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

Line 37:

::::: --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 21:42, 31 March 2026 (UTC)

:::::: So if you mean 1/(24:20:16:14:11:9) and 1/(11:9:7:6:5:4), then no, I strongly disagree. 1/(24:20:16:14:11:9) is a much more consonant voicing cuz it's more regularly tertian and more notes are on the consonant categories, like the minor third, the perfect fifth, even the ~~semidiminished~~ ninth and the perfect eleventh. The perfect fifth above the bass is especially significant here, as it suits itself much better to traditional chord naming systems. I mean, if you don't mind me using a similar logic as yours, 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, on average?

:::::: So if you mean 1/(24:20:16:14:11:9) and 1/(11:9:7:6:5:4), then no, I strongly disagree. 1/(24:20:16:14:11:9) is a much more consonant voicing cuz it's more regularly tertian and more notes are on the consonant categories, like the minor third, the perfect fifth, even the neutral ninth and the perfect eleventh. The perfect fifth above the bass is especially significant here, as it suits itself much better to traditional chord naming systems. I mean, if you don't mind me using a similar logic as yours, 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, on average?

:::::: From there, 1/(24:20:16:14:9) and 1/(24:20:16:14:11) are one-note omissions of 1/(24:20:16:14:11:9), which makes them likewise notable. But anyway, I call these chords sixth-eleventh, sixth added-eleventh, and sixth-ninth chords, so there's no conflict in names. The only special case is 1/(9:7:6:5:4), for which I think we can agree this could be the subharmonic ninth chord, but that again points to 1/(9:7:6:5) as the subharmonic seventh chord, cuz what's the ninth being added to?

Line 43:

:::::: Also, inflecting the third and sixth by 36/35 turns the subharmonic sixth chord into the harmonic sixth chord. Since we're using 36/35 to flip the o/utonality without changing the intervals' degrees or qualities, all we need to do in the names is to flip the harmonic/subharmonic part. It follows that inflecting the third and seventh by the same interval should similarly turn the harmonic seventh chord into the subharmonic seventh chord. This bond is so simple and clear. I don't see why you ignored it in your nomenclature.

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

:::::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:17, 1 April 2026 (UTC) (last edited [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:28, 3 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.

Line 85:

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

:::::::: > 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?

:::::::: I agree. However, complexities of individual ratios aren't the only factor for consonance. If anything, notes above the root deserve more weight. Tertian chords deserve to be favored. Chords with a perfect fifth above the bass in particular deserve a big plus.

:::::::: So, to get to your example, in 1–6/5–3/2–5/3 there's 25/18, which is ''discordant'', and not examining all the component intervals in the chord means failing to spot this, and incorrectly cataloguing it as a consonant chord. Perhaps by consonance you just mean concordance, but consonance is really more than that. Anyway, in 1/(24:20:16:14:11:9) and 1/(11:9:7:6:5:4) all the component intervals are concordant already since they're all 11-odd-limit, so the chord structure plays the major role of determining which chord is more consonant here.

:::::::: > What's more important, a chord's sound or its name?

:::::::: The question is out of context, and besides the point anyway. Of course sound is more important, but we're here to resolve a name conflict. So name is our focus.

:::::::: > Is this still true when you consider all 15 ratios? I don't know how you define "consonant category", …

:::::::: A consonant category is literally an interval category that is considered consonant in tonal harmony … like the major and minor third. Of course, the note should be at least fairly concordant to begin with, which is satisfied in our case. So, since all the notes are on the consonant categories, each component interval have clear functions. Some of them are neutral, but neutral intervals occuring between the notes is much less of a dissonance than on the bass.

:::::::: > I agree that [1/(9:7:6:5:4)] is the subharmonic ninth chord. But …

:::::::: I didn't choose this over 1/(24:20:16:14:9). I've consistently argued that 1/(24:20:16:14:9) is the more significant voicing and only brought up 1/(9:7:6:5:4) as an answer to "what is the subharmonic ninth chord if there is one" cuz 1/(24:20:16:14:9) is clearly not a ninth chord. And again I strongly disagree that 1/(24:20:16:14:9) is a more dissonant voicing than 1/(9:7:6:5:4) (see above).

:::::::: > I view subharmonic chords as being extended downwards, not upwards.

:::::::: In negative harmony practice, subharmonic chords are also extended downwards, but starts on the perfect fifth. This has many advantages, including making chord extensions intuitive. Surely one expects a dominant ninth chord to extend a dominant seventh chord, not a half-diminished seventh chord?

:::::::: > Converting harmonic to subharmonic by commatic inflections holds for the 7-limit, but breaks down in the 11-limit.

:::::::: I don't call it "break down". There's more to it in the 11-limit, like in the 7-limit, you have the pairs 4:5:6:7 ↔ 1/(12:10:8:7) and 6:7:9:10 ↔ 1/(9:7:6:5), whereas in the 11-limit commatic inflection gives you 4:5:6:7:9 ↔ 1/(24:20:16:14:11) and 4:5:6:7:11 ↔ 1/(24:20:16:14:9), but 1/(24:20:16:14:9) is the inverse of 4:5:6:7:9 and 1/(24:20:16:14:11) the inverse of 4:5:6:7:11. It's a little different, but there's still logic to it.

:::::::: > 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.

:::::::: As I said, inflecting the third and sixth by 36/35 flips the o/utonality without changing the intervals' degrees or qualities. This is a very useful property, very helpful for memorizing the 7-limit chords, and I think you should start to consider it, in addition to all the other things I've shown and explained to you.

:::::::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:28, 3 April 2026 (UTC)

@@ Line 37: / Line 37: @@
 ::::: --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 21:42, 31 March 2026 (UTC)
-:::::: So if you mean 1/(24:20:16:14:11:9) and 1/(11:9:7:6:5:4), then no, I strongly disagree. 1/(24:20:16:14:11:9) is a much more consonant voicing cuz it's more regularly tertian and more notes are on the consonant categories, like the minor third, the perfect fifth, even the semidiminished ninth and the perfect eleventh. The perfect fifth above the bass is especially significant here, as it suits itself much better to traditional chord naming systems. I mean, if you don't mind me using a similar logic as yours, 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, on average?
+:::::: So if you mean 1/(24:20:16:14:11:9) and 1/(11:9:7:6:5:4), then no, I strongly disagree. 1/(24:20:16:14:11:9) is a much more consonant voicing cuz it's more regularly tertian and more notes are on the consonant categories, like the minor third, the perfect fifth, even the  neutral ninth and the perfect eleventh. The perfect fifth above the bass is especially significant here, as it suits itself much better to traditional chord naming systems. I mean, if you don't mind me using a similar logic as yours, 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, on average?
 :::::: From there, 1/(24:20:16:14:9) and 1/(24:20:16:14:11) are one-note omissions of 1/(24:20:16:14:11:9), which makes them likewise notable. But anyway, I call these chords sixth-eleventh, sixth added-eleventh, and sixth-ninth chords, so there's no conflict in names. The only special case is 1/(9:7:6:5:4), for which I think we can agree this could be the subharmonic ninth chord, but that again points to 1/(9:7:6:5) as the subharmonic seventh chord, cuz what's the ninth being added to?
@@ Line 43: / Line 43: @@
 :::::: Also, inflecting the third and sixth by 36/35 turns the subharmonic sixth chord into the harmonic sixth chord. Since we're using 36/35 to flip the o/utonality without changing the intervals' degrees or qualities, all we need to do in the names is to flip the harmonic/subharmonic part. It follows that inflecting the third and seventh by the same interval should similarly turn the harmonic seventh chord into the subharmonic seventh chord. This bond is so simple and clear. I don't see why you ignored it in your nomenclature.
-:::::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:17, 1 April 2026 (UTC)
+:::::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:17, 1 April 2026 (UTC) (last edited [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:28, 3 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.
@@ Line 85: / Line 85: @@
 ::::::: --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 22:32, 2 April 2026 (UTC)
+:::::::: > 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?
+:::::::: I agree. However, complexities of individual ratios aren't the only factor for consonance. If anything, notes above the root deserve more weight. Tertian chords deserve to be favored. Chords with a perfect fifth above the bass in particular deserve a big plus.
+:::::::: So, to get to your example, in 1–6/5–3/2–5/3 there's 25/18, which is ''discordant'', and not examining all the component intervals in the chord means failing to spot this, and incorrectly cataloguing it as a consonant chord. Perhaps by consonance you just mean concordance, but consonance is really more than that. Anyway, in 1/(24:20:16:14:11:9) and 1/(11:9:7:6:5:4) all the component intervals are concordant already since they're all 11-odd-limit, so the chord structure plays the major role of determining which chord is more consonant here.
+:::::::: > What's more important, a chord's sound or its name?
+:::::::: The question is out of context, and besides the point anyway. Of course sound is more important, but we're here to resolve a name conflict. So name is our focus.
+:::::::: > Is this still true when you consider all 15 ratios? I don't know how you define "consonant category", …
+:::::::: A consonant category is literally an interval category that is considered consonant in tonal harmony … like the major and minor third. Of course, the note should be at least fairly concordant to begin with, which is satisfied in our case. So, since all the notes are on the consonant categories, each component interval have clear functions. Some of them are neutral, but neutral intervals occuring between the notes is much less of a dissonance than on the bass.
+:::::::: > I agree that [1/(9:7:6:5:4)] is the subharmonic ninth chord. But …
+:::::::: I didn't choose this over 1/(24:20:16:14:9). I've consistently argued that 1/(24:20:16:14:9) is the more significant voicing and only brought up 1/(9:7:6:5:4) as an answer to "what is the subharmonic ninth chord if there is one" cuz 1/(24:20:16:14:9) is clearly not a ninth chord. And again I strongly disagree that 1/(24:20:16:14:9) is a more dissonant voicing than 1/(9:7:6:5:4) (see above).
+:::::::: > I view subharmonic chords as being extended downwards, not upwards.
+:::::::: In negative harmony practice, subharmonic chords are also extended downwards, but starts on the perfect fifth. This has many advantages, including making chord extensions intuitive. Surely one expects a dominant ninth chord to extend a dominant seventh chord, not a half-diminished seventh chord?
+:::::::: > Converting harmonic to subharmonic by commatic inflections holds for the 7-limit, but breaks down in the 11-limit.
+:::::::: I don't call it "break down". There's more to it in the 11-limit, like in the 7-limit, you have the pairs 4:5:6:7 ↔ 1/(12:10:8:7) and 6:7:9:10 ↔ 1/(9:7:6:5), whereas in the 11-limit commatic inflection gives you 4:5:6:7:9 ↔ 1/(24:20:16:14:11) and 4:5:6:7:11 ↔ 1/(24:20:16:14:9), but 1/(24:20:16:14:9) is the inverse of 4:5:6:7:9 and 1/(24:20:16:14:11) the inverse of 4:5:6:7:11. It's a little different, but there's still logic to it.
+:::::::: > 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.
+:::::::: As I said, inflecting the third and sixth by 36/35 flips the o/utonality without changing the intervals' degrees or qualities. This is a very useful property, very helpful for memorizing the 7-limit chords, and I think you should start to consider it, in addition to all the other things I've shown and explained to you.
+:::::::: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:28, 3 April 2026 (UTC)