Would it be safe to say...

[Wheels]

any dominant in any situation is satisfied to lead back to its 1, whether that 1 is a major, a minor, or even another dominant?

[JonR]

Interesting question.

First - to be irritatingly pedantic - "dominant" means V (5th step of the scale, and/or the chord built there). And V always leads back to I.
But I guess you mean a "dominant 7th chord type" - which are not always V chords, functionally.

Your question is a little confusing, because the "situation" a chord is in actually contains the chord it's leading to, and is presumably "satisfied" to lead to (even if that target chord is delayed a little, as it sometimes is). But just to lay out the common uses of dom7 chord types, which will hopefully answer your question:

1. V chord in major key.
Symbols 7, 9, 13. Occasionally has alterations, but these usually signify a borrowing from minor.
Resolves to I, but can often go via other chords, such as IV, or can be part of a "deceptive cadence" (ie by resolving anywhere but I, such as to the vi chord).
Can often occur in cycles, such as the bridge of Rhythm changes. (These tend to be assumed to be mixolydian chords, but can often be altered.) This sequence is what's known as a "backcycle", where the V of the key is given its own V ("secondary dominant" - see below) and so on back through the sequence.

2. V chord in minor key.
Symbols 7, 7b9, 7#9, 7alt (any combination of altered 5th and 9th).
Resolves to I. Rarely goes via any other chord.
Can be used as sub for a major key V. (Rarely vice versa).

3. bII chord in minor key.
Symbols 7#11, 9#11, 13#11 (lydian dominant)
This is a tritone sub for the altered V7 (harmonized from the same notes, often just the same chord tones with a different bass).
Has a very strong tendency to resolve down the half-step to I. (Stronger than the V).

4. bII in major key. Essentially same as above.

5. bVII in major key. Usually lydian dominant, but a weaker resolution tendency (up a whole step) than a bII. (See point 9 below.)

6. bVI in minor key. Usually lydian dominant, a tritone sub for the secondary dominant of V. (Eg, C7 in key of E minor is bII of B, sub for F#7 (V/V) and usually has a strong tendency to lead to B or B7.)
However, bVI7 chords are sometimes used as subs for the iv chord. Eg, in key of E minor, you might get a C7 in place of Am7, leading back to the tonic (Em). Scale-wise, probably lydian dominant again, although it suits the blues scale of the key.

7. Blues I or IV chord. A non-functioning dominant - ie has no tendency to resolve anywhere. The I7 chord does behave as a secondary dominant when leading to IV, but only then. And the IV7 is not the dominant of anything. (Occasionally in jazz, the IV7 will lead to a iii chord instead of back to I, which turns it into the bII of the iii chord.)
A blues tonic chord can sometimes have a #9 alteration, reflecting the flattened blue 3rd. In rock this is known as the "Hendrix chord", but of course it was used in jazz before that. (A 7#9 blues tonic is not quite the same thing as a 7#9 V chord in a minor key: it will have a perfect 5th, and use blues scale.)

8. Key chord of mixolydian mode. Modal music is, by definition (at least in jazz) "non-functional", so no chord type has to do what it usually does in key-based music. In G mixolydian mode, therefore, G7 can be the tonal centre, with no tendency to resolve to C. (In this sense it's similar to a blues tonic.)
Of course, a mixolydian mode chord means 9, sus4 or 13 extensions, not any alterations.

9. Other modal uses could be bVII in aeolian (bVII to a minor I is an "aeolian cadence"), or IV in dorian. The latter is very common in Latin (Afro-Cuban) jazz.

10. I'll leave this one blank . I'm sure there are other uses of dom7s I can't think of right now, and you can probably invent your own. This is jazz after all - we need room to improvise!

Secondary dominants can occur on the I, II, III, VI and VII steps of a major key, and have the same function as V chords relative to their targets. Eg, a D7 chord in key of C, is V/V - dominant of the dominant (G).
Secondary dominants also occur in minor keys, but seem to be rarer. V/V does occur, but its tritone sub seems to be more common, perhaps because its root is diatonic (eg C7 in Em).

Common subs for dom7s (esp V7s) are dim7 chords, rooted on the 3rd of the dom7 (or half-step above the root).
Eg, Bdim7 in key of C minor is a "dominant-function" chord, resolving to Cm. It is a chord in its own right (vii of C harmonic minor) but can be seen as a rootless G7b9.
Dim7 chords have strong resolution tendencies: one of the notes - usually the root - resolves up a half-step, usually to a minor tonic, sometimes to a major tonic. (Dim7s chords are symmetrical, so any note can be the root, but in derivation terms they are vii chords - "leading tone 7ths" - in minor keys.)

The vii chord in a major key (m7b5 or half-dim) can have a similar function - resolving up a half-step, like a rootless version of the dom9 chord - but in jazz is almost never used that way. It's much more common as a ii chord (subdominant function) in a minor key.
Eg, Bm7b5 could resolve to C (major), as a natural leading tone chord, but is more often seen moving to E7(b9) and then to Am.

[cnsky54]

Well, out of all the theory books I have bought over the years, that is about the most condensed and succinct bunch of paragraphs I have read. I'm printing that to go in my lesson folder for the next time I get confused (happens on a daily basis, I'm afraid). Thanks for that!

[BigDaddyLoveHandles]

Yes, that's great, Jon. You said a lot there.

[Wheels]

Thanks for that JonR. That was great. Like cnsky54, I'm gonna put that post in my lesson folder too.

[Reg]

Originally Posted by Wheels

any dominant in any situation is satisfied to lead back to its 1, whether that 1 is a major, a minor, or even another dominant?

Simple answer... No. ( that part, "in any situation", kind of blows your premise out of the water). Of course you theoretically could set up your own rules... and presto... I would be saying "yes". But you didn't.
Jon gave a lot of info... most of which can have very different tendencies in jazz. But good traditional start. We could run down his lists and add quite a bit on each topic... I'm sure we would all fall asleep. But if anyone is interested... I'm always game...
So where are you heading with your question about dominant function...
Reg

[JonR]

Reg is quite right, of course. Those "rules" are just a set of common practices, in functional (pre-modal) jazz. Open to interpretation and being messed with. Eg a bII chord doesn't have to be lydian dominant. It just is more often than not.
(Those damn jazz musicians just can't leave anything alone...)

[Wheels]

Originally Posted by Reg

Simple answer... No. ( that part, "in any situation", kind of blows your premise out of the water). Of course you theoretically could set up your own rules... and presto... I would be saying "yes". But you didn't.
Jon gave a lot of info... most of which can have very different tendencies in jazz. But good traditional start. We could run down his lists and add quite a bit on each topic... I'm sure we would all fall asleep. But if anyone is interested... I'm always game...
So where are you heading with your question about dominant function...
Reg

Well I've read somewhere...maybe it was a theory book (?)...that the strongest cadence in music is from the dominant to its I. If this is so, it seems you could go from any dominant at any point it appears in a progression to its I and it would be technically correct.

Apparently, I'm wrong. Thanks for straitening me out. No need to elaborate. I'd hate this thread to turn into a snore-fest.

[Reg]

Originally Posted by Wheels

Well I've read somewhere...maybe it was a theory book (?)...that the strongest cadence in music is from the dominant to its I. If this is so, it seems you could go from any dominant at any point it appears in a progression to its I and it would be technically correct.

Apparently, I'm wrong. Thanks for straitening me out. No need to elaborate. I'd hate this thread to turn into a snore-fest.

It's not so much that your wrong, there are simply many other harmonic concepts that also control harmonic function. Your not alone in your view. What you read is very common for traditional basic music theory. And it's not wrong in it's limited scope of view. Keep reading... Reg

[Wheels]

Originally Posted by Reg

It's not so much that your wrong, there are simply many other harmonic concepts that also control harmonic function. Your not alone in your view. What you read is very common for traditional basic music theory. And it's not wrong in it's limited scope of view. Keep reading... Reg

So you're referring to context (I think?), as maybe being a more important factor in determining dominant movement than simple cut and dried V-I cadences.

If I get that in your statement, I understand.

[Reg]

Originally Posted by Wheels

So you're referring to context (I think?), as maybe being a more important factor in determining dominant movement than simple cut and dried V-I cadences.

If I get that in your statement, I understand.

Hey Wheels... yes context always is a factor... but there are more harmonic methods of controlling movement besides Dominant cadence,( V-I ), Dominant resolution,(dom 7th chord going to other chord besides I), secondary Doms, extended Doms etc...
Modal cadences are achieved by use of characteristic pitch. Serial or 12 tone music used series of intervals. There are multi tonic systems with new rules and principles for governing harmonic movement. There are sequential and melodic methods for controlling harmonic movement. Constant structure, lydian chromatic, modal interchange organizational concepts.... And on and on and there are many versions of each and you can combine them... so yes, it's not that cut and dry.
It's not really required to be aware of all these methods of controlling harmonic movement, to play jazz, but it really helps. You do need to understand basic modal concepts, which open the modal interchange doors, which will basically teach your ears to be able to hear harmonic movement with out always relating to traditional dominant functional principles and voice leading... yea... I'm putting myself asleep.... John is right... I am one of those dam jazz musicians...Reg

[whatswisdom]

Originally Posted by Reg

...there are more harmonic methods of controlling movement besides Dominant cadence,( V-I ), Dominant resolution,(dom 7th chord going to other chord besides I), secondary Doms, extended Doms etc...Modal cadences are achieved by use of characteristic pitch.

This is a thread I've been digging so I thought I'd put it up as 'flavor of the day.' #2 by JonR deserves to be viewed by more... I'm still hung up on the modal "Characteristic Pitch" subject as discussed here and more recently in other related threads. Reg, JonR, et al, please break this down some more if you could. "Characteristic Pitch" first, if you please. (I'm on solid ground when dealing with dominant>tonic resolution)...

[JonR]

Originally Posted by whatswisdom

This is a thread I've been digging so I thought I'd put it up as 'flavor of the day.' #2 by JonR deserves to be viewed by more... I'm still hung up on the modal "Characteristic Pitch" subject as discussed here and more recently in other related threads. Reg, JonR, et al, please break this down some more if you could. "Characteristic Pitch" first, if you please. (I'm on solid ground when dealing with dominant>tonic resolution)...

As I understand it, the "characteristic pitch" of a mode is the note that distinguishes it from the nearest major or natural minor scale.
Eg, mixolydian mode = major with b7, ie, the b7 would the "characteristic pitch".
lydian = major with #4, so that's the characteristic pitch.

Other characteristic pitches:
Dorian: major 6th
Phrygian: b2

For Locrian it would be the b5, but maybe combined with the b2.

It's also arguable that a mode really has two defining pitches (aside from the root), so as to determine whether it's major or minor.
So mixolydian and lydian would require the M3 along with b7 or #4, just to nail it. The other notes could then be pretty much assumed. (Although one could argue that lydian requires the maj7 too, to distinguish it from lydian dominant...)

I don't know if one would talk about characteristic pitches of Ionian or Aeolian themselves. Maybe P4 and M7 for Ionian, and m3 and m6 for Aeolian (plus m7?)

Reg knows his stuff, but I'm not sure what he means by a modal cadence being achieved by the characteristic pitch. Eg, a cadence in Dorian wouldn't necessarily feature the major 6th. It could just be C-Dm, or Am-Dm - no B in either chord. (Of course that does mean the cadence could be Aeolian in both cases.)

[whatswisdom]

Originally Posted by JonR

Other characteristic pitches:
Dorian: major 6th

(Example using D Dorian.) So this is because D natural minor = DEFGABbC, and in Dorian the sixth is raised?

[John Curran]

Originally Posted by whatswisdom

(Example using D Dorian.) So this is because D natural minor = DEFGABbC, and in Dorian the sixth is raised?

Yes. dorian would be DEFGABC.

Flat the second in the natural minor (Eb) and you have phrygian DEbFGABbC.

Flat the second and the fifth and you have locrian, DEbFGAbBbC.

[Gitarguy]

Originally Posted by Wheels

So you're referring to context (I think?), as maybe being a more important factor in determining dominant movement than simple cut and dried V-I cadences.

We cannot call every V-I movement a cadence. Cadences require certain events to take place...technically.

Originally Posted by John Curran

Yes. dorian would be DEFGABC.

Since we're being technical, I'll have to say no.

When the Dorian mode was in use, B natural was not a part of the lexicon. This is why the Germans call it "H": Bb is called by the name B.

Also, genuine modes are hexatonic scales. So, Dorian is DEFGABb. Later, it became normal to see C# as well in order to make stronger cadences.

A Phrygian mode would have contained the notes: EFGABbC. Unlike the other modes which have the reciting tone on a P5 above tonic, the Phrygian mode uses C as the reciting tone, as Bb is a tritone away. This explains why a cadence in the Phrygian mode moves down a half-step to tonic rather than up a half-step, as no dominant is possible in the Phrygian mode.

[BigDaddyLoveHandles]

Originally Posted by Gitarguy

When the Dorian mode was in use, B natural was not a part of the lexicon. This is why the Germans call it "H": Bb is called by the name B.

Also, genuine modes are hexatonic scales. So, Dorian is DEFGABb. Later, it became normal to see C# as well in order to make stronger cadences.

A Phrygian mode would have contained the notes: EFGABbC. Unlike the other modes which have the reciting tone on a P5 above tonic, the Phrygian mode uses C as the reciting tone, as Bb is a tritone away. This explains why a cadence in the Phrygian mode moves down a half-step to tonic rather than up a half-step, as no dominant is possible in the Phrygian mode.

Interesting, but is it jazz? I mean, this is a jazz forum and these terms have different meanings in a jazz context. But carry on.

[JakeAcci]

Originally Posted by Gitarguy

Since we're being technical, I'll have to say no.

When the Dorian mode was in use, B natural was not a part of the lexicon. This is why the Germans call it "H": Bb is called by the name B.

Also, genuine modes are hexatonic scales. So, Dorian is DEFGABb. Later, it became normal to see C# as well in order to make stronger cadences.

A Phrygian mode would have contained the notes: EFGABbC. Unlike the other modes which have the reciting tone on a P5 above tonic, the Phrygian mode uses C as the reciting tone, as Bb is a tritone away. This explains why a cadence in the Phrygian mode moves down a half-step to tonic rather than up a half-step, as no dominant is possible in the Phrygian mode.

I get that you might be referencing the original use of the modes and how they are different than the modes we use today, but is there any relevance or use to this information or perspective at all?

We all know that when "dorian" is referenced in 2012, we are talking about a 7 note pitch collection that is R, 2, b3, 4, 5, 6, b7. If in some context the word "dorian" meant a different collection, how could that possibly be anything other than confusing to reference in anything other than a conversation about the historical origins of modes?

[whatswisdom]

Mode - Characteristic Pitch

Ionian - None
Dorian - Raised Sixth
Phrygian - Lowered Second
Lydian - Raised Fourth
Mixolydian - Lowered Seventh
Aeolian - None
Locrian - Lowered Second

[mr. beaumont]

I'd include the b5 on that Locrian.

[whatswisdom]

Originally Posted by mr. beaumont

I'd include the b5 on that Locrian.

I wouldn't. Scale built on 7th degree of the harmonized major scale is a minor scale, with b5 naturally occuring because of the half-dim. The only odd man out is b2, which to me is the Characteristic Pitch. I put this out and welcome any correction if I'm wrong...

[Reg]

Using characteristic pitches... to create a source of controlling harmonic movement is simply one method which helps explain how jazz players... played and composed jazz tunes which now are called Modal Jazz... from the late 50's to early 70's.
As I always say in jazz there are generally many musical concepts simultaneously being employed... if we're looking for single exact detail examples... we might be looking at the wrong style of music.
When I use the term cadence... I'm stretching definitions to try and help us understand the Modal Concept... Jazz application of use of term Modal has very little to do with Church Modes, counterpoint, Organum... basic 8 modes, then 12... with 3rd being the defining character... Modality being harmonic and melodic formations based on church modes etc....
And even though Dominant Cadence refers to a V7 chord going to the I chord and Dominant Resolution refers to V7 chord going to other chord besides I chord... Secondary Dominants resolve to Diatonic chords other than I...and Extended Dominants resolve to either... secondary Doms. ,another extended Dom., the related II- of another extended or secondary Dom....
Most of us understand and hear that when different chords move to other chords, (harmonic movement), there appear to be reasons why. The point I'm leading to is... we can design or create concepts which may become methodology for controlling different Harmonic movement... some are simple... some are a little more complex. How they work... can be subjective... but the methods can, have and will be used to compose and solo.
Most jazz tunes are not simple, by simple I mean one compositional or improvisational concept being employed.
Anyway using the CP was simply one of those concepts... The more important point now...(modal jazz is very dated), but that use of that concept, jazz use of characteristic pitches to be one of the methods to control harmonic movement, has opened many other doors as far as controlling harmonic movement.
If we use traditional European Classical framework for trying to understand and play jazz... that's what it will sound like... not good or bad... but very different. Since this is a Jazz Guitar site... I take it for granted, we're talking about Jazz and jazz tendencies... of which that European classical tradition is very much a part... One of Many.
Reg

[JakeAcci]

Originally Posted by Reg

Using characteristic pitches... to create a source of controlling harmonic movement is simply one method which helps explain how jazz players... played and composed jazz tunes which now are called Modal Jazz... from the late 50's to early 70's.

As I always say in jazz there are generally many musical concepts simultaneously being employed... if we're looking for single exact detail examples... we might be looking at the wrong style of music.

When I use the term cadence... I'm stretching definitions to try and help us understand the Modal Concept... Jazz application of use of term Modal has very little to do with Church Modes, counterpoint, Organum... basic 8 modes, then 12... with 3rd being the defining character... Modality being harmonic and melodic formations based on church modes etc....

And even though Dominant Cadence refers to a V7 chord going to the I chord and Dominant Resolution refers to V7 chord going to other chord besides I chord... Secondary Dominants resolve to Diatonic chords other than I...and Extended Dominants resolve to either... secondary Doms. ,another extended Dom., the related II- of another extended or secondary Dom....

Most of us understand and hear that when different chords move to other chords, (harmonic movement), there appear to be reasons why. The point I'm leading to is... we can design or create concepts which may become methodology for controlling different Harmonic movement... some are simple... some are a little more complex. How they work... can be subjective... but the methods can, have and will be used to compose and solo.

Most jazz tunes are not simple, by simple I mean one compositional or improvisational concept being employed.

Anyway using the CP was simply one of those concepts... The more important point now...(modal jazz is very dated), but that use of that concept, jazz use of characteristic pitches to be one of the methods to control harmonic movement, has opened many other doors as far as controlling harmonic movement.

If we use traditional European Classical framework for trying to understand and play jazz... that's what it will sound like... not good or bad... but very different. Since this is a Jazz Guitar site... I take it for granted, we're talking about Jazz and jazz tendencies... of which that European classical tradition is very much a part... One of Many.
Reg

I couldn't resist...probably means I'm going to hell...

[JakeAcci]

Originally Posted by whatswisdom

I wouldn't. Scale built on 7th degree of the harmonized major scale is a minor scale, with b5 naturally occuring because of the half-dim. The only odd man out is b2, which to me is the Characteristic Pitch. I put this out and welcome any correction if I'm wrong...

I don't understand. The b2 naturally occurs as well, so why make the distinction? The pitches that differ from natural minor are b2 and b5.

[Reg]

Thanks Jake... Reg

[whatswisdom]

Originally Posted by whatswisdom

Mode - Characteristic Pitch

Ionian - None
Dorian - Raised Sixth
Phrygian - Lowered Second
Lydian - Raised Fourth
Mixolydian - Lowered Seventh
Aeolian - None
Locrian - Lowered Second; Lowered Fifth

Originally Posted by JakeAcci

I don't understand. The b2 naturally occurs as well, so why make the distinction? The pitches that differ from natural minor are b2 and b5.

Okay, Jake. My bad...

So, the above list revised to correct my error.

Modes of C Major.

Characteristic Pitches:

B F F# F C F

What does it all mean? Well, I see 2 tritones...

[Fred Pepper]

Originally Posted by Wheels

any dominant in any situation is satisfied to lead back to its 1, whether that 1 is a major, a minor, or even another dominant?

This is a neatly phrased question, to which the answer is actually "yes". Any dominant in any situation is satisfied to lead back to it's 1.

Whether it should, or will, or may find satisfaction leading elsewhere, are entirely different questions, as the poster probably already realises (if he is still conscious).

[cosmic gumbo]

There is nothing safe about jazz. It is dangerous, and if it's not, then it's not jazz. They call that safe stuff "smooth" jazz.

[JonR]

"Beautiful music.... dangerous rhythm..."
(from "The Continental", 1935)
Django Reinhardt / Stephane Grappelly - The Continental - YouTube

[whatswisdom]

Originally Posted by JonR

1. V chord in major key.
Symbols 7, 9, 13. Occasionally has alterations, but these usually signify a borrowing from minor.
Resolves to I, but can often go via other chords, such as IV, or can be part of a "deceptive cadence" (ie by resolving anywhere but I, such as to the vi chord).
Can often occur in cycles, such as the bridge of Rhythm changes. (These tend to be assumed to be mixolydian chords, but can often be altered.) This sequence is what's known as a "backcycle", where the V of the key is given its own V ("secondary dominant" - see below) and so on back through the sequence.

2. V chord in minor key.
Symbols 7, 7b9, 7#9, 7alt (any combination of altered 5th and 9th).
Resolves to I. Rarely goes via any other chord.
Can be used as sub for a major key V. (Rarely vice versa).

3. bII chord in minor key.
Symbols 7#11, 9#11, 13#11 (lydian dominant)
This is a tritone sub for the altered V7 (harmonized from the same notes, often just the same chord tones with a different bass).
Has a very strong tendency to resolve down the half-step to I. (Stronger than the V).

4. bII in major key. Essentially same as above.

5. bVII in major key. Usually lydian dominant, but a weaker resolution tendency (up a whole step) than a bII. (See point 9 below.)

6. bVI in minor key. Usually lydian dominant, a tritone sub for the secondary dominant of V. (Eg, C7 in key of E minor is bII of B, sub for F#7 (V/V) and usually has a strong tendency to lead to B or B7.)
However, bVI7 chords are sometimes used as subs for the iv chord. Eg, in key of E minor, you might get a C7 in place of Am7, leading back to the tonic (Em). Scale-wise, probably lydian dominant again, although it suits the blues scale of the key.

7. Blues I or IV chord. A non-functioning dominant - ie has no tendency to resolve anywhere. The I7 chord does behave as a secondary dominant when leading to IV, but only then. And the IV7 is not the dominant of anything. (Occasionally in jazz, the IV7 will lead to a iii chord instead of back to I, which turns it into the bII of the iii chord.)
A blues tonic chord can sometimes have a #9 alteration, reflecting the flattened blue 3rd. In rock this is known as the "Hendrix chord", but of course it was used in jazz before that. (A 7#9 blues tonic is not quite the same thing as a 7#9 V chord in a minor key: it will have a perfect 5th, and use blues scale.)

8. Key chord of mixolydian mode. Modal music is, by definition (at least in jazz) "non-functional", so no chord type has to do what it usually does in key-based music. In G mixolydian mode, therefore, G7 can be the tonal centre, with no tendency to resolve to C. (In this sense it's similar to a blues tonic.)
Of course, a mixolydian mode chord means 9, sus4 or 13 extensions, not any alterations.

9. Other modal uses could be bVII in aeolian (bVII to a minor I is an "aeolian cadence"), or IV in dorian. The latter is very common in Latin (Afro-Cuban) jazz.

10. I'll leave this one blank . I'm sure there are other uses of dom7s I can't think of right now, and you can probably invent your own. This is jazz after all - we need room to improvise!

Secondary dominants can occur on the I, II, III, VI and VII steps of a major key, and have the same function as V chords relative to their targets. Eg, a D7 chord in key of C, is V/V - dominant of the dominant (G).
Secondary dominants also occur in minor keys, but seem to be rarer. V/V does occur, but its tritone sub seems to be more common, perhaps because its root is diatonic (eg C7 in Em).

Common subs for dom7s (esp V7s) are dim7 chords, rooted on the 3rd of the dom7 (or half-step above the root).
Eg, Bdim7 in key of C minor is a "dominant-function" chord, resolving to Cm. It is a chord in its own right (vii of C harmonic minor) but can be seen as a rootless G7b9.
Dim7 chords have strong resolution tendencies: one of the notes - usually the root - resolves up a half-step, usually to a minor tonic, sometimes to a major tonic. (Dim7s chords are symmetrical, so any note can be the root, but in derivation terms they are vii chords - "leading tone 7ths" - in minor keys.)

The vii chord in a major key (m7b5 or half-dim) can have a similar function - resolving up a half-step, like a rootless version of the dom9 chord - but in jazz is almost never used that way. It's much more common as a ii chord (subdominant function) in a minor key.
Eg, Bm7b5 could resolve to C (major), as a natural leading tone chord, but is more often seen moving to E7(b9) and then to Am.

Great post! I've copied and printed for reference.