Translate

Monday, August 31, 2020

338. THE LIPOPHONE CHALUMEAUX A CORNETTI TYPE WIND INSTRUMENT EASILY PLAYABLE , WITH THE ACOUSTICS OF THE CLARINET AND CHALUMEAUX RATHER THAN THE TRUMPET

This is AN INNOVATIVE IDEA,  CLASSICAL wind instrument combining the advantages of cornett, trumpet and clarinet.

1) It utilizes as sound generation method of buzzing the lips with trumpet mouthpieces (or wooden cornett mouthpieces ) , as brass instruments do. Thus for those that love this sound of the human lips in a trumpet mouthpiece  as modulated by a material tube , the lip-o-phone, it is an instrument that they like too.
2) It utlizes the simpler method of diatonic scales notes layout and fingering system of a clarinet (e.g. if no keys an only holes a 8front +1 thump fingering system) based on the 1st and 3rd overtone mainly , which is simpler fingering for 7-notes diatonic scales melodies compared to a valved trumpet which based on at least 5 overtones and which with the valves  favors the 12-notes chromatic scale

3) Its size compared to the root pitch is like that of the clarinet and in overall the wind instrument resembles a classical wooden cornett which also generates sound by buzzing the lips inside very small trumpet-like mouthpiece, except that it is not conical as the cornett but of straight tube as the clarinets.

4) Because it is not utilizing a cone or bell at  the end the sound is not penetarting and loud but gendle silky, and soft as the other wind instruments (flute, clarinett, cornett etc).  It must be noticed though that  the art of buzzing the lips at a stable resonating pitch  to the tube, as it is known from the brass instruments,  is not easy.  Playing brass instruments is more difficult than playing a duduk, a clarinet, or a saxophone just because of the lips buzzing stability issues not to mention the chromatic and non-diatonic layout of the notes by the valves (or slide). Still the lipophone is easier to play compared to a trumpet and most brass instruments and about as easy as playing the wooden cornett. Still more difficult than a duduk, a  clarinet or a saxophone. If it is utlilized wooden cornett mouthpieces instead of brass trumpet mouthpieces, the pitch of the lips buzzing is more stable.

5) Sizes of 70 cm and root Bb3 are normal , but if someone would like lower roots Bb2 F2 , C2 etc and still be able to play them easily we should use flexible plastic pipes or tubes coiled around a cylinder, so that we can put the 8+1 holes close,  and cover themeasily as if playing an alto A4, or Bb4 flute. A method much like that of the medieval wooden rackett wind instrument or the coiling of the tube of the brass wind instruments. 

In the next picture is such Lipophone rooted at D3 and in the 2nd photo for comparison a conical type cornett (diatonic piccolo trumpet) . The cornett has a  fingering system much like a whistle and saxophone (slightly different) , while the Lipophone a fingering system excatly as the clarinet. 



And if for  the body we utilize a  clarinet tube and for mouth piece a french horn mouthpiece then this is shown in the next pictures











The picture below is of a mute cornett (diatonic piccolo  trumpet) . The trumpet-like small cornett mouthpiece is inside the narrow upper hole of the wooden tube.

The picture below is a trumpet-like cornetti mouthpiece which is smaller than the trumpets (inner diameter from 12mm to 14mm, Trumpet mouthpieces have usually inner diameter 16mm-17mm.) .






A cornetti (diatonic piccolo trumet) mouthpiece can fit best  after appropriate adoption to a 





piccolo size clarinet tube or chalumeaux to give a  more modern  type of a soprano Lip-o-phone. Cornetti types mouthoieces are optimalin the 4th and 5th octaves.

1) As it turned out after experimentaion the various sizes of cornetti and brass winds mouthpieces are optimally correlated to particular octaves rather than particular instruments

2) Under this approach and classification the optimal octaves and mouthpieces go like this

 a) Cornetti mouthpieces (11mm-15mm) are optimal in the 5th octave of the piano

b) French horn mouthpieces and mega 7C trumpet mouthpieces  are optimal in the 4th octave of the piano

c) Alto-horn mouthpieces are optimal in the 3rd octave of the piano

d) Double trombone mouthpieces are optimal in  the 2nd octave of the piano

3) From this point of view   cornetti mouthpieces have a market musical need (besides cornetti players) for a big population of piccolo trumpet players! Inspite of the fact that  due to industry tradition the musician themselves do not know it because they have not tried it! 

I have tried it and they make greatly easier the playing of the piccolo trumpet compared to standard piccolo trumpet mouthpieces that are too big for the 5th octave! 

4) Also the use cornetti mouthpieces for the oboe did not give very satisfactory results as the playing for some reason was falling to start from one octave lower than that of oboe.  Instead the french horn mouthpieces for oboe were much satisfactory and besides a bit of volatility in the sound depending on the embouchure the intsrument was functional

The same exactly with the soprano saxophone and cornetti and French horn mouthpieces.

The correlation of mouthpieces and octaves holds also even for overtones flutes when instead of a fipple lips-base mouthpieces a re used.












Thursday, August 27, 2020

337. HARMONY -MELODY AND SIMPLICITY-COMPLEXITY

Historically the harmony was created at the 2nd generation of music (classical polyphonic music) as  a   drone simple countermelody of  rather complicated melodies So there is the pre-occupation that melodies are complicated and accompanying harmonies are simple. And indeed there is a large number of famous folk and artistic songs that it is so.

Nevertheless after the 3rd and 4th generations of music (Jazz, folk jazz and digital music) we notice the reversing of this and we have a large number of beatiful songs where the melody is very simple while the parallele chord progression is complicated. Sometimes  there is a larger number of chords compared to  notes in the melody, or we have a single note in the melody having two accomanying chords etc. Here the harmony of the accompanying chord progression is like a polyphonic countermelody which is more complicated than the melody itself. 
A classical example the famous Lous Armstrong song What a wonderful world
https://www.youtube.com/watch?v=uBs82KnJllg

In the 4th generation of music , the digital music with looping and arpeggiators , this mode of songs with simple melody and complicated harmony is more often and also easier to compose, when you are a (jazz)  guitarist who has spent much time in learning and feeling chord progressions.



Saturday, August 22, 2020

336. HOW TO COMPOSE SONGS WITHIN THE CHROMATIC TONALITY

FOR THE CONCEPT OF CHROMATIC TONALITY SEE POST 263


As chords of the full chromatic tonality we will use the

1M 2m (and 2M) 3m (amd 3M7) 4M  5M (and 5m) 6m (and (6M7) 7d (and 7M7) 

We may conseive them also as a connected arc in the wheel by 4ths

7M-3M-6m-2m-5M-1M-4M  where some of them are turned from minor to major and vice versa

Full chromatic tonality means that we intent to utilize in the melody initially the 7 notes of the diatonic scale (tonality) but thenalso all the 12 notes (plus 5 additional blue or chromatic notes)


We assume that the song will have a sad part and session which is denoted by A and called couple because it will repeat before  the refrain, and a session part B called the refrain which is the happy part. So in a  minimal way it is A A B A A B.

The sad  couple part will have chords from the triad of minors  3m , 6m, 2m and the happy refrain part will have chords from the triad of majors 1M 4M 5M.

We may also use poetic lyrics that correspond to the  simple 2-parts structure AA B AA B. (in exceptional cases we may have a 3 parts structure AA B  C C B or A A B  A A C)

For the arrangment we will utilize

1) A beat by a percusrion organ (usially by a digital instrument) Usually a multiple of 60 bpm which is  the tempo of  calm heart,
2) The chord progression, where we must determine how many beats is each chord Usually 2 beats per chord if we have many chords or or 4 beats per chord if we use few only chords (e.g. played by the guitar or ukulele, or the digital instruments in the ipad toucscaper  , chordion etc)
3) A bass playing a simplicial submelody (e.g. by an acoustic bass, or a ukulele bass or a midi controller like  Artiphone, or Sylphyo, or warbl, or DM48 connected to  the sounds of the application thumpjam in the ipad)
4) The melody (played by a wind istrument , or by a Celtic harp, or by a midi controller as above connected to  the sounds of the Thumpjam in ipad)
5) Possibly a loop playing an arpeggiation from an arpeggiator (e.g. by the applications  arpeggionome , or Reason)

6) We record channel by channel the sessions in an appropriate recording software e.g. the simple audacity. The digital created sounds go directly to the recording application without using speakers and microphones, But the sound of the analogue instruments and especially the voice is recorded with a good quality microphone which is plagged in to a mixer (like focurite) before it enters the computer as a microphone signal. Inthe mixer goes also the signal of an electric guitar if we use one.
After the recording of each channel we make some corrections in volume, timing , pitch, or  apply filters high pass or low pass etc and we put effects like echo etc Finally we export the song in mp3 and wav sound file format.


Chromatic tonality can be very well conducted and played not only with chromatic string instruments like guitar, mandolin, ukulele, bouzouki but also with diatonic Celtic harps with levers which are used in real time as we play to create the 5 blue or chromatic notes in the chords or in the melody.  This is a common  practice in latib=n amrica diatobic harps too (colombia,  bolivia, Peru etc) 

So a simple method to compose a song is the next


0) We compose simulteneously the chord progression and the melodic themes. We use mainly melodic themes for pairs of chords or chord transitions. (rarely simple melodic themes within one only chord).


1)  The chord progression as polyphonic counter melody.
We must notice that the chord progression within the chromatic tonality need not be the simplest possible chord progression that accomoanies the melody .Thus  the chord progression simpler than the melody. It may be that the melody is much simpler than the chord progression.  The chord progression is an independent counterpoint polyphonic counter-melody that fits with the solo melody and not just accompanioe the solo melody. An example is the famous song of Louis Armstrong "What a wonderful world" which has very simple melody but rather complicatd chord progression , with chords that change over a constant solo note which does not change. The melody of this song is very simple around the melodic centers 1-(2-3) and (5-6) of the 7 notes of the diatonic scale.

https://www.youtube.com/watch?v=uBs82KnJllg

We must also notice that the concept of full chromatic tonality , in other words utilizing all 12 notes c of the chromatic scale, may occur in the chord progression not in the melody, while the melody is so simple that it may have even less notes than the default 7-notes diatonic scale.

2)   We start with melodic themes within one chord or a pair of chords which are not in the major triad of the default diatonic scale 1M 4M 5M , e.g. 2m or 3m or 3M or 6m or 7M or pairs (1M-2m)  (1M-6m), (3M-6m) , (4M-7d) , (3m-4M) , (5M-6m)  etc 

Notice that an intense oppositions song would start in the chords 2m, 3m ,3M 6m , 7d etc and end in the triad of majors (1M, 4M, 5M)  while a more soft song would start with pairs (X1,X2) with X1 in (2m, 3m, 3M, 6m ,7d) and X2 in (1M, 4M, 5M ) 


3) And  then in the happy part  of the song shift to the triad of majors (1M, 4M, 5M). 


4) In the melody we translate the melodic themes of one or pair of chords to the next or we invert them. More rarely we mutate them or rotate them (meaning that we entirely change their rhythmic and pitch order structure which is termed in this book as Dolphin word structure) we may utilize the application Dot melody and Fugue machine. 


As alternative and even simpler method we start 

1) With start with melodies in one chord or pair of chords in the triad of majors 1M 4M 5M and we substitute one only chord each time with its corresponding lower relative minor or even the same root major hord converted to minor (e.g. instaed of 5M the 5m etc)  Notice that this stanrd corespondence of majors to minor preserves the chord-transition relations of  being chromatic, or harmonic. Therefore inside the parts-sessions A and B we deal mainly with chord transitions in chromatic and harmonic relations which means short (2nds) steps in the melody or large (4ths and 5ths) while moving from part=session a to B and vice versa mainly with chord-relations transitions of the melodic relation  (intervals of 3rds).   Thus at first and within a single part-session A or B for the melody we only have to decide where we will have shorts steps (intervals of 2nds) and where long steps (intervals of 4ths-5ths) and the rest will follow from the prediceded structure of the songs , and transition from part-session A to B and vice-versa

From the emotional point o view: 
1) chromatic transition=short step in melody (2nds) =just a necessary change in emotion in higher or lower pitch
2)Harmonic transition: large step in the melody (4ths-5ths)= a resolution of tension 
3)Melodic transition: middle step in melody (3rds)= Shift from minor(sad) to major(joy) or vice veesa

2) and also we modify the melodic theme. This is the couple (sad) A part, 


3) Then we return to the happy refrain B part in the (1M, 4M, 5M) or in the  ( 3M, 6M, 2M)   or in the (7M, 3M, 6M).





Here we use of course the idea  of  harmony based on a connected arc of 6 , 7 or even 8 chords in the cycle of 5ths, with mutations from major to minor on it and the involved multi tonality and chromatic tonality .

The concept of chromatic tonality is to enhance the melodiy from the 7 notes of a diatonic scale to the 12 notes of the chromatic.
The concept of multi tonality can do the same but it is done usally here by shifting from the initial diatonic scale e.g. C major here to the A major and E major (notice that the relative chords in melodic relation of the root C major chord is the Am and Em) . All these three major scales are included as triads of major chords in an a connected arc of  7 or 8 chords in the cycle of 5ths (or 4ths). And in particular they are the triads 3M-6M-2M (6 major) and 7M-3M-6M (3 major).

E.g. A characteristoc example is a well known tarditional song Brazilian song  in G major with the arc of chords F#7-B7-Em-Am-D7-G7-C , or in the G major diatonic 7M7-3M7-6m-2m-5M7-1M7-4M where in the refrain from the  more sad to more happy part of the song, the Em (6m) becomes E7 (6M7) and the Am (2m) becomes A (2M) . When from the sad part of the song (3M7-6m-2m) it goes to the happy part with triad of majors 1M7-4M-5M7 , the song it falls the 4M to 4m (to do so the common pair of relative chords 2m-4M is inverted to 2M-4m) which also gives it the chance to translate to 3m (which so far it was 3M7) and thus all 12 chords 7M7-3m7-6m-2m-5M7-1M7-4M and 7M7-3M7-6M-2M-5M7-1M7-4m  occur in the song which also gives all 12 notes in the melody when starting with only the 7 notes.

We must also notice that in such a  connected arc of chords not only the harmonic relation of chords occurs (chords a 5th or 4th apart) but also the melodic and chromatic relation of chords occurs.

The corresponding psychological feelings are

1) Harmonic relation of chords=resolution and nice shift of the melodic theme by a 4th or 5th
2) Melodic relation of chords=ususlly a transition of a major chord to same root minor or upper or lower relative minor , thus a mutation of a happy feeling to a sad and vice versa
3) Chromatic relation of chords=translation of the same feeling a semitone or tone higher or lower



All the above techniques are very common in harmonies and melodies of Gypsy Jazz , Latin Jazz, traditional Brazilian music etc.

The connected arc of chords in the wheel of 4th or 5yh as we said contains pairs of chirds chromatically or melodically related.


We dicsuss also 2 simple methods of how at  the melody in a  diatonic scale we may enhance it from the 7 notes of the diatonic scale to the 12 notes of the chromatic scale (This is called full chromatic tonality see post 263)   which is a usual nice feeling of completness.

A) The first method is to conceive the full pentatonic scale of the chromatic or blue notes 5b 6b 7b 2b 3b and utilize its two main chords 5b major (=5b-7b-2b) and 5bsus2 (=5b-6b-2b)as chromatic transition 4M 5bM 5M and 4M 5bsus2 5M then  the 3b minor (=3b-5b-7b) as chromatic transition 2m 2bm 3m . This will give all the 5 blue or chromatic notes of the 7-notes of the diatonic scale

B) The 2nd method is to involve the transition ofthe involved natural minor to harmonic minor and double harmonic minor and thus convert the chords 2m 3m , 6m , 7d to 2M, 3M7, 6M7 and 7M7 which again will give all the 5 blue notes 5b 6b 7b 2b 3b

E.g. A characteristoc example is a well known tarditional song Brazilian song  in G major with the arc of chords F#7-B7-Em-Am-D7-G7-C , or in the G major diatonic 7M7-3M7-6m-2m-5M7-1M7-4M where in the refrain from the  more sad to more happy part of the song, the Em (6m) becomes E7 (6M7) and the Am (2m) becomes A (2M) . When from the sad part of the song (3M7-6m-2m) it goes to the happy part with triad of majors 1M7-4M-5M7 , the song it falls the 4M to 4m (to do so the common pair of relative chords 2m-4M is inverted to 2M-4m) which also gives it the chance to translate to 3m (which so far it was 3M7) and thus all 12 chords 7M7-3m7-6m-2m-5M7-1M7-4M and 7M7-3M7-6M-2M-5M7-1M7-4m  occur in the song which also gives all 12 notes in the melody when starting with only the 7 notes.


All the above techniques are very common in harmonies and melodies of Gypsy Jazz , Latin Jazz, traditional Brazilian music etc.


As we mentioned in the full chromatic tonality the major chords 1M 4M 5M may turn to minor chords
1m, 4m, 5m and good ways to do it are the next 1) we may turn the 4M to 4m as invesions of the resulotion 1M->4M, thus 1M-4M->4m->1M (see also post 29) . Similarly the 1M to 1m atthe inversion of the resolution 5M->1M->1m->5M. Finally the 5M is turned to 5m in agood way if we temporarily shift to the 7b major diatonic scale which will  turn the 5M to 5m (as 6m in 7b major) and also turn the 1M to 1m (as 2m in 7b major).

Examples of chord progressions  in chromatic tonality in Portugues guitar folk music (E.g. Jorge Fontes )

1) 
triad of major chords=5M 1M 4M

cycle of chords with minors=1M-4m-7bm

2) 

triad of major chords=5M 1M 4M

cycle of chords with minors=6M-2m-(5M)

3) 
triad of major chords=5M 1M 4M

cycle of chords with minors=5M-1M-4m

4) 

triad of major chords=5M 1M 4M

cycle of chords with minors=5M-1m-4m


5) 
triad of major chords=5M 1M 4M

cycle of chords with minors=2M-5m

6) 
triad of major chords=5M 1M 4M

cycle of chords with minors=3M-6m-2m

7) The 5) and 6) together

1st triad of major chords=5M 1M 4M
1st cycle of chords with minors=7M7-3M-6m-2m (double harmonic minor)

2nd triad of majors  7M7-3M7-6M       (shifts in the upper relative major scale) 
2nd cycle of chords with minors=4#M7-7m (as if harmonic minor in in   2 major scale) 

8) 

triad of major chords=5M 1M 4M

cycle of chords with minors=6m-2m-5M

9) 

1st triad of major chords=5M 1M 4M

1st cycle of chords with minors=3M-6m-2m

2nd triad of major chords=7M7 3M7 6M  (upper relative major scale) 

2nd cycle of chords with minors=4#m-7m-3M-6M

10) 

1st triad of major chords=5M 1M 4M

1st cycle of chords with minors=1M-4m-7bm

2nd cycle of chords with minors=2M-5m

Monday, August 17, 2020

335. TWO SIMPLE METHODS TO ENHANCE MELODIES FROM THE 7 NOTES OF THE DIATONIC SCALE TO THE 12 NOTES OF THE CHROMATIC SCALE IN MULTI TONALITY AND CHROMATIC TONALITY

Here we dicsuss 2 simple methods of how at  the melody in a  diatonic scale we may enhance it from the 7 notes of the diatonic scale to the 12 notes of the chromatic scale (This is called full chromatic tonality see post 263)   which is a usual nice feeling of completness.

A) The first method is to conceive the full pentatonic scale of the chromatic or blue notes 5b 6b 7b 2b 3b and utilize its two main chords 5b major (=5b-7b-2b) and 5bsus2 (=5b-6b-2b)as chromatic transition 4M 5bM 5M and 4M 5bsus2 5M then  the 3b minor (=3b-5b-7b) as chromatic transition 2m 2bm 3m . This will give all the 5 blue or chromatic notes of the 7-notes of the diatonic scale

B) The 2nd method is to involve the transition ofthe involved natural minor to harmonic minor and double harmonic minor and thus convert the chords 2m 3m , 6m , 7d to 2M, 3M7, 6M7 and 7M7 which again will give all the 5 blue notes 5b 6b 7b 2b 3b

E.g. A characteristoc example is a well known tarditional song Brazilian song  in G major with the arc of chords F#7-B7-Em-Am-D7-G7-C , or in the G major diatonic 7M7-3M7-6m-2m-5M7-1M7-4M where in the refrain from the  more sad to more happy part of the song, the Em (6m) becomes E7 (6M7) and the Am (2m) becomes A (2M) . When from the sad part of the song (3M7-6m-2m) it goes to the happy part with triad of majors 1M7-4M-5M7 , the song it falls the 4M to 4m (to do so the common pair of relative chords 2m-4M is inverted to 2M-4m) which also gives it the chance to translate to 3m (which so far it was 3M7) and thus all 12 chords 7M7-3m7-6m-2m-5M7-1M7-4M and 7M7-3M7-6M-2M-5M7-1M7-4m  occur in the song which also gives all 12 notes in the melody when starting with only the 7 notes.


All the above techniques are very common in harmonies and melodies of Gypsy Jazz , Latin Jazz, traditional Brazilian music etc.

334. THE BEST SIMPLE CONCEPT FOR COMPLICATED HARMONIES IN MULTI TONALITY AND CHROMATIC TONALITY

Here we discuss the idea  of  harmony based on a connected arc of 6 , 7 or even 8 chords in the cycle of 5ths, with mutations from major to minor on it and the involved multi tonality and chromatic tonality .

The concept of chromatic tonality is to enhance the melodiy from the 7 notes of a diatonic scale to the 12 notes of the chromatic.
The concept of multi tonality can do the same but it is done usally here by shifting from the initial diatonic scale e.g. C major here to the A major and E major (notice that the relative chords in melodic relation of the root C major chord is the Am and Em) . All these three major scales are included as triads of major chords in an a connected arc of  7 or 8 chords in the cycle of 5ths (or 4ths). And in particular they are the triads 3M-6M-2M (6 major) and 7M-3M-6M (3 major).

E.g. A characteristoc example is a well known tarditional song Brazilian song  in G major with the arc of chords F#7-B7-Em-Am-D7-G7-C , or in the G major diatonic 7M7-3M7-6m-2m-5M7-1M7-4M where in the refrain from the  more sad to more happy part of the song, the Em (6m) becomes E7 (6M7) and the Am (2m) becomes A (2M) . When from the sad part of the song (3M7-6m-2m) it goes to the happy part with triad of majors 1M7-4M-5M7 , the song it falls the 4M to 4m (to do so the common pair of relative chords 2m-4M is inverted to 2M-4m) which also gives it the chance to translate to 3m (which so far it was 3M7) and thus all 12 chords 7M7-3m7-6m-2m-5M7-1M7-4M and 7M7-3M7-6M-2M-5M7-1M7-4m  occur in the song which also gives all 12 notes in the melody when starting with only the 7 notes.

We must also notice that in such a  connected arc of chords not only the harmonic relation of chords occurs (chords a 5th or 4th apart) but also the melodic and chromatic relation of chords occurs.

The corresponding psychological feelings are

1) Harmonic relation of chords=resolution and nice shift of the melodic theme by a 4th or 5th
2) Melodic relation of chords=ususlly a transition of a major chord to same root minor or upper or lower relative minor , thus a mutation of a happy feeling to a sad and vice versa
3) Chromatic relation of chords=translation of the same feeling a semitone or tone higher or lower



All the above techniques are very common in harmonies and melodies of Gypsy Jazz , Latin Jazz, traditional Brazilian music etc.

The connected arc of chords in the wheel of 4th or 5yh as we said contains pairs of chirds chromatically or melodically related.

So a simple method to compose a song is  to start with melodic themes within one chord or a pair of chords which are not in the major triad of the default diatonic scale 1M 4M 5M , e.g. 2m or 3m or 3M or 6m or 7M or pairs (1M-2m)  (1M-6m), (3M-6m) , (4M-7d) , (3m-4M) , (5M-6m)  etc Notice that a intense oppositions song would start in the chords 2m, 3m ,3M 6m , 7d etc and end in the triad of majors (1M, 4M, 5M)  while a more soft song would start with pairs (X1,X2) with X1 in (2m, 3m, 3M, 6m ,7d) and X2 in (1M, 4M, 5M ) and and then in the happy part  of the song shift to the triad of majors (1M, 4M, 5M). In the melody we translate the melodic themes of one or pair of chords to the next or we invert them. As alternative and even simpler method we start with melodies in one chord or pair of chords in the triad of majors 1M 4M 5M and we substitute one only chord each time with its corresponding lower relative minor or even the same root major hord converted to minor (e.g. instaed of 5M the 5m etc)  and also we modify the melodic theme. This is the couple (sad) part, Then we return to the happy refrain part in the (1M, 4M, 5M) or in the  ( 3M, 6M, 2M)   or in the (7M, 3M, 6M).


As we mentioned in the full chromatic tonality the major chords 1M 4M 5M may turn to minor chords
1m, 4m, 5m and good ways to do it are the next 1) we may turn the 4M to 4m as invesions of the resulotion 1M->4M, thus 1M-4M->4m->1M (see also post 29) . Similarly the 1M to 1m atthe inversion of the resolution 5M->1M->1m->5M. Finally the 5M is turned to 5m in agood way if we temporarily shift to the 7b major diatonic scale which will  turn the 5M to 5m (as 6m in 7b major) and also turn the 1M to 1m (as 2m in 7b major).