2d:null 2e:["$","title",null,{"children":"MIDI note to freq - using 16-bit integers only | maddie lim ✨ | Observable"}] 33:T535,In MIDI, or other sequencing systems, notes are typically stored as an integer value representing the semitone. This is commonly known as a "note number". Many standards use 60 as middle C. So the C major scale from middle C would be: ``` C D E F G A B C 60, 62, 64, 65, 67, 69, 71, 72 ``` In order to play notes on a synthesizer the note number must be converted to a frequency (in Hz). Many synthesizers would take care of this conversion, however the DSP registers of the SNES will only take a Hz value. Therefore the music engine needs to do this conversion itself. The formula for calculating the frequency of a note is: ``` f = BASE_FREQ * 2 ^ ((n - BASE_NOTE) / 12) ``` This is derived from [equal temperament](https://en.wikipedia.org/wiki/Equal_temperament) which is the modern western standard of tuning. Each octave can be logarithmically divided into 12 parts (semitones). To move up or down a semitone, you respectively multiply or divide by the 12th root of 2 (in other words 2^(1/12)). An octave is simply doubling or halving the frequency (since `12 * 2^(1/12)` = `2^(12/12)` = `2^1` = `2`). So for example if we wanted to calculate the frequency of C above middle C, we can take the standard of middle A = 440Hz. C above middle C is 3 semitones above middle A, so the calculation would look like:34:T4bd,The SPC-700 is not powerful enough, nor has a math library, to reasonably compute 2 ^ (1/12), and so a common way around this is to create a frequency table. Some engines had an entire table with the frequency of every note in every octave (typically a table of up to 128 values). This is great if your base frequency is known (for e.g., tone generators like the 5A22/2A03 on an NES, where 440Hz is definitely middle A). However, since the SPC-700 uses sampled instruments, the base frequency for each sample is set by the user, based on the recorded sample. For example, a sample of a piano playing a middle C note might have been recorded at 8khz, therefore it's base frequency is 8khz. So every instrument might need its own table! That's a lot of tables!! We can generalize this much more and use a single, and much smaller table, for an instrument of any arbitrary base frequency. Given that we can navigate octaves by simply multiplying or dividing by 2 (in assembly we can simply shift bits around to do this), the missing piece is then performing the multiplication needed to get to the note within that octave. For this we will need a lookup table to represent the values we will need to multiply by.35:T8ab,midiNoteToFreqInt = (n) => { const baseOctave = 5; /* HELPER FUNCTIONS to simulate some SPC behaviour */ const mul = (y, a) => { const m = ((a & 0xff) * (y & 0xff)) & 0xffff; return [m >> 8, m & 0xff]; }; const div = (y, a, x) => { const ya = (((y & 0xff) << 8) + a) & 0xff; const oa = (ya / x) & 0xff; const oy = ya % x; return [oy < 0 ? oy + x : oy, oa]; }; const adc = (a, b) => { const add = (a & 0xff) + (b & 0xff); const c = add > 0xff ? 1 : 0; return [add & 0xff, c]; }; const split = (n) => [n >> 8, n & 0xff]; const combine = (msb, lsb) => ((msb & 0xff) << 8) + (lsb & 0xff); /* END HELPER FUNCTIONS */ /* Integer division and modulo (remainder) can be done with a single instruction on an SPC-700 using the DIV YA, X instruction Y <- YA % X and A <- YA / X */ const [octaveNote, octave] = div(0, n, 12); const octaveOffset = octave - baseOctave; // double/halve our base frequency to get it into the target offset var octaveFreq = FreqBaseNote; if (octaveOffset > 0) { for (var i = 0; i < octaveOffset; i++) { octaveFreq <<= 1; // ASL } } else if (octaveOffset < 0) { for (var i = 0; i > octaveOffset; i--) { octaveFreq >>= 1; // LSR } } if (octaveNote === 0) { // if C, we don't need to do anything further return octaveFreq; } // index into the frequency table to work out how much we need to multiply by const noteMultiply = FreqMultiplyTable[octaveNote]; /* these next four lines perform long multiplication */ const [ofHi, ofLo] = split(octaveFreq); const [nmHi, nmLo] = split(noteMultiply); const [p1H, p1L] = mul(ofLo, nmLo); // p1L is unused const [p2H, p2L] = mul(ofLo, nmHi); const [p3H, p3L] = mul(ofHi, nmLo); const [p4H, p4L] = mul(ofHi, nmHi); // p4H is unused // | hi lo | // |---------| // | p1H | p1L // | p2H p2L | // | p3H p3L | // p4H | p4L | // |---------| // | oHi oLo | // CLC const [oLo, oC] = adc(p1H, p2L); const oHi = adc(p2H, p3H)[0] + oC; // CLC const [oLo2, o2C] = adc(oLo, p3L); const oHi2 = adc(oHi, p4L)[0] + o2C; return combine(oHi2, oLo2); }36:Ta7e,midiNoteToFreqIntSpc = (note) => { const memOctFreq = 0x10; const memFreqTable = 0x20; const memNoteMultiply = 0x00; const memResult = 0x02; const baseOct = 5; var s = SPC.createState(); // Write initial values to memory addresses s = SPC.write16(s, memOctFreq, FreqBaseNote); // Load multiplication table s = FreqMultiplyTable.reduce( (s, fm, i) => SPC.write16(s, memFreqTable + i * 2, fm), s ); // Divide note by 12 to figure out octave number, and note index within octave. s = SPC.ldy(s, 0); s = SPC.lda(s, note); s = SPC.ldx(s, 12); // This instruction results in A = YA / X, Y = YA % X s = SPC.div(s); /* Y has the note index A has the octave number We'll subtract with the base octave so we know how much to double or halve. */ s = SPC.sec(s); s = SPC.sbc(s, baseOct); // loop where we double / halve the octave if (SPC.bne(s)) { if (SPC.bmi(s)) { do { s = SPC.clc(s); // divide in half (16-bit LSR) s = SPC.rorAddr(s, addrOctFreq + 1); s = SPC.rorAddr(s, addrOctFreq); s = SPC.inc(s); } while (SPC.bne(s)); } else { do { s = SPC.clc(s); // multiply by two (16-bit ASL) s = SPC.rolAddr(s, addrOctFreq); s = SPC.rolAddr(s, addrOctFreq + 1); s = SPC.dec(s); } while (SPC.bne(s)); } } /* Take the note index in Y and double it into X to use as an index into the freq table. Store the multiplier in memory. */ s = SPC.tya(s); s = SPC.asl(s); s = SPC.tax(s); s = SPC.ldaAddrX(s, memFreqTable + 1); s = SPC.staAddr(s, memNoteMultiply + 1); s = SPC.ldaAddrX(s, memFreqTable); s = SPC.staAddr(s, memNoteMultiply); /* Begin the long process of applying the note multiplier to the octave frequency. This is where the complex integer based floating point multiplication starts. */ s = SPC.ldyAddr(s, memOctFreq); // This instruction results in YA = Y * A s = SPC.mul(s); s = SPC.tya(s); s = SPC.ldy(s, 0); s = SPC.styaAddr(s, memResult); s = SPC.ldyAddr(s, memOctFreq); s = SPC.ldaAddr(s, memNoteMultiply + 1); s = SPC.mul(s); s = SPC.addw(s, memResult); s = SPC.styaAddr(s, memResult); s = SPC.ldyAddr(s, memOctFreq + 1); s = SPC.ldaAddr(s, memNoteMultiply); s = SPC.mul(s); s = SPC.addw(s, memResult); s = SPC.styaAddr(s, memResult); s = SPC.ldyAddr(s, memOctFreq + 1); s = SPC.ldaAddr(s, memNoteMultiply + 1); s = SPC.mul(s); s = SPC.tay(s); s = SPC.lda(s, 0); s = SPC.addw(s, memResult); s = SPC.styaAddr(s, memResult); // By now we have our calculated frequency value! return SPC.read16(s, memResult); }37:[] 31:{"id":"f4f096344922691c","slug":"spc-midi-note-to-freq","title":"MIDI note to freq - using 16-bit integers only","thumbnail":"75a601e88340299c9314562dc5c022c2ce0dc88308f4cd90c21705842555aed1","access_level":"public","create_time":"$D2022-01-26T17:20:54.187Z","update_time":"$D2022-10-09T02:56:00.726Z","view_time":null,"first_public_time":"$D2022-02-22T00:04:16.760Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"408ee840d040526a","login":"maddievision","name":"maddie lim ✨","avatar_url":"https://avatars-next.observableusercontent.com/44fc4f0f8be73321b571127eefd9853a031c5c33e9985648c91e6aa827258ce0","tier":"starter_2024"},"version":1297,"publish_version":1297,"role":null,"authored":false,"authors":[{"type":"individual","id":"578d96c86967f83d","login":"maddievision","name":"maddie lim ✨","avatar_url":"https://avatars-next.observableusercontent.com/44fc4f0f8be73321b571127eefd9853a031c5c33e9985648c91e6aa827258ce0","tier":null}],"members":[{"type":"individual","id":"578d96c86967f83d","login":"maddievision","name":"maddie lim ✨","avatar_url":"https://avatars-next.observableusercontent.com/44fc4f0f8be73321b571127eefd9853a031c5c33e9985648c91e6aa827258ce0","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":2,"collection":{"id":"3e84a05cdcdeb25f","slug":"low-level-stuff","title":"Low Level Stuff","owner":{"id":"408ee840d040526a","login":"maddievision","name":"maddie lim ✨"}},"type":"notebook","body":{"title":"MIDI note to freq - using 16-bit integers only","cells":[{"id":0,"value":"# MIDI note to freq - using 16-bit integers only\nFor use in future SNES / SPC-700 music engine","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":3,"value":"$33","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":334,"value":"C_above_middle_C_freq = 440 * Math.pow(2, 3 / 12)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":337,"value":"In our implementations below, we'll use a standard of middle C = 2616 (based on A = 440). We're using x10 to reflect what a typical sampled instrument might use as a base tuning value for C.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":328,"value":"# 16-bit implementation","pinned":true,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":319,"value":"Frequency of middle C (note 60 in MIDI)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":45,"value":"FreqBaseNote = 2616 // frequency of middle C","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":341,"value":"$34","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":344,"value":"FreqMultipliers = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11].map((o) =>\n Math.pow(2, o / 12)\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":346,"value":"So by doubling/halving the base frequency to get to the right octave, we simply need to index the note into this table and multiply to get the result frequency, using only table of size 12. Awesome!!\n\nNot so fast though, we have a problem here! The SPC-700 doesn't have floating point numbers. It is natively an 8-bit system, which can do multiplication and division with the _result_ being in 16-bits.\n\nThe `DIV YA,X` opcode essentially does Y * A and stores the result using YA combined to create 16-bits. Then the remainder (modulo) is stored in X.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":353,"value":"**TODO:** Insert blabble about how we can do floating point arithmetic using only integers.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":30,"value":"FreqMultiplyTable = FreqMultipliers.map((fm) => Math.round(fm * Math.pow(2, 8)))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1150,"value":"Reference implementation that will be turned into pseudo-SPC assembly:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":195,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1156,"value":"# SPC Implementation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1146,"value":"The breakdown of how this SPC function works is [further below](https://observablehq.com/d/f4f096344922691c#cell-550).","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1018,"value":"$36","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":253,"value":"## Test","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":275,"value":"Generate 3 octaves of notes starting from note 48 (C below middle C):","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":271,"value":"notes = Array.from(Array(3 * 12).keys(), (n) => n + 48)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":301,"value":"Frequencies calculated by integer algorithm:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":199,"value":"testFrequencies = notes.map(midiNoteToFreqIntSpc)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":304,"value":"Frequencies calculated using the floating point algorithm (which is a direct translation of the mathematical formula):","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":20,"value":"floatReference = notes.map((n) => Math.round(midiNoteToFreq(n)))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":309,"value":"Comparison between the two, by measuring variance: (ideally, no more than +/- 0.2%)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":234,"value":"variation = testFrequencies.map((f, i) =>\n pct(roundTo(3, (f - floatReference[i]) / floatReference[i]))\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1248,"value":"roundTo = (c, n) => Math.round(n * Math.pow(10, c)) / Math.pow(10, c)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1254,"value":"pct = (n) => (n * 100).toString() + \"%\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":282,"value":"**TODO:** can we plot these on a graph?","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":550,"value":"## SPC Step-by-step Simulation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":584,"value":"simInputNote = 88","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1160,"value":"This is a step by step walkthrough of how the [consolidated function, above](https://observablehq.com/d/f4f096344922691c#cell-1156), was derived.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":586,"value":"simBaseFreq = FreqBaseNote","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1014,"value":"simBaseOct = 5","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":598,"value":"addrOctFreq = 0x10","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":888,"value":"addrFreqTable = 0x20","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":891,"value":"addrNoteMultiply = 0","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":892,"value":"addrResult = 2","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":556,"value":"s0 = SPC.createState()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1104,"value":"Write initial values to memory addresses:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":762,"value":"s0a = SPC.write16(s0, addrOctFreq, simBaseFreq)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":768,"value":"SPC.memSlice(s1, addrOctFreq, 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1108,"value":"Load multiplication table:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":601,"value":"s1 = FreqMultiplyTable.reduce(\n (s, fm, i) => SPC.write16(s, addrFreqTable + i * 2, fm),\n s0a\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":755,"value":"SPC.memSlice(s1, addrFreqTable, 24)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1114,"value":"Divide note by 12 to figure out octave number, and note index within octave.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":566,"value":"s2 = SPC.ldy(s1, 0)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":583,"value":"s3 = SPC.lda(s2, simInputNote)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":590,"value":"s4 = SPC.ldx(s3, 12)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1260,"value":"This instruction results in `A = YA / X`, `Y = YA % X`","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":592,"value":"s5 = SPC.div(s4)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1118,"value":"Y has the note index\n\nA has the octave number\n\nWe'll subtract with the base octave so we know how much to double or halve.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":701,"value":"s6 = SPC.sec(s5)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":699,"value":"s7 = SPC.sbc(s6, simBaseOct)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1192,"value":"loop where we double / halve the octave","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1182,"value":"SPC.memSlice(s7, addrOctFreq, 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":991,"value":"s7a = {\n var s = s7;\n\n if (SPC.bne(s)) {\n if (SPC.bmi(s)) {\n return SPC.bloop(\n s,\n (s) => {\n s = SPC.clc(s);\n // divide in half (16-bit LSR)\n s = SPC.rorAddr(s, addrOctFreq + 1);\n s = SPC.rorAddr(s, addrOctFreq);\n return SPC.inc(s);\n },\n SPC.bne\n );\n } else {\n return SPC.bloop(\n s,\n (s) => {\n s = SPC.clc(s);\n // multiply by two (16-bit ASL)\n s = SPC.rolAddr(s, addrOctFreq);\n s = SPC.rolAddr(s, addrOctFreq + 1);\n return SPC.dec(s);\n },\n SPC.bne\n );\n }\n }\n\n return s;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":998,"value":"SPC.memSlice(s7a, addrOctFreq, 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1128,"value":"Take the note index in Y and double it into X to use as an index into the freq table. Store the multiplier in memory.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":772,"value":"s8 = SPC.tya(s7a)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":774,"value":"s9 = SPC.asl(s8)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":776,"value":"s10 = SPC.tax(s9)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":778,"value":"s11 = SPC.ldaAddrX(s10, addrFreqTable + 1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":780,"value":"s12 = SPC.staAddr(s11, addrNoteMultiply + 1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":782,"value":"s13 = SPC.ldaAddrX(s12, addrFreqTable)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":784,"value":"s14 = SPC.staAddr(s13, addrNoteMultiply)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":971,"value":"SPC.memSlice(s14, addrNoteMultiply, 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1135,"value":"Begin the long process of applying the note multiplier to the octave frequency. This is where the complex integer based floating point multiplication starts.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":791,"value":"s15 = SPC.ldyAddr(s14, addrOctFreq)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1265,"value":"This instruction results in `YA = Y * A`","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":804,"value":"s16 = SPC.mul(s15)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":914,"value":"s16a = SPC.tya(s16)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":822,"value":"s16b = SPC.ldy(s16a, 0)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":809,"value":"s17 = SPC.styaAddr(s16b, addrResult)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":811,"value":"SPC.memSlice(s17, addrResult, 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":816,"value":"s18 = SPC.ldyAddr(s17, addrOctFreq)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":817,"value":"s19 = SPC.ldaAddr(s18, addrNoteMultiply + 1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":827,"value":"s20 = SPC.mul(s19)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":829,"value":"s21 = SPC.addw(s20, addrResult)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":831,"value":"s22 = SPC.styaAddr(s21, addrResult)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":833,"value":"SPC.memSlice(s22, addrResult, 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":839,"value":"s23 = SPC.ldyAddr(s22, addrOctFreq + 1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":841,"value":"s24 = SPC.ldaAddr(s23, addrNoteMultiply)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":845,"value":"s26 = SPC.mul(s24)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":847,"value":"s27 = SPC.addw(s26, addrResult)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":849,"value":"s28 = SPC.styaAddr(s27, addrResult)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":851,"value":"SPC.memSlice(s28, addrResult, 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":855,"value":"s29 = SPC.ldyAddr(s28, addrOctFreq + 1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":857,"value":"s30 = SPC.ldaAddr(s29, addrNoteMultiply + 1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":860,"value":"s31 = SPC.mul(s30)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":875,"value":"s31a = SPC.tay(s31)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":876,"value":"s31b = SPC.lda(s31a, 0)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":864,"value":"s32 = SPC.addw(s31b, addrResult)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":871,"value":"s33 = SPC.styaAddr(s32, addrResult)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":873,"value":"SPC.memSlice(s33, addrResult, 2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1141,"value":"By now we have our calculated frequency value!","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":978,"value":"simExpected = Math.round(midiNoteToFreq(simInputNote))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":979,"value":"simActual = SPC.read16(s33, addrResult)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":982,"value":"simVariance = pct(roundTo(3, (simActual - simExpected) / simExpected))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":286,"value":"# References","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":7,"value":"## Floating Point Algorithm (for comparison)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":14,"value":"MIDDLE_A_NOTE = 69","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"MIDDLE_A_FREQ = 4400","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"midiNoteToFreq = (n) => Math.pow(2, (n - 69) / 12) * MIDDLE_A_FREQ","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":236,"value":"## Working space for figuring out 16-bit algo","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":136,"value":"shift = 8","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":204,"value":"BaseFreq = 5233","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":48,"value":"NoteBase = 60","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":29,"value":"note = 69","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":50,"value":"offset = note - NoteBase","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":53,"value":"octave = Math.floor(offset / 12)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":62,"value":"octaveBase = {\n var f = BaseFreq;\n if (octave == 0) return f;\n for (\n var i = 0;\n (octave > 0 && i < octave) || (octave < 0 && i > octave);\n i += octave > 0 ? 1 : -1\n ) {\n if (octave > 0) {\n f = f << 1;\n continue;\n }\n f = f >> 1;\n }\n return f;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":75,"value":"noteMultiplier = FreqMultiplyTable[offset]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":155,"value":"loNoteMultiplier = (noteMultiplier & 0xff) << 8","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":157,"value":"hiNoteMultiplier = noteMultiplier & 0xff00","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":78,"value":"loFreqToMultiply = (BaseFreq >> 8) << shift","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":151,"value":"hiFreqToMultiply = (BaseFreq & 0xff) << shift","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":82,"value":"multiplied = multx(BaseFreq, noteMultiplier)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":85,"value":"result = multiplied","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":121,"value":"mult = (x, y) =>\n Math.round((x << shift) * Math.round(y * Math.pow(2, shift))) >> (shift * 2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":123,"value":"mult(200, 1.5)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":163,"value":"9*9","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":164,"value":"9*90","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":295,"value":"writing a function to multiply x * y using only 16-bit integers","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":173,"value":"multx = (x, y) => {\n const p1 = ((x & 0xff) * (y & 0xff)) & 0xffff;\n const p2 = (((x & 0xff) * (y >> 8)) & 0xffff) << 8;\n\n const p3 = ((x >> 8) * (y & 0xff)) & 0xffff;\n const p4 = (((x >> 8) * (y >> 8)) & 0xffff) << 8;\n\n return (((p1 + p2) & 0xffff) >> 8) + ((p3 + p4) & 0xffff);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":176,"value":"multx(512, 384)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":542,"value":"import { SPC } from \"@maddievision/spc\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1297,"value":"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W37","stdlib":"1","titling":"auto"}} 32:"$31:body"