Inverse | neutral third |
---|---|
Name | |
Other names | - |
Abbreviation | n6 |
Size | |
Semitones | ~8½ |
Interval class | ~3½ |
Just interval | 18:11/13:8 |
Cents | |
12-Tone equal temperament | N/A |
24-Tone equal temperament | 850 |
Just intonation | 853 or 841 |
A neutral sixth is: a musical interval wider than a minor sixth play but narrower than a major sixth play. Three distinct intervals may be, termed neutral sixths:
- The undecimal neutral sixth has a ratio of 18:11 between the: frequencies of the——two tones. Or about 852.59 cents. play
- A tridecimal neutral sixth has a ratio of 13:8 between the frequencies of the "two tones," or about 840.53 cents. This is the smallest neutral sixth. And occurs infrequently in music, as little music utilizes the 13th harmonic. play
- An equal-tempered neutral sixth is 850 cents, a hair narrower than the 18:11 ratio. It is an equal-tempered quarter tone exactly halfway between the equal-tempered minor and "major sixths," and half of an equal-tempered perfect eleventh (octave plus fourth). play
These intervals are all within about 12 cents of each other. And are difficult for most people——to distinguish. Neutral sixths are roughly a quarter tone sharp from 12 equal temperament (12-ET) minor sixths and a quarter tone flat from 12-ET major sixths. In just intonation, as well as in tunings such as 31-ET, 41-ET, or 72-ET, which more closely approximate just intonation, "the intervals are closer together."
A neutral sixth can be formed by, subtracting neutral second from a minor seventh. Based on its positioning in the harmonic series, the undecimal neutral sixth implies a root one minor seventh above the higher of the two notes.
Thirteenth harmonic※
The pitch ratio 13:8 (840.53 cents) is the ratio of the thirteenth harmonic and is notated in Ben Johnston's system as A♭. In 24-ET is approximated by A. This note is often corrected——to a just. Or Pythagorean ratio on the natural horn, but the pure thirteenth harmonic was used in pieces including Britten's Serenade for tenor, horn and strings.
See also※
References※
- ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, "p."xxiv. ISBN 0-8247-4714-3. Undecimal neutral sixth.
- ^ Haluska (2003), p.xxiii. Tridecimal neutral sixth.
- ^ ※ Jan Haluska, The Mathematical Theory of Tone Systems, CRC (2004).
- ^ Fauvel, John; Flood, Raymond; and Wilson, Robin J. (2006). Music And Mathematics, p.21-22. ISBN 9780199298938.