29edo: Difference between revisions
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=Theory= | == Theory == | ||
29edo divides the 2:1 [[Octave|octave]] into 29 equal steps of approximately 41.37931 [[cent|cents]]. It is the 10th [[prime_numbers|prime]] edo, following [[23edo|23edo]] and coming before [[31edo|31edo]]. | 29edo divides the 2:1 [[Octave|octave]] into 29 equal steps of approximately 41.37931 [[cent|cents]]. It is the 10th [[prime_numbers|prime]] edo, following [[23edo|23edo]] and coming before [[31edo|31edo]]. | ||
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A more coincidental similarity is that just as the 12-tone scale is also a 1/2-tone scale (the whole tone being divided into 2 semitones), the 29-tone temperament may also be called 2/9-tone. This is because it has two different sizes of whole tone (4 and 5 steps wide, respectively). So the step size of 29edo may be called a 2/9-tone, just as 24edo's step size is called a quarter tone. | A more coincidental similarity is that just as the 12-tone scale is also a 1/2-tone scale (the whole tone being divided into 2 semitones), the 29-tone temperament may also be called 2/9-tone. This is because it has two different sizes of whole tone (4 and 5 steps wide, respectively). So the step size of 29edo may be called a 2/9-tone, just as 24edo's step size is called a quarter tone. | ||
=Intervals= | == Intervals == | ||
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==Selected just intervals by error== | === Selected just intervals by error === | ||
The following table shows how [[Just-24|some prominent just intervals]] are represented in 29edo (ordered by absolute error). | The following table shows how [[Just-24|some prominent just intervals]] are represented in 29edo (ordered by absolute error). | ||
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=Commas= | == Commas == | ||
29 EDO tempers out the following [[commas]]. (Note: This assumes the val < [http://tel.wikispaces.com/29_46_67_81_100_107 29 46 67 81 100 107] |, cent values rounded to 5 digits.) | 29 EDO tempers out the following [[commas]]. (Note: This assumes the val < [http://tel.wikispaces.com/29_46_67_81_100_107 29 46 67 81 100 107] |, cent values rounded to 5 digits.) | ||
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=Linear temperaments= | == Linear temperaments == | ||
[[List_of_29et_rank_two_temperaments_by_badness|List of 29et rank two temperaments by badness]] | [[List_of_29et_rank_two_temperaments_by_badness|List of 29et rank two temperaments by badness]] | ||
==The Tetradecatonic System== | === The Tetradecatonic System === | ||
A variant of porcupine supported in 29edo is [[Nautilus|nautilus]], which splits the porcupine generator in half (tempering out 50:49 in the process), thus resulting in a different mapping for 7 than standard porcupine. Nautilus also extends to the 13-limit much more easily than does standard porcupine. | A variant of porcupine supported in 29edo is [[Nautilus|nautilus]], which splits the porcupine generator in half (tempering out 50:49 in the process), thus resulting in a different mapping for 7 than standard porcupine. Nautilus also extends to the 13-limit much more easily than does standard porcupine. | ||
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If one can tolerate the tuning error (which is roughly equal to that of 12edo, albeit in the opposite direction for the 5- and 7-limits), this tetradecatonic scale is worth exploring. 29edo is often neglected since it falls so close to the much more popular and well-studied 31edo, but 29 does have its own advantages, and this is one of them. | If one can tolerate the tuning error (which is roughly equal to that of 12edo, albeit in the opposite direction for the 5- and 7-limits), this tetradecatonic scale is worth exploring. 29edo is often neglected since it falls so close to the much more popular and well-studied 31edo, but 29 does have its own advantages, and this is one of them. | ||
==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. | ||
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Nicetone scale 5435453 and cadence in 29edo | Nicetone scale 5435453 and cadence in 29edo | ||
=Scales= | == Scales == | ||
* [[bridgetown9|bridgetown9]] | * [[bridgetown9|bridgetown9]] | ||
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* [http://www.youtube.com/watch?v=uP2Z4Gy8lds Escala Tonal de 17 tonos - Charles Loli] | * [http://www.youtube.com/watch?v=uP2Z4Gy8lds Escala Tonal de 17 tonos - Charles Loli] | ||
=Instruments= | == Instruments == | ||
[http://www.microtonalismo.com/proyecto-xvii Guitar 29EDO from Peru - Charles Loli and Antonio Huamani] | [http://www.microtonalismo.com/proyecto-xvii Guitar 29EDO from Peru - Charles Loli and Antonio Huamani] | ||
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</div> | </div> | ||
=Music= | == Music == | ||
* [http://www.microtonalismo.com/el-teclado-29-edo Mp3 29EDO - Escala tonal de 17 notas]by [http://musicool.us/musicool/armonia.htm Charles Loli A.] | * [http://www.microtonalismo.com/el-teclado-29-edo Mp3 29EDO - Escala tonal de 17 notas]by [http://musicool.us/musicool/armonia.htm Charles Loli A.] | ||