-1+1892 
Introduction to Scale Theory with Applications

What is a musical scale? What is a "mode"? How many scales are there and what are they like?

This course presents some notions from pitch class set theory that are useful in thinking about these questions. From the standard ideas in the first session it develops themes related to scale classification that are the subject of current research. As well as presenting theoretical ideas "in the abstract", the course makes practical connections with the real-life musical activities of learning and making music with scales.

The course takes the form of three illustrated video lectures. A thread for questions and discussion pertaining to each lecture will be created in /r/guitarlessons. Additional printed material can be found in the author's books, all of which are available free online.

Lectures
  1. Foundations

    a. Pitch, notes and pitch classes

    b. Definition of a "scale"

    c. The numbering system

    d. Modality

  2. The Space of All Scales

    a. Binary representations of scales

    b. Counting scales

    c. Some classification methods and their applications

  3. Subsets and Supersets

    a. Harmonizations of scales

    b. "Spectral" analysis and its applications

Prerequisites

The course is largely self-contained, since everything is built from the ground up, although if the student knows nothing about music the pace will most likely be too fast. I assume you have some experience of playing a pitched instrument in some Western tradition (classical, pop etc). You need not be a competent player or be able to read music.

A note to music theorists is in order. I've tried to provide a non-rigorous introduction to the subject, not a college-level course. That means I've sometimes allowed myself some hand-waving in the interests of keeping it accessible and moving along at a reasonable pace.

A note is also in order for practical musicians. The course doesn't teach you how to apply specific scales in your chosen style of music. By the end of Session 3, though, I hope it will have given you some useful tools to help you do that.

Syllabus

The difference between a pitch, a note and a pitch class. Octave equivalence. Pitch class numbers. Transposition invariance of scales. Definitions of "scale". Interval maps. Modality and the definition of "mode".

Binary representations of scales. Simple examples of binary operations (inversion and complementation). How many scales are there? Cardinality, interval composition, modality and symmetry as classificatory attributes. Hamming distance and other metrics (mentioned only).

"Harmonization" of a scale at the root position. Some very basic notions from chord-scale theory. Applications of subsets and supersets of scales; generalisation of these ideas.

Additional information

Although "scale theory" is a somewhat marginal topic in the academic world, almost all of the topics covered on the course are standard and have been in the musicological literature for at least forty years. In one or two places I'll present an idea that I believe to be either original or stated in a non-standard way; I'll give an explicit warning when that happens.

Some representative sources for the course are the following. They're a bit of an odd mixture, and most assume a technical background in music theory that this course doesn't. You do not need to buy or read any of these books to follow the course.

These texts represent very different approaches and this course only presents (at most) a few ideas from each, but they might give some idea of where it's "coming from" to students who already know a bit about the subject.

The instructor is primarily a guitarist and anticipates that a majority of students will be as well. Nothing in the course, however, is guitar-specific and players of other instruments are very welcome.

Teacher qualifications

I received my PhD in the philosophy of music in 1997. Since then I've written three books on scale theory, played and composed in various situations and taught guitar regularly. I now teach freelance full-time. Feel free to contact me on reddit.

Latest Update
Intro to Scale Theory session 3 is now available (2013-03-01 21:32:39)

"The third and final lecture in the UReddit Scale Theory course is now available. Sorry for the delay -- I hope you get something useful out of it.

Rich"

Roster
1. fruitbattery
2. Extemporaryalias
3. tbui02721
4. shmach
5. machetemike
6. DMLydian
7. hat_experience
8. procyon
9. scaredofplanes
10. hsckid
11. southberm
12. Eghri
13. whoisthedizzle83
14. gmcerveny
15. Joubin
16. Lizard
17. lemonsforlimeaid
18. drnelson88
19. schako
20. axolotlkips
21. Smurfe
22. ana
23. broda
24. greggyj
25. afclu13
26. erbarad
27. FTZ
28. revofife
29. wowboyooo
30. londonskater
31. pickles46
32. kearnsrj
33. bluesgtr
34. bigum
35. PotatoPaulKim
36. musicman5000
37. phweo
38. neonknights
39. chinsi
40. BlackKoma
41. fryingpan
42. pandamonium1142
43. brainbigging
44. riverfunk
45. EdGG
46. actsman
47. jorgeyp
48. Phrontistery
49. cokert
50. sprinky
51. Crunchybeats
52. hittingal
53. stent_removal
54. UpTheIrons
55. dinodev
56. BSFmatt
57. butchered
58. lowcracks
59. usbcarl
60. PeterSellers
61. coitalwitticism
62. jaredks
63. WastedJack
64. marioodc
65. Natfly
66. otsbear
67. yawnz0r
68. Literally_Everyone
69. iamdeadbeat
70. Magillicuttymerf
71. karma_fountain
72. bolsadebasura
73. perfopt
74. vuptiman
75. somethingsmart6
76. c_mon_man
77. katarinka
78. perianal
79. mzda_rx7
80. seasonal
81. lshepher
82. chowell2010
83. Namali
84. campbellfay
85. teline
86. martin_t
87. Scholar_of_Sarcasm
88. 47bennyg
89. aiurx
90. phrits
91. Batchmuffin
92. Donnernalder
93. sierra1bravo
94. IJWilliams
95. doomscythe
96. deathtech00
97. mola-fich
98. weescottishchic
99. CappyPig
100. andy_1
101. fiskarinfo
102. CompetentAlloy
103. greenm01
104. Chantal
105. minmax
106. gnaghi
107. lovett
108. catastrophic
109. vjvswan
110. rollinrosie
111. meedel
112. Hoobes
113. leroybad
114. camyvedder
115. subliminalj
116. laughs_and_agrees
117. Kirbinator
118. billyman37
119. yeswecatan
120. rellonaut
121. cthulhu_saves
122. jrtera
123. CoolaColada
124. padume
125. Jellyninja
126. juanpev
127. csdeal
128. Barkt
129. norlevo
130. mar0ux
131. aweller3
132. dr_unlikely
133. barry.banjaxed
134. norussel
135. menacel
136. stevenmeara
137. furystryker
138. thefightscene
139. DanielCrook
140. akhilshah
141. ArtorTheAwesome
142. snstrmstch
143. areyouacop
144. Aquavis
145. makeinstall
146. eijere
147. msingh92
148. thewisedog
149. thelandon
150. Gilgethan
151. gtpfbod
152. JcbChpmn
153. jl2013
154. radioterati
155. ybespalko
156. corianderpanic
157. zerodashzero
158. qzpmwxin
159. Cephalic
160. biko
161. Berdy
162. r3dpill
163. erik_shea
164. Psyclone
165. carlsagansnose
166. SandwichesFtw
167. stefie413
168. RIleyDavidson
169. jonkanookid
170. TheRealRyanSmith
171. NBischoff
172. BigMacsAreGood
173. weinee
174. robertbfw
175. jonny_deep
176. clusk
177. salemosophy
178. tmascia1
179. musecian
180. patrickowtf
181. GMS
182. freesoulJAH
183. maxfreakout
184. pocket_eggs
185. jbrookeiv
186. sileegranny
187. SomeBreh
188. aedf
189. Symbiotx
190. bewbie
191. armlz
192. 10splitmind
193. Austinnick99
194. Rowebot
195. stone4487
196. tenaciouszep
197. personjones
198. blazingtruth
199. Dorian
200. ltx
201. seepoe
202. thebasayou
203. clouddrone
204. ShredMarmot
205. ontheintarnet
206. chaoticrendition
207. beachutman
208. evoskate
209. crod242
210. martirodge
211. nisou
212. smellskindaphishy
213. jcarpanini
214. opeth1022
215. Lerke
216. fmpossum
217. DDMsage
218. cheapEgo
219. travischron123
220. zxrossco
221. Kiddoguvna
222. BurgerWolf
223. idlevoid
224. Voodooduffman
225. RockitBoy
226. wheresmywhiskey
227. saputello
228. chaley91
229. arthur.ravet
230. justtryharder
231. stonenbone
232. ch0mp3r
233. exscape
234. Poekicker
235. Raxxiz
236. assiduousBadger
237. Phaedrus49er
238. DelphiEx
239. Robot_Animal
240. Maxwells_Equations
241. steveforbesnash
242. amaninthemaking
243. bwkittinger
244. Proud_Mongol01
245. lalbeiruph
246. haisuli
247. pederng
248. Punisher11292
249. zombiesinthehallway
250. Creanja
251. rdrew
252. massatari
253. cococrispies
254. dirtsman
255. kualahugs
256. snwboardguy
257. Cordanjo
258. dinhmq1
259. calm_batman
260. tomaytto
261. jcassper
262. SausageMcNasty
263. Kris_Rothe
264. wasurenai
265. mindful_drone
266. Satellitess
267. cosmicwonder
268. aethier
269. sunnymonkey
270. nedsdeadnedsdead
271. woodsda
272. armoul
273. McGuirk808
274. someteochewguy
275. tsubom33
276. windziarz
277. Cygnus2112
278. wavemancer
279. Missedirection
280. Alexander10110
281. sabogalcc
282. Gintoki
283. kidkolumbo
284. SecretlyAPenguin
285. Wilfinlock
286. organicfunk
287. MmmCheeze
288. chiminage
289. WowThisIsGreat
290. mitchlangdon
291. TrustyDrusty
292. mokacoffay
293. 010ron
294. educ210student
295. batsh1t
296. metaladdi
297. kneeups2
298. apemandune
299. tre2cool
300. karimhigazy
301. duziboomboom
302. dreamingOfInfinity
303. Bhane
304. mrdeathllama
305. musfiqniaz
306. HAMBOOONE
307. packersfan25
308. br0die
309. ant_l_p
310. archflames
311. johnd41
312. dime100
313. RoyceJulius
314. dankers
315. johnny_who
316. rypry
317. ryankeeler
318. diamondium
319. otisfunkmeyer
320. paster
321. recycledair
322. slappedhams
323. wanwan
324. sobtiankit
325. mdfewkes
326. Mr.Jagil
327. ort
328. josef
329. Hg-Mercurious
330. timrichard
331. llwybyr
332. viceroyjenkins
333. shouldbefun
334. n2ishin
335. fer_puricelli
336. fetzko
337. Jules91
338. Neuroleptic
339. stuebm
340. barfolamew
341. VikingScholar
342. Pip2071
343. Perplexity
344. ogen
345. ncms1990
346. jtrance
347. Kurdt99
348. Thirza
349. MrReaperX
350. mystache
351. DreamAeon
352. asianrower
353. _suited_up
354. cpnbbp
355. vath
356. Lochivan
357. mikerude90
358. sz320
359. JCarter
360. andrew.asf
361. princessbjm1114
362. danpupz
363. boredkids123
364. godlikeinu
365. pao.maneepairoj
366. tushuguan
367. zachsalvetta
368. James_Hetfield
369. jrs09a
370. Jiantjames
371. zaephyrion
372. weegreenlassie
373. oxymoron
374. stanford_winnet
375. surfwookie
376. DoubleMajor
377. mgbrennan
378. ShroudedCriminal
379. vibrant_pastel
380. Thrasyboulus
381. Taurat715
382. pjdog
383. csbadfish90
384. st1ckman67
385. ZeCoimas
386. muhaimin01
387. wocks
388. astronate
389. robbiej5
390. lostandround
391. nateharr
392. meowrox
393. kakihara
394. theso
395. tboje
396. nswittman
397. nullsignature
398. ballsofstjohn
399. lukegonzalez
400. bourgeoisplatypus
401. VitriolHumor
402. weeeird
403. xmarimbafaggotx
404. Clemenreau
405. kronomancer
406. tana.r
407. Jalp
408. wongse
409. rmondoz
410. henky81
411. cwleo
412. manzer
413. purpange_octopus
414. MikaelBirger
415. swathiroyalenfield
416. punkrockjesus
417. schrute_Farms_
418. megzieroe
419. nbrown10
420. JenelleCT
421. sunupu
422. jl.da
423. Grungo
424. Bensterism
425. squarewaffles
426. artemesiaISM
427. QuiltedVino
428. ytsejammer
429. camel
430. typhy
431. Nicole.k.d
432. jussyjus
433. ju4n
434. sayingallineed
435. smileyblob
436. moreslack
437. BusJACK
438. nanunanu98
439. wildlark
440. mmmcheese
441. Initiatrix
442. pao.esta
443. wshipman96
444. trodz24
445. andystrucible
446. neotheicebird
447. markfoobar
448. footietues
449. jillianthien
450. Charlboro_lights
451. chlobonibo
452. misterbland
453. Marxist_fiend
454. thesuityman
455. moonraker_elite
456. kiwikiller
457. Mementomori
458. waldenemile
459. mongolbaatar
460. worldisimagination
461. tiffanynfitzz
462. Zolii95
463. AndrewSides
464. thehumptydance
465. gyalrin
466. dopesoap
467. JAWE
468. Superawe
469. ArsonistNightfire
470. gardengoesforth
471. ofthreeminds
472. jdsmith25
473. kcig
474. etkt
475. Mistryjhjd
476. onoffon
477. crvernon
478. adamnemecek
479. jafs
480. humbager
481. mkulaczk
482. defun
483. shibutani
484. frazzl
485. ted_dreadful
486. kaaz89
487. rakeeb11
488. jimmyjamsd
489. allanthegrreat
490. grunsten
491. jammyburger
492. effieg
493. LisaMCooper
494. Hedgewolf
495. hcjxm5
496. asobel
497. worthless_your_Supply
498. NikittyTesla
499. notapotatoyet
500. suedou
501. wizard_holt
502. Kelaab
503. Semmo
504. yokento
505. Sain4847
506. ariellecherie
507. malei06
508. jona
509. jstaples
510. moon-boy
511. ihad2reload
512. moonstomper
513. rockthecatskills89
514. poojachaturvedi
515. RedManWalking
516. timetoacceptmyself
517. DC888
518. awesomeness1498
519. ropper1
520. Azulalnacer
521. sowhatifidont
522. imakemusic27
523. owlite
524. SingMeToSleep
525. pootpoot
526. bjh
527. mrjlevin
528. b_radgeezy17
529. babe.rainbow
530. cayle
531. Yannie
532. Yanni123
533. timmaha
534. nakkefame
535. rhyth
536. jj0123
537. dreamingrevenge
538. doppioslash
539. f3rq
540. Lethotep
541. RATwashingM
542. MisterHahn
543. philomath
544. v00d00StYL3
545. Jonii3
546. echd
547. achickendidit
548. alerion617
549. SweetVerdandi
550. rider
551. FalloutShuffle
552. Scabe
553. Jeyson
554. billpersilja
555. Giraffosaurus
556. mysound
557. cultculture
558. charizade
559. abjindal
560. lancexoxo
561. spunkbomb
562. Tewisp
563. cunningham91
564. fr240
565. riku_32191
566. uraeus
567. ajmori2
568. dug
569. MrBrizola
570. ashleybriana0203
571. tctippens
572. deafleopard13
573. buntyinthesky
574. brianna.derevjanik
575. aamirazeem
576. Heyheyhey
577. ThePigeonMan
578. birdonawire88
579. jelli96
580. washedfugur
581. omen2k
582. hobn
583. pejoseph
584. mumbra
585. ethahous1
586. waraoka
587. tnscott99
588. ShrewdMoose
589. dethmonkey
590. Sits-when-pees
591. kodakidd
592. ctaylor905
593. luxiia
594. Mrlenz
595. truenym
596. intelligentfail
597. nicco
598. undbecks
599. Frogger8675309
600. snowgoose
601. sant333
602. darkchidori
603. evilbee
604. Kizartik
605. king718
606. Vasckin
607. piarose
608. Durelo
609. IndaSkies
610. Fh-Fh
611. CorneliusJack
612. cdin
613. aileenconnors
614. youreaatowel
615. keeran_tamu
616. skbounce
617. wwryan
618. puffinorchid
619. wzpgsr
620. jack_main
621. miles377
622. LachRobster
623. Ppohlus
624. Sneaky_p
625. zantefresco
626. demivisage
627. TullyTaargus
628. plokij909
629. hates_novelty_accts
630. stillsweet2
631. consciouscoward
632. mrbokonon
633. m-smith
634. ilyaunoiseau
635. Maddie16
636. mnml
637. chumb
638. draculatreeforest
639. music_player99
640. witchgrass
641. penischarles
642. Ailuropoda
643. EXICON
644. PaszerRatiug
645. postballistics
646. TwilieIsBestPony
647. useeeeee
648. RenegadeoftheWastes
649. japhy11
650. gigantic_panda
651. takomako
652. curiousdevice
653. conchobe
654. CwazyBear666
655. thepeopleskey
656. ncastell77
657. feliperro
658. sjohnb1989
659. sallydkang
660. ryustreetfighter
661. Curious_Device
662. rturns
663. micahlandall
664. owensrs
665. isaaclee96
666. Iroxtion
667. UnorthodoxScholar
668. tbrown983
669. MightAsWellGG
670. tibincrunch
671. starjocelyn8
672. full_metal_avatar
673. efildriew
674. no_ta_ching
675. epomzo
676. koalaver
677. handleson
678. lakmalrupasinghe
679. AntCGallagher
680. LQTMS
681. highbrowalcoholic
682. mrfuzz
683. donkadillo
684. film_guy01
685. ailurophilia
686. beautiful_llama
687. Adorism
688. bkopf
689. thegreatdivide
690. garygetsgrapes
691. masenfim
692. jonnyquin
693. suckarpuncharr
694. kadirgunel
695. NanayawGeoff
696. harleygatt
697. mrfresh44
698. wonderwilly
699. DanielNHarber
700. alfonsosn
701. mudsauce
702. dnnysn
703. 222botany
704. themortal
705. pando
706. Josqu
707. jeffrey_mcpooper
708. Elphabaization
709. laceymarie
710. deltawolf9000
711. maktig
712. Brown.Chicken.Brown.Cow
713. deepit6431
714. Ironklemp
715. hilu
716. alery
717. alemeno
718. utsabgiri
719. Billybobangel
720. 400Lux
721. pallu
722. Mr_WazanskiiiiGoesToSchool
723. nineteen-hundred
724. JuberasTargaryan
725. corycruse
726. Rupen144
727. visvim
728. fkgtz013
729. flowerchild
730. abrarmh
731. November
732. aaronjeo
733. thegeorge
734. deAlchemist
735. jdrush
736. tkirk513
737. christieezhao
738. Marliz
739. mlephotographe
740. Foschi
741. Riovov
742. Mozartny
743. SpicyBabySauce
744. cloudfunk
745. ChannelSERFER
746. nonojr
747. luciafernandez
748. HeartOfAtlas
749. jj57347
750. einarsw
751. BulletMassage
752. john1212
753. quadres
754. melmackian
755. ldudew
756. lulwutamidoin
757. alekspitts
758. Sub0x0one
759. Tjwhore
760. chaditude10
761. arcoty
762. EdwinArcilla
763. sonyasavova
764. vinay1997
765. coyotequark
766. SMETA
767. dariak
768. adqg
769. SockRabbit
770. Adheip.Pai
771. poxto
772. andresf17
773. mobyxe
774. chbeir
775. mecenas
776. Driftw00d
777. TheSilentPianist
778. RossAyRoss
779. christuffa2000
780. rvinay88
781. kkalligeros
782. jeremydrinkard
783. SwiftOwls
784. awdcvgyjm
785. lookingforsome
786. mikyor1
787. dylanpieper
788. claudiav
789. starwarsfien
790. gregorytj
791. gmc51
792. monom3
793. liebstraum
794. ManiDProductions
795. Cheesekicksass
796. kapli
797. reid
798. riccieoriach
799. onederricktion
800. kibieyes
801. doe9
802. hammerhedd
803. VeeShip
804. Jogobello
805. narwhalfam
806. r3os
807. winfield.brookins
808. potatoemagic
809. Twicebakedbuckeye
810. maniacodomachado
811. Tigah
812. sicnarf
813. limvolution
814. cobbless
815. Milkisabadchoice
816. lildre
817. PoundlandBurrito
818. Livin_The_High_Life
819. WadeFU
820. PriscillaVesper
821. zillahdryke
822. davoomac
823. gimel
824. Adollo
825. JimmyNuggets
826. anunez89nyc
827. nosuchusernamefound
828. hockeymullet
829. perceheadies
830. PesterT
831. arielkiss
832. justeastofwest
833. lucasplaysbass
834. xcortez
835. creedofwheat
836. OkThings
837. VermillionFox
838. WiserMelon
839. eddz423
840. PiNapL
841. nickr33
842. Daegarn
843. theodyssey_
844. tlien
845. feebarscevicius
846. mAd_Lib_kid
847. InesTeles
848. derz_mcgerz
849. darrenpic
850. muthafunkah
851. tomasloureirogomes
852. returnofthaking
853. ecNate
854. Peiatro
855. olds0ul
856. DroHanSolo
857. ilr1
858. phy133
859. pmcinern
860. thewolfman
861. chrisdiaz808
862. Cmder
863. austinn596
864. BarbieCastoldi
865. Alex78
866. AcidRap786
867. fishsmash
868. Jorozo
869. murasa
870. safister
871. ficar
872. moishaha
873. anmuydarp
874. Aumnescience
875. raios168
876. crookedteeth
877. chrawrles
878. godofthesun
879. goflvhxj963
880. mowgli-kun
881. Omnified
882. ilive12
883. tillyt
884. sowhat
885. jdfuhr10
886. Beezlo
887. zenovance_dev
888. syntaxidermy
889. Ivanrose
890. Mashia
891. sparkleinyourchina
892. mrsparklee
893. vrk_92
894. shefster
895. PayneMcDowell
896. big_red_fuck_you
897. NeuralLotus
898. RadKenfo
899. clare_neal
900. Dzigly
901. Alliecompton
902. ValiantEntity
903. WaywardWanderer14
904. fatty_mcturdenstein
905. teck7878
906. cloudland3
907. owenlewis90
908. midnyght219
909. ogaragav
910. dextorg
911. penfold
912. wellrightyothen
913. indigox
914. Lelouch08
915. waterlilyslim
916. BuryMeInSmoke
917. adzash
918. STFUandLove
919. i_am_squish
920. Fitzy257
921. DEADBEEFdd
922. bobbibee
923. leonbasin
924. maicorral
925. NihilisticPriest
926. jaxmanation
927. SandBoxKing
928. moondesu
929. cmcmorrow
930. gfunkel
931. raineou