29edo: Difference between revisions
Move temperament measures to RTT properties section |
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! colspan="2" | [[ | ! colspan="2" | [[Nearest edomapping]] | ||
| 29 | | 29 | ||
| 17 | | 17 | ||
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| 20 | | 20 | ||
|- | |- | ||
! colspan="2" | [[ | ! colspan="2" | [[Fifthspan]] | ||
| 0 | | 0 | ||
| +1 | | +1 | ||
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== Intervals == | == Intervals == | ||
{{See also| 29edo solfege }} | |||
{| class="wikitable center-all right-2 left-3" | {| class="wikitable center-all right-2 left-3" | ||
|- | |- | ||
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| | | | ||
|} | |} | ||
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors: | Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors: | ||
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|} | |} | ||
== | == JI approximation == | ||
=== 15-odd-limit interval mappings === | |||
The following table shows how [[15-odd-limit intervals]] are represented in 29edo. Prime harmonics are in '''bold'''. | The following table shows how [[15-odd-limit intervals]] are represented in 29edo. Prime harmonics are in '''bold'''. | ||
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|} | |} | ||
== | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | |||
{| class="wikitable center- | ! rowspan="2" | Subgroup | ||
! | ! rowspan="2" | [[Comma list]] | ||
! | ! rowspan="2" | [[Mapping]] | ||
! | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! | ! colspan="2" | Tuning error | ||
! | |- | ||
! | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | |||
| {{monzo| 46 -29 }} | |||
| [{{val| 29 46 }}] | |||
| -0.47 | | -0.47 | ||
| 0.47 | |||
| 1.14 | |||
|- | |||
| 2.3.5 | |||
| 250/243, 16875/16384 | |||
| [{{val| 29 46 67 }}] | |||
| +1.68 | | +1.68 | ||
| 3.07 | |||
| 7.41 | |||
|- | |||
| 2.3.5.7 | |||
| 49/48, 225/224, 250/243 | |||
| [{{val| 29 46 67 81 }}] | |||
| +2.78 | | +2.78 | ||
| 3.28 | |||
| 7.91 | |||
|- | |||
| 2.3.5.7.11 | |||
| 49/48, 55/54, 100/99, 225/224 | |||
| [{{val| 29 46 67 81 100 }}] | |||
| +3.00 | | +3.00 | ||
| 2.97 | |||
| 7.15 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 49/48, 55/54, 100/99, 105/104, 225/224 | |||
| [{{val| 29 46 67 81 100 107 }}] | |||
| +3.09 | | +3.09 | ||
| 2.71 | | 2.71 | ||
| 6.54 | | 6.54 | ||
|} | |} | ||
== Commas == | === Commas === | ||
29edo [[tempers out]] the following [[comma]]s. This assumes the [[patent val]] {{val| 29 46 67 81 100 107 }}. Cent values are rounded to 5 digits. | 29edo [[tempers out]] the following [[comma]]s. This assumes the [[patent val]] {{val| 29 46 67 81 100 107 }}. Cent values are rounded to 5 digits. | ||
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<references/> | <references/> | ||
== Linear temperaments == | === Linear temperaments === | ||
* [[List of 29et rank two temperaments by badness]] | * [[List of 29et rank two temperaments by badness]] | ||
Important MOSes include: | Important MOSes include: | ||
* [[leapfrog]] diatonic [[5L 2s]] 5552552 (17\29, 1\1) | * [[leapfrog]] diatonic [[5L 2s]] 5552552 (17\29, 1\1) | ||
* [[leapfrog]] chromatic [[5L 7s]] 3232323223232322 (17\29, 1\1) | * [[leapfrog]] chromatic [[5L 7s]] 3232323223232322 (17\29, 1\1) | ||
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=== Nicetone === | === Nicetone === | ||
29edo is not a meantone system, but it could nonetheless be used as a basis for common-practice music if one considers the superfourth as a consonant, alternative type of fourth, and the 11:13:16 as an alternative type of consonant "doubly minor" triad. We can then use a diatonic scale such as 5435453 (which resembles Didymus' 5-limit JI diatonic scale, but with the syntonic comma being exaggerated in size). This scale has a very similar harmonic structure to a meantone diatonic scale, except that one of its minor triads is doubly-minor. | 29edo is not a meantone system, but it could nonetheless be used as a basis for common-practice music if one considers the superfourth as a consonant, alternative type of fourth, and the 11:13:16 as an alternative type of consonant "doubly minor" triad. We can then use a diatonic scale such as 5435453 (which resembles Didymus' 5-limit JI diatonic scale, but with the syntonic comma being exaggerated in size). This scale has a very similar harmonic structure to a meantone diatonic scale, except that one of its minor triads is doubly-minor. | ||