User:TallKite/41edo: Difference between revisions
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An example of how to make hovering over primes reveal their cents through invalid links! BTW the lack of decimal places is deliberate, it's extremely difficult to hear a tenth of a cent, and even harder to care about it! |
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Two examples of how I personally prefer to round off cents and percentages to whole numbers or 2 significant figures, whichever is more accurate. | |||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 4: | Line 5: | ||
|+Approximation of prime harmonics in 41edo | |+Approximation of prime harmonics in 41edo | ||
! colspan="2" |Harmonic | ! colspan="2" |Harmonic | ||
!2 | ![[1200¢|2]] | ||
!3 | ![[702¢|3]] | ||
!5 | ![[386¢|5]] | ||
!7 | ![[969¢|7]] | ||
!11 | ![[551¢|11]] | ||
!13 | ![[841¢|13]] | ||
!17 | ![[105¢|17]] | ||
!19 | ![[298¢|19]] | ||
![[628¢|23]] | ![[628¢|23]] | ||
![[1030¢|29]] | ![[1030¢|29]] | ||
| Line 24: | Line 25: | ||
| +4.8 | | +4.8 | ||
| +8.3 | | +8.3 | ||
| +12 | | +12 | ||
| -4.8 | | -4.8 | ||
| - | | -14 | ||
| -5.2 | | -5.2 | ||
| -3.6 | | -3.6 | ||
| Line 33: | Line 34: | ||
| +0.0 | | +0.0 | ||
| +1.7 | | +1.7 | ||
| -19 | | -20 | ||
| - | | -10 | ||
| + | | +16 | ||
| + | | +28 | ||
| + | | +41 | ||
| - | | -17 | ||
| - | | -47 | ||
| - | | -18 | ||
| -12 | | -12 | ||
|- | |||
! colspan="2" |Steps | |||
([[Octave reduction|reduced]]) | |||
|41 | |||
(0) | |||
|65 | |||
(24) | |||
|95 | |||
(13) | |||
|115 | |||
(33) | |||
|142 | |||
(19) | |||
|152 | |||
(29) | |||
|168 | |||
(4) | |||
|174 | |||
(10) | |||
|185 | |||
(21) | |||
|199 | |||
(35) | |||
|203 | |||
(39) | |||
|} | |||
{| class="wikitable" | |||
|+Approximation of prime harmonics in 41edo | |||
! colspan="2" |Harmonic | |||
!2 | |||
!3 | |||
!5 | |||
!7 | |||
!11 | |||
![[13/8|13]] | |||
!17 | |||
!19 | |||
!23 | |||
!29 | |||
!31 | |||
|- | |||
! colspan="2" |Just cents ([[Octave reduction|reduced]]) | |||
!1200 | |||
!702 | |||
!386 | |||
!969 | |||
!551 | |||
!841 | |||
!105 | |||
!298 | |||
!628 | |||
!1030 | |||
!1145 | |||
|- | |||
! rowspan="2" |Error | |||
!Absolute ([[Cent|¢]]) | |||
| +0.0 | |||
| +0.5 | |||
| -5.8 | |||
| -3.0 | |||
| +4.8 | |||
| +8.3 | |||
| +12 | |||
| -4.8 | |||
| -14 | |||
| -5.2 | |||
| -3.6 | |||
|- | |||
![[Relative interval error|Relative]] ([[Relative cent|%]]) | |||
| +0.0 | |||
| +1.7 | |||
| -20 | |||
| -10 | |||
| +16 | |||
| +28 | |||
| +41 | |||
| -17 | |||
| -47 | |||
| -18 | |||
| -12 | |||
|- | |- | ||
! colspan="2" |Steps | ! colspan="2" |Steps | ||
Latest revision as of 21:45, 6 December 2024
Two examples of how I personally prefer to round off cents and percentages to whole numbers or 2 significant figures, whichever is more accurate.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | +0.5 | -5.8 | -3.0 | +4.8 | +8.3 | +12 | -4.8 | -14 | -5.2 | -3.6 |
| Relative (%) | +0.0 | +1.7 | -20 | -10 | +16 | +28 | +41 | -17 | -47 | -18 | -12 | |
| Steps
(reduced) |
41
(0) |
65
(24) |
95
(13) |
115
(33) |
142
(19) |
152
(29) |
168
(4) |
174
(10) |
185
(21) |
199
(35) |
203
(39) | |
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Just cents (reduced) | 1200 | 702 | 386 | 969 | 551 | 841 | 105 | 298 | 628 | 1030 | 1145 | |
| Error | Absolute (¢) | +0.0 | +0.5 | -5.8 | -3.0 | +4.8 | +8.3 | +12 | -4.8 | -14 | -5.2 | -3.6 |
| Relative (%) | +0.0 | +1.7 | -20 | -10 | +16 | +28 | +41 | -17 | -47 | -18 | -12 | |
| Steps
(reduced) |
41
(0) |
65
(24) |
95
(13) |
115
(33) |
142
(19) |
152
(29) |
168
(4) |
174
(10) |
185
(21) |
199
(35) |
203
(39) | |