User:BudjarnLambeth/1ed237.8c: Difference between revisions
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{{Infobox ET|1ed187/163}} | {{Infobox ET|1ed187/163}} | ||
'''1 equal division of 237.8¢''' ('''1ed237.8c'''), also known as '''arithmetic pitch sequence of 237.8¢''' ('''APS237.8¢'''), is an [[Equal|equal]] [[ | '''1 equal division of 237.8¢''' ('''1ed237.8c'''), also known as '''arithmetic pitch sequence of 237.8¢''' ('''APS237.8¢'''), is an [[Equal-step tuning|equal]] and [[nonoctave]] scale generated by making a continuous chain of intervals of exactly 237.8¢. | ||
It is almost exactly [[8edt]], but retuned to have a slightly more acceptable pseudo-[[octave]]. It could be seen as a compromise between 8edt and [[5edo]], though leaning heavily towards 8edt. | |||
It can also be thought of as '''1ed187/163''' as [[187/163]] equals 237.800 cents. | |||
==Methodology== | |||
[[Budjarn Lambeth]] arrived at this scale by looking at every possible 1ed23x.y¢ and 1ed24x.y¢ in [[Scale Workshop]], noodling in each of them, adjusting the [[generator]] up and down by 0.1-cent increments until he found the one that sounded most pleasing to his ear. | |||
==Harmonics== | |||
{{harmonics in cet|237.8|prec=1|columns=11}} | |||
5edo, [[8edt]], [[14ed7]] for comparison: | |||
{{Harmonics in equal|5|intervals=integer|prec=1|collapsed=1}} | |||
{{Harmonics in equal|8|3|1|intervals=integer|prec=1|collapsed=1}} | |||
{{Harmonics in equal|14|7|1|intervals=integer|prec=1|collapsed=1}} | |||
==Intervals== | ==Intervals== | ||
| Line 9: | Line 25: | ||
! | Degree of 1ed65c | ! | Degree of 1ed65c | ||
! | Cents Value | ! | Cents Value | ||
! | Approximate ratio | |||
|- | |- | ||
| | 0 | | | 0 | ||
| | 0 | | | 0 | ||
| | 1/1 | |||
|- | |- | ||
| | 1 | | | 1 | ||
| | 237.8 | | | 237.8 | ||
| | 8/7 | |||
|- | |- | ||
| | 2 | | | 2 | ||
| | 475.6 | | | 475.6 | ||
| | 37/28 | |||
|- | |- | ||
| | 3 | | | 3 | ||
| | 713.4 | | | 713.4 | ||
| | 3/2 | |||
|- | |- | ||
| | 4 | | | 4 | ||
| | 951.2 | | | 951.2 | ||
| | 7/4 | |||
|- | |- | ||
| | 5 | | | 5 | ||
| | 1189.0 | | | 1189.0 | ||
| | 2/1 | |||
|- | |- | ||
| | 6 | | | 6 | ||
| | 1426.8 | | | 1426.8 | ||
| | 16/7 | |||
|- | |- | ||
| | 7 | | | 7 | ||
| | 1664.6 | | | 1664.6 | ||
| | 73/28 | |||
|- | |- | ||
| | 8 | | | 8 | ||
| | 1902.4 | | | 1902.4 | ||
| | 3/1 | |||
|} | |} | ||
==Scala files == | |||
<pre> | |||
! 1ed237pt8oct.scl | |||
! | |||
1 equal division of 237.8, octave repeating | |||
5 | |||
! | |||
237.800000 | |||
475.600000 | |||
713.400000 | |||
951.200000 | |||
1189.000000 | |||
</pre> | |||
<pre> | |||
! 1ed237pt8tri.scl | |||
! | |||
1 equal division of 237.8, tritave repeating | |||
8 | |||
! | |||
237.800000 | |||
475.600000 | |||
713.400000 | |||
951.200000 | |||
1189.000000 | |||
1426.800000 | |||
1664.600000 | |||
1902.400000 | |||
</pre> | |||
== See also == | |||
* [[Gallery of arithmetic pitch sequences]] | |||
[[Category:5-tone scales]] | |||
[[Category:Tempered scales]] | |||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
[[Category: | [[Category:Pages with Scala files]] | ||