Posted December 8, 20177 yr Dear Friends, I'm working with pcs now. A lot of pcs have inverted forms. For example: Pcs 3-11 correspond to the minor triad (037) and also the major triad (047) since both have the same interval vector. But when I evaluate the expression below, I get only the prime form (037) and not the IF (047). Is it possible to retrieve also the inverted form, like the example below ? (setf pcset (pcs '3-11)) >> (0 4 7) ??? Thanks a lot
December 8, 20177 yr (pcs-analysis '(0 3 7)) ? pcs-analysis Sequence: (0 3 7) Set: 3-11 Prime Form: (0 3 7) Pitch: (c4 eb4 g4) Normal Order: (0 3 7) Complement: (1 2 4 5 6 8 9 10 11) Inversion: (0 9 5) Vector: (0 0 1 1 1 0) (pcs-analysis '(0 4 7)) ? pcs-analysis Sequence: (0 4 7) Set: 3-11 Prime Form: (0 3 7) Pitch: (c4 eb4 g4) Normal Order: (0 4 7) Complement: (1 2 3 5 6 8 9 10 11) Inversion: (0 8 5) Vector: (0 0 1 1 1 0) Note: The pitch output form PCS-ANALYSIS is the pitch form prime form.
December 8, 20177 yr Author Really Cool, Janusz ! But what I was refering would be getting the inverted form from the Forte Number, i.e., from 3-11 and not the opposite, informing the integer list and getting all the info, although this can be very useful too. In my book, I specify this by adbing a "b" after the set: 3-11 = 037 3-11b = 047 like this, from http://composertools.com/Tools/PCSets/PCSRelations.html Best ! Julio
December 8, 20177 yr To do this I would need to rewrite the pitch class set functions. The functions where based on Allen Forte 'The Structure of Atonal Music' book.
December 9, 20177 yr Author Very cool, Janusz! Im doing my doctoral dissertation now and I'm doing some thing interesting related to rhythm that certainly could be transformed in a function. I'll tell you soon. This Will be useful there. Best Julio
December 9, 20177 yr Author It's a really interesting issue to study the different approaches of the post tonal Theory. The more hardcore atonal side does not consider prime and inverted form as different things, ontologically but in fact, our tonal oriented ear really can tell the difference between a major and a minor triad as a clear episthemological distinction. Counting or not counting the inverted forms also have implications on the Problems of enumeration of the types of series, as Frippertinger & Lackner recent studies related to group theory and a more modern approach to Hauer Tropes demonstrates. Best Julio
December 9, 20177 yr 3 hours ago, JulioHerrlein said: It's a really interesting issue to study the different approaches of the post tonal Theory. The more hardcore atonal side does not consider prime and inverted form as different things, ontologically but in fact, our tonal oriented ear really can tell the difference between a major and a minor triad as a clear episthemological distinction. Counting or not counting the inverted forms also have implications on the Problems of enumeration of the types of series, as Frippertinger & Lackner recent studies related to group theory and a more modern approach to Hauer Tropes demonstrates. Best Julio I agree totally !!! S.
December 11, 20177 yr The PCS-ANALYSIS function returns two more results: inverted-form and interval-class: (pcs-analysis '(4 1 8 10 3 7)) => Sequence: (4 1 8 10 3 7) Set: 6-z29 Prime Form: (0 2 3 6 7 9) Inverted Form: nil Pitch: (c4 d4 eb4 fs4 g4 a4) Normal Order: (1 3 4 7 8 10) Complement: (0 2 5 6 9 11) Inversion: (8 11 4 2 9 5) Vector: (2 2 4 2 3 2) Interval Class: (3 5 2 5 4) (pcs-analysis '(0 3 7)) => Sequence: (0 3 7) Set: 3-11 Prime Form: (0 3 7) Inverted Form: (0 4 7) Pitch: (c4 eb4 g4) Normal Order: (0 3 7) Complement: (1 2 4 5 6 8 9 10 11) Inversion: (0 9 5) Vector: (0 0 1 1 1 0) Interval Class: (3 4) (pcs-analysis '(0 4 7)) => Sequence: (0 4 7) Set: 3-11b Prime Form: (0 3 7) Inverted Form: (0 4 7) Pitch: (c4 e4 g4) Normal Order: (0 4 7) Complement: (1 2 3 5 6 8 9 10 11) Inversion: (0 8 5) Vector: (0 0 1 1 1 0) Interval Class: (4 3) The new function PCS-FORMS takes care of both forms: prime-form and inverted-form. The inverted form set ends with letter b: (pcs-forms '((0 4 7) (0 3 7)) :type :set) => (3-11b 3-11)
December 11, 20177 yr Author Really Cool, Janusz !! Thanks a lot. Can we do the reverse ? Typing the Forte code 3-11b and getting the integer list (0 4 7) ?
December 11, 20177 yr of course: (pcs '3-11b) => (0 4 7) INTERVAL-CLASS: (interval-class '(0 1 2 11 10 9 5 4 3 6 7 8)) => (1 1 3 1 1 4 1 1 3 1 1) (interval-class '(0 1 3 8 4 9 10 7 6 5 11 2)) => (1 2 5 4 5 1 3 1 1 6 3) (interval-class '(0 11 5 7 6 1 3 4 2 9 8 10)) => (1 6 2 1 5 2 1 2 5 1 2)
December 11, 20177 yr Author WOW !!! GREAT ! Thanks ! It was really a lot of work done ! Lots of sets, but it's really useful, I think. Best ! Julio This will be in the next release, I think. Looking Forward ! added 2 minutes later If you like Set Theory and Guitar, you gonna like my book. Please, Check it out ! https://www.melbay.com/Products/Default.aspx?bookid=30042BCDEB Best, Julio
December 13, 20177 yr On December 11, 2017 at 9:15 AM, JulioHerrlein said: Please, Check it out ! https://www.melbay.com/Products/Default.aspx?bookid=30042BCDEB Best, Julio Going to, looks good...thanks for the notice ;-)
December 17, 20177 yr 15 hours ago, JulioHerrlein said: Thanks a lot LOOPYC! Hope you like it! Best Julio I opted for a 'physical copy', so will have to wait until Dec. 21st...just in time for a Christmas gift to myself ;-)
December 17, 20177 yr Author 3 hours ago, Stephane Boussuge said: Hey, Stephane! Thank you! Hope you like it. What a lovely combination! I feel very honored with this picture! Best! Julio added 2 minutes later 4 hours ago, loopyc said: I opted for a 'physical copy', so will have to wait until Dec. 21st...just in time for a Christmas gift to myself ;-) Thank you, LOOPYC! It's really cool to have a physical book. Best regards and happy xmas to you! Best Julio
December 18, 20177 yr Author 12 hours ago, lviklund said: Nice work and a good companion to Allan Forte. /Lasse Thank you, Iviklund! Best Julio
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