Anyway, The 1st Trumpet and the trombone are inversions of each other. So are the 2nd trumpet and the bass trombone but these two are an augmentation os the former two.
(click on image to enlarge)
Lahti
1 year ago
Sunday, May 31, 2009
Canon in mensuration and inversion
I seem to be drawn towards making some of these short canons into fanfares -- not sure why...
Anyway, The 1st Trumpet and the trombone are inversions of each other. So are the 2nd trumpet and the bass trombone but these two are an augmentation os the former two.
(click on image to enlarge)
Anyway, The 1st Trumpet and the trombone are inversions of each other. So are the 2nd trumpet and the bass trombone but these two are an augmentation os the former two.
(click on image to enlarge)
Saturday, May 30, 2009
Pentatonic Canon at the Octave
Busy day (how often do I say that?) -- Maggi and I had a concert followed by a dinner with our audience (a group of Japanese tourists visiting Salem).
So, I took the easy way out and wrote a simple pentatonic canon at the octave for harpsichord.
(click on image to enlarge)
Busy day (how often do I say that?) -- Maggi and I had a concert followed by a dinner with our audience (a group of Japanese tourists visiting Salem).
So, I took the easy way out and wrote a simple pentatonic canon at the octave for harpsichord.
(click on image to enlarge)
Friday, May 29, 2009
Hidden Elaboration
Elaboration of yesterday's canon.
The basic canon in inversion stays the same but is hidden by the different types of elaboration in the two parts.
(click on image to enlarge)
The basic canon in inversion stays the same but is hidden by the different types of elaboration in the two parts.
(click on image to enlarge)
Thursday, May 28, 2009
More Pentatonic Inversion
Taking the information about inversion that led to the last two canons, I quickly realized that since inverting at the tonic of the first scale will generate a scale a major third lower, if I wanted to maintain the same scale, i would simply need to begin the inversion a major third higher than the dux.
(click on image to enlarge)
(click on image to enlarge)
Wednesday, May 27, 2009
Finally Caught Up Again!
I'm finally caught up again after falling behind with my posting during the grading of finals.
Today's canon is an elaboration of yesterday's 1st species-style canon in inversion.
(click on image to enlarge)
Today's canon is an elaboration of yesterday's 1st species-style canon in inversion.
(click on image to enlarge)
Tuesday, May 26, 2009
Pentatonic Canon is Inversion
If you invert a major pentatonic scale from its tonic, the result is a major pentatonic with a tonic pitch a major third lower.
To be more precise: the result is another pentatonic set a major 3rd lower but the intervals are inverted.
Major pentatonic -- M2 M2 m3 M2 m3 -- Ascending
from C -- C D E G A C --C major pentatonic.
to invert we use the same intervals descending:
from C -- C Bb Ab F Eb C
If we rearrange these pitches to start on Ab, you'll see that we have an Ab major pentatonic scale:
Ab Bb C Eb F Ab
I used this material for the canon today -- the common tone of C is used as the tonic.
(click on image to enlarge)
If you invert a major pentatonic scale from its tonic, the result is a major pentatonic with a tonic pitch a major third lower.
To be more precise: the result is another pentatonic set a major 3rd lower but the intervals are inverted.
Major pentatonic -- M2 M2 m3 M2 m3 -- Ascending
from C -- C D E G A C --C major pentatonic.
to invert we use the same intervals descending:
from C -- C Bb Ab F Eb C
If we rearrange these pitches to start on Ab, you'll see that we have an Ab major pentatonic scale:
Ab Bb C Eb F Ab
I used this material for the canon today -- the common tone of C is used as the tonic.
(click on image to enlarge)
Tuesday, May 26, 2009
Monday, May 25, 2009
An elaboration of yesterday's canon -- quite different from either Friday's or Saturday's canons.
The instrumentation is a combination that I've always wanted to try...
(click on image to enlarge)
The instrumentation is a combination that I've always wanted to try...
(click on image to enlarge)
Sunday, May 24, 2009
Phrygian canon in 3 voices.
I took Friday's canon and removed the sharps from the upper two voices. This gave me a slightly odd by mostly workable canon in E phrygian. I tweaked it a bit to eliminate some voice leading problems and harsh dissonances.
Here it is (in whole and half notes):
(click on image to enlarge)
I took Friday's canon and removed the sharps from the upper two voices. This gave me a slightly odd by mostly workable canon in E phrygian. I tweaked it a bit to eliminate some voice leading problems and harsh dissonances.
Here it is (in whole and half notes):
(click on image to enlarge)
Saturday, May 23, 2009
An elaboration of yesterday's canon using only the tones of those three scales:
(click on image to enlarge)
(click on image to enlarge)
Friday, May 22, 2009
Canon on Three Pentatonic scales.
I chose Comes I to enter a major third above the dux and Comes II to enter a major 6th above the dux (a perfect 4th above Comes I).
This gave me the following pitch material:
Dux -- C major pentatonic C D E G A
Comes I -- E major pentatonic E F# G# B C#
Comes II -- A major pentatonic A B C# E F#
But, I didn't treat them as being in these three keys. Since E is the common tone between these three scales I chose to use it as a tonal center. This makes the top two voices sound like they are in E major and the lowest voice sound like E phrygian.
Again, 1st species-style:
(click on image to enlarge)
I chose Comes I to enter a major third above the dux and Comes II to enter a major 6th above the dux (a perfect 4th above Comes I).
This gave me the following pitch material:
Dux -- C major pentatonic C D E G A
Comes I -- E major pentatonic E F# G# B C#
Comes II -- A major pentatonic A B C# E F#
But, I didn't treat them as being in these three keys. Since E is the common tone between these three scales I chose to use it as a tonal center. This makes the top two voices sound like they are in E major and the lowest voice sound like E phrygian.
Again, 1st species-style:
(click on image to enlarge)
Thursday, May 21, 2009
Elaboration of yesterday's 1st species-style canon.
It almost seems like cheating to write a whole-note canon one day and then elaborate it the next but I do it for numbar of reasons:
1) It facilitates composition on days that I have limited time (all too often!)
2) It explicates the process for others who may wish to try their hand at contrapuntal and/or canonic composition.
3) habit (at least by now it seems to be so...)
(click on image to enlarge)
It almost seems like cheating to write a whole-note canon one day and then elaborate it the next but I do it for numbar of reasons:
1) It facilitates composition on days that I have limited time (all too often!)
2) It explicates the process for others who may wish to try their hand at contrapuntal and/or canonic composition.
3) habit (at least by now it seems to be so...)
(click on image to enlarge)
Wednesday, May 20, 2009
A pentatonic canon at the tritone.
Not very traditional sounding because there are no common tones shared by these two scales.
Also, I stuck with the sharp names of the notes throughout, even though the consonances would be made more clear by occasionally spelling them enharmonically. Needless to say, this canon must be in equal temperament to work...
(click on image to enlarge)
Not very traditional sounding because there are no common tones shared by these two scales.
Also, I stuck with the sharp names of the notes throughout, even though the consonances would be made more clear by occasionally spelling them enharmonically. Needless to say, this canon must be in equal temperament to work...
(click on image to enlarge)
Saturday, May 23, 2009
Tuesday, May 19, 2009
Elaborated 3-Voice Pentatonic Canon
Yesterday's canon elaborated:
(click on image to enlarge)
Yesterday's canon elaborated:
(click on image to enlarge)
Monday, May 18, 2009
Three-Voice Pentatonic Canon at the 4th above and below.
As I stated on Saturday, combining major pentatonic scales a fifth or fourth apart gives a set of pitches contained in the major (heptatonic) scale.
If we combine a pentatonic with one a fourth above and another a fourth below, we get the complete diatonic set.
Here the dux is C major pentatonic -- C, D, E, G, A
Comes I is F major pentatonic -- F, G, A, C, D
Comes II is G major pentatonic -- G, A, B, C, D
The complete set of pitches is C, D, E, F, G, A, B (C major)
In 1st species style:
(click on image to enlarge)
sunday, May 17, 2009
Elaborated Pentatonic Canon at the 4th
Yesterday's canon elaborated.
(click on image to enlarge)
Yesterday's canon elaborated.
(click on image to enlarge)
Saturday, May 16, 2009
Pentatonic canon at the fourth.
If one takes the major pentatonic scale (scale degrees 1, 2, 3, 5 & 6) and writes a canon at the fourth (or fifth for that matter), the resulting combined scales still only use pitches contained in the major (heptatonic) scale.
That's what I explored here. The dux is in C major pentatonic C, D, E, G, A and the comes is in F major pentatonic -- F, G, A, C, D. All of the pitches are members of the C major scale.
Today, first species--elaboration tomorrow.
(click on image to enlarge)
If one takes the major pentatonic scale (scale degrees 1, 2, 3, 5 & 6) and writes a canon at the fourth (or fifth for that matter), the resulting combined scales still only use pitches contained in the major (heptatonic) scale.
That's what I explored here. The dux is in C major pentatonic C, D, E, G, A and the comes is in F major pentatonic -- F, G, A, C, D. All of the pitches are members of the C major scale.
Today, first species--elaboration tomorrow.
(click on image to enlarge)
Tuesday, May 19, 2009
Friday, May 15, 2009
4-Voice Pentatonic Canon
One interesting feature of the major pentatonic scale is that it has no half steps. A technical name for it that is sometimes used is anhemitonic pentatonic (literally "5 tone scale with no half steps").
In a practical sense this means that it is pretty difficult to produce harsh dissonance with only these tones. To demonstrate that fact, I offer this setting for string quartet of yesterday's melody. because the rhythm varies sufficiently from measure to measure, the parts will be distinct enough.
I have not altered any of the tones (except, of course, the simple transposition to a suitably resonant key for strings). Consecutive voices enter an octave apart.
(click on image to enlarge)
One interesting feature of the major pentatonic scale is that it has no half steps. A technical name for it that is sometimes used is anhemitonic pentatonic (literally "5 tone scale with no half steps").
In a practical sense this means that it is pretty difficult to produce harsh dissonance with only these tones. To demonstrate that fact, I offer this setting for string quartet of yesterday's melody. because the rhythm varies sufficiently from measure to measure, the parts will be distinct enough.
I have not altered any of the tones (except, of course, the simple transposition to a suitably resonant key for strings). Consecutive voices enter an octave apart.
(click on image to enlarge)
Thursday, May 14, 2009
The elaboration of yesterday's canon.
I used only the scale tones of each voice in the elaboration.
(click on image to enlarge)
I used only the scale tones of each voice in the elaboration.
(click on image to enlarge)
Wednesday, May 13, 2009
Here is a 1st-species-style canon using the same two scales as yesterday but in reversed position.
I'll elaborate it tomorrow.
(click on image to enlarge)
I'll elaborate it tomorrow.
(click on image to enlarge)
Tuesday, May 12, 2009
...still playing catch-up with my posts, though I have managed to continue to write my canons daily.
Maggi and I had a concert at the Fitchburg Art Museum on Sunday that took up much of our time in preparation and rehearsal.
Here is a canon on the major pentatonic scale 1, 2, 3, 5, 6.
Because it imitates at the minor tenth, each voice is in a different scale.
Lower: C D E G A
Upper: Eb F G Bb C
(click on image to enlarge)
Maggi and I had a concert at the Fitchburg Art Museum on Sunday that took up much of our time in preparation and rehearsal.
Here is a canon on the major pentatonic scale 1, 2, 3, 5, 6.
Because it imitates at the minor tenth, each voice is in a different scale.
Lower: C D E G A
Upper: Eb F G Bb C
(click on image to enlarge)
Thursday, May 14, 2009
Monday, May 11, 2009
Another elaboration of Saturday's canon. This one using notes of the D minor scale. Again, recall that this symmetrical enharmonic pentatonic is a subset of the D minor scale...
(click on image to enlarge)
(click on image to enlarge)
Sunday, May 10, 2009
Another very busy day.
I simply elaborated yesterday's canon using tones of the scale>
(click on image to enlarge)
I simply elaborated yesterday's canon using tones of the scale>
(click on image to enlarge)
Saturday, May 9, 2009
A three-voice canon in symmetrical enharmonic pentatonic.
Working on grading finals, this needed to be quick. It's in 1st species style.
(click on image to enlarge)
Working on grading finals, this needed to be quick. It's in 1st species style.
(click on image to enlarge)
Wednesday, May 13, 2009
Friday, May 8, 2009
A second elaboration of the May 6th canon.
For yesterday's elaboration, I used only pitches of the symmetrical enharmonic scale that I used to compose the original first-species canon.
Today -- a different approach. I used the original canon as a skeletal outline and elaborated with pitches from the D minor scale. You'll notice that the sym/enh/pent is a subset of D minor...
(click on image to enlarge)
For yesterday's elaboration, I used only pitches of the symmetrical enharmonic scale that I used to compose the original first-species canon.
Today -- a different approach. I used the original canon as a skeletal outline and elaborated with pitches from the D minor scale. You'll notice that the sym/enh/pent is a subset of D minor...
(click on image to enlarge)
Wednesday, May 6, 2009
This is another first-species-style canon -- this one using the same scale as my May 3 canon.
I'll elaborate it tomorrow...
(click on image to enlarge)
I'll elaborate it tomorrow...
(click on image to enlarge)
Tuesday, May 5, 2009
Elaboration of Yesterday's Canon
Simple elaboration using tones of the symmetrical enharmonic pentatonic:
(click on image to enlarge)
Simple elaboration using tones of the symmetrical enharmonic pentatonic:
(click on image to enlarge)
Monday, May 4, 2009
Another Symmetrical Enharmonic Scale
For this scale, I simply reversed the two tetrachords of the scale that I used for yesterday's canon.
A G# E D Bb A
A simple, first-species-style canon:
(click on image to enlarge)
For this scale, I simply reversed the two tetrachords of the scale that I used for yesterday's canon.
A G# E D Bb A
A simple, first-species-style canon:
(click on image to enlarge)
Sunday, May 3 2009
Well, now that the semester is done, finals given and graded and semester grades submitted, I'll finally have time to catch up.
I have continued to write my daily canons but didn't have the time to enter them into Finale and post them. I will post several a day until I'm caught up.
Canon in the Symmetrical Enharmonic Pentatonic
The ancient Greek Enharmonic Pentatonic is a scale with two identical tetrachords (as were most Greek scales).
In modern terminology, a tetrachord is a group of pitches spanning the interval of a perfect fourth. The Enharmonic begins with a major third. The remaining minor second completes the tetrachord.
Example (The Greeks constructed their scales in a descending manner):
A F E (A-F is a major 3rd, F-E is a minor second)
As I said, the ancient Greek version used identical tetrachords to make a scale. These are connected by a major second so that the two tetrachords are a perfect fifth apart and will complete the octave.
A F E D Bb A
I wanted to have a scale that was symmetrical around that connective major second, so I created two versions of a symmetrical enharmonic pentatonic. Today's canon uses one of them, I'll get to the other later this week.
A F E is the first tetrachord -- M3, m2
D C# A is the second -- m2, M3
The complete scale is A F E D C# A.
As befits a symmetrical scale, here is a canon in inversion.
(click on image to enlarge)
I have continued to write my daily canons but didn't have the time to enter them into Finale and post them. I will post several a day until I'm caught up.
Canon in the Symmetrical Enharmonic Pentatonic
The ancient Greek Enharmonic Pentatonic is a scale with two identical tetrachords (as were most Greek scales).
In modern terminology, a tetrachord is a group of pitches spanning the interval of a perfect fourth. The Enharmonic begins with a major third. The remaining minor second completes the tetrachord.
Example (The Greeks constructed their scales in a descending manner):
A F E (A-F is a major 3rd, F-E is a minor second)
As I said, the ancient Greek version used identical tetrachords to make a scale. These are connected by a major second so that the two tetrachords are a perfect fifth apart and will complete the octave.
A F E D Bb A
I wanted to have a scale that was symmetrical around that connective major second, so I created two versions of a symmetrical enharmonic pentatonic. Today's canon uses one of them, I'll get to the other later this week.
A F E is the first tetrachord -- M3, m2
D C# A is the second -- m2, M3
The complete scale is A F E D C# A.
As befits a symmetrical scale, here is a canon in inversion.
(click on image to enlarge)
Tuesday, May 5, 2009
Saturday, May 2, 2009
Another Canon at the Tritone.
This one is based on a scale that combines two minor chords a tritone apart.
A C E and Eb Gb Bb
The scale spelled enharmonically:
A Bb C D# E F#
See the April 30th canon.
(click on image to enlarge)
This one is based on a scale that combines two minor chords a tritone apart.
A C E and Eb Gb Bb
The scale spelled enharmonically:
A Bb C D# E F#
See the April 30th canon.
(click on image to enlarge)
Lá Bealtaine 2009
Lá Bealtaine is the traditional Celtic celebration of May Day.
I have adapted phrases from a Bealtaine ritual song that Maggi and I wrote together for our book, The Measure of the Year: Singing Through the Seasons
This is an unusual canon in that the intervals of imitation change halfway through. For the first half, each following voice imitates a step lower. Beginning with the upper voice in measure six, each following voice imitates a step higher.
The title, Dlí Bealtaine is Gaeilge (Irish) for Beltane Canon.
(click on image to enlarge)
I have adapted phrases from a Bealtaine ritual song that Maggi and I wrote together for our book, The Measure of the Year: Singing Through the Seasons
This is an unusual canon in that the intervals of imitation change halfway through. For the first half, each following voice imitates a step lower. Beginning with the upper voice in measure six, each following voice imitates a step higher.
The title, Dlí Bealtaine is Gaeilge (Irish) for Beltane Canon.
(click on image to enlarge)
Thursday, April 30, 2009
A canon at the Tritone
This six-tone scale is made of two major triads a tritone apart.
C E G and F# A# C#
Written enharmonically, the scale is C Db E F# G Bb
Imitation at the tritone in this scale is a no-brainer.
(click on image to enlarge)
This six-tone scale is made of two major triads a tritone apart.
C E G and F# A# C#
Written enharmonically, the scale is C Db E F# G Bb
Imitation at the tritone in this scale is a no-brainer.
(click on image to enlarge)
Sunday, May 3, 2009
Wednesday, April 29, 2009
A canon on a scale built from the overtone series.
An equal-tempered version of the scale is:
C D E F# G A Bb C
(click on image to enlarge)
An equal-tempered version of the scale is:
C D E F# G A Bb C
(click on image to enlarge)
Tuesday, April 28, 2009
A canon at the octave, adapted from an earlier rhythmic canon.
(Click on image to enlarge)
(Click on image to enlarge)
Monday, April 27, 2009
I have been keeping up with my canon writing even during the very busy end-of semester time. I have been falling behind with the posting though. Bear with me and I'll be caught up soon.
I have kept the canons pretty simple, though -- just a function of the schedule...
This one is a canon in augmentation based on a rhythmic canon that I wrote a month or so back.
(click on image to enlarge.)
I have kept the canons pretty simple, though -- just a function of the schedule...
This one is a canon in augmentation based on a rhythmic canon that I wrote a month or so back.
(click on image to enlarge.)
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