Ruby, Rock & Roll

1. Ruby, Rock and Roll Chang Sau Sheong HP Labs Singapore May 2012

2. About

4. About

6. About

8. About

10. About

11. me

12. About

13. me

14. About

15. me

16. About

17. me

18. Muse http://github.com/sausheong/muse

20. (pure)

21. Ruby

22. domain- specific

23. language

24. for

25. synthesizing

26. music

30. Creating

31. Muse •Create

32. sound •Organize

33. sound

34. into

35. music

36. notes •Write

37. notes

38. to

39. file •Wrap

40. around

41. with

43. domain- specific

44. language

45. About

46. sound •Sound

47. is

48. produced

49. by

50. vibration

51. of

52. something

53. (air,

54. water

55. etc) •Vibration

56. produces

57. waves

58. •Properties

59. of

60. sound

61. wave

62. include

63. amplitude

64. (volume)

65. and

66. frequency

67. (pitch)

68. Higher

69. amplitude

70. means

71. louder

72. volume amplitude frequency

74. number

75. of

76. cycles

77. in

79. second cycle More

80. cycles

81. in

83. second

84. mean

85. higher

86. frequency,

87. higher

88. pitch

89. Make

91. sound •Sine

92. wave

93. is

94. pure

95. sound,

96. all

97. other

98. sounds

99. made

100. by

101. combining

102. various

103. sine

104. waves •To

105. make

106. a

107. sound,

108. generate

109. sine

110. waves •To

111. make

112. a

113. digital

114. sound,

115. generate

116. digital

117. sine

118. waves

119. and

120. put

121. them

122. into

123. sound

124. files

125. The

126. physics

127. of

128. music •Music

129. is

130. organized

131. sound •Music

132. notes

133. are

134. sounds

135. with

136. specific

137. pitches

138. (frequencies)

139. and

140. durations •Each

141. note

142. corresponds

143. to

144. a

145. particular

146. frequency,

147. expressed

148. in

149. hertz

150. (Hz) •Most

151. music

152. use

153. a

154. scale

155. (sequence

156. of

157. notes)

158. with

159. 12

160. notes

161. called

162. the

163. chromatic

164. scale

165. same

166. pitch

167. class

168. (octave) C# D# F# G# A# C D E F G A B C 1

169. octave

170. =

171. 12

172. semi-tone

173. notes

174. The

175. physics

176. of

177. music •The

178. frequencies

179. of

180. the

181. notes

182. are

183. related

184. to

185. each

186. other

187. in

188. a

189. mathematical

190. formula •The

191. frequencies

192. are

193. defined

194. around

195. the

196. standard

197. pitch

198. A4,

199. which

200. is

201. 440

202. Hz

203. (ISO

204. 16:1975

205. standard) •Notes

206. of

207. the

208. same

209. pitch

210. class

211. (octave)

212. are

213. in

214. the

215. ratio

216. of

217. a

218. power

219. of

220. 2

221. (1/4,

222. 1/2,

223. 2,

224. 4,

225. 8

226. etc)

228. A A7 3520Hz A A6 1760Hz A A5 880Hz A A4 440Hz

229. 12 difference

230. between

231. 12

232. semi-tones

233. (1

234. octave)

235. is

237. 2

240. ×

241. f

243. or

244. 2f

247. 12 1 difference

248. between

249. 2

250. semi-tones

251. is

255. 2

256. ×

257. f

259. or

260. 2

262. 12 12 ×f

263. Getting

264. the

265. frequency •Get

266. the

267. frequency

268. of

269. the

270. note

271. (f),

272. as

273. compared

274. to

275. A4

276. (440Hz)

277. using

278. the

279. formula n f = 2 × 440Hz 12 •where

280. n

281. =

282. distance

283. from

284. A4.

285. For

286. eg

287. C5

288. is

289. 3

290. notes

291. (semi-tones)

292. after

293. A4,

294. so

295. frequency

296. of

297. C5

298. is

299. 3 f = 2 12 × 440Hz = 523.25Hz

300. Create

301. music

302. notes •To

303. get

304. a

305. sine

306. wave

307. representing

308. a

309. note s = sin(2π f ) • We

310. multiple

311. f

312. with

313. 2

316. because

317. we

318. need

319. to

321. π turn

322. the

323. frequency

324. into

325. radians

326. Get

327. note

328. data

329. samples 1250 626 0 44100

330. samples take

331. samples

332. at

333. regular

334. intervals

335. (44,100

336. samples

337. over

338. a

339. period

340. of

341. 1

342. second)

343. and

344. calculate

345. the

346. wave

347. value

348. at

349. that

350. sample

351. NOTES = %w(a ais b c cis d dis e f fis g gis) FREQUENCIES = { d4:-7, dis4:-6, e4:-5, f4: -4, fis4:-3, g4:-2, gis4:-1, a4: 0, ais4: 1, b4: 2, c5: 3, cis5: 4, d5: 5 } # get the frequency of the pitch def frequency_of(step) 440.0*(2**(step.to_f/12.0)) end sample_rate = 44100.0 # 44100 Hz duration = 1 # 1 sec stream = [] # data stream for left and right channels frequency = frequency_of(FREQUENCIES[:a4]) # for the duration of 1 sec, step every 1/44100 times and # write the value (0.0..duration.to_f).step(1/sample_rate) do |i| x = (10000 * Math.sin(2 * Math::PI * frequency * i)).to_i stream [x,x] end

352. [[0, 0], [626, 626], [1250, 1250], [1869, 1869], [2481, 2481], [3083, 3083], [3673, 3673], [4248, 4248], [4807, 4807], [5347, 5347], [5866, 5866], [6362, 6362], [6832, 6832], [7276, 7276], [7692, 7692], [8077, 8077], [8431, 8431], [8751, 8751], [9037, 9037], [9287, 9287], [9501, 9501], [9678, 9678], [9816, 9816], [9916, 9916], [9978, 9978], [9999, 9999], [9982, 9982], [9925, 9925], [9830, 9830], [9696, 9696], [9523, 9523], [9313, 9313], [9067, 9067], [8785, 8785], [8469, 8469], [8119, 8119], [7737, 7737], [7325, 7325], [6884, 6884], [6416, 6416], [5923, 5923], [5407, 5407], [4869, 4869], [4313, 4313], [3739, 3739], [3151, 3151], [2550, 2550], [1939, 1939], [1321, 1321], [697, 697], [71, 71], [-555, -555], [-1179, -1179], [-1799, -1799], [-2412, -2412], [-3015, -3015], [-3606, -3606], [-4184, -4184], [-4744, -4744], [-5287, -5287], [-5808, -5808], [-6307, -6307], [-6780, -6780], [-7227, -7227], [-7646, -7646], stream [-8035, -8035], [-8392, -8392], [-8716, -8716], [-9006, -9006], [-9261, -9261], [-9479, -9479], [-9660, -9660], [-9803, -9803], [-9907, -9907], [-9973, -9973], [-9999, -9999], [-9986, -9986], [-9934, -9934], [-9843, -9843], [-9713, -9713], [-9545, -9545], [-9339, -9339], [-9097, -9097], [-8819, -8819], [-8506, -8506], [-8160, -8160], [-7782, -7782], [-7373, -7373], [-6936, -6936], [-6471, -6471], [-5981, -5981], [-5467, -5467], [-4931, -4931], [-4377, -4377], [-3805, -3805], [-3218, -3218], [-2619, -2619], [-2009, -2009], [-1391, -1391], [-768, -768], [-142, -142], [484, 484], [1109, 1109], [1729, 1729], [2343, 2343], [2947, 2947], [3540, 3540], [4119, 4119], [4682, 4682], [5226, 5226], [5750, 5750], [6251, 6251], [6728, 6728], [7178, 7178], [7600, 7600], [7992, 7992], [8353, 8353], [8681, 8681], [8975, 8975], [9234, 9234], [9456, 9456], [9641, 9641], [9788, 9788], [9897, 9897], [9967, 9967], [9998, 9998], [9989, 9989], [9942, 9942], [9855, 9855], [9729, 9729], [9566, 9566], [9364, 9364], [9126, 9126], [8852, 8852], [8544, 8544], [8201, 8201], [7827, 7827], [7421, 7421], [6987, 6987], [6525, 6525], [6038, 6038], [5526, 5526], [4993, 4993], [4441, 4441], [3871, 3871], [3285, 3285], [2687, 2687], [2079, 2079], [1462, 1462], [839, 839], [213, 213], [-413, -413], [-1038, -1038], [-1659, -1659], [-2273, -2273], [-2879, -2879], [-3473, -3473], [-4054, -4054], [-4619, -4619], [-5165, -5165], [-5691, -5691], [-6195, -6195], [-6675, -6675], [-7128, -7128], [-7554, -7554], [-7949, -7949], [-8314, -8314], [-8645, -8645], [-8943, -8943], [-9206, -9206], [-9432, -9432], [-9622, -9622], [-9774, -9774], [-9887, -9887], [-9961, -9961], [-9996, -9996], [-9992, -9992], [-9949, -9949], [-9867, -9867], [-9746, -9746], [-9586, -9586], [-9389, -9389], [-9155, -9155], [-8885, -8885], [-8580, -8580], [-8242, -8242], [-7871, -7871], [-7469, -7469], [-7038, -7038], [-6579, -6579], [-6094, -6094], [-5586, -5586], [-5055, -5055], [-4504, -4504], ...]

353. [[0, 0], [626, 626], [1250, 1250], [1869, 1869], [2481, 2481], [3083, 3083], [3673, 3673], [4248, 4248], [4807, 4807], [5347, 5347], [5866, 5866], [6362, 6362], [6832, 6832], [7276, 7276], [7692, 7692], [8077, 8077], [8431, 8431], [8751, 8751], [9037, 9037], [9287, 9287], [9501, 9501], [9678, 9678], [9816, 9816], [9916, 9916], [9978, 9978], [9999, 9999], [9982, 9982], [9925, 9925], [9830, 9830], [9696, 9696], [9523, 9523], [9313, 9313], [9067, 9067], [8785, 8785], [8469, 8469], [8119, 8119], [7737, 7737], [7325, 7325], [6884, 6884], [6416, 6416], [5923, 5923], [5407, 5407], [4869, 4869], [4313, 4313], [3739, 3739], [3151, 3151], [2550, 2550], [1939, 1939], [1321, 1321], [697, 697], [71, 71], [-555, -555], [-1179, -1179], [-1799, -1799], [-2412, -2412], [-3015, -3015], [-3606, -3606], [-4184, -4184], [-4744, -4744], [-5287, -5287], [-5808, -5808], [-6307, -6307], [-6780, -6780], [-7227, -7227], [-7646, -7646], stream [-8035, -8035], [-8392, -8392], [-8716, -8716], [-9006, -9006], [-9261, -9261], [-9479, -9479], [-9660, -9660], [-9803, -9803], [-9907, -9907], [-9973, -9973], [-9999, -9999], [-9986, -9986], [-9934, -9934], [-9843, -9843], [-9713, -9713], [-9545, -9545], [-9339, -9339], [-9097, -9097], [-8819, -8819], [-8506, -8506], [-8160, -8160], [-7782, -7782], [-7373, -7373], [-6936, -6936], [-6471, -6471], [-5981, -5981], [-5467, -5467], [-4931, -4931], [-4377, -4377], [-3805, -3805], [-3218, -3218], [-2619, -2619], [-2009, -2009], [-1391, -1391], [-768, -768], [-142, -142], [484, 484], [1109, 1109], [1729, 1729], [2343, 2343], [2947, 2947], [3540, 3540], [4119, 4119], [4682, 4682], [5226, 5226], [5750, 5750], [6251, 6251], [6728, 6728], [7178, 7178], [7600, 7600], [7992, 7992], [8353, 8353], [8681, 8681], [8975, 8975], [9234, 9234], [9456, 9456], [9641, 9641], [9788, 9788], [9897, 9897], [9967, 9967], [9998, 9998], [9989, 9989], [9942, 9942], [9855, 9855], [9729, 9729], [9566, 9566], [9364, 9364], [9126, 9126], [8852, 8852], [8544, 8544], [8201, 8201], [7827, 7827], [7421, 7421], [6987, 6987], [6525, 6525], [6038, 6038], [5526, 5526], [4993, 4993], [4441, 4441], [3871, 3871], [3285, 3285], [2687, 2687], [2079, 2079], [1462, 1462], [839, 839], [213, 213], [-413, -413], [-1038, -1038], [-1659, -1659], [-2273, -2273], [-2879, -2879], [-3473, -3473], [-4054, -4054], [-4619, -4619], [-5165, -5165], [-5691, -5691], [-6195, -6195], [-6675, -6675], [-7128, -7128], [-7554, -7554], [-7949, -7949], [-8314, -8314], [-8645, -8645], [-8943, -8943], [-9206, -9206], [-9432, -9432], [-9622, -9622], [-9774, -9774], [-9887, -9887], [-9961, -9961], [-9996, -9996], [-9992, -9992], [-9949, -9949], [-9867, -9867], [-9746, -9746], [-9586, -9586], [-9389, -9389], [-9155, -9155], [-8885, -8885], [-8580, -8580], [-8242, -8242], [-7871, -7871], [-7469, -7469], [-7038, -7038], [-6579, -6579], [-6094, -6094], [-5586, -5586], [-5055, -5055], [-4504, -4504], ...]

354. Harmonics •Sine

355. wave

356. is

357. the

358. most

359. basic

360. waveform

361. and

362. produces

363. the

364. fundamental

365. frequency,

366. a

367. pure

368. sound •Any

369. other

370. sounds

371. can

372. be

373. created

374. by

375. adding

376. other

377. waves

378. at

379. different

380. frequencies

381. and

382. amplitudes

383. (called

384. harmonics) •Adding

385. sine

386. waves

387. at

388. different

389. multiples

390. of

391. the

392. same

393. frequency

394. changes

395. how

396. the

397. same

398. note

399. sounds

400. y=sin(x) y

401. =

402. sin(2x) y

403. =

404. sin(x)

405. +

406. sin(2x)

407. def harmonics(input) Math.sin(2 * Math::PI * input) + Math.sin(2 * Math::PI * input * 2) end # for the duration of 1 sec, step every 1/44100 times and # write the value (0.0..duration.to_f).step(1/sample_rate) do |i| x = (10000 * harmonics(frequency * i)).to_i stream [x,x] end

408. def harmonics(input) Math.sin(2 * Math::PI * input) + Math.sin(2 * Math::PI * input * 2) end # for the duration of 1 sec, step every 1/44100 times and # write the value (0.0..duration.to_f).step(1/sample_rate) do |i| x = (10000 * harmonics(frequency * i)).to_i stream [x,x] end

409. Envelopes •Changing

410. the

411. volume

412. of

413. the

414. note

415. over

416. the

417. duration

418. also

419. changes

420. how

421. the

422. note

423. sounds def envelope(input, duration) Math.cos((Math::PI*input)/(2*duration.to_f)) end # for the duration of 1 sec, step every 1/44100 times and # write the value (0.0..duration.to_f).step(1/sample_rate) do |i| x = (10000 * Math.sin(2 * Math::PI * frequency * i) * envelope(i, duration)).to_i stream [x,x] end

424. input

425. x

426. sin(duration) input

427. x

428. cos(duration)

429. input

430. x

432. x

433. cos(duration)

434. input

435. x

437. x

438. cos(duration)

439. Digital

440. sound •Digital

441. sound

442. stored

443. in

444. compressed

445. or

446. uncompressed

447. formats •Main

448. uncompressed

449. format

450. is

451. PCM

452. (Pulse

453. Code

454. Modulation),

455. stored

456. as

457. WAV

458. (Windows)

459. or

460. AIFF

461. (Mac)

462. files •Standard

463. form

464. for

465. all

466. digital

467. audio,

468. digital

469. representation

470. of

471. an

472. analog

473. signal

474. The

475. WAV

476. format •Audio

477. file

478. format

479. for

480. Windows,

481. derived

482. from

483. RIFF

484. (Resource

485. Interchange

486. File

487. Format) •Bitstream

488. format

489. store

490. data

491. in

492. chunks •Linear

493. PCM

494. encoded,

495. 2

496. channels

497. of

498. 44,100

499. samples

500. per

501. second,

502. 16

503. bits

504. per

505. sample

508. Create

509. WAV

510. files •Write

511. manually

512. using

513. Array#pack

514. (read

515. manually

516. using

517. String#unpack) •Use

518. the

519. BinData

520. library

521. (http:// bindata.rubyforge.org)

522. to

523. represent

524. WAV

525. format

526. and

527. stuff

528. data

529. in •Data

530. is

531. just

532. integers

533. representing

534. the

535. sample

536. require 'bindata' class RiffChunk BinData::Record int32be :chunk_id int32le :chunk_size int32be :format end class FormatChunk BinData::Record int32be :chunk_id int32le :chunk_size int16le :audio_format int16le :num_channels int32le :sample_rate int32le :byte_rate int16le :block_align int16le :bits_per_sample end class DataChunk BinData::Record int32be :chunk_id int32le :chunk_size array :stream do int16le :left int16le :right end end class WavFormat BinData::Record riff_chunk :riff_chunk format_chunk :format_chunk data_chunk :data_chunk end

537. class Wav SAMPLE_RATE = 44100 attr :wav, :file, :sample_rate, :format_chunk, :riff_chunk, :data_chunk def initialize(filename) @sample_rate = SAMPLE_RATE @file = File.open(filename, wb) @riff_chunk = RiffChunk.new @riff_chunk.chunk_id = RIFF.unpack(N).first @riff_chunk.format = WAVE.unpack(N).first @format_chunk = FormatChunk.new @format_chunk.chunk_id = fmt .unpack(N).first @format_chunk.chunk_size = 16 @format_chunk.audio_format = 1 @format_chunk.num_channels = 2 @format_chunk.bits_per_sample = 16 @format_chunk.sample_rate = @sample_rate @format_chunk.byte_rate = @format_chunk.sample_rate * @format_chunk.num_channels * @format_chunk.bits_per_sample/2 @format_chunk.block_align = @format_chunk.num_channels * @format_chunk.bits_per_sample/2 @data_chunk = DataChunk.new @data_chunk.chunk_id = data.unpack(N).first end

538. def write(stream_data) stream_data.each_with_index do |s,i| @data_chunk.stream[i].left = s[0] @data_chunk.stream[i].right = s[1] end @data_chunk.chunk_size = stream_data.length * @format_chunk.num_channels * @format_chunk.bits_per_sample/8 @riff_chunk.chunk_size = 36 + @data_chunk.chunk_size @wav = WavFormat.new @wav.riff_chunk = @riff_chunk @wav.format_chunk = @format_chunk @wav.data_chunk = @data_chunk @wav.write(@file) end def close @file.close end end wav_file = Wav.new('sine.wav') wav_file.write(stream) wav_file.close

539. Putting

540. it

541. all

542. together

543. NOTES = %w(a ais b c cis d dis e f fis g gis) FREQUENCIES = { d4:-7, dis4:-6, e4:-5, f4:-4, fis4:-3, g4:-2, gis4:-1, a4: 0, ais4: 1, b4: 2, c5: 3, cis5: 4, d5: 5 } # get the frequency of the pitch def frequency_of(step) 440.0*(2**(step.to_f/12.0)) end sample_rate = 44100.0 # 44100 Hz duration = 1 # 1 sec stream = [] # data stream for left and right channels frequency = frequency_of(FREQUENCIES[:a4]) # for the duration of 1 sec, step every 1/44100 times and # write the value (0.0..duration.to_f).step(1/sample_rate) do |i| x = (10000 * Math.sin(2 * Math::PI * frequency * i)).to_i stream [x,x] end wav_file = Wav.new('sine.wav') wav_file.write(stream) wav_file.close

544. Domain

545. specific

546. language •Designed

547. for

548. a

549. specific

550. domain •Captures

551. concepts

552. of

553. the

554. domain

555. including

556. jargon •Is

557. still

558. Ruby!

559. Techniques

560. used

561. in

562. Muse •DSL

563. are

564. methods

565. in

566. Song

567. and

568. Bar •Use

569. instance_eval

570. to

571. evaluate

572. music

573. score •Use

574. method_missing

575. to

576. catch

577. names

578. of

579. notes

580. and

581. chords

582. class Song DSL

583. are

584. methods def self.record(name, options ={}, block) ... def bar(id, options={}) ... @bars[id] Bar.new(id, options) @bars[id].last end end class Bar def notes(block) ... end end end require muse include Muse Song.record 'hotel_california', harmonic: 'guitar', bpm: 100 do bar(1).notes { d4 b:2; e4; fis4;} ... end

585. instance_eval class Bar ... def notes(block) instance_eval block end end require muse include Muse Song.record 'hotel_california', harmonic: 'guitar', bpm: 100 do bar(1).notes { d4 b:2; e4; fis4;} ... end

586. method_missing class Bar ... def method_missing(name, *args, block) name = name.to_s if name.start_with? *NOTES ... end end end require muse include Muse Song.record 'hotel_california', harmonic: 'guitar', bpm: 100 do ... bar(3).notes { a3_d4_fis4; fis4; fis4 b:0.5;} ... end

587. Turk!h March

588. Wait,

589. there’s

590. more

591. ...

592. Otto the Algorithmic Composer

593. Algorithmic composition is the technique of using algorithms to create music - Wikipedia

594. Grab tweet from Twitter, create music from it

595. Scan a picture Grab tweet from Twitter, create music from it

596. Get today’s weather report Scan a picture Grab tweet from Twitter, create music from it

597. The algorithm

598. Melody + Chords = Music

599. Grab tweet from Twitter text = Twitter.search(#reddot).last.text

600. Split tweet into words words = text.split

601. Convert each word into a number using the touch tone keypad algorithm

603. KEYPAD = {a:2,b:2,c:2, d:3,e:3,f:3, g:4,h:4,i:4, j:5,k:5,l:5, m:6,n:6,o:6, p:7,q:7,r:7,s:7, t:8,u:8,v:8, w:9,x:9,y:9,z:9} def word_to_num(a_word) a_word.downcase.chars.inject() { |memo,obj| memo + KEYPAD[obj.to_sym].to_s } end

604. Find the 7 most frequently found notes music = [] words.each do |w| music NOTES[note(w)] end sorted = music.counts.sort_by {|obj| obj[1]}.reverse most_frequent_7_notes = sorted.map {|obj| obj[0]}.first(7)

605. Determine the musical scale from the 7 notes MAJOR = { 0 = %w(c d e f g a b c d), 1 = %w(g a b c d e fis g a), 2 = %w(d e fis g a b cis d e), 3 = %w(a b cis d e fis gis a b), 4 = %w(e fis gis a b cis dis e fis), 5 = %w(b cis dis e fis gis ais b cis), 6 = %w(fis gis ais b cis dis f fis gis) } num_of_sharps = most_frequent_7_notes.inject(0) { |memo, obj| obj.end_with? (is) ? memo + 1 : memo } scale = MAJOR[num_of_sharps]

606. Get the chord progression for the scale (using I-IV-V) scale_chords = {} scale_chords[0] = [#{scale[0]}, #{scale[2]}, #{scale[4]}] scale_chords[1] = [#{scale[3]}, #{scale[5]}, #{scale[7]}] scale_chords[2] = [#{scale[4]}, #{scale[6]}, #{scale[8]}]

607. ✓ Melody + Chords = Music

608. Start with the ﬁrst note of the scale

609. Calculate the ‘distance’ between the current note and the next def distance(a_word) word_to_num(a_word).to_i % 5 end

610. Determine if the next note goes ‘up’ or ‘down’ the scale def direction(a_word) (word_to_num(a_word).to_i % 2) == 0 ? 1 : -1 end

611. Get number of syllables for each word, each syllable is 1 beat def syllables(a_word) word = a_word.downcase return 1 if word.length = 3 word.sub!(/(?:[^laeiouy]es|ed|[^laeiouy]e)$/, '') word.sub!(/^y/, '') word.scan(/[aeiouy]{1,2}/).size end

612. Move from current note to next note if direction(word) 0 bar_notes scale.next(distance(word)) else bar_notes scale.previous(distance(word)) end

613. ✓ ✓ Melody + Chords = Music

614. Break down into 4 words per bar, use Muse to write to WAV ﬁle

615. quadruplets.reverse.each_with_index do |quad, index| beats = 0.0 bar(index).notes { beats, bar_notes = [], [] quad.each do |word| beats syllables(word).to_f/2 if direction(word) 0 bar_notes scale.next(distance(word)) else bar_notes scale.previous(distance(word)) end end total_beats = beats.inject(:+) bar_notes.each_with_index do |n,i| note = n.chop octave = n[n.size-1] b = (beats[i]*4.0)/total_beats add_to_stream note_data(note, octave, b:b) end } bar(index, v:1.5).notes { ch = scale_chords[index % 3] chord = [ch[1], ch[2], ch[0]] add_to_stream note_data(ch[0].chop, 3, b:1) add_to_stream chord(chord, b:1) add_to_stream chord(chord, b:1) add_to_stream chord(chord, b:1) }

616. Demo

619. @sausheong +Sau Sheong Chang sausheong@gmail.com sausheong@hp.com http://blog.saush.com

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