« Harmonics » project

2.1 Presentation generale. Sauvegarde des parametres.

1. Lancer le programme “StandAlone”, voir section 3.1.
2. Verifier la version avec la souris, et visiter la page web avec ses rubriques dont cette section 2.
3. Brancher clavier/EWI. Dans “Options”, connecter Audio et MIDI devices et faire Reset_Default_State.
4. Changer un parametre comme ch_in et faire menu_Options/save_current_state puis menu_Options/load_a_saved_state

2.2 Jouer avec l’EWI et/ou avec le clavier.

1. Identifier son canal: affiche sur la note de tunplot.
2. Choisir le son dans Audio_out
3. Mode Hold on/off (case à cocher ou messages expression) et “reset notes”
4. Mode Leader on/off, aussi affiche par « L » sur la note de tunplot.

2.3 Jouer avec la souris

1. Choisir le cannal ch_in.
2. Jouer sur tunplot et netplot
3. Modifier le volume des notes avec le scroll de la souris. (attention de bien choisir le canal ch_in).
4. Choisir le son: “Audio out”

2.4 Chords save/load

1. Save/Load d’accords
2. Panneau “sequence”.
3. Export/Import et on echange le fichier par whatsapp ou mail.

2.5 Change chords

1. Change chord et ses parametres.
2. Utilisation de Automate pour “read chords” et “change chords”.

2.6 Enregistrer l’audio et capture video+son

1. avec Garage Band ou Audacity, etc, cf section 3.2.

2.7 Jouer avec un synthe externe (ex: Diva)

1. Sur la premiere ligne, cocher “mute” et “midi_out” pour demander de couper le son interne et envoyer les messages midi en sortie (mais on peut choisir de garder le son interne pour comparer).
2. Brancher les bus midi: Tonnetz-> Bus1 virtuel-> Live piste Midi avec plugin Diva. Il faut configurer le plugin Diva avec tuning range Up=2, Down=2.
3. Enregistrer la piste midi et la rejouer. Cf section 3.3.

2.8 Network

1. Se connecter et voir la liste des autres personnes.
2. Jouer avec les autres: Id_input = all. Chacun choisit un Id_output différent (car on ne recoit pas son propre Id). On échange des notes.

2.9 Audio in:

1. Vérifier que l’on a un signal audio_in venant du micro: OPtions/Audio_Midi_Settings/Input: il devrait y avoir un jauge de signal. Sinon, il faut lancer le programme Tonnetz depuis un terminal pour avoir l’autorisation du micro: /Applications/Fred.../Fred_Tonnetz
2. Cocher detect_audio_pitch, ouvrir la fenetre “Show audio in”. Jouer un instrument acoustique. Ajuster le volume.

2.10 Presentation a MACI:

• Preparer quelques slides qui presentent
  • les bases historiques
    • les bases mathématiques et physiques
    • Nos motivations
    • Question de lutherie,division à N notes.
    • présenter le programme et les controlleurs: clavier, souris, EWI, flute et flute a nez,
  • Demonstrations:
    • Extraits archives pre-enregistrées:
      • Hexagone
      • Essais de chez moi. Demander à Alex.
      • Nouveaux exemples pedagogiques
        • Melodie identique mais avec differents temperaments fixes, puis adaptatifs. C/E/G/C/D\C\Bb/C\A\G\F#/A\G.../Ab\G\F\Eb\Db\B/C/E/G\E\D/E\C
        • Idem avec une suite d’accords
        • Temperament adaptatif, harmonie positive / negative, modes differents selon l’octave
        • Fred fait des accords: canal 3 en leader. Sans memoire.
          • Ex: Intevalles de quinte: C/G -> \F -> \B -> \E etc ..
          • Ex: grande cadence majeure en C (ordre non important).
          • ex: grande cadence mineure en A: A\F\D\B, -> G#\E -> A/C -> F\D -> G#/B -> E\C ->F/a ->d\b -> E/G# -> C\A -> C pour stabiliser
        • Malik improvise :
          • canal 1 ou 2, avec 4 keys/oct, adaptative, non leader son sinus avec chorus., et toujours le meme parttern sur 2 ou trois octaves en descente (idem griots)
          • idem en 6 keys/oct, adaptative, non leader
      • Nouveaux exemples artistiques
    • Petit Live
      • Avec ancrage, sans ancrage, sans memoire.
  • Conclusion: parler du projet à Royaumont, musique en live.

3.1 Lancement du programme

3.2 Comment enregistrer des sessions audio et video

3.3 Comment enregistrer (et rejouer) des sessions Midi

21/01/2024, version 1.1.1

• Jouer avec l’ewi ou clavier. Choisir le son dans ’audio out’. Choisir le tempérament.
• Avec l’ewi, passer/sortir du mode ’hold’ en mordant un peu et effacer les notes en mordant fort. Il y a une jauge ’crunch’ qui montre le seuil. Ainsi, en mode hold, on peut poser des accords.
• Si on rejoue une note existante, cela l’éteind.
• On peut jouer sur differents canaux de l’EWI, par exemple
  • canal 1: en mode hold pour construire des accords,
  • canal 2: en mode hold off, pour jouer un solo.
• On peut modifier les accords avec la souris, en cliquant sur les notes (on/off) et modifier la force des notes avec la molette.
• Save/Load des accords et faire evoluer des accords en choisissant différents paramètres.
• Jouer en temperament adaptatif ou fixe et décaler les tempéraments fixes selon les directions $3,5,7$ .

19/02/2024, version 1.1.9

• Il y a un seul package appelé Tonnetz qui contient:
  • Un programme indépendant de tout logiciel DAW, appelé Tonnetz StandAlone que l’on peut utiliser directement dans Applications/Fred/Tonnetz
  • des plugins:
    • Tonnetz_Synth qui est un synthétizer for LogicPro or GarageBand, etc. This is an AU Plugin.
      The suffix Synth means “synthetizer” and that on output it gives some sounds from an internal synthetizer (by Alex or Fred).
    • Tonnetz_MidiFX est un plugin for LogicPro, this is a AU Plugin.
      The suffix MidiFX means “midi effect” and that on output it gives midi events. Beware that it is not accepted by GarageBand. On LogicPro, to have sound, you need to put after this plugin, any external synthetizer which accepts pitch-bend and calibrate the pitch bend to the range $\pm 2$ (e.g. Diva).
    • Tonnetz_Analyzer is for LogicPro or GarageBand, etc. This is an AU Plugin.
      The suffix Analyzer means “audio effect” and that on input and output it takes some audio. on peut jouer avec un instrument acoustique et en particulier la flute à coulisse.

19/02/2024, version 1.1.10

• Dans la section, “1 Temperaments/ 8 For dev”, un mot de passe est requis pour accéder à l’onglet “8 For developpers”.
• Représentation en portée musicale “Staff” dans “1 Temperaments/ 3 Display Settings”.
• On peut éditer un tempérament fixe dans la section “1 Temperaments/5 Edit”
  • Il faut au préalable sélectionner un tempérament fixe.
  • On modifie les notes, soit à la souris sur la fenetre tunplot ou la fenetre netplot, soit avec les widgets.
  • Penser à utiliser le bouton droit de la souris pour basculer en mode freeze.
• On peut sauvegarder et rejouer des accords dans la section “1 Temperaments/2 Chords/ 1 Save/Load” et faire évoluer les accords dans la section “1 Temperaments/2 Chords/ 2 Change Chord”

23/05/2024, version 1.1.13

• On peut programmer et faire jouer un automate dans la section “4 Markov Automate”. Il composera en direct selon des suites d’instructions situées sur les sommets d’un graphe de Markov.

21/07/2024, version 1.1.16

• Il y a une interface graphique (comme des pads) pour jouer la suite d’accords: dans “1_Tempéraments/2_Chords/Show_sequence”.

30/07/2024, version 1.1.17

• Pour chaque canal midi entrant (ch_in sélectionné en haut à gauche) on peut associer un instrument et des effets spécifiques (voir “2 Audio/Audio_out”). On peut aussi décider ou non d’une sortie midi_out pour enchainer avec un synthe externe.

01/08/2024, version 1.1.18

• On peut jouer en reseau via internet avec d’autres utilisateurs distants, cfonglet “5 Network”.

02/09/2024, version 1.2.0

• Dans le menu “1 Temperament/ 3 Display / 1 Tunplot” il y a un mode “edit forest” qui peut aussi se (des)actionner avec le bouton droit de la souris sur les fenetres tunplot et netplot. Il permet d’accèder à toutes les notes de la forêt en cliquant avec le bouton gauche, et donc pas seulement aux seules notes du tempérament.

29/09/2024, version 1.2.3

• Mémoire des notes anciennes (“ghost note”). Au moment de s’éteindre, au lieu de disparaitre, une note leader devient “ghost” pour une certaine durée avec toujours son rôle de leader qui influence le tempérament adaptatif, mais le son est eteind. Elles sont dessinées en transparence.

6.1 First ojectives

6.2 Some conferences?

6.3 Objectives

• Un disque
• Documentaire de 15’ + 30’ de morceaux

7.1 Summary of the tonnetz plugin with few key-words

8.1 Harmonics and just intervals

8.1.2 What are the harmonics

The harmonics of the fundamental note $C_3$ for example (subscript $3$ here means octave $3$ ), is the following series of notes (and correction in half-tone)

where the index is the harmonic number $1,2,3,\dots$ and the subscript is the correction with respect to the equal temperament. For example, harmonic 3 is $G$ with a correction $+0.02$ of halftone. Harmonic $7$ is $B♭$ with a correction $-0.31$ of halftone, that is very perceptible. What is important to observe and enough to remember for after is:

• Harmonic $1$ is called the fundamental.
• Harmonic $2$ is an octave from the fundamental.
• Harmonic $3$ is a fifth (plus an octave) from the fundamental with $+0.02$ of halftone (not perceptible).
• Harmonic $5$ is a major third (plus two octaves) from the fundamental with $-0.14$ of halftone.
• Harmonic $7$ is a minor seventh (plus two octaves) from the fundamental with $-0.31$ of halftone.
• Harmonic $11$ is a augmented fourth (plus three octaves) from the fundamental with $-0.49$ of halftone.
• Harmonic $13$ is a major sixth (plus three octaves) from the fundamental with $+0.40$ of halftone.

Numbers $2,3,5,7,\dots$ are prime numbers and are enough to construct every other numbers, e.g. harmonic $6=2\times 3$ is one octave above harmonic $3$ , hence $2$ octaves and a fifth above the fundamental. Harmonic $9=3\times 3$ is a fifth and an octave above harmonic $3$ , hence two octaves and two fifth above the fundamental, etc.

Frequency of the harmonics:

if $f=f_{C_3}$ is the frequency of the fundamental, then the frequency of harmonic $3$ is $f_{G_4}=3f$ , and frequency of harmonic $5$ is $f_{E_5}=5f$ , etc. These frequencies are slightly different from the frequency obtained in equal temperament (more on this below). More informations about harmonics are in the appendix sec:Harmonics.

8.2 Tunplot: the pitch space

Exemple 8.1. On the following example, three notes have been played with the keys $F_4,C_5,E_5$ . They are represented by the green disks. Their horizontal position gives their pitch $x$ , and the dashed lines are is the equal temperament, i.e. for integer value of $x$ . (In black are other accessible notes by the temperament, but not yet played).

In this example, we observe that $x_{E_5}$ is a little lower than the equal temperament line. The number on the left of each line is the octave range number.

8.4 Formula for pitch values

• Intervals along the $n_3$ axis, i.e. fifths, do not differ from the equal temperament intervals by a perceptible quantity. And similarly for $n_{17},n_{19}$ axis.
• Intervals along the $n_5$ axis of major third get a strong pitch correction $\Delta x\approx -0.14$ (of half-tone) for each positive step.
• Intervals along the $n_7$ axis of minor seventh get a strong pitch correction $\Delta x\approx -0.31$ (of half-tone) for each positive step.

8.5 Temperaments

8.5.1 Fixed temperament

Watch a video.

If this choice is fixed, we say that we play with a fixed temperament. The program will allow to play with different fixed temperament, like the famous “Pythagorean temperament”, the “Zarlino temperament”, the “Harmonic temperament” etc.. but also on some fixed temperament build by the user. The advantage of fixed temperament is that some fixed “musical mode color” can be explored. The dis-advantage of fixed temperament is that not all the just intervals are available, and some intervals sometimes sound bad.

Zarlino temperament in C:

Here is the picture for available notes

We observe on the tonnetz space that it is made with just fifths and just major thirds. On the pitch space, we observe that the temperament is the same on each octave range. One advantage of the Zarlino temperament is that we have just major triads chords like $\left\{C,E,G\right\}$ , $\left\{Eb,G,Bb\right\}$ . But beware that some other triads are not the usual just like: $\left\{E,Ab,B\right\}$ or $\left\{Gb,Bb,Db\right\}$ .

Harmonics temperament in C:

Here is the picture for available notes

We observe on the tonnetz space and pitch space that it is made from the first few harmonics of $C$ (up to harmonics 25).

8.5.2 Adaptative temperament

Watch video.

Adaptative temperament has been defined and proposed in the paper [1].

Instead of using a fixed temperament, it is also possible to adapt the frequency of some key to the present situation, depending on the notes that are played currently (or recently) and depending on some (deterministic) rules. We say that we play with adaptative temperament. The advantage of adaptative temperament is that all the just intervals may be available. The disadvantage is that the frequency associated to a key may change, and this can be a difficulty to the player. To overcome this difficulty this is very useful for the player to look at the available notes on the tonnetz space and on the pitch space.

Definition of the adaptative temperament:

Suppose that there is already a set of notes, i.e. a chord $A$ that sounds. The adaptative temperament depends on this chord $A$ . We have to choose how many keys per octave we want to be able to use. This is $N_{oct}=4,6,12$ . Then the octave range is divided in $N_{oct}$ equal intervals and in each of these intervals, we choose the note that is the most consonant with the notes already present in the chord $A$ (among the infinity of rational numbers in this interval).

More precisely we use the dissonance function $d_A\left(n\right)$ of a note $n$ with respect to the chord $A=\left\{n_j,j=1\dots N\right\}$ made of $N$ notes. $$d_A\left(n\right):=\sum _{j}d\left(n_j,n\right)$$ where $d\left(n_j,n\right)=ln\left(ab\right)$ is the dissonance of the just interval $\frac{f}{f_j}=\frac{a}{b}$ made by the pair of notes $n_j,n$ . (On the tonnetz $d\left(n_j,n\right)$ is just the $L^1$ distance). The resonance function is just the opposite $R_A\left(n\right)=-d_A\left(n\right)$ .

Exemple 8.6. In this example, the chord is made of the only note $A=\left\{C_5\right\}$ . We choose $N_{oct}=6$ notes per octave. For this we are allowed to use only the keys $C,D,E,F,G,A$ in each octave. On the first pitch space we represent a vertical bar at (almost) every rational number, i.e. possible new note $n$ , and the hight of the bar is the resonance $R_A\left(n\right)=-d_A\left(n\right)$ . Each octave is decomposed in $N_{oct}=6$ equal intervals and the black lines is the selection in each interval that gives the highest bar, i.e. the most resonance note, with respect to $A$ . This is the adaptative temperament with $N_{oct}=6$ notes per octave, for the chord $A=\left\{C_5\right\}$ . The other pictures are as above.

Observe that the temperament is not the same at each octave. We observe interestingly that the scale in octave $5$ is the “blues scale”.

Exemple 8.7. In this example, the chord is made of four notes $A=\left\{E_4,G_4,C_5,E_6\right\}$ . We choose $N_{oct}=6$ notes per octave.

We observe that the adaptative temperament depends indeed on the chord $A$ .

9.1 Great cadence

10.1 Automation

10.2 Adaptative temperament with different N_keys and levels

• Choose adaptative temperament with 4 keys/octave
• Choose adaptative temperament with 6 keys/octave
• Choose adaptative temperament with 3/6/12
  • In octave 4, put hold notes in leader mode: C,Ab,E, this play a minor triad. Then play in follower mode, not hold, in higher octaves.

10.3 Many musicians, how to use in session

• On input there are audio (in green) and midi (in red) signals. Each input is connected to an individual midi track with a tonnetz plugin. In fact all the plugins communicate in the computer and share the same list of notes and the same tonnetz space. Beware that a plugin VST3 can not communicate with a AU plugin, so all the plugins should be of the same type VST3 or AU.
• On output of the plugin we can choose to use the internal synthetizer (IS) of Alex that gives an audio output. This audio output is then sent to a mixer table.
• On output of the plugin we can choose not to use the internal synthetizer of Alex but send the midi signal to an external synthe, and after the audio signal to the mixer table.
• The musicians have a direct access to the plugin parameters through a computer console. They can also send automatic commands to the plugin using a Foot-Pad midi controller. The commands can be assigned from the computer console.
• In practice the developpers can have also an access to the computer from an external computer, using “AnyDesk”.

A.1 EWI USB

A.2 EWI 5000