m7 20/11, 11/6, 9/5
14 1120 major seventh M7 Supermajor 7th Mi7 Major 7th diminished octave pao-P8 vM7, v8 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
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