I'm interested in making a tune that uses the harmonic series found in a saw wave, instead of the 12 tone set.
Does anyone know if I can lay out all (well, 120) the harmonics of say, a C1 saw wave, with a TUN file and a synth with tuning support?
TUN files for microtonal music?
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- KVRAF
- 6388 posts since 8 Jun, 2009
You should be able to. The TUN spec is here:http://www.mark-henning.de/files/Tuning_File_V2_Doc.pdf. But using Scala or something is going to be a lot easier.
However, you can get the first 20 partials (a saw is all the even and odd partials summed together), more or less, by simply leaving notes out of a regular scale (it winds up being like a blues scale but with a raised third in the G clef region). After the 20th (somewhere around E5 or F5) it starts going microtonal: http://en.wikipedia.org/wiki/Harmonic_series_(music)
So you might the results a bit less interesting than you were expecting.
However, you can get the first 20 partials (a saw is all the even and odd partials summed together), more or less, by simply leaving notes out of a regular scale (it winds up being like a blues scale but with a raised third in the G clef region). After the 20th (somewhere around E5 or F5) it starts going microtonal: http://en.wikipedia.org/wiki/Harmonic_series_(music)
So you might the results a bit less interesting than you were expecting.
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- KVRian
- Topic Starter
- 797 posts since 23 Apr, 2009
Yeah that's true, it's quite fascinating actually that so many of the intervals in the series are so close to the 12 tone series. But I'm just as interested in the small derivations from the 12 tone in the early partials, like the 7th partial of C2 is A4+69 cents. Stuff like that.Gamma-UT wrote:You should be able to. The TUN spec is here:http://www.mark-henning.de/files/Tuning_File_V2_Doc.pdf. But using Scala or something is going to be a lot easier.
However, you can get the first 20 partials (a saw is all the even and odd partials summed together), more or less, by simply leaving notes out of a regular scale (it winds up being like a blues scale but with a raised third in the G clef region). After the 20th (somewhere around E5 or F5) it starts going microtonal: http://en.wikipedia.org/wiki/Harmonic_series_(music)
So you might the results a bit less interesting than you were expecting.
Thanks for the link.
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- KVRAF
- 6388 posts since 8 Jun, 2009
That might be one of the reasons why quarter notes were incorporated into early Greek and Middle Eastern music. The deviation from Pythagorean tuning is slightly smaller and I think works out to be much closer to A plus a quarter (haven't checked - might be wrong on the direction).TankEyes wrote:Yeah that's true, it's quite fascinating actually that so many of the intervals in the series are so close to the 12 tone series.
This researcher reckons it's not a coincidence: http://eceserv0.ece.wisc.edu/~sethares/ (The sawtooth was intended to emulate the frequency response of a bowed or plucked string).
TankEyes wrote:But I'm just as interested in the small derivations from the 12 tone in the early partials, like the 7th partial of C2 is A4+69 cents. Stuff like that.
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- KVRian
- Topic Starter
- 797 posts since 23 Apr, 2009
that's right, the word is deviation...
I'll have to study the different tunings like the Pythagorean one.
Out of interest, You know the saw is odd + even, the square is odd only, do the even only (or even + fundamental) harmonics produce a distinctive shape when summed to nyquist? I tried it on my additive with a bunch of partials and got a short pulse type shape. Maybe if I inverted a square and added a saw I could get a good result?
I'll have to study the different tunings like the Pythagorean one.
Out of interest, You know the saw is odd + even, the square is odd only, do the even only (or even + fundamental) harmonics produce a distinctive shape when summed to nyquist? I tried it on my additive with a bunch of partials and got a short pulse type shape. Maybe if I inverted a square and added a saw I could get a good result?
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- KVRAF
- 26033 posts since 20 Oct, 2007 from gonesville
the thing about harmonics is that they are spaced closer and closer together as higher partials.
to transpose that down into an octave range and formulate as a tuning will be fraught with problems, in terms of useful musicality IME.
> per the seventh partial, I don't know that a 31¢ deviation off a dollar is that small, btw.
your odd harmonics are just not reflected in 12T ET; you get past the sixth partial and it's a whole nother ballgame in terms of 'notes'. Harmonic reality is other than equally tempered.
the Arabs played around for centuries with the arithmetics of just - and other, higher limit rational - intonations to come up with their intervals, which are not well described as quarter tones. That is a conventionally used term but it's about as off in many cases as that other 'small' deviation.
to transpose that down into an octave range and formulate as a tuning will be fraught with problems, in terms of useful musicality IME.
> per the seventh partial, I don't know that a 31¢ deviation off a dollar is that small, btw.
your odd harmonics are just not reflected in 12T ET; you get past the sixth partial and it's a whole nother ballgame in terms of 'notes'. Harmonic reality is other than equally tempered.
the Arabs played around for centuries with the arithmetics of just - and other, higher limit rational - intonations to come up with their intervals, which are not well described as quarter tones. That is a conventionally used term but it's about as off in many cases as that other 'small' deviation.
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- KVRAF
- 6388 posts since 8 Jun, 2009
It's called the parabola waveform apparently (I had to go search for the name). Quite soothing though, like a sawtooth that's retired for the night with a pipe and slippers.TankEyes wrote:that's right, the word is deviation...
I'll have to study the different tunings like the Pythagorean one.
Out of interest, You know the saw is odd + even, the square is odd only, do the even only (or even + fundamental) harmonics produce a distinctive shape when summed to nyquist? I tried it on my additive with a bunch of partials and got a short pulse type shape. Maybe if I inverted a square and added a saw I could get a good result?
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- KVRian
- Topic Starter
- 797 posts since 23 Apr, 2009
Yeah I agree Jan. That's why I was asking about the TUN format because I don't want to have to work in an octave based framework. Basically I'm imagining a drone type ambient piece where the harmonics play little decorations and mini melodies and such.
Last edited by TankEyes on Mon Nov 09, 2009 9:10 pm, edited 1 time in total.
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- KVRian
- Topic Starter
- 797 posts since 23 Apr, 2009
hehe no way! a parabola? cool.Gamma-UT wrote:It's called the parabola waveform apparently (I had to go search for the name). Quite soothing though, like a sawtooth that's retired for the night with a pipe and slippers.
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Aroused by JarJar Aroused by JarJar https://www.kvraudio.com/forum/memberlist.php?mode=viewprofile&u=191505
- KVRian
- 1048 posts since 16 Oct, 2008
Scala will let you do this, and innumerable other things. IIRC, there's even a command for harmonic series scales where you just type in the first and last harmonic you want. Have to check in the studio later.
Once you have your .scl format scale, you convert it to .tun with the following commands:
set synth
112
send/file
YourTuning.tun
Most stuff in Scala is in the menus, with many keyboard shortcuts as well, but
these format conversions and some scale-generating/modifying commands are entered on the command line (which is right there in the GUI anyway)
With octave reduction and duplicate pitches, you'll have quite a bit less than 120 notes.
The first 20 partials will give you a kind of Atlantis-BeBop-Klezmer kind of scale, the notes appearing in this order:
1:1, 2:1, 3:2, 5:4, 7:4, 9:8, 11:8, 13:8, 15:8, 17:16, 19:16
C....c.....G....E....Bb...D.....F#....Ab....B....C#......Eb
0, 1200, 702, 386, 969, 208, 551, 841, 1086, ~100, ~300
(cent values from memory, you have to check for the exact amounts) The relationships between interals here give you all kinds of other intervals found in Persian and Arabic music for example- between 9:8 and 11:8 there is middle third of 11:9 (~342 cents), between 13:8 and 2:1 a middle/major third of 16:13 (~359 cents), etc. as well as your church-choir-sounding or Indian intervals like the minor third of 316 cents (6:5) between 5:4 and 3:2, and so on.
Because of the spacing of the intervals, errors in approximation by equal division get compounded, so just the first 20 partials actually take big ETs to approximate well: 53-ET (Turkish and older European theory), 68-ET (Eastern Orthodox), 72-ET (Russian, and Western "underground" approach) are the most known ways.
At any rate, I hope the OP does try this out. There is a great thing about this spectral-drone approach: a tight resonant filter sweep of a droning tonic will play your scale!
Once you have your .scl format scale, you convert it to .tun with the following commands:
set synth
112
send/file
YourTuning.tun
Most stuff in Scala is in the menus, with many keyboard shortcuts as well, but
these format conversions and some scale-generating/modifying commands are entered on the command line (which is right there in the GUI anyway)
With octave reduction and duplicate pitches, you'll have quite a bit less than 120 notes.
The first 20 partials will give you a kind of Atlantis-BeBop-Klezmer kind of scale, the notes appearing in this order:
1:1, 2:1, 3:2, 5:4, 7:4, 9:8, 11:8, 13:8, 15:8, 17:16, 19:16
C....c.....G....E....Bb...D.....F#....Ab....B....C#......Eb
0, 1200, 702, 386, 969, 208, 551, 841, 1086, ~100, ~300
(cent values from memory, you have to check for the exact amounts) The relationships between interals here give you all kinds of other intervals found in Persian and Arabic music for example- between 9:8 and 11:8 there is middle third of 11:9 (~342 cents), between 13:8 and 2:1 a middle/major third of 16:13 (~359 cents), etc. as well as your church-choir-sounding or Indian intervals like the minor third of 316 cents (6:5) between 5:4 and 3:2, and so on.
Because of the spacing of the intervals, errors in approximation by equal division get compounded, so just the first 20 partials actually take big ETs to approximate well: 53-ET (Turkish and older European theory), 68-ET (Eastern Orthodox), 72-ET (Russian, and Western "underground" approach) are the most known ways.
At any rate, I hope the OP does try this out. There is a great thing about this spectral-drone approach: a tight resonant filter sweep of a droning tonic will play your scale!
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- KVRAF
- 26033 posts since 20 Oct, 2007 from gonesville
sounds like a great idea to me.TankEyes wrote:Yeah I agree Jan. That's why I was asking about the TUN format because I don't want to have to work in an octave based framework. Basically I'm imagining a drone type ambient piece where the harmonics play little decorations and mini melodies and such.
I'd like something similiar, in this case. Last I looked at scala, you had to be far more geekified to get it to work on OSX and I quit looking at it.
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- KVRian
- Topic Starter
- 797 posts since 23 Apr, 2009
Aroused by Jarjar (lol @ username)- thanks for the great reply man. Unfortunately a lot of it when over my head!
Can you explain what the third row of your table means?
What's an ET?
You couldn't make me a TUN file could you? I don't really want to have to learn a programming language to do this. I've got Visual Studio and I'm OK with C++. I wonder if there's some kinda scale making library I could use.
I can use a narrow band spectral filter like iZotope Spectron to approximate the effect. I could also individually sample each partial of an additive synth, then map it in a sampler, that would give me accurate volume levels as well as pitch, but it's a lot of work
Can you explain what the third row of your table means?
What's an ET?
You couldn't make me a TUN file could you? I don't really want to have to learn a programming language to do this. I've got Visual Studio and I'm OK with C++. I wonder if there's some kinda scale making library I could use.
I can use a narrow band spectral filter like iZotope Spectron to approximate the effect. I could also individually sample each partial of an additive synth, then map it in a sampler, that would give me accurate volume levels as well as pitch, but it's a lot of work
Last edited by TankEyes on Tue Nov 10, 2009 10:56 pm, edited 1 time in total.
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- KVRAF
- 26033 posts since 20 Oct, 2007 from gonesville
ET is equal temperament. eg., an octave divided into twelve equal parts.
the last row in that table is relative to cents in that 12 tones equal temperament -
C to c is 1200, one octave, 12$; then you see that an ET perfect fifth is 2¢ flatter (700 vs 702¢) than a 'just intoned' fifth (3:2), and that an ET major third is 14¢ sharper (400 vs 386¢) than a 5:4 third etc.
the last row in that table is relative to cents in that 12 tones equal temperament -
C to c is 1200, one octave, 12$; then you see that an ET perfect fifth is 2¢ flatter (700 vs 702¢) than a 'just intoned' fifth (3:2), and that an ET major third is 14¢ sharper (400 vs 386¢) than a 5:4 third etc.
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- KVRAF
- 6388 posts since 8 Jun, 2009
If you go to the Scala page, there's a ZIP file full of tunings - something like harm30 in that lot should do the trick. But you'll have to install Scale to be able to convert them into a file format that you can use with a synth (unless you've got one that will read .scl directly).