1/1: Difference between revisions

(2 intermediate revisions by 2 users not shown)

Line 5:

The '''unison''' (interval ratio '''1/1''') is the [[interval]] between two tones that are identical in pitch. In the [[harmonic series]], 1/1 is the 1st [[harmonic]], and likewise in the [[subharmonic series]] 1/1 is the first [[subharmonic]] – this is because it acts as the fundamental to both series.

Measured in [[cent]]s (or any other logarithmic measure such as [[~~2/1|~~octave]]s, [[edo|edosteps]], etc.), the unison's size is exactly 0. This is because the distance between two identical pitches is zero. As such, the unison can be considered as a degenerate interval.

Measured in [[cent]]s (or any other logarithmic measure such as [[octave]]s, [[edo|edosteps]], etc.), the unison's size is exactly 0. This is because the distance between two identical pitches is zero. As such, the unison can be considered as a degenerate interval.

In [[just intonation]], 1/1 represents the base frequency from which an interval is measured.

In any [[temperament]], any [[comma]] [[tempering out|tempered out]] by that temperament is equated with 1/1, and thus intervals that differ by that comma in JI become equal in that temperament. For example, [[meantone]] sends [[81/80]] to the unison, and thus [[81/64]] and [[5/4]], which differ by [[81/80]] in JI, are equated to the same interval.

== As an interval region ==

Line 23:

Line 25:

As an interval region, the unison usually refers precisely to the 0-cent interval. However, there can be a tiny difference between any two intervals that are practically "the same note" (more pedantically, an ~~extremely small~~ [[~~Unnoticeable~~ comma|comma]]), that might be considered a "unison" (or at least too small to be a meaningful interval). This range usually goes up to 3.5 cents, as that is the just-noticeable difference.

As an interval region, the unison usually refers precisely to the 0-cent interval. However, there can be a tiny difference between any two intervals that are practically "the same note" (more pedantically, an [[unnoticeable comma|extremely small comma]]), that might be considered a "unison" (or at least too small to be a meaningful interval). This range usually goes up to 3.5 cents, as that is the [[just-noticeable difference]].

In some practices, this bound goes up to about 6 cents, which is the most precisely one is expected to intonate a pitch on certain instruments, and is a bit smaller than a [[Kleisma (interval region)|kleisma]] (hence the kleisma's significance in the context of intonation).

In some practices, this bound goes up to about 6 cents, which is the most precisely one is expected to intonate a pitch on certain instruments, and is a bit smaller than a [[Kleisma #As an interval region|kleisma]] (hence the kleisma's significance in the context of intonation).

As a diatonic interval category, unisons represent [[subchromatic]] motions – i.e. the difference between a note and itself (though perhaps in a different tuning or using a non-diatonic accidental, though that's more generally covered by [[comma and diesis]]). Every note in every scale has a unison, which is that note itself.

As a diatonic interval category, unisons represent [[subchromatic]] motions – i.e. the difference between a note and itself (though perhaps in a different tuning or using a non-diatonic accidental, though that is more generally covered by [[comma and diesis]]). Every note in every scale has a unison, which is that note itself.

In functional harmony, the unison over the root serves as the [[tonic]].

@@ Line 5: / Line 5: @@
 The '''unison''' (interval ratio '''1/1''') is the [[interval]] between two tones that are identical in pitch. In the [[harmonic series]], 1/1 is the 1st [[harmonic]], and likewise in the [[subharmonic series]] 1/1 is the first [[subharmonic]] – this is because it acts as the fundamental to both series.
-Measured in [[cent]]s (or any other logarithmic measure such as [[2/1|octave]]s, [[edo|edosteps]], etc.), the unison's size is exactly 0. This is because the distance between two identical pitches is zero. As such, the unison can be considered as a degenerate interval.
+Measured in [[cent]]s (or any other logarithmic measure such as [[octave]]s, [[edo|edosteps]], etc.), the unison's size is exactly 0. This is because the distance between two identical pitches is zero. As such, the unison can be considered as a degenerate interval.
 In [[just intonation]], 1/1 represents the base frequency from which an interval is measured.
+In any [[temperament]], any [[comma]] [[tempering out|tempered out]] by that temperament is equated with 1/1, and thus intervals that differ by that comma in JI become equal in that temperament. For example, [[meantone]] sends [[81/80]] to the unison, and thus [[81/64]] and [[5/4]], which differ by [[81/80]] in JI, are equated to the same interval.
 == As an interval region ==
@@ Line 23: / Line 25: @@
 {{Wikipedia|Unison}}
-As an interval region, the unison usually refers precisely to the 0-cent interval. However, there can be a tiny difference between any two intervals that are practically "the same note" (more pedantically, an extremely small [[Unnoticeable comma|comma]]), that might be considered a "unison" (or at least too small to be a meaningful interval). This range usually goes up to 3.5 cents, as that is the just-noticeable difference.
+As an interval region, the unison usually refers precisely to the 0-cent interval. However, there can be a tiny difference between any two intervals that are practically "the same note" (more pedantically, an [[unnoticeable comma|extremely small comma]]), that might be considered a "unison" (or at least too small to be a meaningful interval). This range usually goes up to 3.5 cents, as that is the [[just-noticeable difference]].
-In some practices, this bound goes up to about 6 cents, which is the most precisely one is expected to intonate a pitch on certain instruments, and is a bit smaller than a [[Kleisma (interval region)|kleisma]] (hence the kleisma's significance in the context of intonation).
+In some practices, this bound goes up to about 6 cents, which is the most precisely one is expected to intonate a pitch on certain instruments, and is a bit smaller than a [[Kleisma #As an interval region|kleisma]] (hence the kleisma's significance in the context of intonation).
-As a diatonic interval category, unisons represent [[subchromatic]] motions – i.e. the difference between a note and itself (though perhaps in a different tuning or using a non-diatonic accidental, though that's more generally covered by [[comma and diesis]]). Every note in every scale has a unison, which is that note itself.
+As a diatonic interval category, unisons represent [[subchromatic]] motions – i.e. the difference between a note and itself (though perhaps in a different tuning or using a non-diatonic accidental, though that is more generally covered by [[comma and diesis]]). Every note in every scale has a unison, which is that note itself.
 In functional harmony, the unison over the root serves as the [[tonic]].