-1+1969 
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. tushuguan
366. zachsalvetta
367. James_Hetfield
368. jrs09a
369. Jiantjames
370. zaephyrion
371. weegreenlassie
372. oxymoron
373. stanford_winnet
374. surfwookie
375. DoubleMajor
376. mgbrennan
377. ShroudedCriminal
378. vibrant_pastel
379. Thrasyboulus
380. Taurat715
381. pjdog
382. csbadfish90
383. st1ckman67
384. ZeCoimas
385. muhaimin01
386. wocks
387. astronate
388. robbiej5
389. lostandround
390. nateharr
391. meowrox
392. kakihara
393. theso
394. tboje
395. nswittman
396. nullsignature
397. ballsofstjohn
398. lukegonzalez
399. bourgeoisplatypus
400. VitriolHumor
401. weeeird
402. xmarimbafaggotx
403. Clemenreau
404. kronomancer
405. tana.r
406. Jalp
407. wongse
408. rmondoz
409. henky81
410. cwleo
411. manzer
412. purpange_octopus
413. MikaelBirger
414. swathiroyalenfield
415. punkrockjesus
416. schrute_Farms_
417. megzieroe
418. nbrown10
419. JenelleCT
420. sunupu
421. jl.da
422. Grungo
423. Bensterism
424. squarewaffles
425. artemesiaISM
426. QuiltedVino
427. ytsejammer
428. camel
429. typhy
430. Nicole.k.d
431. jussyjus
432. ju4n
433. sayingallineed
434. smileyblob
435. moreslack
436. BusJACK
437. nanunanu98
438. wildlark
439. mmmcheese
440. Initiatrix
441. pao.esta
442. wshipman96
443. trodz24
444. andystrucible
445. neotheicebird
446. markfoobar
447. footietues
448. jillianthien
449. Charlboro_lights
450. chlobonibo
451. misterbland
452. Marxist_fiend
453. thesuityman
454. moonraker_elite
455. kiwikiller
456. Mementomori
457. waldenemile
458. mongolbaatar
459. worldisimagination
460. tiffanynfitzz
461. Zolii95
462. AndrewSides
463. thehumptydance
464. gyalrin
465. dopesoap
466. JAWE
467. Superawe
468. ArsonistNightfire
469. gardengoesforth
470. ofthreeminds
471. jdsmith25
472. kcig
473. etkt
474. Mistryjhjd
475. onoffon
476. crvernon
477. adamnemecek
478. jafs
479. humbager
480. mkulaczk
481. defun
482. shibutani
483. frazzl
484. ted_dreadful
485. kaaz89
486. rakeeb11
487. jimmyjamsd
488. allanthegrreat
489. grunsten
490. jammyburger
491. effieg
492. LisaMCooper
493. Hedgewolf
494. hcjxm5
495. asobel
496. worthless_your_Supply
497. NikittyTesla
498. notapotatoyet
499. suedou
500. wizard_holt
501. Kelaab
502. Semmo
503. yokento
504. Sain4847
505. ariellecherie
506. malei06
507. jona
508. jstaples
509. moon-boy
510. ihad2reload
511. moonstomper
512. rockthecatskills89
513. poojachaturvedi
514. RedManWalking
515. timetoacceptmyself
516. DC888
517. awesomeness1498
518. ropper1
519. Azulalnacer
520. sowhatifidont
521. imakemusic27
522. owlite
523. SingMeToSleep
524. pootpoot
525. bjh
526. mrjlevin
527. b_radgeezy17
528. babe.rainbow
529. cayle
530. Yannie
531. Yanni123
532. timmaha
533. nakkefame
534. rhyth
535. jj0123
536. dreamingrevenge
537. doppioslash
538. f3rq
539. Lethotep
540. RATwashingM
541. MisterHahn
542. philomath
543. v00d00StYL3
544. Jonii3
545. echd
546. achickendidit
547. alerion617
548. SweetVerdandi
549. rider
550. FalloutShuffle
551. Scabe
552. Jeyson
553. billpersilja
554. Giraffosaurus
555. mysound
556. cultculture
557. charizade
558. abjindal
559. lancexoxo
560. spunkbomb
561. Tewisp
562. cunningham91
563. fr240
564. riku_32191
565. uraeus
566. ajmori2
567. dug
568. MrBrizola
569. ashleybriana0203
570. tctippens
571. deafleopard13
572. buntyinthesky
573. brianna.derevjanik
574. aamirazeem
575. Heyheyhey
576. ThePigeonMan
577. birdonawire88
578. jelli96
579. washedfugur
580. omen2k
581. hobn
582. pejoseph
583. mumbra
584. ethahous1
585. waraoka
586. tnscott99
587. ShrewdMoose
588. dethmonkey
589. Sits-when-pees
590. kodakidd
591. ctaylor905
592. luxiia
593. Mrlenz
594. truenym
595. intelligentfail
596. nicco
597. undbecks
598. Frogger8675309
599. snowgoose
600. sant333
601. darkchidori
602. evilbee
603. Kizartik
604. king718
605. Vasckin
606. piarose
607. Durelo
608. IndaSkies
609. Fh-Fh
610. CorneliusJack
611. cdin
612. aileenconnors
613. youreaatowel
614. keeran_tamu
615. skbounce
616. wwryan
617. puffinorchid
618. wzpgsr
619. jack_main
620. miles377
621. LachRobster
622. Ppohlus
623. Sneaky_p
624. zantefresco
625. demivisage
626. TullyTaargus
627. plokij909
628. hates_novelty_accts
629. stillsweet2
630. consciouscoward
631. mrbokonon
632. m-smith
633. ilyaunoiseau
634. Maddie16
635. mnml
636. chumb
637. draculatreeforest
638. music_player99
639. witchgrass
640. penischarles
641. Ailuropoda
642. EXICON
643. PaszerRatiug
644. postballistics
645. TwilieIsBestPony
646. useeeeee
647. RenegadeoftheWastes
648. japhy11
649. gigantic_panda
650. takomako
651. curiousdevice
652. conchobe
653. CwazyBear666
654. thepeopleskey
655. ncastell77
656. feliperro
657. sjohnb1989
658. sallydkang
659. ryustreetfighter
660. Curious_Device
661. rturns
662. micahlandall
663. owensrs
664. isaaclee96
665. Iroxtion
666. UnorthodoxScholar
667. tbrown983
668. MightAsWellGG
669. tibincrunch
670. starjocelyn8
671. full_metal_avatar
672. efildriew
673. no_ta_ching
674. epomzo
675. koalaver
676. handleson
677. lakmalrupasinghe
678. AntCGallagher
679. LQTMS
680. highbrowalcoholic
681. mrfuzz
682. donkadillo
683. film_guy01
684. ailurophilia
685. beautiful_llama
686. Adorism
687. bkopf
688. thegreatdivide
689. garygetsgrapes
690. masenfim
691. jonnyquin
692. suckarpuncharr
693. kadirgunel
694. NanayawGeoff
695. harleygatt
696. mrfresh44
697. wonderwilly
698. DanielNHarber
699. alfonsosn
700. mudsauce
701. dnnysn
702. 222botany
703. themortal
704. pando
705. Josqu
706. jeffrey_mcpooper
707. Elphabaization
708. laceymarie
709. deltawolf9000
710. maktig
711. Brown.Chicken.Brown.Cow
712. deepit6431
713. Ironklemp
714. hilu
715. alery
716. alemeno
717. utsabgiri
718. Billybobangel
719. 400Lux
720. pallu
721. Mr_WazanskiiiiGoesToSchool
722. nineteen-hundred
723. JuberasTargaryan
724. corycruse
725. Rupen144
726. visvim
727. fkgtz013
728. flowerchild
729. abrarmh
730. November
731. aaronjeo
732. thegeorge
733. deAlchemist
734. jdrush
735. tkirk513
736. christieezhao
737. Marliz
738. mlephotographe
739. Foschi
740. Riovov
741. Mozartny
742. SpicyBabySauce
743. cloudfunk
744. ChannelSERFER
745. nonojr
746. luciafernandez
747. HeartOfAtlas
748. jj57347
749. einarsw
750. BulletMassage
751. john1212
752. quadres
753. melmackian
754. ldudew
755. lulwutamidoin
756. alekspitts
757. Sub0x0one
758. Tjwhore
759. chaditude10
760. arcoty
761. EdwinArcilla
762. sonyasavova
763. vinay1997
764. coyotequark
765. SMETA
766. dariak
767. adqg
768. SockRabbit
769. Adheip.Pai
770. poxto
771. andresf17
772. mobyxe
773. chbeir
774. mecenas
775. Driftw00d
776. TheSilentPianist
777. RossAyRoss
778. christuffa2000
779. rvinay88
780. kkalligeros
781. jeremydrinkard
782. SwiftOwls
783. awdcvgyjm
784. lookingforsome
785. mikyor1
786. dylanpieper
787. claudiav
788. starwarsfien
789. gregorytj
790. gmc51
791. monom3
792. liebstraum
793. ManiDProductions
794. Cheesekicksass
795. kapli
796. reid
797. riccieoriach
798. onederricktion
799. kibieyes
800. doe9
801. hammerhedd
802. VeeShip
803. Jogobello
804. narwhalfam
805. r3os
806. winfield.brookins
807. potatoemagic
808. Twicebakedbuckeye
809. maniacodomachado
810. Tigah
811. sicnarf
812. limvolution
813. cobbless
814. Milkisabadchoice
815. lildre
816. PoundlandBurrito
817. Livin_The_High_Life
818. WadeFU
819. PriscillaVesper
820. zillahdryke
821. davoomac
822. gimel
823. Adollo
824. anunez89nyc
825. nosuchusernamefound
826. hockeymullet
827. perceheadies
828. PesterT
829. arielkiss
830. justeastofwest
831. lucasplaysbass
832. xcortez
833. creedofwheat
834. OkThings
835. VermillionFox
836. WiserMelon
837. eddz423
838. PiNapL
839. nickr33
840. Daegarn
841. theodyssey_
842. tlien
843. feebarscevicius
844. mAd_Lib_kid
845. InesTeles
846. derz_mcgerz
847. darrenpic
848. muthafunkah
849. tomasloureirogomes
850. returnofthaking
851. ecNate
852. Peiatro
853. olds0ul
854. DroHanSolo
855. ilr1
856. phy133
857. pmcinern
858. thewolfman
859. chrisdiaz808
860. Cmder
861. austinn596
862. BarbieCastoldi
863. Alex78
864. AcidRap786
865. fishsmash
866. Jorozo
867. murasa
868. safister
869. ficar
870. moishaha
871. anmuydarp
872. Aumnescience
873. raios168
874. crookedteeth
875. chrawrles
876. godofthesun
877. goflvhxj963
878. mowgli-kun
879. Omnified
880. ilive12
881. tillyt
882. sowhat
883. jdfuhr10
884. Beezlo
885. zenovance_dev
886. syntaxidermy
887. Ivanrose
888. Mashia
889. sparkleinyourchina
890. mrsparklee
891. vrk_92
892. shefster
893. PayneMcDowell
894. big_red_fuck_you
895. NeuralLotus
896. RadKenfo
897. clare_neal
898. Dzigly
899. Alliecompton
900. ValiantEntity
901. WaywardWanderer14
902. fatty_mcturdenstein
903. teck7878
904. cloudland3
905. owenlewis90
906. midnyght219
907. ogaragav
908. dextorg
909. penfold
910. wellrightyothen
911. indigox
912. Lelouch08
913. waterlilyslim
914. BuryMeInSmoke
915. adzash
916. STFUandLove
917. i_am_squish
918. Fitzy257
919. DEADBEEFdd
920. bobbibee
921. leonbasin
922. maicorral
923. NihilisticPriest
924. jaxmanation
925. SandBoxKing
926. moondesu
927. cmcmorrow
928. gfunkel
929. raineou
930. dml1989
931. Advils_Devocate
932. teddy16246
933. PanKarol
934. fitofrijolito
935. luxarus
936. BallinDalin
937. Scarlet_honey
938. lifeinpancakes
939. heepster
940. dnptrs
941. Dreadneck22
942. Evangelion92
943. shradha
944. gasquie
945. voidofman
946. bobbydylan.12
947. jowhica
948. senoresteban
949. brentshermana
950. DamnyouMongarians
951. Dusando
952. mattzimel
953. rough_ER
954. futurespacecadet
955. blobmoe
956. aviator1
957. alexwjohnson
958. Anjello
959. Urca
960. anphex
961. cheef_resident
962. bonhasgone
963. gtarjohnson
964. MasonHoberg
965. pipin574
966. MADXT
967. corntastic
968. Shadeslayr
969. E-than8211
970. prncezmimi
971. crastinator
972. bluffles
973. sl4327
974. Reggeatron
975. Bennymoonbase
976. keller452
977. funkshake
978. soniclizard
979. VSVWB
980. jd95
981. Seacrab
982. jonyuhas15
983. conorobrien50
984. Delusi0n
985. losergetsnothing
986. circulo
987. jayashraj
988. redditreporter424
989. daCostaDave
990. christianblough
991. Djmoyer
992. sfg
993. complainerslament
994. Merallak
995. Jamesjkr
996. LarryThreezor
997. conspiracyofqueens
998. iwishiwasryan
999. dergster
1000. learning_stuff
1001. infaustment
1002. jibicationaire
1003. fariq1mohd
1004. yippohappo
1005. katiewiththeboyds
1006. Lazydude88
1007. braindamage
1008. maagjoel
1009. thephotograph
1010. smk2541
1011. bernardosgr
1012. fotwentylife
1013. Bazzabazza
1014. AliceSAysNo
1015. sssnuff
1016. simha