Chord inversions book recommendations???

maybe a expand circle of fiths (a 8 octave keyboard as circle)

theerrorofpythagoras.jpg

red shows the octave

green shows the quint

blue shows the mathematical difference between octave and quint

after 1 octave humans dont hear (the small) differnece between octave and quint, after 8 octaves we hear the ( bigger) difference

that is why there is a tempered mood (every octave is slightly a little out of tune) we here with tempered no differnce between the 8 octaves

source/link (sadly no english) - the error of pythagoras

https://www.youtube.com/watch?v=Dt7Ihzyae6I&t=2508s

this book (free pdf) write about this too: music a mathematical offering - dave benson

http://homepages.abdn.ac.uk/d.j.benson/html/music.pdf

I’m just looking for a way to extract all possible chords from any given scale. I think it requires a computer program.

You are writing about the pythagorean comma and the equal temperament tuning system which allows for key changes using only one keyboard or fretboard.

It is quite a subtle difference between ‘just’ and ‘equal’. Basically the chords in ‘equal’ warble slightly a bit like detuning a supersaw. The chords in ‘just’ are completely stable when you see them in lissajous oscilloscope…Its a complete headache to try and understand fully and describe but this video describes it well:

Thanks for that hardcore 500+ page .pdf. It looks great. It will definitely take some time to try and read it and understand it.

I don’t really need to understand everything about the mathematics and physics of harmony and tuning. I’m just looking for a way to compute all possible chords from any scale and a way to use other scales ( other than vanilla major and minor ) around the cycle of fifths.

ts a complete headache to try and understand fully

had occupied me for a long time, as that is exactly
so good as nobody writes, talk about or know it (i asked here too)

it is really easy (know that only since 3 days, the yt link - the error of pythagoras - help me)
1: 2 = octave
2: 3 = quint
they are not compatibel, the bill does not work, not mathematically, graphically or musically (it works there logarithmically - look at the strings at a guitar or inside a piano)
the keyboard is a lie but works self-contained with tempered-tuning and the circle of 5th

think that is a good basis for everything else, understand the mathematically, graphically and musically view, can switch between and build up on that

musically something behaves differently, it requires a trained hearing, recognize the notes chords and scales by listening, need a musical education, i do not have

electronic music often plays with modulation, filter, microtuning and so on, the classical harmonic theory probably does not work there so easily

no limits today but it certainly does not hurt to know the rules (the cultural influence is connected as disharmonious/harmoniously with it) before to break them

THE NEVERENDING STORY

ABOUT

THAT CHORDINVERSION THINGY

Already #bookmarked by Me & checking in&out on a regular

THANKS Y’ALL!

:ph34r: :drummer: :ph34r:

electronic music often plays with modulation, filter, microtuning and so on, the classical harmonic theory probably does not work there so easily

no limits today but it certainly does not hurt to know the rules (the cultural influence is connected as disharmonious/harmoniously with it) before to break them

If using fat, thick, detuned, multiple oscillator, layered sounds the theory about chords and harmony doesn’t really apply as much.

Same goes for weird, metallic FM bell sounds.

The harmony theory is really useful for building things up from single cycle waveform samples though.

My computer is not so powerful and my wallet not so fat and thick with bills, so I’m not a big VSTi user.

I do mostly almost chip things but with VSTi for the bass and breakbeat samples for drums ( single hits layered with free 808 and 909 from magazine cover CD). Its good. I can’t afford big hardware or flashy vintage PSP tube valve warmer stuff but I can do stuff with harmonies, bass and breaks. I’m all about arpeggiators and phrases right now, so for that stuff the harmony is essential knowledge.

If anyone knows a way to get all possible chords + voicings, inversions out from a scale please let me know the technique or computer program yo.

If anyone knows a way to get all possible chords + voicings, inversions out from a scale please let me know the technique or computer program yo.

It only requires a simple brute-force algorithm matching two tables - one table containing the pitch degrees of the scale, and one table containing all chord figures you want to search for in an 047-format. You will have to provide the chord figures yourself. The only thing “complex” about the operation is to use modulo in the correct way, and to search for all rotations (inversions) of the chord figure. Also, you’d want to “compact” the figure beforehand, with a simple modulo operation.

I’ve done it, as can be seen in the chord navigator I scripted. http://forum.renoise.com/index.php/topic/49986-ras-renoise-accompaniment-system/page-3#entry359032

I can give you a Testpad.lua version that will generate a table with all chords in a specified scale/key… I’m pretty sure that the scalefinder tool has the same functionality, so you should be able to rip it from there as well. You’d probably want to provide it with more chord figures, though, but that should be a simple task. https://www.renoise.com/tools/scale-finder

Regarding voicings specifically, it makes no sense. There is a large amount of voicings per chord, as the only thing specific to a voicing is the choice of octave/doublings for each pitch. However, some usable generators can be made for inverting chords and generating some popular/standard voicings, but this territory is a bit more complex and very much to taste. For example, there is no absolute set standard as to exactly what voices that make up an “open voicing”. Furthermore, there is the common drop2 voicing, which is rather an “operation” on a voicing than a specific voicing itself (I believe).

Thanks. These tools look awesome. Inversions, voicings and chord naming seems complicated maybe unnecessary. I prefer ‘semitones up from root note’ style chord description anyway ( 047, 037 etc.).

As for the traditional way of naming chords for instrumentalists I would usually name a chord based on the major scale of its root note as it appears in cycle of 5ths… However, if I have a note in my scale / key signature which differs from cycle of 5ths representation I am unsure how to name the chords with that note as the root.

For example,

A harmonic minor ( A B C D E F G# ) has a G# ( like normal A minor scale but altered ).

G# usually appears in cycle of 5th’s as Ab ( 8 o’clock, 4-b )

In the case of creating a ‘chords from scale’ guide specifically for A harmonic minor, should I name the chords based on root G# as Ab chords or convert everything and describe them as G# chords?

It will require a double sharp or ‘x’. ( the scales book im working from has no # or b in the key sig for A harmonic minor scale in traditional notation, that is, it has key sig of A natural minor with the G# of harmonic minor marked as # every time it appears in the score but not in the key sig )

G-sharp major is a theoretical key based on the musical note G-sharp, consisting of the pitches G♯, A♯, B♯, C♯, D♯, E♯ and F7px-DoubleSharp.svg.png. Its key signature has six sharps and one double sharp.

  1. If you’re following the CIRCLE of fifths, you’re gonna be out of key pretty soon. You do know that? The CIRCLE of fifths isn’t very helpful in defining a key, as far as I know.

  2. http://www.themusicalear.com/sharps-or-flats-how-to-spell-notes-correctly/

the cicle of fifths is a handy tool to know which keys share common notes ., and how many sharp/flats the kay has

If your moving from key G to D , you are adding 1 sharp .‘C#’

You now have 2 sharps 'f# and g# .

I wouldn’t use the circle as a composition tool

Thanks for the link and all these informative answers. Its a shame I don’t know lua.

I’m building a traditional chords from scales guide just as .txt files for reference.

I know the cycle of fifths is good for determining how many sharps or flats a major or minor scale has. This is the ‘scales only’ version of the cycle.

There is also a version of the cycle that gives a chord for each scale degree (image below). Pretty good as as compositional tool. Its the basis of all classical music. I’m not a big classical fan to be honest but I want to name chords correctly for my guide.

My problem is to do with describing chords from scales other than major or minor.

In cycle of fifths G# would usually be described as Ab, but specifically in the context of A harmonic minor chords from scale guide I guess I should probably name the chords with G# as the root note as ‘G# chords’ rather than ‘Ab chords’ because to get a harmonic minor from normal minor I have to sharpen (G to G#).

A minor ( A B C D E F G )

A harmonic minor ( A B C D E F G# )

Its a problem because the chords should be named according to the notes of the G# major scale (usually Ab Major).

G# Major is a funky and stupid looking major scale with six sharps and one double sharp. Ab Major would be better if only describing the scale ( and not naming chords in the context of A harmonic minor ) as it just has 4 flats, no double flats, nothing weird (Ab Bb C Db Eb F G).

I just wanted to check here if G# or Ab is better for naming G# chords in the context of chords from scale - A harmonic minor…I think I will end up going with G#, but it will be annoying ( six sharps and a double sharp ). Any advice for me?

Sorry I know the classical stuff is unnecessary and boring for renoise (renoise doesnt have diatonic rule or flats).

diatonic rule - for example, you cant have an A and then an A# in one scale. A must progress to B, so it must be described as A then Bb.

You must always go from A to B, B to C etc…the point I’m making is that trackers don’t have this rule. In trackers its always all sharps and chords are described ( as in the arp command ) with number formulas representing semitones up from the root note rather than being described in terms of intervals (based on harmonic series) such as minor 3rd, Major 3rd, Perfect 5th and so on…for example: All Major chords are just 047 chords, all minor chords are just 037 chords, the notes are always written with sharps, never flats.

I just want to get these chords named correctly in context. There are many per scale. I dont want to have to go back and do corrections afterwards, its a big job to get this guide finished. Consider all the other chords for each note in a a scale apart from the main ones:

Even just for the note D (in the context of ‘chords from scale - A harmonic minor’) so far I have these ‘D chords’:

Dmin: D F A
Dm7: D F A C
Dm9: D F A C E
Dm6: D F A B
Dmadd9: D F A E
Dm6add9: D F A B E
D5: D A
Dsus2: D E A
Ddim: D F G#

There are many more than just these to be made and all off them have inversions and voicings…If I get all this information extracted I will be arpeggiator and phrase king. Plus, if I name them in two ways; ‘the renoise way’ (all sharps, no diatonic rule) and the ‘classical way’ I can not only write quickly and accurately but also describe my chord progressions and arps to fancy instrumentalists like ukelele players, guitarists or keyboardists.

Cycle of fifths - chords (mentioned at the beginning):

51nkXcFaSmL.jpg

A harmonic minor ( A B C D E F G# ) has a G# ( like normal A minor scale but altered ).

G# usually appears in cycle of 5th’s as Ab ( 8 o’clock, 4-b )

In the case of creating a ‘chords from scale’ guide specifically for A harmonic minor, should I name the chords based on root G# as Ab chords or convert everything and describe them as G# chords?

In A harmonic minor, the reason it’s G# and not Ab is that you already have an A and you’ll have a more readable score if you have notes on different lines instead of constantly needing accidentals.

I do not understand what you are trying to do with the circle of fifths, but the reason G# is given as Ab on there is the same reason (Ab major is much more readable key sig than G# even though they are the exact same thing described 2 different ways…)

The triad built on the G# in A harmonic minor is G#dim you could call it Abdim, but you wouldn’t want to for the same reason of readability.

Its a problem because the chords should be named according to the notes of the G# major scale (usually Ab Major).

Not if you’re playing in A (harmonic) minor though. I think you are misunderstanding something fundamental, but I’m also not sure what you’re trying to achieve, so I could be wrong.

Edit:

in the context of chords from scale - A harmonic minor…I think I will end up going with G#, but it will be annoying ( six sharps and a double sharp ). Any advice for me?

Like this is just completely wrong.
Whether you call it a flat or a sharp, theres only one black-key note in the scale. So the G#dim chord it gives you (or G#dim7 or how ever many notes you add), you only have the 1 sharp from the scale and certainly no double sharps. (unless you use chords with non-scale tones which is both possible and something what you seem to be trying to build won’t allow for.)

Thanks for your reply.

I think it will make sense to name them as ‘G# chords’.

I will have to do chord spelling for the ‘G# chords’ using notes from the theoretical scale G# Major ( rather than the usual Ab Major )…because chords are named according to the Major scale of their root note.

For example:

A Harmonic minor - 1st A, 2nd B, b3rd C, 4th D, 5th E, b6th F, 7th G#
( Note that the 3rd is flattened because A Major scale contains C#, the 6th is flattened because A Major scale has F# )

[To spell the G# chords I must use G# Major scale - 1st G#, 2nd A#, 3rd B#, 4th C#, 5th D#, 6th E#, 7th Fx]
[G# Major scale is enharmonically equivalent to Ab Major scale - 1st Ab, 2nd Bb, 3rd C, 4th Db, 5th Eb, 6th F, 7th G]

G#dim :

Renoise spelling - G# B D

Normal classical spelling - 1st Ab, b3rd Cb, b5th Ebb = Abdim
( based on Ab Major scale degrees)

Classical spelling in context of describing it as a chord from A harmonic minor - 1st G#, b3rd B, b5th D = G#dim
( based on G# Major scale degrees )

G#dim7 :

Renoise spelling - G# B D F

Normal classical spelling - 1st Ab, b3rd Cb, b5th Ebb, bb7th Gbb = Abdim7
( based on Ab Major scale degrees)

Classical spelling in context of describing it as a chord from A harmonic minor - 1st G#, b3rd B, b5th D, bb7th F = G#dim7
( based on G# Major scale degrees )

( Note that the 3rd is flattened because A Major scale contains C#, the 6th is flattened because A Major scale has F# )

So these notes are flattened compared to major scale, but I don’t understand why you need to make everything relative to the major scale?
These are just a_minor 3rd_ and minor 6th.

[To spell the G# chords I must use G# Major scale - 1st G#, 2nd A#, 3rd B#, 4th C#, 5th D#, 6th E#, 7th Fx]

This is one of the bits I don’t understand. Why aren’t you describing G#dim in it’s own terms - root ( G# ), minor 3rd ( B ), dim 5th ( F ) instead of doing everything relative to an irrelevant major scale ?

As I understand it its like this:

Both the A harmonic minor scale and the G#dim chord ( and all scales and chords ) are properly described in terms of how they differ from the Major scale of their root note.

So to describe ‘A harmonic minor’ I have to define it in terms of how it differs from ‘A Major’ ( it has flattened 3rd and flattened 6th degrees of A Major ), same for the G#dim chord. To spell the notes of G#dim properly I have to use G# Major scale. I wouldn’t define the G#dim chord in terms of which notes it contains from A harmonic minor, but rather in terms of how its notes differ from the scale degrees of G# Major scale.

Descriptions of harmonic intervals also describe a Major scale.

Take C Major, for example:

1st C

2nd D - major 2nd …2 semitones up from C

3rd E - Major 3rd …4 semitones up from C

4th F - Perfect 4th …5 semitones up from C

5th G - Perfect 5th …7 semitones up from C

6th A - Major 6th …9 semitones up from C

7th B - Major 7th …11 semitones up from C

8th C - perfect 8th ( octave ) …12 semitones up from C

So when describing Cdim I would use C Major scale as well.

Diminished triads contain a minor 3rd ( 3 semitones up from root note ) and a diminished 5th ( 6 semitones up from root note )…036.

Minor 3rd is minor because its ‘less than’ Major 3rd ( flattened by 1 semitone ), diminished 5th is also a way to say ‘less than’ a perfect 5th ( flattened by 1 semitone ). So Cdim chord spelling must be:

1st - C, ‘b3rd / m3rd - Eb’ and ‘b5th / dim5th’ - Gb… Cdim = C Eb Gb.

It is the same in the description of the C diminished scale ( It has b3rd, b5th and b6th degrees of C Major scale ) :

1st C - root / tonic

2nd D - Major 2nd …2 semitones up from C

b3rd Eb - minor 3rd …3 semitones up from C

4th F - Perfect fourth …5 semitones up from C

b5th Gb - diminished 5th …6 semitones up from C

b6th Ab - minor 6th …8 semitones up from C

6th A - Major 6th …9 semitones up from C

7th B - Major 7th …11 semitones up from C

8th C - perfect 8th ( octave ) …12 semitones up from C

So, as A harmonic minor has a G# and not an Ab, if I want to spell G#dim correctly for the chord guide (regarding chords from scale - A harmonic minor ) I must use the notes of G# Major.

1st G#

2nd A#

3rd B#

4th C#

5th D#

6th E#

7th Fx

1st - G#, ‘b3rd / m3rd’ - B, ‘b5th / dim5th’ D… G#dim = G# B D ( 036 )

Another one G#dim7 :

1st - G#, ‘b3rd / m3rd’ - B, ‘b5th / dim5th’ - D, 'bb7th / dim7th - F…G#dim7 = G# B D F ( 0369 )

As it turns out, it is the same chord spelling both in terms of writing the chords into the renoise pattern editor ( G#dim = G# B D, G#dim7 = G# B D F ) and in terms of writing the chords using the notes within A harmonic minor - ABCDEFG# ( G#dim = G# B D, G#dim7 = G# B D F )

Hooktheorychapter 5 is about inversions. It’s easy to follow with good examples.

Hook theory ( and now hook theory 2 ) looks awesome.

Thanks, Great book recommendation.

I will have to save up to buy it. Quite expensive. Next month.

@lettuce : you’ll probably dig this site: http://guitardashboard.com/

nice !

complemets with:

https://www.guitaristsreference.com/?action=chords&id=1

Here are a bunch of links I found useful for studying various aspects of music theory.

They are in a completely random order, sorry about that.

Havent sorted them out yet. Still, many useful sites.

http://www.guitar-chords.org.uk/modes/c-dorian-mode.html
www.guitar-chords.org.uk/modes/gsharp-locrian-mode.html
http://www.all-guitar-chords.com/scales-to-chords.php
https://en.wikibooks.org/wiki/Piano/Fingering
http://www.piano-keyboard-guide.com/piano-chords.html
http://www.bandcoach.org/
http://www.pianochorddictionary.com/chords/c/major-inversion1.shtml
http://scottdavies.net/chords_and_scales/music.html (CREATE CHORDS FROM SCALES)
https://www.wolframalpha.com/input/?i=scale+A,+C%23,+E (chords to scale)
http://www.piano-keyboard-guide.com/piano-chords.html
https://www.basicmusictheory.com/e-flat-harmonic-minor-scale
http://www.themusicalear.com/sharps-or-flats-how-to-spell-notes-correctly/
https://www.hooktheory.com/music-theory-for-songwriting
https://www.ultimate-guitar.com/lessons/guitar_techniques
https://www.theguitarlesson.com/guitar-techniques/harmonics/
http://www.michaelnorris.info/theory/harmonicseriescalculator
https://en.wikipedia.org/wiki/Piano_key_frequencies
http://www.jeff-brent.com/Lessons/AdvancedPianoFingerings.html
http://blog.dubspot.com/music-theory-modes/
https://en.wikibooks.org/wiki/Music_Theory/Scales_and_Intervals#Simple_intervals
https://www.moderndrummer.com/article/january-1978-jazz-drummers-workshop-polyrhythms/
http://pianoencyclopedia.com/scales/diminished/C-diminished.html ( for diminished scales traditional )
https://www.chordsscales.com/chords/piano/Csharp_/sus2sus4/
https://www.pianochord.org/d-dim7.html
https://en.wikipedia.org/wiki/Borrowed_chord
http://www.jazclass.aust.com/improvisation/im12.htm
http://www.tonalcentre.org/Diatonic.html
https://www.ars-nova.com/Theory%20Q&A/Q144.html
https://www.jamplay.com/articles/5-guides/153-harmonic-minor-modes
https://www.musictheoryacademy.com/understanding-music/primary-chords/
https://en.wikipedia.org/wiki/Primary_triad
https://en.wikipedia.org/wiki/Function_(music)#Diatonic_functions_of_notes_and_chords
http://guitardashboard.com/
https://www.guitaristsreference.com/?action=chords&id=1

I have a Chord inversion click recommendation.

I have developed over 1/3rd of this tool for Renoise 3. It features 235 chord types to listen to (with OSC server enabled) and serve them into the pattern (with Record enabled). I have also invested in the translations.

You can inverse any chord with the Inversion value selection.

Forum topic: https://forum.renoise.com/t/hurray-for-ChordLord/62253
English version: https://renoise.com/tools/ChordLord
Version en Español: https://renoise.com/tools/AcordeSenor
Version en Português: https://renoise.com/tools/SenhorAcordes
Version en Français: https://renoise.com/tools/AccordSeigneur
Version in Italiano: https://renoise.com/tools/AccordoSignore