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Thread: 18 musical tunings/with links
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| 18 musical tunings/with links |
|
2006-12-08 13:42:44 |
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.r
obertschroeter.de/diplom.pdf
http://
www.robertschroeter.de/stimmungen.html
http://www.sengpielaudio.com/Rechner-centfrequenz.htm
http://www.xs4a
ll.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://e
n.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://e
n.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
htt
p://en.wikipedia.org/wiki/Meantone_temperament
2a) 1/4 comma meantone
http://de.wikipe
dia.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
ht
tp://de.wikipedia.org/wiki/Werckmeister-Stimmung
3a-3) Werckmeister III
h
ttp://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
h
ttp://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
h
ttp://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
h
ttp://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
h
ttp://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
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|
|
| 18 musical tunings/with links |
|
2006-12-12 00:41:10 |
On Fri, 8 Dec 2006, Hanno wrote:
> 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.
thanks, it's (thanks to your assistance on IRC) in SVN now.
please review the tooltips that i had to cook up for the
different tunings:
bsecore.idl:
+ /* musical tunings: http://en
.wikipedia.org/wiki/Musical_tuning */
+ choice MusicalTuningType {
+ /* Equal Temperament: http:/
/en.wikipedia.org/wiki/Equal_temperament */
+ MUSICAL_TUNING_12_TET = (1, _("12
Tone Equal Temperament"), // http:/
/en.wikipedia.org/wiki/Equal_temperament
+ _("The
most common tuning system for modern Western music, "
+ "is the
twelve-tone equal temperament, abbreviated as 12-TET, "
+ "which
divides the octave into 12 equal parts.")),
+ MUSICAL_TUNING_7_TET = (_("7 Tone
Equal Temperament"), // http:/
/en.wikipedia.org/wiki/Equal_temperament
+ _("A
fairly common tuning system is the seven-tone equal
temperament tuning system, "
+
"abbreviated as 7-TET. It divides the octave into 7
equal parts using 171 cent steps.")),
+ MUSICAL_TUNING_5_TET = (_("5 Tone
Equal Temperament"), // http:/
/en.wikipedia.org/wiki/Equal_temperament
+ _("A
fairly common tuning system is the five-tone equal
temperament tuning system, "
+
"abbreviated as 5-TET. It divides the octave into 5
equal parts using 240 cent steps.")),
+ /* Rational Intonation: http://e
n.wikipedia.org/wiki/Just_intonation */
+ MUSICAL_TUNING_DIATONIC_SCALE =
(_("Diatonic Scale"), // http://en
.wikipedia.org/wiki/Diatonic_scale
+ _("In
music theory, a diatonic scale (also: heptatonia prima) is a
seven-note "
+ "musical
scale comprising five whole-tone and two half-tone steps.
"
+ "The
half tones are maximally separated, so between two half-tone
steps "
+ "there
are either two or three whole tones, repeating per
octave.")), // Werckmeister I
+ MUSICAL_TUNING_INDIAN_SCALE = (_("Indian
Scale"), // http://en.wikipedia.org/wiki/Just_intonation#Indian_sc
ales
+
_("Diatonic scale used in Indian music with wolf
interval at Dha, close to 3/2")),
+ MUSICAL_TUNING_PYTHAGOREAN_TUNING =
(_("Pythagorean Tuning"), // http:
//en.wikipedia.org/wiki/Pythagorean_tuning
+
_("Pythagorean tuning is the oldest way of tuning the
12-note chromatic scale, "
+ "in
which the frequency relationships of all intervals are based
on the ratio 3:2. "
+ "Its
discovery is generally credited to Pythagoras.")),
+ MUSICAL_TUNING_PENTATONIC_5_LIMIT =
(_("Pentatonic 5-limit"), // http://
en.wikipedia.org/wiki/Pentatonic_scale
+
_("Pentatonic scales are used in modern jazz and
pop/rock contexts "
+ "because
they work exceedingly well over several chords diatonic
"
+ "to the
same key, often better than the parent scale.")),
+ MUSICAL_TUNING_PENTATONIC_BLUES =
(_("Pentatonic Blues"), // http://
en.wikipedia.org/wiki/Pentatonic_scale
+ _("The
blues scale is the minor pentatonic with an additional
augmented fourth, "
+ "which
is referred to as the "blues note".")),
+ MUSICAL_TUNING_PENTATONIC_GOGO =
(_("Pentatonic Gogo"), // http://
en.wikipedia.org/wiki/Pentatonic_scale
+ _("The
Pentatonic Gogo scale is an anhemitonic pentatonic scale
used to tune the "
+
"instruments of the Gogo people of Tanzania.")),
+ /* Meantone Temperament: htt
p://en.wikipedia.org/wiki/Meantone_temperament */
+ MUSICAL_TUNING_QUARTER_COMMA_MEANTONE =
(_("Quarter-Comma Meantone"), // h
ttp://en.wikipedia.org/wiki/Quarter-comma_meantone
+
_("Quarter-comma meantone was the most common meantone
temperament in the "
+
"sixteenth and seventeenth centuries and sometimes used
later.")), // Werckmeister II
+ MUSICAL_TUNING_SILBERMANN_SORGE =
(_("Silbermann-Sorge Temperament"), // http://de.wikipedia.org/wiki/Silbermann-Sorge-Temperatur
+ _("The
Silbermann-Sorge temperament is a meantone temperament used
for "
+ "Baroque
era organs by Gottfried Silbermann.")),
+ /* Well Temperament: http://
en.wikipedia.org/wiki/Well_temperament */
+ MUSICAL_TUNING_WERCKMEISTER_3 =
(_("Werckmeister III"), // http://en.wikipedia.org/wiki/Werckmeister_temperament
+ _("This
tuning uses mostly pure (perfect) fifths, as in Pythagorean
tuning, but each "
+ "of the
fifths C-G, G-D, D-A and B-F# is made smaller, i.e. tempered
by 1/4 comma. "
+
"Werckmeister designated this tuning as particularly
suited for playing chromatic music.")),
+ MUSICAL_TUNING_WERCKMEISTER_4 =
(_("Werckmeister IV"), // http://en.wikipedia.org/wiki/Werckmeister_temperament
+ _("In this
tuning the fifths C-G, D-A, E-B, F#-C#, and Bb-F are
tempered narrow by 1/3 comma, "
+ "and the
fifths G#-D# and Eb-Bb are widened by 1/3 comma. The other
fifths are pure. "
+ "Most of
its intervals are close to sixth-comma meantone. "
+
"Werckmeister designed this tuning for playing mainly
diatonic music.")),
+ MUSICAL_TUNING_WERCKMEISTER_5 =
(_("Werckmeister V"), // http://en.wikipedia.org/wiki/Werckmeister_temperament
+ _("In this
tuning the fifths D-A, A-E, F#-C#, C#-G#, and F-C are
narrowed by 1/4 comma, "
+ "and the
fifth G#-D# is widened by 1/4 comma. The other fifths are
pure. "
+ "This
temperament is closer to equal temperament than Werckmeister
III or IV.")),
+ MUSICAL_TUNING_WERCKMEISTER_6 =
(_("Werckmeister VI"), // http://en.wikipedia.org/wiki/Werckmeister_temperament
+ _("This
tuning is also known as Septenarius tuning is based on a
division of the monochord "
+ "length
into 196 = 7 * 7 * 4 parts. "
+ "The
resulting scale has rational frequency relationships, but in
practice involves pure "
+ "and
impure sounding fifths. "
+
"Werckmeister described the Septenarius as a
"temperament which has nothing at all to do "
+ "with
the divisions of the comma, nevertheless in practice so
correct that one can be really "
+
"satisfied with it".")),
+ MUSICAL_TUNING_KIRNBERGER_3 =
(_("Kirnberger III"), // http://en.wikipedia.org/wiki/Johann_Philipp_Ki
rnberger_temperament
+
_("Kirnberger's method of compensating for and closing
the circle of fifths is to split the "wolf"
"
+
"interval known to those who have used meantone
temperaments between four fifths instead, "
+
"allowing for four 1/4-comma wolves to take their
place. "
+
"1/4-comma wolves are used extensively in meantone and
are much easier to tune and to listen to. "
+
"Therefore, only one third remains pure (between C and
E).")),
+ MUSICAL_TUNING_YOUNG = (_("Young
Temperament"), // http:/
/en.wikipedia.org/wiki/Young_temperament
+ _("Thomas
Young devised a form of musical tuning to make the harmony
most perfect in those keys which "
+ "are the
most frequently used (give better major thirds in those
keys), but to not have any unplayable keys. "
+ "This is
attempted by tuning upwards from C a sequence of six pure
fourths, "
+ "as well
as six equally imperfect fifths.")),
+ };
bsesong.c:
+ bse_object_class_add_param (object_class,
_("Tuning"),
+ PROP_MUSICAL_TUNING,
+ bse_param_spec_enum
("musical_tuning", _("Musical Tuning"),
+
_("The tuning system which specifies the tones or
pitches to be used. "
+
"Due to the psychoacoustic properties of tones, various
pitch combinations can "
+
"sound "natural" or "pleasing"
when used in combination, the musical "
+
"tuning system defines the number and spacing of
frequency values applied."),
+
BSE_MUSICAL_TUNING_EQUAL_TEMPERAMENT,
BSE_TYPE_MUSICAL_TUNING_TYPE,
+
SFI_PARAM_STANDARD ":unprepared:skip-default"));
below, i'll adress changes in SVN from your email for the
record.
>
> Hanno
> 3a-4) Werckmeister IV
> h
ttp://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),
wikipedia and text_T017.html are wrong on this one,
it's: 9 / 8.0 * 4 ^ (1 / 3).
> 4096/2187
> };
>
> 3a-5) Werckmeister V
> h
ttp://www.groenewald-berlin.de/text/text_T018.html
>
> interval[12]={
> 1,
> 8*2^.25/9,
> 9/8,
> 2^.25,
> 8*2^.5/9,
text_T018.html is wrong here, wikipedia get's it right: 3 /
2.0
> 9/4*8^.25,
> 2^.5,
> 3/2,
> 128/81,
> 8^.25,
> 3/8^.25,
> 4*2^.5/3
> };
>
> 3a-6) Werckmeister VI
> h
ttp://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))
the wikipedia formulas are pretty different here in using
shorter fractions.
i did pick the wikipedia version. the tables are still
similar
within 2 decimal digits though.
> };
> 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
> };
we have Kirnberger III in SVN now, but i didn't pick
Kirnberger II,
because aparently (according to wikipedia) Kirnberger
himself didn't
like II after a while which is why he devised III.
> 3b-2) Kirnberger III
> http:
//groenewald-berlin.de/text/text_T032.html
[...]
---
ciaoTJ
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