19 equal temperament
A Neunzehnstufiges sound system organizes the musical pitch in 19 steps per Oktavraum. Are these levels of equal size, one speaks of the uniform Neunzehntönigen mood in which direct neighboring tones a height difference of about 63.16 cents or a frequency ratio of
Have.
All neunzehntönigen tempered tunings have the same specific enharmonic, which clearly differs from the usual at 12 -tone temperaments. So the tones F-sharp and G flat sound actually varies, for example, and a 19 -stage cycle of fifths could be the interface, for example, lay between Ai and Fez. This results from the traditional 12 -step modulation differing ways.
Another important aspect, namely that some basic intervals can be approximated well in 19 -tone systems, was apparently already in the late 16th century, when it concluded its ongoing effort to optimal Mean Tone for the first time.
- 5.1 For the 16th century
- 5.2 On the 20th and 21st centuries
- 5.3 sound samples
First approaches in the 16th century
In the 16th century, several theorists tried ( with reference to the ancient theory of music of Greece, whose keys were trying to reproduce it ) to balance the tradeoff between perfect intervals and the displacements by additional tones within the octave and enharmonic "Versions" to the existing twelve tones with additional keys (with a keyboard ) to realize. Trying always to find more precise differentiations for enharmonic scales, led to proposals for 19 - as well as for 24 - and 36 -step scales, and keyboards, for which instruments were built. 19 -stage harpsichords were apparently quite common in the 16th century. This gave the opportunity to sound relatively more pure intervals and thus can play more tones sounding harmony. In all this, however, succeeded in the mathematical representation easily than the vocal practice and the construction of such instruments.
Already in 1558 mentioned the Italian composer and theorist Gioseffo Zarlino in his work Le Istituzioni harmoniche a mood that was referring to nineteen tone steps within the octave, without to be more explicit. It is obviously to the 1577 proposed by the theorist Francisco de Salinas 1/3-Komma Mean Tone that the then customary twelve notes of the scale -, C, C #, D, Eb, E, F, F #, G, G # A, B and H - seven more enharmonic variants - His, In, Dis, ice, Gifts, As and Ais - supplemented. According to a contemporary witness of the blind Salinas could very skillful to play on a constructed according to his plans 19 -stage instrument in this temperature. Klaus Lang writes about this
" In this mood the fifths and major thirds are about 1/3-inch ( syntonic ) comma reduced, while the major sixths remain pure. Zarlino himself says that this method is not as good sound like the other two methods. An interesting feature of this Temperierungsmethode is, however, that if you let a close, the match relatively widespread instruments with 19 steps per octave with their help in the 16th century, the circle of fifths, so the wolf fifth is eliminated "
The chanson Seigneur Dieu ta Pity the French composer Guillaume Costeley is composed for a 19 -stage sound system; because Costeley reported in 1570 from the fact that he had composed this chromatic - enharmonic chanson spiritual " well before the age of twelve " ( " il y bien douze ans" ), or about 1557 as an exercise in the use of a 19 -step scale. He explained the way also quite detailed, as you have to build 19 -stage keyboard, and thought of one same division of the octave.
Gleichstufige division of the octave since the 19th century
In the 19th century the research on alternatives to the 12 -tone equal temperament tuning began. 53 -level divisions of the octave, for pragmatic reasons, and the 19 -stage particularly examined, it is the closest - To create purer intervals, was next to 31 -, 43 -, 50. The theorist Wesley Woolhouse propagated in his Essay on Musical Intervals, Harmonics, and the Temperament of the Musical Scale in 1835 alongside other equally- tuned a tone system, which divides (contrary to the conventional flow ) in 19 (instead of 12) equal intervals the octave. The remarkable thing is that for large and small thirds and sixths frequency conditions arise that are much closer to the pure interval, as in the usual equal temperament tuning. All other intervals, however, are further away from their pure equivalents.
For the uniform neunzehnstufige mood there is a whole series of compositions with both classic claim as well as rock and pop sector. The development in the field of electronic musical instruments or computer-based systems for sound synthesis give compositions in this and other alternate tunings significant advance.
The clay material
The mathematical procedure for determining the frequency of a pitch of 19 -step equal temperament is
Where f ( 0) is the frequency of a desired reference tone, f (i ) is the frequency of the sound is increased by i 19tel -octave steps.
The smallest representable tone difference of the system is therefore
As in the twelve -step equal temperament, can be described as multiples of the smallest representable interval for the neunzehnstufige equal temperament interval sizes. This gives the following values for step - intervals:
Properties of selected intervals
The in classical music -conceived as consonances intervals of Pure cue will be played by the 19 -stage mood partially better (thirds and sixths ), some less good ( fourth and fifth). For this purpose, a tabular comparison ( the differences are given in cents, each better approach is highlighted):
The following table shows the values of all intervals in gleichstufiger and pure mood as well as their deviation from each other in cents:
Notes: 1) Excessive fourth, sometimes called a tritone, defined as: Major third ( 5/4) plus major second (9 /8). This is equivalent to: fifth ( 3/2) minus diatonic semitone (16 /15). 2) If the difference is negative, the interval is narrower than the same temperature-controlled pure.