45/28: Difference between revisions
Jump to navigation
Jump to search
+ twelfth complement |
Rework to reflect the progress thanks to the establishment of the aberschisma |
||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox Interval | {{Infobox Interval | ||
| Name = septimal wide minor sixth, marvel-ptolemaic minor sixth, | | Name = septimal wide minor sixth, marvel-ptolemaic minor sixth, aberschismic augmented fifth | ||
| Color name = ry5, ruyo 5th | | Color name = ry5, ruyo 5th | ||
}} | }} | ||
'''45/28''', the '''septimal wide minor sixth''' | '''45/28''', conventionally known as the '''septimal wide minor sixth''' or '''marvel-ptolemaic minor sixth''', is an interval that is sharp of the [[128/81|Pythagorean minor sixth]] by [[3645/3584]], i.e. a [[81/80|syntonic comma]] plus a [[225/224|marvel comma]]. However, it functions more commonly as an augmented fifth, sharp of the [[6561/4096|Pythagorean augmented fifth]] by an [[aberschisma]]. This gives rise to the more precise name '''aberschismic augmented fifth''', and in fact it arises as the result of stacking certain [[9-odd-limit]] consonances – of [[5/4]] and [[9/7]], and of [[9/8]] and [[10/7]]. | ||
== Temperaments == | |||
[[Marvel]] tempering equates this interval with the [[8/5|classical minor sixth]] and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into [[essentially tempered chord]]s. | |||
== Approximation == | |||
This interval is only a third of a [[cent]] sharper than 13\19, the minor sixth of [[19edo]]. | |||
{{Interval edo approximation|45/28}} | |||
== See also == | == See also == | ||
| Line 14: | Line 22: | ||
[[Category:Fifth]] | [[Category:Fifth]] | ||
[[Category:Augmented fifth]] | [[Category:Augmented fifth]] | ||
[[Category: | [[Category:Aberschismic]] | ||
{{Todo|add sound example}} | {{Todo|add sound example}} | ||
Latest revision as of 19:32, 30 July 2026
| Interval information |
marvel-ptolemaic minor sixth,
aberschismic augmented fifth
45/28, conventionally known as the septimal wide minor sixth or marvel-ptolemaic minor sixth, is an interval that is sharp of the Pythagorean minor sixth by 3645/3584, i.e. a syntonic comma plus a marvel comma. However, it functions more commonly as an augmented fifth, sharp of the Pythagorean augmented fifth by an aberschisma. This gives rise to the more precise name aberschismic augmented fifth, and in fact it arises as the result of stacking certain 9-odd-limit consonances – of 5/4 and 9/7, and of 9/8 and 10/7.
Temperaments
Marvel tempering equates this interval with the classical minor sixth and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into essentially tempered chords.
Approximation
This interval is only a third of a cent sharper than 13\19, the minor sixth of 19edo.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 3 | 2\3 | 800.00 | -21.40 | -5.35 |
| 16 | 11\16 | 825.00 | +3.60 | +4.80 |
| 19 | 13\19 | 821.05 | -0.35 | -0.55 |
| 22 | 15\22 | 818.18 | -3.22 | -5.90 |
| 32 | 22\32 | 825.00 | +3.60 | +9.61 |
| 35 | 24\35 | 822.86 | +1.46 | +4.26 |
| 38 | 26\38 | 821.05 | -0.35 | -1.09 |
| 41 | 28\41 | 819.51 | -1.89 | -6.44 |
| 51 | 35\51 | 823.53 | +2.13 | +9.06 |
| 54 | 37\54 | 822.22 | +0.82 | +3.71 |
| 57 | 39\57 | 821.05 | -0.35 | -1.64 |
| 60 | 41\60 | 820.00 | -1.40 | -6.99 |
| 70 | 48\70 | 822.86 | +1.46 | +8.51 |
| 73 | 50\73 | 821.92 | +0.52 | +3.16 |
| 76 | 52\76 | 821.05 | -0.35 | -2.19 |
| 79 | 54\79 | 820.25 | -1.14 | -7.54 |