Dear John, John Wiedenhoeft wrote:
> Dear all, > > I know Lilypond is mainly a program for writing classical scores. But for the modernists among us, I really think support for the so-called "Extended Helmholtz-Ellis JI Pitch notation" should be included. > > It's nothing special, just some accidentals used for microtonal composition. To my opinion this is the most convincing way of writing microtonal pitches, however it's much more convincing than the system currently used in Lilypond. This notation is the first one which clearly has a mathematically sound origin! I give an example (for others reading the mails). All notes have upper harmonics. Consider frequency 442 Hz, which is c'. Its upper harmonics are multiples of the basic frequency: 2*442 Hz = 884 Hz, 3*442 Hz = 1322 Hz, etc. Let us say that you want to play a Perfect Fifth, with c' and g' played together. In that case, the 3rd harmonics of c', 3*442 Hz, and the 2nd harmonics of g', 2*662 Hz, exactly match at 3*442 Hz = 2*662 Hz = 1322 Hz. And, there is no wobbling in the sound! Let us also calculate what frequencies that interval would correspond in Equal Tempered Semitones (logarithmic scale). The (approximated) frequencies of the scale are (calculated using GNU Octave) octave:1> 442 * 2.^([0:24]/12) ans = Columns 1 through 8: 442.00 468.28 496.13 525.63 556.89 590.00 625.08 662.25 Columns 9 through 16: 701.63 743.35 787.55 834.38 884.00 936.57 992.26 1051.26 Columns 17 through 24: 1113.77 1180.00 1250.16 1324.50 1403.26 1486.70 1575.11 1668.77 Column 25: 1768.00 of which the frequencies of our interest are octave:2> 442 * 2.^([0 7 12 19]/12) ans = 442.00 662.25 884.00 1324.50 Now we got 1324.50 Hz. This is by 2.50 Hz larger than in a perfect fifth. What does this mean? If you have had two tuning forks, one of them at 442 Hz, and the other at 440 Hz, you may guess what happens. The sound appears and disappers two times in a second, which means that the sound waves interfere either constructively (summing up to maximum) or destructively (summing up to zero). A similar phenomenon will happen when you play the organ. > Please refer to http://www.plainsound.de/research/legendE.pdf for a chart, or http://www.plainsound.de/MSscores.html#research for further information (fonts are provided there). I really like the idea behind this system. The quarter tones themselves are rarely interesting, but microtonal music, when it tries to make interval more sound and pure, is valuable in everyday life. If you prefer to sing pure major thirds, it is not a bad idea to show explicitly that in this place and in that place you should sing the pure major third in stead of an equally tempered and wobbling major third. Referring to the PDF-file, seems like the notation for the 3-limit (Pythagorean) intervals and the 11-limit (undecimal) intervals is already included in LilyPond. We would need to add the notation for the 5-limit (Ptolemaic) intervals, which provides for example a pure major third (with matching 5th and 4th harmonics) and a pure minor third (with matching 6th and 5th harmonics). In addition, the notations for the 7-limit (Septimal) intervals, the 3-limit (Tridecimal) intervals, and the irrational-and-tempered intervals need to be included in LilyPond. The 'extended' part of the notation is for tones which match at at primes higher than 13 (which are 17, 19, 23, 29, 31, 37, etc.). > It can also be used for writing just intonation. For example, research is going on on intonation of Bach pieces... it really sounds impressive! Bach used to play the organ. The organ produces very pure single sounds. When you add two pure sound together, you may hear wobbling of upper harmonics which is characteristic to the tempering in hand. Bach must have been aware of different temperings; he wrote his Preludes and Fugues für ``Das wohltemperierte Klavier'', for the well-tempered piano. For me, it is an interesting question who did tune the organ Bach played? And, how much Bach was involved in the tuning of the organs he played? > I'd appreciate your opinion on this request, > Best regards, > John Wiedenhoeft > In my opinion, there are four requests, of which at least three are easily specifiable: (1) the microtonal notation of pitches with a number representation showing cents to be added or removed, which is Alexander Ellis' part of the pitch notation, (2) the microtonal notation of pitches for irrational-and-tempered intervals, one of the extensions, (3a) the microtonal notation of pitches with accidentals which are based on primes, which is Hermann von Helmholz's part of the pitch notation, (3b) the extended Hermann von Helmholz's notation which is based on primes higher than 13. Implementation could be the following: (1) make a command called \cents, which produces a text markup. Example: <c' g'\cents{-2.5}>. (2) make a command called \tempered, which only ensures that there is an accidental of the irrational-and-tempered type. Example: <c' g'\tempered> (3a) make commands called \syntonic, \septimal, \undecimal, and \tridecimal, which bring the accidental symbols. Example 5: <c' g'\syntonic{-1}> = a pure fifth, (allowed range for the argument is -3 ... +3) Example 7: c'\septimal{+1}, (allowed range for the argument is -2 ... -2) Example 11: c'\undecimal{+1} = cih', (allowed range for the argument is -4 ... +4) Example 13: c'\tridecimal{+1}, (allowed range for the argument is -1... +1) (3b) the extended part is tricky, I could not figure out the system at first sight. In conclusion, commands \cents, \tempered, \syntonic, \septimal, \undecimal, and \tridecimal, can be implemented rather straightforwardly. No big changes will appear in the code, as long as only markup commands are implemented. Best wishes, Heikki Junes _______________________________________________ lilypond-devel mailing list lilypond-devel@gnu.org http://lists.gnu.org/mailman/listinfo/lilypond-devel
