In most instances, it's a logical progression of increasing the outer integers. When it comes to trichords, for example, (012) is Forte label 3–1, (013) is 3–2, (014) is 3–3, and so on.
But that's not very helpful with something like (0158); you don't want to walk through all tetrachords to try to determine which one it is, and with tetrachords the algorithm becomes a bit more complex. Really, your best bet is to just have a chart nearby with all of the Forte numbers on them. I know of several music theorists and analysts of twentieth-century music that have such a chart just taped on the wall for easy reference.
And if you'll be spending a lot of time with these, I recommend keeping track of the six set classes that are different based on the Forte and Rahn labeling systems; see more in the table here.
Answer from Richard on Stack ExchangeMusic Theory
musictheory.pugetsound.edu › mt21c › PrimeForm.html
33.3 Prime Form
Let’s determine normal form and prime form of the first set from the Webern excerpt. ... The first chord contained E♭, B, and D (3, 11, and 2). ... The normal form is [11, 2, 3]. Below is the calculation to determine prime form.
EasyCalculation
easycalculation.com › other › fun › musical-set-theory.php
Musical Set Theory Calculator | PC Set Calculation
A branch of music that is concerned about the pitches and pitch classes, which can be either ordered or unordered, and can also be related to operations in music like transposition, inversion, and complementation is called as a musical set theory. Here is the online musical set theory calculator for you to make the PC set calculations with ease. Enter the prime form and choose an algorithm in the set finder, the tool will display the output for forte code, interval vector and prime inversion.
theory - How do I calculate the Forte number from the Prime form? - Music: Practice & Theory Stack Exchange
I know of several music theorists ... music that have such a chart just taped on the wall for easy reference. And if you'll be spending a lot of time with these, I recommend keeping track of the six set classes that are different based on the Forte and Rahn labeling systems; see more in the table here. ... Find the answer to your question by asking. Ask question ... See similar questions with these tags. 10 How was the ordering of Allen Forte's list of prime forms ... More on music.stackexchange.com
theory - Error computing prime form of a pitch class set - Music: Practice & Theory Stack Exchange
I'm working on coming up with prime forms. I've been using this calculator online to check my work. My problem is that the prime form I compute for a certain PCS doesn't agree with the calculator... More on music.stackexchange.com
Calculate the prime form (Pitch-Class Set Theory)
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February 8, 2023What is the Prime Form of D F# G Bb B in Set Theory? (Exercise from Robert Hutchinson's "Music Theory for the 21st-Century Classroom")
Looks to me like you've found a mistake in their answer key. Your reasoning is sound. Here's one more way to demonstrate that the notes provided can't possibly be [0, 1, 4, 5, 7]: look at intervals between some of the numbers and compare to the original set. For example, between 1 and 7 we have 6 semitones (or a tritone). However, looking at the original set, no two pitch classes you select can create a tritone. Similarly, 5 to 7 is 2 semitones, but no two pitch classes you select are a whole tone apart. More on reddit.com
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January 10, 2023Trainedear
trainedear.net › other › pc-set-class-calculator
pc Set-Class Calculator
Use the tool below to calculate the normal order, prime form, etc. for any pitch class set. Click the button for each pitch class in the set. If you make a mistake or need to go back, click the "DEL" button to remove the last entry. Press the "CLR" button to start over. ... (There are also many options for mobile devices. Try searching for "music set theory" in your device's download center.)
Wikipedia
en.wikipedia.org › wiki › Forte_number
Forte number - Wikipedia
October 29, 2024 - There are two prevailing methods of computing prime form. The first was described by Forte, and the second was introduced in John Rahn's Basic Atonal Theory and used in Joseph N. Straus's Introduction to Post-Tonal Theory, and is now generally more popular. For example, the Forte prime form for 6-31 is [011232538193] whereas the Rahn algorithm chooses [011341527293], where adjacency intervals are shown here by subscripts between pitch-class numerals.
Google Play
play.google.com › store › apps › details
Pitch Class Set Calculator - Apps on Google Play
December 22, 2016 - This is a calculator which can be used to generate normal form, prime form, interval vector, and Forte number metadata for every applicable pitch class set. Included within it is also a comprehensive list of pitch class sets ranging from ...
YouTube
youtube.com › watch
Music Theory: How to find the Normal Form & Prime Form of a PC set - YouTube
AboutPressCopyrightContact usCreatorsAdvertiseDevelopersTermsPrivacyPolicy & SafetyHow YouTube worksTest new featuresNFL Sunday Ticket · © 2025 Google LLC
Published March 30, 2020
Jaytomlin
jaytomlin.com › music › settheory
Set Theory Calculator – Post-Tonal Set Theory
Musical Set Theory app for iPhone · For pitch sets you define, the app will: Calculate Normal Form and Prime Form · Display the Forte Number · Calculate the interval class vector · Show transposed and inverted sets · Display a set matrix · Sort, invert or complement the set ·
Sc
in.music.sc.edu › fs › bain › software › aa-v2.20d › help › index.htm
Atonal Assistant Help
When you click the Get button, Atonal Assistant calculates the prime form of the current set and uses it to look up the following information in its Set Class Database: the Forte name, the number of Distinct members in the set class, the ic vector, the Z-relation (if any), and M-relation (see ...
Strcalculator
strcalculator.com
Set Theory Relationship Calculator
Calculator that analyzes relationships in musical set theory
LearnMusicTheory.net
learnmusictheory.net › PDFs › pdffiles › 06-10-SetTheorySimplified.pdf pdf
LearnMusicTheory.net 6.10 Set Theory Simplified
Prime form: Parentheses, NO commas, e.g. (014). Use "T" for ten and "E" for eleven. It is possible to calculate the normal order entirely with pitch class numbers. Simply write down the pitch class · numbers without the music notation and continue all calculations from there.
Jaytomlin
jaytomlin.com › music › settheory › help.html
Post-Tonal Set Theory – All About Musical Set Theory
To get help defining and manipulating pitch class sets, and to determine their normal form, prime form, Forte number and interval class vectors, you can use the Post-Tonal Theory Calculator for iPhone.
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As the PC Set Calculator you link to shows, [0, 1, 2, 3, 5] is the Prime Inversion of [0, 2, 3, 4, 5]. However, as [0, 1, 2, 3, 5] has a lower interval at the bottom, it is considered the correct prime form of these two equivalent PC Sets.
Another page on the website you link to gives a rigorous method for determining the Prime Form of any PC Set. The last of 8 steps asks you to find:
Which form, the original or the inverted, is most packed to the left (has the smallest numbers)? That will be the Prime Form.
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I think you forgot to test inversions -- you should measure the distance between the first two and last two classes, and find the form that packs the smaller intervals to the left.
If you invert [0 2 3 4 5], you get [0 1 2 3 5], which succeeds in packing the shorter distance to the left of the form (starts with a distance of 1 instead of 2).
Reddit
reddit.com › r/maxmsp › calculate the prime form (pitch-class set theory)
r/MaxMSP on Reddit: Calculate the prime form (Pitch-Class Set Theory)
February 8, 2023 -
Has anyone any idea on how to calculate the prime forms of pitch-class sets?
I am aware of the bach objects that deal with set theory, but I am looking for ways to do it more manually.
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Found this on Google: https://viva.pressbooks.pub/openmusictheory/chapter/set-class-and-prime-form/ Not Max-related, but if you detect the pitches and throw them in an array, you should be able to apply these techniques.
Intmus
intmus.github.io › inttheory22-23 › 23-intro-to-post-tonal › e1-ex-primeform.html
Integrated Music Theory | 23e Lesson - PC Set Prime Form
There are a number of helpful online resources that will help you quickly find the normal and prime forms of a pitch-class set, but these tools are only useful if you know where to use them. In order to do so, you must understand how the pcs calculator finds the new forms, so I hope that you ...
Amazon
amazon.com › Alex-Worland-Inc-Pitch-Calculator › dp › B01G1CXCDM
Amazon.com: Pitch Class Set Calculator : Alexa Skills
This skill is designed to aid in the calculation of the prime and normal forms of a pitch class set of one to twelve different musical notes.
Intmus
intmus.github.io › inttheory19-20 › 23-intro-to-post-tonal › c2-tx-primeform.html
Integrated Music Theory | 23c Lesson - PC Set Prime Form
And set the inversion’s normal form on zero [0,2,6,7]. NOW you compare the two normal forms on zero. ... first you find the smallest interval between the first and 4th intergers (in this case it is the same). then you check the interval between the first and 3rd intergers (in this case the first option has a smaller interval). Our prime form is (0157).
Smbutterfield
smbutterfield.github.io › ibmt17-18 › 23-intro-to-post-tonal › c1-ex-primeform.html
Inquiry-Based Music Theory | 23c Examples - PC Set Prime Form
In the above trichords, we had ... form, we apply the same tie-breakers that we used when determining normal form: start by comparing the outermost intervals and then work your way inward....
Mount Allison University
mta.ca › pc-set › calculator › pc_calculate.html
PC Set Calculator
PC Set Calculator · Type your set here: · Forte name: · Subset: · cardinality · Trichords · Tetrachords · Pentachords · Hexachords
Astate
clt.astate.edu › tcrist › theory4 › findingasetsprimeform.pdf pdf
3 M2 m2 M6 N.O. 0 2 3 3 1 0 0 1 3 M2 m3 m2 m3 0 ( B.N.O 1 3 ) Prime Form f
Prime Form · f · Theory Dr. Crist · Steps for Finding a Set's Prime Form · (1) Identify a pitch segment. (2) Remove redundant pitch classes (pcs). (3) Arrange the pcs in an ascending scale that spans · an octave · (4) Find the largest interval between adjacent notes ·