User:BudjarnLambeth/1ed148.5c: Difference between revisions
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{{Infobox ET|8ed1869/941}} | {{Infobox ET|8ed1869/941}} | ||
'''1 equal division of 148.5¢''' ('''1ed148.5c'''), also known as '''arithmetic pitch sequence of 148.5¢''' ('''APS148.5¢'''), is an [[ | '''1 equal division of 148.5¢''' ('''1ed148.5c'''), also known as '''arithmetic pitch sequence of 148.5¢''' ('''APS148.5¢'''), is an [[equal]] and [[nonoctave]] scale generated by making a continuous chain of intervals of exactly 148.5 [[cents]]. | ||
It is closely related to [[8edo]]. 1ed148.5c can be seen as a [[octave shrinking|compressed-octave]] version of 8edo. | It is closely related to [[8edo]]. 1ed148.5c can be seen as a [[octave shrinking|compressed-octave]] version of 8edo. | ||
It can be treated as an equalized variant of the [[octatonic scale]] from mainstream 12edo music theory, a.k.a. the scale [[diminished]][8]. | It can be treated as an equalized variant of the [[octatonic scale]] from mainstream [[12edo]] music theory, a.k.a. a variant of the scale [[diminished]][8]. | ||
== Harmonics == | == Harmonics == | ||
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In other words, 1ed148.5c upgrades 8edo into a strong low-[[complexity]] tuning for the 2.11.13.17.31 [[subgroup]]. | In other words, 1ed148.5c upgrades 8edo into a strong low-[[complexity]] tuning for the 2.11.13.17.31 [[subgroup]]. | ||
{{Harmonics in cet| 148.5 |intervals=prime|columns=11}} | {{Harmonics in cet| 148.5 |intervals=prime|columns=11}} | ||
{{Harmonics in equal| 29 | 12 | 1 |intervals=prime|columns=11|title=29ed12, for comparison|collapsed=yes}} | |||
{{Harmonics in equal| 8 |intervals=prime|columns=11|title=8edo, for comparison|collapsed=yes}} | {{Harmonics in equal| 8 |intervals=prime|columns=11|title=8edo, for comparison|collapsed=yes}} | ||
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So while the composite subgroup of 8edo could be described as '''2.19.27''', the composite subgroup of 1ed148.5c could be described as '''2.6.11.13.17.20.25'''. This provides 1ed148.5c with a comparatively larger, more diverse array of [[consonance]]s. | So while the composite subgroup of 8edo could be described as '''2.19.27''', the composite subgroup of 1ed148.5c could be described as '''2.6.11.13.17.20.25'''. This provides 1ed148.5c with a comparatively larger, more diverse array of [[consonance]]s. | ||
==== Integer harmonics in | ==== Integer harmonics in 1ed148.5c ==== | ||
{{Harmonics in cet| 148.5 |intervals=integer|columns=8|start=1|title= | {{Harmonics in cet| 148.5 |intervals=integer|columns=8|start=1|title=1ed148.5c}} | ||
{{Harmonics in cet| 148.5 |intervals=integer|columns=9|start=9|title=contd.}} | {{Harmonics in cet| 148.5 |intervals=integer|columns=9|start=9|title=contd.}} | ||
{{Harmonics in cet| 148.5 |intervals=integer|columns=9|start=18|title=contd.}} | {{Harmonics in cet| 148.5 |intervals=integer|columns=9|start=18|title=contd.}} | ||
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|2 | |2 | ||
|297.0 | |297.0 | ||
|13/11 | |13/11, 24/20 | ||
| | |Reduces to 6/5 | ||
|- | |- | ||
|3 | |3 | ||
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|4 | |4 | ||
|594.0 | |594.0 | ||
|17/12 | |17/12, 24/17 | ||
| | |17/6 in the next octave | ||
|- | |- | ||
|5 | |5 | ||
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|1039.5 | |1039.5 | ||
|11/6, 20/11 | |11/6, 20/11 | ||
| | |11/3 in the next octave | ||
|- | |- | ||
|8 | |8 | ||
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Scale degrees 0, 4, 6, 7, 8 create the [[pentad]] 12:17:20:22:24. Any subset of this chord can be a consonance in its own right too. | Scale degrees 0, 4, 6, 7, 8 create the [[pentad]] 12:17:20:22:24. Any subset of this chord can be a consonance in its own right too. | ||
Scale degrees 0, 3, 4, 8 create the [[tetrad]] 17:22:24:34. Any subset of this chord can be a consonance in its own right too. | |||
== Notation == | == Notation == | ||