Kite's thoughts on enharmonic unisons: Difference between revisions

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The notation of every temperament, including every edo, has at least one '''enharmonic unison''', abbreviated as '''EU''' (with one rare exception, see below). An EU is by definition enharmonically equivalent to a perfect unison. (''Enharmonically equivalent'' is used here in the modern sense of "the same exact pitch, merely named differently".) Any note or interval can be respelled by adding or subtracting an EU.

For example, in 12edo, {{nowrap|A4 {{=}} d5}} and {{nowrap|F♯ {{=}} G♭}}. Such equivalences result from adding or subtracting a diminished 2nd, abbreviated as d2. But in 19edo, {{nowrap|A4 {{=}} dd5}} and {{nowrap|F♯ {{=}} G𝄫}}. 19edo's EU is the dd2.

For example, in 12edo, {{nowrap|A4 {{=}} d5}} and {{nowrap|F♯ {{=}} G♭}}. Such equivalences result from adding or subtracting a diminished 2nd, abbreviated as d2. But in 19edo, {{nowrap|A4 {{=}} dd5}} and {{nowrap|F♯ {{=}} G𝄫}}. 19edo's EU is the dd2, a double-diminished 2nd. As these two examples show, an enharmonic unison may actually be not a unison but a second.

EUs are very useful for respelling notes and intervals less awkwardly. For example, in 12edo we can add a d2 to {{nowrap|B♯}} to convert it to C, or we can subtract a d2 from a diminished 4th to get a major 3rd.

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 The notation of every temperament, including every edo, has at least one '''enharmonic unison''', abbreviated as '''EU''' (with one rare exception, see below). An EU is by definition enharmonically equivalent to a perfect unison. (''Enharmonically equivalent'' is used here in the modern sense of "the same exact pitch, merely named differently".) Any note or interval can be respelled by adding or subtracting an EU.
-For example, in 12edo, {{nowrap|A4 {{=}} d5}} and {{nowrap|F&#x266F; {{=}} G&#x266D;}}. Such equivalences result from adding or subtracting a diminished 2nd, abbreviated as d2. But in 19edo, {{nowrap|A4 {{=}} dd5}} and {{nowrap|F&#x266F; {{=}} G&#x1D12B;}}. 19edo's EU is the dd2.
+For example, in 12edo, {{nowrap|A4 {{=}} d5}} and {{nowrap|F&#x266F; {{=}} G&#x266D;}}. Such equivalences result from adding or subtracting a diminished 2nd, abbreviated as d2. But in 19edo, {{nowrap|A4 {{=}} dd5}} and {{nowrap|F&#x266F; {{=}} G&#x1D12B;}}. 19edo's EU is the dd2, a double-diminished 2nd. As these two examples show, an enharmonic unison may actually be not a unison but a second.
 EUs are very useful for respelling notes and intervals less awkwardly. For example, in 12edo we can add a d2 to {{nowrap|B&#x266F;}} to convert it to C, or we can subtract a d2 from a diminished 4th to get a major 3rd.