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210 Beacon of Hope

About Enthalpy

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  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

    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
  3. 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
  4. 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.
  5. 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
  6. 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!
  7. 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.
  8. 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
  9. 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.
  10. 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
  11. 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!
  12. 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:
  13. Quasi Sine Generator

    Ahum. Ism generators, not Rfid.
  14. 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
  15. 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