User:FloraC/Reasonable commas: Difference between revisions

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Thanks to @Dead Shaman.  
Thanks to @Dead Shaman.  


A reasonable comma in a subgroup is one which cannot be factored into two simpler commas.  
Dead Shaman defines the reasonable comma as one such that there is not a number between the numerator and denominator which is in the subgroup.
 
My redefinition: a reasonable comma is one which cannot be factored into two simpler commas in a given subgroup.  


{| class="wikitable"
{| class="wikitable"
Line 22: Line 24:
| 10/9 || {{monzo| 1 -2 1 }} || Classic major second
| 10/9 || {{monzo| 1 -2 1 }} || Classic major second
|-
|-
| 16/15 || {{monzo| 4 -1 -1 }} || Classic minor second
| 16/15 || {{monzo| 4 -1 -1 }} || Father comma
|-
|-
| 25/24 || {{monzo| -3 -1 2 }} || Classic chroma
| 25/24 || {{monzo| -3 -1 2 }} || Dicot comma
|-
|-
| 27/25 || {{monzo| 0 -3 2 }} || Large limma
| 27/25 || {{monzo| 0 -3 2 }} || Bug comma
|-
|-
| 81/80 || {{monzo| -4 4 -1 }} || Syntonic comma
| 81/80 || {{monzo| -4 4 -1 }} || Syntonic comma
|-
|-
| 128/125 || {{monzo| 7 0 -3 }} || Diesis
| 128/125 || {{monzo| 7 0 -3 }} || Augmented comma
|-
|-
| 250/243 || {{monzo| 1 -5 3 }} || Porcupine comma
| 250/243 || {{monzo| 1 -5 3 }} || Porcupine comma
Line 67: Line 69:
|-
|-
| 450359962737049600/450283905890997363 || {{monzo| 54 -37 2 }} || Monzisma
| 450359962737049600/450283905890997363 || {{monzo| 54 -37 2 }} || Monzisma
|}
{| class="wikitable"
|+ List of 7-limit reasonable commas
|-
! Ratio !! Monzo !! Name
|-
| 2/1 || {{monzo| 1 }} || Octave
|-
| 3/2 || {{monzo| -1 1 }} || Perfect fifth
|-
| 4/3 || {{monzo| 2 -1 }} || Perfect fourth
|-
| 5/4 || {{monzo| -2 0 1 }} || Classic major third
|-
| 6/5 || {{monzo| 1 1 -1 }} || Classic minor third
|-
| 7/6 || {{monzo| -1 -1 0 1 }} || Septimal minor third
|-
| 8/7 || {{monzo| 3 0 0 -1 }} || Septimal major second
|-
| 9/8 || {{monzo| -3 2 }} || Major second
|-
| 10/9 || {{monzo| 1 -2 1 }} || Classic major second
|-
| 15/14 || {{monzo| -1 1 1 -1 }} || Septimal major semitone
|-
| 16/15 || {{monzo| 4 -1 -1 }} || Father comma
|-
| 21/20 || {{monzo| -2 1 -1 1 }} || Septimal minor semitone
|-
| 25/24 || {{monzo| -3 -1 2 }} || Dicot comma
|-
| 27/25 || {{monzo| 0 -3 2 }} || Bug comma
|-
| 28/27 || {{monzo| 2 -3 0 1 }} || Trienstonic comma
|-
| 36/35 || {{monzo| 2 2 -1 -1 }} || Mint comma
|-
| 49/48 || {{monzo| -4 -1 0 2 }} || Slendro diesis
|-
| 50/49 || {{monzo| 1 0 2 -2 }} || Jubilisma
|-
| 64/63 || {{monzo| 6 -2 0 1 }} || Septimal comma
|-
| 81/80 || {{monzo| -4 4 -1 }} || Syntonic comma
|-
| 126/125 || {{monzo| 1 2 -3 1 }} || Starling comma
|-
| 225/224 || {{monzo| -5 2 2 -1 }} || Marvel comma
|-
| 245/243 || {{monzo| 0 -5 1 2 }} || Sensamagic comma
|-
| 1029/1024 || {{monzo| -10 1 0 3 }} || Gamelisma
|-
| 1728/1715 || {{monzo| 6 3 -1 -3 }} || Orwellisma
|-
| 2048/2025 || {{monzo| 11 -4 -2 }} || Diaschisma
|-
| 2401/2400 || {{monzo| -5 -1 -2 4 }} || Breedsma
|-
| 3125/3087 || {{monzo| 0 -2 5 -3 }} || Gariboh comma
|-
| 3136/3125 || {{monzo| 6 0 -5 2 }} || Hemimean comma
|-
| 4000/3969 || {{monzo| 5 -4 3 -2 }} || Octagar comma
|-
| 4375/4374 || {{monzo| -1 -7 4 1 }} || Ragisma
|-
| 5120/5103 || {{monzo| 10 -6 1 -1 }} || Hemifamity comma
|-
| 6144/6125 || {{monzo| 11 1 -3 -2 }} || Porwell comma
|-
| 16875/16807 || {{monzo| 0 3 4 -5 }} || Mirkwai comma
|-
| 19683/19600 || {{monzo| -4 9 -2 -2 }} || Cataharry comma
|-
| 32805/32768 || {{monzo| -15 8 1 }} || Schisma
|-
| 118098/117649 || {{monzo| 1 10 0 -6 }} || Stearnsma
|-
| 250047/250000 || {{monzo| -4 6 -6 3 }} || Landscape comma
|-
| 589824/588245 || {{monzo| 16 2 -1 -6 }} || Hewuermera comma
|-
| 703125/702464 || {{monzo| -11 2 7 -3 }} || Meter comma
|-
| 2460375/2458624 || {{monzo| -10 9 3 -4 }} || Sesquiquartisma
|-
| 14348907/14336000 || {{monzo| -14 15 -3 -1 }} || Skeetsma
|-
| 29360128/29296875 || {{monzo| 22 -1 -10 1 }} || Quasiorwellisma
|-
| 33554432/33480783 || {{monzo| 25 -14 0 -1 }} || Garischisma
|-
| 43046721/43025920 || {{monzo| -9 16 -1 -5 }} || Trienstonisma
|-
| 52734375/52706752 || {{monzo| -6 3 9 -7 }} || Supermatertisma
|-
| 67108864/66976875 || {{monzo| 26 -7 -4 -2 }} || Decovulture comma
|-
| 78125000/78121827 || {{monzo| 3 -13 10 -2 }} || Euzenius comma
|}
|}

Latest revision as of 18:47, 30 May 2022

Thanks to @Dead Shaman.

Dead Shaman defines the reasonable comma as one such that there is not a number between the numerator and denominator which is in the subgroup.

My redefinition: a reasonable comma is one which cannot be factored into two simpler commas in a given subgroup.

List of 5-limit reasonable commas
Ratio Monzo Name
2/1 [1⟩ Octave
3/2 [-1 1⟩ Perfect fifth
4/3 [2 -1⟩ Perfect fourth
5/4 [-2 0 1⟩ Classic major third
6/5 [1 1 -1⟩ Classic minor third
9/8 [-3 2⟩ Major second
10/9 [1 -2 1⟩ Classic major second
16/15 [4 -1 -1⟩ Father comma
25/24 [-3 -1 2⟩ Dicot comma
27/25 [0 -3 2⟩ Bug comma
81/80 [-4 4 -1⟩ Syntonic comma
128/125 [7 0 -3⟩ Augmented comma
250/243 [1 -5 3⟩ Porcupine comma
2048/2025 [11 -4 -2⟩ Diaschisma
3125/3072 [-10 -1 5⟩ Magic comma
15625/15552 [-6 -5 6⟩ Kleisma
20000/19683 [5 -9 4⟩ Tetracot comma
32805/32768 [-15 8 1⟩ Schisma
78732/78125 [2 9 -7⟩ Sensipent comma
393216/390625 [17 1 -8⟩ Würschmidt comma
1600000/1594323 [9 -13 5⟩ Amity comma
1224440064/1220703125 [8 14 -13⟩ Parakleisma
4294967296/4271484375 [32 -7 -9⟩ Escapade comma
6115295232/6103515625 [23 6 -14⟩ Vishnuzma
10485760000/10460353203 [24 -21 4⟩ Vulture comma
274877906944/274658203125 [38 -2 -15⟩ Luna comma
7629394531250/7625597484987 [1 -27 18⟩ Ennealimma
9010162353515625/9007199254740992 [-53 10 16⟩ Kwazy comma
50031545098999707/50000000000000000 [-16 35 -17⟩ Minortone comma
450359962737049600/450283905890997363 [54 -37 2⟩ Monzisma
List of 7-limit reasonable commas
Ratio Monzo Name
2/1 [1⟩ Octave
3/2 [-1 1⟩ Perfect fifth
4/3 [2 -1⟩ Perfect fourth
5/4 [-2 0 1⟩ Classic major third
6/5 [1 1 -1⟩ Classic minor third
7/6 [-1 -1 0 1⟩ Septimal minor third
8/7 [3 0 0 -1⟩ Septimal major second
9/8 [-3 2⟩ Major second
10/9 [1 -2 1⟩ Classic major second
15/14 [-1 1 1 -1⟩ Septimal major semitone
16/15 [4 -1 -1⟩ Father comma
21/20 [-2 1 -1 1⟩ Septimal minor semitone
25/24 [-3 -1 2⟩ Dicot comma
27/25 [0 -3 2⟩ Bug comma
28/27 [2 -3 0 1⟩ Trienstonic comma
36/35 [2 2 -1 -1⟩ Mint comma
49/48 [-4 -1 0 2⟩ Slendro diesis
50/49 [1 0 2 -2⟩ Jubilisma
64/63 [6 -2 0 1⟩ Septimal comma
81/80 [-4 4 -1⟩ Syntonic comma
126/125 [1 2 -3 1⟩ Starling comma
225/224 [-5 2 2 -1⟩ Marvel comma
245/243 [0 -5 1 2⟩ Sensamagic comma
1029/1024 [-10 1 0 3⟩ Gamelisma
1728/1715 [6 3 -1 -3⟩ Orwellisma
2048/2025 [11 -4 -2⟩ Diaschisma
2401/2400 [-5 -1 -2 4⟩ Breedsma
3125/3087 [0 -2 5 -3⟩ Gariboh comma
3136/3125 [6 0 -5 2⟩ Hemimean comma
4000/3969 [5 -4 3 -2⟩ Octagar comma
4375/4374 [-1 -7 4 1⟩ Ragisma
5120/5103 [10 -6 1 -1⟩ Hemifamity comma
6144/6125 [11 1 -3 -2⟩ Porwell comma
16875/16807 [0 3 4 -5⟩ Mirkwai comma
19683/19600 [-4 9 -2 -2⟩ Cataharry comma
32805/32768 [-15 8 1⟩ Schisma
118098/117649 [1 10 0 -6⟩ Stearnsma
250047/250000 [-4 6 -6 3⟩ Landscape comma
589824/588245 [16 2 -1 -6⟩ Hewuermera comma
703125/702464 [-11 2 7 -3⟩ Meter comma
2460375/2458624 [-10 9 3 -4⟩ Sesquiquartisma
14348907/14336000 [-14 15 -3 -1⟩ Skeetsma
29360128/29296875 [22 -1 -10 1⟩ Quasiorwellisma
33554432/33480783 [25 -14 0 -1⟩ Garischisma
43046721/43025920 [-9 16 -1 -5⟩ Trienstonisma
52734375/52706752 [-6 3 9 -7⟩ Supermatertisma
67108864/66976875 [26 -7 -4 -2⟩ Decovulture comma
78125000/78121827 [3 -13 10 -2⟩ Euzenius comma
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