“I learn even from my most stupid students” Theodor Leschetizky
climateoax.ca@gmail.com
MP3 Files
Federal Inmate: Randoph Duey, Release Date 05/01/2043
Prelude 3: Randy Duey 1999
Will You Be Good to Me? : John LaPorta 1920-2004
Laplace Transform with Step Function
Pythagorean Birds: Computer program at bottom of page
Kyrie: Hans Leo Hassler 1564-1612
The Lone, Wild Bird: Walker’s Southern Harmony
Church Modes
Around 1500 there is a transition from Gregorian Chant to what we have today. This composition by William Byrd starts in Lydian mode. The subdominante is a tritone distant from the tonic and to avoid problems this fourth degree is flattened. It is changed again, sharp, so that it becomes the leading note for the supertonic. In other words, each bar has a chromatic alteration.
The Woods so Wild: Wiiliam Byrd, 1590
Equal Temperament: Is Your Guitar in Tune?
There is this fantasy that the music scale is derived from the overtone series. With a concoction of second and third overtones we can say that a major second, such as c to d will be in the ratio of 9/8. Since there are 6 whole tones in an octave, 9/8 is raised to the 6th power and we get 2.02728. This is not an octave higher and is referred to as the Pythagorean comma. Keyboards and guitars have to use equal temperament to get around this problem. You can also use the computer to see if your guitar is playable. I am using PRAAT to check the spectrum. The music note ‘A’ should be 110 for the 5th open string. Here is what I get
The ‘E’ string 3/2 times 220 = 330
Equal temperament = 2^7/12 times 220 = 329.6
Measured = 329.47
Alignment of Frets
We can use the spectrum again to check the frets; it would otherwise be too difficult to measure without specialized instruments. The E string is played (on a different day) and we get 329.43 Hz. The B note on the 7th fret should be 2^(7/12) times E = 493.5873 Hz. The measured note is slightly higher at 494.05 Hz., which is to be expected since the finger is pushing down on the string. This is still lower than a perfect fifth, which is equal to 494.145.
- The guitar sounds an octave lower than it is written.
- Praat sofware is here https://www.fon.hum.uva.nl/praat/
; climatehoax.ca@gmail.com
;writeInfoLine (“Pythagorean Bird Sequence (3/2)^ed * 100”)
pitchTier = do (“Create PitchTier…”, “source”, 0, 0.95)
t0 = 0.0
tinc = 0.1
for i from 1 to 45
ed = randomInteger(1,10)
do (“Add point…”, t0 + 0.05, (3/2)^ed*100 )
t0 = t0 + tinc
; appendInfoLine ( “ed = “, ed)
endfor
t0 = 0.05 ; between 0.1 and 0.2
pulses = To PointProcess
for i from 1 to 45
do (“Remove points between…”, t0-0.02, t0+0.02)
t0 = t0 + tinc
endfor
do (“To Sound (phonation)…”, 44100, 1, 0.05, 0.7, 0.03, 3, 4)
do (“Filter (pass Hann band)…”, 2000, 3000, 200)
do (“Scale peak…”, 0.75)
do (“Play”)
Ape Town 