### **Triangle Wave** - Contains only odd harmonics like the square wave but with amplitudes falling off as 1/n² and alternating phase on every second harmonic, resulting in a softer, flute-like tone  . This is the waveform produced by an integrator ramping alternately positive and negative by equal amounts and at the same rate. Analysis of its harmonics shows that it contains only odd multiples of the fundamental frequency, i.e. a triangle wave of frequency 100 Hz contains sine waves of 100, 300, 500, 700, 900...Hz (f, 3f, 5f, 7f, 9f...). The amplitude of each harmonic is inversely proportional to the square of its harmonic number, i.e. if the fundamental is at relative amplitude A, then 3f is at A/9, 5f is at A/25, 7f is at A/49. This can also be expressed by saying that the harmonics decrease by 12 dB per octave. Thus although it contains all the odd harmonics, most of them are too faint to be heard; however beats between adjacent harmonics may contribute to the overall sound. Something approaching a triangle wave is produced when a string is plucked exactly at its mid-point. Figure 1 shows how the triangle wave can be built up. ![[image-3.png]] ### **Square (and Pulse) Wave** - Ideal square waves (50% duty) contain only odd harmonics (1f, 3f, 5f…); detuning multiple squares creates rich chorusing effects  . - Pulse waves generalize this by varying duty cycle, introducing controlled even harmonics for timbral variation  . These are all members of the same family and a simple rule explains their harmonic content. The ratio of the proportions of high and low, or on and off is called the duty cycle or mark:space ratio. Thus a wave which is high for 25% of the time has a duty cycle of 25% and a mark:space ratio of 1:3. The reciprocal of the duty cycle is called the L-number, and for a duty cycle of 25% (=¼), L=4. A rectangular wave contains all the harmonics except those divisible by the L-number, in this case 4f, 8f, 12f etc. The amplitudes of the high harmonics are very strong. The square wave is a special case; its duty cycle is 50%, giving L=2, so it contains only odd harmonics. Their amplitudes are inversely proportional to the harmonic number (3f=A/3, 5f=A/5 etc.). This means that the harmonics fall off at 6dB per octave (compare with the triangle wave). See Figure 2. ![[image-2.png]] ## Sawtooth wave **The Sawtooth (ramp) Wave**: This very useful waveform contains all odd and even harmonics, and their amplitudes are inversely proportional to the harmonic number, just like the square wave (6dB per octave fall-off). In a good quality sawtooth up to about the thirtieth harmonic will be detectable. See Figure 3. ![[image-1.png]] # SSL VHD ![[Saturation Characteristics _0.excalidraw.svg]] # Clarinet The clarinet behaves acoustically like a stopped (closed) cylindrical pipe, which reinforces resonances at the fundamental frequency and its odd harmonics (3rd, 5th, 7th, etc.) while largely suppressing even harmonics in its lower registers  . Because the mouthpiece and reed effectively close one end of the bore, the clarinet overblows at the twelfth rather than the octave, a hallmark of odd-only harmonic series in stopped pipes ![[Saturation Characteristics .excalidraw.svg]] # Distressor It’s not only a compressor but a ... "Distortion Generator" The Distressor is a modern digitally controlled analog device that attempts to offer some of the "musical non-linearities" exhibited by the older tube, class A discrete, and magnetic tape mediums. The old, sought after vintage gear is not anywhere near as accurate (or linear) as devices made today, but certain "faults" or non-linearities are exactly the reason some sell today at 10 times their original value. They color the sound with distortion and frequency response shaping. Getting the frequency response flat to 20kHz and having distortion below .5% used to be an achievement. Today, a 35 cent op amp is flat to 3 MHz and produces distortion below .002%. Getting things accurate in the digital age is relatively cheap and easy. But getting the expert user to think a piece of gear is "musical" and fun to use is something else. The Distortion Modes By using a design that allows pinpoint control of nonlinear analog devices, the Distressor is trimmed to produce three controllable distortion modes: 1. Normal (Clean) No induced distortion. THD hovering between .025 and .3% 2. Dist 2 THD hovering between .05 and 3% Emphasized 2nd Harmonic 3. Dist 3 THD hovering between .1% and 20% 3rd Harmonic increased. Dist 2 Mode It is well known that the triode distortion in tube circuits produces lots of 2nd and 3rd harmonics, in somewhat varying ratios. These lower order harmonics form "the octave" and "the octave and a fifth" to the fundamental musical tones. They are actually "musical" distortion. Harmonics well above the 2nd and 3rd are usually considered more harsh and unmusical, and therefore should be lower in amplitude (<-60 dB) to keep with our line of thinking. Second harmonic is considered to be the warmest and most "consonant" harmonic distortion and is usually very hard to hear, especially on single tracks. The Dist 2 mode on the Distressor emphasizes the 2nd harmonic (octave), especially while compressing. Dist 3 mode & the Distortion indicators This mode emphasizes the third harmonic. This is basically caused by nonlinear gain that results with the top and the bottom of waveforms being flattened out. Analog tape saturates in this manner. The 3rd harmonic is induced in the Distressor by increasing VCA output level. We have provided distortion indicator lights that come on most frequently in Dist 3 mode. A yellow LED light indicates .25% THD and the red "redline" LED indicates 3% THD or more. Though not always an exact indication of the distortion, these LED's are an excellent guide to where the user is in the "Grunge Department" and can help to avoid turning the music into an "overwell" mess. You will find that the harmonic distortion is generally more obvious on overall mixes and complex programs. On individual instruments, sometimes 3% distortion sounds "fat" and "analog" and isn't heard as distortion at all.