201. TRADITIONAL IMPROVISATIONAL FAST DANCING SOLOING GREEK CRETAN (CONDILIES OR DACHTILIES) AND IRISH (REELS) THAT ARE ACCOMPANIED WITH UP TO TWO MAJOR/MINOR CHORDS ONLY

VECTORS, WAVES AND SPIKES

The identification and method of composition of them is based on the next concepts

1) As melody it has 3 layers (Simplicial submelody of the harmony, melodic arpeggio , diatonic chromatic arpeggio or ostinado)

2) Within each chord, it has 

2.0) A single note from the simplicial submelody

2.1) A projected and simplified melodic arpeggio

2.2) The full diatonic chromatic ostinado, which consists from

a) Diatonic chromatic maxima VECTORS

b) Diatonic chromatic RIPPLES or waves or cycles or oscillations

c) SPIKES (jumps with intervals higher than 2nd)

THE ANCIENT MUSICAL THEORY SIMPLE DESCRIPTION OF RAPSODY MUSIC STIL LIVING IN THE AEGEAN ISLANDS LIKE THAN OF CRETE IN GREECE :

Such music was created in ancient times it  is mesmerizing with complicated melodic lines but in reality very simple musical description.

For example for Aegean islands (Greece) improvisational folk melodies (mandinades) condylies) with violin or Lyra, the next factors prevail.

1) "Poetic meters" over the same note sometimes notes up to 8 notes. The density of the notes is high. E.g. with 4 notes per  measure-bar and a beat of 80-100 bars per minute gives a tempo of 320-400 beats-notes per minute.

3) Straight vectors ascending or descending usually of 4 or 5 notes so as to reach a new chord neighborhood.

2) Mainly waves by intervals of 2nds (chromatic) inside intervals of 3rds (melodic, either standing or ascending descending, and usually inside a chord  so as to reach the neighborhood of a new chord. The simplistic sub-melody of such a waving melody is essentially an arpeggio of the underlying chord.

A) THE UNDERLYNG CHORD OF THE SONG IS ONLY ONE AND IS A POWER  CHORD AT ROOT POSITION OF SAY A DIATONIC SCALE (ALTHOUGH IN ANCIENT TIMES THEY DID NOT HAVE THE CONCEPT OF A  7-NOTES SCALE BUT ONLY OF A 4-NOTES SCALE THE  TETRACHORD WHICH WAS A SCALE SPANING ONLY AN INTERVAL OF 4TH INSTEAD OF AN INTERVAL OF 8TH, THUS POWER CHORD WOULD BE THE ROOT POSITION ON THE TETRACHORD). 

B) THE SOLOING IS ANY REPEATING PROGRESSION OF SHORT RYTHMIC MELODIC THEMES WITHIN A TETRACHORD WHICH  IS USUALLY  THE 1-2-2 IN SEMITONES THUS THE FRYGIAN TETRACHORD AT THE 3RD POSITION OF A  DIATONIC SCALE WITH UNDERLYING POWER CHORD AT THE ROOT POSITION OF THE TETRACHORD OR THE 3RD POSITIONOF A MODERN 7-NOTES DIATONIC SCALE. (SOMETIMES ALTERNATING WITH ANOTHER TETRACHORD E.G. THE IONIAN TETARCHORD AT ROOT POSITION OF THE 7-NOTES DIATONIC SCALE , AND IN ANY CASE THE ACCOMPANYING CAN BE ALSO BY THE POWER CHORD AT THE ROOT POSITION OF THE 7-NOTES DIATONIC SCALE IN INSTEAD OF THE 3RD POSITION OF THE DIATONIC SCALE)

EXAMPLE

ΚΑΣΤΡΙΝΟ ΜΟΥ ΦΟΥΛΙ (=αραβικο γιασεμι) (η ΧΑΝΙΩΤΙΚΟ ΜΟΥ ΓΙΑΣΕΜΙ Οταν τραγουδιεται στα Χανια αντι στο Ηρακλειο) ΕΝΑ ΟΜΟΡΦΟ ΤΡΑΓΟΥΔΙ ΑΠΟ ΤΑ ΑΥΤΟΣΧΕΔΙΑΣΤΙΚΑ ΤΩΝ ΡΑΨΩΔΙΩΝ Με την Ειρηνη Δερεμπεη στο θιαμπολι και τον Καρολο Κουκλακι στο μπουγλαρι https://www.youtube.com/watch?v=762B3kiJroY&ab_channel=KarolosKouklakis ΡΑΨΩΔΙΕΣ ΣΕ ΕΝΑ (ΔΙΑΤΟΝΙΚΟΥ ΓΕΝΟΥΣ ΣΥΝΤΟΝΟ) ΤΕΤΡΑΧΟΡΔΟ ΜΟΝΟ ΜΕ ΣΥΝΟΔΕΙΑ σταθερη ΤΟ POWER-5 CHORD στην ριζα του τετραχορδου . Η σε 7-τονικη κλιμακα, ειναι το τετραχορδο σε ημιτονια και ανιουσα 1-2-2 που ξεκινα απο την 3 νοτα (Φρυγιος τροπος) με συνωδεια σταθερη ενα power-5 chord το 3-7-3'. Το πολυ ενδιαφερον με αυτα τα τραγουδια (οπως και με τις περισσοτερες κοντυλιες η δακτυλιες η σαιθιες, η μαντινοδιες) ειναι πως ειναι φτιαγμενες με βαση την θεωρια της αρχαιας Ελληνικης μουσικη και οχι την συγχρονη. Δηλ κανονικα δεν παιζονται σε 7-τονικη κλιμακα αλλα σε 4-τονικη που λεγοταν τετραχορδο. Συνηθως στο διατονικο γενους συντονο (Qurdi, κιουρντι) τετραχορδο δηλ σε ημιτονια σε ανιουσα σε υψος 1-2-2 με ακολουδια απο μικρα ρυθμικα μελωδικα θεματα που επαμαλαμβανονται και συνοδευονται με μια μονο σταθερη συγχορδια τυπου power-5 chord δηλ 1-5-1' (σε ντο ματζορε θα ηταν ντο-σολ-ψηλο ντο) που δεν ειναι ουτε ματζορε ουτε μινορε συγχορδια. Επειδη τετοια τετραχορδα εμφανιζοντα σε μια συγχρονη 7-τονικη κλιμακα στην τριτη θεση (φρυγιος τροπος) το power-5 chord ειναι στην 3η θεση δηλ 3-7-3ψηλο. Στο προηγουμενο τραγουδι το καστρινο φουλι η αντιστοιχη συγχρονη διατονικη κλιμακα ειναι η μι-υφεση, η συγχορδια ειναι η Σολ-Ρε-Σολψηλο και η μελωδια στριφογυριζει κυριως στο τετραχορδο σολ- λα υφεση-σι υφεση-ντο που ειναι στην 3η θεση (φρυγιος τροπος) της μι-υφεση Στην αρχαια εποχη δεν υπηρχαν 7-τονικες κλιμακες μονο 4-χορδα με 4-νοτες σε ενα διαστημα 4ης,και οι μονες συγχορδιες ηταν οι διφθογγες συνηθως 1-5-1ψηλο (power5 chord). Η δε λυρα ηταν μικρη αρπα με 4 μονο χορδες ακριβως σε ενα τεταρχορδο. Ετσι παιζαν τις ραψωδιες (αλλα και οι μαντιναδες ειναι ραψωδια) Συχνα αλλαζαν το κουρδισμα της 4-χορδης λυρας (ιδιο και αυτο σε ολο το τραγουδι) απο το διατονικου γενους συντονο τετραχορδο σε καμια ντουζινα αλλα (εναρμονιου και χρωματικου γενους τετραχορδα) αλλα που δεν ανηκουν στην δυστικη 12-τονικη κλιμακα του Μπαχ και δεν παιζονται στο πιανο η στην κιθαρα μονο στο βιολι, στην λυρα η στο τρομπονι. Συνοδευαν παντα με μια power5 chord. Συνοδευαν σχεδον παντα ολο το τραγουδι με μια μονο μονο συγχορδια που ηταν και μινορε και ματζορε 1-5-1' (π.χ. ντο-σολ-ντο) η και τυπου τριτης αντι πεμπτης 1-3-1' (power3 chord) και διναν τρομερη ελευθερια στους ρυθμικους συνδυασμους στη μελωδια, ενω απο την αλλη δεν χανοντα σε 7-νοτες ειχαν μονο 4-νοτες να παιξουν και ετσι το ταξιμι ηταν ευκολο.Ετσι γινοταν μια ομορφη υπνωτιστικη μεθυστικη μουσικη, και το μη μονοτονο ηταν τα λογια η μαντιναδες της ραψωδιας που ειτε τα επαναλαμβαναν οπως στην ιλιαδα και οδυσσεια ειτε τα σκαρφιζονταν εκεινη την στιγμη αφου η μουσικη ηταν σταθερη βαση. Αρκετα απο τα εγχορδα οργανα μου τα κουρδιζω σε σειρα απο 4 η 6 (αναλογα με το πληθος χορδων) απο διαδοχικες αρμονικες της φυσικης σαλπιγκας . Το power-5 chord εμφανιζεται ως διαδοχικξ σειρα αρμονικων και στην δευτρη οκταβα των αρμονικων η στην 1η οκταβα της φυσικης αρχαιας σαλπιγκας χωρις βαλβιδες (η στο overtones flutes των σκανδιναβων και βορειων που δεν εχουν τρυπες παιζουν μονο με τις αρμονικες) Το ιδιο το κουρδισμα του 3-χορδου μπουζουκιου Ρε-Λα-Ρεψηλο που καταγεται απο την αρχαια ελληνικη πανδουρις (=εξολκληρου απο ξυλο σε αντιδιαστολη με την λυρα που φαινεται ειχε και μηξυλινα μερη ) ειναι επισης μια τετοια συγχορδια power-5 chord, οπως και ενα απο τα πολλα κουρδισματα στο 3-χορδο μπουλγαρι η στο σαζι ,ταμπουρα κλπ. Υπηρχαν δε και παληα τετοια κουρδισματα κρητικης λυρας, οπως ακομα σωζοντα τετοια κουρδισματα σειρας αρμονικων στο βιολι στην σκανδιναβια.

H πιο βασικη αρμονια και κλιμακες βγαινουν απο τις αρμονικες π.χ. στην αρχαια φυσικη σαλπιγκα χωρις βαλβιδες (η τα φλαουτα αρμονικων).

1. Οι αρμονικες (overtones) στην πρωτη οκταβα 1-2 δινουν την τονικη
2. Οι αρμονικες (overtones) στην δευτερη οκταβα 2-3-4 δινουν το power5 chord (και μινορε και ματζορε)
3. Οι αρμονικες (overtones) στην τριτη οκταβα 4-5-6-7-8 δινουν την μειζωνα συγχορδια
4. Οι αρμονικες (overtones) στην τεταρτη οκταβα 8-9-10-11--12-13-14-15-16 λογω του οτι πεφτουν εξω απο την δυτικη κλιμακα του μπαχ δινουν αναλογα με την στρογγυλοποιηση , την διατονικη 7-τονικη κλιμακα, την αρμονικη μινορε (χιτζαζ), την μελοδικη μινορε, την 6-τονικη κλιμακα των μπλουζ, την νεαπολιτανικη (neapolitan) κλπ.

ΣΥΝΟΨΙΖΟΝΤΑΣ ΤΟΠΟΛΥ ΕΝΔΙΑΦΕΡΟΝ ΟΤΙ ΟΙ ΑΡΧΑΙΕΣ ΔΑΚΤΥΛΙΕΣ-ΤΑΞΙΜΙΑ ΠΑΙΖΟΝΤΑΝ ΜΕ ΜΙΑ ΜΟΝΟ ΣΥΓΧΟΡΔΙΑ ΤΥΠΟΥ 1-5-1 ΠΟΥ ΕΙΝΑΙ ΟΥΤΕ ΜΑΤΖΟΡΕ ΟΥΤΕ ΜΙΝΟΡΕ Η ΚΑΙ ΤΑ ΔΥΟ ΚΑΙ ΜΟΝΟ ΜΕΣΑ ΣΕ ΕΝΑ ΤΕΤΡΑΧΟΡΔΟ ΣΥΝΗΘΩΣ ΤΟ ΔΙΑΤΟΝΙΚΟΥ ΓΕΝΟΥΣ ΣΥΝΤΟΝΟ ΣΕ ΑΝΙΟΥΣA ΣΕ ΗΜΙΤΟΝΙΑ 1-2-2.

THE MORE COMPLICATED BUT NOT  ALWAYS MORE ENLIGHTENING DESCRIPTION WITH MODERN SCALES AND CHORDS: 

Such Greek Cretan soloing is very similar to the Irish reels. 

SHORT DESCRIPTION


THERE ARE HUNDREDS OF DIFFERENT SONGS ON THE SAME CHORD-CYCLE  AND THOUSANDS OF DIFFERENT IMPROVISATIONAL SONGS ON THE SAME CHORD-CYCLE.


E.G.

1) 1M


2) 5M7->1M


3) 6m->1M



4) 1M->4M->5M->1M    (Cretan matinodies, kondilies) 
or only 1M (3rd note) ->1M->5M7(5th note)->1M (3rd note)
or only 1M (3rd note) ->1M->1M->1M (3rd note)
e.g. as order of notes in adiatonic scale 
(3 3 3 4 )(3 5 5 5) (4  2 3 4) (5 5 3) (15 syllables) and spans an interval of 4th.
As intervals of a scale they are 1-2-2
Or a different again of cyclic type:
(1'2'3'3')(1'1'2'2')(771'1')(7655)
556671'2'2'1'71'1'1'1'(again 16+14 half syllables  or 8+7 syllables) and spans an interval of 4th.

As intervals of a scale they are 1-2-2
Alternatively the action of the melody can be in the upper minor 3rd and in detail  descending from 3' to 5 (in intervals of semitones 2-2-1-2-2) , or in the lower major 3rd, or in detail from 1' to 3 (in in intervals of semitones 1-2-2-2-1)
as rhythm from 15-syllables poetry
(1M         )
10010100
(5M7)1M
1001010
(combination of anapestik  100 with trochaic 10 )

Other thythms are 

100111010 or a more extreme that spans 3 powers of 2 , 10000011100100
(e.g. in Bardakis castrines condilies) .

DANCING FAST INSTRUMENTAL MELODY
Most often each half line of the poetic line is with 8 notes , thus all the first 8-syllables line 
16 notes, and the 2nd 7-syllables line from 16 notes again or possible 14 notes, in total 32 or 28. This is the dancing fast instrumental melody.
The half-poetic line is the middle melodic theme, and also one measure, that follows the pattern of the above rhythm most of the time, and is translated up or down , and also changing shape. The trasnlations are melodic (intervals of 3rd) harmonic (intervals of 4th or 5th) or more rarely (less than 30% of the cases) chromatic (intervals of 2nd).
But inside each measure and middle melodic theme, there are the micro-melodic-themes that are oscilaltions around one note, most often by intervals of 2nds.
SLOW SINGING MELODY: this is by no means following in syllables the exact pattern of the 15-syllables poetry. Maybe it was in ancient times. But in modern times, is may vary significaly depending on the  emotional state ofthe singer.


In addition to  rhythm, scale and chord progression we need also the statistical profile of the progression of the simplical melodic themes (see post 282) so as to determine the local style of the particular improvisations.
E.g. in Cretan Kondilies (mandinodies)  that have usually only two underlying chords (e.g. 1M->5M7->1M ) this progression during each chord (statistically determined rather than deterministically) defines the local style of the improvisational melody. E,g, 2 simplicial melodic themes for first 1M one for 5M7 and one back to 1M. In total 4 simplicial themes, the first 3 in a kind of variational repetition (translation or inversion) and one last and 4th closing one that may be mutated.

Examples of such progressions of simplicial melodic themes (or Dolphin words) are the next  (each vector-arrow is an oriented interval that fits to a single or more  underlying chord(s)).

Or

Or

Or

etc (See also post 280)

Other determinations of these songs or improvisations;

0) THE HARMONY.

Although the cycle of chords is fixed, the order and duration that these chords are played may vary, from song to song, or even inside the same song ("random" permutation of the chords of the cycle).
E.g. 1M->4M->5M->1M    (Cretan matinodies, kondilies) 
or only 1M (3rd note) ->1M->5M(5th note)->1M (3rd note)
or only 1M (3rd note) ->1M->1M->1M (3rd note)



1) The rhythm:
The duration of the beat is determined by clock-standards. Then each chord of the cycle is determined how many beats has duration. Furthermore, the rhythm is specified as in post 10. Usually, the powers of 2 are utilized. So a triad of chords will have a repetition of a chord in duration. E.g. a cyclic pattern A B C A, of 4 groups of beats so that each chord has equal duration will also determine a variational repetition pattern of the variating melodic themes, usually 3 variations and the last time a resolution.  The melody itself can be classified to the simplicial say in 4 chord-durations, or the normal in 8 chord half durations, or embellishing in 16  chord quarter durations, or fast embellishing  32 , eighths chord durations etc.
Initially, it seems that the rhythm of the main melody was patterned over 15-syllables poetry, with 4+4 beats at the first line of 8 syllables and 4+3 beats at the 2nd line of 7 syllables.
The term mantinodies is quite similar and meanings and methods with the term rhapsody of the ancient poetry of homer (Iliada, Odyssia etc)

E.g. for Cretan mantinodies (condilies)

as rhythm from 15-syllables poetry

10010100

1001010

(a combination of anapestik  100 with trochaic 10 )

2)  The pitch order pattern of the roots of the chords of the chord-cycle.
In general, there are 4 classes:
1)The ascending (happy)
2) The descending (unhappy)
3) The upper cyclic (happily sad),
4) The lower cyclic (sadly happy).

This is a general pitch order pattern which of course has emotional significance: Increasing pitch order in the roots =joy, decreasing pitch order in the roots=sadness.

e.g. as order of notes in adiatonic scale 
3 3 3 4 3 5 5 5 4  2 3 4 5 5 3


3) The pitch order pattern of the induced by the melody harpism (permutation) of the notes of each chord.  

Although the part of the melody accompanied by a single chord may have notes outside the chord, it will have also notes of the chord that it is expected that they have a longer duration. Thus this part of the melody induces a permutation or harpist of the notes of the chord.

4) The variational repetition pattern of the melodic themes as part of the melody accompanied by a single chord.


MORE DETAILED ANALYSIS:


THE MAIN IDEA TO COMPOSE AND IMPROVISE SUCH FAST DANCING SOLOING IS TO RESTRICT THE HARMONY AND USED NOTES TO REALLY SIMPLEST POSSIBLE  SCHEMES AND CONVERSELY ENHANCE THE COMPLEXITY IN WAVING OR ROTATING, VARIATIONAL PATTERNS

In Greek island of Creta they are considered as restrained improvisation, in the sense that each time the instrument player plays them they are a bit different but the overall musical sense and feeling is the same. The term "Condilies" or "dactilies" means in the Cretan language fingering.

See also post 159

CONDILIES=WAVING ROTATIONS INSIDE A VECTOR-CHORD , OR TETRA-CHORD OR PENTA-CHORD OR HEXA-CHORD. (CONNECTED SUBSCALES OF 4,5 OR 6 NOTES AND TOTAL LENGTH AN INTERVAL OF 4th  OR 5th OR 6th)
THE VARIATIONS OF THE BASIC MICRO-THEMES (CALLED "STROFES" OR "GYRISMATA") ARE AS USUALLY TRANSLATION, INVERSION (IN TIME OR PITCH) , EXPANSION-CONTRACTION AND MUTATION

The waving such rotations are part of the melodic personality of "dachtilia" and has a name of the player, area or composer. The "rotations" are called in the Greek language "gyrismata", or "strofes" which means rotations 

Very often the rotational waving inside a vector chord (in Creta it is called condilies as it was played with wind instruments from cane and the thicker rings of it are called Condili)  (e.g. major chord 1-3-5 as root chord of a diatonic scale) is a waving by intervals of 2nds of a full walkthrough of the vector chord 3-4-5-4-3-2-1-1 , which restricted to the notes of the chord is 3-5-3-1 .Other times as cycle waving starting and ending on the same note of the chord (e.g. 3rd middle note). For every type of "Condilies" or "dactilies" there is a "projection trace" of it as an almost  repetitive harping on the arpeggio of an  underlying chord. It is almost certain though that it includes notes outside the arpeggio of the chord.

RHYTHMIC  MICRO-THEMES AND IMPROVISATION OF THEM.
At another side nevertheless, such fast dancing solos have a "projection trace" to the rhythm exclusively as note durations and position in time irrespectively of what pitch is each note. Then the melodic micro-themes or "rotations" ("gyrismata" or  "strofes") become rhythmic micro-themes, and the melodic improvisation of them becomes rhythmic improvisation. Such rhythmic improvisations obviously could be carried out with single note or on percussion instrument only (see Djembe music). When one tries to compose or improvise such melodic "rotations" the underlying rhythmic micro-themes and their variations are of primary importance as they choose where in time you put a note and how long it would sound. having chosen the rhythmic micro-themes and their variations will greatly make easy the final choice of the pitch too of each not and the melodic patterns. The rhythm here will be like a road of the mountains where we eventually drive our melodic vehicle , and this "road" is not straight by changing directions and slopes. The rhythmic variations are similar to the melodic themes variations: They have inversions in time, translation of patterns in rhythms increased or decreased by powers of 2, and mutations.



Another insight about Condilies or Dachtilies  is the next: Let us remember the well known Andalusian cadenza patterned on the sub-scale 1-2-2 semitones (See post 17 and also above about Ancient Greek syntono tetrachord ) which is played by chord e.g. iv->V->IV->III . Here for condilies we  may have a melodic version of it where instead of chords we play waving patterns around the notes of pitch order 1-2-2 in semitones . 
Or so as to have a pure interval of 5 , 1-2-2-2 or 2-2-2-1 . And also an interval of 
minor 6 : 1-2-2-2-1 

If we combine the 6-notes  1-2-2-2-1 with the 4 notes 1-2-2 at one semitone distance we get the 1-2-2-2-1-1-1-2-2 which is a modulation to 2 different diatonic scales. We may also combine a diatonic scale with a 6-notes blues scale by having the 4 note of the major diatonic scale with a sharp and apply wavings by intervals of 2nd going up and down it.
Or we may combine two or 3 diatonic scales deriving a bebop 8-notes or 9-notes scale. 

Other examples of subscales from here http://mantolinokrhth.blogspot.com/2012/08/blog-post.html give in semitones

1-1-2-2-1
2-2-1-2-2-1
2-1-1-1-2-2-1-2  (Bebop dominant)
1-1-1-2-2-1
2-1-1-1-2-2

It is used as we notice the Bebop dominant scale as in post 139 which fas interval structure in semitones   2-2-1-2-2-1-1-1

If we want to avoid thinking about chords or arpeggios when playing, improvising or composing such solos, then the simplest idea is the triads of notes or intervals of 3rds with all their intermediate notes in some scale. By alternating such major and minor intervals of 3rds we may give the melody an underlying good harmonic content (see also post 159 about vector-intervals)


Somewhere in the wavings by 2nds we double the speed of waving for 2-3 such oscillations
Usual rhythms are, Cretan dance (pidichtos) and reels dancing (1110). But also (1010100010001000)

We very often  in condillies may use the descending sequence of notes 1'-7-6-5-4-3 as steps of the diatonic scale (in semitones 1-2-2-2-1) in 3  melodic triads, one descending and two cyclic :  1'-1'-7-6 the  5-7-7-6-5,  3-4-4-4-5-4-4-3 (chord progression of 5 steps  on 3 chords  I-IV-V-IV-I) Or it could be with three waves one   ascending and two  cyclic 3-4-5   6-7-6-6-5-5    3-4-4-4-5-4-4-3 and with chord progression of 5 steps on three chords  I-IV-I-V-I
As harmony it is usually a permutation of the the chords I, IV,V. But as melody it is usually three melodic triads (vector intervals of 3rds see post  208) two minor and one major. 
The rhythm is from a 15-syllables poetry so the first two minor/major melodic triads count 8 syllables (beats) while the last melodic triad or last two melodic triads count  7 beats or syllables. Nevertheless the melody of the voice and the counter melody of the instrument  maybe different although on the same sub-scale (usually in semitones 1-2-2-2-1 or in steps of the scale 1'-7-6-5-4-3  )  and with the same chord progression on the I, IV V. In some cases the melody of the voice may use only 2 or only 1 of the  melodic triads with a sub-chord progression  fewer chords , but from the same chord progression.
We may count each of the poetic lines, the 1st of 8 beats and syllables and the 2nd of 7 beats or syllables as 1) The Upper cycles 2) the Lower cycles 3) The ascending 4) the descending,
Obviously the most sad are the Descending-Descending and the most joyful the ascending ascending. While interpediateare e.g. Descending-upper cycle (sad) , or Upper-cycle-upper cycle (a little happy) or Ascending-upper-cycle (a bit more happy) , lower cycle - lower cycle ( a little happier) and ascending-lower cycle (much happier).

POETIC MEASURE FOR THE PATTERN OF REPETITIONS IN DACHTILIES (CONDILIES). 

The dactilies are correlated with poetic improvisation as well, called in Creta mandinades (mandiniades) that are usually pairs of poetic lines in iambic 15-syllables poetic measure. 
Somehow all dactilies (condilies) could be considered "the same big tune" with unlimited variations, open to continuing by the players and also with known words (maninades) but also open to unlimited variations and be continued by the players and singers. 
This is similar to songs of Portuguese fado, where a single chord progression patterned on the intervals 1-2-2 makes an unlimited pattern of tunes and variations. 
Here in dactlilies (condilies) also there are unique characteristic morphological patterns which are 2 or 3 waving by intervals of 2nd cadenzas of 3-4 notes , and all of them within an interval of 4 or 5th (1-2-2 or 1-2-2-2).
This some how determine repetition patterns of rotations (gyrismata or strifes) .

A good source for the pattern of repetitions of the melodic themes is the syllables poetic measure.

For example of an underlying poem exists for lyrics , with syllables measure pairs of lines with 8 syllables the first and 7 syllables  the second, (8+7=15-syllables poetic measure) , the notation is repetitions of 8 and 7 beats one pause bear and then again.

Now the correspondence of the poetic measure to the melodic measure can be

1) Each line is one  8-beats musical measure of the melody

or

2) Each line is two consecutive 4-beats musical measures of the melody.

In the first case we have two repetitions of melodic themes one by 8 notes and one almost repeated by 7 notes. In the second case we have a repetition three times of   a melodic theme of 4-notes and beats, which correspond to the two half parts of the first line and one first half part the second line while after these three repetitions occurs also a different melodic theme of 4 beats and 3 notes and one beat pause.

The harmonization of the Condillies in the  5-chordo 1-2-2-2 is not a iii minor chord (1-2)-(2-2) (e.g. Em in C major scale or F#m in D major) but two major chord V=5M and I=1M (G-C in C major or D-A in D major), Where the upper -(2-2) part is the lower major 3rd of V=5M chord and the lower (1-2)- is  the upper minor 3rd ofthe I-1M chord. In general this might be a way also to substitute a minor chord in a melody in a diatonic scale with two major chords. If we want to accompany it with intervals of 5th strictly speaking it should be two intervals of 5th 4-1! and 1-5 as steps of the diatonic scale. An harmonization of the Condillies in the 4-chord 1-2-2 , it could be an upper part -(2-2) which is the lower major 3rd of the IV=4M chord (in D major it would be G major) and the (1-2)- (overlapping with the 2-2 part) it would be the upper minor 3rd of the I =1M chord (In D major the D major chord).

Of course in some cases depending on the waving we may use the chords progression 
I->V->IV->I, where the 3rd chord is of very short duration.




In Greek Cretan such soloing (dachtilies) only up to two major chords are used as above. 
But if someone wants a more free composition and improvisation of them then minor chords can be included as below.


If we want to accompany such condillies  melodies not with one power chord but with major or minor triads then they should be as few as possible e.g. 2 or 3. For happy melodies obviously, they are the I, IV, V. According to the degree of sadness we want to impose, we substitute any of the major chords with its lower minor relative. In other words  vi for I, ii for IV and iii for V. 

About the symbols: In a C major scale the symbols denote the next chords

I=1M=C
ii=2m=Dm
iii=3m=Em
IV=4M=F
V=5M=G
vi=6m=Am
vii=7d=Bdim

So the possible combinations are 

I, IV, V   or only I, V

vi , IV, V or only vi, V

I , ii, V 

I, IV, iii   or only I, iii

iv , ii, V or only iv, V

I , ii, iii or only I, iii

vi, IV, iii   or only I, iii

vi, ii, iii   or only vi, iii


We must understand that the dancing melodies of melodic improvisation that are of a high degree of freedom in changes and are accompanied only by a root power chord 1-5-1' are a different class of melodies of harmonic improvisation  that are  those that during not very short intervals of time are accompanied by a 3-notes chord of the scale. An example of a melody that the only reasonable accompanying chord is a root power chord is to go up and down several times all the 7 notes scale and fast enough. Theoretically, one could accompany it with very fast changing 3-notes chords but exactly because it is very fast changing it is meaningless and it is better only a root power chord. On the other hand, singing melodies that can be divided into a small number and of significant duration time intervals during which they have clear 3-notes major or minor or diminished accompanying chord (preferably with another instrument than the soloing instrument) have better harmony if accompanied by such major or minor chords rather than a single root power chord. 

A basic "signature" of a condilia is the simplicial submelody basic melodic theme as shape and pattern,which of course is parallel to the chord-progression pattern as rhythm and repetitions. 

Examples of Cretan Condilies

https://www.youtube.com/watch?v=xqc92Y9zPqA

https://www.youtube.com/watch?v=UDmwVbhA9No

https://www.youtube.com/watch?v=jXok6nsT17M

https://www.youtube.com/watch?v=ejmMrb2r2ic

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

https://www.youtube.com/watch?v=AjH68cAuoD8

http://mantolinokrhth.blogspot.com/2012/08/blog-post.html

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



Irish Reels

https://www.youtube.com/watch?v=njgAjaAGebw
https://www.youtube.com/watch?v=N2iHNSlJMfc


HERE WE LIST AND DISCUSS SHORT SUBSCALES OF THE CHROMATIC 12-TONE SCALE THAT CAN BE USED FOR REPETITIVE SOLOING. SOME OF  THEM ARE KNOWN 4-CHORDS 5-CHORD 6-CHORDS OR SIMPLY CONNECTED PIECES FROM BEBOP SCALES DERIVED FROM THE SUPERPOSITION OF 2 OR 3 DIATONIC SCALES.  THIS DOES NOT MEAN THAT THEY ARE MET ALL OF THEM IN CRETAN DACHTILIES AND IRISH REELS BUT THAT CAN BE USED FOR OUR OWN INSPIRED COMPOSITION AND IMPROVISATION 

3-NOTES SUBSCALES (TRIADS E.G. VECTOR-INTERVALS OF 3 ), 16 IN TOTAL

THE TRIADS ESPECIALLY THE ONES OF LENGTH AN INTERVAL OF 3 (vector-interval of 3) ARE THE MAIN BUILDING BLOCK OF HARMONIC-MELODIC IMPROVISATIONS AS ALSO CHORDS ARE BUILD FROM INTERVALS OF 3.

WHEN WE SHIFT A MELODIC THEME BY A CHROMATIC  INTERVAL OF 2 USUALLY WE APPLY A TRANSLATIONAL-VARIATION. WHEN WE SHIFT BY A MELODIC  INTERVAL OF 3 USUALLY WE APPLY AN INVERSION -VARIATION. WHEN WE SHIFT BY AN HARMONIC  INTERVAL OF 4 OR 5 USUALLY WE APPLY A MUTATION-VARIATION . IF WE STAY IN THE SAME INTERVAL WE HAVE A ROTATION OR PERMUTATION VARIATION

By alternating major and minor such vector-intervals of 3 we impose also underlying hidden harmony of triad chords

Chromatic triad

 1-1

Melodic triads:

minors 2-1,  1-2,

Majors 2-2 , 1-3, 3-1,

Blue :diminished chord 3-3

2-4, 4-2

(When improvising it is familiar melody if we alternate major-minor such vector-intervals of 3 because in diatonic scales this is the case and also in the formation of major and minor triad chords)  

Harmonic triads

2-3 , 3-2,

4-1, 1-4 ,

Chords: major:4-3, minor: 3-4.

 augmented chord 4-4

4-NOTES SUBSCALES  (TETRADS) WITH TOTAL LENGTH 5 0R 7 SEMITONES

6+10 IN TOTAL

The most common are 2-2-1, 1-2-2. 1-3-1, 2-2-3, 3-2-2

TOTAL LENGTH 5 SEMITONES, 6 IN TOTAL

1-2-2, 2-2-1, 2-1-2,

3-1-1, 1-1-3, 1-3-1

The 1-1-3  is called by Aristoxenus the tonal tetrachord of the Chromatic generation and it exists in the double harmonic minor scale.

TOTAL LENGTH 7 SEMITONES, 10  IN TOTAL (We call such subscales vector-chords as they contain the first and last note of 3-notes chord)

4-2-1, 2-4-1, 1-2-4, 1-4-2,

3-2-2. 2-3-2, 2-2-3

1-3-3, 3-3-1, 3-1-3

We must notice here that according to Aristoxenos (see post 25 page 40 of the manuscript) in ancient Greece there were the tetrachords (4 strings of the lyra) of total range an interval of 4 (5 semitones) that were tuned outside the Back 12-notes scale as follows

Enharmonic   generation 

1/4 of tone -- 1/4 of tone --2 tones

The closest in Bach scale would be or 1-1-3 in semitones

Chromatic generation

Soft: 1/3 of tone -1/3 tone - 11/6 tone=about 2 tones

The closest in Bach scale would be  or 1-1-3   in semitones

3/8 tone --3/8 tone --7/4 tones

The closest in Bach scale would be  1-1-3  in semitones

tonal    1-1-3 in semitones

Diatonic generation

Uniform: 1-3/2-15/6 semitones

The closest in Bach scale would be  1-2-2  in semitones

Syntono  1-2-2 in semitones

5-NOTES SUBSCALES (INTERVALS OF 5) TOTAL LENGTH 7 SEMITONES 18 IN TOTAL

(We call such subscales vector-chords as they contain the first and last note of  a 3-notes chord)

1-2-2-2 (=a vector minor chord)  ,     2-2-2-1(=a vector major chord),      2-1-2-2(=a vector minor chord),    2-2-1-2=(=a vector major chord)

The 1-2-2-2 might be called the syntono 5-chord of the Diatonic generation according to the terminology of Aristoxenus for the ancient Greek music (actually it is mentioned the syntonon tetrachord 1-2-2)

1-1-2-3=(=a vector major chord),   1-1-3-2,  2-3-1-1, 3-2-1-1,

The 1-1-3-2,  2-3-1-1  might be also called tonal 5-chords of the Chromatic generation in the the terminology of Aristoxenus for the ancient Greek music (actually it is mentioned the tonal tetrachord 1-1-3)

1-2-1-3(=a vector minor chord),  3-1-2-1(=a vector major chord),   1-3-1-2(=a vector major chord) , 2-1-3-1(=a vector minor chord),

1-2-3-1(=a vector minor chord),   1-3-2-1(=a vector major chord),

1-1-1-4(=a vector minor chord), 4-1-1-1(=a vector major chord), 1-4-1-1  1-1-4-1

We will formulate rules of combinations of intervals of 1,2,3,4,5,7 semitones  (Intervals of 2 of 3 of 4 or of 5 as it is used to say) so as to compose beautiful melodic themes.

Obviously usually intervals of 1, 2 or 3,4 semitones are played horizontally on a single string while intervals of 3,4 of 5 of 7 are played vertically among strings. 

(3,4)

1) Combination of intervals of 3, in other words of 3 or 4 semitones

We combine the 3+4=7 mostly as it gives arpeggios of minor major chords ans rarely the 3+3=6 and 4+4-8 that give arpeggios of diminished and augmented chords.

We also alternate the 3+4 with the 4+3 as so it  mainly in the chords of a diatonic scale.

(3,4-5)

2) Combination of intervals of 3, in other words of 3 or 4 semitones and intervals of 5 in other words of 7 semitones.

We combine by alternating them around the 5 : 3-5-4 and 4-5-3, 4-5-3-5-4 etc

(3,4-7)

3)  Combination of intervals of 4, in other words of 5 semitones and intervals of 5 in other words of  7 semitones

Similarly for the 7 : 3-7-4 and 4-7-3, 4-7-3-7-4 etc

(5-7)

4)  Combination of intervals of 4, in other words of 5 semitones and intervals of 5 in other words of  7 semitones

We alternate 5 and 7 : 5-7-5 etc

 (5-5)

5)  Combination of intervals of 4, in other words of 5 semitones

We avoid repetitions of 5

6)  (7-7)

Combination of intervals of 5, in other words of 7 semitones

We allow up to 3 repetitions  of 7 7-7 , 7-7-7

(1,2-3,4)

7) Combination of intervals of 3, in other words of 3 or 4 semitones and intervals of 2 in other words of 1 or 2 semitones

We combine 1 freely with 3, 4  1-3, 1-4 as it gives intervals of minor 3 and of 4 that exist in arpeggios of major minor chords.

(1,2-5)

8) Combination of intervals of 4, in other words of 5 semitones and intervals of 2 in other words of 1 or 2 semitones

We  combine only 2 with 5 2+5 =7, 5+2=7  as it gives intervals of 5 that exist in arpeggios of minor and major chords.

(1,2-7)

9) Combination of intervals of 4, in other words of 5 semitones and intervals of 2 in other words of 1 or 2 semitones

We combine freely the 1, 2 with 7  1+8= 2+7=9 as it gives intervals of 6 that exist in arpeggios of (inverted) minor and major chords.

10) (1,2-1,2)

We combine freely 1-2 and 2-2 as it gives intervals of 3 of the major minor chord arpeggios

Here is a group of musicians playing simultaneously Cretan codilies and Irish reels over the same chord progressions , for dancing

https://www.youtube.com/watch?v=hiksW0XdFg4

THE KEY-WORD HERE IN THE 4TH GENERATION DIGITAL MUSIC FOR THE MUSICAL-THEORETIC IDEAS OF THIS   POST (AS FAR AS MORDEN SOFTWARE FOR MUSIC MAKING IS ) IS MELODY-SEQUENCERS AND ARPEGGIATORS

THE TERM  SEQUENCER MEANS HERE A LOOP OR RHYTHMIC CYCLE OF   A  MELODIC THEME THAT IS VARIATED INTERACTIVELY BY THE USER  IN A MELODIC SEQUENCER.

THERE MANY GOOD SOFTWARE PROGRAMS FOR THIS COMPOSITION AND IMPROVISATION LIKE FUGUE MACHINE, YAMAHA MOBILE SEQUENCER, THUMPJAM ETC. ALSO ARPIO  AND ARPEGGIONOME FOR GENERAL ARPEGGIOS ALTERNATED WITH MELODIC IMPROVISATIONS

200. MULTI-OCTAVE SCALES THAT GIVE EXACTLY THE NOTES OF A DIATONIC SCALE AND ARE MADE EXCLUSIVELY FROM INTERVALS OF 3,4,5,7,8,9 SEMITONES.

We already know  such scales E.g. the Wheel of 4ths or Wheel of %th and the Wheel of alternating major minor 3rds posts 32 , 79 . Also the scales in posts 184 ,185 ,186, 190.

More abstractly we  may include them in the general scheme of MULTI-OCTAVE DIATONIC SCALES (IN THE SENSE THAT GIVE WHEN REDUCED TO A SINGLE OCTAVE EXACTLY THE NOTES OF THE DIATONIC SCALE) BUT ARE MADE EXCLUSIVELY  NOT FROM INTERVALS OF 2NDS BUT OF INTERVALS OF 3RDS, OR COMPLEMENTARY 6THS , 4THS, AND 5THS (OR IN SEMITONES 3,4,5,7,8,9).

They are used for 

1) Alternative tunings of string instruments

2) Schemes of  melodies centers to improvise around theme waving patterns.

We enumerated below some more such scales.

199. ΤΗΕ BEST DESIGN FOR AEROPHONE END-BLOWN (WITH FIPPLE) FLUTES.COMPARISON OF GERMAN RECORDERS, IRISH WHISTLES, CHINESE SUCH FLUTES AND QUENAS-LIKE PINQUILO OF ANDES

BEST DESIGN FOR AEROPHONE END-BLOWN (WITH FIPPLE) FLUTES.COMPARISON OF GERMAN RECORDERS, IRISH WHISTLES, CHINESE SUCH FLUTES AND QUENAS-LIKE PINQUILO OF ANDES .

We are accustomed to the traditional design of the aerophone end-blown flutes with fipple , like recorder , by big companies like Hohner , Yamaha etc and we have the illusion that it is an optimal design. This is by far not true.

Some obvious disadvantages of the classical recorders are the next

1) The sound hole of the fipple at the tenor (C4) or even alto (F4) size has very short longitudinal length and in total it is of rather small area, which makes it difficult to make sound at the lowest root note . And when the sound is made we have to blow drastically at lower strength compared to the other notes and it is a sound of very low volume. In addition a little only if we increase the blowing strength it mutates to a note of the next octave which makes in total unstable.

This disantange has been corrected carefully by the Irish low D4 and C4 folk whistles. The sound hole is of greater longitudinal length

2) The holes are of small size which makes a continuous glissandi from say a high note to the same note one octave lower very difficult are almost impossible. Small size holes also give lower sound volume and a bias to higher frequencies, that it is not good for the lowest octave. Small holes are convenient for very fast melodies like Irish reels and Cretan condyles because the are less probabilities of finger covering errors. But such very fast melodies are rather rare in the general context of music.

This disadvantage does not exist say in Incas quenas of Andes folk music , that have large holes which give louder sound and easy sharps-flats and octave glissandi.

This somehow was discovered by Bohm in his modern concert Bohm flute (that is large diameter holes are better ) but because of the keys over them the ability of glissanti and rolling around the holes has been lost. In addition modern analysis for optimal designs has proved that the position of the keys of the modern Bohm concert flute are not really the best as the intuitive linearity of the pitch is lost and there are designs that correct it but they sell such flutes for more than 20,000 dollars!

3) The diameter of the recorder tube is rather small and the ratio total length to average diameter is rather high which is an advantage for the higher octaves but disadvantage for the lower octave and makes mutation to higher harmonics rather unstable. To correct this the recorders have inverse conical diameters and also small barrel-like thicker walls after the sound hole and before the end of the tube. This also makes the total length less. Nevertheless this requires more blowing for the same volume sound, and the perfect sinusoidal harmonic sound is lost . Such smaller average diameters give a sound with bias to higher frequencies and of low volume. The idea to include 3 octaves to the same flute is not really good as only at the first two octaves the playing is easy and symmetric . Better use flutes of different sizes and scales for higher octaves, and keep a smart design for an end-blown flute for only 2 octaves.

Such disadvantages do not exist in Incas quenas that have wider diameters and thus low ratio of length to diameter. Wider diameters will make the higher octaves harder, but that is why they have a thump hole almost at half of the length so that with partial holing of it they ignite the 2nd harmonic and make the second octave easy. Irish whistles do not have such thump hole because they do not need it as they have narrower diameters compared to quenas but larger compared to recorders

4) Besides the thump hole there is an extra hole in recorders , in total 8 holes, which allow for playing to modes of the diatonic scale , the ionian and the dorian, but in overall it is a confusing redantuntly complicated system to play straight and in a minimal way a diatonic scale . The best minimal system of holes to play a diatonic scale is of course only 6 holes in front , which is more or less a universal preference all over the planet (Chinese, Incas, Irish , Greece, Japan, Africa, Scandinavia etc) Irish whistles are a perfect example of it. The next minimal number of holes (to play a diatonic scale) is the 6+1 system with an additional thumb-hole (often called "soul" as it doubles the frequency) and it necessary only when the diameter is rather large (ratio of total length to diameter rather low) which requires partial holing on the thumb to excite the 2nd harmonic and play easily with almost the same blowing strength the 2nd octave.

After these realizations and combining the corrections of such design inefficiency that have already been discovered and implemented by various countries and their folk ethnic music (Irish, Greek, Andes, Chinese, etc)

 In winds there two types of impedance a) the vibration impedance responsible of propagating the vibration from the air column of the mouthpiece to the air column of the tube,and then outside the tube b) The air-flow impedance which is the resistance of the flow of the air. Large bore tubes have reverse effects on the two types of impedance: They increase the vibration impedance because a larger mass of air must vibrate , but they decrease the air-flow impedance because lower flow speeds are necessary to drive the blowing outside the tube compared to thin bore tubes. The air-flow impedance is by far of larger effect on the felt "resistance in playing and producing sound compared to the vibration impedance. 

A summary of a best such design is

THE BEST DESIGN FOR END-BLOWN FLUTES WITH FIPPLES

1) CONSTANT DIAMETER TUBE AS THE GOAL IS OPTIMAL FUNCTIONING AT ONLY TWO OCTAVES AND A PERFECT HARMONIC SINUSOIDAL SOUND

2) MEDIUM TO LARGE DIAMETER OR RATIO OF TOTAL LENGTH TO DIAMETER SO AS TO HAVE A STABLE AND ROBUST SOUND AT THE FIRST OCTAVE WHERE MOST OF THE ACTION IS INTENDED TO TAKE PLACE. THE CHOICES OF INCAS AND ANDES QUENAS AND SLIGHTLY ONLY NARROWER DIAMETER BUT LARGER THAN THE IRISH WHISTLES DIAMETERS IS A GUIDE FOR THIS. THIS RATIO TUBE-LENGTH/BORE INTERNAL DIAMETER SHOULD NOT BE LESS THAN 20 OTHERWISE THE 2ND OCTAVE WILL BE SERIOUSLY OUT OF TUNE IN THE HIGHER NOTES. (THIS IS THE MAIN REASON WHY THE NATIVE AMERICAN INDIAN FLUTES DO NOT PLAY A 2ND OCTAVE AS THE HAVE SUCH RATIO LESS THAN 20 . IF SOMEONE INSISTS IN HAVING THIS RATIO LESS THAN 20, THEN WITH APPROPRIATE MOUTHPIECE (e.g. very narrow layer of air thus very high speed of air falling on the edge of the fipple or fipples with membrane [see post 243] ) HE MIGHT BE TO PLAY A 2ND OCTAVE BUT HE MIGHT ALSO NEED SPECIAL MODIFIED FINGERING. E.G. At about 24 celsius degrees temperature, the speed of sound is 345 meters/second and for the frequency 587.33 of high D, D5 the half-wavelength is 29.37 cm. So a high D5 whistle normally has length 29.37, and the minimum ratio 20 of the pipe-length/bore internal diameter gives a maximum internal diameter for the pipe of 14.68 mm !) CONVERSELY WHISTLES WITH LENGTH/BORE INNER DIAMETER RATIO LARGER THAN 48 WILL HARDLY HAVE A FIRST OCTAVE FROM THE 1ST HARMONIC BUT ONLY 2ND OCTAVE AND HIGHER FROM THE 2ND HARMONIC AND HIGHER. MANY OVERTONE FLUTES LIKE GUJARA WHICH HAS SUCH RATIO 55 BELONG TO THIS CLASS. WE DISCUSS AT THE END OF THIS ARTICLE SUCH CASES OF DIATONIC-OVERTONE WHISTLES. Normally whistles with the intention to play robust and mainly in the first octave should not have L/B ratio larger than 28.

3) LARGE SIZE HOLES. A GUIDE IS THE SIZE OF THE HOLES OF ANDES QUENAS THAT ARE LARGER EVEN COMPARED TO THE IRISH WHISTLES THAT ARE OF COURSE ALREADY OF LARGER HOLES COMPARED THE RECORDERS. THIS ALLOWS FOR EASY SHARPS AND FLATS BY PARTIAL HOLING AND SMOOTH GLISSANDI OF A FULL OCTAVE. THERE IS THOUGH ONE CASE THAT LARGE HOLES ARE NOT THE BEST WHEN VERY FAST MELODIES ARE PLAYED WHERE SMALLER HOLES ARE MORE CONVENIENT NO TO MAKE FINGER-COVERING MISTAKES. BUT SUCH VERY FAST MELODIES ARE RATHER RARE. ALSO TOO LARGE HOLES FOR SOPRANO WHISTLES MAY RESULT IN TO NON-TUNED AND DIFFICULT 2ND OCTAVE.

4) A FIPPLE OF THE TYPE OF IRISH WHISTLES WHICH IS LARGER THAN THE FIPPLES OF RECORDERS CHINESE RECORDERS AND ANDES PINQUILAS. THE SOUND HOLE OF THE FIPPLE SHOULD BE SLIGHTLY ONLY LESS THAN THE SIZE OF THE HOLES ON THE TUBE.

5) IT IS BEST TO HAVE THEM TUNABLE AND WITH AN ABILITY TO CHANGE THE FIPPLE MOUTHPIECE WITH A RIM-BLOWING MOUTHPIECE AS IN QUENAS OR JAPANESE SHAKUHACHI OR CHINESE XIAO FOR VERY SKILLFUL PLAYERS OF RIM-BLOWING MOUTHPIECES WHICH ALLOWS FOR MORE CONTROL FROM THE PLAYER.

6) WE MAY ADOPT THE CHINESE TRICK OF DIZI FLUTES OF AN EXTRA HOLE COVERED PERMANENTLY BY A MEMBRANE E.G. ORDINARY TRANSPARENT OR NOT PLASTIC TAPE, ANYWHERE BETWEEN THE SOUND HOLE AND THE FIRST NOTE HOLE. THIS HOLE IS NOT USED TO PLAY A NOTE BUT ONLY TO MAKE A SPOT OF VERY THING WALL OF THE TUBE WHICH VIBRATES AND MAKES THE OVERALL SOUND MORE SWEET. IN ADDITION IT MAKES THE FIRST OCTAVE MORE STABLE NOT TO MUTATE TO THE 2ND OCTAVE ACCIDENTALLY.

IT SEEMS THAN MANY VERY EXPERIENCED HANDCRAFTED IRISH WHISTLES MAKERS TURN TO SUCH A DESIGN EVEN FOR D5 WHISTLES AND THE PRICES THAT APPEAR ARE FROM THE HIGHEST THAT ONE CAN FIND FOR IRISH WHISTLES.

Greek such flutes that are called souravli in Greece and habioli or thiaboli in Creta had such a design but gradually it was lost by the influence of the German recorders.

I have made plenty many such optimal design end-blown flutes with fipple from PVC. From Bb3 , B3, C4, D4, E4 F4 , A4 F4 Bb4 C5 to D5 .

I have used for the body the designs of Andes quenas with large diameter and large holes 6 front plus 1 thump , while I have used ready-made Irish whistles fipples. The results is a sound and easy playing better than the German recorders , better (deeper and more stable in the first octave ) than the Irish whistles and easier to play compared to Andes quenas. Compared to Irish whistles they have deeper ,louder and more stable sound in the first octave but more difficult sound in the second octave , that is why one must use partial holing by the thump hole to make it adequate easy. Compared to recorders they have a deeper and more bass sound stable and loud first octave and abilities of easy sharps flats and octave glissanti. Compared to Pinquilo of andes (like quenas with fipples) they have more bass sound as the sounding hole of Irish whistles is rather larger than the sounding hole of Bolivian Pinquilo.

The opening of the holes is by the acoustics of the perfect pipe. In other words  The reduction of the length of the  pipe so as to make the sound of pitch higher by one semitone is (1/2)^(1/12)=94.38% shorter. While so as to make sound of pitch one tone higher is (1/2)^(1/6)=89.08% shorter. This means that the distances of the holes become shorter as we go closer to the mouthpiece by a quantitative rule similar to that of the frets in the guitar.
Nevertheless because these calculations are for cutting vertically the pipe, while we just open holes, there should exist a correction to it, and the correction for holes at about a fraction of the  internal diameter of the pipe, is the we make the hole closer to the mouthpiece by about 80%-83% of ID where ID is the internal diameter of the pipe. Probably this empirical correction formula can be refined to one that  the correction is less the higher the pitch of the hole thus a formula like correction=(0.8*ID)/(a*pitch_of_the_hole) , and the coefficient a is again to be empirically found by experiment. Of course in practice we cut the pipe length at the correct initial note and then for the first highest pitch hole we just make a small hole about there (taking in to account the above correction) and then we widen (which means that we raise the pitch) it it till we reach the correct pitch.
 If we want all the holes to be of less diameter as in recorders we start the first (lower pitch) hole closer to the mouthpiece than above estimations and we proceed.   The converse if we want all the holes of larger diameter.
Other practical rules for opening the holes as we move from the lower to the higher pitch holes involve measuring the relative distance  of the holes for tones,semitones, etc that we have opened so far and repeating them by shortening them a  little as we move to higher pitch holes. Or if we already have another flute that we have successfully made and well tuned, we copy the holes distances.

High chimneys in holes (e.g. by thick walls tube or by branched tubes) lower the pitch.

Some flute makers prefer equal distance holes , for the convenience of the fingers, which will mean that the diameter if the holes will become larger as we go closer to the mouth piece. In general the thickness of the pipe plays also a role.
More thick walls pipe more bass the sound and shorter the length and holes closer to the mouthpiece . If we utilize inverse cone pipe, in other words larger diameter closer to the mouthpiece and shorter at the end (as with Clarke whistles ad German recorders) , this will mean shorter length and holes closer to the mouthpiece , but also more blowing.
The size of the sound-hole at the mouthpiece is also very important. It is a good rule to make it (e.g. square or circular) but as a percentage of the size of the internal diameter of the pipe (e.g. circular of diameter 2R equal to the half the internal diameter of the pipe 2R=ID/2 or in general 2R=aID 0<a<1.
 E.g. a=33%-66% A good practical rule for a is to be so that the size of the sound hole is the average size of the finger-holes. The larger the sound hole the higher the pitch, but also the more breathy the sound, good for the first octave but difficult 2nd octave. The shorter the sound hole the lower the pitch , easier 2nd octave but very low volume 1st octave , which easily may jump in an unintended way to the 2nd octave. Also of the sound hole is not rectangular but an orthogonal shape, if the length along the axis of the pipe  is longer than the side vertical to the axis of the pipe, then the sound is more sweet and breathy. If it is conversely  the length along the axis of the pipe  is shorter than the side vertical to the axis of the pipe, then the sound (as it is usually in Yamaha and Hohner recorders and low D Irish whistles ) is more acute like Shakuhachi sound, and the first lower octave is more unstable. E.g. if  the short side of the orthogonal sound hole , parallel to the pipe's axis is r then the vertical longer side is 2r and 2r=ID/2, where ID is the internal diameter of the pipe.
If ones what to have easier 2nd octave than 1st octave, then a square hole not larger than 1/3 of the ID of the tube is a good choice while the finger holes can be larger.

Open cylindrical tubes resonate at the approximate frequencies:

${\displaystyle f={nv \over 2L}}$

where n is a positive integer (1, 2, 3...) representing the resonance node, L is the length of the tube and v is the speed of sound in air (which is approximately 343 metres per second [770 mph] at 20 °C [68 °F]).

A more accurate equation considering an end correction is given below:

${\displaystyle f={nv \over 2(L+0.8d)}}$

where d is the diameter of the resonance tube. This equation compensates for the fact that the exact point at which a sound wave is reflecting at an open end is not perfectly at the end section of the tube, but a small distance outside the tube.

(See https://en.wikipedia.org/wiki/Acoustic_resonance )

A closed tube will have approximate resonances of:

${\displaystyle f={nv \over 4L}}$

where "n" here is an odd number (1, 3, 5...). This type of tube produces only odd harmonics and has its fundamental frequency an octave lower than that of an open cylinder (that is, half the frequency).

A more accurate equation is given below:

${\displaystyle f={nv \over 4(L+0.4d)}}$.

We may also copare with  the Helmholtz resonator formula (which applies for ocarinas also )


where f is the frequency  at a hole, p0 is the pressure and ρ the density ofthe air, while V0 is the volume of the tube till the whole (thus the intenal diameter of the tube is involved) , l is the lenght ofthe tube  till the hole, and A is the total area of the soundhole plus the fingerhole.
where  is just a number, depending on what kind of gas we have. For dry air at 20°C or 68°F, we have 

See
https://en.wikipedia.org/wiki/Helmholtz_resonance#cite_note-physicsocarinaforest-7
and
https://web.archive.org/web/20130314100538/http://ocarinaforest.com/info/physics/how-ocarinas-work/

There are flutes that behave half like ocarina and half like a tube-flute . E.g.

https://www.youtube.com/watch?time_continue=16&v=Y-HOlxDQQLQ&feature=emb_title

A good question of course is if such ocraina-flute hybrid winds have all harmonics or only the odd number harmonics.

Since we are discussing here innovative improvements if folk instruments, here area couple of  interesting questions for reed winds.

1) FREE-REED OR FREE-MEMBRANE OR  FIPPLE-AEROPHONES  WITH ALTERNATING OPEN/CLOSE-OPEN TUBE ACOUSTICS WITH BOTH ODD AND EVEN+ODD  HARMONICS ? It is known that by adding a hole (actually a branched pipe) just after the mouthpiece in a closed-open acoustics non-free reed wind (as in Venova of yamaha https://www.youtube.com/watch?v=3XCan3cV76Q) or simple similar versions as the cylisax here https://www.youtube.com/watch?v=J0Ka4M_CvVY&t=95s  and https://www.youtube.com/watch?v=6wa0mPEmJI0  or https://www.youtube.com/watch?v=1B5fTwSC4QQ) the acoustics become open-open having all the odd and even harmonics (overtones)  The question here is, can we apply the same idea for free-reed winds like Bawu , Hulusi etc so that they become from close-open acoustics to open-open acoustics? Could we manufacture such a free-reed open-open pipe acoustics wind? Or alternatively if we use the long and fast increase diameter cone instead of pipe as in the saxophone would we not result to a sound with all the odd and even overtones as with saxophone? Could we manufacture such a free-reed saxophone wind? The same would apply of course if we utilize free-membranes for open-open acoustics instead of free-membranes for cose-open acoustics . All we need to do is to  make sure that the environment of the membrane has environmental air pressure. The reed and membranophone winds with alternating closed-open and open-open acoustics will function for the first octave with the 1st harmonic as closed-open or open-closed tubes and for the 2nd octave again with the 1st harmonic as open-open acoustics! For the reed-instruments like soprillo saxophone this is achieved by a registry hole on the mouthpiece close tthe reed, which converts closed-open acoustics to open-open acoustics. What is remarkable is that even the fipple-aerophones that are considered open-open acoustics can have conversion to alternating close/open-open acoustics! A fipple is normally open,but we can design fipples internal to the tube that are of closed-open acoustics!    ALL THE ABOVE INTRODUCE NEW FAMILIES OF ADVANTAGEOUS WINDS WITH SHORTER HALF LENGTH THAT HAVE NOT BEEN PRODUCED SO FAR ESPECIALLY BY THE INDUSTRIES.

2) FREE-REED OR FREE OR NOT MEMBRANE OPEN-OPEN TUBE ACOUSTICS WITH BOTH ODD AND EVEN HARMONICS. A free wind instrument like Bawu and  Hulusi , or piper (mantouri) the blowing is from around the free-reed therefore the pressure at this end is not of the open air and the acoustics are closed-open pipe acoustic, s with the odd overtones only. But what if we blow from inside the pipe so that the free-reed vibrates at open air  (as in harmonica) ? Would not have then open-open pipe acoustics with all the odd and even overtones? Could we manufacture such a free-reed open-open pipe acoustics wind? Here is a video with an informal experiment from a young anonymous guy, with seemingly free-reed and open-open acoustics as ocarina in plastic bottle https://www.youtube.com/watch?v=hx0CoDQVtvo&fbclid=IwAR3y5VBvxh7QUUvfxXzMVRuvSBEBB01mRsJlXmDRgH-BbuMCHmItY2EliH8

On the other hand if for a cane-reed instrument like clarinet the opening of a registry hole very close the the mouthpiece converts it to a  reed-instrument with open-open acoustics (like Venova or Soprillo Sax) , then applying it to have permanently open-open acoustics we have easier fingering for the 2nd octave (6+1 holes) like quenas by using 1st and 2nd harmonics (overtones) instead of only the 1st harmonic. Why not then design and make such open-open acoustics reed-instruments? 

Here is an photo of a memraphone which normally it would have a closed-open tube acoustics but with a long chimney right after the mouthpiece it becomes open-open accoyutsics with all the odd and even harmonics compared for example with the standard mebraphone clariphons (like the claricano here https://www.youtube.com/watch?v=64Uy7BQHMgg ) with closed open acoustics. The sound is more open and closer to saxophone rather than  closer to clarinet. The straight branch is so as to blow while the curved is as in the case of yamaha Venova, to create open-open acoustics.

3) SINGLE TUBE RIM-BLOWING OPEN-CLOSE  ACOUSTIC DIATONIC WINDS? It is known that the pan-flute as rim-blowing winds has a very nice breathy sound closer to the human voice, compared to a concert flute, and that the pipes of it are closed to the end so that acoustics are open-closed pipe acoustics with the odd only overtones. What if we design a pan-flute with a single only pipe and rim-blowing like a quena , and instead of holes we put mechanical valves that change the pipe length by closing the pipe at particular height so that all the required notes and pitches are produced? Would it not such a  rim-blowing single pipe open-closed pipe acoustics wind be easier to play at least for one or two octaves? It could also be a sliding wind with a slit and a moving bottom, as long as the part of the slit is always covered, or it could be sliding wind with a second pipe moving in it.

4)AEROPHONE WITH FIPPLE  TRUMPETS? AEROPHONE DIDGERIDOOS(FUJARAS)  WITH TRUMPET ACOUSTICS.

LONG TUBE AEROPHONES (CHROMATIC/HARMONIC WINDS)  WITH FIPPLE ,SIMILAR TO FUJARAS/DIDGERIDOOS, TRUMPETS AND BRASS WINDS (ratio 80< Length/Bore and about equal 125 as in trumpets ) ?

It is known that many  long tube winds have been invented with cane reeds (like  coils either double reeds  https://www.youtube.com/watch?v=QwPgiVCVxEA or single reed like Mr curly of Lindsay Polak https://www.youtube.com/watch?v=Iu60MwpMiow ) or lips-reeds in trumpets and other brass winds. But what if the same acoustics are used for aerophone winds with fipples? Fujara and didgeridoos are simplistic  cases of them with close air acoustics at the side of the mouth but they can be rendered to open-open acoustics with fipples. Such winds have not been elaborated in the same way with valves etc as the brass lips-reeds winds.

The fujaras that are know if they have large bore inner diameter and thus length/bore ratio less than 80 will not belong to the acoustic and musical effect described here (sliding whistle over a desne scale of higher harmonics)
Examples of Fujaras
https://www.youtube.com/watch?v=y8Wzb3tLPCs

I made one such aerophone didgeridoo from a 97 cm long PVC pipe with inner diameter 12mm (thus Length/bore ratio= 970/12=80.83) and with a fipple from a Sweet tone Clarke whistle C5. I opened 4 holes above the middle of the tube (corresponding to the 2nd harmonic) that as in the trumpet keys give an increase of the tone by 1 semitone by 2 by 3 and by 4 semitones (one more key than trumpets) .The action is mainly on the 6th and 5th octave. The base not is F5.

Then I made a 2nd one. I made this 2nd   aerophone didgeridoo from a 172 cm long PVC pipe with inner diameter 16.5 mm (thus Length/bore ratio= 172/1,65=104.24) and with a fipple from a generation whistle at Bb . I did not opened holes as the variation of pitch was relatively easy and desne in the harmonics.The action is mainly on the 6th  and 5th octave. The base not is G5.
These winds should not be confused with the Mosenos that are similarly long and with a fipple but they still play at the 1st 2 harmonics with small Length/bore ratio compared to 80.

More experiments that are not irrelevant by Nikolas Brass

https://www.youtube.com/watch?v=R35N43h8M5U&t=684s

https://www.youtube.com/watch?v=D8YJXMCSbLg

https://www.youtube.com/watch?v=oKnK5h_y3pg


5) LONG CHIMNEY (BRANCHE TUBE) IN LOW AND BASS WHISTLES TO LOWER THE TOTAL LENGTH AND MAKE THEM EASIER  FOR FINGERING

The idea (and patent) of Yamaha with a long chimney or brach-tube just after the mouthpiece and of about 2/3 of bore size compared to main tube was so as to convert close-open acoustics (with odd only harmonics ) to open-open (with both odd and even harmonics). But it has another effect too: It lowers the total length of the tube. This technique applied to low and bass whistles will make them of considerably shorter length . This will make the covering of  the holes with the fingers a lot easier . Even the "pipers grip"might not be necessary now.
In  the next photo we see a  D4 clariphon (chalumeaux) with along chimney which converts it from closed-open acoustics to open-open acoustics. Nevertheless the same technique will make a Low D4 whistles with a fipple a lot shorter!

6) WHISTLE WITH A MEMBRANE  REED ON THE FIPPLE WHICH REDUCES THE VIBRATION IMPEDANCE.
It is possible to have a reed on the soundhole of the fipple of a whistle! For this the sound hole must be larger, and then cover the extra part with a plastic or other material membrane reed. It could also be a cane reed. The vibration of the air which is vertical to the surface of the membrane will set in vibration the membrane-reed also which will influence the color and quality of the sound.  This idea exist also in the dizi chinese flutes, but they put the membrane not on the soundhole but on an extra hole just after the mouthpiece. It adds to the sound of the flute the sound of the membrane which vibrates as the air flows parallel to it. I used a membrane-reed from a white balloon, and actually I put it in double sheet as it was the balloon before inflating. It has to be well stretched and fixed on the fipple by tape. In the photo we see an example on a wooden-plastic Fipple of a Low D4 whistle with thin wall aluminum body of inner diameter 25 mm . The open sound hole that is left, has ratio of transverse to longitudinal sides 2:1.  The area that the membrane-reed covers is about double the uncovered one (Uncovered : 10mm*5mm Covered about 10mm*10mm ) Before the balloon reed, the fipple had large sound hole with very breathy sound and difficult 2nd octave. After the balloon reed the sound hole become 10mm*5mm and the low octave acquired very clear (not breathy) and soft sweet sound, while the 2nd octave acquired again very clear (not breathy) and loud melo sound,and somehow it is  more pleasant and easy to play in the higher octave than in the lower as is the case with the concert Bohm flute too.  This suggest happier melodies that star in the 2nd octave move in the low 1st octave and finally end again in the 2nd octave as in the upper registry whistles (see below THE UPPER REGISTRY WHISTLES (28< Length / bore ID ratio  <48) FOR HAPPIER MELODIES ) . The overall result was a substantial improvement of the sound and easier playing response of the whistle.  Suddenly this cheap Low D4 whistle become the best sounding and playing Low D4 whistle among many other expensive ones that I have! The material of the reed influences the color of the sound. I did not try it but I assume that if I would put a cane reed from say an alto sax cane reed, the sound would be more woody. Obviously this can apply also to soprano C5 and D5 whistles and might allow rather wide bore such whistles (more than 14 mm)  to have easier , clear and loud 2nd octave, even if the Length/bore ratio is less than 20.
 In winds there two types of impedance a) the vibration impedance responsible of propagating the vibration from the air column of the mouthpiece to the air column of the tube,and then outside the tube b) The air-flow impedance which is the resistance of the flow of the air. Large bore tubes have reverse effects on the two types of impedance: They increase the vibration impedance because a larger mass of air must vibrate , but they decrease the air-flow impedance because lower flow speeds are necessary to drive the blowing outside the tube compared to thin bore tubes. The air-flow impedance is by far of larger effect on the felt "resistance in playing and producing sound compared to the vibration impedance. The membrane on the fipple does not affect much the air-flow impedance but lessents the vibration impedance.

TWO  OTHER CLASSES OF AEROPHONE WINDS WITH FIPPLE

A) THE UPPER REGISTRY WHISTLES (28< Length / bore ID ratio  <48) FOR HAPPIER MELODIES
In  this category belongs also the concert flute (especially if we substitute the upper head join with a fipple) Its ratio L/B=33. Other traditional flutes in this category are many recorders and also it is the Ney if we adopt a fipple instead of rim-blowing and also the kaval flutes too. Such types of  flutes and whistles are designed for happier music and melodies where we start at the higher registry (octave) we may move to the lower registry (octave) and we end the melody in the higher registry (octave_ again. Such whistles when blowing normally they play directly to the 2nd registry (octave) while when we want to play to the lower 1st registry (octave) we have to underblow carefully. This is  the inverse with the standard whistles that when we blow normally they play in the 1st registry and in order to play in the 2nd registry we must overblow.
In the next picture we see two such whistles one in D4 and one in C4 with L/B ratios respectively the D4  55cm/1.65cm=33.33
and the C4 63cm/1.65cm= 38.18

I have made on more in F4 with L/B ratio equal to 47.5cm/1.2 cm=39.58

B) THE  DIATONIC AND CHROMATIC OVERTONE WHISTLES (48< Length / bore ID ratio <80 ) FOR CHORD ARPEGGIOS AT EACH HOLE.
These whistles are relatively unknown and I am not aware of any traditional flute in this category. The closest traditional flutes are the overtone flutes but they do not have many holes for a diatonic or other scale. This flutes have the peculiar characteristic that they are so long and with thin tupe (L/B ratio above 48) that when blowing or even under-blowing they cannot lay the 1str harmonic registry (octave). They only play with the 2nd or higher harmonics. They have more than 8 harmonics that sound easily with blowing softer or stronger. These flutes are a combination of the traditional overtone flutes and the standard diatonic flutes like irish whistles. As far as it is  concerned the acoustics relevant to the L/B ratio (which is between 48 and 80  ) , they are in between the trumpet acoustics with ratio around 125 and classical flutes and whistles with ratio between 16 to 48.
They play with less than half action  "horizontally" with their holes as diatonic scale (e.g. 2 octaves) and more than half action  "vertically" at each hole more than 8 overtones (3 ,4 octaves) that are essentially arpeggios of major chords (up to the 7nth harmonic).  Up to the 10 harmonic, the overtones of each hole belong to the scale (with the exception of the 7nth harmonic which makes the arpeggio , that of a major chord with  7nth). The playing is best when it is improvisational. It is nice to play a melodic theme and be able to play also over each note of it the arpeggio of  power-chord or major chord. The overall range of such flute is considerably larger than the standard whistles. The fipple sound hole is preferably smaller than the usual to help the higher overtones.Such winds are so much so as to read an existing  written melody from musical notes and play but a melody inside you to improvise and meditate .

The fujaras that are known if they have large bore inner diameter and thus length/bore ratio less than 80 will also belong to the acoustic and musical effect described here if made by smaller size bore and thus also shorter length (thus maybe not bass flutes). The fujaras use to have only 3 holes at the diatonic 4-chord in semitones 2-2-1. E.g. if the root is C3, then the holes give the notes D3-E3-F3 but at the 3rd harmonic G4 they will give the notes  A , B , C  thus eventually all the diatonic scale. Similarly if we open 5 holes chromatically in semitones 1-1-1-1 as in the style of valves of trumpet,  for the first harmonic it would be C#3-D3-D#3-E3-F3, the 3rd harmonic will give on the same holes G#, A , Bb, B, C , thus eventually all the 12-note chromatic scale
Examples of Fujaras
https://www.youtube.com/watch?v=y8Wzb3tLPCs

See also

https://www.youtube.com/watch?v=qzOLO5YHL9Q


The general rule to make an overtone whistle say in X base tone (e.g. C5, G4, D4, C4 etc) is to utilize the same bore inner diameter size with the ordinary whostre but about double the length. This is expected in general to give the Length/Bore ratio between 48 and 80. The resulting whistle is an overtone whistle that the basic tone (one octave lower than the corresponding whistle tone) cannot be played in the instrument , but the next octave (2nd Harmonic) is playable which is the original whistles root note.  Furthermore if we want a diatonic overtone whistle we utilize only 3 holes (the  lower pitch 3 holes if it would be an ordinary whistle) If the length is very long (for alto or low whistles) we "coil" the tube with turns and rounds as in t he brass wind instruments.  If we want a chromatic such overtone whistle we simple fill-up the gaps of the 3-holes of the diatonic overtones whistle as above with all their sharps or flats getting so 5 holes in the same area , which is about the lower 1/3 of the tupe. In thsi way with the 2nd and 3rd overtone we have all the 7-notes diatonic scale or all the 12-notes chromatic scale.  
In the next picture I made from 16 mm bore  (inner diameter 12 mm) PVC and sweet tone Clarke whistles mouthpieces (fipples of D5 and C5 ) two such "magical" diatonic overtone whistles in D5 and C5 (although the length is as if of Low D4 and C4).The have respectively L/B ratios the D5 57/1.2=47.5 and the C5 64cm/1.2cm=53.33
They have 6+1 holes, but if we seal with a tape all except the highest 3, as in Fujara, we still have with the 1st and 3rd harmonic all the 7 notes of the diatonic scale.

In the next photo we see  a C5 and aF5 overtone diatonic whistles only 3 holes are opened and suffice for a full 7-notes diatonic scale even only with the 2nd and 3rd harmonic.

Here is a bass in Bb3 diatonic from PVC of 32mm external diameter ,  of length about 148.2 cm (the same length with a Bb4 trumpet) , again with only 3 holes. In semitone intervals 2-2-1 or in notes Bb3 C4  D4 Eb4 . That is all it is necessary for a 7notes scale because it already starts with the 2n harmonic (due to the double than normal length)   and the 3rd harmonic gives in the same octave and on the same 3 holes  the the notes  F4-G4-A4-Bb4 thus all the Bb3 7-notes major scale. As it is a bass one, it falls in the category of Fujara. The high pitch ones I call overtone whistles. By changing the last part of the coil-tubes with another of appropriate length and holing we may have more roots on the same upper body.

In the next 2 photo we see a  C5 full chromatic overtone whistle that utilizes practically the 2nd and 3rd harmonic and with the 5 holes to give the chromatic half octave C5 C5# D5 D#5 E5 F5 F#5 with the 2nd harmonic and with the 3rd harmonic to give on the same holes the G5  G#5 A5 A#5 B5 C5 C#5 gives thsu a full chromatic 12 notes octave. The 1s tharmonic  is hardly listened or of sound it is fused with the 2nd harmonic due to the membrane fipple (see post 243) and gives to this part of the 5th octave a more bass sound. It is made again by PVC tube of external diameter 25 mm. The lenghth to bore ratio Length/bore=34 , thus strictly speaking an upper registry whistle (see post 199 ) rather than an overtone whistle. That is why it does not give more than the 3rd harmonic. The idea is the same with the trumpet and the valves that produce 5 notes each a semitone away from the previous. We see 7 holes in the front (there is not thump hole) but the highest pitch hole is a tuning hole for C5, thus 6 holes covered 3+3 by the two hands. These 5 notes that divide a 5th (laso a 4th) give the concept of ancient Greek 4-chords and 5-chords as basic building block for an octave scale. If we close that tuning hole too it will give a Bb4 note as in aC4 Ney. The whistle as it has a breathy harsh sound due to the membrane fipple sounds almost exactly like a C4 Ney flute (which normally is rim blowing ) and if we exclude the 1st harmonic of the Ney is identical with what the Ney is playing (of course the semitones are in the equal tempered scale rather than deviating scale)

A trumpet that the sound is produced by the lips is a  lips-reed wind with closed-open acoustics that normally have only odd number harmonics (overtones) . Nevertheless because of the gradual cone at the end, as with the saxophone  eventually because of a complicated phenomenon of acoustics  both odd and even number of overtones. Still strictly speaking an aerophone is not producing the sound from a reed, but by a fipple or rim blowing. A modern trumpet at Bb was tube length of 1.482 m and is producing 8 overtones, the first is not possible to play so from 2nd to 8th are C4 G4 C5 E5 G5 A5 C6. These 7 notes are essentially part of an arpeggio of the C major chord with 7nth within 2 octaves. The keys-valves allow for 6 more series of such harmonics each one a semitone lower. 

So what if the same acoustics are derived as aerophone winds with fipples? Fujara and didgeridoos are simplistic  cases of them with close air acoustics at the side of the mouth but they can be rendered to open-open acoustics with fipples. Such winds have not been elaborated in the same way with valves etc as the brass lips-reeds winds.

The fujaras that are know if they have large bore inner diameter and thus length/bore ratio less than 80 will not belong to the acoustic and musical effect described here (sliding whistle over a desne scale of higher harmonics)
Examples of Fujaras
https://www.youtube.com/watch?v=y8Wzb3tLPCs

I made one such aerophone trumpet from a 97 cm long PVC pipe with inner diameter 12mm (thus Length/bore ratio= 970/12=80.83) and with a fipple from a Sweet tone Clarke whistle C5. I opened 4 holes above the middle of the tube (corresponding to the 2nd harmonic) that as in the trumpet keys give an increase of the tone by 1 semitone by 2 by 3 and by 4 semitones (one more key than trumpets) .The action is mainly on the 6th and 5th octave. The base not is F5.

As 2nd version o the holes we open a hole at the 2/3 of the length (corrected higher by above 80% of the more diameter) which corresponds the 3rd harmonic and two holes  that give sequentially 2 semitones above it. And we also we mark the middle of the tube (that would correspond to  thump hole giving the roo one octave higher, thus 2nd harmonic) but we do not open a hole there, we only open again 3 holes that give sequentially 1 tone  1  semitone and 1 semitone above it. In this setting of 5 holes (3+2) we incorporate almost the natural minor, the double harmonic minor and the harmonic minor in the main octave (which contains the 1-3-1 semitones pattern and has 5# and 2# in place of 5 and 2. The harmonic minor has only 5# in place of 5 and 2 while the natural minor has 5 and 2 ) which is chromatic feeling that complements the strongly harmonic feeling of the arpeggio of the major chord of each hole as higher harmonics). Strictly speaking the holes scale is the parachromatic Byzantine which is in semitones 1-2-3-2-1-1-3 (in steps of  F major it is 5, 5# 6, 1, 2, 2# 3 5).When we open all the lower 3 holes a major 3rd interval appears , while of we open only the upper two holes a minor 3rd interval appears. Alternating these two we get nice harmony.

Then I made a 2nd one which feels even better (because the ratio is higher 104 and the bore larger) without holes  . I made this 2nd   aerophone didgeridoo from a 172 cm long PVC pipe with inner diameter 16.5 mm (thus Length/bore ratio= 172/1,65=104.24) and with a fipple from a generation whistle at Bb . I did not opened holes as the variation of pitch was relatively easy and desne in the harmonics.The action is mainly on the 6th  and 5th octave. The base note is G5.

These winds should not be confused with the Mosenos that are similarly long and with a fipple but they still play at the 1st and 2 harmonics mainly with small Length/bore ratio (e.g. 20) compared to 80.

The most important characteristic of these aerophone trumpet, winds are

1) They need not be bass , but on octaves from 7nth to 4th etc
2) The sound is not really one note but rather like a chord with many hidden harmonics
3) They must have very high Length/bore ratio above 80 and preferably around 125
4) They behave in the pitch of the sound like sliding whistles with a continuum of pitches but not entirely on all frequencies but on a dense grid of harmonics (certainly more than 12 chromatic notes in the octave) 
5) They are very satisfying in playing like natural human whistling but unlike it or unlike the violin without frets, the harmonics give a natural scale of "frets"  that the pitch falls in it which is very harmonic to listen . It is so because the relative change o the pitch is determined always by harmonics.
6) The harmonics are very easy to obtain not by overblowing (as in standard overtone whistles)  but by simple blowing even under-blowing. 
7) Holes are not necessary for hem. Only if the Length/bore ratio is much less than 125, e.g. 80 then 4 choles (reachable by the hands) at equal pitch distances of one semitone are adequate to help small chromatic changes of 1, 2 3 or 4 semitones (in trumpets the 3 keys help for 1,2 and 3 semitones). The reason that 4 semitones is added is because  a  sequence of alternating minor-major thirds gives chords on every 3 notes.
8) Such winds are so much so as to read an existing  written melody from musical notes and play but a melody inside you to improvise and meditate .

More experiments that are not irrelevant by Nikolas Brass

https://www.youtube.com/watch?v=R35N43h8M5U&t=684s

https://www.youtube.com/watch?v=D8YJXMCSbLg

https://www.youtube.com/watch?v=oKnK5h_y3pg

198.The DADGAD tuning for 6-string guitar

We should not forget of course the very famous and well known in Irish tunes music, D2A2D3G3A3D4 tuning

https://en.wikipedia.org/wiki/DADGAD