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Showing posts from April, 2022

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 terms the ha

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 also improved to ‘Five-tone

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, it can be changed on line 15. The default harmonic pattern is based on harmonic serie

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 holes,The calcula

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 finding downwar