User talk:FloraC: Difference between revisions

Line 76:

== Subsets and Supersets af AFDOs (Pages AFDO, 2afdo, 3afdo, …n-afdo) ==

Flora, you have put so much effort and time into maintaining and editing the ''AFDO'' pages - thank you for that.

There is one aspect of these pages that I'm not sure I understood correctly, so I'll just address my question directly to you. It's about the terms ''subset'' and ''superset'' of an AFDO.

Line 94:

Line 93:

I've been playing around with overtone scales for a while now, in order to construct a prototype keyboard with dynamic intonation control. Personally I would summarize my experience with this project as follows:

• To create a '''superset''' of an n-afdo , I’d multiply ''n'' by a (preferably small) integer number including 2 (i.e. 9-afdo is a superset of 3-afdo).

* To create a '''superset''' of an n-afdo , I’d multiply ''n'' by a (preferably small) integer number including 2 (i.e. 9-afdo is a superset of 3-afdo).

* To create a '''subset''' of an n-afdo , I’d divide ''n'' by any of its prime factors

• To create a '''subset''' of an n-afdo , I’d divide ''n'' by any of its prime factors

(i.e. 5-afdo and 3-afdo are both subsets of 15-afdo).

Your comment is very much appreciated – thanks for your time.<br>

All the best --[[User:Holger Stoltenberg|Holger Stoltenberg]] ([[User talk:Holger Stoltenberg|talk]]) 11:35, 12 December 2024 (UTC)

: You might be missing the fact that afdos are octave-repeating tunings and that octave-equivalent rotation is a thing. For edos it's the prime factor rule, since each edo only has one mode. For afdos, ''n''-afdo has ''n'' distinct modes. So in the 2- and 3afdo example, 2afdo has two modes: 2:3:4 and 3:4:6. 3afdo has three modes: 3:4:5:6, 4:5:6:8, and 5:6:8:10. 3:4:5:6 is a superset of 3:4:6, so 3afdo is a superset of 2afdo. The same is true for any two distinct afdos and any two distinct ifdos. I hope that answers your question. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:03, 12 December 2024 (UTC)

@@ Line 76: / Line 76: @@
 == Subsets and Supersets af AFDOs (Pages AFDO, 2afdo, 3afdo, …n-afdo) ==
 Flora, you have put so much effort and time into maintaining and editing the ''AFDO'' pages - thank you for that.
 There is one aspect of these pages that I'm not sure I understood correctly, so I'll just address my question directly to you. It's about the terms ''subset'' and ''superset'' of an AFDO.
@@ Line 94: / Line 93: @@
 I've been playing around with overtone scales for a while now, in order to construct a prototype keyboard with dynamic intonation control. Personally I would summarize my experience with this project as follows:
-•	To create a '''superset''' of an n-afdo , I’d multiply ''n'' by a (preferably small) integer number including 2 (i.e. 9-afdo is a superset of 3-afdo).
+* To create a '''superset''' of an n-afdo , I’d multiply ''n'' by a (preferably small) integer number including 2 (i.e. 9-afdo is a superset of 3-afdo).
+* To create a '''subset''' of an n-afdo , I’d divide ''n'' by any of its prime factors
-•	To create a '''subset''' of an n-afdo , I’d divide ''n'' by any of its prime factors
 (i.e. 5-afdo and  3-afdo are both subsets of 15-afdo).
 Your comment is very much appreciated – thanks for your time.<br>
 All the best --[[User:Holger Stoltenberg|Holger Stoltenberg]] ([[User talk:Holger Stoltenberg|talk]]) 11:35, 12 December 2024 (UTC)
+: You might be missing the fact that afdos are octave-repeating tunings and that octave-equivalent rotation is a thing. For edos it's the prime factor rule, since each edo only has one mode. For afdos, ''n''-afdo has ''n'' distinct modes. So in the 2- and 3afdo example, 2afdo has two modes: 2:3:4 and 3:4:6. 3afdo has three modes: 3:4:5:6, 4:5:6:8, and 5:6:8:10. 3:4:5:6 is a superset of 3:4:6, so 3afdo is a superset of 2afdo. The same is true for any two distinct afdos and any two distinct ifdos. I hope that answers your question. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:03, 12 December 2024 (UTC)