User:TallKite/41edo: Difference between revisions
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→Prime harmonics: another way to show cents |
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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 | ||
| - | | -20 | ||
| -10 | | -10 | ||
| +16 | | +16 | ||
| +28 | | +28 | ||
| +41 | | +41 | ||
| - | | -17 | ||
| - | | -47 | ||
| - | | -18 | ||
| -12 | | -12 | ||
|- | |- | ||
! colspan="2" |Steps | ! colspan="2" |Steps | ||
| Line 70: | Line 71: | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Approximation of prime harmonics in 41edo | |+Approximation of prime harmonics in 41edo | ||
! colspan | ! colspan="2" |Harmonic | ||
!2 | !2 | ||
!3 | !3 | ||
| Line 76: | Line 77: | ||
!7 | !7 | ||
!11 | !11 | ||
!13 | ![[13/8|13]] | ||
!17 | !17 | ||
!19 | !19 | ||
| Line 83: | Line 84: | ||
!31 | !31 | ||
|- | |- | ||
! | ! colspan="2" |Just cents ([[Octave reduction|reduced]]) | ||
! | !1200 | ||
! | !702 | ||
! | !386 | ||
! | !969 | ||
! | !551 | ||
! | !841 | ||
! | !105 | ||
! | !298 | ||
! | !628 | ||
! | !1030 | ||
!1145 | |||
|- | |- | ||
! rowspan="2" |Error | ! rowspan="2" |Error | ||
| Line 103: | Line 105: | ||
| +4.8 | | +4.8 | ||
| +8.3 | | +8.3 | ||
| +12 | | +12 | ||
| -4.8 | | -4.8 | ||
| - | | -14 | ||
| -5.2 | | -5.2 | ||
| -3.6 | | -3.6 | ||
| Line 112: | Line 114: | ||
| +0.0 | | +0.0 | ||
| +1.7 | | +1.7 | ||
| - | | -20 | ||
| -10 | | -10 | ||
| +16 | | +16 | ||
| +28 | | +28 | ||
| +41 | | +41 | ||
| - | | -17 | ||
| - | | -47 | ||
| - | | -18 | ||
| -12 | | -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) | |