“23 equal temperament”的意思、由来-开放百科全书

词条

23 equal temperament

释义

History and use
Notation
Interval size
Scale diagram
Modes
See also
References

In music, 23 equal temperament, called 23-TET, 23-EDO ("Equal Division of the Octave"), or 23-ET, is the tempered scale derived by dividing the octave into 23 equal steps (equal frequency ratios). Each step represents a frequency ratio of {{radic|2|23}}, or 52.174 cents. This system is the largest EDO that has an error of at least 20 cents for the 3rd (3:2), 5th (5:4), 7th (7:4), and 11th (11:8) harmonics, which makes it unusual in microtonal music.

History and use

23-EDO was advocated by ethnomusicologist Erich von Hornbostel in the 1920s,^[1] as the result of "a cycle of 'blown' (compressed) fifths"^[2] of about 678 cents that may have resulted from "overblowing" a bamboo pipe. Today, [https://en.xen.wiki/w/23edo#Music dozens of songs] have been composed in this system.

Notation

There are two ways to notate the 23-tone system with the traditional letter names and system of sharps and flats, called Melodic Notation and Harmonic Notation.

Harmonic Notation preserves harmonic structures and interval arithmetic, but sharp and flat have reversed meanings. Because it preserves harmonic structures, 12-EDO music can be reinterpreted as 23-EDO Harmonic Notation, so it's also called Conversion Notation.

An example of these harmonic structures is the Circle of Fifths below (shown in 12-EDO, Harmonic Notation, and Melodic Notation.)

Circle of Fifths in 12-EDO			Circle of Fifths in 23-EDO Harmonic Notation				Circle of Fifths in 23-EDO Melodic Notation
Sharp Side	Enharmonicity	Flat Side	Sharp Side	Enharmonicity	Flat Side	Enharmonicity	Flat Side	Enharmonicity	Sharp Side	Enharmonicity
C	=	doubleflat}}	C	doubleflat}}	doublesharp}}	C	doublesharp}}	doubleflat}}
G	=	doubleflat}}	G	doubleflat}}	doublesharp}}	G	doublesharp}}	doubleflat}}
D	=	doubleflat}}	D	doubleflat}}	D	doublesharp}}
A	=	doubleflat}}	A	doubleflat}}	A	doublesharp}}
E	=	flat}}	E	flat}}	E	sharp}}
B	=	flat}}	B	flat}}	B	sharp}}
sharp}}	=	flat}}	sharp}}	flat}}	flat}}	sharp}}
sharp}}	=	flat}}	sharp}}	flat}}	flat}}	sharp}}
sharp}}	=	flat}}	sharp}}	flat}}	flat}}	sharp}}
sharp}}	=	flat}}	sharp}}	flat}}	flat}}	sharp}}
sharp}}	=	flat}}	sharp}}	flat}}	flat}}	sharp}}
sharp}}	=	F	sharp}}	doubleflat}}	F	flat}}	doublesharp}}	F
sharp}}	=	C	sharp}}	doubleflat}}	C	flat}}	doublesharp}}	C

Melodic Notation preserves the meaning of sharp and flat, but harmonic structures and interval arithmetic no longer work.

Interval size

{{Missing information|section|the interval size|date=February 2019}}

Scale diagram

Step (cents)	52	52	52	52	52	52	52	52	52	52	52	52	52	52	52	52	52	52	52	52	52	52	52
Melodic Notation note name	A	A{{music\|sharp}}	B{{music\|flat}}	B	B{{music\|sharp}}	B{{music\|doublesharp}} C{{music\|doubleflat}}	C{{music\|flat}}	C	C{{music\|sharp}}	D{{music\|flat}}	D	D{{music\|sharp}}	E{{music\|flat}}	E	E{{music\|sharp}}	E{{music\|doublesharp}} F{{music\|doubleflat}}	F{{music\|flat}}	F	F{{music\|sharp}}	G{{music\|flat}}	G	G{{music\|sharp}}	A{{music\|flat}}	A
Harmonic Notation note name	A	A{{music\|flat}}	B{{music\|sharp}}	B	B{{music\|flat}}	B{{music\|doubleflat}} C{{music\|doublesharp}}	C{{music\|sharp}}	C	C{{music\|flat}}	D{{music\|sharp}}	D	D{{music\|flat}}	E{{music\|sharp}}	E	E{{music\|flat}}	E{{music\|doubleflat}} F{{music\|doublesharp}}	F{{music\|sharp}}	F	F{{music\|flat}}	G{{music\|sharp}}	G	G{{music\|flat}}	A{{music\|sharp}}	A
Interval (cents)	0	52	104	157	209	261	313	365	417	470	522	574	626	678	730	783	835	887	939	991	1043	1096	1148	1200

Modes

References

1. ^{{cite web |last1=Monzo |first1=Joe |title=Equal-Temperament |url=http://tonalsoft.com/enc/e/equal-temperament.aspx#edo-table |website=Tonalsoft Encyclopedia of Microtonal Music Theory |publisher=Joe Monzo |accessdate=20 February 2019 |date=2005}}
2. ^{{cite book |last1=Sethares |first1=William |title=Tuning, Timbre, Spectrum, Scale |date=1998 |publisher=Springer |isbn=9781852337971 |page=211 |url=https://books.google.com/books?id=KChoKKhjOb0C&lpg=PP1&pg=PA211#v=onepage&q&f=false |accessdate=20 February 2019}}

2 : Equal temperaments|Microtonality

随便看