43edo-interval names

From Xenharmonic Wiki
Jump to: navigation, search
Degree Cents Piotr Grochowski, Extended meantone notation (named) Igs' Input Kite's Correction Margo's Method Aaron's Answer SagiSpeak Ups and downs Gareth's Go Keenan Category Represented Ratios
0 0 Unison P1 1/1
1 27.907 high unison, diminished second Comma L1/Nm2 pai-P1, d2 ^1, d2 d2 64/63, 81/80
2 55.814 low augmented unison Low Subminor 2nd Chromatic Minor 2nd Sm2 (Small M2) pao-A1, pai-m2 vA1, ^d2 *Unicond sA1, Sd2 33/32
3 83.721 augmented unison High Subminor 2nd Neutral Minor 2nd m2 A1, pao-m2 A1, vm2 A1 21/20
4 111.628 Minor 2nd Diatonic Minor 2nd Lm2 m2 17/16, 16/15, 15/14
5 139.535 low neutral second Superminor 2nd Small Neutral 2nd Wm2/NM2 (Narrow M2) pai-m2 ^m2 Sm2 12/11, 13/12, 14/13
6 167.442 high neutral second Submajor 2nd Large Neutral 2nd, Chromatic Major 2nd d.SM2 pao-M2 vM2 sM2 11/10
7 195.349 Major 2nd Low Neutral Major 2nd (S)M2 M2 9/8, 10/9
8 223.256 high major second, diminished third Supermajor 2nd High Neutral Major 2nd LM2 pai-M2, d3 ^M2, d3 SM2, d3 8/7
9 251.163 low augmented second, high diminished third Super 2nd, Sub 3rd Diatonic Major 2nd, Interseptimal 2nd-3rd A.LM2/d.Sm3 pao-A2, pai-d3 vA2, ^d3 Serd* sA2, Sd3 15/13
10 279.07 augmented second, low minor third Subminor 3rd Small Minor 3rd Sm3 A2, pao-m3 A2, vm3 sm3. A2 7/6, 13/11
11 306.977 Minor 3rd Large Minor 3rd (L)m3 m3 6/5
12 334.884 low neutral third Superminor 3rd Small Neutral 3rd Wm3 pai-m3 ^m3 Sm3 17/14, 39/32
13 362.791 high neutral third Submajor 3rd Large Neutral 3rd NM3 pao-M3 vM3 sM3 11/9, 16/13
14 390.698 Major 3rd Small Major 3rd (S)M3 M3 5/4
15 418.605 diminished fourth, high major third Low Supermajor 3rd Large Major 3rd M.M3/LM3 d4, pai-M3 ^M3 SM3, d4 9/7, 14/11
16 446.512 low augmented third, high diminished fourth High Supermajor 3rd Interseptimal 3rd-4th S4 (Small 4) pao-A3, pai-d4 vA3, ^d4 *Thorth sA3, Sd4 13/10
17 474.419 augmented third, low fourth Sub 4th Small Perfect 4th A3, pao-P4 A3, v4 A3 21/16
18 502.326 fourth Perfect 4th Medium Perfect 4th P4/L4 P4 4/3
19 530.233 high fourth Super 4th Large Perfect 4th A.L4 pai-P4 ^4 S4 15/11
20 558.139 low augmented fourth Sub Tritone Small Tritone NA4/Sd5 pao-A4 vA4 sA4 11/8, 18/13
21 586.046 augmented fourth Narrow Tritone Narrow Medium Tritone d5 pao-d5, A4 A4, vd5 A4 7/5
22 613.953 diminished fifth Wide Tritone Wide Medium Tritone A4 pai-A4, d5 ^A4, d5 d5 10/7
23 641.86 high diminished fifth Super Tritone Large Tritone La4/Wd5 pai-d5 ^d5 Sd5 16/11, 13/9
24 669.767 low fifth Sub 5th Small Perfect 5th d.S5 pao-P5 v5 s5 22/15
25 697.674 fifth Perfect 5th Medium Perfect 5th S5/P5 P5 3/2
26 725.581 diminished sixth, high fifth Super 5th Large Perfect 5th L5 d6, pai-P5 ^5 d6 32/21
27 753.488 low augmented fifth, high diminished sixth Low Subminor 6th Interseptimal 5th-6th pao-A5, pai-d6 vA5, ^d6 sA5, Sd6 20/13
28 781.395 low minor sixth High Subminor 6th Small Minor 6th Sm6/m.m6 A5, pao-m6 vm6 sm6, A5 14/9, 11/7
29 809.302 Minor 6th MediuenMinor 6th (L)m6 m6 8/5
30 837.209 low neutral sixth Superminor 6th Large Minor 6th Wm6 pai-m6 ^m6 Sm6 18/11, 13/8
31 865.116 high neutral sixth Submajor 6th Large Neutral 6th NM6 pao-M6 vM6 sM6 28\17, 64\39
32 893.023 Major 6th Small Major 6th (S)M6 M6 5/3
33 920.93 high major sixth Supermajor 6th Large Major 6th LM6 pai-M6, d7 ^M6 SM6, d7 12/7
34 948.837 low augmented sixth, high diminished seventh Super 6th, Sub 7th Diatonic Minor 7th, Interseptimal 6th-7th A.LM6/d.Sm7 pao-A6, pai-d7 vA6, ^d7 Sinth* sA6, Sd7 26/15
35 976.744 low minor seventh, augmented sixth Subminor 7th Low Neutral Minor 7th Sm7 pao-m7, A6 vm7 sm7, A6 7/4
36 1004.651 Minor 7th High Neutral Minor 7th (L)m7 m7 16/9, 9/5
37 1032.558 low neutral seventh Superminor 7th Chromatic Minor 7th, Small Neutral 7th A.Lm7 pai-m7 ^m7 Sm7 20/11
38 1060.465 high neutral seventh Submajor 7th Large Neutral 7th Wm7/NM7 pao-M7 vM7 sM7 11/6, 24/13, 13/7
39 1088.372 Major 7th Diatonic Major 7th SM7 M7 15/8, 28/15
40 1116.279 diminished octave Low Supermajor 7th Neutral Major 7th M7 d8, pai-M7 ^M7 SM7. d8 40/21
41 1144.186 high diminished octave High Supermajor 7th Chromatic Major 7th LM7 pai-d8, pao-A7 vA7, ^d8 *Septave sA7, Sd8 64/33
42 1172.093 low octave, augmented seventh Ultramajor 7th S8/WM7 pao-P8, A7 A7, v8 A7 63/32, 160/81
43 1200 Octave P8 2/1

*'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.

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 as well.