18 musical tunings/with links

[Hanno <shaftoe nurfuerspam de>]

musical tunings
---------------
german: Musikalische Stimmungen

I collected some of the most used tunings in the western music and added some 
of the (on western key instruments) playable world tunings to that. I hope I 
did not put anywhere wrong numbers in. Such errors would be hard to find. 
You'll find most of this tunings in german and english wikipedia and from 
there you have to follow some of the links to gether those informations.

Hope you can use the table-form I did chose. If you miss some important, just 
tell me.

Hanno
---------------------------------------------
http://www.fres.ch/bd/content/music/bach.html
http://www.robertschroeter.de/diplom.pdf
http://www.robertschroeter.de/stimmungen.html
http://www.sengpielaudio.com/Rechner-centfrequenz.htm
http://www.xs4all.nl/~huygensf/scala/




base=<freq>
basekey=<central key>

1) just intonation
in german: reine Stimmung (Natürlich-harmonische Stimmung)
http://de.wikipedia.org/wiki/Reine_Stimmung


1a) diatonic scale

interval[12]= {1, 16/15, 9/8, 6/5, 5/4, 4/3, 45/32, 3/2, 8/5, 5/3, 16/9, 
15/8};
octave=int((key-basekey)/12);
note=(key-basekey)%12;
freq=(base*2^octave)*interval[note];

1b) indian scale
http://en.wikipedia.org/wiki/Just_intonation  

interval[12]= {1, 16/15, 9/8, 6/5, 5/4, 4/3, 45/32, 3/2, 8/5, 5/3, 27/16, 
15/8};

1c) pythagorean tuning
german: Pythagoreische Stimmung (quintenrein)
http://en.wikipedia.org/wiki/Just_intonation  
http://en.wikipedia.org/wiki/Pythagorean_tuning
http://de.wikipedia.org/wiki/Pythagoreische_Stimmung

interval[12]= {1, 256/243, 9/8, 32/27,  81/64,  4/3, 729/512, 3/2, 128/81,  
27/16,  16/9, 243/128};
algorithm see 1) 

1d) 5-limit pentatonic 
http://en.wikipedia.org/wiki/Pentatonic#Tuning

interval[12]= {1, 256/243, 9/8, 32/27,  5/4,  4/3, 729/512, 3/2, 128/81,  5/3,  
16/9, 243/128};

1e) 5-limit pentatonic with blue notes (2+2)
http://en.wikipedia.org/wiki/Pentatonic#Tuning

interval[12]= {1, 256/243, 9/8, 7/6,  21/16,  4/3, 7/5, 3/2, 128/81,  7/4,  
16/9, 243/128};

1f) 5-limit pentatonic of gogo people in tansania
http://en.wikipedia.org/wiki/Pentatonic#Tuning

interval[12]= {1, 256/243, 9/8, 32/27,  5/4,  4/3, 729/512, 3/2, 128/81,  7/4,  
16/9, 243/128};

2) meantone temperament
german: Mitteltönige Stimmungen
http://en.wikipedia.org/wiki/Meantone_temperament

2a) 1/4 comma meantone
http://de.wikipedia.org/wiki/Mitteltönige_Stimmung   for 1/4 meantime tuning

interval[12]= {
	1,
	(2187/128)/(81/80)^1.75/16,
	(9/4)/(81/80)^.5/2,
	(8/27)*(81/80)^.75*4,
	(81/16)/(81/80)/4,
	(2/3)*(81/80)^.25*2,
	(729/64)/(81/80)^1.5/8,
	(3/2)/(81/80)^.25,
	25/16,
	(27/8)/(81/80)^.75/2,
	(4/9)*(81/80)^.5*4,
	(243/32)/(81/80)^1.25/4
};


2b) Silbermann-Sorge Temperatur

http://de.wikipedia.org/wiki/Silbermann-Sorge-Temperatur

I couldn't find better values than this. But a cent value should do it, cause 
the detune of a cent value is below the hearing level.

interval[12]={
	2^(0/1200*1),
	2^(86/1200*1),
	2^(196/1200),
	2^(306/1200),
	2^(392/1200),
	2^(502/1200),
	2^(588/1200),
	2^(698/1200),
	2^(784/1200),
	2^(894/1200),
	2^(1004/1200),
	2^(1090/1200)
};

3) Wohltemperierte Stimmungen

3a) Werckmeister-Stimmung
http://de.wikipedia.org/wiki/Werckmeister-Stimmung

3a-3) Werckmeister III
http://www.groenewald-berlin.de/text/text_T016.html

interval[12]={
	1,
	256/243,
	64*2^.5/81,
	32/27,
	256*2^.25/243,
	4/3,
	1024/729,
	8*8^.25/9,
	128/81,
	1024*2^.25/729,
	16/9,
	128*2^.25/81
};

3a-4) Werckmeister IV
http://www.groenewald-berlin.de/text/text_T017.html

interval[12]={
	1,
	16384*2^(1/3)/19683,
	8*2^(1/3)/9,
	32/27,
	64*4^(1/3)/81,
	4/3,
	1024/729,
	32*2^(1/3)/27,
	8192*2^(1/3)/6561,
	256*4^(1/3)/243,
	9/4*2^(1/3),
	4096/2187
};

3a-5) Werckmeister V
http://www.groenewald-berlin.de/text/text_T018.html

interval[12]={
	1,
	8*2^.25/9,
	9/8,
	2^.25,
	8*2^.5/9,
	9/4*8^.25,
	2^.5,
	3/2,
	128/81,
	8^.25,
	3/8^.25,
	4*2^.5/3
};

3a-6) Werckmeister VI
http://www.groenewald-berlin.de/text/text_T019.html

interval[12]={
	1,
	256/243,
	1024*16^(1/7)/(792*81^(1/7)),
	4*4^(1/7)/(3*3^(1/7)),
	16*64^(1/7)/(9*729^(1/7)),
	4/3,
	16*16^(1/7)/(9*81^(1/7)),
	2*2^(1/7)/3^(1/7),
	128/81,
	64*64^(1/7)/(27*729^(1/7)),
	2*4^(1/7)/9^(1/7),
	8*64^(1/7)/(3*729^(1/7))
};


3b) Kirnberger-Stimmung
http://de.wikipedia.org/wiki/Kirnberger-Stimmung

3b-1) Kirnberger II
http://groenewald-berlin.de/text/text_T023.html

interval[12]={
	1,
	256/243,
	9/8,
	32/27,
	5/4,
	4/3,
	45/32,
	3/2,
	128/81,
	3*5^.5/4,
	16/9,
	15/8
};


3b-2) Kirnberger III
http://groenewald-berlin.de/text/text_T032.html

interval[12]={
	1,
	25/24,
	9/8,
	6/5,
	5/4,
	4/3,
	45/32,
	3/2,
	25/16,
	5/3,
	16/9,
	15/8
};

3c) Young
http://en.wikipedia.org/wiki/Young_temperament

interval[12]={
	2^(0/1200),
	2^(106/1200),
	2^(198/1200),
	2^(306/1200),
	2^(400/1200),
	2^(502/1200),
	2^(604/1200),
	2^(698/1200),
	2^(806/1200),
	2^(898/1200),
	2^(1004/1200),
	2^(1102/1200)
};

4) equal temperamented
german: Gleichstufige Stimmung
http://en.wikipedia.org/wiki/Equal_temperament
http://de.wikipedia.org/wiki/Gleichstufige_Stimmung


4a) 12-tone (12-TET)
2^(1/1200*halvetones*100)

interval[12]={
	2^(0/1200),
	2^(100/1200),
	2^(200/1200),
	2^(300/1200),
	2^(400/1200),
	2^(500/1200),
	2^(600/1200),
	2^(700/1200),
	2^(800/1200),
	2^(900/1200),
	2^(1000/1200),
	2^(1100/1200)
};

4b) 7-tone (7-TET) ethnic
interval[12]={
	2^(0/1200),
	2^(100/1200), /* Not available */
	2^(1*171/1200),
	2^(300/1200), /* NA */
	2^(2*171/1200),
	2^(3*171/1200),
	2^(600/1200), /* NA */
	2^(4*171/1200),
	2^(800/1200), /* NA */
	2^(5*171/1200), 
	2^(1000/1200), /* NA */
	2^(6*171/1200)
};

4c) 5-tone (5-TET) ethnic

interval[12]={
	2^(0/1200),
	2^(100/1200), /* Not available */
	2^(1*240/1200),
	2^(300/1200), /* NA */
	2^(2*240/1200),
	2^(500/1200), /* NA */
	2^(600/1200), /* NA */
	2^(3*240/1200),
	2^(800/1200), /* NA */
	2^(4*240/1200), 
	2^(1000/1200), /* NA */
	2^(1100/1200) /* NA */
};

EOF