29edo: Difference between revisions
→21st century: Add Claudi Meneghin's ''Porcupine Canon 3-in-1 on the Lament Bass (29EDO)'' (2026) |
m →Stacking fifths: link chords |
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Another possible use for 29edo is as an equally tempered para-pythagorean scale. Using its fifth as a generator leads to a variant of [[garibaldi temperament]] which is not very accurate but which has relatively low 13-limit complexity. However, it gives the POL2 generator for [[Subgroup temperaments #Edson (2.3.7/5.11/5.13/5 subgroup)|edson temperament]] with essentially perfect accuracy, only 0.034 cents sharp of it. | Another possible use for 29edo is as an equally tempered para-pythagorean scale. Using its fifth as a generator leads to a variant of [[garibaldi temperament]] which is not very accurate but which has relatively low 13-limit complexity. However, it gives the POL2 generator for [[Subgroup temperaments #Edson (2.3.7/5.11/5.13/5 subgroup)|edson temperament]] with essentially perfect accuracy, only 0.034 cents sharp of it. | ||
Edson is a 2.3.7/5.11/5.13/5 subgroup temperament, and 29edo represents the 2.3.11/5.13/5 subgroup to very high accuracy, and the 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 (7:11:13) chord, the [[The Archipelago|barbados | Edson is a 2.3.7/5.11/5.13/5 subgroup temperament, and 29edo represents the 2.3.11/5.13/5 subgroup to very high accuracy, and the 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the [[7:11:13|1-11/7-13/7 (7:11:13)]] chord, the [[The Archipelago|barbados]] triad [[10:13:15|1-13/10-3/2 (10:13:15)]], the minor barbados triad [[26:30:39|1-15/13-3/2 (26:30:39)]], the [[22:28:33|1-14/11-3/2 (22:28:33)]] triad, the [[22:26:33|1-13/11-3/2 (22:26:33)]] triad, and the [[petrmic triad]], a 13-limit [[Dyadic chord|essentially tempered dyadic chord]]. | ||
29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the [[k*N subgroups|3*29 subgroup]] 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the [[k*N subgroups|2*29 subgroup]] 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas. | 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the [[k*N subgroups|3*29 subgroup]] 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the [[k*N subgroups|2*29 subgroup]] 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas. | ||