User:Dummy index/Chromatic pairs and how we define haplotonic: Difference between revisions
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= Proposal to simplify the definition = | |||
* In order to distinguish between the fixed category of [[:Category:Haplotonic scales]], etc., and the reciprocal relationship (haplotonic) + (albitonic) = (chromatic), the latter will be called, for example, MOS triplet. Every 3 successive generations of MOS that satisfies the above relationship will be called a MOS triplet. | |||
** Or moshaplotonic as a parent MOS, moschromatic as a descendant MOS, like that [[moschroma]] and [[mosdiesis]] are relative from any MOS scale of interest. | |||
* If the number of notes in the scale is important, consider using the [[Pentatonic]] and [[Heptatonic]] pages. | |||
* Based on the above equation and the nature of MOS, the chromatic must be a direct descendant of the albitonic. So I don't like the existence of mega-albitonic between albitonic and chromatic, even though the meanings of relational and categorical usages don't have to be exactly the same. (I will also withdraw the mini-albitonic that I said.) | |||
* Categorical haplotonic scales include the last MOS that s ≥ 125 ¢ and some subset of such scales. in <nowiki>[[Chromatic pairs]]</nowiki>, such subsets all may be labelled mini-haplotonic (even if there are more than one). | |||
* Categorical albitonic scale is the first MOS that s < 125 ¢. | |||
** If the interval that appears is too narrow to be a semitone, it may be a [[Cluster MOS]]. | |||
* Categorical chromatic scales include direct descendant of albitonic (by adding corresponding haplotonic) and further descendant <del>(by adding same haplotonic)</del>. in <nowiki>[[Chromatic pairs]]</nowiki>, such further descendants all may be labelled mega-chromatic (even if there are more than one). | |||
= Memos = | |||
I couldn't find a comprehensive explanation of haplotonic, so I'm going to consider the current situation in my own way. | I couldn't find a comprehensive explanation of haplotonic, so I'm going to consider the current situation in my own way. | ||
| Line 9: | Line 19: | ||
haplotonic is something similar to the black keys of a piano. hmm... | haplotonic is something similar to the black keys of a piano. hmm... | ||
# Number of notes. about 5-notes. here I tentatively state the best is | # Number of notes. about 5-notes. here I tentatively state the best is 4–6 notes. | ||
# (haplotonic)+(albitonic)=(chromatic). strong. | # (haplotonic)+(albitonic)=(chromatic). strong. (strict, but local) | ||
# Semitone-free MOS. some authors might consider this property. All labelled scales are s > 125 ¢. | # Semitone-free MOS. some authors might consider this property. All labelled scales are s > 125 ¢. | ||
In fact, it can be seen from condition 3 that the haplotonic scale is up to 9 notes. | In fact, it can be seen from condition 3 that the haplotonic scale is up to 9 notes. | ||
( | By the way, many of the scale-lists listed on <nowiki>[[Chromatic pairs]]</nowiki> are actually "chain of albitonic-chromatic pairs". Moreover, the part that is a arithmetic sequence is composed by repeatedly adding the same strong haplotonic scale. And the strong haplotonic is direct parent MOS of first albitonic of the arithmetic chain. | ||
* Nestoria[7], Nestoria[12], Nestoria[17] — adding Nestoria[5] repeatedly | |||
* (memo: strong haplotonic is "L will be new s if cutting s from L anymore" so soft-of-basic) | |||
* What I mean of albitonic-chromatic pairs is strict operation of equation of condition 2. And with MOS tree, albitonic-chromatic relation usually results in direct parent-daughter. Exception is (1L ''x''s)+(1L ''y''s)=(1a (1+''x''+''y'')b) (i dunno another case). Or adopt [[User:Ganaram inukshuk/Notes #Strict definition|his strict definition]]. You can then use ''n''*(haplotonic)+(albitonic)=(...) to move a few steps at once (<q>possibly multiple copies of one of them</q>). | |||
~~ Exercise ~~ | |||
* I would like to exclude 1L ''x''s from the albitonic-chromatic pair. To reason this... excluding 1L from strong haplotonic. | |||
* First two strong haplotonic of Barton are Barton[2] and Barton[11]. Barton[2] is too few notes. Barton[11] is too many notes. Barton[3] and all descendants aren't semitone-free. Strong haplotonic can be obtained for any rank-2, but not always any haplotonic (in condition 1 and 3) can be. | |||
* Seni[5] and Sensi[8] both are labelled Category:Haplotonic scales. Only Sensi[8] is strong haplotonic, but Sensi[5] is shorter genchain, obviously more haplo than Sensi[8]. both haplotonic? mini-haplotonic and haplotonic? haplotonic and strong-haplotonic? Well, shouldn't both be haplotonic? Isn't it just that we want to differentiate it because we're trying to include it in the scale-list? | |||
** If there are multiple haplotonic scale in condition 1 and 3, it may be nice to name most-notes scale (must be strong haplotonic!) "strong haplotonic" or "maximum haplotonic" or "the end of haplotonic". | |||
*** Baldy[5] and Baldy[6] both are strong haplotonic, so we need to use different terms to distinguish them. e.g. Baldy4/5/6 are haplotonic and Baldy6 is max-haplotonic. Until Baldy5 become listed, Baldy6 is simply called haplotonic. | |||
* Fractional-octave? | |||
* Are they undoubtedly haplotonic? neutral third 3L 4s, mavila 2L 5s, ... | |||
= Category:Haplotonic scales (November 2024) = | = Category:Haplotonic scales (November 2024) = | ||
{| class="wikitable" | |||
|+ Caption text | |||
|- | |||
! Name !! Size of s (¢) !! # of notes<br>1–3: −, 4–6: ☆, 7–9: △ !! Strong !! Remarks | |||
|- | |||
| Baldy6 || 180 || ☆ || Yes || Baldy5 is also strong haplotonic for Baldy6-Baldy11 pair | |||
|- | |||
| Bleu8 || 140 || △ || Yes || | |||
|- | |||
| Roulette6 || 195 || ☆ || Yes || | |||
|- | |||
| Sensi5 || 130 || ☆ || No || direct parent of Sensi8 | |||
|- | |||
| Sensi8 || 130 || △ || Yes || | |||
|- | |||
| Silver7 || 128 || △ || Yes || | |||
|- | |||
| Tutone6 || 194 || ☆ || Yes || | |||
|} | |||
= Chromatic pairs (November 2024) = | = Chromatic pairs (November 2024) = | ||
| Line 40: | Line 75: | ||
[[Comma list]]: [[250047/250000]] | [[Comma list]]: [[250047/250000]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 3 0 -4 | 0 1 2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }} | ||
: [[gencom]]: [63/50 10/9; 250047/250000] | : [[gencom]]: [63/50 10/9; 250047/250000] | ||
| Line 68: | Line 103: | ||
[[Comma list]]: [[2200/2197]] | [[Comma list]]: [[2200/2197]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 1| 0 3 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 -1/3 0 -1/3 2/3 | 0 0 -4/3 0 5/3 -1/3 }} | ||
: [[gencom]]: [2 13/10; 2200/2197] | : [[gencom]]: [2 13/10; 2200/2197] | ||
| Line 94: | Line 129: | ||
[[Comma list]]: [[2200/2197]], [[6656/6655]] | [[Comma list]]: [[2200/2197]], [[6656/6655]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 6 3 6 | 0 -8 1 -5 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 6 0 3 6 | 0 0 -8 0 1 -5 }} | ||
: gencom: [2 11/8; 2200/2197 6656/6655] | : gencom: [2 11/8; 2200/2197 6656/6655] | ||
| Line 120: | Line 155: | ||
[[Comma list]]: [[28672/28561]] | [[Comma list]]: [[28672/28561]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 4 4 | 0 -4 -1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 4 0 4 | 0 0 0 -4 0 -1 }} | ||
: [[gencom]]: [2, 16/13; 28672/28561] | : [[gencom]]: [2, 16/13; 28672/28561] | ||
| Line 141: | Line 176: | ||
[[Comma list]]: [[847/845]], [[1001/1000]] | [[Comma list]]: [[847/845]], [[1001/1000]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 0 1 | 0 -4 3 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 -3/4 5/4 -3/4 1/4 | 0 0 0 -4 3 1 }} | ||
: [[gencom]]: [2 13/10; 847/845 1001/1000] | : [[gencom]]: [2 13/10; 847/845 1001/1000] | ||
| Line 179: | Line 214: | ||
[[Comma list]]: [[65536/65219]] | [[Comma list]]: [[65536/65219]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 4 | 0 3 -2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 2 4 | 0 0 0 3 -2 }} | ||
: [[gencom]]: [2 77/64; 65536/65219] | : [[gencom]]: [2 77/64; 65536/65219] | ||
| Line 205: | Line 240: | ||
[[Comma list]]: [[325/324]] | [[Comma list]]: [[325/324]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 2 | 0 1 -2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -1/6 5/6 0 0 -1/3 | 0 -1/2 -3/2 0 0 1 }} | ||
: [[gencom]]: [2 6/5; 325/324] | : [[gencom]]: [2 6/5; 325/324] | ||
| Line 243: | Line 278: | ||
[[Comma list]]: [[352/351]], [[676/675]] | [[Comma list]]: [[352/351]], [[676/675]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -6 -1 | 0 2 9 3 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 2 -5/3 0 4/3 1/3 | 0 -2 4 0 -5 1 }} | ||
: [[gencom]]: [2 15/13; 352/351 676/675] | : [[gencom]]: [2 15/13; 352/351 676/675] | ||
| Line 272: | Line 307: | ||
[[Comma list]]: [[352/351]], [[676/675]], [[847/845]] | [[Comma list]]: [[352/351]], [[676/675]], [[847/845]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 10 -6 -1 | 0 2 -12 9 3 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 2 -3/4 -11/4 9/4 5/4 | 0 -2 0 12 -9 -3 }} | ||
: [[gencom]]: [2 15/13; 352/351 676/675 847/845] | : [[gencom]]: [2 15/13; 352/351 676/675 847/845] | ||
| Line 322: | Line 357: | ||
[[Comma list]]: [[640/637]], [[10985/10976]] | [[Comma list]]: [[640/637]], [[10985/10976]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 5 4 4 | 0 -9 -4 -1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 5 4 0 4 | 0 0 -9 -4 0 -1 }} | ||
: [[gencom]]: [2 16/13; 640/637 10985/10976] | : [[gencom]]: [2 16/13; 640/637 10985/10976] | ||
| Line 348: | Line 383: | ||
[[Comma list]]: [[243/242]], [[676/675]] | [[Comma list]]: [[243/242]], [[676/675]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 2 0 -1 -2 | 0 2 5 3 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 2 4 -2 0 9 2 | 0 -2 3/2 0 -5 -3/2 }} | ||
: [[gencom]]: [55/39 15/13; 243/242 676/675] | : [[gencom]]: [55/39 15/13; 243/242 676/675] | ||
| Line 375: | Line 410: | ||
[[Comma list]]: [[352/351]], [[364/363]] | [[Comma list]]: [[352/351]], [[364/363]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 7 12 | 0 1 -4 -7 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }} | ||
: [[gencom]]: [2 3/2; 352/351 364/363] | : [[gencom]]: [2 3/2; 352/351 364/363] | ||
| Line 400: | Line 435: | ||
[[Comma list]]: [[15625/15488]] | [[Comma list]]: [[15625/15488]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 2 0 -7 | 0 1 3 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 2 0 4 0 5 | 0 0 1 0 3 }} | ||
: [[gencom]]: [125/88 5/4; 15625/15488] | : [[gencom]]: [125/88 5/4; 15625/15488] | ||
| Line 424: | Line 459: | ||
[[Comma list]]: [[1573/1568]], [[15488/15379]] | [[Comma list]]: [[1573/1568]], [[15488/15379]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 1 3 | 0 8 7 2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 0 1 3 | 0 0 0 8 7 2 }} | ||
: [[gencom]]: [2 14/11; 1573/1568 15488/15379] | : [[gencom]]: [2 14/11; 1573/1568 15488/15379] | ||
| Line 457: | Line 492: | ||
[[Comma list]]: [[265837/262144]] | [[Comma list]]: [[265837/262144]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 6 | 0 3 -2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 0 3 4 | 0 0 0 0 3 -2 }} | ||
: [[gencom]]: [2 143/128; 265837/262144] | : [[gencom]]: [2 143/128; 265837/262144] | ||
| Line 481: | Line 516: | ||
[[Comma list]]: [[225/224]] | [[Comma list]]: [[225/224]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 5 | 0 1 -2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 2/5 2 -1/5 | 0 -4/5 1 2/5 }} | ||
: [[gencom]]: [2 5/4; 225/224] | : [[gencom]]: [2 5/4; 225/224] | ||
| Line 505: | Line 540: | ||
[[Comma list]]: [[196/195]] = {{monzo| 2 -1 2 0 -1 }}, [[352/351]] = {{monzo| 5 -3 0 1 -1 }}, [[364/363]] = {{monzo| 2 -1 1 -2 1 }} | [[Comma list]]: [[196/195]] = {{monzo| 2 -1 2 0 -1 }}, [[352/351]] = {{monzo| 5 -3 0 1 -1 }}, [[364/363]] = {{monzo| 2 -1 1 -2 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 10 17 22 | 0 1 -6 -10 -13 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 1 -5 -1 2 4 | 0 1 29/4 5/4 -11/4 -23/4 }} | ||
: [[gencom]]: [2 3/2; 196/195, 352/351, 364/363] | : [[gencom]]: [2 3/2; 196/195, 352/351, 364/363] | ||
| Line 565: | Line 600: | ||
[[Comma list]]: [[170/169]], [[640/637]], [[5525/5488]] | [[Comma list]]: [[170/169]], [[640/637]], [[5525/5488]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 5 4 4 2 | 0 -9 -4 -1 7 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 -4 0 0 3 9 | 0 0 9 4 0 1 -7 }} | ||
: [[gencom]]: [2 13/8; 170/169 640/637 5525/5488] | : [[gencom]]: [2 13/8; 170/169 640/637 5525/5488] | ||
| Line 593: | Line 628: | ||
[[Comma list]]: [[225/224]], [[325/324]], [[640/637]] | [[Comma list]]: [[225/224]], [[325/324]], [[640/637]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 15 25 -28 | 0 1 -4 -7 10 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 3/2 3 4 0 2 | 0 1/2 -4 -7 0 10 }} | ||
: [[gencom]]: [2 9/8; 225/224 325/324 640/637] | : [[gencom]]: [2 9/8; 225/224 325/324 640/637] | ||
| Line 619: | Line 654: | ||
[[Comma list]]: [[176/175]], [[540/539]] | [[Comma list]]: [[176/175]], [[540/539]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 2 -2 | 0 3 -1 5 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }} | ||
: [[gencom]]: [2 7/6; 176/175 540/539] | : [[gencom]]: [2 7/6; 176/175 540/539] | ||
| Line 652: | Line 687: | ||
[[Comma list]]: [[275/273]], [[847/845]] | [[Comma list]]: [[275/273]], [[847/845]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 0 0 | 0 3 5 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }} | ||
: [[gencom]]: [2 13/11; 275/273 847/845] | : [[gencom]]: [2 13/11; 275/273 847/845] | ||
| Line 684: | Line 719: | ||
[[Comma list]]: [[245/243]] | [[Comma list]]: [[245/243]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 0 | 0 2 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 0 | 0 0 2 -1 }} | ||
: [[gencom]]: [2 9/7; 245/243] | : [[gencom]]: [2 9/7; 245/243] | ||
| Line 728: | Line 763: | ||
[[Comma list]]: 1071875/1048576 | [[Comma list]]: 1071875/1048576 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 5 | 0 3 -5 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 1 5 | 0 0 3 -5 }} | ||
: [[gencom]]: [2 175/128; 1071875/1048576] | : [[gencom]]: [2 175/128; 1071875/1048576] | ||
| Line 754: | Line 789: | ||
[[Comma list]]: [[3025/3024]], [[3125/3087]] | [[Comma list]]: [[3025/3024]], [[3125/3087]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 0 2 | 0 6 10 -1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -1/2 -1/2 -1/2 3/2 | 0 -15/4 9/4 25/4 -19/4 }} | ||
: [[gencom]]: [2 12/11; 3025/3024 3125/3087] | : [[gencom]]: [2 12/11; 3025/3024 3125/3087] | ||
| Line 782: | Line 817: | ||
[[Comma list]]: [[126/125]] | [[Comma list]]: [[126/125]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -1 | 0 1 3 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -1 0 1 | 0 4/3 1/3 -5/3 }} | ||
: [[gencom]]: [2 6/5; 126/125] | : [[gencom]]: [2 6/5; 126/125] | ||
| Line 806: | Line 841: | ||
[[Comma list]]: [[1352/1331]] | [[Comma list]]: [[1352/1331]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 3 | 0 2 3 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 0 3 3 | 0 0 0 0 2 3 }} | ||
: [[gencom]]: [2 13/11; 1352/1331] | : [[gencom]]: [2 13/11; 1352/1331] | ||
| Line 832: | Line 867: | ||
[[Comma list]]: [[29282/28561]] | [[Comma list]]: [[29282/28561]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 4 0 1 | 0 1 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 4 0 0 0 12 13 | 0 0 0 0 1 1 }} | ||
: [[gencom]]: [13/11 11/8; 29282/28561] | : [[gencom]]: [13/11 11/8; 29282/28561] | ||
| Line 856: | Line 891: | ||
[[Comma list]]: [[144/143]], [[176/175]], [[196/195]] | [[Comma list]]: [[144/143]], [[176/175]], [[196/195]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 2 -2 6 | 0 3 -1 5 -5 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -5/4 3 -1/4 7/4 -1/4 | 0 -1/4 -3 3/4 -21/4 19/4 }} | ||
: [[gencom]]: [2 7/6; 144/143 176/175 196/195] | : [[gencom]]: [2 7/6; 144/143 176/175 196/195] | ||
| Line 891: | Line 926: | ||
[[Comma list]]: [[121/120]], [[126/125]] | [[Comma list]]: [[121/120]], [[126/125]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 2 2 | 0 -2 -6 -1}} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }} | ||
: [[gencom]]: [2 11/10; 121/120 126/125] | : [[gencom]]: [2 11/10; 121/120 126/125] | ||
| Line 919: | Line 954: | ||
[[Comma list]]: [[121/120]], [[169/168]], [[275/273]] | [[Comma list]]: [[121/120]], [[169/168]], [[275/273]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 5 3 4 | 0 -6 -10 -3 -5 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -3 0 2 0 1 | 0 24/5 -6/5 -26/5 9/5 -1/5 }} | ||
: [[gencom]]: [2 13/10; 121/120 169/168 275/273] | : [[gencom]]: [2 13/10; 121/120 169/168 275/273] | ||
| Line 944: | Line 979: | ||
[[Comma list]]: [[99/98]] | [[Comma list]]: [[99/98]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 1 | 0 1 2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }} | ||
: [[gencom]]: [2 7/6; 99/98] | : [[gencom]]: [2 7/6; 99/98] | ||
| Line 968: | Line 1,003: | ||
[[Comma list]]: [[99/98]], [[176/175]] | [[Comma list]]: [[99/98]], [[176/175]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 5 -9 | 0 1 -2 4 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 4/9 2 -1/9 -1/9 | 0 -4/3 1 -2/3 4/3 }} | ||
: [[gencom]]: [2 5/4; 99/98 176/175] | : [[gencom]]: [2 5/4; 99/98 176/175] | ||
| Line 1,014: | Line 1,049: | ||
[[Comma list]]: 100/99 = {{monzo| 2 2 0 -1 }}, 385/384 = {{monzo| -7 1 1 1 }} | [[Comma list]]: 100/99 = {{monzo| 2 2 0 -1 }}, 385/384 = {{monzo| -7 1 1 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 5 2 | 0 1 -3 2 }} | ||
: mapping generators: ~2, ~5/3 | : mapping generators: ~2, ~5/3 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }} | ||
: [[gencom]]: [2 6/5; 100/99 385/384] | : [[gencom]]: [2 6/5; 100/99 385/384] | ||
| Line 1,056: | Line 1,091: | ||
[[Comma list]]: 100/99, 245/242 | [[Comma list]]: 100/99, 245/242 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 1 0 | 0 -2 3 4 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }} | ||
: [[gencom]]: [2 21/20; 100/99 245/242] | : [[gencom]]: [2 21/20; 100/99 245/242] | ||
| Line 1,077: | Line 1,112: | ||
[[Comma list]]: 343/338, 847/832 | [[Comma list]]: 343/338, 847/832 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 3 1 | 0 4 1 6 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 1 3 1| 0 0 0 4 1 6 }} | ||
: [[gencom]]: [2 11/8; 343/338 847/832] | : [[gencom]]: [2 11/8; 343/338 847/832] | ||
| Line 1,153: | Line 1,188: | ||
[[Comma list]]: 99/98, 9317/9216 | [[Comma list]]: 99/98, 9317/9216 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 1 3 | 0 7 4 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 1 3 | 0 7/2 0 4 1 }} | ||
: [[gencom]]: [2 11/8; 99/98 9317/9216] | : [[gencom]]: [2 11/8; 99/98 9317/9216] | ||
| Line 1,205: | Line 1,240: | ||
[[Comma list]]: 65/64, 170/169, 221/220 | [[Comma list]]: 65/64, 170/169, 221/220 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 15 6 11 | 0 1 -5 -1 -3 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 2 0 5 4 5 | 0 0 1 0 -5 -1 -3 }} | ||
: [[gencom]]: [2 5/4; 65/64 170/169 221/220] | : [[gencom]]: [2 5/4; 65/64 170/169 221/220] | ||
| Line 1,294: | Line 1,329: | ||
[[Comma list]]: 56/55, 91/90, 100/99 | [[Comma list]]: 56/55, 91/90, 100/99 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -1 2 2 | 0 1 3 2 -2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }} | ||
: [[gencom]]: [2 6/5; 56/55 91/90 100/99] | : [[gencom]]: [2 6/5; 56/55 91/90 100/99] | ||
| Line 1,318: | Line 1,353: | ||
[[Comma list]]: 56/55, 128/125 | [[Comma list]]: 56/55, 128/125 | ||
{{Mapping|legend= | {{Mapping|legend=3| 3 7 0 2 | 0 0 1 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 3 0 7 9 11| 0 0 0 -1 -1 }} | ||
: [[gencom]]: [5/4 8/7; 56/55 128/125] | : [[gencom]]: [5/4 8/7; 56/55 128/125] | ||
| Line 1,355: | Line 1,390: | ||
[[Comma list]]: 56/55, 78/77, 91/90 | [[Comma list]]: 56/55, 78/77, 91/90 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 1 2 2 | 0 -3 -2 1 -1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -5/4 2 -1/4 3/4 3/4 | 0 -1/2 3 3/2 -3/2 1/2 }} | ||
: [[gencom]]: [2 13/12; 56/55 78/77 91/90] | : [[gencom]]: [2 13/12; 56/55 78/77 91/90] | ||
| Line 1,377: | Line 1,412: | ||
[[Comma list]]: 55/54, 64/63, 100/99 | [[Comma list]]: 55/54, 64/63, 100/99 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 1 5 2 | 0 3 4 -3 2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 2 3 2 4 | 0 -3/2 -5/2 3 -2 }} | ||
: [[gencom]]: [2 6/5; 55/54 64/63 100/99] | : [[gencom]]: [2 6/5; 55/54 64/63 100/99] | ||
| Line 1,409: | Line 1,444: | ||
[[Comma list]]: 45/44, 65/64, 81/80 | [[Comma list]]: 45/44, 65/64, 81/80 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -4 -6 10 | 0 1 2 3 -2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 3/2 2 0 3 4 | 0 1/2 2 0 3 -2 }} | ||
: [[gencom]]: [2 9/8; 45/44 65/64 81/80] | : [[gencom]]: [2 9/8; 45/44 65/64 81/80] | ||
| Line 1,442: | Line 1,477: | ||
[[Category:Listen]] | [[Category:Listen]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||