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Blackwood's diatonic behaviour of xenharmonic equal temperament

 Blackwood's Modes and Chord Progressions in Equal Tunings (1991) put the traditional functional harmony and chord progression into a new context, non-12 equal temperament, in other equal temperament numbers, nineteen, seventeen, sixteen, and fifteen. His article describes what if the subdominants, dominants, or tonic chords are applied in these ET. Blackwood proposes two major concepts of interval property, Dissonance versus Discordance. Dissonance describes the interval property between, it is not based on the sonic experience to our ears, pure or harsh. If the interval is defined as major 3rd, perfect 5th, major 6th or octave etc. It is always described as a consonant; if verse versa, dissonant. A chord that contains a combination of tendency notes, such as a dominant seventh, a diminished seventh, or an augmented sixth; these latter are dissonant intervals/chords whatever the tuning, disregarding the how it sounds. Consonant and dissonant are paired to describe in te...

The neumatic notation - the Buddhist of smooth melodic movement

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 Western music uses staff notation while Chinese music uses solfege or ideogram notation. These two notations have a common point one symbol represents a pitch. The player perceives the pitches block by block, one note or chord at a time and one after. However, some Buddhist chanting music uses curved lines to notate the music, and emphasise the contour of the voice. It is similar to the western glissando but not in a linear way. The connection between of each text is smooth and flowing. Japanese Shōmyō In Japanese Shōmyō, a type of Buddhist chant in Japan, they have a contrasting notation method to the West. The neumatic notation, generally known as hakase (- bakase ). straight and curved lines (Tokita, 2008). Same with the Western neume, these notations lack any systematic way of indicating pitch. The lines appear to represent the up-and-down movement of the vocal melody in a simple visual manner.  A Shōmyō  hakase  score (Tokita,2008) The Shomyo notation als...

Equal temperament finder - effectively finding temperament fits the all consonants

 This program finds a suitable number of equal temperaments for a series of notes or ratios. It is useful for inharmonic tuning, a more accurate and way more effective way to find the number in the previous calculation . Separate individual items with a space bar. There are two ways to use this program: 1, enter the frequencies (Hz) from tonic to the octave;  An example of entering an inharmonic scale in frequency:      220  259.2   302.5   329.6296296   362.3290203   432.8 (The inharmonic pattern of a bar percussion .) 2, enter the ratio of every note relates to the tonic form to the octave An example of entering a major scale in ratios (just intonation):      1 1.12246 1.25992 1.33483 1.49831 1.68179 1.88775 2 The boundary of matching frequency is +/-15 cents which is an average number of comparing 12-TET and just intonation. Can be changed on lines 7 and 9. The upper limit of finding the ET is 40, i...

Keys in woodwind- the physical cut off frequency

When a tone is produced on a wind instrument, the bore of the instrument works as a resonator, to produce a pitch, but the internal surface of the bore is not a perfect smooth parallel surface. In woodwind, the keyholes even in a closed situation, still add (drill tone hole) or attach a little bit some space (plug/attach tone hole)in the bore. The rough and uneven surface of the bore causes energy loss, especially the high frequencies with short wavelengths. Diffraction refers to various phenomena that occur when a wave encounters an obstacle or opening. The tone hole, the lattice rough surface, is the obstacle to the sound wave. When covering most and all tone holes of the woodwind instrument, short-wavelength in high frequency have trouble the get around corners and obstacles by traveling the whole length of the pipe, while the high frequencies (>1000Hz) are lost (Benada,1990).  For fingering in woodwind instrument, it creates different patterns of open and close hol...

Central Pitch Processor Model -a program helps finding the make up fundamental in our mind

 The combination tone effect is discussed in the previous article. In short, when two tones are played in the high range, our brain will make a low frequency as a fundamental frequency. I developed a program here on Github. Two playing frequencies are fa and fb. fb>fa The fundamental frequency is f1 . n is number of partials The fa and fb frequencies are considered two successive harmonics of fa = n*f1 and fb = (n+1)*f1.   For example, the main, 1000Hz and 800Hz are playing at the same time, in the previous article , the result is 200Hz, and the program returns a perfect fit message. If the pair with no harmonic relationship, the program tries all possible partials from 1 to 24, to find the closest result of the fundamental. The main v2 can work with complex harmonic partials and inharmonic partials, up the 4 partials, both found down in harmonic series patterns. All individual partials are treated as a pair of sine tones, performing the same process above and f...

The timbre of woodwind - unique sound and shape of each woodwind instrument

 In the string family, each member has a similar look to each others. People who do not have deep knowledge of music would call every string instrument a violin. The vibration of a string follows the harmonic series pattern. In the woodwind family, every instrument's shape and timbre is very unique, the spectrum may or may not follow the harmonic series. In short, to break down the shape of the woodwind instrument, there are three main types of shape: open cylindrical, close-ended cylindrical, conical.  For cylinder instruments like flute and recorder with both open ends, the spectra follow the harmonic series, ideally. The vibration stops at both ends resulting in a string with both ends fastened. But the vibration would still fade out after leaving the end, in other words, the length of vibration is slightly longer than the pipe itself, that is the topic of end correction. fn=n*(v/2L) For closing one end in cylindrical instruments like the clarinet, one end is stopped by a r...

A program convert measure dissonance level

To run to code, just copy and paste the code on an online python compiler, or download a python interpreter on your computer. This program automatically converts sound pressure level to loudness and calculates the dissonance level between notes with harmonics considered up to the 7th partials. First, you have to enter the fundamental frequency, the lower note you want to work with. It only accepts one frequency. There are two modes, enter 0 for drawing dissonance curve; enter 1 for calculating dissonance between two notes or even more. To calculate multiple notes (a chord), use a spacebar to separate individual frequencies. The default harmonic pattern is based on harmonic series (f,2f,3f,4f,5f,6f,7f) and sound pressure level in decibel (dBSPL) corresponds to harmonics 60, 50, 40, 40, 30, 30, 30 dBSPL respectively. You can customize the parameters in the code for inharmonic instruments like percussion, and wind. The dissonance curve drawing is based on the resolution of  2^1/120 fo...