The Sagittal forum

So I'm running into several qualms with sagittal chord names. Assuming we already know what to call accidentals, we have Pai, Pao, Pai-flat, pao-sharp. Here's my proposed system based on Cam's system with a few modifications for special chords. This post is mainly for 22 TET but applies to everything as well I guess.

1. Chord names begin with Root which is exactly the same as the note name (duh but it's good to clarify this.)

2. Immediately following the Root is the suffix pertaining to the third of the chord. Major chords can have one but don't need a suffix.
Example, C Minor has a minor third. Gmaj9 has a major third. F is a F major chord etc...
In addition, there are suffixes which effect the fifth as well such as augmented but we'll talk about that in a bit.

3. If no third exists, then a 5 is placed after the Root. G5 has no third at all, it's just a power chord on G.

4. Immediately following the suffix for the third is the suffix for the quality of the seventh. When we the seventh is the same quality as the third i.e. it's a fifth away then we only need to name them once. Example Gpao7 has pao-maj3 and pao-maj7 in it.

5. Chord names are based on how they FIT in a scale rather than a harmonic interpretation. That means C major in 22 EDO is C E G not C E G. I also think the 7th chord should NOT be 4:5:6:7 in tunings like 22 EDO because it should be the chord that exists in superpyth[7] as the dominant chord. Making C7 as C E G B. This makes it consistent with the chord notation. 4:5:6:7 in 22 EDO would be called a "harmonic-seventh" or "major-minor-seventh" which since it's so common having some kind of symbol such as "$" to be harmonic. Otherwise just say "h7" or "Mm7". This chord also is a C-pao dominant seventh.

6. Alterations to other chord degrees are done so by the accidental as well. Cmaj7pao5 = C E G B in 22 EDO. To make names shorter ^ and v can be used in chord names. The same chord can be written Cmaj7v5.

7. When the name of a chord becomes confusing, use "Root" possibly "Dot" or a CLEAR HELD pause to distinguish. Example C7 vs Cpao7. THIS IS COMMON PROBLEM WITH THE NAMING SCHEME. A dot can be used in confusing chord names. So the two chords would be written C\!7 as C pao seventh and C.\!7 C pao major seventh.

BUT another possibility which may work well is NEVER using those as modifications but instead using the letter by itself of the accidental. so C\!7 = C Pao-Seventh, but C major with a pao-seventh is Cp7. Pronounced C "Pee" "Seventh" and C-"Pao" "Seventh". I think this may be a good way to avoid this confusion.

8. Augmented and diminished should refer to their literal meaning of stacked major thirds or stacked minor thirds. In 22 EDO, an augmented chord is C E G#: and a C diminished is C Eb Gb: . IF we feel these get confusing, it might be better just to use explicit alterations to the 5 at all times and avoid confusion altogether. C diminished is a C minor pai-flat5 or possibly
Cm^b5. C augmented is a C major pao-sharp 5 or C.v#5 .

9. Slash chords are indicated normally with slash marks BUT in ascii we bracket each side of the chord. G7/B written in Ascii looks loke [G7]/[B\!].

10. Major and Minor are based on a stack of fifths. The 11th harmonic is notated as a raised fourth so in 22 EDO it's a pai-11 or ^11.

That should cover everything, but tell me what you guys think.

William Lynch wrote:So I'm running into several qualms with sagittal chord names. Assuming we already know what to call accidentals, we have Pai, Pao, Pai-flat, pao-sharp. Here's my proposed system based on Cam's system with a few modifications for special chords. This post is mainly for 22 TET but applies to everything as well I guess.

I'm sorry I haven't had time to address this before now. I don't like it because I think it is inconsistent in the way it treats thirds versus sevenths, and I think this is due to a bug in Cam's system, which I finally think I understand well enough to criticise.

I think Cam's system for naming intervals (and hence chords) using Sagispeak, can only work if you always use the Sagispeak prefixes for the commas that vanish as well as those that do not. i.e. if you never use plain "major" but only "pao-major" or "tao-major" and you never use plain "minor" but only "pai-minor" or "tai-minor". It's just that tai and tao happen to vanish in 22-edo pitch notation.

So in 22-edo, C:E is a pao-major third (approx 4:5) while C:E is a tao-major third (approx 7:9). In 22-edo, C:B is a pai-minor seventh (approx 5:9) while C:B is a tai-minor seventh (approx 4:7).

In conventional music, a dominant 7th chord is exactly the same thing as a major minor seventh chord, and I think it should stay that way.

So in 22-edo, C:E:G:B (an approximate 4:5:6:7) could be called a C pao-major tai-minor seventh, and C:E:G:B [Edit: That should have been C:E:G:B] could be called a C pao-major pai-minor seventh.

But then I'd be perfectly happy to always allow dropping the "pao"s and "pai"s no matter whether they vanish in the tuning or not. So then in 22-edo, C:E:G:B (an approximate 4:5:6:7) could be called a C major tai-minor seventh, and C:E:G:B could be called a C major minor seventh.

And then the existing convention of dropping "major" when applied to thirds and dropping "minor" when applied to sevenths, leads us finally to:

In 22-edo,
C:E:G:B (an approximate 4:5:6:7) could be called a C tai-minor seventh, and
C:E:G:B could be called a C seventh.

Dave Keenan wrote:

William Lynch wrote:So I'm running into several qualms with sagittal chord names. Assuming we already know what to call accidentals, we have Pai, Pao, Pai-flat, pao-sharp. Here's my proposed system based on Cam's system with a few modifications for special chords. This post is mainly for 22 TET but applies to everything as well I guess.

I'm sorry I haven't had time to address this before now. I don't like it because I think it is inconsistent in the way it treats thirds versus sevenths, and I think this is due to a bug in Cam's system, which I finally think I understand well enough to criticise.

I think Cam's system for naming intervals (and hence chords) using Sagispeak, can only work if you always use the Sagispeak prefixes for the commas that vanish as well as those that do not. i.e. if you never use plain "major" but only "pao-major" or "tao-major" and you never use plain "minor" but only "pai-minor" or "tai-minor". It's just that tai and tao happen to vanish in 22-edo pitch notation.

So in 22-edo, C:E is a pao-major third (approx 4:5) while C:E is a tao-major third (approx 7:9). In 22-edo, C:B is a pai-minor seventh (approx 5:9) while C:B is a tai-minor seventh (approx 4:7).

In conventional music, a dominant 7th chord is exactly the same thing as a major minor seventh chord, and I think it should stay that way.

So in 22-edo, C:E:G:B (an approximate 4:5:6:7) could be called a C pao-major tai-minor seventh, and C:E:G:B could be called a C pao-major pai-minor seventh.

But then I'd be perfectly happy to always allow dropping the "pao"s and "pai"s no matter whether they vanish in the tuning or not. So then in 22-edo, C:E:G:B (an approximate 4:5:6:7) could be called a C major tai-minor seventh, and C:E:G:B could be called a C major minor seventh.

And then the existing convention of dropping "major" when applied to thirds and dropping "minor" when applied to sevenths, leads us finally to:

In 22-edo,
C:E:G:B (an approximate 4:5:6:7) could be called a C tai-minor seventh, and
C:E:G:B could be called a C seventh.

Well in that case, I wouldn't even use major and minor, just the suffixes because it's too long winded to say all that. so 4:5:6:7 is C-pao-tai-7 or CPt7 for short possibly. C:E:G:B can be called a C-pao-pai7 or CPp7 for short.

Thus p and t is pai and tai, P and T is Pao and Tao. i agree though, I'm certainly not against dropping major and minor for the actual comma things. All intervals with #, b and the naturals are Tai/tao/perfect, and all intervals with combination accidentals from naturals would be pai/pao/paoaug/paidim etc...

William Lynch wrote:Well in that case, I wouldn't even use major and minor, just the suffixes because it's too long winded to say all that. so 4:5:6:7 is C-pao-tai-7 or CPt7 for short possibly. C:E:G:B can be called a C-pao-pai7 or CPp7 for short.

Why not go the next step and drop the p and P and just call them Ct7 and C7? If the approximate 4:5:6:7 happened to be in a meantone like 36 or 43-edo, where pai and pao vanish but tai and tao don't, you'd have no qualms about calling it a Ct7. And the second one is a stack of an approximate 4:5 then 5:6 then 5:6, which you'd call a C7 in 12-edo.

I note that the one place where I wrote C:E:G:B was a typo. It should have been C:E:G:B as it was everywhere else. I've added a note in the original and fixed it in the quote above.

Dave Keenan wrote:

William Lynch wrote:Well in that case, I wouldn't even use major and minor, just the suffixes because it's too long winded to say all that. so 4:5:6:7 is C-pao-tai-7 or CPt7 for short possibly. C:E:G:B can be called a C-pao-pai7 or CPp7 for short.

Why not go the next step and drop the p and P and just call them Ct7 and C7? If the approximate 4:5:6:7 happened to be in a meantone like 36 or 43-edo, where pai and pao vanish but tai and tao don't, you'd have no qualms about calling it a Ct7. And the second one is a stack of an approximate 4:5 then 5:6 then 5:6, which you'd call a C7 in 12-edo.

I note that the one place where I wrote C:E:G:B was a typo. It should have been C:E:G:B as it was everywhere else. I've added a note in the original and fixed it in the quote above.

Because we don't do that in 12 EDO anyway, Cm7 means C Eb G Bb so Ct7 implies there is both a tai 3rd and tai 7th.

William Lynch wrote:

Dave Keenan wrote:Why not go the next step and drop the p and P and just call them Ct7 and C7?

Because we don't do that in 12 EDO anyway, Cm7 means C Eb G Bb so Ct7 implies there is both a tai 3rd and tai 7th.

Good point regarding Ct7. It would need to be written "C.t7" for it to be the approximate 4:5:6:7. But "C7" would be fine for C:E:G:B in 22-edo.

One can choose to generalise the 12-edo conventions in various ways. You can consider them as:
1. No need to qualify the triad if it's Major, and
2. No need to qualify the 7th if it's minor.

So we can parse these standard 7th chords as follows:
C7 -> C.7 -> CM.m7 (no qualifiers, so triad defaults to major and 7th defaults to minor)
Cm7 -> Cm.7 -> Cm.m7 (we know the original "m" applies to the triad because we don't need to qualify the 7th if it's minor)
CM7 -> C.M7 -> CM.M7 (we know the original "M" applies to the 7th because we don't need to qualify the triad if it's Major)
CmM7 -> Cm.M7 (already fully qualified)

So in 22-edo,
C:E:G:B could be called C7,
C:E:G:B could be called C.t7 or CMt7, and
C:E:G:B could be called CTt7.

Dave Keenan wrote:

William Lynch wrote:

Dave Keenan wrote:Why not go the next step and drop the p and P and just call them Ct7 and C7?

Because we don't do that in 12 EDO anyway, Cm7 means C Eb G Bb so Ct7 implies there is both a tai 3rd and tai 7th.

Good point regarding Ct7. It would need to be written "C.t7" for it to be the approximate 4:5:6:7. But "C7" would be fine for C:E:G:B in 22-edo.

One can choose to generalize the 12-edo conventions in various ways. You can consider them as:
1. No need to qualify the triad if it's Major, and
2. No need to qualify the 7th if it's minor.

So we can parse these standard 7th chords as follows:
C7 -> C.7 -> CM.m7 (no qualifiers, so triad defaults to major and 7th defaults to minor)
Cm7 -> Cm.7 -> Cm.m7 (we know the original "m" applies to the triad because we don't need to qualify the 7th if it's minor)
CM7 -> C.M7 -> CM.M7 (we know the original "M" applies to the 7th because we don't need to qualify the triad if it's Major)
CmM7 -> Cm.M7 (already fully qualified)

So in 22-edo,
C:E:G:B could be called C7,
C:E:G:B could be called C.t7 or CMt7, and
C:E:G:B could be called CTt7.

Hmm, so you're suggesting we use the pai7 as the default 7? Why not the tao7? Then C7 becomes C:E:G:B and the other chord you had as C7 is a "C.p7" or "C root pai-seventh chord".

I would modify the above as:
1. No need to qualify the triad if it's Pao-3, and
2. No need to qualify the 7th if it's Tao-7.

I know I said originally that C7 was C:E:G:B but what is the reasoning for this? I'm starting to wonder if this is better than C7 being the harmonic seventh chord, C9 being the harmonic ninth chord, and C.11 being the harmonic 11th chord.

Ok so just to clarify. P and p means Pao-major and Pai-minor, T and t mean Tai-major, and Tao-minor. Right?

Triads are named by third, omitted quality suffix in Cam's system was assumed to be the M3 but am I correct in saying you Dave prefer it to be M3? So C in cam's is C E G but here, you are saying it should be C E:/!: G? I used to feel this way but I'm starting to think that messes up chord naming.

In Cam's system, C E G is Tai-major, C E G is Pao-major, C Eb G is Tao-Minor, C E G is Pai-Minor. We can abbreviate these T, P, t and p but chords without suffixes are assumed to be T because it follows chain of fifths logic. That was his idea anyway. Now cam omitted tai/tao but you think we should keep those if not omit major/minor altogether.

SEVENTHS

We assume 7 unspecified to mean a pai minor seventh but I think it should be a tao-minor seventh BECAUSE we use the harmonic seventh chord so often it might as well be C7. But how often would we use C E G B ? It's not a bad chord but we are better off making the harmonic chord the plain 7.

The rest of sevenths are notated with alterations of course. if only the seventh is altered, we can attach T to the chord name or I suppose the dot. So the chord C E G B is a C.p7 or CTp7, right? Omitting the dot or major suffix assumes both 3 and 7 to be altered thus Ct7 is C Eb G Bb. and CT7 is C E G B.

William Lynch wrote:Hmm, so you're suggesting we use the pai7 as the default 7? Why not the tao7?

Because the pai-flat 7 is the default in conventional music (where pai vanishes). The default 7th in 12-edo is not the tao-flat 7th (harmonic seventh).

I would modify the above as:
1. No need to qualify the triad if it's Pao-3, and
2. No need to qualify the 7th if it's Tao-7.

I agree with 1 because to me a pao-3 is a major 3rd, so it's the same as what I had, and it agrees with existing convention.
But 2 does not agree with existing convention. The convention is that the default 7th is the minor seventh (approx 5:9), not the harmonic seventh (4:7).

William Lynch wrote:Ok so just to clarify. P and p means Pao-major and Pai-minor, T and t mean Tai-major, and Tao-minor. Right?

I thought I understood your intention there and was willing to go along with it and see how it panned out. But I thought you would use uppercase P for Pai because it is an upward alteration and lowercase p for pao because it is downward. And therefore I thought pao-major would be lowercase p and Pai-minor would be uppercase P. And I think of these as the ordinary kind of major and minor and so I don't think they actually need any "p" or "P".

BTW, I think you mean "prefix" rather than "suffix". A suffix comes at the end.

Triads are named by third,

Don't forget that triads can also be named by their fifth. "Diminished" and "augmented" triads have diminished and augmented fifths, not thirds. A diminished triad has a minor third and an augmented triad a major third.

omitted quality suffix in Cam's system was assumed to be the M3

No, the omitted qualifier in Cam's system is whatever happens to vanish in the tuning you are using. So in 22-edo it happens to be M3 as you say, but in 36-edo and 43-edo, where does not vanish, a plain major or minor would be 5-limit not 7-limit. This is what I consider a bug in Cam's system, and propose to remedy by using the tai and tao (and vai and vao) whether they vanish or not. Cam's system was almost naming according to how the interval sounds. The only time it didn't was when some comma vanished in some tuning, like pai and pao in meantones and tai and tao in superpythagoreans.

I'm sure Cam doesn't consider that a bug. So I'm really suggesting a different way of using sagispeak for interval names.
6:7 tao-minor third
5:6 pai-minor third = minor third
4:5 pao-major third = major third = third
7:9 tai-major third

4:7 tao-minor seventh
5:9 pai-minor third = minor seventh = seventh
4:5 pao-major third = major seventh
7:9 tai-major seventh

4:9 major ninth = ninth

3:8 perfect eleventh = eleventh
4:11 vai eleventh

but am I correct in saying you Dave prefer [omitted prefix] to be M3?

If you really meant M3 (an approximate 4:5), then yes.

So C in cam's is C E G but here, you are saying it should be C E:/!: G?

Again, if you really mean C E G for the latter, then yes. And of course it would be C E G in any tuning where vanishes, as it does in 12-edo.

I used to feel this way but I'm starting to think that messes up chord naming.

In Cam's system, C E G is Tai-major, C E G is Pao-major, C Eb G is Tao-Minor, C E G is Pai-Minor.

No. C E G is never tai-major and C Eb G is never tao-minor in Cam's system. They are only ever plain "major" and "minor" no matter whether there is a 7-comma or a 5-comma vanishing in the given tuning. That's the aspect I don't like.

We can abbreviate these T, P, t and p but chords without suffixes are assumed to be T because it follows chain of fifths logic. That was his idea anyway.

Cam did not suggest chords without prefixes should be assumed to be T. That would only happen to be the case in tunings where tai and tao vanish, like 22-edo.

Now cam omitted tai/tao but you think we should keep those if not omit major/minor altogether.

Cam omits tai/tao in 22-edo because they don't appear in its pitch notation, and they don't appear in its pitch notation because 7-commas are tempered out by 22-edo. But you began this thread with a proposal for a chord naming system that might be useful for more EDOs than just 22-edo. Yes, I think we should keep tai and tao in interval and chord names based on Sagispeak. And I think we can drop pai and pao, and we can further drop major for thirds and we can drop minor for sevenths (the standard conventions).

SEVENTHS

We assume 7 unspecified to mean a pai minor seventh but I think it should be a tao-minor seventh BECAUSE we use the harmonic seventh chord so often it might as well be C7. But how often would we use C E G B ? It's not a bad chord but we are better off making the harmonic chord the plain 7.

I guess we'll never agree. I prefer to retain the ability to communicate with musicians still working in 12-edo. I prefer to remain backwards-compatible with existing chord names.

The rest of sevenths are notated with alterations of course. if only the seventh is altered, we can attach T to the chord name or I suppose the dot. So the chord C E G B is a C.p7 or CTp7, right?

I can see how this could be called a C.p7, but I still find it confusing that you use lowercase p when it's the upward symbol. However I can't see any way that it could be called a CTp7 as the triad is an approximate 4:5:6, not a 7-limit triad, so the T is not appropriate.

Omitting the dot or major suffix assumes both 3 and 7 to be altered thus Ct7 is C Eb G Bb. and CT7 is C E G B.

Yes, I could go along with those.