Delta-rational chord: Difference between revisions
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A '''delta-rational''' ('''DR''') chord is a [[chord]] that has integer ratios between frequency ''differences'' of some pair of dyads, called '''deltas''', with the dyads in question assumed to be between successive notes (Δ, capital delta, is often used to denote "difference"). | A '''delta-rational''' ('''DR''') chord is a [[chord]] that has integer ratios between frequency ''differences'' of some pair of dyads, called '''deltas''', with the dyads in question assumed to be between successive notes (Δ, capital delta, is often used to denote "difference"). | ||
DR chords generalize JI chords, in which all frequency differences of dyads are exactly integer ratios. But unlike JI chords, a DR chord need not have integer ratios between frequencies of notes. For example, the [[13edo]] chord 0 | DR chords generalize JI chords, in which all frequency differences of dyads are exactly integer ratios. But unlike JI chords, a DR chord need not have integer ratios between frequencies of notes. For example, the [[13edo]] chord {{dash|0, 3, 8, 10|med}}\13 ({{dash|0¢, 277¢, 738¢, 923¢|med}}) is close to being delta-rational, because the frequency difference of the dyad 8–10\13 is 0.994 times the frequency difference of the dyad 0–3\13. (In the exactly DR chord {{dash|0\13, 3\13, 8\13, 924.159¢}}, the 3rd and 4th notes have exactly the same frequency difference as the dyad 0-3\13.) | ||
[[JI]] chords and chords that are subsets of [[Delta-rational chord#Isodifferential chord|isodifferential chord]]s (these correspond to all chords of the form α : α + ''k''<sub>1</sub> : ... : α + ''k''<sub>''n''</sub> for any positive (possibly irrational) number α and integers ''k''<sub>1</sub>, ..., ''k''<sub>''n''</sub>) are special cases of delta-rational chords, but in these chords ''all'' dyads are rationally related in frequency space, which we call either '''fully delta-rational''' (FDR) or '''linear'''. | [[JI]] chords and chords that are subsets of [[Delta-rational chord#Isodifferential chord|isodifferential chord]]s (these correspond to all chords of the form α : {{nowrap|α + ''k''<sub>1</sub>}} : ... : {{nowrap|α + ''k''<sub>''n''</sub>}} for any positive (possibly irrational) number α and integers ''k''<sub>1</sub>, ..., ''k''<sub>''n''</sub>) are special cases of delta-rational chords, but in these chords ''all'' dyads are rationally related in frequency space, which we call either '''fully delta-rational''' (FDR) or '''linear'''. | ||
Delta-rational chords provide a non-JI-based approach to concordance, since chords that are delta-rational with simple ratios between dyads (when measured as absolute frequency differences) tend to be perceived as more concordant than other chords. This acoustic effect is thought to be caused by synchronized interference beating among the fundamentals and among lower harmonics of the fundamentals; the effect may be more or less pronounced depending on register, timbre, the complexity of the linear relationship, etc. For example, the delta-rational acoustic effect is expected to be weaker in chords with wider voicings, as well as chords played in timbres with loud higher harmonics (because the higher harmonics would make the delta-rational relationships less obvious). The justification for only considering dyads between adjacent notes is that the resulting notes within the dyads could psychoacoustically interfere with the beating of the dyads. | Delta-rational chords provide a non-JI-based approach to concordance, since chords that are delta-rational with simple ratios between dyads (when measured as absolute frequency differences) tend to be perceived as more concordant than other chords. This acoustic effect is thought to be caused by synchronized interference beating among the fundamentals and among lower harmonics of the fundamentals; the effect may be more or less pronounced depending on register, timbre, the complexity of the linear relationship, etc. For example, the delta-rational acoustic effect is expected to be weaker in chords with wider voicings, as well as chords played in timbres with loud higher harmonics (because the higher harmonics would make the delta-rational relationships less obvious). The justification for only considering dyads between adjacent notes is that the resulting notes within the dyads could psychoacoustically interfere with the beating of the dyads. | ||
| Line 16: | Line 16: | ||
* Two delta signatures are equivalent if one can be obtained from the other by scaling by a positive real number. For example, +2+e+3 is equivalent to +2φ+eφ+3φ, and both signatures imply a delta-rational chord. | * Two delta signatures are equivalent if one can be obtained from the other by scaling by a positive real number. For example, +2+e+3 is equivalent to +2φ+eφ+3φ, and both signatures imply a delta-rational chord. | ||
For example, a chord with a +1+2+1 delta signature is ''a'':(''a''+1):(''a''+3):(''a''+4) for some possibly irrational ''a''. | For example, a chord with a +1+2+1 delta signature is ''a'':({{nowrap|''a'' + 1}}):({{nowrap|''a'' + 3}}):({{nowrap|''a'' + 4}}) for some possibly irrational ''a''. | ||
Deltas that are ''free'', i.e. not required to be related to any other deltas are indicated with +?. For example, saying that a tetrad is "+1 +? +1" means the first two notes and the last two notes have almost equal frequency difference (thus the ratio between the differences is 1/1), but the middle two notes are not in any simple relationship with the two outer dyads. The example 13edo chord is approximately +1 +? +1. | Deltas that are ''free'', i.e. not required to be related to any other deltas are indicated with +?. For example, saying that a tetrad is "{{nowrap|+1 +? +1}}" means the first two notes and the last two notes have almost equal frequency difference (thus the ratio between the differences is 1/1), but the middle two notes are not in any simple relationship with the two outer dyads. The example 13edo chord is approximately {{nowrap|+1 +? +1}}. | ||
If you have some sets of deltas related to each other but not to other sets of increments, you could write the related sets with variables a, b, c or use one fewer letter by writing one set with positive integers without variables: an +a +b +a +b chord can also be written +1 +c +1 +c where c = b/a. | If you have some sets of deltas related to each other but not to other sets of increments, you could write the related sets with variables a, b, c or use one fewer letter by writing one set with positive integers without variables: an {{nowrap|+a +b +a +b}} chord can also be written {{nowrap|+1 +c +1 +c}} where {{nowrap|c = b/a}}. | ||
Fully delta-rational chords always have a delta signature with no irrational ratios between terms. | Fully delta-rational chords always have a delta signature with no irrational ratios between terms. | ||
| Line 34: | Line 34: | ||
== Finding a tuning of a MOS scale with an exact DR chord == | == Finding a tuning of a MOS scale with an exact DR chord == | ||
Let ''a'' | Let ''a'' and ''b'' be positive integers and suppose {{nowrap|gcd(''a'', ''b'') {{=}} 1}}. Let {{nowrap|''E'' > 1}} be the frequency ratio of the equave. Consider a MOS ''a'''''L'''''b'''''s'''{{angbr|''E''}} with generator range <math>I \subseteq (1, \sqrt{E})</math> (in the linear frequency domain), and consider a pair ({{nowrap|'''u''', '''v'''}}) of notes from the root of a given triad in the MOS, {{nowrap|'''0''' (unison) < '''u''' < '''v'''}}. Let '''p''', '''g''' be a basis formally representing the MOS scale's period and generator. Write | ||
<math>\begin{align} | <math>\begin{align} | ||
| Line 48: | Line 48: | ||
<math>\displaystyle{r_{\mathbf{u}, \mathbf{v}}(x) = \frac{E^{v_p}x^{v_g}- E^{u_p}x^{u_g}}{E^{u_p}x^{u_g} - 1} }.</math> | <math>\displaystyle{r_{\mathbf{u}, \mathbf{v}}(x) = \frac{E^{v_p}x^{v_g}- E^{u_p}x^{u_g}}{E^{u_p}x^{u_g} - 1} }.</math> | ||
Then, provided that the positive rational number <math>m/n</math> lies in the image <math>r_{\mathbf{u}, \mathbf{v}}(I),</math> we can solve for the frequency ratio <math>g \in I</math> that satisfies <math>r_{\mathbf{u}, \mathbf{v}}(g) = m/n,</math> making the specified chord ('''0''', '''u''', '''v''') a +''n''+''m'' DR chord. | Then, provided that the positive rational number <math>m/n</math> lies in the image <math>r_{\mathbf{u}, \mathbf{v}}(I),</math> we can solve for the frequency ratio <math>g \in I</math> that satisfies <math>r_{\mathbf{u}, \mathbf{v}}(g) = m/n,</math> making the specified chord {{nowrap|('''0''', '''u''', '''v''') a + ''n'' + ''m''}} DR chord. | ||
The existence of an exact tuning for a delta signature specification is only guaranteed to hold when we only care about a ratio between ''two'' terms in the delta signature being exact. If we want to optimize an arbitrary specified delta signature (with some deltas possibly held free), we can use a least-squares-error solution instead to minimize the error. | The existence of an exact tuning for a delta signature specification is only guaranteed to hold when we only care about a ratio between ''two'' terms in the delta signature being exact. If we want to optimize an arbitrary specified delta signature (with some deltas possibly held free), we can use a least-squares-error solution instead to minimize the error. | ||
== Least-squares error measures == | == Least-squares error measures == | ||
Say we want the error of a chord 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> (in increasing order), with ''n'' | Say we want the error of a chord 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> (in increasing order), with {{nowrap|''n'' > 1}}, in the linear domain as an approximation to a fully delta-rational chord with signature {{nowrap|+δ<sub>1</sub> +δ<sub>2</sub> ... +δ<sub>''n''</sub> | ||
}} (where the delta signature is written based on the chord written to have root 1), i.e. a chord | |||
<math> 1 : 1 + \delta_1 : \cdots : 1 + \sum_{l=1}^n \delta_l </math> | <math> 1 : 1 + \delta_1 : \cdots : 1 + \sum_{l=1}^n \delta_l </math> | ||
| Line 106: | Line 107: | ||
Shown below are approximate DR triads in edos < 24 with symmetric least-squared error < 0.05. All delta signatures are in the 3-integer limit. | Shown below are approximate DR triads in edos < 24 with symmetric least-squared error < 0.05. All delta signatures are in the 3-integer limit. | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! | ! EDO | ||
! | ! Steps | ||
! | ! Delta signature | ||
! | ! Naive LS error | ||
! | ! Symmetric LS error | ||
|- | |- | ||
|6 | | 6 | ||
|0, 2, 5 | | 0, 2, 5 | ||
| +1+2 | | +1+2 | ||
|0.0025 | | 0.0025 | ||
|0.0026 | | 0.0026 | ||
|- | |- | ||
|6 | | 6 | ||
|0, 4, 5 | | 0, 4, 5 | ||
| +3+1 | | +3+1 | ||
|0.0043 | | 0.0043 | ||
|0.0044 | | 0.0044 | ||
|- | |- | ||
|7 | | 7 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0447 | | 0.0447 | ||
|0.0449 | | 0.0449 | ||
|- | |- | ||
|7 | | 7 | ||
|0, 2, 5 | | 0, 2, 5 | ||
| +1+2 | | +1+2 | ||
|0.0242 | | 0.0242 | ||
|0.0247 | | 0.0247 | ||
|- | |- | ||
|7 | | 7 | ||
|0, 4, 5 | | 0, 4, 5 | ||
| +3+1 | | +3+1 | ||
|0.0273 | | 0.0273 | ||
|0.0277 | | 0.0277 | ||
|- | |- | ||
|7 | | 7 | ||
|0, 4, 6 | | 0, 4, 6 | ||
| +3+2 | | +3+2 | ||
|0.0046 | | 0.0046 | ||
|0.0047 | | 0.0047 | ||
|- | |- | ||
|8 | | 8 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0391 | | 0.0391 | ||
|0.0392 | | 0.0392 | ||
|- | |- | ||
|8 | | 8 | ||
|0, 4, 7 | | 0, 4, 7 | ||
| +1+1 | | +1+1 | ||
|0.0060 | | 0.0060 | ||
|0.0065 | | 0.0065 | ||
|- | |- | ||
|8 | | 8 | ||
|0, 2, 5 | | 0, 2, 5 | ||
| +1+2 | | +1+2 | ||
|0.0442 | | 0.0442 | ||
|0.0450 | | 0.0450 | ||
|- | |- | ||
|8 | | 8 | ||
|0, 5, 7 | | 0, 5, 7 | ||
| +2+1 | | +2+1 | ||
|0.0416 | | 0.0416 | ||
|0.0432 | | 0.0432 | ||
|- | |- | ||
|8 | | 8 | ||
|0, 4, 5 | | 0, 4, 5 | ||
| +3+1 | | +3+1 | ||
|0.0443 | | 0.0443 | ||
|0.0447 | | 0.0447 | ||
|- | |- | ||
|8 | | 8 | ||
|0, 4, 6 | | 0, 4, 6 | ||
| +3+2 | | +3+2 | ||
|0.0322 | | 0.0322 | ||
|0.0325 | | 0.0325 | ||
|- | |- | ||
|9 | | 9 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0347 | | 0.0347 | ||
|0.0348 | | 0.0348 | ||
|- | |- | ||
|9 | | 9 | ||
|0, 4, 7 | | 0, 4, 7 | ||
| +1+1 | | +1+1 | ||
|0.0089 | | 0.0089 | ||
|0.0094 | | 0.0094 | ||
|- | |- | ||
|9 | | 9 | ||
|0, 5, 7 | | 0, 5, 7 | ||
| +2+1 | | +2+1 | ||
|0.0231 | | 0.0231 | ||
|0.0238 | | 0.0238 | ||
|- | |- | ||
|10 | | 10 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0312 | | 0.0312 | ||
|0.0313 | | 0.0313 | ||
|- | |- | ||
|10 | | 10 | ||
|0, 4, 7 | | 0, 4, 7 | ||
| +1+1 | | +1+1 | ||
|0.0207 | | 0.0207 | ||
|0.0217 | | 0.0217 | ||
|- | |- | ||
|10 | | 10 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0392 | | 0.0392 | ||
|0.0427 | | 0.0427 | ||
|- | |- | ||
|10 | | 10 | ||
|0, 2, 7 | | 0, 2, 7 | ||
| +1+3 | | +1+3 | ||
|0.0463 | | 0.0463 | ||
|0.0468 | | 0.0468 | ||
|- | |- | ||
|10 | | 10 | ||
|0, 5, 7 | | 0, 5, 7 | ||
| +2+1 | | +2+1 | ||
|0.0085 | | 0.0085 | ||
|0.0087 | | 0.0087 | ||
|- | |- | ||
|10 | | 10 | ||
|0, 6, 9 | | 0, 6, 9 | ||
| +3+2 | | +3+2 | ||
|0.0195 | | 0.0195 | ||
|0.0197 | | 0.0197 | ||
|- | |- | ||
|11 | | 11 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0283 | | 0.0283 | ||
|0.0284 | | 0.0284 | ||
|- | |- | ||
|11 | | 11 | ||
|0, 4, 7 | | 0, 4, 7 | ||
| +1+1 | | +1+1 | ||
|0.0303 | | 0.0303 | ||
|0.0315 | | 0.0315 | ||
|- | |- | ||
|11 | | 11 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0265 | | 0.0265 | ||
|0.0283 | | 0.0283 | ||
|- | |- | ||
|11 | | 11 | ||
|0, 6, 10 | | 0, 6, 10 | ||
| +1+1 | | +1+1 | ||
|0.0415 | | 0.0415 | ||
|0.0454 | | 0.0454 | ||
|- | |- | ||
|11 | | 11 | ||
|0, 3, 8 | | 0, 3, 8 | ||
| +1+2 | | +1+2 | ||
|0.0454 | | 0.0454 | ||
|0.0465 | | 0.0465 | ||
|- | |- | ||
|11 | | 11 | ||
|0, 4, 10 | | 0, 4, 10 | ||
| +1+2 | | +1+2 | ||
|0.0193 | | 0.0193 | ||
|0.0202 | | 0.0202 | ||
|- | |- | ||
|11 | | 11 | ||
|0, 2, 7 | | 0, 2, 7 | ||
| +1+3 | | +1+3 | ||
|0.0301 | | 0.0301 | ||
|0.0304 | | 0.0304 | ||
|- | |- | ||
|11 | | 11 | ||
|0, 5, 7 | | 0, 5, 7 | ||
| +2+1 | | +2+1 | ||
|0.0034 | | 0.0034 | ||
|0.0034 | | 0.0034 | ||
|- | |- | ||
|11 | | 11 | ||
|0, 8, 10 | | 0, 8, 10 | ||
| +3+1 | | +3+1 | ||
|0.0106 | | 0.0106 | ||
|0.0108 | | 0.0108 | ||
|- | |- | ||
|11 | | 11 | ||
|0, 6, 9 | | 0, 6, 9 | ||
| +3+2 | | +3+2 | ||
|0.0088 | | 0.0088 | ||
|0.0089 | | 0.0089 | ||
|- | |- | ||
|12 | | 12 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0260 | | 0.0260 | ||
|0.0260 | | 0.0260 | ||
|- | |- | ||
|12 | | 12 | ||
|0, 4, 7 | | 0, 4, 7 | ||
| +1+1 | | +1+1 | ||
|0.0383 | | 0.0383 | ||
|0.0395 | | 0.0395 | ||
|- | |- | ||
|12 | | 12 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0159 | | 0.0159 | ||
|0.0168 | | 0.0168 | ||
|- | |- | ||
|12 | | 12 | ||
|0, 3, 8 | | 0, 3, 8 | ||
| +1+2 | | +1+2 | ||
|0.0321 | | 0.0321 | ||
|0.0327 | | 0.0327 | ||
|- | |- | ||
|12 | | 12 | ||
|0, 4, 10 | | 0, 4, 10 | ||
| +1+2 | | +1+2 | ||
|0.0025 | | 0.0025 | ||
|0.0026 | | 0.0026 | ||
|- | |- | ||
|12 | | 12 | ||
|0, 2, 7 | | 0, 2, 7 | ||
| +1+3 | | +1+3 | ||
|0.0165 | | 0.0165 | ||
|0.0166 | | 0.0166 | ||
|- | |- | ||
|12 | | 12 | ||
|0, 3, 10 | | 0, 3, 10 | ||
| +1+3 | | +1+3 | ||
|0.0310 | | 0.0310 | ||
|0.0316 | | 0.0316 | ||
|- | |- | ||
|12 | | 12 | ||
|0, 2, 3 | | 0, 2, 3 | ||
| +2+1 | | +2+1 | ||
|0.0489 | | 0.0489 | ||
|0.0490 | | 0.0490 | ||
|- | |- | ||
|12 | | 12 | ||
|0, 5, 7 | | 0, 5, 7 | ||
| +2+1 | | +2+1 | ||
|0.0132 | | 0.0132 | ||
|0.0133 | | 0.0133 | ||
|- | |- | ||
|12 | | 12 | ||
|0, 8, 11 | | 0, 8, 11 | ||
| +2+1 | | +2+1 | ||
|0.0125 | | 0.0125 | ||
|0.0130 | | 0.0130 | ||
|- | |- | ||
|12 | | 12 | ||
|0, 8, 10 | | 0, 8, 10 | ||
| +3+1 | | +3+1 | ||
|0.0043 | | 0.0043 | ||
|0.0044 | | 0.0044 | ||
|- | |- | ||
|12 | | 12 | ||
|0, 6, 9 | | 0, 6, 9 | ||
| +3+2 | | +3+2 | ||
|0.0322 | | 0.0322 | ||
|0.0325 | | 0.0325 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0240 | | 0.0240 | ||
|0.0240 | | 0.0240 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 2, 4 | | 0, 2, 4 | ||
| +1+1 | | +1+1 | ||
|0.0481 | | 0.0481 | ||
|0.0485 | | 0.0485 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 4, 7 | | 0, 4, 7 | ||
| +1+1 | | +1+1 | ||
|0.0451 | | 0.0451 | ||
|0.0462 | | 0.0462 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0070 | | 0.0070 | ||
|0.0074 | | 0.0074 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 7, 12 | | 0, 7, 12 | ||
| +1+1 | | +1+1 | ||
|0.0087 | | 0.0087 | ||
|0.0095 | | 0.0095 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 3, 8 | | 0, 3, 8 | ||
| +1+2 | | +1+2 | ||
|0.0207 | | 0.0207 | ||
|0.0210 | | 0.0210 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 4, 10 | | 0, 4, 10 | ||
| +1+2 | | +1+2 | ||
|0.0119 | | 0.0119 | ||
|0.0122 | | 0.0122 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 5, 12 | | 0, 5, 12 | ||
| +1+2 | | +1+2 | ||
|0.0215 | | 0.0215 | ||
|0.0225 | | 0.0225 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 2, 7 | | 0, 2, 7 | ||
| +1+3 | | +1+3 | ||
|0.0049 | | 0.0049 | ||
|0.0050 | | 0.0050 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 3, 10 | | 0, 3, 10 | ||
| +1+3 | | +1+3 | ||
|0.0145 | | 0.0145 | ||
|0.0147 | | 0.0147 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 2, 3 | | 0, 2, 3 | ||
| +2+1 | | +2+1 | ||
|0.0451 | | 0.0451 | ||
|0.0452 | | 0.0452 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 5, 7 | | 0, 5, 7 | ||
| +2+1 | | +2+1 | ||
|0.0214 | | 0.0214 | ||
|0.0217 | | 0.0217 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 8, 11 | | 0, 8, 11 | ||
| +2+1 | | +2+1 | ||
|0.0005 | | 0.0005 | ||
|0.0005 | | 0.0005 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 8, 10 | | 0, 8, 10 | ||
| +3+1 | | +3+1 | ||
|0.0167 | | 0.0167 | ||
|0.0170 | | 0.0170 | ||
|- | |- | ||
|13 | | 13 | ||
|0, 8, 12 | | 0, 8, 12 | ||
| +3+2 | | +3+2 | ||
|0.0275 | | 0.0275 | ||
|0.0279 | | 0.0279 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0222 | | 0.0222 | ||
|0.0223 | | 0.0223 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 2, 4 | | 0, 2, 4 | ||
| +1+1 | | +1+1 | ||
|0.0447 | | 0.0447 | ||
|0.0449 | | 0.0449 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0006 | | 0.0006 | ||
|0.0006 | | 0.0006 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 6, 11 | | 0, 6, 11 | ||
| +1+1 | | +1+1 | ||
|0.0401 | | 0.0401 | ||
|0.0426 | | 0.0426 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 7, 12 | | 0, 7, 12 | ||
| +1+1 | | +1+1 | ||
|0.0186 | | 0.0186 | ||
|0.0201 | | 0.0201 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 1, 3 | | 0, 1, 3 | ||
| +1+2 | | +1+2 | ||
|0.0468 | | 0.0468 | ||
|0.0469 | | 0.0469 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 3, 8 | | 0, 3, 8 | ||
| +1+2 | | +1+2 | ||
|0.0110 | | 0.0110 | ||
|0.0111 | | 0.0111 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 4, 10 | | 0, 4, 10 | ||
| +1+2 | | +1+2 | ||
|0.0242 | | 0.0242 | ||
|0.0247 | | 0.0247 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 5, 12 | | 0, 5, 12 | ||
| +1+2 | | +1+2 | ||
|0.0363 | | 0.0363 | ||
|0.0377 | | 0.0377 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 2, 7 | | 0, 2, 7 | ||
| +1+3 | | +1+3 | ||
|0.0050 | | 0.0050 | ||
|0.0050 | | 0.0050 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 3, 10 | | 0, 3, 10 | ||
| +1+3 | | +1+3 | ||
|0.0002 | | 0.0002 | ||
|0.0002 | | 0.0002 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 4, 13 | | 0, 4, 13 | ||
| +1+3 | | +1+3 | ||
|0.0294 | | 0.0294 | ||
|0.0301 | | 0.0301 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 2, 3 | | 0, 2, 3 | ||
| +2+1 | | +2+1 | ||
|0.0418 | | 0.0418 | ||
|0.0419 | | 0.0419 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 5, 7 | | 0, 5, 7 | ||
| +2+1 | | +2+1 | ||
|0.0284 | | 0.0284 | ||
|0.0287 | | 0.0287 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 8, 11 | | 0, 8, 11 | ||
| +2+1 | | +2+1 | ||
|0.0116 | | 0.0116 | ||
|0.0119 | | 0.0119 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 4, 9 | | 0, 4, 9 | ||
| +2+3 | | +2+3 | ||
|0.0461 | | 0.0461 | ||
|0.0464 | | 0.0464 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 7, 9 | | 0, 7, 9 | ||
| +3+1 | | +3+1 | ||
|0.0393 | | 0.0393 | ||
|0.0397 | | 0.0397 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 8, 10 | | 0, 8, 10 | ||
| +3+1 | | +3+1 | ||
|0.0273 | | 0.0273 | ||
|0.0277 | | 0.0277 | ||
|- | |- | ||
|14 | | 14 | ||
|0, 8, 12 | | 0, 8, 12 | ||
| +3+2 | | +3+2 | ||
|0.0046 | | 0.0046 | ||
|0.0047 | | 0.0047 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0208 | | 0.0208 | ||
|0.0208 | | 0.0208 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 2, 4 | | 0, 2, 4 | ||
| +1+1 | | +1+1 | ||
|0.0417 | | 0.0417 | ||
|0.0419 | | 0.0419 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0071 | | 0.0071 | ||
|0.0074 | | 0.0074 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 6, 11 | | 0, 6, 11 | ||
| +1+1 | | +1+1 | ||
|0.0319 | | 0.0319 | ||
|0.0336 | | 0.0336 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 7, 12 | | 0, 7, 12 | ||
| +1+1 | | +1+1 | ||
|0.0273 | | 0.0273 | ||
|0.0291 | | 0.0291 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 8, 14 | | 0, 8, 14 | ||
| +1+1 | | +1+1 | ||
|0.0149 | | 0.0149 | ||
|0.0164 | | 0.0164 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 1, 3 | | 0, 1, 3 | ||
| +1+2 | | +1+2 | ||
|0.0437 | | 0.0437 | ||
|0.0437 | | 0.0437 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 3, 8 | | 0, 3, 8 | ||
| +1+2 | | +1+2 | ||
|0.0025 | | 0.0025 | ||
|0.0025 | | 0.0025 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 4, 10 | | 0, 4, 10 | ||
| +1+2 | | +1+2 | ||
|0.0349 | | 0.0349 | ||
|0.0355 | | 0.0355 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 2, 7 | | 0, 2, 7 | ||
| +1+3 | | +1+3 | ||
|0.0137 | | 0.0137 | ||
|0.0137 | | 0.0137 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 3, 10 | | 0, 3, 10 | ||
| +1+3 | | +1+3 | ||
|0.0122 | | 0.0122 | ||
|0.0123 | | 0.0123 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 4, 13 | | 0, 4, 13 | ||
| +1+3 | | +1+3 | ||
|0.0134 | | 0.0134 | ||
|0.0137 | | 0.0137 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 2, 3 | | 0, 2, 3 | ||
| +2+1 | | +2+1 | ||
|0.0390 | | 0.0390 | ||
|0.0391 | | 0.0391 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 5, 7 | | 0, 5, 7 | ||
| +2+1 | | +2+1 | ||
|0.0345 | | 0.0345 | ||
|0.0348 | | 0.0348 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 7, 10 | | 0, 7, 10 | ||
| +2+1 | | +2+1 | ||
|0.0415 | | 0.0415 | ||
|0.0423 | | 0.0423 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 8, 11 | | 0, 8, 11 | ||
| +2+1 | | +2+1 | ||
|0.0211 | | 0.0211 | ||
|0.0216 | | 0.0216 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 3, 7 | | 0, 3, 7 | ||
| +2+3 | | +2+3 | ||
|0.0496 | | 0.0496 | ||
|0.0498 | | 0.0498 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 4, 9 | | 0, 4, 9 | ||
| +2+3 | | +2+3 | ||
|0.0294 | | 0.0294 | ||
|0.0296 | | 0.0296 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 5, 11 | | 0, 5, 11 | ||
| +2+3 | | +2+3 | ||
|0.0356 | | 0.0356 | ||
|0.0359 | | 0.0359 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 7, 9 | | 0, 7, 9 | ||
| +3+1 | | +3+1 | ||
|0.0304 | | 0.0304 | ||
|0.0306 | | 0.0306 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 8, 10 | | 0, 8, 10 | ||
| +3+1 | | +3+1 | ||
|0.0364 | | 0.0364 | ||
|0.0368 | | 0.0368 | ||
|- | |- | ||
|15 | | 15 | ||
|0, 8, 12 | | 0, 8, 12 | ||
| +3+2 | | +3+2 | ||
|0.0151 | | 0.0151 | ||
|0.0152 | | 0.0152 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0195 | | 0.0195 | ||
|0.0195 | | 0.0195 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 2, 4 | | 0, 2, 4 | ||
| +1+1 | | +1+1 | ||
|0.0391 | | 0.0391 | ||
|0.0392 | | 0.0392 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0129 | | 0.0129 | ||
|0.0132 | | 0.0132 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 6, 11 | | 0, 6, 11 | ||
| +1+1 | | +1+1 | ||
|0.0248 | | 0.0248 | ||
|0.0259 | | 0.0259 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 7, 12 | | 0, 7, 12 | ||
| +1+1 | | +1+1 | ||
|0.0348 | | 0.0348 | ||
|0.0368 | | 0.0368 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 8, 14 | | 0, 8, 14 | ||
| +1+1 | | +1+1 | ||
|0.0060 | | 0.0060 | ||
|0.0065 | | 0.0065 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 9, 15 | | 0, 9, 15 | ||
| +1+1 | | +1+1 | ||
|0.0373 | | 0.0373 | ||
|0.0410 | | 0.0410 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 1, 3 | | 0, 1, 3 | ||
| +1+2 | | +1+2 | ||
|0.0410 | | 0.0410 | ||
|0.0410 | | 0.0410 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 3, 8 | | 0, 3, 8 | ||
| +1+2 | | +1+2 | ||
|0.0049 | | 0.0049 | ||
|0.0050 | | 0.0050 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 4, 10 | | 0, 4, 10 | ||
| +1+2 | | +1+2 | ||
|0.0442 | | 0.0442 | ||
|0.0450 | | 0.0450 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 5, 13 | | 0, 5, 13 | ||
| +1+2 | | +1+2 | ||
|0.0386 | | 0.0386 | ||
|0.0398 | | 0.0398 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 6, 15 | | 0, 6, 15 | ||
| +1+2 | | +1+2 | ||
|0.0257 | | 0.0257 | ||
|0.0268 | | 0.0268 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 2, 7 | | 0, 2, 7 | ||
| +1+3 | | +1+3 | ||
|0.0213 | | 0.0213 | ||
|0.0213 | | 0.0213 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 3, 10 | | 0, 3, 10 | ||
| +1+3 | | +1+3 | ||
|0.0231 | | 0.0231 | ||
|0.0233 | | 0.0233 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 4, 13 | | 0, 4, 13 | ||
| +1+3 | | +1+3 | ||
|0.0007 | | 0.0007 | ||
|0.0008 | | 0.0008 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 2, 3 | | 0, 2, 3 | ||
| +2+1 | | +2+1 | ||
|0.0365 | | 0.0365 | ||
|0.0366 | | 0.0366 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 5, 7 | | 0, 5, 7 | ||
| +2+1 | | +2+1 | ||
|0.0398 | | 0.0398 | ||
|0.0401 | | 0.0401 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 7, 10 | | 0, 7, 10 | ||
| +2+1 | | +2+1 | ||
|0.0334 | | 0.0334 | ||
|0.0340 | | 0.0340 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 8, 11 | | 0, 8, 11 | ||
| +2+1 | | +2+1 | ||
|0.0294 | | 0.0294 | ||
|0.0300 | | 0.0300 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 10, 14 | | 0, 10, 14 | ||
| +2+1 | | +2+1 | ||
|0.0416 | | 0.0416 | ||
|0.0432 | | 0.0432 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 11, 15 | | 0, 11, 15 | ||
| +2+1 | | +2+1 | ||
|0.0010 | | 0.0010 | ||
|0.0010 | | 0.0010 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 3, 7 | | 0, 3, 7 | ||
| +2+3 | | +2+3 | ||
|0.0383 | | 0.0383 | ||
|0.0384 | | 0.0384 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 4, 9 | | 0, 4, 9 | ||
| +2+3 | | +2+3 | ||
|0.0148 | | 0.0148 | ||
|0.0149 | | 0.0149 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 5, 11 | | 0, 5, 11 | ||
| +2+3 | | +2+3 | ||
|0.0178 | | 0.0178 | ||
|0.0179 | | 0.0179 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 6, 13 | | 0, 6, 13 | ||
| +2+3 | | +2+3 | ||
|0.0348 | | 0.0348 | ||
|0.0352 | | 0.0352 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 7, 9 | | 0, 7, 9 | ||
| +3+1 | | +3+1 | ||
|0.0227 | | 0.0227 | ||
|0.0228 | | 0.0228 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 8, 10 | | 0, 8, 10 | ||
| +3+1 | | +3+1 | ||
|0.0443 | | 0.0443 | ||
|0.0447 | | 0.0447 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 12, 15 | | 0, 12, 15 | ||
| +3+1 | | +3+1 | ||
|0.0162 | | 0.0162 | ||
|0.0166 | | 0.0166 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 8, 12 | | 0, 8, 12 | ||
| +3+2 | | +3+2 | ||
|0.0322 | | 0.0322 | ||
|0.0325 | | 0.0325 | ||
|- | |- | ||
|16 | | 16 | ||
|0, 10, 15 | | 0, 10, 15 | ||
| +3+2 | | +3+2 | ||
|0.0325 | | 0.0325 | ||
|0.0330 | | 0.0330 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0183 | | 0.0183 | ||
|0.0183 | | 0.0183 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 2, 4 | | 0, 2, 4 | ||
| +1+1 | | +1+1 | ||
|0.0367 | | 0.0367 | ||
|0.0369 | | 0.0369 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0179 | | 0.0179 | ||
|0.0184 | | 0.0184 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 6, 11 | | 0, 6, 11 | ||
| +1+1 | | +1+1 | ||
|0.0185 | | 0.0185 | ||
|0.0192 | | 0.0192 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 7, 12 | | 0, 7, 12 | ||
| +1+1 | | +1+1 | ||
|0.0414 | | 0.0414 | ||
|0.0434 | | 0.0434 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 8, 14 | | 0, 8, 14 | ||
| +1+1 | | +1+1 | ||
|0.0019 | | 0.0019 | ||
|0.0020 | | 0.0020 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 9, 15 | | 0, 9, 15 | ||
| +1+1 | | +1+1 | ||
|0.0454 | | 0.0454 | ||
|0.0494 | | 0.0494 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 9, 16 | | 0, 9, 16 | ||
| +1+1 | | +1+1 | ||
|0.0327 | | 0.0327 | ||
|0.0360 | | 0.0360 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 1, 3 | | 0, 1, 3 | ||
| +1+2 | | +1+2 | ||
|0.0386 | | 0.0386 | ||
|0.0386 | | 0.0386 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 3, 8 | | 0, 3, 8 | ||
| +1+2 | | +1+2 | ||
|0.0115 | | 0.0115 | ||
|0.0116 | | 0.0116 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 5, 13 | | 0, 5, 13 | ||
| +1+2 | | +1+2 | ||
|0.0281 | | 0.0281 | ||
|0.0288 | | 0.0288 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 6, 15 | | 0, 6, 15 | ||
| +1+2 | | +1+2 | ||
|0.0134 | | 0.0134 | ||
|0.0139 | | 0.0139 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 2, 7 | | 0, 2, 7 | ||
| +1+3 | | +1+3 | ||
|0.0280 | | 0.0280 | ||
|0.0281 | | 0.0281 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 3, 10 | | 0, 3, 10 | ||
| +1+3 | | +1+3 | ||
|0.0328 | | 0.0328 | ||
|0.0331 | | 0.0331 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 4, 13 | | 0, 4, 13 | ||
| +1+3 | | +1+3 | ||
|0.0133 | | 0.0133 | ||
|0.0135 | | 0.0135 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 5, 16 | | 0, 5, 16 | ||
| +1+3 | | +1+3 | ||
|0.0164 | | 0.0164 | ||
|0.0168 | | 0.0168 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 2, 3 | | 0, 2, 3 | ||
| +2+1 | | +2+1 | ||
|0.0344 | | 0.0344 | ||
|0.0344 | | 0.0344 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 5, 7 | | 0, 5, 7 | ||
| +2+1 | | +2+1 | ||
|0.0444 | | 0.0444 | ||
|0.0447 | | 0.0447 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 7, 10 | | 0, 7, 10 | ||
| +2+1 | | +2+1 | ||
|0.0264 | | 0.0264 | ||
|0.0267 | | 0.0267 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 8, 11 | | 0, 8, 11 | ||
| +2+1 | | +2+1 | ||
|0.0366 | | 0.0366 | ||
|0.0373 | | 0.0373 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 10, 14 | | 0, 10, 14 | ||
| +2+1 | | +2+1 | ||
|0.0318 | | 0.0318 | ||
|0.0328 | | 0.0328 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 11, 15 | | 0, 11, 15 | ||
| +2+1 | | +2+1 | ||
|0.0110 | | 0.0110 | ||
|0.0114 | | 0.0114 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 12, 16 | | 0, 12, 16 | ||
| +2+1 | | +2+1 | ||
|0.0477 | | 0.0477 | ||
|0.0499 | | 0.0499 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 3, 7 | | 0, 3, 7 | ||
| +2+3 | | +2+3 | ||
|0.0283 | | 0.0283 | ||
|0.0284 | | 0.0284 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 4, 9 | | 0, 4, 9 | ||
| +2+3 | | +2+3 | ||
|0.0020 | | 0.0020 | ||
|0.0020 | | 0.0020 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 5, 11 | | 0, 5, 11 | ||
| +2+3 | | +2+3 | ||
|0.0021 | | 0.0021 | ||
|0.0021 | | 0.0021 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 6, 13 | | 0, 6, 13 | ||
| +2+3 | | +2+3 | ||
|0.0163 | | 0.0163 | ||
|0.0164 | | 0.0164 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 7, 15 | | 0, 7, 15 | ||
| +2+3 | | +2+3 | ||
|0.0389 | | 0.0389 | ||
|0.0394 | | 0.0394 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 3, 4 | | 0, 3, 4 | ||
| +3+1 | | +3+1 | ||
|0.0499 | | 0.0499 | ||
|0.0500 | | 0.0500 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 7, 9 | | 0, 7, 9 | ||
| +3+1 | | +3+1 | ||
|0.0159 | | 0.0159 | ||
|0.0160 | | 0.0160 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 11, 14 | | 0, 11, 14 | ||
| +3+1 | | +3+1 | ||
|0.0474 | | 0.0474 | ||
|0.0483 | | 0.0483 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 12, 15 | | 0, 12, 15 | ||
| +3+1 | | +3+1 | ||
|0.0053 | | 0.0053 | ||
|0.0054 | | 0.0054 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 13, 16 | | 0, 13, 16 | ||
| +3+1 | | +3+1 | ||
|0.0310 | | 0.0310 | ||
|0.0318 | | 0.0318 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 8, 12 | | 0, 8, 12 | ||
| +3+2 | | +3+2 | ||
|0.0472 | | 0.0472 | ||
|0.0476 | | 0.0476 | ||
|- | |- | ||
|17 | | 17 | ||
|0, 10, 15 | | 0, 10, 15 | ||
| +3+2 | | +3+2 | ||
|0.0133 | | 0.0133 | ||
|0.0135 | | 0.0135 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0173 | | 0.0173 | ||
|0.0173 | | 0.0173 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 2, 4 | | 0, 2, 4 | ||
| +1+1 | | +1+1 | ||
|0.0347 | | 0.0347 | ||
|0.0348 | | 0.0348 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0224 | | 0.0224 | ||
|0.0229 | | 0.0229 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 6, 11 | | 0, 6, 11 | ||
| +1+1 | | +1+1 | ||
|0.0129 | | 0.0129 | ||
|0.0134 | | 0.0134 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 7, 12 | | 0, 7, 12 | ||
| +1+1 | | +1+1 | ||
|0.0472 | | 0.0472 | ||
|0.0493 | | 0.0493 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 7, 13 | | 0, 7, 13 | ||
| +1+1 | | +1+1 | ||
|0.0430 | | 0.0430 | ||
|0.0452 | | 0.0452 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 8, 14 | | 0, 8, 14 | ||
| +1+1 | | +1+1 | ||
|0.0089 | | 0.0089 | ||
|0.0094 | | 0.0094 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 9, 16 | | 0, 9, 16 | ||
| +1+1 | | +1+1 | ||
|0.0246 | | 0.0246 | ||
|0.0267 | | 0.0267 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 10, 17 | | 0, 10, 17 | ||
| +1+1 | | +1+1 | ||
|0.0145 | | 0.0145 | ||
|0.0160 | | 0.0160 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 1, 3 | | 0, 1, 3 | ||
| +1+2 | | +1+2 | ||
|0.0364 | | 0.0364 | ||
|0.0365 | | 0.0365 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 3, 8 | | 0, 3, 8 | ||
| +1+2 | | +1+2 | ||
|0.0173 | | 0.0173 | ||
|0.0174 | | 0.0174 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 5, 13 | | 0, 5, 13 | ||
| +1+2 | | +1+2 | ||
|0.0186 | | 0.0186 | ||
|0.0191 | | 0.0191 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 6, 15 | | 0, 6, 15 | ||
| +1+2 | | +1+2 | ||
|0.0025 | | 0.0025 | ||
|0.0026 | | 0.0026 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 7, 17 | | 0, 7, 17 | ||
| +1+2 | | +1+2 | ||
|0.0038 | | 0.0038 | ||
|0.0040 | | 0.0040 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 2, 7 | | 0, 2, 7 | ||
| +1+3 | | +1+3 | ||
|0.0340 | | 0.0340 | ||
|0.0341 | | 0.0341 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 3, 10 | | 0, 3, 10 | ||
| +1+3 | | +1+3 | ||
|0.0414 | | 0.0414 | ||
|0.0417 | | 0.0417 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 4, 13 | | 0, 4, 13 | ||
| +1+3 | | +1+3 | ||
|0.0244 | | 0.0244 | ||
|0.0248 | | 0.0248 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 5, 16 | | 0, 5, 16 | ||
| +1+3 | | +1+3 | ||
|0.0028 | | 0.0028 | ||
|0.0028 | | 0.0028 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 2, 3 | | 0, 2, 3 | ||
| +2+1 | | +2+1 | ||
|0.0324 | | 0.0324 | ||
|0.0325 | | 0.0325 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 5, 7 | | 0, 5, 7 | ||
| +2+1 | | +2+1 | ||
|0.0485 | | 0.0485 | ||
|0.0488 | | 0.0488 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 7, 10 | | 0, 7, 10 | ||
| +2+1 | | +2+1 | ||
|0.0201 | | 0.0201 | ||
|0.0204 | | 0.0204 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 8, 11 | | 0, 8, 11 | ||
| +2+1 | | +2+1 | ||
|0.0430 | | 0.0430 | ||
|0.0437 | | 0.0437 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 10, 14 | | 0, 10, 14 | ||
| +2+1 | | +2+1 | ||
|0.0231 | | 0.0231 | ||
|0.0238 | | 0.0238 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 11, 15 | | 0, 11, 15 | ||
| +2+1 | | +2+1 | ||
|0.0198 | | 0.0198 | ||
|0.0205 | | 0.0205 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 3, 7 | | 0, 3, 7 | ||
| +2+3 | | +2+3 | ||
|0.0194 | | 0.0194 | ||
|0.0194 | | 0.0194 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 4, 9 | | 0, 4, 9 | ||
| +2+3 | | +2+3 | ||
|0.0094 | | 0.0094 | ||
|0.0095 | | 0.0095 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 5, 11 | | 0, 5, 11 | ||
| +2+3 | | +2+3 | ||
|0.0119 | | 0.0119 | ||
|0.0120 | | 0.0120 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 6, 13 | | 0, 6, 13 | ||
| +2+3 | | +2+3 | ||
|0.0002 | | 0.0002 | ||
|0.0002 | | 0.0002 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 7, 15 | | 0, 7, 15 | ||
| +2+3 | | +2+3 | ||
|0.0198 | | 0.0198 | ||
|0.0201 | | 0.0201 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 8, 17 | | 0, 8, 17 | ||
| +2+3 | | +2+3 | ||
|0.0453 | | 0.0453 | ||
|0.0461 | | 0.0461 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 3, 4 | | 0, 3, 4 | ||
| +3+1 | | +3+1 | ||
|0.0471 | | 0.0471 | ||
|0.0472 | | 0.0472 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 7, 9 | | 0, 7, 9 | ||
| +3+1 | | +3+1 | ||
|0.0099 | | 0.0099 | ||
|0.0099 | | 0.0099 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 11, 14 | | 0, 11, 14 | ||
| +3+1 | | +3+1 | ||
|0.0380 | | 0.0380 | ||
|0.0386 | | 0.0386 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 12, 15 | | 0, 12, 15 | ||
| +3+1 | | +3+1 | ||
|0.0043 | | 0.0043 | ||
|0.0044 | | 0.0044 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 13, 16 | | 0, 13, 16 | ||
| +3+1 | | +3+1 | ||
|0.0407 | | 0.0407 | ||
|0.0417 | | 0.0417 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 5, 8 | | 0, 5, 8 | ||
| +3+2 | | +3+2 | ||
|0.0495 | | 0.0495 | ||
|0.0497 | | 0.0497 | ||
|- | |- | ||
|18 | | 18 | ||
|0, 10, 15 | | 0, 10, 15 | ||
| +3+2 | | +3+2 | ||
|0.0036 | | 0.0036 | ||
|0.0036 | | 0.0036 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0164 | | 0.0164 | ||
|0.0164 | | 0.0164 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 2, 4 | | 0, 2, 4 | ||
| +1+1 | | +1+1 | ||
|0.0329 | | 0.0329 | ||
|0.0330 | | 0.0330 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 3, 6 | | 0, 3, 6 | ||
| +1+1 | | +1+1 | ||
|0.0494 | | 0.0494 | ||
|0.0498 | | 0.0498 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0264 | | 0.0264 | ||
|0.0269 | | 0.0269 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 6, 11 | | 0, 6, 11 | ||
| +1+1 | | +1+1 | ||
|0.0079 | | 0.0079 | ||
|0.0082 | | 0.0082 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 7, 13 | | 0, 7, 13 | ||
| +1+1 | | +1+1 | ||
|0.0371 | | 0.0371 | ||
|0.0387 | | 0.0387 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 8, 14 | | 0, 8, 14 | ||
| +1+1 | | +1+1 | ||
|0.0151 | | 0.0151 | ||
|0.0159 | | 0.0159 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 9, 16 | | 0, 9, 16 | ||
| +1+1 | | +1+1 | ||
|0.0174 | | 0.0174 | ||
|0.0187 | | 0.0187 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 10, 17 | | 0, 10, 17 | ||
| +1+1 | | +1+1 | ||
|0.0220 | | 0.0220 | ||
|0.0239 | | 0.0239 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 1, 3 | | 0, 1, 3 | ||
| +1+2 | | +1+2 | ||
|0.0345 | | 0.0345 | ||
|0.0345 | | 0.0345 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 3, 8 | | 0, 3, 8 | ||
| +1+2 | | +1+2 | ||
|0.0225 | | 0.0225 | ||
|0.0227 | | 0.0227 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 4, 11 | | 0, 4, 11 | ||
| +1+2 | | +1+2 | ||
|0.0433 | | 0.0433 | ||
|0.0439 | | 0.0439 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 5, 13 | | 0, 5, 13 | ||
| +1+2 | | +1+2 | ||
|0.0102 | | 0.0102 | ||
|0.0104 | | 0.0104 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 6, 15 | | 0, 6, 15 | ||
| +1+2 | | +1+2 | ||
|0.0073 | | 0.0073 | ||
|0.0075 | | 0.0075 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 7, 17 | | 0, 7, 17 | ||
| +1+2 | | +1+2 | ||
|0.0149 | | 0.0149 | ||
|0.0155 | | 0.0155 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 2, 7 | | 0, 2, 7 | ||
| +1+3 | | +1+3 | ||
|0.0393 | | 0.0393 | ||
|0.0394 | | 0.0394 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 3, 10 | | 0, 3, 10 | ||
| +1+3 | | +1+3 | ||
|0.0492 | | 0.0492 | ||
|0.0495 | | 0.0495 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 4, 13 | | 0, 4, 13 | ||
| +1+3 | | +1+3 | ||
|0.0345 | | 0.0345 | ||
|0.0349 | | 0.0349 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 5, 16 | | 0, 5, 16 | ||
| +1+3 | | +1+3 | ||
|0.0095 | | 0.0095 | ||
|0.0097 | | 0.0097 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 2, 3 | | 0, 2, 3 | ||
| +2+1 | | +2+1 | ||
|0.0307 | | 0.0307 | ||
|0.0307 | | 0.0307 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 7, 10 | | 0, 7, 10 | ||
| +2+1 | | +2+1 | ||
|0.0145 | | 0.0145 | ||
|0.0147 | | 0.0147 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 8, 11 | | 0, 8, 11 | ||
| +2+1 | | +2+1 | ||
|0.0487 | | 0.0487 | ||
|0.0494 | | 0.0494 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 10, 14 | | 0, 10, 14 | ||
| +2+1 | | +2+1 | ||
|0.0154 | | 0.0154 | ||
|0.0158 | | 0.0158 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 11, 15 | | 0, 11, 15 | ||
| +2+1 | | +2+1 | ||
|0.0277 | | 0.0277 | ||
|0.0285 | | 0.0285 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 13, 18 | | 0, 13, 18 | ||
| +2+1 | | +2+1 | ||
|0.0327 | | 0.0327 | ||
|0.0342 | | 0.0342 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 3, 7 | | 0, 3, 7 | ||
| +2+3 | | +2+3 | ||
|0.0115 | | 0.0115 | ||
|0.0115 | | 0.0115 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 4, 9 | | 0, 4, 9 | ||
| +2+3 | | +2+3 | ||
|0.0197 | | 0.0197 | ||
|0.0197 | | 0.0197 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 5, 11 | | 0, 5, 11 | ||
| +2+3 | | +2+3 | ||
|0.0244 | | 0.0244 | ||
|0.0245 | | 0.0245 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 6, 13 | | 0, 6, 13 | ||
| +2+3 | | +2+3 | ||
|0.0150 | | 0.0150 | ||
|0.0151 | | 0.0151 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 7, 15 | | 0, 7, 15 | ||
| +2+3 | | +2+3 | ||
|0.0028 | | 0.0028 | ||
|0.0028 | | 0.0028 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 8, 17 | | 0, 8, 17 | ||
| +2+3 | | +2+3 | ||
|0.0260 | | 0.0260 | ||
|0.0264 | | 0.0264 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 3, 4 | | 0, 3, 4 | ||
| +3+1 | | +3+1 | ||
|0.0446 | | 0.0446 | ||
|0.0446 | | 0.0446 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 7, 9 | | 0, 7, 9 | ||
| +3+1 | | +3+1 | ||
|0.0045 | | 0.0045 | ||
|0.0045 | | 0.0045 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 11, 14 | | 0, 11, 14 | ||
| +3+1 | | +3+1 | ||
|0.0296 | | 0.0296 | ||
|0.0300 | | 0.0300 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 12, 15 | | 0, 12, 15 | ||
| +3+1 | | +3+1 | ||
|0.0128 | | 0.0128 | ||
|0.0130 | | 0.0130 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 5, 8 | | 0, 5, 8 | ||
| +3+2 | | +3+2 | ||
|0.0412 | | 0.0412 | ||
|0.0413 | | 0.0413 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 7, 11 | | 0, 7, 11 | ||
| +3+2 | | +3+2 | ||
|0.0464 | | 0.0464 | ||
|0.0466 | | 0.0466 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 10, 15 | | 0, 10, 15 | ||
| +3+2 | | +3+2 | ||
|0.0187 | | 0.0187 | ||
|0.0189 | | 0.0189 | ||
|- | |- | ||
|19 | | 19 | ||
|0, 12, 18 | | 0, 12, 18 | ||
| +3+2 | | +3+2 | ||
|0.0359 | | 0.0359 | ||
|0.0365 | | 0.0365 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0156 | | 0.0156 | ||
|0.0156 | | 0.0156 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 2, 4 | | 0, 2, 4 | ||
| +1+1 | | +1+1 | ||
|0.0312 | | 0.0312 | ||
|0.0313 | | 0.0313 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 3, 6 | | 0, 3, 6 | ||
| +1+1 | | +1+1 | ||
|0.0469 | | 0.0469 | ||
|0.0472 | | 0.0472 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0300 | | 0.0300 | ||
|0.0305 | | 0.0305 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 6, 11 | | 0, 6, 11 | ||
| +1+1 | | +1+1 | ||
|0.0035 | | 0.0035 | ||
|0.0036 | | 0.0036 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 7, 13 | | 0, 7, 13 | ||
| +1+1 | | +1+1 | ||
|0.0317 | | 0.0317 | ||
|0.0330 | | 0.0330 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 8, 14 | | 0, 8, 14 | ||
| +1+1 | | +1+1 | ||
|0.0207 | | 0.0207 | ||
|0.0217 | | 0.0217 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 9, 16 | | 0, 9, 16 | ||
| +1+1 | | +1+1 | ||
|0.0109 | | 0.0109 | ||
|0.0116 | | 0.0116 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 10, 17 | | 0, 10, 17 | ||
| +1+1 | | +1+1 | ||
|0.0287 | | 0.0287 | ||
|0.0310 | | 0.0310 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 10, 18 | | 0, 10, 18 | ||
| +1+1 | | +1+1 | ||
|0.0392 | | 0.0392 | ||
|0.0427 | | 0.0427 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 11, 19 | | 0, 11, 19 | ||
| +1+1 | | +1+1 | ||
|0.0036 | | 0.0036 | ||
|0.0039 | | 0.0039 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 1, 3 | | 0, 1, 3 | ||
| +1+2 | | +1+2 | ||
|0.0328 | | 0.0328 | ||
|0.0328 | | 0.0328 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 3, 8 | | 0, 3, 8 | ||
| +1+2 | | +1+2 | ||
|0.0272 | | 0.0272 | ||
|0.0274 | | 0.0274 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 4, 11 | | 0, 4, 11 | ||
| +1+2 | | +1+2 | ||
|0.0369 | | 0.0369 | ||
|0.0374 | | 0.0374 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 5, 13 | | 0, 5, 13 | ||
| +1+2 | | +1+2 | ||
|0.0026 | | 0.0026 | ||
|0.0026 | | 0.0026 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 6, 15 | | 0, 6, 15 | ||
| +1+2 | | +1+2 | ||
|0.0162 | | 0.0162 | ||
|0.0166 | | 0.0166 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 7, 17 | | 0, 7, 17 | ||
| +1+2 | | +1+2 | ||
|0.0250 | | 0.0250 | ||
|0.0259 | | 0.0259 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 7, 18 | | 0, 7, 18 | ||
| +1+2 | | +1+2 | ||
|0.0467 | | 0.0467 | ||
|0.0485 | | 0.0485 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 8, 19 | | 0, 8, 19 | ||
| +1+2 | | +1+2 | ||
|0.0271 | | 0.0271 | ||
|0.0283 | | 0.0283 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 2, 7 | | 0, 2, 7 | ||
| +1+3 | | +1+3 | ||
|0.0442 | | 0.0442 | ||
|0.0443 | | 0.0443 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 4, 13 | | 0, 4, 13 | ||
| +1+3 | | +1+3 | ||
|0.0436 | | 0.0436 | ||
|0.0440 | | 0.0440 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 4, 14 | | 0, 4, 14 | ||
| +1+3 | | +1+3 | ||
|0.0463 | | 0.0463 | ||
|0.0468 | | 0.0468 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 5, 16 | | 0, 5, 16 | ||
| +1+3 | | +1+3 | ||
|0.0206 | | 0.0206 | ||
|0.0209 | | 0.0209 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 6, 19 | | 0, 6, 19 | ||
| +1+3 | | +1+3 | ||
|0.0076 | | 0.0076 | ||
|0.0078 | | 0.0078 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 2, 3 | | 0, 2, 3 | ||
| +2+1 | | +2+1 | ||
|0.0292 | | 0.0292 | ||
|0.0292 | | 0.0292 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 7, 10 | | 0, 7, 10 | ||
| +2+1 | | +2+1 | ||
|0.0095 | | 0.0095 | ||
|0.0096 | | 0.0096 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 10, 14 | | 0, 10, 14 | ||
| +2+1 | | +2+1 | ||
|0.0085 | | 0.0085 | ||
|0.0087 | | 0.0087 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 11, 15 | | 0, 11, 15 | ||
| +2+1 | | +2+1 | ||
|0.0348 | | 0.0348 | ||
|0.0357 | | 0.0357 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 13, 18 | | 0, 13, 18 | ||
| +2+1 | | +2+1 | ||
|0.0238 | | 0.0238 | ||
|0.0247 | | 0.0247 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 14, 19 | | 0, 14, 19 | ||
| +2+1 | | +2+1 | ||
|0.0087 | | 0.0087 | ||
|0.0091 | | 0.0091 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 3, 7 | | 0, 3, 7 | ||
| +2+3 | | +2+3 | ||
|0.0043 | | 0.0043 | ||
|0.0043 | | 0.0043 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 4, 9 | | 0, 4, 9 | ||
| +2+3 | | +2+3 | ||
|0.0289 | | 0.0289 | ||
|0.0290 | | 0.0290 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 5, 11 | | 0, 5, 11 | ||
| +2+3 | | +2+3 | ||
|0.0356 | | 0.0356 | ||
|0.0358 | | 0.0358 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 6, 13 | | 0, 6, 13 | ||
| +2+3 | | +2+3 | ||
|0.0283 | | 0.0283 | ||
|0.0285 | | 0.0285 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 7, 15 | | 0, 7, 15 | ||
| +2+3 | | +2+3 | ||
|0.0125 | | 0.0125 | ||
|0.0127 | | 0.0127 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 8, 17 | | 0, 8, 17 | ||
| +2+3 | | +2+3 | ||
|0.0086 | | 0.0086 | ||
|0.0087 | | 0.0087 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 9, 19 | | 0, 9, 19 | ||
| +2+3 | | +2+3 | ||
|0.0335 | | 0.0335 | ||
|0.0341 | | 0.0341 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 3, 4 | | 0, 3, 4 | ||
| +3+1 | | +3+1 | ||
|0.0423 | | 0.0423 | ||
|0.0424 | | 0.0424 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 7, 9 | | 0, 7, 9 | ||
| +3+1 | | +3+1 | ||
|0.0003 | | 0.0003 | ||
|0.0003 | | 0.0003 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 11, 14 | | 0, 11, 14 | ||
| +3+1 | | +3+1 | ||
|0.0221 | | 0.0221 | ||
|0.0223 | | 0.0223 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 12, 15 | | 0, 12, 15 | ||
| +3+1 | | +3+1 | ||
|0.0205 | | 0.0205 | ||
|0.0208 | | 0.0208 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 5, 8 | | 0, 5, 8 | ||
| +3+2 | | +3+2 | ||
|0.0336 | | 0.0336 | ||
|0.0337 | | 0.0337 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 7, 11 | | 0, 7, 11 | ||
| +3+2 | | +3+2 | ||
|0.0361 | | 0.0361 | ||
|0.0362 | | 0.0362 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 10, 15 | | 0, 10, 15 | ||
| +3+2 | | +3+2 | ||
|0.0322 | | 0.0322 | ||
|0.0325 | | 0.0325 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 12, 18 | | 0, 12, 18 | ||
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|0.0195 | | 0.0195 | ||
|0.0197 | | 0.0197 | ||
|- | |- | ||
|20 | | 20 | ||
|0, 13, 19 | | 0, 13, 19 | ||
| +3+2 | | +3+2 | ||
|0.0460 | | 0.0460 | ||
|0.0468 | | 0.0468 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 1, 2 | | 0, 1, 2 | ||
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|0.0148 | | 0.0148 | ||
|0.0148 | | 0.0148 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 2, 4 | | 0, 2, 4 | ||
| +1+1 | | +1+1 | ||
|0.0297 | | 0.0297 | ||
|0.0298 | | 0.0298 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 3, 6 | | 0, 3, 6 | ||
| +1+1 | | +1+1 | ||
|0.0447 | | 0.0447 | ||
|0.0449 | | 0.0449 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0333 | | 0.0333 | ||
|0.0338 | | 0.0338 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 6, 11 | | 0, 6, 11 | ||
| +1+1 | | +1+1 | ||
|0.0006 | | 0.0006 | ||
|0.0006 | | 0.0006 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 7, 13 | | 0, 7, 13 | ||
| +1+1 | | +1+1 | ||
|0.0269 | | 0.0269 | ||
|0.0278 | | 0.0278 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 8, 14 | | 0, 8, 14 | ||
| +1+1 | | +1+1 | ||
|0.0257 | | 0.0257 | ||
|0.0268 | | 0.0268 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 9, 16 | | 0, 9, 16 | ||
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|0.0051 | | 0.0051 | ||
|0.0054 | | 0.0054 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 10, 17 | | 0, 10, 17 | ||
| +1+1 | | +1+1 | ||
|0.0348 | | 0.0348 | ||
|0.0372 | | 0.0372 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 10, 18 | | 0, 10, 18 | ||
| +1+1 | | +1+1 | ||
|0.0325 | | 0.0325 | ||
|0.0351 | | 0.0351 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 11, 19 | | 0, 11, 19 | ||
| +1+1 | | +1+1 | ||
|0.0033 | | 0.0033 | ||
|0.0036 | | 0.0036 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 12, 20 | | 0, 12, 20 | ||
| +1+1 | | +1+1 | ||
|0.0350 | | 0.0350 | ||
|0.0387 | | 0.0387 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 1, 3 | | 0, 1, 3 | ||
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|0.0312 | | 0.0312 | ||
|0.0313 | | 0.0313 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 3, 8 | | 0, 3, 8 | ||
| +1+2 | | +1+2 | ||
|0.0315 | | 0.0315 | ||
|0.0317 | | 0.0317 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 4, 11 | | 0, 4, 11 | ||
| +1+2 | | +1+2 | ||
|0.0311 | | 0.0311 | ||
|0.0315 | | 0.0315 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 5, 13 | | 0, 5, 13 | ||
| +1+2 | | +1+2 | ||
|0.0043 | | 0.0043 | ||
|0.0044 | | 0.0044 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 6, 15 | | 0, 6, 15 | ||
| +1+2 | | +1+2 | ||
|0.0242 | | 0.0242 | ||
|0.0247 | | 0.0247 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 7, 17 | | 0, 7, 17 | ||
| +1+2 | | +1+2 | ||
|0.0341 | | 0.0341 | ||
|0.0351 | | 0.0351 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 7, 18 | | 0, 7, 18 | ||
| +1+2 | | +1+2 | ||
|0.0372 | | 0.0372 | ||
|0.0385 | | 0.0385 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 8, 19 | | 0, 8, 19 | ||
| +1+2 | | +1+2 | ||
|0.0372 | | 0.0372 | ||
|0.0388 | | 0.0388 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 8, 20 | | 0, 8, 20 | ||
| +1+2 | | +1+2 | ||
|0.0290 | | 0.0290 | ||
|0.0303 | | 0.0303 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 1, 4 | | 0, 1, 4 | ||
| +1+3 | | +1+3 | ||
|0.0476 | | 0.0476 | ||
|0.0477 | | 0.0477 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 2, 7 | | 0, 2, 7 | ||
| +1+3 | | +1+3 | ||
|0.0485 | | 0.0485 | ||
|0.0486 | | 0.0486 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 3, 11 | | 0, 3, 11 | ||
| +1+3 | | +1+3 | ||
|0.0475 | | 0.0475 | ||
|0.0478 | | 0.0478 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 4, 14 | | 0, 4, 14 | ||
| +1+3 | | +1+3 | ||
|0.0378 | | 0.0378 | ||
|0.0382 | | 0.0382 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 5, 16 | | 0, 5, 16 | ||
| +1+3 | | +1+3 | ||
|0.0306 | | 0.0306 | ||
|0.0311 | | 0.0311 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 5, 17 | | 0, 5, 17 | ||
| +1+3 | | +1+3 | ||
|0.0451 | | 0.0451 | ||
|0.0459 | | 0.0459 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 6, 19 | | 0, 6, 19 | ||
| +1+3 | | +1+3 | ||
|0.0042 | | 0.0042 | ||
|0.0043 | | 0.0043 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 2, 3 | | 0, 2, 3 | ||
| +2+1 | | +2+1 | ||
|0.0278 | | 0.0278 | ||
|0.0278 | | 0.0278 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 7, 10 | | 0, 7, 10 | ||
| +2+1 | | +2+1 | ||
|0.0050 | | 0.0050 | ||
|0.0051 | | 0.0051 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 10, 14 | | 0, 10, 14 | ||
| +2+1 | | +2+1 | ||
|0.0023 | | 0.0023 | ||
|0.0023 | | 0.0023 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 11, 15 | | 0, 11, 15 | ||
| +2+1 | | +2+1 | ||
|0.0411 | | 0.0411 | ||
|0.0421 | | 0.0421 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 13, 18 | | 0, 13, 18 | ||
| +2+1 | | +2+1 | ||
|0.0157 | | 0.0157 | ||
|0.0163 | | 0.0163 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 14, 19 | | 0, 14, 19 | ||
| +2+1 | | +2+1 | ||
|0.0169 | | 0.0169 | ||
|0.0176 | | 0.0176 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 15, 20 | | 0, 15, 20 | ||
| +2+1 | | +2+1 | ||
|0.0458 | | 0.0458 | ||
|0.0480 | | 0.0480 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 3, 7 | | 0, 3, 7 | ||
| +2+3 | | +2+3 | ||
|0.0022 | | 0.0022 | ||
|0.0022 | | 0.0022 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 4, 9 | | 0, 4, 9 | ||
| +2+3 | | +2+3 | ||
|0.0372 | | 0.0372 | ||
|0.0373 | | 0.0373 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 5, 11 | | 0, 5, 11 | ||
| +2+3 | | +2+3 | ||
|0.0458 | | 0.0458 | ||
|0.0460 | | 0.0460 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 6, 13 | | 0, 6, 13 | ||
| +2+3 | | +2+3 | ||
|0.0403 | | 0.0403 | ||
|0.0406 | | 0.0406 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 7, 15 | | 0, 7, 15 | ||
| +2+3 | | +2+3 | ||
|0.0264 | | 0.0264 | ||
|0.0266 | | 0.0266 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 8, 17 | | 0, 8, 17 | ||
| +2+3 | | +2+3 | ||
|0.0071 | | 0.0071 | ||
|0.0072 | | 0.0072 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 9, 19 | | 0, 9, 19 | ||
| +2+3 | | +2+3 | ||
|0.0160 | | 0.0160 | ||
|0.0162 | | 0.0162 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 3, 4 | | 0, 3, 4 | ||
| +3+1 | | +3+1 | ||
|0.0403 | | 0.0403 | ||
|0.0403 | | 0.0403 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 7, 9 | | 0, 7, 9 | ||
| +3+1 | | +3+1 | ||
|0.0046 | | 0.0046 | ||
|0.0046 | | 0.0046 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 11, 14 | | 0, 11, 14 | ||
| +3+1 | | +3+1 | ||
|0.0153 | | 0.0153 | ||
|0.0155 | | 0.0155 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 12, 15 | | 0, 12, 15 | ||
| +3+1 | | +3+1 | ||
|0.0273 | | 0.0273 | ||
|0.0277 | | 0.0277 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 16, 20 | | 0, 16, 20 | ||
| +3+1 | | +3+1 | ||
|0.0191 | | 0.0191 | ||
|0.0196 | | 0.0196 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 5, 8 | | 0, 5, 8 | ||
| +3+2 | | +3+2 | ||
|0.0268 | | 0.0268 | ||
|0.0269 | | 0.0269 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 7, 11 | | 0, 7, 11 | ||
| +3+2 | | +3+2 | ||
|0.0268 | | 0.0268 | ||
|0.0269 | | 0.0269 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 9, 14 | | 0, 9, 14 | ||
| +3+2 | | +3+2 | ||
|0.0480 | | 0.0480 | ||
|0.0483 | | 0.0483 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 10, 15 | | 0, 10, 15 | ||
| +3+2 | | +3+2 | ||
|0.0444 | | 0.0444 | ||
|0.0448 | | 0.0448 | ||
|- | |- | ||
|21 | | 21 | ||
|0, 12, 18 | | 0, 12, 18 | ||
| +3+2 | | +3+2 | ||
|0.0046 | | 0.0046 | ||
|0.0047 | | 0.0047 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0141 | | 0.0141 | ||
|0.0141 | | 0.0141 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 2, 4 | | 0, 2, 4 | ||
| +1+1 | | +1+1 | ||
|0.0283 | | 0.0283 | ||
|0.0284 | | 0.0284 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 3, 6 | | 0, 3, 6 | ||
| +1+1 | | +1+1 | ||
|0.0426 | | 0.0426 | ||
|0.0429 | | 0.0429 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0362 | | 0.0362 | ||
|0.0367 | | 0.0367 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 6, 11 | | 0, 6, 11 | ||
| +1+1 | | +1+1 | ||
|0.0042 | | 0.0042 | ||
|0.0043 | | 0.0043 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 7, 13 | | 0, 7, 13 | ||
| +1+1 | | +1+1 | ||
|0.0225 | | 0.0225 | ||
|0.0232 | | 0.0232 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 8, 14 | | 0, 8, 14 | ||
| +1+1 | | +1+1 | ||
|0.0303 | | 0.0303 | ||
|0.0315 | | 0.0315 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 8, 15 | | 0, 8, 15 | ||
| +1+1 | | +1+1 | ||
|0.0461 | | 0.0461 | ||
|0.0481 | | 0.0481 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 9, 16 | | 0, 9, 16 | ||
| +1+1 | | +1+1 | ||
|0.0003 | | 0.0003 | ||
|0.0003 | | 0.0003 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 10, 17 | | 0, 10, 17 | ||
| +1+1 | | +1+1 | ||
|0.0403 | | 0.0403 | ||
|0.0428 | | 0.0428 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 10, 18 | | 0, 10, 18 | ||
| +1+1 | | +1+1 | ||
|0.0265 | | 0.0265 | ||
|0.0283 | | 0.0283 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 11, 19 | | 0, 11, 19 | ||
| +1+1 | | +1+1 | ||
|0.0096 | | 0.0096 | ||
|0.0104 | | 0.0104 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 12, 20 | | 0, 12, 20 | ||
| +1+1 | | +1+1 | ||
|0.0415 | | 0.0415 | ||
|0.0454 | | 0.0454 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 12, 21 | | 0, 12, 21 | ||
| +1+1 | | +1+1 | ||
|0.0182 | | 0.0182 | ||
|0.0201 | | 0.0201 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 1, 3 | | 0, 1, 3 | ||
| +1+2 | | +1+2 | ||
|0.0298 | | 0.0298 | ||
|0.0298 | | 0.0298 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 3, 8 | | 0, 3, 8 | ||
| +1+2 | | +1+2 | ||
|0.0354 | | 0.0354 | ||
|0.0355 | | 0.0355 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 4, 11 | | 0, 4, 11 | ||
| +1+2 | | +1+2 | ||
|0.0259 | | 0.0259 | ||
|0.0261 | | 0.0261 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 5, 13 | | 0, 5, 13 | ||
| +1+2 | | +1+2 | ||
|0.0106 | | 0.0106 | ||
|0.0108 | | 0.0108 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 6, 15 | | 0, 6, 15 | ||
| +1+2 | | +1+2 | ||
|0.0315 | | 0.0315 | ||
|0.0321 | | 0.0321 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 6, 16 | | 0, 6, 16 | ||
| +1+2 | | +1+2 | ||
|0.0454 | | 0.0454 | ||
|0.0465 | | 0.0465 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 7, 17 | | 0, 7, 17 | ||
| +1+2 | | +1+2 | ||
|0.0424 | | 0.0424 | ||
|0.0435 | | 0.0435 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 7, 18 | | 0, 7, 18 | ||
| +1+2 | | +1+2 | ||
|0.0286 | | 0.0286 | ||
|0.0295 | | 0.0295 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 8, 19 | | 0, 8, 19 | ||
| +1+2 | | +1+2 | ||
|0.0465 | | 0.0465 | ||
|0.0482 | | 0.0482 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 8, 20 | | 0, 8, 20 | ||
| +1+2 | | +1+2 | ||
|0.0193 | | 0.0193 | ||
|0.0202 | | 0.0202 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 9, 21 | | 0, 9, 21 | ||
| +1+2 | | +1+2 | ||
|0.0459 | | 0.0459 | ||
|0.0481 | | 0.0481 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 1, 4 | | 0, 1, 4 | ||
| +1+3 | | +1+3 | ||
|0.0455 | | 0.0455 | ||
|0.0455 | | 0.0455 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 3, 11 | | 0, 3, 11 | ||
| +1+3 | | +1+3 | ||
|0.0415 | | 0.0415 | ||
|0.0418 | | 0.0418 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 4, 14 | | 0, 4, 14 | ||
| +1+3 | | +1+3 | ||
|0.0301 | | 0.0301 | ||
|0.0304 | | 0.0304 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 5, 16 | | 0, 5, 16 | ||
| +1+3 | | +1+3 | ||
|0.0398 | | 0.0398 | ||
|0.0404 | | 0.0404 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 5, 17 | | 0, 5, 17 | ||
| +1+3 | | +1+3 | ||
|0.0357 | | 0.0357 | ||
|0.0363 | | 0.0363 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 6, 19 | | 0, 6, 19 | ||
| +1+3 | | +1+3 | ||
|0.0151 | | 0.0151 | ||
|0.0154 | | 0.0154 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 2, 3 | | 0, 2, 3 | ||
| +2+1 | | +2+1 | ||
|0.0265 | | 0.0265 | ||
|0.0265 | | 0.0265 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 7, 10 | | 0, 7, 10 | ||
| +2+1 | | +2+1 | ||
|0.0010 | | 0.0010 | ||
|0.0010 | | 0.0010 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 9, 13 | | 0, 9, 13 | ||
| +2+1 | | +2+1 | ||
|0.0478 | | 0.0478 | ||
|0.0485 | | 0.0485 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 10, 14 | | 0, 10, 14 | ||
| +2+1 | | +2+1 | ||
|0.0034 | | 0.0034 | ||
|0.0034 | | 0.0034 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 11, 15 | | 0, 11, 15 | ||
| +2+1 | | +2+1 | ||
|0.0469 | | 0.0469 | ||
|0.0478 | | 0.0478 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 12, 17 | | 0, 12, 17 | ||
| +2+1 | | +2+1 | ||
|0.0457 | | 0.0457 | ||
|0.0469 | | 0.0469 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 13, 18 | | 0, 13, 18 | ||
| +2+1 | | +2+1 | ||
|0.0085 | | 0.0085 | ||
|0.0088 | | 0.0088 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 14, 19 | | 0, 14, 19 | ||
| +2+1 | | +2+1 | ||
|0.0242 | | 0.0242 | ||
|0.0251 | | 0.0251 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 3, 7 | | 0, 3, 7 | ||
| +2+3 | | +2+3 | ||
|0.0080 | | 0.0080 | ||
|0.0081 | | 0.0081 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 4, 9 | | 0, 4, 9 | ||
| +2+3 | | +2+3 | ||
|0.0448 | | 0.0448 | ||
|0.0449 | | 0.0449 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 7, 15 | | 0, 7, 15 | ||
| +2+3 | | +2+3 | ||
|0.0390 | | 0.0390 | ||
|0.0393 | | 0.0393 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 8, 17 | | 0, 8, 17 | ||
| +2+3 | | +2+3 | ||
|0.0214 | | 0.0214 | ||
|0.0216 | | 0.0216 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 9, 19 | | 0, 9, 19 | ||
| +2+3 | | +2+3 | ||
|0.0000 | | 0.0000 | ||
|0.0000 | | 0.0000 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 10, 21 | | 0, 10, 21 | ||
| +2+3 | | +2+3 | ||
|0.0240 | | 0.0240 | ||
|0.0244 | | 0.0244 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 3, 4 | | 0, 3, 4 | ||
| +3+1 | | +3+1 | ||
|0.0384 | | 0.0384 | ||
|0.0384 | | 0.0384 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 7, 9 | | 0, 7, 9 | ||
| +3+1 | | +3+1 | ||
|0.0085 | | 0.0085 | ||
|0.0085 | | 0.0085 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 11, 14 | | 0, 11, 14 | ||
| +3+1 | | +3+1 | ||
|0.0092 | | 0.0092 | ||
|0.0093 | | 0.0093 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 12, 15 | | 0, 12, 15 | ||
| +3+1 | | +3+1 | ||
|0.0335 | | 0.0335 | ||
|0.0339 | | 0.0339 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 15, 19 | | 0, 15, 19 | ||
| +3+1 | | +3+1 | ||
|0.0415 | | 0.0415 | ||
|0.0423 | | 0.0423 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 16, 20 | | 0, 16, 20 | ||
| +3+1 | | +3+1 | ||
|0.0106 | | 0.0106 | ||
|0.0108 | | 0.0108 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 17, 21 | | 0, 17, 21 | ||
| +3+1 | | +3+1 | ||
|0.0171 | | 0.0171 | ||
|0.0175 | | 0.0175 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 5, 8 | | 0, 5, 8 | ||
| +3+2 | | +3+2 | ||
|0.0207 | | 0.0207 | ||
|0.0207 | | 0.0207 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 7, 11 | | 0, 7, 11 | ||
| +3+2 | | +3+2 | ||
|0.0184 | | 0.0184 | ||
|0.0184 | | 0.0184 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 9, 14 | | 0, 9, 14 | ||
| +3+2 | | +3+2 | ||
|0.0372 | | 0.0372 | ||
|0.0374 | | 0.0374 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 12, 18 | | 0, 12, 18 | ||
| +3+2 | | +3+2 | ||
|0.0088 | | 0.0088 | ||
|0.0089 | | 0.0089 | ||
|- | |- | ||
|22 | | 22 | ||
|0, 14, 21 | | 0, 14, 21 | ||
| +3+2 | | +3+2 | ||
|0.0384 | | 0.0384 | ||
|0.0391 | | 0.0391 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 1, 2 | | 0, 1, 2 | ||
| +1+1 | | +1+1 | ||
|0.0135 | | 0.0135 | ||
|0.0135 | | 0.0135 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 2, 4 | | 0, 2, 4 | ||
| +1+1 | | +1+1 | ||
|0.0271 | | 0.0271 | ||
|0.0272 | | 0.0272 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 3, 6 | | 0, 3, 6 | ||
| +1+1 | | +1+1 | ||
|0.0408 | | 0.0408 | ||
|0.0410 | | 0.0410 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 5, 9 | | 0, 5, 9 | ||
| +1+1 | | +1+1 | ||
|0.0389 | | 0.0389 | ||
|0.0394 | | 0.0394 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 6, 11 | | 0, 6, 11 | ||
| +1+1 | | +1+1 | ||
|0.0076 | | 0.0076 | ||
|0.0077 | | 0.0077 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 7, 13 | | 0, 7, 13 | ||
| +1+1 | | +1+1 | ||
|0.0185 | | 0.0185 | ||
|0.0190 | | 0.0190 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 8, 14 | | 0, 8, 14 | ||
| +1+1 | | +1+1 | ||
|0.0345 | | 0.0345 | ||
|0.0357 | | 0.0357 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 8, 15 | | 0, 8, 15 | ||
| +1+1 | | +1+1 | ||
|0.0415 | | 0.0415 | ||
|0.0431 | | 0.0431 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 9, 16 | | 0, 9, 16 | ||
| +1+1 | | +1+1 | ||
|0.0051 | | 0.0051 | ||
|0.0053 | | 0.0053 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 10, 17 | | 0, 10, 17 | ||
| +1+1 | | +1+1 | ||
|0.0453 | | 0.0453 | ||
|0.0478 | | 0.0478 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 10, 18 | | 0, 10, 18 | ||
| +1+1 | | +1+1 | ||
|0.0210 | | 0.0210 | ||
|0.0223 | | 0.0223 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 11, 19 | | 0, 11, 19 | ||
| +1+1 | | +1+1 | ||
|0.0153 | | 0.0153 | ||
|0.0164 | | 0.0164 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 11, 20 | | 0, 11, 20 | ||
| +1+1 | | +1+1 | ||
|0.0448 | | 0.0448 | ||
|0.0484 | | 0.0484 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 12, 21 | | 0, 12, 21 | ||
| +1+1 | | +1+1 | ||
|0.0118 | | 0.0118 | ||
|0.0129 | | 0.0129 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 13, 22 | | 0, 13, 22 | ||
| +1+1 | | +1+1 | ||
|0.0176 | | 0.0176 | ||
|0.0195 | | 0.0195 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 1, 3 | | 0, 1, 3 | ||
| +1+2 | | +1+2 | ||
|0.0285 | | 0.0285 | ||
|0.0285 | | 0.0285 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 3, 8 | | 0, 3, 8 | ||
| +1+2 | | +1+2 | ||
|0.0389 | | 0.0389 | ||
|0.0391 | | 0.0391 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 4, 11 | | 0, 4, 11 | ||
| +1+2 | | +1+2 | ||
|0.0211 | | 0.0211 | ||
|0.0213 | | 0.0213 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 5, 13 | | 0, 5, 13 | ||
| +1+2 | | +1+2 | ||
|0.0163 | | 0.0163 | ||
|0.0166 | | 0.0166 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 6, 15 | | 0, 6, 15 | ||
| +1+2 | | +1+2 | ||
|0.0381 | | 0.0381 | ||
|0.0388 | | 0.0388 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 6, 16 | | 0, 6, 16 | ||
| +1+2 | | +1+2 | ||
|0.0385 | | 0.0385 | ||
|0.0393 | | 0.0393 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 7, 18 | | 0, 7, 18 | ||
| +1+2 | | +1+2 | ||
|0.0207 | | 0.0207 | ||
|0.0213 | | 0.0213 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 8, 20 | | 0, 8, 20 | ||
| +1+2 | | +1+2 | ||
|0.0105 | | 0.0105 | ||
|0.0109 | | 0.0109 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 9, 22 | | 0, 9, 22 | ||
| +1+2 | | +1+2 | ||
|0.0059 | | 0.0059 | ||
|0.0062 | | 0.0062 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 1, 4 | | 0, 1, 4 | ||
| +1+3 | | +1+3 | ||
|0.0435 | | 0.0435 | ||
|0.0435 | | 0.0435 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 3, 11 | | 0, 3, 11 | ||
| +1+3 | | +1+3 | ||
|0.0360 | | 0.0360 | ||
|0.0362 | | 0.0362 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 4, 14 | | 0, 4, 14 | ||
| +1+3 | | +1+3 | ||
|0.0230 | | 0.0230 | ||
|0.0232 | | 0.0232 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 5, 16 | | 0, 5, 16 | ||
| +1+3 | | +1+3 | ||
|0.0482 | | 0.0482 | ||
|0.0488 | | 0.0488 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 5, 17 | | 0, 5, 17 | ||
| +1+3 | | +1+3 | ||
|0.0271 | | 0.0271 | ||
|0.0275 | | 0.0275 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 6, 19 | | 0, 6, 19 | ||
| +1+3 | | +1+3 | ||
|0.0250 | | 0.0250 | ||
|0.0254 | | 0.0254 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 6, 20 | | 0, 6, 20 | ||
| +1+3 | | +1+3 | ||
|0.0403 | | 0.0403 | ||
|0.0412 | | 0.0412 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 7, 22 | | 0, 7, 22 | ||
| +1+3 | | +1+3 | ||
|0.0012 | | 0.0012 | ||
|0.0013 | | 0.0013 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 2, 3 | | 0, 2, 3 | ||
| +2+1 | | +2+1 | ||
|0.0253 | | 0.0253 | ||
|0.0253 | | 0.0253 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 7, 10 | | 0, 7, 10 | ||
| +2+1 | | +2+1 | ||
|0.0028 | | 0.0028 | ||
|0.0028 | | 0.0028 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 9, 13 | | 0, 9, 13 | ||
| +2+1 | | +2+1 | ||
|0.0428 | | 0.0428 | ||
|0.0433 | | 0.0433 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 10, 14 | | 0, 10, 14 | ||
| +2+1 | | +2+1 | ||
|0.0085 | | 0.0085 | ||
|0.0086 | | 0.0086 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 12, 17 | | 0, 12, 17 | ||
| +2+1 | | +2+1 | ||
|0.0392 | | 0.0392 | ||
|0.0401 | | 0.0401 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 13, 18 | | 0, 13, 18 | ||
| +2+1 | | +2+1 | ||
|0.0019 | | 0.0019 | ||
|0.0020 | | 0.0020 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 14, 19 | | 0, 14, 19 | ||
| +2+1 | | +2+1 | ||
|0.0309 | | 0.0309 | ||
|0.0320 | | 0.0320 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 16, 22 | | 0, 16, 22 | ||
| +2+1 | | +2+1 | ||
|0.0199 | | 0.0199 | ||
|0.0208 | | 0.0208 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 3, 7 | | 0, 3, 7 | ||
| +2+3 | | +2+3 | ||
|0.0134 | | 0.0134 | ||
|0.0134 | | 0.0134 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 8, 17 | | 0, 8, 17 | ||
| +2+3 | | +2+3 | ||
|0.0344 | | 0.0344 | ||
|0.0347 | | 0.0347 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 9, 19 | | 0, 9, 19 | ||
| +2+3 | | +2+3 | ||
|0.0146 | | 0.0146 | ||
|0.0148 | | 0.0148 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 10, 21 | | 0, 10, 21 | ||
| +2+3 | | +2+3 | ||
|0.0079 | | 0.0079 | ||
|0.0080 | | 0.0080 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 3, 4 | | 0, 3, 4 | ||
| +3+1 | | +3+1 | ||
|0.0367 | | 0.0367 | ||
|0.0367 | | 0.0367 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 7, 9 | | 0, 7, 9 | ||
| +3+1 | | +3+1 | ||
|0.0121 | | 0.0121 | ||
|0.0121 | | 0.0121 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 11, 14 | | 0, 11, 14 | ||
| +3+1 | | +3+1 | ||
|0.0036 | | 0.0036 | ||
|0.0037 | | 0.0037 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 12, 15 | | 0, 12, 15 | ||
| +3+1 | | +3+1 | ||
|0.0392 | | 0.0392 | ||
|0.0396 | | 0.0396 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 15, 19 | | 0, 15, 19 | ||
| +3+1 | | +3+1 | ||
|0.0338 | | 0.0338 | ||
|0.0344 | | 0.0344 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 16, 20 | | 0, 16, 20 | ||
| +3+1 | | +3+1 | ||
|0.0028 | | 0.0028 | ||
|0.0028 | | 0.0028 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 17, 21 | | 0, 17, 21 | ||
| +3+1 | | +3+1 | ||
|0.0249 | | 0.0249 | ||
|0.0255 | | 0.0255 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 5, 8 | | 0, 5, 8 | ||
| +3+2 | | +3+2 | ||
|0.0150 | | 0.0150 | ||
|0.0151 | | 0.0151 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 7, 11 | | 0, 7, 11 | ||
| +3+2 | | +3+2 | ||
|0.0107 | | 0.0107 | ||
|0.0107 | | 0.0107 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 9, 14 | | 0, 9, 14 | ||
| +3+2 | | +3+2 | ||
|0.0274 | | 0.0274 | ||
|0.0276 | | 0.0276 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 12, 18 | | 0, 12, 18 | ||
| +3+2 | | +3+2 | ||
|0.0210 | | 0.0210 | ||
|0.0213 | | 0.0213 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 14, 21 | | 0, 14, 21 | ||
| +3+2 | | +3+2 | ||
|0.0240 | | 0.0240 | ||
|0.0244 | | 0.0244 | ||
|- | |- | ||
|23 | | 23 | ||
|0, 15, 22 | | 0, 15, 22 | ||
| +3+2 | | +3+2 | ||
|0.0325 | | 0.0325 | ||
|0.0331 | | 0.0331 | ||
|} | |} | ||
| Line 2,837: | Line 2,838: | ||
|- | |- | ||
! colspan="11" | Coefficients of terms | ! colspan="11" | Coefficients of terms | ||
!rowspan=2| Chord | ! rowspan="2" | Chord | ||
!rowspan=2| Delta signature | ! rowspan="2" | Delta signature | ||
!rowspan=2| Temperament | ! rowspan="2" | Temperament | ||
!rowspan=2| Generator (cents) | ! rowspan="2" | Generator (cents) | ||
!rowspan=2| Edos | ! rowspan="2" | Edos | ||
|- | |- | ||
! g^10 | ! g^10 | ||
| Line 3,093: | Line 3,094: | ||
| 22, 31, 53 | | 22, 31, 53 | ||
|} | |} | ||
=== Limitations === | === Limitations === | ||
Interpreting simple JI chords as signatures/templates for delta-rational chords is reasonable, as the psychoacoustic effect of DR is more robust to detuning than that of JI for many people, but it is no panacea. If the temperament is too inaccurate, other inversions and voicings of a given JI chord will not have the DR signatures preserved acceptably, and compromising will make all of them inaccurate, though this of course depends on what error tolerance you prefer. This is because DR simplicity is only preserved by inversion and revoicing if the chord in question is low-complexity JI. | Interpreting simple JI chords as signatures/templates for delta-rational chords is reasonable, as the psychoacoustic effect of DR is more robust to detuning than that of JI for many people, but it is no panacea. If the temperament is too inaccurate, other inversions and voicings of a given JI chord will not have the DR signatures preserved acceptably, and compromising will make all of them inaccurate, though this of course depends on what error tolerance you prefer. This is because DR simplicity is only preserved by inversion and revoicing if the chord in question is low-complexity JI. | ||
| Line 3,099: | Line 3,101: | ||
== Higher-order differences of frequency == | == Higher-order differences of frequency == | ||
Generalizing, one could consider chords where differences between its frequency deltas (as Tom Price has called them, '''precessions''') are rationally related, while the deltas themselves may not be. This corresponds to chords where differences between various interference beatings go in and out of sync in a periodic manner. One precession-rational chord is 5:5.4142...:6.8284...:9.2426..., a +(sqrt(2) − 1) +sqrt(2) +(sqrt(2) + 1) chord. | Generalizing, one could consider chords where differences between its frequency deltas (as Tom Price has called them, '''precessions''') are rationally related, while the deltas themselves may not be. This corresponds to chords where differences between various interference beatings go in and out of sync in a periodic manner. One precession-rational chord is 5:5.4142...:6.8284...:9.2426..., a {{nowrap|+(sqrt(2) − 1) +sqrt(2) +(sqrt(2) + 1)}} chord. | ||
Precession being the second-order difference (Δ<sup>2</sup>) of frequency, we similarly have the theoretical notions of Δ<sup>3</sup>-rationality, Δ<sup>4</sup>-rationality, and so on. The practical consequences of higher-order differences are as of yet speculative, though a few people have reported finding precession psychoacoustically meaningful. | Precession being the second-order difference (Δ<sup>2</sup>) of frequency, we similarly have the theoretical notions of Δ<sup>3</sup>-rationality, Δ<sup>4</sup>-rationality, and so on. The practical consequences of higher-order differences are as of yet speculative, though a few people have reported finding precession psychoacoustically meaningful. | ||
==Isodifferential chord== | == Isodifferential chord == | ||
In an '''isodifferential chord''' (known variously by '''linear chord''', '''equal-hertz chord''', '''equal-beating chord''', and '''proportional-beating chord'''), the frequencies of the pitches are in an arithmetic sequence, or in other words, there is an equal difference in cycles per second between successive pitches. | In an '''isodifferential chord''' (known variously by '''linear chord''', '''equal-hertz chord''', '''equal-beating chord''', and '''proportional-beating chord'''), the frequencies of the pitches are in an arithmetic sequence, or in other words, there is an equal difference in cycles per second between successive pitches. | ||
===Isoharmonic chord=== | == =Isoharmonic chord === | ||
An '''isoharmonic chord''' is a specific type of isodifferential chord, where the ratios between the notes are rational numbers, and therefore the chord is in just intonation. Such a chord can be built by successive jumps up the [[harmonic series]] by some number of steps. Since the harmonic series is arranged such that each higher step is smaller than the one before it, all isoharmonic chords have this same shape—with diminishing step size as one ascends. | An '''isoharmonic chord''' is a specific type of isodifferential chord, where the ratios between the notes are rational numbers, and therefore the chord is in just intonation. Such a chord can be built by successive jumps up the [[harmonic series]] by some number of steps. Since the harmonic series is arranged such that each higher step is smaller than the one before it, all isoharmonic chords have this same shape—with diminishing step size as one ascends. | ||
| Line 3,836: | Line 3,837: | ||
{| class="wikitable" | {| class="wikitable" | ||
! colspan="4" rowspan="3" | | ! colspan="4" rowspan="3" | Chord type | ||
! colspan="7" rowspan="1" | | ! colspan="7" rowspan="1" | Illustrative examples | ||
|- | |- | ||
! colspan="2" | | ! colspan="2" | Actual chord | ||
! colspan="3" rowspan="1" | | ! colspan="3" rowspan="1" | Deltas | ||
! colspan="2" | | ! colspan="2" | Delta ratio set | ||
|- | |- | ||
! | ! Frequency ratio | ||
! | ! Are items all integers? | ||
! | ! Delta signature | ||
! | ! Reduced delta signature (class) | ||
! | ! Are items all the same? | ||
! | ! Unique undirected ratios between the deltas | ||
! | ! Are items all rational? | ||
|- | |- | ||
! colspan="1" rowspan="17" |DR | ! colspan="1" rowspan="17" | DR | ||
! colspan="1" rowspan="14" |FDR | ! colspan="1" rowspan="14" | FDR | ||
! colspan="2" rowspan="3" |JI, <i>not</i> isodifferential | ! colspan="2" rowspan="3" | JI, <i>not</i> isodifferential | ||
|4:5:7:8 | | 4:5:7:8 | ||
| rowspan="11" |yes, all | | rowspan="11" | yes, all | ||
| +1+2+1 | | +1+2+1 | ||
| rowspan="2" | +1+2+1 | | rowspan="2" | +1+2+1 | ||
| rowspan="3" |no, not all | | rowspan="3" | no, not all | ||
| rowspan="2" |{ 1, 2 } | | rowspan="2" | {{(}}1, 2{{)}} | ||
| rowspan="14" |yes | | rowspan="14" | yes | ||
|- | |- | ||
|3:5:9:11 | | 3:5:9:11 | ||
| +2+4+2 | | +2+4+2 | ||
|- | |- | ||
|3:4:7:9 | | 3:4:7:9 | ||
| +1+3+2 | | +1+3+2 | ||
| +1+3+2 | | +1+3+2 | ||
|{ 3/2, 2, 3 } | | {{(}}3/2, 2, 3{{)}} | ||
|- | |- | ||
! rowspan="8" | | ! rowspan="8" | Isoharmonic | ||
(JI | (JI ''and'' isodifferential) | ||
! rowspan="3" | | ! rowspan="3" | Class i | ||
|4:5:6 | | 4:5:6 | ||
| +1+1 | | +1+1 | ||
| +1+1 | | +1+1 | ||
| rowspan="10" | | | rowspan="10" | Yes, all | ||
| rowspan="10" |{ 1 } | | rowspan="10" | {{(}}1{{)}} | ||
|- | |- | ||
|4:5:6:7 | | 4:5:6:7 | ||
| rowspan="2" | +1+1+1 | | rowspan="2" | +1+1+1 | ||
| rowspan="9" | +1+1+1 | | rowspan="9" | +1+1+1 | ||
|- | |- | ||
|3:4:5:6 | | 3:4:5:6 | ||
|- | |- | ||
! rowspan="2" |class ii | ! rowspan="2" | class ii | ||
|3:5:7:9 | | 3:5:7:9 | ||
| rowspan="2" | +2+2+2 | | rowspan="2" | +2+2+2 | ||
|- | |- | ||
|5:7:9:11 | | 5:7:9:11 | ||
|- | |- | ||
! rowspan="2" |class iii | ! rowspan="2" | class iii | ||
|1:4:7:10 | | 1:4:7:10 | ||
| rowspan="2" | +3+3+3 | | rowspan="2" | +3+3+3 | ||
|- | |- | ||
|2:5:8:11 | | 2:5:8:11 | ||
|- | |- | ||
!... | ! ... | ||
|... | | ... | ||
|... | | ... | ||
|- | |- | ||
! colspan="2" rowspan="2" | | ! colspan="2" rowspan="2" | Not JI, but isodifferential | ||
|ɸ:(ɸ+1):(ɸ+2):(ɸ+3) | | ɸ:(ɸ+1):(ɸ+2):(ɸ+3) | ||
| rowspan="7" | | | rowspan="7" | No, not all or none | ||
| +1+1+1 | | +1+1+1 | ||
|- | |- | ||
|1:ɸ:(2ɸ-1):(3ɸ-2) | | 1:ɸ:(2ɸ-1):(3ɸ-2) | ||
| +(ɸ-1)+(ɸ-1)+(ɸ-1) | | +(ɸ-1)+(ɸ-1)+(ɸ-1) | ||
|- | |- | ||
! colspan="2" rowspan="1" | | ! colspan="2" rowspan="1" | Not JI or isodifferential | ||
|ɸ:(ɸ+1):(ɸ+3) | | ɸ:(ɸ+1):(ɸ+3) | ||
| +1+2 | | +1+2 | ||
| +1+2 | | +1+2 | ||
| Line 3,916: | Line 3,917: | ||
| { 2 } | | { 2 } | ||
|- | |- | ||
! colspan="3" rowspan="3" |( | ! colspan="3" rowspan="3" | (Incompletely) DR | ||
|4:5:τ:7:9 | | 4:5:τ:7:9 | ||
| +1+(τ-5)+(7-τ)+2 | | +1+(τ-5)+(7-τ)+2 | ||
| +1+(τ-5)+(7-τ)+2 | | +1+(τ-5)+(7-τ)+2 | ||
| rowspan="5" |(irrelevant for categorization) | | rowspan="5" | (irrelevant for categorization) | ||
|{ (7-τ)/(τ-5), 7-τ, τ-5, 2/(τ-5), 2, 2/(7-τ) } | | {{(}}(7-τ)/(τ-5), 7-τ, τ-5, 2/(τ-5), 2, 2/(7-τ){{)}} | ||
| rowspan="3" |no, but at least one | | rowspan="3" | no, but at least one | ||
|- | |- | ||
|5:τ:8:(3+τ) | | 5:τ:8:(3+τ) | ||
| +(τ-5)+(8-τ)+(τ-5) | | +(τ-5)+(8-τ)+(τ-5) | ||
| +1+(8-τ)/(τ-5)+1 | | +1+(8-τ)/(τ-5)+1 | ||
|{ 1, (8-τ)/(τ-5) } | | {{(}}1, (8-τ)/(τ-5) {{)}} | ||
|- | |- | ||
|1:(1+a):(1+a+b):(1+a+2b):(1+3a+2b), with a/b irrational | | 1:(1+a):(1+a+b):(1+a+2b):(1+3a+2b), with a/b irrational | ||
| +a+b+b+2a | | +a+b+b+2a | ||
| +a+b+b+2a | | +a+b+b+2a | ||
|{ a/b, 1, 2, 2a/b } | | {{(}}a/b, 1, 2, 2a/b{{)}} | ||
|- | |- | ||
! colspan="4" rowspan="2" | | ! colspan="4" rowspan="2" | Not DR | ||
|4:5:τ:7 | | 4:5:τ:7 | ||
| +1+(τ-5)+(7-τ) | | +1+(τ-5)+(7-τ) | ||
| +1+(τ-5)+(7-τ) | | +1+(τ-5)+(7-τ) | ||
|{ (7-τ)/(τ-5), 7-τ, τ-5 } | | {{(}}(7-τ)/(τ-5), 7-τ, τ-5{{)}} | ||
| rowspan="2" | | | rowspan="2" | No, none | ||
|- | |- | ||
|5:τ:7 | | 5:τ:7 | ||
| +(τ-5)+(7-τ) | | +(τ-5)+(7-τ) | ||
| +1+(7-τ)/(τ-5) | | +1+(7-τ)/(τ-5) | ||
|{ (7-τ)/(τ-5) } | | {{(}}(7-τ)/(τ-5){{)}} | ||
|} | |} | ||