Spiral chart: Difference between revisions
→Spirals of twelve fifths: added 41edo spiral in table form |
→Spirals of other amounts, other intervals: added a table of 27edo |
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A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] into a self-similar spiral shape, so that it may be compared with a circle of the same interval in a smaller coprime edo. | A '''spiral chart''' is an illustration which converts a circle of repeats of an interval in one [[edo]] into a self-similar spiral shape, so that it may be compared with a circle of the same interval in a smaller coprime edo. | ||
Spiral charts were invented by [[Kite Giedraitis]] | Spiral charts were invented by [[Kite Giedraitis]] no later than April 2014. | ||
== Spirals of twelve fifths == | == Spirals of twelve fifths == | ||
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Such a spiral chart can be made for any two edos, as long as they are coprime. It's often a spiral of something other than fifths. In fact, it's a spiral of the [[User:TallKite/The delta method|nearest miss]]. | Such a spiral chart can be made for any two edos, as long as they are coprime. It's often a spiral of something other than fifths. In fact, it's a spiral of the [[User:TallKite/The delta method|nearest miss]]. | ||
For example, consider [[8edo]] and [[27edo]]. The near misses are 3\8 and 10\27. You get an 8-spoke spiral of 27edo major 3rds. This might be useful for someone researching [[octatonic]] scales in 27edo. | For example, consider [[8edo]] and [[27edo]]. The near misses are 3\8 and 10\27. You get an 8-spoke spiral of 27edo major 3rds. This might be useful for someone researching [[octatonic]] scales in 27edo. To follow the circle of 3rds, read the columns left to right, and within each column read top to bottom. | ||
{| class="wikitable" | |||
|+27edo intervals as a circle of major 3rds, grouped into 8 categories | |||
!Tritones | |||
| | |||
|A4 = v5 | |||
|vA4 = vv5 | |||
|^^4 = ^d5 | |||
|^4 = d5 | |||
|- | |||
!Middish 7ths | |||
| | |||
|vM7 | |||
|~7 | |||
|^m7 | |||
|m7 | |||
|- | |||
!Minorish 3rds | |||
| | |||
|~3 | |||
|^m3 | |||
|m3 | |||
|(M2) | |||
|- | |||
!Minorish 6ths | |||
| | |||
|^m6 | |||
|m6 | |||
|vm6 | |||
| | |||
|- | |||
!Perfectish 1sns / 8ves | |||
| | |||
|^1 | |||
|P1 | |||
|v8 | |||
| | |||
|- | |||
!Majorish 3rds | |||
| | |||
|^M3 | |||
|M3 | |||
|vM3 | |||
| | |||
|- | |||
!Majorish 6ths | |||
|(m7) | |||
|M6 | |||
|vM6 | |||
|~6 | |||
| | |||
|- | |||
!Middish 2nds | |||
|M2 | |||
|vM2 | |||
|~2 | |||
|^m2 | |||
| | |||
|- | |||
!Tritones | |||
|A4 = v5 | |||
|vA4 = vv5 | |||
|^^4 = ^d5 | |||
|^4 = d5 | |||
| | |||
|} | |||
== Relationship to the scale tree == | == Relationship to the scale tree == | ||