Talk:70:90:105:126: Difference between revisions

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:::::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:17, 1 April 2026 (UTC)

::::::: I actually listened to the voicings of all these chords using normal harmonic timbres, and both Praveen and I agreed that the ones with the 11th subharmonic in the bass sound better.

::::::: "Surely we can agree that 6/5, 3/2, 12/7, 24/11, and 8/3 sound better than 11/9, 11/7, 11/6, 11/5, and 11/4?" I don't agree. Consider these two chords 1/1 6/5 3/2 5/3 (min6) vs. 1/1 6/5 3/2 9/5 (min7). Which is more consonant? By your logic, considering only the 3 intervals from the root, since 5/3 is more consonant than 9/5, the min6 is more consonant. But what one actually hears is not just those 3 intervals, but all 6 intervals within the chord. Min6 has 6/5 5/4 10/9, 3/2 25/18, 5/3. Min7 has 6/5 5/4 6/4, 3/2 3/2, 9/5. Ignoring the ratios they have in common, we have 10/9 vs 6/5 and 25/18 vs 3/2 and 5/3 vs 9/5. The dissonant 25/18 makes min7 the clear winner.

::::::: Can we agree that when judging a chord's consonance, one must take into account all intervals within the chord, not just the ones from the root?

::::::: Assuming your answer is yes, here are all 15 intervals in 24:20:16:14:11:9

:::::::: 6/5 5/4 8/7 14/11 11/9

:::::::: 3/2 10/7 16/11 14/9

:::::::: 12/7 20/11 16/9

:::::::: 24/11 20/9

:::::::: 8/3

::::::: And here are all 15 intervals in 11:9:7:6:5:4

:::::::: 11/9 9/7 7/6 6/5 5/4

:::::::: 11/7 3/2 7/5 3/2

:::::::: 11/6 9/5 7/4

:::::::: 11/5 9/4

:::::::: 11/4

::::::: Discarding those ratios in common, we have 11 ratios left. Let's compare them using Weil height, Bernadetti height, and Wilson height.

:::::::: 8/7 vs 7/6 and 14/11 vs 9/7 -- the latter wins both times

:::::::: 14/9 vs 3/2 and 10/7 vs 7/5 and 16/11 vs 11/7 -- the latter wins all 3 times

:::::::: 16/9 vs 7/4 and 12/7 vs 9/5 and 20/11 vs 11/6 -- the latter wins all 3 times

:::::::: 20/9 vs 9/4 and 24/11 vs 11/5 -- the latter wins both times

:::::::: 8/3 vs 11/4 -- the former wins

::::::: The latter wins 10 out of 11 times, no matter which height you use.

::::::: "It suits itself much better to traditional chord naming systems." What's more important, a chord's sound or its name?

::::::: "More notes are on the consonant categories." Is this still true when you consider all 15 ratios? I don't know how you define "consonant category", but surely it can't contradict all 3 of the heights I used.

::::::: I agree that 9:7:6:5:4 is the subharmonic ninth chord. But by the rules of negative harmony, this should be 1/1 6/5 3/2 12/7 8/3, a min6add11 chord 24:20:16:14:9. In choosing 9:7:6:5:4 over this, you're actually arguing against using negative harmony. Note that 24:20:16:14:9 is a more dissonant voicing than 9:7:6:5:4. Analyzing the ratios as before, we have the latter winning 8/7 vs 7/6 and 10/7 vs 7/5 and 16/9 vs 7/4 and 14/9 vs 3/2 and 12/7 vs 9/5 and 20/9 vs 9/4. Whereas the former wins only 8/3 vs 9/7.

::::::: "What's the ninth being added to?" Again, I view subharmonic chords as being extended downwards, not upwards. Because the subharmonic series itself extends downwards, not upwards. You may or may not agree with me on this, but it is in fact a logical and consistent approach. So the 9th is added to 7:6:5:4 to make 9:7:6:5:4. And adding the 11th makes 11:9:7:6:5:4.

::::::: "Inflecting the third and sixth by 36/35... why you ignored it in your nomenclature." I ignored it for two reasons. One, converting harmonic to subharmonic by commatic inflections holds for the 7-limit, but breaks down in the 11-limit. 11/8 and 18/11 differ by 301c. Two, IMO the significance of a subharmonic chord should be determined not by whether it's commatically close to a harmonic chord, but by its consonance. 7:6:5:4 is more consonant than 9:7:6:5, because 5/4 beats 9/7 and 7/4 beats 9/5.

::::::: --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 22:32, 2 April 2026 (UTC)

@@ Line 44: / Line 44: @@
 :::::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:17, 1 April 2026 (UTC)
+::::::: I actually listened to the voicings of all these chords using normal harmonic timbres, and both Praveen and I agreed that the ones with the 11th subharmonic in the bass sound better.
+::::::: "Surely we can agree that 6/5, 3/2, 12/7, 24/11, and 8/3 sound better than 11/9, 11/7, 11/6, 11/5, and 11/4?" I don't agree. Consider these two chords 1/1 6/5 3/2 5/3 (min6) vs. 1/1 6/5 3/2 9/5 (min7). Which is more consonant? By your logic, considering only the 3 intervals from the root, since 5/3 is more consonant than 9/5, the min6 is more consonant. But what one actually hears is not just those 3 intervals, but all 6 intervals within the chord. Min6 has 6/5 5/4 10/9, 3/2 25/18, 5/3. Min7 has 6/5 5/4 6/4, 3/2 3/2, 9/5. Ignoring the ratios they have in common, we have 10/9 vs 6/5 and 25/18 vs 3/2 and 5/3 vs 9/5. The dissonant 25/18 makes min7 the clear winner.
+::::::: Can we agree that when judging a chord's consonance, one must take into account all intervals within the chord, not just the ones from the root?
+::::::: Assuming your answer is yes, here are all 15 intervals in 24:20:16:14:11:9
+:::::::: 6/5 5/4 8/7 14/11 11/9
+:::::::: 3/2 10/7 16/11 14/9
+:::::::: 12/7 20/11 16/9
+:::::::: 24/11 20/9
+:::::::: 8/3
+::::::: And here are all 15 intervals in 11:9:7:6:5:4
+:::::::: 11/9 9/7 7/6 6/5 5/4
+:::::::: 11/7 3/2 7/5 3/2
+:::::::: 11/6 9/5 7/4
+:::::::: 11/5 9/4
+:::::::: 11/4
+::::::: Discarding those ratios in common, we have 11 ratios left. Let's compare them using Weil height, Bernadetti height, and Wilson height.
+:::::::: 8/7 vs 7/6 and 14/11 vs 9/7 -- the latter wins both times
+:::::::: 14/9 vs 3/2 and 10/7 vs 7/5 and 16/11 vs 11/7 -- the latter wins all 3 times
+:::::::: 16/9 vs 7/4 and 12/7 vs 9/5 and 20/11 vs 11/6 -- the latter wins all 3 times
+:::::::: 20/9 vs 9/4 and 24/11 vs 11/5 -- the latter wins both times
+:::::::: 8/3 vs 11/4 -- the former wins
+::::::: The latter wins 10 out of 11 times, no matter which height you use.
+::::::: "It suits itself much better to traditional chord naming systems." What's more important, a chord's sound or its name?
+::::::: "More notes are on the consonant categories." Is this still true when you consider all 15 ratios? I don't know how you define "consonant category", but surely it can't contradict all 3 of the heights I used.
+::::::: I agree that 9:7:6:5:4 is the subharmonic ninth chord. But by the rules of negative harmony, this should be 1/1 6/5 3/2 12/7 8/3, a min6add11 chord 24:20:16:14:9. In choosing 9:7:6:5:4 over this, you're actually arguing against using negative harmony. Note that 24:20:16:14:9 is a more dissonant voicing than 9:7:6:5:4. Analyzing the ratios as before, we have the latter winning 8/7 vs 7/6 and 10/7 vs 7/5 and 16/9 vs 7/4 and 14/9 vs 3/2 and 12/7 vs 9/5 and 20/9 vs 9/4. Whereas the former wins only 8/3 vs 9/7.
+::::::: "What's the ninth being added to?" Again, I view subharmonic chords as being extended downwards, not upwards. Because the subharmonic series itself extends downwards, not upwards. You may or may not agree with me on this, but it is in fact a logical and consistent approach. So the 9th is added to 7:6:5:4 to make 9:7:6:5:4. And adding the 11th makes 11:9:7:6:5:4.
+::::::: "Inflecting the third and sixth by 36/35... why you ignored it in your nomenclature." I ignored it for two reasons. One, converting harmonic to subharmonic by commatic inflections holds for the 7-limit, but breaks down in the 11-limit. 11/8 and 18/11 differ by 301c. Two, IMO the significance of a subharmonic chord should be determined not by whether it's commatically close to a harmonic chord, but by its consonance. 7:6:5:4 is more consonant than 9:7:6:5, because 5/4 beats 9/7 and 7/4 beats 9/5.
+::::::: --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 22:32, 2 April 2026 (UTC)