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Everything posted by Enthalpy

  1. Sound Perception

    Intervals tuned to simple frequency ratios are often more pleasant to our ears. Violin and viola players tune their instrument that way. Some texts claim that "good tune" follows simple ratios. So can we generalize? No. First, some harmonics sound out of tune. Here's the uncorrected scale of a natural horn, and within the west European musical culture, 7*F is badly low, 11*F isn't a note, and many higher multiples are bad. Hear Beat2_1_NaturalHorn.wav from the upload Beat2.7z 11*F is about three-quarter-tone, which serves in Romania, Greece, Iran and many more. "Proper intonation" is a matter of culture. West European musicians can train the three-quarter-tone by whistling Beat2_2_TrainQuarterTone.wav (here equal-tempered) with equal tongue movements. ---------- Then, they may be individually nice, but simple ratios combine to derail the intonation. Hear the small thirds in Beat2_3_ F_Ab_B_D_F.wav: tuned to 6/5 here, they sum to an octave a third-tone too big. One goal of the equal-tempered scale is to avoid this. Trombone and bowed string players learn to follow it, not just to play together with a piano, but in their own interest. ---------- This is the correction from simple ratios to the equal-tempered scale, in cent (0.01 half-tone). I've taken big intervals complementary to the small ones, like 16/9 rather than 7/4 for the minor seventh. The fifth and fourth (whose sum is an octave) have simple ratios only 2 cents wrong. Bowed strings are tuned to zero beat or by sounding the harmonics, which cumulates 6 cents over four strings, an error imperceptible to most people. Beat2_4_Fifth32BachFourth43Bach.wav plays both intervals according to simple ratios (no beat) and to equal temper. At the major and minor thirds and their complements, things get ugly. Zero-beat intonation sounds better and is tempting, but violinists and others must learn and train to follow the unpleasant equal temper to avoid other trouble. The height difference is patent even with single notes. Some guitarists tune the G-B strings by sounding their harmonics 5 and 4, which is questionable. Hear Beat2_5_ThirdMajor54BachMinor65Bach.wav. We hear beats at the major and minor seconds even when they follow simple ratios. Other ratios nearby explain it: only 37Hz separate the harmonics 8 and 7 when this interval is 9/8 and 20Hz separate the harmonics 15 and 14 in the 16/15 interval. At least, training them equal-tempered costs less. Hear Beat2_6_SecondMajor98BachMinor1615Bach.wav. At the tempered minor second, slow beats result from the harmonics 18 and 17. Marc Schaefer, aka Enthalpy
  2. Sound Perception

    Hello everybody and everyone! I'd like to share some thoughts about sound perception here. ========== First, does the phase of the harmonics matter in a periodic sound? This was a debated question when Hi-Fi was fashionable, and is still interesting. Here's a piece of software I made for more general purposes. It creates a file Tut.wav playable by Winamp, Windows' Sndrec32.exe, Media Player and probably more. The user defines a spectrum (hence of a periodic sound), the soft writes the sound in the file. TutD.zip I recommend to listen with headphones rather than PC loudspeakers that create misleading distortion even at low level. And this is a 440Hz sound with H1, H2 and H3 of equal amplitude, where the phase of H2 or H3 vary between two seconds intervals: 0s 2s 4s 6s 8s 10s 12s 14s 16s =========================================================== H1 (0dB) | 0° 0° 0° 0° 0° 0° 0° 0° H2 (0dB) | 0° 45° 90° 135° 180° 180° 180° 180° H3 (0dB) | 0° 0° 0° 0° 0° 0° 180° 45° =========================================================== H123Phase.zip And the net result is: I hear no difference at all. The phase of the harmonics does not matter. Marc Schaefer, aka Enthalpy
  3. Sound Perception

    How quickly do we perceive sound intensity? My TutTrem.exe writes in TutTrem.wav a tone at frequency f whose amplitude is modulated with depth 0 <= m <= 1 by a sine at frequency g TutTrem.7z and here are the sounds Tremolo.7z Trem_1_A880sine_3Hz10Hz30Hz50Hz70Hz.wav modulates a 880Hz sine, with 0.25 depth like the others, at 3Hz, 10Hz, 30Hz, 50Hz, 70Hz. I perceive a tremolo at 30Hz but a steady sum of notes at 70Hz, the limit being around 50Hz. Trem_2_C131sine_3Hz10Hz30Hz.wav. The sine C note is at 130.8Hz, about where the cello and bassoon begin their second octave. I perceive no tremolo at 30Hz already, so the ears are slower on lower notes. Well, the same happens with an amplitude detector made of electronic components. Trem_3_C131bassoon_3Hz10Hz30Hz50Hz70Hz.wav plays a 130.8Hz C note with already cited bassoon spectrum containing strong harmonics. The limit is around 50Hz again, so the ears discern quick changes through the harmonics of low notes. These observations are compatible with hair cells in our ears that measure amplitudes each over a band, supposedly wide bands with much overlap. https://en.wikipedia.org/wiki/Ear https://en.wikipedia.org/wiki/Hair_cell Trem_4_C65bassoon_3Hz10Hz30Hz50Hz.wav. The 65.4Hz C is about where the cello and bassoon begin. Here the limit is at 30Hz or less, quite fast for a 65Hz fundamental. Trem_5_D293A440violin_3Hz10Hz30Hz50Hz70Hz.wav. Made by the programme tutut uploaded in a previous message, the wav contains a fifth with violin spectrum: an A at 440Hz and a D above 293.33Hz so their harmonics 2 and 3 beat. Here too, the beat limit is around 50Hz. These observations are compatible with our ears measuring the amplitude in a band that contains the harmonics of both notes and perceiving the interferences as beats. Marc Schaefer, aka Enthalpy
  4. Quasi Sine Generator

    Here's the aspect of the waveform with T=210 a=5 b=14 c=16 from Mar 04, 2018 9:05 pm. Adding two of them with 60° lag or subtracting them with 120° gives the same wave. Electric motors sometimes run slower: at start on an electric plane, more often on an electric or hybrid car. The same waveform and filter would then drive the motor with a jagged voltage, but the drive electronics can use the same power components in PWM mode when running slowly. For an electric motor, a counter with fixed frequency suffices to place the transitions. Maybe a fast microcontroller can create the waveforms directly from its clock, or the controller tells the dates of the coming transitions to comparators that refer to one fast big counter. This can be integrated on a special chip, optionally the same as the controller. Marc Schaefer, aka Enthalpy
  5. Quasi Sine Generator

    Hello you all! Here's a means to produce a sine wave voltage, very pure, with metrologic amplitude, whose frequency can be varied over 2+ octaves in the audio range - this combination may serve from time to time. It uses sums of square waves with accurate shape and timeshift. A perfectly symmetric square wave has no even harmonics. Adding two squares shifted by T/6 suppresses all 3N hamonics as the delay puts them in opposition; this makes the waveform well-known for power electronics. Two of these waveforms can be added with T/10 shift to suppress all 5N harmonics, then two of the latter with T/14 shift, and so on. A filter removes the higher harmonics as needed. The operation makes sense, and may be preferred over direct digital synthesis, because components and proper circuits may provide superior performance. Counters produce accurate timings. If a fast output flip-flop outputs a zero 1ns earlier or later than a one, at 20kHz it leaves -90dBc of second harmonic and at 1kHz -116dBc, but at 1MHz less interesting -56dBc. If the propagation times of the output flip-flops match to 0.5ns, at 20kHz they leave -100dBc of third, fifth, seventh... harmonic and at 1kHz -126dBc. 74AC Cmos output buffers have usually less than 15ohm and 25ohm impedance at N and P side. On a 100kohm load, the output voltage equals the power supply to +0 -200ppm. 5ohm impedance mismatch contributes -102dBc to the third harmonic, less at higher ones. Common resistor networks achieve practically identical temperatures and guarantee 100ppm matching, but measures give rather 20ppm. This contributes -110dBc to the third harmonic, less at higher ones. This diagram example would fit 74AC circuits. Programmable logic, Asic... reduce the package count and may use an adapted diagram. To suppress here the harmonics multiple of 2, 3, 5 and 7, it uses 8 Cmos outputs and resistors. As 3 divides 9, the first unsqueezed harmonic is the 11th. A counter by 210 has complementary outputs so that sending the proper subsets to 8-input gates lets RS flip-flops change their state at adequate moment. Programmable logic may prefer GT, LE comparators and no RS. I would not run parallel counters by 6, 5 and 7 instead of 210 as these would inject harmonics. The RS flip-flops need strong and fast outputs. Adding an octuple D flip-flop is reasonable, more so with programmable logic. I feel paramount that the output flip-flops have their own regulated and filtered power supplies, for instance +-2.5V, and the other logic circuits separated supplies like +-2.5V not touching the analog ground. That's a reason to add an octuple D flip-flop to a programmable logic chip. For metrologic amplitude, the output supplies must be adjusted. All the output flip-flops must share the same power supplies, unless the voltages are identical to 50ppm of course. A fixed filter can remove the higher harmonics if the fundamental varies by less than 11 minus margin, and a tracking filter for wider tuning is easy as its cutoff frequency is uncritical. The filter must begin with passive components due to the slew rate, and must use reasonably linear components. ---------- I tried almost three decades ago the circuit squeezing up to the fifth harmonic, and it works as expected. Squeezing up to the third is even simpler, with a Johnson counter by 6 and two resistors. Measuring the spectrum isn't trivial, for instance Fft spectrometers can't do it; most analog spectrometers need help by a linear high-pass filter that attenuates the fundamental. Marc Schaefer, aka Enthalpy
  6. Quasi Sine Generator

    On the right side of the last message's diagram, I suggested separate supplies for the output flip-flops. While it can be useful to filter individual supply lanes for the flip-flops (in separate packages with LC cells), the phased outputs attenuate the target harmonics only if the supply potentials match very accurately, and this is best obtained from a common regulator.
  7. Quick Electric Machines

    The quick machines need AC in the kHz range, and sometimes MW power. PWM inverters are then difficult. I had suggested to provide square voltages rather than sines to reduce the number of lossy transitions per cycle http://www.scienceforums.net/topic/73798-quick-electric-machines/?do=findComment&comment=736205 but now there is an alternative, with my waveforms that suppress harmonics using few transitions. In the thread "quasi sine generators", for instance there https://www.scienceforums.net/topic/110665-quasi-sine-generator/?do=findComment&comment=1041409
  8. Quick Electric Machines

    Hello, heirs of James Clerk, Nikola and the others! It is well known, but by too few people : in an electric machine, only the force means losses and heavy parts, the speed comes for free. When a motor or generator runs quickly, say 50 or 100m/s at a power plant, it is smaller than a turbine. Quick machines with rotating permanent magnets use to hold them in a tight sleeve of strong steel to counter the centrifugal force. I propose to wind a composite of graphite fibres around the magnets instead of the steel sleeve. Graphite fibres are lighter than steel and produce less eddy current losses where they cross the stator's windings; better, while the accurate diameter of a steel sleeve is difficult, fibres are commonly wound tight over varied cores, even with a pre-tension useful here. A unidirectional composite looks best here, and pre-impregnated graphite is usual at wound pressure tanks for instance - other fibres may emerge. Some thin elastic material below the magnets can prevent cracks. To run at 200m/s, 5mm thick magnets weighing 7500kg/m3 need 1.5mm of graphite composite withstanding 1000MPa - or scale both thicknesses. Neodymium magnets like Thyssen-Krupp's 300/110 still achieve 0.78T through the graphite plus 1.5mm radial gap. I already described a small electric motor turning a rocket engine pump, there http://www.scienceforums.net/topic/73571-rocket-engine-with-electric-pumps/#entry734225 and http://saposjoint.net/Forum/viewtopic.php?f=66&t=2272&start=80#p41298 the following one outputs 2083kW like the PW127M gas turbine that moves the ATR-72 and other successful planes. http://www.pwc.ca/en/engines/pw127m http://de.wikipedia.org/wiki/Pratt_%26_Whitney_Canada_PW100 http://en.wikipedia.org/wiki/ATR_72 The motor rotates at 255Hz, so a gear drives the propeller at 20Hz - but a turbofan would need none. 5mm thick magnets at D=250mm run at 200m/s. The 355mm long stator has 3 phases and 18 poles. The windings are one turn of square 5mm*5mm copper that makes 36 passes through the shared 54 slits. The induced coil voltage is 1726Vpk (reduce the length if I botched a cos30°...) and the current 804Apk, nice for an inverter supplied with 3kVdc maximum. Coil resistance is 13mohm (or a bit more as the skin depth is 1.4mm at 2292Hz) so ohmic losses are 13kW or 0.6%; core losses are small with the proper material. This electric motor weighs ~120kg, is ~400mm long and 312mm wide , while the PW127M is 660mm wide and ~1.2m long without the gear, and weighs 481kg with the gear. Direct retrofit, though we still lack proper fuel cells. Marc Schaefer, aka Enthalpy
  9. Rocket engine with electric pumps

    The already cited Rocket Lab company has reached orbit in January with electrically pumped oxygen and kerosene https://www.rocketlabusa.com/news/updates/rocket-lab-successfully-reaches-orbit-and-deploys-payloads-january-21-2018/ https://www.rocketlabusa.com/news/updates/rocket-lab-successfully-circularizes-orbit-with-new-electron-kick-stage/ congrats! I like much their target market segment. Transporting only small satellites as main payloads, they offer more flexibility than a big launcher taking secondary payloads. At (announced!) 6Musd per launch, a split among many customers can be as cheap as a back seat elsewhere. Very important too, their working culture may be closer to that of teams building micro payloads, as the size and style of their user's manual suggests. Besides selling launches, they might consider to provide upper stages or engines, as well as roll and injection verniers, to other launchers: Falcon 9, Zenit, Chang Zhen 7, Soyuz and more. Long life, and get rich!
  10. Hello dear friends! As an alternative to heavy pressurized tanks and to complicated turbopumps, an electric pump can feed the propellants in the chamber(s). Conceivable at small chemical thrusters, where a high pressure improves the efficiency and injects enthalpy from the Solar panels. ----- Scale up: electronics can control 1MW motors from the main's voltage. A 70% efficient centrifugal pump brings then 72kg/s of oxygen and farnesane C15H32 to 96b; expansion from 80b to 0.02b in a 2.6m nozzle to push 260kN with Isp=375s, enough for the main engine of a 30t upper stage. Rotating at 780Hz in vacuum, the motor is small. Its rotor can be a permanent magnet of Magnetoflex 93, D=250mm L=200mm. The D=350mm 3-phase 8-pole stator loses <1kW in its braided "Litz" wires and 70W in the Nanoperm magnetic circuit; it's cooled by the fuel. The motor weighs 140kg. It accelerates in 30s. The safer Li-MnO2 primary battery brings ~650kJ/kg in the too quick discharge. The stage bringing 5900m/s would burn 24t; at full thrust, this would require a 470kg battery (20kg per ton of propellants), but throttling is easy, useful, and lightens the battery. The battery is easy to integrate and welcome for the gimbal actuators, the igniters... ----- Pressurized steel tanks for the same 24t but with only 36b in the chamber, throttling to 20b, would weigh 1930kg and provide 13s less Isp. Graphite tanks could weigh about 1100kg. A gas generator cycle could waste 42kg per ton of propellants, later ejected at 1500m/s thus counting as 35kg/t - but this equivalent overhead is ejected all the way and a battery supposedly not. Staged combustion is more efficient. ----- Scale up further: power components control 6MW railway engines. This would provide 1MN thrust with 120b in the chamber, enough for 115t at a second stage or 70t per 6MW slice at a first stage. ----- Smaller roll and vernier engines can also have electric pumps, for instance at a solid engine stage. For a lander or descent-ascent module, I like the ease of starting and restarting electric pumps. ----- Fuel cells would have been fantastic for a hydrogen-oxygen engine with electric pumps, but are still too heavy. Marc Schaefer, aka Enthalpy ===================================================================================== At an RL-10B equivalent with electric pumps, injectors shall drop 17% pressure and pumps be 65% efficient, then the shafts need 145kW and 399kW, and the motors cumulate 80kg. The Li-MnO2primary battery weighs 36kg per ton of propellants, a bit less by throttling. This is mass where not desired, and an expansion cycle performs better, but the electric pump is simpler. The battery mass is a good surprise, this is how I compute it: 1kg of oxygen-hydrogen m5.88:1 occupies 2.8dm3 as liquids boiling at 1 atm. Because no turbine is needed and I forgot the drop in the cooling jacket, the pumps must bring the propellants to 52.3b at the injectors. The power electronics shall be 97% efficient, the motor 99.9%, the pumps 65% because of hydrogen. 23kJ of electricity is used per kg of propellants. Li-MnO2 batteries use to store 240Wh/kg = 864kJ/kg or 33Ah*2,7V/355g = 904kJ/kg at room temperature http://media.duracell.com/media/en-US/pdf/gtcl/Technical_Bulletins/Lithium%20Technical%20Bulletin.pdf http://www.saftbatteries.com/doc/Documents/primary/Cube656/FRI_M62.2cf814ca-1181-4dc6-85f1-7c679f35054c.pdf but are meant for multi-hour discharge. Winding the electrodes and electrolyte thinner must permit a faster discharge (and self-discharge); I take only 650kJ/kg because of the redesign. Hence the 36kg per ton of propellants. This extra mass is similar to a gas generator cycle because both energy sources are chemical, and both happen to be equally inefficient. 36kg/t is as much as the Shuttle's external tank, alas, so a lower pressure is probably better. Throttling permits to reduce the pump pressure at the end, saving energy. Li-SOCl2 and others are lighter, fit fast discharge, cold... but they catch fire, explode or emit toxic gas if crushed or pierced. I don't want half a ton of them over 20t of explosive gas. ----- The power electronics needs a special design cooled by the fuel. An eight-pole motor at 780 Hz (46,800 rpm) needs three-phase at 3120 Hz so the electronics makes probably a 1/3 - 2/3 waveform instead of a sine by pwm. The motor is exotic. Its permanent magnet rotor is uncooled; Magnetoflex 93 with HV=950 rotates at 613m/s, key to the tiny design. A stepper motor would accept more banal materials but demands vacuum, and might combine with the impeller - maybe perhaps. ===================================================================================== Many hydrogen engines for upper stages offer no roll control. Vernier thrusters control the roll, the launcher's attitude at spacecraft separation, the precise injection speed to orbit. Instead of toxic and less efficient hydrazine, these thrusters could use the hydrogen and oxygen, but they must operate after the main engine shuts off, and a restartable extra turbopump is too complicated for them. Propellants at ~1.5b from the tanks may cavitate and need bigger thrusters. Electric pumps would improve this. This holds for other propellants as well, but pressure vessels are especially bad for hydrogen, hence the pumps. As roll actuators, they could push only when needed, saving further electricity hence battery mass. A positive displacement pump can be considered here. A thruster taking 5b hydrogen-oxygen exists already at DLR. For this purpose? Marc Schaefer, aka Enthalpy ===================================================================================== Many communication satellites are put by the launcher on Geosynchronous Tranfer Orbit and reach Geo-Synchronous Orbit with a 1600m/s kick by their MMH+N2O4 apogee motor. While better than solids, these motors use inefficient propellants pressure-fed by heavy tanks to burn at a low pressure. Electric pumps would improve. The satellite shall weigh 4000kg including the engine - wherever this one is. The nozzle is 0.6m wide. 1600m/s are brought in 2000s, needing about 4kN. Hydrogen-oxygen in the satellite improves most. The satellite's existing battery loaded by Sunlight brings all electricity (75MJ) for 100b in the chamber, hence the Isp and inert mass. Though, the hydrogen takes a 1.7m sphere. The sphere can be multilayer-insulated and held to a truss by polymer straps. Hydrogen-oxygen in a launcher's special stage takes an extra battery of 16kg/t to achieve only 20b. No big improvement over a Vinci stage for instance, but some launchers (Zenit, Falcon...) could then offer GSO delivery to satellites without an apogee motor or to replace MHM. Syntin-oxygen in the satellite can burn at 250b, or even more if the apogee kick is spread over several orbits. A strained amine is as efficient as Syntin and possibly cheaper. Syntin-oxygen in a launcher's special stage burns at good 80b. All-kerosene launchers may prefer it. The gain over MMH is still impressive. Space probes have similar needs, for instance to get captured by Saturn. A cryocooler can keep the propellants liquid. Un pensamiento para Don Hugo. Marc Schaefer, aka Enthalpy ===================================================================================== An oxygen screw pump fits a 4kN apogee motor burning Syntin. http://en.wikipedia.org/wiki/Rotary_screw_compressor Its two rotors can have (before optimization) D=20mm and a core of d=16mm, a single thread of 10mm pitch and 50% solid, for instance of nearly-sine profile. Drive at 418Hz and 3.3N*m (8.6kW) achieves 96bar and 669cm3/s if efficiency is 75%. With 10 screw turns in 100mm length, oxygen inertia lets it leak at 41m/s; 20µm radial clearance limit the leak to 104cm3/s - less if the pump is smaller. The stator and rotors need roughly matched temperatures and expansion coefficients. Turning or milling tools are made to the desired tiny profile. The pump weighs about 3kg. The electric motor can have a D=40mm L=60mm rotor (only 53m/s) with four poles of Nd-magnets held by a steel sleeve. The three-phase stator then looses about 60W. The motor weighs 2.5kg. Example of an electrically pumped apogee stage: Marc Schaefer, aka Enthalpy ===================================================================================== A main hydrogen-oxygen stage pushing 1MN with 40bar in the chamber(s) is feasible with battery power. The impeller for the hydrogen centrifugal pump for 33kg/s or 467dm3/s at 48bar has for instance D=214mm (not optimized), its channels are 19mm high, and it rotates at 503Hz. If 60% efficient, it needs 3.9MW and 1.2kN*m at the shaft. I won't detail the booster pump. The electric motor can have 10mm thick Nd-Fe-B magnets moving at 200m/s at the D=126mm L=400mm rotor, held by a 3mm thick sleeve. The 3-phase 4-pole (or more) stator loses about 20kW in its coils with few turns of rectangular wire, and the motor weighs 200kg. The traditional sleeve is cold-rolled austenitic steel. It could instead be helix-rolled and welded Maraging sheet to offer permeability. But for precision, and to reduce eddy currents in the sleeve, I'd prefer the same 3mm wound of unidimensional graphite prepreg. Thin elastic material can fit between the steel core and the magnets. A stepper motor, with a D=400mm L=50mm rotor and overlapped phases and coils, may work and weigh 70kg, but I won't invest more time to check this attempt. The oxygen pump can have symmetric inlets, then D=174mm lets it rotate at 165Hz, so a ring motor can have D~380mm with many poles and be flat - I won't detail it. The magnets cost 1000€ per motor. 80t of propellants need 2.7t of Li-MnO2 batteries, which sell for ~50€/kg in small amount. Marc Schaefer, aka Enthalpy ===================================================================================== A booster burning 225:100 of O2:Pmdeta expanded from 110b to 0.35b in a D=2.4m nozzle to produce 2MN and 337s @vac needs 419kg/s and 367dm3/s of oxygen. The centrifugal pump with symmetric inlets can rotate at 217Hz with a D=204mm impeller; being 72% efficient, it receives 6.75MW and 4.95kN*m from the shaft. (Click to magnify) A corresponding electric motor has 10mm thick Nd-Fe-B magnets moving at 200m/s on D=290mm. 3mm thick wound unidimensional graphite composite holds the magnets. 18 poles allow 16mm thin iron at the stator and the hollow rotor, and a single turn (36 passes, 36 grooves, 3 phases) of D=8mm twisted "Litz" wire gets 1.7kVpk induced, while 2.0kApk take 12 big IGBT. Copper looses some 50kW and the motor weighs 160kg for almost 7MW: it's lighter than a gas turbine. On an aeroplane, it can drive a fan directly, or a propeller through a gear. We still lack light fuel cells. Marc Schaefer, aka Enthalpy
  11. Violin non-linearity

    As it looks, a non-linearity isn't necessary to let sounds beat https://www.scienceforums.net/topic/113243-sound-perception/?do=findComment&comment=1042336 The two bows experiment remains interesting to check if it changes the sound quality.
  12. Violin non-linearity

    Hi dear music lovers! The violin and all bowed instruments has an important non-linear behaviour. It is noticed when playing two notes simultaneously on one instrument: the nonlinearity produces an additional beat, absent if two instruments produce the notes separately. When the frequencies are far from a ratio of integers, for instance in an equal-tempered small third interval, the beat is unpleasantly fast and seems out of tune, so violonists must train to play equal-tempered. The equal-tempered octave, fourth and fifth in contrast are nearly ratios of integers, the beat can be unnoticeable for being slow; violonists use it to tune the instrument. No source of non-linearity is expected in a violin, because all vibration strains and stresses are small. I claim (others may have done it) that the bow-string contact is the source. In favour of this: we don't hear the beat if playing pizzicato, that is, by plucking the strings. Also: the beat is still audible if playing piano, while a non-linearity in the violin would decrease the relative strength of the beat when the notes weaken. The bow-string contact operates in a well-understood fashion. Rosin makes the bow sticky; the moving bow pulls the string to the side and gives it energy until the string's stiffness wins, then the sticky contact breaks, the string relaxes back, until one-half to one period later, the speeds again similar permit the string to stick again to the bow. By the way, this stick-slip process is somewhat random as sticking uses to be. As a consequence, sticking ceases within a period at a moment that fluctuates, and the sound isn't really periodic. It is known meanwhile (but not enough) that for a listener to recognize a violin, the sound must be non-periodic. Attempts to synthesize it from a harmonic spectrum, hence producing a periodic sound, consistently failed over decades - but a primitive synthesis with a simple sawtooth signal shape, whose transition had intentional jitter, was immediately "violin-like". This experiment (in a French university I believe) was among the first proofs that musical sounds are, and must be, non-periodic. Relying on a threshold, the stick-slip is as nonlinear as possible. Several processes can couple the strings so that the instant phase at one string influences the moment when the other string tears off the bow: - The strings' movement is knowingly elliptic, not just parallel to the bow's speed. As one string moves perpendicularly to the bow, it changes the bow's pressure on the other, hence the maximum sticking force, and influences the tear-off instant. - The horsehairs at the bow have some elasticity. When a first string tears off the bow, the horsehairs reduce their strain, pulling suddenly stronger the other string, which tears off if it was about to do so. - The violin's bridge is compliant. Less so than a string, to make there a displacement node, but enough to move the sounding boards. The movement of one string displaces the other a bit, which again influences the instant when the other string tears off. These processes keep a beat amplitude essentially constant relative to both notes, which a nonlinearity downstream the oscillator can't. Marc Schaefer, aka Enthalpy
  13. Sound Perception

    When you play simultaneous notes on a violin, you hear them beat, depending on the interval and the intonation. It's weak but well perceiveable at the violinist' distance. The same happens on the viola, and supposedly other polyphonic instruments with sustained sound. To investigate the beat, I reproduce it with sounds synthesized by my software Tutut.7z and here are the sound samples Beat1.7z As a violin spectrum, I thankfully use these measures of an empty D string http://nagyvaryviolins.com/tonequality.html and again, a spectrum synthesizes a periodic sound that fails to imitate a music instrument. The four Beat1... wav play simultaneously a 440Hz A and a D nearly a fifth lower like violin strings. In the first 2s, the frequency ratio is 3/2, and for the next 2s, D is raised by 1Hz. Beat1_A_DA32harm.wav uses the measured spectrum. You hear 3 beats per second when D is raised by 1Hz because the harmonics 3 of D and 2 of A interfere. This happens without intentional nonlinearity, on summed sounds, and the intensity of the beat resembles what the violinist hears. I had supposed some nonlinearity is requested at the instrument, there http://www.scienceforums.net/topic/80768-violin-non-linearity/ and as it looks I was wrong. Our ears perceive sound intensities on a logarithmic scale more or less, so they aren't linear. A measurement of the intensity is by nature a nonlinear process anyway. So the instrument can behave linearly, and the perception makes the interference. Beat1_B_DA32onlyH23.wav contains a fundamental and only the harmonics 2 and 3 of the measured spectrum. It beats like the complete spectrum: 3 times per second, similar amplitude. Beat1_C_DA32removedH23.wav uses the spectrum minus the harmonics 2 and 3. It beats more weakly and about 6 times per second, like the interference of the weaker harmonics 4 and 6. Beat1_D_DA32sine.wav contains sine waves. I perceive no beat at medium amplitude, and only a faint one when playing loudly, when the amplifier's power supply drops. Until I improve the amplifier, I consider the power supply produces the faint beat with sines, but not the stronger beat when harmonics are present. All is consistent with a linear interference of harmonics. Marc Schaefer, aka Enthalpy
  14. Sound Perception

    Aggiornamento to the second message of Feb 18, 2018 https://www.scienceforums.net/topic/113243-sound-perception/?do=findComment&comment=1038957 I have now bigger loudspeakers. No Hi-fi, but better than Pc hardware. They are connected to the usual amplifier. With them, I hear easily a difference between a sine and 3% mild distortion (a tanh deformation that compresses the sine crest by 3%), and 1% is the limit once knowing what to listen at. Which implies that, even at modest power, the previous Pc loudspeakers and headphones deformed the sound enough to make 3% distortion barely discernible. Ouch. The following wav distorts mildly the 330Hz sine by 0%, 1%, 3% in 2s samples. DistortionB.7z So maybe 1% of mild distortion is our perception limit - or my present hardware still creates as much distortion. My sensitivity to hard clipping and to 8-bit coding has not changed.
  15. Quasi Sine Generator

    The stone-old Proms like 2716 make the waveforms easily, as they receive all addresses at once on pins distinct from the data. They are still available in small amount. I didn't check if more recent components exist nor how they are addressed. Of the diagrams, the left example provides the drive signals for a three-phase power stage driving a motor, a transformer and transport line... The Prom behaves statically, so a counter and a set of flip-flops suffice. One of the eight output bits defines each waveform, possibly more than three to stack transformers. Only the switching losses in the power components limit the number of transitions per cycle. The right example makes a sine exempt of H5 and H7 thanks to the chosen transitions, and of H3 and H9 by summing two waveforms shifted by 60°. T=210 a=5 b=14 c=16 is a logic candidate here, though more transitions can attenuate more harmonics, alone or helped by the resistors. More waveforms and resistors can attenuate more harmonics too. The waveforms can be longer too, for instance to create new phase shifts. Counting by 840 for T=210 here lets the Prom store 0001 and 0111 for each symbol to make tr-tf unimportant. The dinosaur Proms consume power and limit the clock to about 10MHz hence the sine to 50kHz. Newer Proms (in a programmable logic chip?) could be much faster, but the general solution to speed is logic rather than Proms. Marc Schaefer, aka Enthalpy
  16. Hear a Kora

    The Kora, a fabulous plucked string instrument, isn't common where I live, but here are opportunities to hear one - or even two, as Toumani and Sidiki Diabaté play together. https://www.youtube.com/watch?v=-cLAwAOi-hA https://www.youtube.com/watch?v=K8nyjsDj-Is (music begins at 0:25) Enjoy!
  17. Bore width of wind instruments

    The first record of the sonata on a Heckel system bassoon (by Sophie Dartigalongue) was removed from Youtube, but here's one piece of it:
  18. Bore width of wind instruments

    Hello, dear music lovers! I often read that a broader bore gives wind instruments a mellower sound. This comparison holds for the bugle and tuba versus trumpet and trombone, but I claim it should not be extended to woodwinds, especially not to double reed instruments. Make your opinion with two bassoons, both playing very well Saint-Saëns' sonata French system Heckel system More artists have played the sonata, and in every case the Heckel bassoon is prompt to become tinny. The instruments diverged in the 19th century. The French bassoon continued to evolve, but less so than the Heckel system, which was a more radical development from the older instruments. The Heckel system has a broader bore, and its tone holes get wider at the low notes, but it has kept the very long tone holes. The hole system, keyworks and fingerings differ enough to demand re-learning the instrument. The big drawback of the French bassoon: it isn't loud enough! Insufficient in an orchestra. Julien Hardy luckily played with a civilized pianist. And for a solo over a symphonic orchestra: no chance. So it has but disappeared.
  19. Quasi Sine Generator

    Ahum. Ism generators, not Rfid.
  20. Quasi Sine Generator

    We can combine both methods to reduce more harmonics: add or subtract optimized +-1 waveforms with the proper phase shift. This combines the drawbacks, but also the advantages: for instance the number of summing resistors doubles for each suppressed harmonic, which at some point a +-1 waveforms does for cheaper. ---------- Voltage differences appear in power electronics at full bridges and three-phase bridges. If two outputs are out of phase minus a fourteenth of a period, the load between them sees no H7, so using the waveforms of Jan 13, 2018 to Jan 21, 2018 that squeeze H3 and H5, the first strong one is H9. More commonly, the outputs can lag by 120°, which suppresses H3 and H9. This is done with square waves and improves with the coming +-1 waveforms that squeeze H5 and H7, leaving H11 as the first strong one. Three square waves at 0°, 120° and 240° were common with thyristors, especially for very high power. They need an additional regulation of the supply voltage, often a buck. With Igbt, sine waves made by Pwm are more fashionable. They need less filtering, avoid cogging at motors, adjust the output amplitude, but suffer switching losses. The more elaborate +-1 waveforms I propose are intermediate. They need an additional regulation, but have small switching losses, and little filtering avoids harmonics and cogging. Maybe useful for very high power, to minimize switching losses and save on costly filters. I see an emerging use for quick electric motors: http://www.scienceforums.net/topic/73798-quick-electric-machines/ Machine tools demand a fast spindle hence a high three-phase frequency; Centrifugal pumps and compressors demand fast rotating motors too; Electric aeroplanes need a high three-phase frequency to lighten the motor, either with a small fast motor and a gear, or with a large ring motor at the fan's speed but with many poles for a light magnetic path. The high frequency (several kHz) is uneasy to obtain by Pwm as switching losses rise. But for fans, compressors, pumps... whose speed varies little, a fixed LC network filters my waveforms to a nice sine. Rfid generators at low frequencies might perhaps benefit from such waveforms too, since they must filter much their harmonics to avoid interferences, which is costly. RF transmitters maybe, for LW. ---------- The selected +-1 waveforms in this table squeeze H5 and H7 since the phased sum does the rest. 7 transitions per half-period ideally suppress H5 and H7 with T=210, more transitions bring no obvious advantage in this quest. Power electronics tends to reduce the transitions that create switching losses, and want a strong H1 voltage, while spectral purity isn't so stringent, so the table's top fits better, while the bottom is more for signal processing. One single transition more than the square wave puts the H5 voltage at 6% of the fundamental, two transitions at 0.7%. At 2kHz, 100ns accuracy on the transitions suffices easily, so a specialized oscillator isn't mandatory. 0.97 and 0.93 are fractions of the square wave's H1 voltage, and the usual coefficients like sqrt(3)/2 still apply. H1 H3 H5 H7 H9 H11 | T a b c d e =================================================== 0.97 -12 -25 -27 -19 -16 | 36 1 0.93 -15 -43 -43 -21 -14 | 180 8 11 0.90 -9 nil -64 -16 -16 | 180 5 41 42 0.93 -16 nil nil -30 -39 | 210 5 14 16 0.90 -18 nil -51 -21 -12 | 120 1 4 11 12 0.87 -8 nil -61 -21 -15 | 120 2 3 4 26 27 0.77 -10 nil -77 -7 -15 | 120 4 16 17 28 29 0.93 -15 nil -77 -23 -17 | 180 1 7 9 12 13 =================================================== Marc Schaefer, aka Enthalpy
  21. Quasi Sine Generator

    The wide Nand gates that detect the transition times from the counter's outputs are welcome with programmable logic. With packages of fixed logic instead, decoding subgroups of counter outputs allows small Nands. This diagram for T=210 and 27 transitions per half-period needs only 16 packages. The by-105 counter and transition locators in odd number make two cycles per sine period, the output JK rebuilds a complete period. The logic can be pipelined for speed; think with calm at what state decides the reset (or better preload), and then at the other transitions. -------------------- Alternately, diodes-and-resistor circuits can make the logic between a 4-to-16 decoder and an 8-to-1 multiplexer. Few logic packages and 1 diode per transition. Or use a tiny PROM easy to address by the counter. -------------------- We can also split the counter into subfactors, like T=210=6*5*7=14*15. This enables Johnson counters, which comprise D flip-flops plus few gates for N>=7, and are easier to decode and faster. For a count enable, feed the outputs of flip-flops through a multiplexer back. Traditionally, the subcounters run a different paces, and the carry outputs of faster subcounters determine the count enable inputs of slower ones. We can run them all at full speed instead: with factors relatively prime, they pass through all combinations of states in a period. Subcounters ease several phased sine outputs, at 90°, at 120° and 240°... For instance with T=210=6*5*7, common logic can locate transitions from the /5 and /7 subcounters, and these transitions serve not only twice per period, but also for the three sines, as switched by the /6 subcounter. To my incomplete understanding, Or gates can group several located transitions if their interval is no multiple of 6. Notice the T states and RS flip-flops, not T/2 and JK, to ensure the relative phases. A PROM is a strong contender for phased sine outputs. -------------------- Here's a subdiagram to make tr-tf unimportant, as proposed here on Jan 28, 2018. 4T clock ticks per sine period in this example, adding a /4 subcounter whose carry out drives the count enable of the other (sub)counter(s). Or use a PROM 4* bigger. Marc Schaefer, aka Enthalpy
  22. Quasi Sine Generator

    The search programme could gain 10dB on H3, H5 and H7 with +-1 waveforms using 23, 25 and 27 transitions per half-period. Still the dumb algorithm, but the source is better written. Search27357b.zip Here's a selection of waveforms, with 21 transitions too. Among even T, 210 stands widely out. The H1 amplitude refers to a square wave while H3, H5, H7, H9 are dBc. H1 H3 H5 H7 H9 | T a b c d e f g h i j k l m ===================================================================== 0.73 -104 nil nil -23 | 210 2 7 14 16 19 20 26 28 42 43 0.34 -114 nil nil 6 | 210 3 6 7 14 22 35 36 38 43 45 46 0.59 -111 nil nil -19 | 210 5 6 10 14 16 17 19 20 29 32 44 46 0.38 -114 nil nil -8 | 210 1 2 4 6 10 19 25 34 35 39 41 43 46 ===================================================================== Marc Schaefer, aka Enthalpy
  23. Sound Perception

    Clipping the crests of a sine by 0.5% is noticeable previous message here and digitizing on 8 bits creates everywhere steps 0.4% high or more. Expectedly, the difference between 16 bits and 8 bits is strong on a sine: Bits8or16.zip For the 16-bits sine to sound pure, your loudspeakers may need a soft support. The effect is the same through my three audio cards, in the loudspeakers as in two headphone sets. Is it not a result of aliasing, since the original sine is "perfect" (64-bit floats) hence contains no aliasable harmonics. Neither a result of the sampling frequency, always 44.1kHz. If the resolution were unlimited, sampling would introduce no error at all. But here the digitizing noise is strong for our ears, and it resides at frequencies not belonging to the original sound. The complicated interaction with the sampling frequency lets the 330Hz and 329Hz sines sound differently after the 8-bit digitization. The other sounds I provide in the discussion are digitized on 16 bits at 44.1kHz. Marc Schaefer, aka Enthalpy
  24. Sound Perception

    If you record a long sample and reproduce the whole sample, the reproduction will be good. It's called recording and works decently by now. Taking a direct and inverse Fourier transform of the whole long sample introduces arbitrarily low imperfections, provided you record the phase too, or the complex coefficients. As good as recording. What does not work is when people attempt to fourierize one period of the sound and reduce the information to a harmonic spectrum, because this sound is non-periodic in essence. Synthesis from harmonics creates identical periods - be it one recorded period, or a mean of several periods - which our ears do not accept as a saxophone sound. Any PC has already an ADC in its sound card. Not of recording studio quality, but it suffices to record a saxophone and reproduce a convincing sound. You might for instance record a long tone, identify the pseudo-periods, compute a mean value, and observe that the mean period does not sound like a saxophone or a recorder. It doesn't even need a Fourier transform. Researchers at a Brittany university claimed (I didn't hear it) they obtained a more convincing violin sound by taking a sawtooth signal and letting a random noise decide the instant of the transition.
  25. Quasi Sine Generator

    At last, +-1 waveforms that reduce nicely H3, H5 and H7. They take 21 transitions per half-period but only T=210. H3 H5 H7 H1 T a b c d e f g h i j ================================================================= -104 -inf -inf 0.73 210 2 7 14 16 19 20 26 28 42 43 <<<<< -110 -inf -inf 0.23 210 8 10 14 22 32 34 38 41 42 46 <<<<< ================================================================= The amplitudes of H5 and H7 are algebraic zeros almost certainly. The first waveform has its H9 some 23dB below H1, while the second has a weaker H1, about 10dB below H9. A 6 bits up-down counter takes only 11 big And gates to define all the transitions. -------------------- The harmonics that are zero to the rounding accuracy with 64-bits floats remain so with 80-bits floats, both here and for the previous waveform that suppresses H3 and H5 using 11 transitions. Marc Schaefer, aka Enthalpy