Understanding Frequency Ratios, tuning, any tips?

Anything modular synth related that is not format specific.

Moderators: Kent, Joe., analogdigital, infradead, lisa, parasitk, plord, sduck

Damo303
Veteran Wiggler
Posts: 620
Joined: Tue Aug 02, 2011 4:06 pm

Understanding Frequency Ratios, tuning, any tips?

Post by Damo303 » Fri Aug 23, 2013 9:19 pm

I've been learning FM synthesis, i'm trying to understand Frequency ratios.

If I want to tune my oscillators a fifth apart, thats seven semitones right?

So for example if I tune osc 1 to a 'C1' (using the Jones o'Tool) then osc 2 should be tuned to 'G1'.

Going by the TipTop Freq/Note chart C1 = 33Hz and G1 = 49hz, as these are not mathematically even intervals this will give me an Inharmonic overtone, correct?

Or a Inharmonic overtone is only created by subtracting or adding a constant number? (i've googled the definition of 'constant number' and the explanations are confusing to the say the least, anyone explain it in simple terms?)

Basically i'm interested in exploring the different tones I can get out of FM synthesis and subtractive synthesis, I like bass/lead sounds where artists seem to tune their oscs a fifth apart so I wanted to understand it fully and try the same techniques.

cheers

User avatar
VortexRanger
reticulating splines
Posts: 2451
Joined: Fri Mar 04, 2011 12:13 pm
Location: North Carolina

Post by VortexRanger » Fri Aug 23, 2013 9:32 pm

The harmonic overtones based on frequency ratios start with one octave, then an octave and a fifth. So if you want to tune to the second ratio of "C1" it should be "G2".
:hobbes:

User avatar
VortexRanger
reticulating splines
Posts: 2451
Joined: Fri Mar 04, 2011 12:13 pm
Location: North Carolina

Post by VortexRanger » Fri Aug 23, 2013 9:32 pm

:hobbes:

User avatar
VortexRanger
reticulating splines
Posts: 2451
Joined: Fri Mar 04, 2011 12:13 pm
Location: North Carolina

Re: Understanding Frequency Ratios, tuning, any tips?

Post by VortexRanger » Fri Aug 23, 2013 9:38 pm

Damo303 wrote: I like bass/lead sounds where artists seem to tune their oscs a fifth apart so I wanted to understand it fully and try the same techniques.

cheers
This usually is just two oscillators mixed together before the filter, as on a Minimoog or its descendants, rather than modulating each others' frequency, if I'm understanding what you're saying.

FM ratios (and even more so, additive synthesis) are based on harmonic series because different levels of various harmonics over time are the essence of what gives musical sounds their timbre.
:hobbes:

Mans
Super Deluxe Wiggler
Posts: 1097
Joined: Thu Jan 28, 2010 12:20 pm
Location: Rotterdam

Post by Mans » Fri Aug 23, 2013 10:28 pm

This might be of help: http://www.soundonsound.com/sos/may00/a ... /synth.htm

Also with analog oscs sync can be of great help in getting nice integer ratios between two oscs.

User avatar
felixer
Super Deluxe Wiggler
Posts: 4140
Joined: Thu May 13, 2010 9:27 pm
Location: germany

Re: Understanding Frequency Ratios, tuning, any tips?

Post by felixer » Fri Aug 23, 2013 11:12 pm

Damo303 wrote:TipTop Freq/Note chart C1 = 33Hz and G1 = 49hz
they are just off: 33*1,5=49,5 ... the difference would be slow chorusing@0,5Hz.
that would be 'just' intonation, beware that the fifth on an equaltempered keyboard (like a synth or organ) is slightly (2 cents) flatter.
this is a problem and it gets worse with the major third and minor seventh. you can get very deep into theory and go pretty crazy (some pianotuners have suffered serious damage), but in the end it just has to sound good and you tweak until it does :hihi:
forget numbers and displays (or use 'm to get in the ballpark) and use your ears for finetuning.
don't need midi, don't need keys, just want knobs and cables (all together now ;-)

User avatar
LeFreq
Super Deluxe Wiggler
Posts: 1252
Joined: Thu Feb 21, 2013 3:24 pm
Location: LA

Post by LeFreq » Sat Aug 24, 2013 12:22 am

I just listen! :tu:
Support My Gear Addiction:
For Sale/Trade

User avatar
Frankenzappa
Common Wiggler
Posts: 92
Joined: Sat Jul 28, 2012 6:24 pm
Location: Los Angeles

Post by Frankenzappa » Sat Aug 24, 2013 12:35 am

LeFreq wrote:I just listen! :tu:
+1 don't over think fm. just use your ears and have fun :cloud:

User avatar
lego
Common Wiggler
Posts: 151
Joined: Tue Mar 26, 2013 2:16 am
Location: Portland, OR

Post by lego » Sat Aug 24, 2013 12:47 am

G1 to C1 approximates a ratio of 3/2.

G1 ~= 49.00
C1 ~= 32.70
G1 / C1 ~= 1.498

A general rule of thumb is that simple ratios like 3/2 can produce more harmonic FM sounds than complex ratios, which can create more enharmonic or clangorous sounds.

Fifths sound consonant to us and show up all over the place. Stringed instruments like violins and cellos are tuned in fifths. A fifth can be used in a lead or bass patch without contributing to whether a chord is major or minor, and without creating beats and taking up too much sonic space like thirds can. They're used in "power chords" on guitar and bass. I think fifths can be easy and intuitive to dial in when tuning two oscillators to each other.

To answer your question, yes, a fifth is 7 semitones. You can remember a fifth by counting 5 notes of the scale starting with 1 (C D E F G), and you can count 7 semitones but start with 0 (C C# D D# E F F# G). Yay music terminology. :despair:

User avatar
ndkent
Super Deluxe Wiggler
Posts: 3586
Joined: Tue Dec 23, 2008 5:59 am

Post by ndkent » Sat Aug 24, 2013 2:46 am

In a nutshell, for FM you want math numbers like 3 to 2 frequency ratios for a fifth.

Don't look up frequencies of notes in Western music. All scales are compromised somehow because you either get pure harmonic intervals and need a new tuning for every key you write music in. Meaning a melody based in the key of C will sound right but start playing the same melody in say F# and it will sound sour or wrong. Or do what western music has done in the last couple hundred years and use Equal Temperament which means all scales are equally a bit off and harmonically compromised but an equal amount so anything interval sounds the same in any key.

Finally when using frequencies to get things in the right ratio, I think going for ones comfortably high is to your advantage. Lower frequencies are a little harder to work with imho and the frequency count may be rounded more when down low. Obviously you hope your VCOs then track
Last edited by ndkent on Sat Aug 24, 2013 5:01 pm, edited 1 time in total.

StoneLaw
Super Deluxe Wiggler
Posts: 1631
Joined: Mon Feb 04, 2013 9:59 pm
Location: Minneapolis, MN

Post by StoneLaw » Sat Aug 24, 2013 4:32 pm

:popcorn:

User avatar
Nantonos
Super Deluxe Wiggler
Posts: 1267
Joined: Sun Mar 03, 2013 1:00 pm
Location: Boston, MA

Re: Understanding Frequency Ratios, tuning, any tips?

Post by Nantonos » Sat Aug 24, 2013 10:30 pm

Damo303 wrote: Going by the TipTop Freq/Note chart C1 = 33Hz and G1 = 49hz, as these are not mathematically even intervals this will give me an Inharmonic overtone, correct?

Or a Inharmonic overtone is only created by subtracting or adding a constant number? (i've googled the definition of 'constant number' and the explanations are confusing to the say the least, anyone explain it in simple terms?
Forget intervals (subtracting) and adding. Instead think of doubling and halving, ie multiplying and dividing. An octave is a double. Go from there.
ondes | current rack
I am afraid a firmware change will not be able to turn a rather expensive 16-bit DAC into a 16-bit ADC, and flip all those op-amps :)

User avatar
Nantonos
Super Deluxe Wiggler
Posts: 1267
Joined: Sun Mar 03, 2013 1:00 pm
Location: Boston, MA

Post by Nantonos » Sat Aug 24, 2013 10:41 pm

lego wrote: To answer your question, yes, a fifth is 7 semitones. You can remember a fifth by counting 5 notes of the scale starting with 1 (C D E F G), and you can count 7 semitones but start with 0 (C C# D D# E F F# G). Yay music terminology. :despair:
An octave, from the Latin for eight, so called because it has twelve notes :omg: :omg: :omg: :omg: music terminology :roll:
ondes | current rack
I am afraid a firmware change will not be able to turn a rather expensive 16-bit DAC into a 16-bit ADC, and flip all those op-amps :)

User avatar
Samwise
Common Wiggler
Posts: 167
Joined: Mon Apr 15, 2013 12:57 am
Location: Charleston, SC, USA

Post by Samwise » Sat Aug 24, 2013 11:52 pm

lego wrote: An octave, from the Latin for eight, so called because it has twelve notes :omg: :omg: :omg: :omg: music terminology :roll:
Uh...if you're talking about scales, then yeah, it's eight notes per octave.

User avatar
Captain Coconut
Wiggling with Experience
Posts: 367
Joined: Thu May 26, 2011 3:25 pm
Location: Western WA, USA

Post by Captain Coconut » Sun Aug 25, 2013 12:43 am


User avatar
wednesdayayay
Super Deluxe Wiggler
Posts: 1575
Joined: Wed Nov 16, 2011 8:17 am

Post by wednesdayayay » Sun Aug 25, 2013 8:19 am

viewtopic.php?t=91090
there is a diamond tuning table near the end of the first page that may be of some help

http://petermopar.blogspot.com/2013/08/tunings.html

these both give some extra insight into ciat-lonbarde/shbobo instrument tunings but I think you may be able to get something out of them as well

the shbobo shnth can do some amazing things with regard to tunings

User avatar
usw
Veteran Wiggler
Posts: 573
Joined: Sun Aug 14, 2011 4:19 am
Location: Villeurbanne, France

Post by usw » Mon Aug 26, 2013 2:22 am

Samwise wrote:
lego wrote: An octave, from the Latin for eight, so called because it has twelve notes :omg: :omg: :omg: :omg: music terminology :roll:
Uh...if you're talking about scales, then yeah, it's eight notes per octave.
7 notes per octave actually ;)

User avatar
Captain Coconut
Wiggling with Experience
Posts: 367
Joined: Thu May 26, 2011 3:25 pm
Location: Western WA, USA

Post by Captain Coconut » Mon Aug 26, 2013 3:25 am

And the eighth is the octave.

User avatar
felixer
Super Deluxe Wiggler
Posts: 4140
Joined: Thu May 13, 2010 9:27 pm
Location: germany

Post by felixer » Mon Aug 26, 2013 2:14 pm

usw wrote:
Samwise wrote:
lego wrote: An octave, from the Latin for eight, so called because it has twelve notes :omg: :omg: :omg: :omg: music terminology :roll:
Uh...if you're talking about scales, then yeah, it's eight notes per octave.
7 notes per octave actually ;)
some may think that the chromatic scale (all 12 notes) is the basis of all scales. actually it's the other way around: if you stack all scales on top of each other you'll get the cromatic scale. so start thinking in terms of harmonics. then it becomes clear that the octave is a close relative to the fundamental. the fifth is still family, the major third starts to get a bit off and the minor seventh is no more then a cousin. western harmony doesn't use any more harmonics. the others (minor third, fourth etc) are the result of 'a fifth minus major thrid' or 'octave minus fifth' etc

in chords etc (anything you play on a keyboard) you can often get away with equal tempered but within sounds (like fm of additive) it sounds lousy. just intonation sounds right.
so there's the problem. pythagoras found out over 3000 years ago and since then many clever people (like werckmeister, kirnberger et all) tried to solve the puzzle, but all they could come up with were various compromises.

but yes, do study all those things. it's fascinating, but it will not give you 'the answer' so that everthing will be in tune for all times. because that is impossible. not only practical but also theoretical. so we all end up doing our version of some compromise that sounds 'good enough' for us ... we live in an imperfect universe. but you knew that already :mrgreen:
don't need midi, don't need keys, just want knobs and cables (all together now ;-)

User avatar
Tim Stinchcombe
Uncommon Wiggler
Posts: 1418
Joined: Fri Mar 13, 2009 1:55 pm
Location: Cheltenham, Glos, UK

Post by Tim Stinchcombe » Mon Aug 26, 2013 2:51 pm

PDF download of 'Music: A Mathematical Offering':

http://homepages.abdn.ac.uk/mth192/pages/html/music.pdf

from here:

http://homepages.abdn.ac.uk/mth192/page ... music.html

More mathematics than many musicians can shake a stick at!

Tim

n_m
Veteran Wiggler
Posts: 595
Joined: Sat Jan 26, 2013 4:51 pm

Post by n_m » Mon Aug 26, 2013 4:03 pm

Tim Stinchcombe wrote: http://homepages.abdn.ac.uk/mth192/page ... music.html
More mathematics than many musicians can shake a stick at!
Tim
I love threads like this one! :party:

I know what I'll be reading the upcoming weekend. Thank you Tim Stinchcombe :hail:

Don Erskine
Learning to Wiggle
Posts: 4
Joined: Mon Jul 22, 2013 2:21 pm
Location: UK

Post by Don Erskine » Mon Aug 26, 2013 10:28 pm

I just think in integer multiples of 0.0833333333 Volts. :hihi:

User avatar
dkcg
I pity the fool w/o enough VCAs
Posts: 9138
Joined: Mon Jul 14, 2008 12:35 pm
Location: LA

Post by dkcg » Tue Aug 27, 2013 2:16 am

i just use my ears and a little experimentation, aka knob twisting.

User avatar
felixer
Super Deluxe Wiggler
Posts: 4140
Joined: Thu May 13, 2010 9:27 pm
Location: germany

Post by felixer » Tue Aug 27, 2013 6:03 am

Tim Stinchcombe wrote:PDF download of 'Music: A Mathematical Offering':

http://homepages.abdn.ac.uk/mth192/pages/html/music.pdf

from here:

http://homepages.abdn.ac.uk/mth192/page ... music.html

More mathematics than many musicians can shake a stick at!

Tim
thanks :tu:
music used to be an exact science along with mathematics, astronomy and physics. but beware of greek theories as they sound good but are invariably wrong :mrgreen: listening to radiotelescoop output will give you a taste of the 'harmony of the spheres'. sound more like john cage then mozart ...
don't need midi, don't need keys, just want knobs and cables (all together now ;-)

Naive Teen Idol
Common Wiggler
Posts: 163
Joined: Tue Jul 02, 2013 7:37 pm

Post by Naive Teen Idol » Tue May 07, 2019 6:33 pm

Question: is there a Scala scale that aligns to the harmonic series for "easy" ratios in a modular context? If so, I'm thinking you could use, say, Disting's microtonal quantizer mode (algorithm K-5) to set it up.

Post Reply

Return to “Modular Synth General Discussion”