Chain-of-fifths notation: Difference between revisions

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EDOs that are best supported by this system are those whose fifth does not deviate too much from the pure fifth [[3/2]] (702 cent) and that can be represented by only one ring of fifths. 24edo, as a counter-example to this, contains two rings. If we as well demand that whole tones (2*P5 - P8), diatonic semitones (3*P8 - 5*P5), and chromatic semitones (shifts caused by one accidental, 7*P5 - 4*P8), use a positive number of steps, we lose all EDOs below 12 EDO and also {{EDOs| 13, 16, 18, and 23 }}.

EDOs up to 100 are listed in the following table. The unit (if not stated otherwise) is ''steps'' of the corresponding EDO which is given in the first column of each row.

== EDOs up to 100 ==

EDOs up to 100 are listed in the following table. The unit (if not stated otherwise) is ''steps'' of the corresponding EDO which is given in the first column of each row. The list contains only those EDOs whose all degrees can be reached by fifth steps.

{| class="wikitable center-all"

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| 58 || +1.1 ( +8.9%) || 17 || 7 || 10

|}

== See also ==

* [[Alternative symbols for ups and downs notation]] -- system that supports sub-circles

* [[User:Xenwolf/cofn]] -- sortable table with more intervals (all fifths within the interval [4\7, 3\5])

[[Category:Notation]]

[[Category:Method]]

@@ Line 3: / Line 3: @@
 EDOs that are best supported by this system are those whose fifth does not deviate too much from the pure fifth [[3/2]] (702 cent) and that can be represented by only one ring of fifths. 24edo, as a counter-example to this, contains two rings. If we as well demand that whole tones (2*P5 - P8), diatonic semitones (3*P8 - 5*P5), and chromatic semitones (shifts caused by one accidental, 7*P5 - 4*P8), use a positive number of steps, we lose all EDOs below 12 EDO and also {{EDOs| 13, 16, 18, and 23 }}.
-EDOs up to 100 are listed in the following table. The unit (if not stated otherwise) is ''steps'' of the corresponding EDO which is given in the first column of each row.
+== EDOs up to 100 ==
+EDOs up to 100 are listed in the following table. The unit (if not stated otherwise) is ''steps'' of the corresponding EDO which is given in the first column of each row. The list contains only those EDOs whose all degrees can be reached by fifth steps.
 {| class="wikitable center-all"
@@ Line 163: / Line 165: @@
 | 58 ||  +1.1 ( +8.9%) || 17 ||  7 || 10
 |}
+== See also ==
+* [[Alternative symbols for ups and downs notation]] -- system that supports sub-circles
+* [[User:Xenwolf/cofn]] -- sortable table with more intervals (all fifths within the interval [4\7, 3\5])
 [[Category:Notation]]
 [[Category:Method]]