Music Theory: Set Theory, Part 1

This video corresponds with material from chapter 9 in your text. In particular, it focuses on material from pages 166 - 173.
0:00 Introductions
1:41 Pitch Class Notation
4:19 Pitch Class Intervals
7:06 Pitch Class and Mod 12
10:20 Normal Order
14:47 Breaking Ties
17:04 Transpositionally Symmetrical Sets

[@Spykakos88]

For us math and music nerds, this is gold. Job well done.

[@kaileegirl1785]

My study time stamps 11:39 - finding normal order/form -order into octave -invert/rotate -compare and choose the rotation with the smallest outer interval (subtract highest pc by lowest pc in each) -use that rotation order as normal order/form [numbers in brackets] 16:17 - If there's a tie, use the first and penultimate pitch, rather than the first and last to find the smallest outer between the two 17:10 - transpositional symmetry

[@PineAway515]

Been brushing up on my theory so I can start preparing to apply to grad school and I came across a video by one of my former composition instructors! Solid video Dr. Farrell! I hope all is well in your world.

[@ericarnau1987]

Awesome video! Explained it very well! Look forward to your next one. 👍

[@Stephanie-kv2bu]

Very thorough and extremely easy to understand! You've cleared up all the fog and confusion from my undergrad. Thank you!

[@Gilbrass1]

Thank you for these videos. You've made things easier to understand.

[@melissabialecki9688]

Reviewing some stuff for graduate diagnostics, your videos are extremely helpful--brief, not too pedantic, and well-paced. Thanks for posting!

[@DavidEFarrell]

Thanks! Good luck with the diagnostics.

[@merrickmarcel4508]

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[@korbynharrison5899]

@Merrick Marcel Instablaster :)

[@merrickmarcel4508]

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[@merrickmarcel4508]

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[@icecreamforcrowhurst]

Very well explained and very useful. Thank you for posting

[@JJBerthume]

Really clear and concise lecture! 9:25 - you meant to say 10 AM to 2 PM.

[@jamespredisik7074]

Here from your book. :)

[@simonkawasaki4229]

This really comes in handy when studying Webern. Thank you.

[@bergspot]

So clear, thank you!

[@pineapple_1066]

Omg is this so interesting! Better explanation than my uni lecturer I am afraid........

[@ForPropertyInvestors]

I'm learning set theory in a way so far to just identify the normal music theory. I've gone a step further and added a colour to each number as well at the music theory letters the same colour. I know it seems strange but i tried many things and my mind for some reason being dyslexic had eternal trouble to get it the normal way. I even went a step further and associated a natural thing of that colour to the note. For example to me i felt F was green and for Forest so i painted green. When i think of F i instantly think green forest and a green 5. Or simply 5F where the number gives me logic where to go next. You would not believe the difficulty i've had to learn the traditional music theory and i can never get it to flow where the set theory is starting to make logic sense better and with time think i can relearn it like knowing a new language and get it to flow and be spontaneous in decision making while playing music on guitar. My question: I would like to be able to convert the numbers and letters into the arbitrary colours i'd like to use in a set theory program on mac so i can start to get familiar with my learning concept. Would anyone be able to help me to suggest a program with this function built in so it changes all them across all theory? Then be able to do a heap of questions ect so get flowing with the muscle memory and get the theory down. I can tell you a short story and i spent 4 yrs at grade 4 at primary school in private lessons once a week to learn piano and i learned next to nothing and could never understand the music theory my mother wasted her money. At 48 years old i finally self taught myself Uke Guitar.

[@mpdirigent]

Excellent, concise introduction. Small correction @ 06:41, as 8 is a minor sixth. Quibbling detail, but important for pedagogy purposes and worth correcting. Your website was a pleasure to explore. Cheers!

[@JJBerthume]

He said and has on the chart that it's a minor sixth, but also noted that an augmented fifth is the same sounding interval and would be classified as the number 8 in set theory, since set theory disregards enharmonic spelling. Am I missing something?

[@VsevolodTokmakov93]

Thank you very much.

[@Norm64349]

M.Lloyd Tew taught us about pitch class and its uses back in 1970.

[@sebastianmorataboada9795]

Can't the pitches in a pitch class set be reapeated, e. g. the 4's in [0,4,4,5,8,0]? Can't them be in an order other than clockwise on the pitch clock, e. g. the 8 in [0,4,5,6,8,7]?

[@n.gulbrandson2547]

Thank you!

[@FeonaLeeJones]

Well explained

[@averysax6429]

The new music Tonal Scale is as thus: 12 7 5 2 3 : 1 4 5 9 14 Not 12 with 7 & 5 BUT 14 with 9 & 5 [2^(1/14)] These are the Tonal Scales growing from f (by cycles of fifths): All Scales build from the first mode: equivalent to Lydian f White keys are = & Black keys are | 12 with 7 & 5 [2^(1/12)] =|=|=|==|=|= {1,8,3,10,5,12,7,2,9,4,11,6} 1thru7are= 8thru12are| 7 with 5 & 2 [2^(1/7)] ===|==| {1,3,5,7,2,4,6} 1thru5are= 6&7are| 5 with 2 & 3 [2^(1/5)] =||=| {1,3,5,2,4} 1&2are= 3thru5are| Now evolving up the other end 5 with 4 & 1 [2^(1/5)] ==|== {1,3,5,2,4} 1thru4are= 5is| 9 with 5 & 4 [2^(1/9)] =|=|=|==| {1,8,3,7,5,9,2,4,6} 1thru5are= 6thru9are| 14 with 9 & 5 [2^(1/14)] =|=|===|=|===| {1,12,3,14,5,7,9,11,2,13,4,6,8,10} 1thru9are= 10thru14are| Joseph Yasser is the actual originator of the realization, that scales develop by cycles of fifths. www.seraph.it/blog_files/623ba37cafa0d91db51fa87296693fff-175.html www.academia.edu/4163545/A_Theory_of_Evolving_Tonality_by_Joseph_Yasser www.musanim.com/Yasser/ The chromatic scale we use today is divided by 2^(1/12) twelfth root of two Instead of moving to the next higher: the 19 tone scale 2^(1/19) nineteenth root of two I decided to go all the way down and back up the other end: So 12 - 7 is 5 & 7 - 5 is 2 & 5 - 2 is 3 Now we enter to the other side: 2 - 3 is (-1)* & 3 - (-1) is 4* & (-1) - 4 is (-5)* & 4 - (-5) is 9* & (-5) - 9 is (-14)* ignoring the negatives we have * 1 4 5 9 14 Just follow the cycles how each scale is weaved together, as shown above. Each scale has its own division within the frequency doubling, therefore the 14 tone scale is 2^(1/14) fourteenth root of two

[@udomatthiasdrums5322]

cool stuff

[@runnerkidal]

Curious: what's the reference text that you're using... you mention the pages and chapters but no title... much appreciated and thanks for these vids!

[@DavidEFarrell]

Hello! The book from which I teach this stuff is currently "Materials and Techniques of Post-Tonal Music" by Stefan Kostka.

[@still451]

May i know which book you recommend for the theory book? Thanks!

[@DavidEFarrell]

Helen - there are many great texts. If you want to learn set theory, you might consider Straus's Introduction to Post-Tonal Theory. It is very detailed, but really gives you everything you would need to know set theory.

[@benkendall4307]

I don't understand something. If pitch class represents all the possible pitches in that class then why do we need MOD 12? Can't we just limit the pitches given to the same octave without crossing zero?

[@DavidEFarrell]

good question! direction can matter, and so if we are counting up from pc9 to pc3, we like to be able to calculate that pitch class interval.

[@priscilavieira9787]

Is it possible to do this descendent insted of ascendent? I Have Bb-G-F... how do i classify this? What is the "short-form" if i have to make this ascendent? (srry for my bad english, it's not my native language) And thank you so much for your videos, they are very simple and easy to understand!! Wish you all the sucess!!

[@DavidEFarrell]

Priscila Vieira There are a lot of ways to find the normal order. Ultimately, you are looking to group pitches in the smallest overall space. I suppose descending or ascending doesn’t really matter! For the PC set you gave, normal order would have F and Bb as the outer pitches - [5,7,t].

[@priscilavieira9787]

@@DavidEFarrell Ok, that helps a lot!! Thank you so much!!

[@Mukundanghri]

The light just came on...good grief.

[@insanedrummer89]

Music Theory Nerd Level: OVER 9000000!!!!

[@bobbymcloughlin3452]

I Got A 14 Note Chromatic Scale C# D# F# G# H# A# C | D | E F | G | H | A | B C Db Eb Gb Hb Ab Bb 8 = Natural & 6 Accidental Eight Letters Of The Music Alphabet: A B C D E F G H, Then Starts All Over At A C Major Scale: C D E F G H A B C Intervals Mod 14 (A Twensen (Twains O’ Seven) Values) Range: 0 - 13 0 = P1/P9 8 = S8T 1 = m2 9 = P6 2 = M2 10 = m7 3 = m3 11 = M7 4 = M3 12 = m8 5 = P4 13 = M8 6 = Tritone 7 = P5 9ve = Nonave Solfege: Do Re Mi Fa Sol La Ti Be Do Modes Of The Scale 1. Ionian: 1, 2, 3, 4, 5, 6, 7, 8, 9(1) 2. Dorian: 1, 2, b3, 4, 5, 6, 7, b8, 9(1) 3. Phrygian: 1, b2, b3, 4, 5, 6, b7, b8, 9(1) 4. Lydian: 1, 2, 3, #4, #5, 6, 7, 8, 9(1) 5. Hypolydian: 1, 2, 3, #4, 5, 6, 7, b8, 9(1) 6. Mixolydian: 1, 2, 3, 4, 5, 6, b7, b8, 9(1) 7. Aeolian: 1, 2, b3, 4, 5, b6, b7, b8, 9(1) 8. Locrian: 1, b2, b3, 4, b5, b6, b7, b8, 9(1) Major Scale 1. Major 2. Minor 3. Minor 4. Augmented 5. Major 6. Major 7. Minor 8. Diminished 9(1. Major) I ii iii IV+ V VI vii viii° I 1. Tonic (I) 2. Supertonic (ii) 3. Mediant (iii) 4. Sub-Dominant (IV+) 5. Dominant (V) 6. Superdominant (VI) 7. Sub-Mediant (vii) 8. Leading Tone (viii°) 9(1. Tonic) I And So On 8 TET Scale (Mod 8 = 8 Values) Ranging: 0 - 7 Nonal (Base-9) Digits (0, 1, 2, 3, 4, 5, 6, 7, 8) 0 = Unison 1 = Neutral Major Second 2 = Neutral Third 3 = Neutral Major Fourth 4 = Perfect Fifth 5 = Neutral Minor Sixth 6 = Neutral Seventh 7 = Neutral Minor Eighth 8 = Nonave Circle Of Fourths & Sixths C H F E Ab B Db G# Gb D# A A# D G

[@apothecurio]

Music theory always felt so weirdly biased to me. Everything being based around C Major/major in general. With thing about sharps and flats and how G# major is a stupid key. Despite all the notes being the same distance away from eachother. Even though the set theory is still treating C as note 0. This feels much more freeing and “inclusive” if that makes any sense.

[@boyisun]

9:23 You know it's 4 hours from 10 p.m. to 2 p.m.

[@deathhzrd]

Gonna be honest it sounds like you’re talking through a cup my friend I have to squint my ears to understand this