Kite's thoughts on enharmonic unisons: Difference between revisions
Created page with "The notation of every temperament, including every edo, has at least one enharmonic interval, or EI for short (with one exception, see below). An EI is by definition enharmoni..." |
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For example, in 12edo, A4 = d5 and F# = Gb. Such equivalences result from adding or subtracting a diminished 2nd, abbreviated as d2. | For example, in 12edo, A4 = d5 and F# = Gb. Such equivalences result from adding or subtracting a diminished 2nd, abbreviated as d2. | ||
EIs are very useful for | EIs are very useful for respelling notes and intervals less awkwardly. For example, in 12edo we can add a d2 to C## to convert it to D. And we can subtract a d2 from a dim 4th to get a major 3rd. | ||
Just intonation does not have EIs, although as a practical matter just intonation is audibly indistinguishable from certain microtemperaments that do have them. | Just intonation does not have EIs, although as a practical matter just intonation is audibly indistinguishable from certain microtemperaments that do have them. | ||
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!Tuning's rank | !Tuning's rank | ||
!Notation | !Notation | ||
!Notation's rank | !Notation's rank<br>without any EIs | ||
without any EIs | !Minimum #<br>of EIs needed | ||
!Minimum # | |||
of EIs needed | |||
|- | |- | ||
|19edo | |19edo | ||
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|2 | |2 | ||
|- | |- | ||
|Guti | |[[Meantone|Meantone/Guti]] | ||
|rank-2 | |rank-2 | ||
|conventional | |conventional | ||
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|0 | |0 | ||
|- | |- | ||
|Triyoti | |[[Porcupine|Porcupine/Triyoti]] | ||
|rank-2 | |rank-2 | ||
|ups and downs | |ups and downs | ||
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Likewise if an octave of 8edo were notated as J K L M N O P Q J with no sharps or flats, there would be no EIs. This type of notation is obviously only practical for small edos. | Likewise if an octave of 8edo were notated as J K L M N O P Q J with no sharps or flats, there would be no EIs. This type of notation is obviously only practical for small edos. | ||
Some notations, like ups and downs, notate all but the largest edos with only a single additional pair of accidentals. Other notations, like Sagittal and SKULO, notate edos using various commas such as 81/80, 64/63 and 33/32. Thus they notate an edo interval as a nearby JI interval, indicating the "feel" of the interval. For some edos, these notations use multiple such commas. For example, Sagittal notates 41edo using 81/80 and 33/32, and SKULO notates it using all three commas. Each comma used adds a pair of accidentals, and hence adds an EI. Respelling the sum of two intervals becomes much more complicated. | Some notations, like ups and downs, notate all but the largest edos with only a single additional pair of accidentals. Other notations, like Sagittal and SKULO, notate edos using various commas such as 81/80, 64/63 and 33/32. Thus they notate an edo interval as a nearby JI interval, indicating the "feel" of the interval. For some edos, these notations use multiple such commas. For example, Sagittal notates [[41edo]] using 81/80 and 33/32, and SKULO notates it using all three commas. Each comma used adds a pair of accidentals, and hence adds an EI. Respelling the sum of two intervals becomes much more complicated. | ||
== See also == | == See also == | ||
* [[Interval arithmetic]] | |||
* [[Enharmonic intervals in ups and downs notation#Canonical EIs for edos 5-55]] | * [[Enharmonic intervals in ups and downs notation#Canonical EIs for edos 5-55]] | ||
* [[Enharmonic intervals in ups and downs notation#Canonical EIs for various pergens]] | * [[Enharmonic intervals in ups and downs notation#Canonical EIs for various pergens]] | ||