Neutral second: Difference between revisions
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In [[just intonation]], an interval may be classified as a neutral second if it is reasonably mapped to 1\7 and 3[[24edo|\24]] (precisely one step of the diatonic scale and one and a half steps of the chromatic scale). | In [[just intonation]], an interval may be classified as a neutral second if it is reasonably mapped to 1\7 and 3[[24edo|\24]] (precisely one step of the diatonic scale and one and a half steps of the chromatic scale). | ||
As a concrete [[interval region]], it is typically near 150 | As a concrete [[interval region]], it is typically near 150{{cent}} in size, distinct from the [[Semitone (interval region)|semitone]] of roughly 100{{c}} and the [[major second]] of roughly 200{{c}}. A rough tuning range for the neutral second is 130 to 170{{c}} according to [[Margo Schulter]]'s theory of interval regions. | ||
== In just intonation == | == In just intonation == | ||
=== By prime limit === | === By prime limit === | ||
The [[3-limit]] and 5-limit do not have simple neutral seconds, so we start with the 7-limit: | The [[3-limit]] and 5-limit do not have simple neutral seconds, so we start with the 7-limit: | ||
Revision as of 15:03, 3 March 2025
A neutral second (n2) is an interval that spans one step of the diatonic scale with a quality between major and minor. It exists in neutralized diatonic scales as exactly one half of a minor third.
In just intonation, an interval may be classified as a neutral second if it is reasonably mapped to 1\7 and 3\24 (precisely one step of the diatonic scale and one and a half steps of the chromatic scale).
As a concrete interval region, it is typically near 150 ¢ in size, distinct from the semitone of roughly 100 ¢ and the major second of roughly 200 ¢. A rough tuning range for the neutral second is 130 to 170 ¢ according to Margo Schulter's theory of interval regions.
In just intonation
By prime limit
The 3-limit and 5-limit do not have simple neutral seconds, so we start with the 7-limit:
- The 7-limit septimal neutral second
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Todo: complete page |
In moment-of-symmetry scales
Intervals between 120 and 171 ¢ generate the following MOS scales:
These tables start from the last monolarge MOS generated by the interval range.
MOSes with more than 12 notes are not included.
| Range | MOS | |
|---|---|---|
| 120–133 ¢ | 1L 8s | 9L 1s |
| 133–150 ¢ | 1L 7s | 8L 1s |
| 150–171 ¢ | 1L 6s | 7L 1s |
| View • Talk • EditInterval classification | |
|---|---|
| Interval regions | |
| Unison and octave | Unison • Comma and diesis • Octave |
| Seconds | Minor second • Neutral second • Major second |
| Thirds | Minor third • Neutral third • Major third |
| Fourths and fifths | Perfect fourth • Superfourth • Tritone • Subfifth • Perfect fifth |
| Sixths | Minor sixth • Neutral sixth • Major sixth |
| Sevenths | Minor seventh • Neutral seventh • Major seventh |
| Interseptimal intervals | Interseptimal 2nd-3rd • Interseptimal 3rd-4th • Interseptimal 5th-6th • Interseptimal 6th-7th |
| Interval qualities | |
| Diatonic qualities | Diminished • Minor • Perfect • Major • Augmented |
| Tuning ranges | Neutral (interval quality) • Submajor and supraminor • Pental major and minor • Novamajor and novaminor • Neogothic major and minor • Supermajor and subminor • Ultramajor and inframinor |