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=== Backslash notation ===

A common shorthand in use in the microtonal community is ''k''\''N'', written with a backslash (\) instead of a forwardslash (/), to refer to an interval with a frequency ratio of 2''k''/''N''. ''k''\''N'' is pronounced "''k'' steps of ''N'' [[edo]]", and ~~suffices to define~~ the meaning of "[[step]]s" in the context of edos (unless talking about steps of specific subsets/scales of some edo).

A common shorthand in use in the microtonal community is ''k''\''N'', written with a backslash (\) instead of a forwardslash (/), to refer to an interval with a frequency ratio of 2''k''/''N''. ''k''\''N'' is pronounced "''k'' steps of ''N'' [[edo]]", and can be derived from the meaning of "[[step]]s" in the context of edos (unless talking about steps of specific subsets/scales of some edo).

~~It is logarithmic because it's common to see~~ expressions like {{nowrap|11\19 − 6\19 {{=}} 5\19}}, ~~which is an additive notation, though the frequency ratios referred to in the definition are linear, which is to say~~:

Steps are linear in the log-frequency domain, so expressions like {{nowrap|11\19 − 6\19 {{=}} 5\19}} hold. In general, we have

: {{nowrap|''a''\''N'' + ''b''\''N'' {{=}} (''a'' + ''b'')\''N''}}

~~: {{nowrap|''a''\''N'' + ''b''\''N'' {{=}} (''a'' + ''b'')\''N''}}~~ expresses the same thing as {{nowrap|2''a''/''N'' × 2''b''/''N'' {{=}} 2(''a'' + ''b'')/''N''.}}

which expresses the same thing as {{nowrap|2''a''/''N'' × 2''b''/''N'' {{=}} 2(''a'' + ''b'')/''N''.}}

Or equivalently, for subtraction/division:

: {{nowrap|''a''\''N'' − ''b''\''N'' {{=}} (''a'' − ''b'')\''N''}} expresses the same thing as {{nowrap|2''a''/''N'' / 2''b''/''N'' {{=}} 2(''a'' - ''b'')/''N''.}}

: {{nowrap|''a''\''N'' − ''b''\''N'' {{=}} (''a'' − ''b'')\''N''}}

which expresses the same thing as {{nowrap|2''a''/''N'' / 2''b''/''N'' {{=}} 2(''a'' - ''b'')/''N''.}}

Backslash notation can be extended to support [[nonoctave]] [[equal tuning]]s by writing the tuning in full after the backslash. For example, 11\13edt means 11 steps of [[13edt]], 14\9edf means 14 steps of [[9edf]], and 7\12ed12/5 means 7 steps of [[12ed12/5]].

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 === Backslash notation ===
-A common shorthand in use in the microtonal community is ''k''\''N'', written with a backslash (\) instead of a forwardslash (/), to refer to an interval with a frequency ratio of 2<sup>''k''/''N''</sup>. ''k''\''N'' is pronounced "''k'' steps of ''N'' [[edo]]", and suffices to define the meaning of "[[step]]s" in the context of edos (unless talking about steps of specific subsets/scales of some edo).
+A common shorthand in use in the microtonal community is ''k''\''N'', written with a backslash (\) instead of a forwardslash (/), to refer to an interval with a frequency ratio of 2<sup>''k''/''N''</sup>. ''k''\''N'' is pronounced "''k'' steps of ''N'' [[edo]]", and can be derived from the meaning of "[[step]]s" in the context of edos (unless talking about steps of specific subsets/scales of some edo).
-It is logarithmic because it's common to see expressions like {{nowrap|11\19 &minus; 6\19 {{=}} 5\19}}, which is an additive notation, though the frequency ratios referred to in the definition are linear, which is to say:
+Steps are linear in the log-frequency domain, so expressions like {{nowrap|11\19 &minus; 6\19 {{=}} 5\19}} hold. In general, we have
+: {{nowrap|''a''\''N'' + ''b''\''N'' {{=}} (''a'' + ''b'')\''N''}}
-: {{nowrap|''a''\''N'' + ''b''\''N'' {{=}} (''a'' + ''b'')\''N''}} expresses the same thing as {{nowrap|2<sup>''a''/''N''</sup> × 2<sup>''b''/''N''</sup> {{=}} 2<sup>(''a'' + ''b'')/''N''</sup>.}}
+which expresses the same thing as {{nowrap|2<sup>''a''/''N''</sup> × 2<sup>''b''/''N''</sup> {{=}} 2<sup>(''a'' + ''b'')/''N''</sup>.}}
 Or equivalently, for subtraction/division:
-: {{nowrap|''a''\''N'' &minus; ''b''\''N'' {{=}} (''a'' &minus; ''b'')\''N''}} expresses the same thing as {{nowrap|2<sup>''a''/''N''</sup> / 2<sup>''b''/''N''</sup> {{=}} 2<sup>(''a'' - ''b'')/''N''</sup>.}}
+: {{nowrap|''a''\''N'' &minus; ''b''\''N'' {{=}} (''a'' &minus; ''b'')\''N''}}
+which expresses the same thing as {{nowrap|2<sup>''a''/''N''</sup> / 2<sup>''b''/''N''</sup> {{=}} 2<sup>(''a'' - ''b'')/''N''</sup>.}}
 Backslash notation can be extended to support [[nonoctave]] [[equal tuning]]s by writing the tuning in full after the backslash. For example, 11\13edt means 11 steps of [[13edt]], 14\9edf means 14 steps of [[9edf]], and 7\12ed12/5 means 7 steps of [[12ed12/5]].