Re: 18 musical tunings/with links
- From: Tim Janik <timj gtk org>
- To: Hanno <shaftoe nurfuerspam de>
- Cc: beast gnome org, Stefan Westerfeld <stefan space twc de>
- Subject: Re: 18 musical tunings/with links
- Date: Tue, 12 Dec 2006 01:41:10 +0100 (CET)
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://en.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_scales
+ _("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: http://en.wikipedia.org/wiki/Meantone_temperament */
+ MUSICAL_TUNING_QUARTER_COMMA_MEANTONE = (_("Quarter-Comma Meantone"), // http://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_Kirnberger_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
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),
wikipedia and text_T017.html are wrong on this one,
it's: 9 / 8.0 * 4 ^ (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,
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
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))
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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