A neutral interval is a musical interval whose size lies approximately halfway between the corresponding major and minor intervals of the same generic number. In standard Western equal temperament, intervals are classified as either major, minor, perfect, augmented, or diminished. Neutral intervals, by contrast, are characteristic of microtonal and non‑Western tuning systems and are used to describe pitch relationships that do not conform to the conventional twelve‑tone equal temperament (12‑ET) scale.
Definition and classification
- Neutral second: An interval of about 150 cents, positioned between the minor second (100 cents) and the major second (200 cents).
- Neutral third: Approximately 350 cents, halfway between the minor third (300 cents) and the major third (400 cents).
- Neutral sixth: Roughly 850 cents, situated between the minor sixth (800 cents) and the major sixth (900 cents).
- Neutral seventh: About 1050 cents, between the minor seventh (1000 cents) and the major seventh (1100 cents).
These values are approximate because the exact size of a neutral interval can vary depending on the tuning system employed (e.g., 31‑ET, 53‑ET, just intonation, or other microtonal temperaments). In just intonation, neutral intervals may be expressed by specific rational frequency ratios, such as 10:9 for a neutral second or 12:9 (4:3) for a neutral third, though the precise ratios differ among theoretical frameworks.
Notation
Neutral intervals are commonly notated using conventional accidentals augmented with additional symbols to indicate their microtonal nature. In some modern notation systems, a neutral second may be written as a whole tone with a half‑sharp (♯½) or half‑flat (♭½), and similar modifiers are applied to other neutral intervals. Alternative notation schemes, such as those employed in the Helmholtz-Ellis notation or in the extended staff notation of microtonal music, use specific symbols to denote quarter‑tones, sixth‑tones, or other divisions that approximate neutral intervals.
Historical and cultural usage
Neutral intervals appear in various folk and non‑Western musical traditions. For example:
- Certain Middle Eastern maqam systems incorporate intervals that correspond closely to neutral seconds and thirds.
- Some African and Asian musical practices employ pitch inflections that can be described as neutral intervals when analyzed within a Western theoretical framework.
- In contemporary Western microtonal composition, composers such as Harry Partch, Ben Johnston, and Julián Carrillo have utilized neutral intervals to expand the harmonic palette beyond the limits of 12‑ET.
Acoustic and perceptual characteristics
Because neutral intervals fall between the familiar major/minor dichotomy, they are often perceived as “in‑between” or ambiguous in terms of emotional connotation. Listeners may describe them as having a “neutral” or “indeterminate” affect, which aligns with their nomenclature. Psychoacoustic studies indicate that the recognition of neutral intervals depends on cultural exposure and musical training.
Related concepts
- Quarter tone: An interval of 50 cents, representing one quarter of a whole tone; frequently used alongside neutral intervals in microtonal systems.
- Tritone: An interval of 600 cents, historically referred to as “augmented fourth” or “diminished fifth”; distinct from neutral intervals but often discussed in the context of non‑standard tonalities.
- Microtonality: The broader field of music that explores intervals smaller than the semitone of 12‑ET, of which neutral intervals are a subset.
References
Scholarly discussions of neutral intervals can be found in works on microtonal theory, such as:
- Partch, Harry. Genesis of a Music (1974).
- Johnston, Ben. Maximum Clarity and Other Writings on Music (1997).
- Barbour, James. Tuning and Temperament: A Historical Survey (2004).
These sources provide detailed analyses of the tuning ratios, notation, and compositional applications of neutral intervals.