1489edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | |- | ||
! rowspan="2" |[[Comma list | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" |Optimal<br>8ve | ! rowspan="2" | [[Mapping]] | ||
! colspan="2" |Tuning | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
|- | ! colspan="2" | Tuning error | ||
![[TE error|Absolute]] (¢) | |- | ||
![[TE simple badness|Relative]] (%) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo|-2360 1489}} | | {{monzo|-2360 1489}} | ||
| {{mapping|1489 2360}} | | {{mapping|1489 2360}} | ||
| 0.0023 | | +0.0023 | ||
| 0.0023 | | 0.0023 | ||
| 0.29 | | 0.29 | ||
| Line 32: | Line 33: | ||
| {{monzo|54 -37 2}}, {{monzo|-73 -14 41}} | | {{monzo|54 -37 2}}, {{monzo|-73 -14 41}} | ||
| {{mapping|1489 2360 3457}} | | {{mapping|1489 2360 3457}} | ||
| 0.0422 | | +0.0422 | ||
| 0.0564 | | 0.0564 | ||
| 7.00 | | 7.00 | ||
| Line 39: | Line 40: | ||
| 420175/419904, 703125/702464, {{monzo|49 -27 7 -8}} | | 420175/419904, 703125/702464, {{monzo|49 -27 7 -8}} | ||
| {{mapping|1489 2360 3457 4180}} | | {{mapping|1489 2360 3457 4180}} | ||
| 0.0425 | | +0.0425 | ||
| 0.0488 | | 0.0488 | ||
| 6.06 | | 6.06 | ||
| Line 46: | Line 47: | ||
| 3025/3024, 759375/758912, 420175/419904, 32768000000/32750405919 | | 3025/3024, 759375/758912, 420175/419904, 32768000000/32750405919 | ||
| {{mapping|1489 2360 3457 4180 5151}} | | {{mapping|1489 2360 3457 4180 5151}} | ||
| 0.0384 | | +0.0384 | ||
| 0.0444 | | 0.0444 | ||
| 5.51 | | 5.51 | ||
| Line 53: | Line 54: | ||
| 3025/3024, 4225/4224, 91125/91091, 256000/255879, 420175/419904 | | 3025/3024, 4225/4224, 91125/91091, 256000/255879, 420175/419904 | ||
| {{mapping|1489 2360 3457 4180 5151 5510}} | | {{mapping|1489 2360 3457 4180 5151 5510}} | ||
| 0.0303 | | +0.0303 | ||
| 0.0444 | | 0.0444 | ||
| 5.51 | | 5.51 | ||
| Line 60: | Line 61: | ||
| 3025/3024, 2500/2499, 4225/4224, 56595/56576, 57375/57344, 256000/255879 | | 3025/3024, 2500/2499, 4225/4224, 56595/56576, 57375/57344, 256000/255879 | ||
| {{mapping|1489 2360 3457 4180 5151 5510 6086}} | | {{mapping|1489 2360 3457 4180 5151 5510 6086}} | ||
| 0.0325 | | +0.0325 | ||
| 0.0414 | | 0.0414 | ||
| 5.14 | | 5.14 | ||
Latest revision as of 18:21, 20 February 2025
| ← 1488edo | 1489edo | 1490edo → |
1489 equal divisions of the octave (abbreviated 1489edo or 1489ed2), also called 1489-tone equal temperament (1489tet) or 1489 equal temperament (1489et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1489 equal parts of about 0.806 ¢ each. Each step represents a frequency ratio of 21/1489, or the 1489th root of 2.
Theory
1489edo is consistent to the 21-odd-limit. As an equal temperament, it tempers out 3025/3024 in the 11-limit; 4225/4224 and 256000/255879 in the 13-limit; 2500/2499, 5985/5984, and 57375/57344 in the 17-limit; 6175/6174 in the 19-limit. Using the 2.3.11.17.19.37 subgroup, it tempers out 3553/3552. It supports qak.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.007 | -0.283 | -0.122 | -0.075 | +0.036 | -0.187 | -0.132 | +0.335 | +0.376 | +0.163 |
| Relative (%) | +0.0 | -0.9 | -35.1 | -15.1 | -9.4 | +4.5 | -23.2 | -16.4 | +41.6 | +46.6 | +20.2 | |
| Steps (reduced) |
1489 (0) |
2360 (871) |
3457 (479) |
4180 (1202) |
5151 (684) |
5510 (1043) |
6086 (130) |
6325 (369) |
6736 (780) |
7234 (1278) |
7377 (1421) | |
Subsets and supersets
1489edo is the 237th prime edo.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-2360 1489⟩ | [⟨1489 2360]] | +0.0023 | 0.0023 | 0.29 |
| 2.3.5 | [54 -37 2⟩, [-73 -14 41⟩ | [⟨1489 2360 3457]] | +0.0422 | 0.0564 | 7.00 |
| 2.3.5.7 | 420175/419904, 703125/702464, [49 -27 7 -8⟩ | [⟨1489 2360 3457 4180]] | +0.0425 | 0.0488 | 6.06 |
| 2.3.5.7.11 | 3025/3024, 759375/758912, 420175/419904, 32768000000/32750405919 | [⟨1489 2360 3457 4180 5151]] | +0.0384 | 0.0444 | 5.51 |
| 2.3.5.7.11.13 | 3025/3024, 4225/4224, 91125/91091, 256000/255879, 420175/419904 | [⟨1489 2360 3457 4180 5151 5510]] | +0.0303 | 0.0444 | 5.51 |
| 2.3.5.7.11.13.17 | 3025/3024, 2500/2499, 4225/4224, 56595/56576, 57375/57344, 256000/255879 | [⟨1489 2360 3457 4180 5151 5510 6086]] | +0.0325 | 0.0414 | 5.14 |