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🔗Mario Pizarro <piagui@...>

11/16/2012 7:29:53 AM

Mike,

Your idea of presenting the progression in two sections of 306 cells can be applied since any pair of cells (MM, JJ, UU) is consonant with any of the mentioned pairs.

I always had the sensation that 12 TET is formed by 2 parts and that the first part ends on cell # 306, (2^1/2). At the present we notice that the first section starts with (SSS) or 3 sets of MMJJMM. The first U was placed at cell number 23; some times I moved this U to cell # 23 + 6 = Cell # 29. This change made 4 sets of MMJJMM as the initial groups. Consequently, the whole number of UU pairs occupy the following cells: 23-24, ...........595-596 + S + R + *S + S + S. The last M of second *S gives the octave 2.
(R = MMJJ). We also see that cells # 607 up to cell # 624 form SSS that makes a total symmetrical set of 624 cells. The cyclical (9/8)´s makes the number series 1, 2, 3, 4, ..........etc. When continuing the progression, besides the pair numbers, numbers 3, 6, 9, 11.... (+ 10) must appear. Then we can say that the periodical (9/8)^1/2 is the base of the number series.
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
------------------------------------------------ Regards ---------------- Mario ----------- November 16
13 M 13 1.01478782047
14 M 14 1.01593366853
15 J 15 1.01708306653
16 J 16 1.01823376491
17 M 17 1.01938350397
18 M 18 1.02053454125
19 M 19 1.02168687823
20 M 20 1.02284051636
21 J 21 1.02399772856
22 J 22 1.02515625
23 U 23 1.02640047856
24 U 24 1.02764621724
25 M 25 1.02880658437
26 M 26 1.02996826173
27 J 27 1.03113353805
28 J 28 1.03230013274
29 M 29 1.03346575483
30 M 30 1.03463269310

23 U 595 1.96180446806
24 U 596 1.96418550330
25 M 597 1.96640336411
26 M 598 1.96862372925
27 J 599 1.97085097325
28 J 600 1.97308073708
29 M 601 1.97530864197
30 M 602 1.97753906249
31 M 603 1.97977200149
32 M 604 1.98200746182
33 J 605 1.98424984779
34 J 606 1.98649477072
35 M 607 1.98873782207
36 M 608 1.99098340615
37 J 609 1.99323594724
38 J 610 1.99549103679
39 M 611 1.99774424627
40 M 612 2
41 M 613 2.00225830075
42 M 614 2.00451915149
43 J 615 2.00678700653
44 J 616 2.00905742735
45 M 617 2.01132595533
46 M 618 2.01359704485
47 M 619 2.01587069874
48 M 620 2.01814691993
49 J 621 2.02043019303
50 J 622 2.02271604936
51 M 623 2.025
52 M 624 2.02728652952
. = (9/8)^6

Hello Mario - I'm sorry to hear about your health.

I'd like to name a certain musical temperament that's suggested by the
progression of 612 cells "Pizarro temperament"; the 612-note scale
contains two separate chains of 306 notes, each of which is generated
by an approximate 3/2 (the approximation is so close that the error
can't be detected by the human ear). This isn't exactly what you have
in your progression of cells, but it's strongly suggested by it.

Is that alright? YES MIKE, IT IS ALRIGHT ------ MARIO

Thanks and sorry again to hear about your illness; best of luck with
your recovery!

-Mike

🔗RR <djtrancendance@...>

11/16/2012 1:01:42 PM

I wonder if any of you have an interest in working with me to design something like this.

It will hopefully allow you to specify certain "tunefulness" criteria e.g.

A) How many fourth/fifth/any-alternative-semi-equivalence-ratio are allowed in a row far as shifting the root of the chord
B1) What kind of melodic progression is allowed e.g. no larger than a whole tone apart for each note unless shifting by something in A) above
B2) Additionally, what's the maximum total melodic movement per chord switch e.g. if C E G shift to D E A, that's (C-D = 2) + (E-E = 0) + (G to A = 2) = 4 total steps

C) What percentage of the chords must involve (as I understand them) comma pumps (e.g. in a three note chord, keep two of the same notes, but invoke a third that shifts the apparent VF)
D) How many iterations of chords in the progression must return to the root e.g. 3,4,5...
E) What counts as a chord e.g. either specify a list of define criteria such as minimum ratio between any two tones in the chord or average ratio/difference among all tones.

One thing required is the ability to specify the scale and what ratio in the scale you are treating as a fifth and/or semitone...this is needed to make sure all random combinations calculated fit within the scale.

 

________________________________
From: Mario Pizarro <piagui@...>
To: tuning yahoogroups <tuning@yahoogroups.com>
Cc: Mike Battaglia <battaglia01@...>
Sent: Friday, November 16, 2012 9:29 AM
Subject: [tuning] Your question

 
Mike,
 
Your idea of presenting the progression in two
sections of 306 cells can be applied since any pair of cells (MM, JJ, UU)
is consonant with any of the mentioned pairs.
 
I always had the sensation that 12 TET is
formed by 2 parts and that the first part ends on cell # 306, (2^1/2). At the
present we notice that the first section starts with (SSS) or 3 sets
of MMJJMM. The first U was placed at cell
number 23; some times I moved this U to cell # 23 + 6 = Cell
# 29. This change made 4 sets of MMJJMM as the initial
groups. Consequently, the whole number of
UU pairs occupy the following cells:    23-24,
...........595-596 + S + R + *S + S + S. The last M of second 
*S gives the octave 2.  
(R = MMJJ). We also see that cells # 607 up to cell
# 624 form SSS that makes a total symmetrical set of 624 cells. The
cyclical  (9/8)´s makes the number series 1, 2, 3, 4,
..........etc. When continuing the progression, besides the pair
numbers, numbers 3, 6, 9, 11.... (+ 10) must appear. Then we can say
that the periodical (9/8)^1/2 is the base of the number
series.  
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
------------------------------------------------
Regards ---------------- Mario ----------- November 1613 M 13 1.01478782047
14 M 14 1.01593366853
15 J 15 1.01708306653
16 J 16 1.01823376491
17 M 17 1.01938350397
18 M 18 1.02053454125
19 M 19 1.02168687823
20 M 20 1.02284051636
21 J 21 1.02399772856
22 J 22 1.02515625
23 U 23 1.02640047856
24 U 24 1.02764621724
25 M 25 1.02880658437
26 M 26 1.02996826173
27 J 27 1.03113353805
28 J 28 1.03230013274
29 M 29 1.03346575483
30 M 30 1.03463269310
 
  23 U 595 1.96180446806
  24 U 596 1.96418550330
  25 M 597 1.96640336411
  26 M 598 1.96862372925
  27 J 599 1.97085097325
  28 J 600 1.97308073708
  29 M 601 1.97530864197
  30 M 602 1.97753906249
  31 M 603 1.97977200149
  32 M 604 1.98200746182
  33 J 605 1.98424984779
  34 J 606 1.98649477072
  35 M 607 1.98873782207
  36 M 608 1.99098340615
  37 J 609 1.99323594724
  38 J 610 1.99549103679
  39 M 611 1.99774424627
  40 M 612 2
  41 M 613 2.00225830075
  42 M 614 2.00451915149
  43 J 615 2.00678700653
  44 J 616 2.00905742735
  45 M 617 2.01132595533
  46 M 618 2.01359704485
  47 M 619 2.01587069874
  48 M 620 2.01814691993
  49 J 621 2.02043019303
  50 J 622 2.02271604936
  51 M 623 2.025
  52 M 624 2.02728652952
  .  =(9/8)^6
Hello
Mario - I'm sorry to hear about your health.

I'd
like to name a certain musical temperament that's suggested by the
progression
of 612 cells "Pizarro temperament"; the 612-note scale
contains
two separate chains of 306 notes, each of which is generated
by
an approximate 3/2 (the approximation is so close that the error
can't
be detected by the human ear). This isn't exactly what you have
in
your progression of cells, but it's strongly suggested by it.

Is
that alright? YES MIKE, IT IS ALRIGHT ------ MARIO

Thanks
and sorry again to hear about your illness; best of luck with
your
recovery!

-Mike

🔗Keenan Pepper <keenanpepper@...>

11/16/2012 2:10:12 PM

--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>
> I wonder if any of you have an interest in working with me to design something like this.

What is the purpose of this? Seems like it's assigning some scores to pieces of music but it's unclear why you'd want to do that. Algorithmic composition perhaps?

> C) What percentage of the chords must involve (as I understand them) comma pumps (e.g. in a three note chord, keep two of the same notes, but invoke a third that shifts the apparent VF)

That's not what a comma pump is...

Keenan

🔗Mike Battaglia <battaglia01@...>

11/16/2012 2:12:48 PM

On Fri, Nov 16, 2012 at 4:01 PM, RR <djtrancendance@...> wrote:
>
> C) What percentage of the chords must involve (as I understand them) comma
> pumps (e.g. in a three note chord, keep two of the same notes, but invoke a
> third that shifts the apparent VF)

This isn't a comma pump. Comma pumps don't have anything (directly) to
do with VFs; they're just chord progressions that modulate you by some
JI comma. If you do them in the temperament that tempers out that
comma, they bring you back to the tonic.

-Mike

🔗RR <djtrancendance@...>

11/16/2012 3:53:02 PM

   The purpose of it is the crack an issue I heard Igs mention: people are scared of approaching xenharmony because they don't have the first clue what the basic chord progressions are.  This could at least help them uncover some basic chord patterns for any arbitrary scale that found very "tuneful", and give them some sense of what a scale is like in practice so they can quickly chose a one that fits their style, before they move on to more advanced progressions.

>>That's not what a comma pump is...
  Sigh.... (not exactly a useful answer)

  Anyhow, I read up on comma pumps...seems to say that taking consecutive steps of a ratio that would normally result in a non-unison e.g. 6/5^4 = 1296/625 (not 2/1) results in a unison because the error between 1296/625 and 2/1 is tempered out.

-------------------------

    My concern is how I would use this toward creating chord progressions.  I realize, apparently, that you can easily chain a circle of tempered fifths in Blackwood to make a chord progression...but (I'm) wondering how this would work for other interval types. 

For starters, I assume temperaments with tempered 6/5 5/4 3/2's (and I believe I'm being pretty generous here by marking movement of a chord root by 6/5 as "tuneful")...that chain to result in unisons have a huge advantage here...what are some of them (categorized by which simple interval they contain)?
  I want to at least take a crack at seeing which ones can make very efficient chord progressions.

 

________________________________
From: Keenan Pepper <keenanpepper@...>
To: tuning@yahoogroups.com
Sent: Friday, November 16, 2012 4:10 PM
Subject: [tuning] Re: Chord progression program (scale independent within subsets of EDOs)

 
--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>
> I wonder if any of you have an interest in working with me to design something like this.

What is the purpose of this? Seems like it's assigning some scores to pieces of music but it's unclear why you'd want to do that. Algorithmic composition perhaps?

> C) What percentage of the chords must involve (as I understand them) comma pumps (e.g. in a three note chord, keep two of the same notes, but invoke a third that shifts the apparent VF)

That's not what a comma pump is...

Keenan

🔗genewardsmith <genewardsmith@...>

11/17/2012 8:54:19 AM

--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:

> For starters, I assume temperaments with tempered 6/5 5/4 3/2's (and I believe I'm being pretty generous here by marking movement of a chord root by 6/5 as "tuneful")...that chain to result in unisons have a huge advantage here...what are some of them (categorized by which simple interval they contain)?

You seem to be asking what are the important 5-limit temperaments, but then you ask about the simple intervals they contain, so I'm left in doubt as to what the actual question is.

🔗cityoftheasleep <igliashon@...>

11/18/2012 8:28:30 AM

--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>
>    The purpose of it is the crack an issue I heard Igs mention: people are scared of
> approaching xenharmony because they don't have the first clue what the basic chord
> progressions are.  This could at least help them uncover some basic chord patterns for
> any arbitrary scale that found very "tuneful", and give them some sense of what a scale is
> like in practice so they can quickly chose a one that fits their style, before they move on
> to more advanced progressions.

For starters, I don't recall saying that. I don't think people are "scared" of xenharmony; they're just not interested in it, because they aren't experiencing any problems with 12-TET that xenharmonic tunings would solve. 12-TET is plenty in-tune and plenty expressively versatile for most people. Those who do get interested in it do so for a variety of reasons, and they all seem to learn it a little bit differently.

Secondly, I think specific chord progressions are less important than understanding the relationships between notes in the scale. Lattices are good for this, but they get mighty difficult to read once you have more than a couple different kinds of relationship to depict. Another useful way to depict these relationships is with a table showing all the modes of the scale in sequence, which demonstrates which chords of interest are found on each degree of the scale. To take meantone[7] for example, if you start with the major scale (the Ionian mode), you can lay it out so that it's clear that the I, IV, and V degrees all form major triads, the ii, iii, and vi degrees all form minor triads, and the vii is diminished. I do this for most new scales I encounter as a first step to figuring out their deeper harmonic structure.

Thirdly, I generally object to any and all approaches that try to quantify something "useful" about specific chord progressions. The most "tuneful" chord progression might also be the most boring/pedestrian/unremarkable. The Porcupine comma pump--starting at one spot on the Porcupine[8] 5-limit lattice and changing one note at a time to move across the lattice until you end up at the first chord again--is probably one of the least interesting things you can do with Porcupine temperament, IMO. But it's probably the most "tuneful" by some standard. Of course, if you treat Porcupine as a 2.3.5.11 temperament, you end up with all kinds of different comma pumps that are probably a little more interesting. You also get some dyadic chords in there, like 1/1-11/10-6/5, which is sort of a "one-chord comma pump"

-Igs

🔗RR <djtrancendance@...>

11/18/2012 8:01:09 PM

>>"For starters, I don't recall saying that. I don't think people are "scared" of xenharmony; they're just not interested in it"
  And you never said anything along the lines of their thinking there are just too many possibilities and no easy way for them to quickly discover which system works for them?  Maybe scared isn't the right word either...more like too intimidated by to make it worth their while.  I also remember you saying that a huge problem with many of my scale systems is they neglected the fact that musicians like to move along simple intervals, such as 3/2, 5/4...concerning chord progressions and I was neglecting "how musicians actually use/combine the chords, not just how many chords are available".  In fact, if I'm correct, that was a primary motivation behind the BP scale system: to chain triads in a system that allows such simple movement.

>>"12-TET is plenty in-tune and plenty expressively versatile for most people."

     Minus one thing: a vast majority of the most mathematically efficient chord progressions in it have been taken (and taken, and taken again) by musicians in the past.  Look at the proportion of upbeat popular music that has a majority of its melodies based on a combination of scale runs and jumps by fourths, octaves, and fifths (and rarely anything else): it's huge...and there are only a fixed number of such efficient jumps in 12EDO.

  The sheer amount of remixes or tracks with entire sampled melodies on the pop charts is pretty obvious evidence of this, as is the fact we get garbage like AVICII and Leona Lewis suing over who sampled an orchestral track "Perpetuum Mobile" by the Penguin Cafe Orchestra first. 

  There may be few musicians who don't think 12EDO isn't versatile enough...minus the fact musicians are constantly running into and over each others' ideas.  So much so it's often to the point many don't even bother to try original chord progressions and mess around with the phrasing-timing/textures with so-so results.
  Hence there are very few modern "classics" that are considered breakthroughs.  Even in alternative genres and completely outside the major label scene...how hard is it to find a modern jazz artist with a current (less than 10 years old) work considered a classic?

  Personally, I've found myself using things like pivot chords and modulations plus movement in the roots of chord progressions by even odd intervals like minor 6ths plus extensive use of odd inversions, diminished chords, 11th and even 13th chords...in my "basic" dance tracks just to keep them from sounding unoriginal in 12EDO...and boy it is not versatile; takes ages to find a melody or chord progression that's both mathematically elegant (all notes have simplified relations to all other notes played within the last few seconds or more so well as to be hummable) and not taken.  And most of the advanced progressions just plain old don't chain together efficiently and end up sounding academic/forced e.g. even when they are original they are often not even vaguely "tuneful", as you'd find out if you tried to sing them.

>>"To take meantone[7] for example, if you start with the major scale (the
Ionian mode), you can lay it out so that it's clear that the I, IV, and V degrees all form major triads, the ii, iii, and vi degrees all form
minor triads, and the vii is diminished. I do this for most new scales   I encounter as a first step to figuring out their deeper harmonic
structure."
  Good idea, shows you the surface...and it's actually quite along the lines of what I was thinking.

>>"The most "tuneful" chord progression might also be the most boring/pedestrian/unremarkable."
  Within 12EDO, sure.  But within Xenharmony, we have this profound advantage in that even the obvious mathematical progressions usually haven't been covered.  Also, in 12EDO we are forced to move by only a fixed number of simple ratios like 3/2, 5/4, and 6/5...why not do a chord progression moving by something like 9/7 or, as you said, even just a basic comma pump by the usual ratios that doesn't exist in 12EDO?
   Side question...what's a good scale 9 notes or under to find chained supermajor/minor chords?

   Thing is, once we convince people xenharmony can be tuneful along with original, it's only a matter of time before the obvious patterns get taken up and artists start reaching for the more novel ones.  I figure, we have to convince them we have a good "car" for basic comfortable travel before we convince them to race it.

________________________________
From: cityoftheasleep <igliashon@sbcglobal.net>
To: tuning@yahoogroups.com
Sent: Sunday, November 18, 2012 10:28 AM
Subject: [tuning] Re: Chord progression program (scale independent within subsets of EDOs)

 
--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>
>    The purpose of it is the crack an issue I heard Igs mention: people are scared of
> approaching xenharmony because they don't have the first clue what the basic chord
> progressions are.  This could at least help them uncover some basic chord patterns for
> any arbitrary scale that found very "tuneful", and give them some sense of what a scale is
> like in practice so they can quickly chose a one that fits their style, before they move on
> to more advanced progressions.

For starters, I don't recall saying that. I don't think people are "scared" of xenharmony; they're just not interested in it, because they aren't experiencing any problems with 12-TET that xenharmonic tunings would solve. 12-TET is plenty in-tune and plenty expressively versatile for most people. Those who do get interested in it do so for a variety of reasons, and they all seem to learn it a little bit differently.

Secondly, I think specific chord progressions are less important than understanding the relationships between notes in the scale. Lattices are good for this, but they get mighty difficult to read once you have more than a couple different kinds of relationship to depict. Another useful way to depict these relationships is with a table showing all the modes of the scale in sequence, which demonstrates which chords of interest are found on each degree of the scale. To take meantone[7] for example, if you start with the major scale (the Ionian mode), you can lay it out so that it's clear that the I, IV, and V degrees all form major triads, the ii, iii, and vi degrees all form minor triads, and the vii is diminished. I do this for most new scales I encounter as a first step to figuring out their deeper harmonic structure.

Thirdly, I generally object to any and all approaches that try to quantify something "useful" about specific chord progressions. The most "tuneful" chord progression might also be the most boring/pedestrian/unremarkable. The Porcupine comma pump--starting at one spot on the Porcupine[8] 5-limit lattice and changing one note at a time to move across the lattice until you end up at the first chord again--is probably one of the least interesting things you can do with Porcupine temperament, IMO. But it's probably the most "tuneful" by some standard. Of course, if you treat Porcupine as a 2.3.5.11 temperament, you end up with all kinds of different comma pumps that are probably a little more interesting. You also get some dyadic chords in there, like 1/1-11/10-6/5, which is sort of a "one-chord comma pump"

-Igs

🔗Mike Battaglia <battaglia01@...>

11/18/2012 10:54:16 PM

On Sun, Nov 18, 2012 at 11:01 PM, RR <djtrancendance@...> wrote:
>
> Personally, I've found myself using things like pivot chords and
> modulations plus movement in the roots of chord progressions by even odd
> intervals like minor 6ths

Er, a chord progression with a root that moves by a m6 isn't odd. Why
on earth do you think that's odd? Smells like Teen Spirit moves from
goes from Db back to Fm every time the cycle rolls around.

> plus extensive use of odd inversions, diminished
> chords, 11th and even 13th chords...in my "basic" dance tracks just to keep
> them from sounding unoriginal in 12EDO...and boy it is not versatile; takes
> ages to find a melody or chord progression that's both mathematically
> elegant (all notes have simplified relations to all other notes played
> within the last few seconds or more so well as to be hummable) and not
> taken.

You'll get better at it, it gets easier. Extended 12-EDO harmony is
not rocket science; it's just (often) poorly taught.

> And most of the advanced progressions just plain old don't chain
> together efficiently and end up sounding academic/forced e.g. even when they
> are original they are often not even vaguely "tuneful", as you'd find out if
> you tried to sing them.

Then they aren't advanced :)

> Also, in 12EDO we are forced to move by only a fixed number
> of simple ratios like 3/2, 5/4, and 6/5...why not do a chord progression
> moving by something like 9/7 or, as you said, even just a basic comma pump
> by the usual ratios that doesn't exist in 12EDO?

People do this all the time. You'd probably like Gene's or Petr
Parizek's compositions. Petr has a quick improv in Sensi here:
http://dl.dropbox.com/u/8497979/pp_guess_what_this_is.mp3 - lots of
motions by 9/7 in the last part

> Side question...what's a good scale 9 notes or under to find chained
> supermajor/minor chords?

Look at superpyth[7] in 22-EDO, which is 4 4 1 4 4 4 1. Note that it's
just a diatonic scale, but where the fifths are a bit sharp so that
four of them makes 9/7 instead of 5/4, and three fourths makes 7/6
instead of 6/5, and two fourths is 7/4 instead of 9/5. In other words,
it's the most boring possible way to play with supermajor and subminor
chords.

What does it sound like? Well, here's Bach's Fugue in the key of "C
supermajor" in superpyth temperament

http://soundcloud.com/mikebattagliamusic/bach-fugue-in-c-major-bwv952-22-edo

Now here it is in "C major" in meantone

http://soundcloud.com/mikebattagliamusic/bach-fugue-in-c-major-bwv952-31-edo

...So, you may disagree, but I don't think that this is the pinnacle
of xenharmonics right here. Yeah, I hear the intonation is different,
but... meh.

On the other hand, try messing around with hedgehog in 22-EDO; the
scale is 3 3 2 3 3 3 2 3. Now it's like 6/5 is a "major third" and 7/6
is a "minor third", and 1/1 6/5 7/5 and 1/1 7/6 7/5 are somehow otonal
and utonal-sounding inverses, rather than just "different types of
diminished chord." The structure of the scale, in this case, somehow
adds an extra dimension of musical information beyond just what you
get from the ratios involved, and to my ears this extra dimension is
more related to all of this tonal mood/tension/happiness/etc stuff
that you talk about than the ratios themselves are.

> Thing is, once we convince people xenharmony can be tuneful along with
> original, it's only a matter of time before the obvious patterns get taken
> up and artists start reaching for the more novel ones. I figure, we have to
> convince them we have a good "car" for basic comfortable travel before we
> convince them to race it.

There are a lot of us trying to learn how to do this. What you want is
a xenharmonic Mozart, who can write brilliantly "simple" compositions
that outline the basics of functional harmony in some tuning system.
Or for you, specifically, maybe a xenharmonic Deadmau5 is in order.

It's just not an easy thing to actually figure out how to do.

-Mike

🔗Charles Lucy <lucy@...>

11/19/2012 4:03:36 AM

Interesting comments, and valid conclusions.
My approach was to consider this from meantone, having listed which triads are found in 2400 + unique scales.
see:
http://www.lucytune.com/scales/

My obvious next step would be to develop chord sequences/progressions of triads for each scale, when I can find time to get to it.
To also consider all the possible extensions 6,7,13, etc would result in a vast number of possibilities.
Each progression would then require "testing each for singability".
I shall be very interested to see how you progress with this useful direction.

On 19 Nov 2012, at 04:01, RR wrote:

>
> >>"For starters, I don't recall saying that. I don't think people are "scared" of xenharmony; they're just not interested in it"
> And you never said anything along the lines of their thinking there are just too many possibilities and no easy way for them to quickly discover which system works for them? Maybe scared isn't the right word either...more like too intimidated by to make it worth their while. I also remember you saying that a huge problem with many of my scale systems is they neglected the fact that musicians like to move along simple intervals, such as 3/2, 5/4...concerning chord progressions and I was neglecting "how musicians actually use/combine the chords, not just how many chords are available". In fact, if I'm correct, that was a primary motivation behind the BP scale system: to chain triads in a system that allows such simple movement.
>
> >>"12-TET is plenty in-tune and plenty expressively versatile for most people."
>
> Minus one thing: a vast majority of the most mathematically efficient chord progressions in it have been taken (and taken, and taken again) by musicians in the past. Look at the proportion of upbeat popular music that has a majority of its melodies based on a combination of scale runs and jumps by fourths, octaves, and fifths (and rarely anything else): it's huge...and there are only a fixed number of such efficient jumps in 12EDO.
> The sheer amount of remixes or tracks with entire sampled melodies on the pop charts is pretty obvious evidence of this, as is the fact we get garbage like AVICII and Leona Lewis suing over who sampled an orchestral track "Perpetuum Mobile" by the Penguin Cafe Orchestra first.
>
> There may be few musicians who don't think 12EDO isn't versatile enough...minus the fact musicians are constantly running into and over each others' ideas. So much so it's often to the point many don't even bother to try original chord progressions and mess around with the phrasing-timing/textures with so-so results.
> Hence there are very few modern "classics" that are considered breakthroughs. Even in alternative genres and completely outside the major label scene...how hard is it to find a modern jazz artist with a current (less than 10 years old) work considered a classic?
> Personally, I've found myself using things like pivot chords and modulations plus movement in the roots of chord progressions by even odd intervals like minor 6ths plus extensive use of odd inversions, diminished chords, 11th and even 13th chords...in my "basic" dance tracks just to keep them from sounding unoriginal in 12EDO...and boy it is not versatile; takes ages to find a melody or chord progression that's both mathematically elegant (all notes have simplified relations to all other notes played within the last few seconds or more so well as to be hummable) and not taken. And most of the advanced progressions just plain old don't chain together efficiently and end up sounding academic/forced e.g. even when they are original they are often not even vaguely "tuneful", as you'd find out if you tried to sing them.
>
>
> >>"To take meantone[7] for example, if you start with the major scale (the Ionian mode), you can lay it out so that it's clear that the I, IV, and V degrees all form major triads, the ii, iii, and vi degrees all form minor triads, and the vii is diminished. I do this for most new scales I encounter as a first step to figuring out their deeper harmonic structure."
> Good idea, shows you the surface...and it's actually quite along the lines of what I was thinking.
>
> >>"The most "tuneful" chord progression might also be the most boring/pedestrian/unremarkable."
> Within 12EDO, sure. But within Xenharmony, we have this profound advantage in that even the obvious mathematical progressions usually haven't been covered. Also, in 12EDO we are forced to move by only a fixed number of simple ratios like 3/2, 5/4, and 6/5...why not do a chord progression moving by something like 9/7 or, as you said, even just a basic comma pump by the usual ratios that doesn't exist in 12EDO?
> Side question...what's a good scale 9 notes or under to find chained supermajor/minor chords?
>
> Thing is, once we convince people xenharmony can be tuneful along with original, it's only a matter of time before the obvious patterns get taken up and artists start reaching for the more novel ones. I figure, we have to convince them we have a good "car" for basic comfortable travel before we convince them to race it.
>
>
>
> From: cityoftheasleep <igliashon@...>
> To: tuning@yahoogroups.com
> Sent: Sunday, November 18, 2012 10:28 AM
> Subject: [tuning] Re: Chord progression program (scale independent within subsets of EDOs)
>
>
> --- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
> >
> > Â Â The purpose of it is the crack an issue I heard Igs mention: people are scared of
> > approaching xenharmony because they don't have the first clue what the basic chord
> > progressions are. This could at least help them uncover some basic chord patterns for
> > any arbitrary scale that found very "tuneful", and give them some sense of what a scale is
> > like in practice so they can quickly chose a one that fits their style, before they move on
> > to more advanced progressions.
>
> For starters, I don't recall saying that. I don't think people are "scared" of xenharmony; they're just not interested in it, because they aren't experiencing any problems with 12-TET that xenharmonic tunings would solve. 12-TET is plenty in-tune and plenty expressively versatile for most people. Those who do get interested in it do so for a variety of reasons, and they all seem to learn it a little bit differently.
>
> Secondly, I think specific chord progressions are less important than understanding the relationships between notes in the scale. Lattices are good for this, but they get mighty difficult to read once you have more than a couple different kinds of relationship to depict. Another useful way to depict these relationships is with a table showing all the modes of the scale in sequence, which demonstrates which chords of interest are found on each degree of the scale. To take meantone[7] for example, if you start with the major scale (the Ionian mode), you can lay it out so that it's clear that the I, IV, and V degrees all form major triads, the ii, iii, and vi degrees all form minor triads, and the vii is diminished. I do this for most new scales I encounter as a first step to figuring out their deeper harmonic structure.
>
> Thirdly, I generally object to any and all approaches that try to quantify something "useful" about specific chord progressions. The most "tuneful" chord progression might also be the most boring/pedestrian/unremarkable. The Porcupine comma pump--starting at one spot on the Porcupine[8] 5-limit lattice and changing one note at a time to move across the lattice until you end up at the first chord again--is probably one of the least interesting things you can do with Porcupine temperament, IMO. But it's probably the most "tuneful" by some standard. Of course, if you treat Porcupine as a 2.3.5.11 temperament, you end up with all kinds of different comma pumps that are probably a little more interesting. You also get some dyadic chords in there, like 1/1-11/10-6/5, which is sort of a "one-chord comma pump"
>
> -Igs
>
>
>
>
>

Charles Lucy
lucy@lucytune.com

-- Promoting global harmony through LucyTuning --

For more information on LucyTuning go to:

http://www.lucytune.com

LucyTuned Lullabies (from around the world) can be found at:

http://www.lullabies.co.uk

🔗cityoftheasleep <igliashon@...>

11/19/2012 9:42:35 AM

--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>   And you never said anything along the lines of their thinking there are just too many > possibilities and no easy way for them to quickly discover which system works for them?

That hasn't scared anyone away yet, at least not anyone interested enough to dip a toe in the pool. That's one reason the community exists: to help people figure out what a good system to play around with might be.

>I also remember you saying that a huge problem with many of my scale systems is they
> neglected the fact that musicians like to move along simple intervals, such as 3/2,
> 5/4...concerning chord progressions and I was neglecting "how musicians actually
> use/combine the chords, not just how many chords are available".

Right, like I said: it's not specific chord progressions per se, but relationships between the notes, between the chords, etc.

> >>"12-TET is plenty in-tune and plenty expressively versatile for most people."

>      Minus one thing: a vast majority of the most mathematically efficient chord
> progressions in it have been taken (and taken, and taken again) by musicians in the past.

That's not actually a problem, at least not for most people, because music--and especially popular music--runs on more than chord progressions. Most people who listen to music in our culture don't actually like music, they like singing (or rapping, as the case may be). Anyone who wants to make formulaic pop music--i.e. by utilizing "mathematically efficient" chord progressions that are "maximally tuneful" or whatever--is in all likelihood quite content to rely on using the old standbys of 12-TET over and over and over again. It's quite obvious, really, by the fact that almost no one writing pop music even bothers to exploit the myriad other temperaments compatible with 12-TET, like augmented, diminished, or pajara temperaments. If people aren't even interested in those temperaments--which, BTW, are very good temperaments, better than many xenharmonic temperaments, like Magic, Hanson, or Porcupine if the 5-limit error of 12-TET is considered acceptable--they're certainly not going to care about xenharmony.

>   Look at the proportion of upbeat popular music that has a majority of its melodies
> based on a combination of scale runs and jumps by fourths, octaves, and fifths (and
> rarely anything else): it's huge...and there are only a fixed number of such efficient
> jumps in 12EDO.

And yet, musicians seemingly never tire of exploiting them...and apparently never will. In fact, scientists have discovered that popular music is moving toward *simpler* progressions, *simpler* melodies, and *simpler* orchestration. It's basically commercial suicide these days to try to do something harmonically or melodically adventurous.

>   Hence there are very few modern "classics" that are considered breakthroughs.  Even > in alternative genres and completely outside the major label scene...how hard is it to find > a modern jazz artist with a current (less than 10 years old) work considered a classic?

It usually takes a few decades for a song to be deemed a "classic". But I think you'll find that many "classic rock" stations are now playing hits from the '90s in heavy rotation. I can't think of any more definitive way to establish a song as a "classic". But in any case, the whole notion of a "classic" is a fiction of the commercial music industry, which feeds heavily on nostalgia. Over-play a song during someone's youth, and that person will think it's a classic a few decades later, and then you can hit them with the re-issue/re-master/box set/etc. If you think classics have anything to do with having adventurous or novel chord progressions, you better reconsider.

> >>"The most "tuneful" chord progression might also be the most boring/pedestrian/unremarkable."
>   Within 12EDO, sure.  But within Xenharmony, we have this profound advantage in
> that even the obvious mathematical progressions usually haven't been covered.  Also,
> in 12EDO we are forced to move by only a fixed number of simple ratios like 3/2, 5/4,
> and 6/5...why not do a chord progression moving by something like 9/7 or, as you said, > even just a basic comma pump by the usual ratios that doesn't exist in 12EDO?

Because there is no sensible way to quantify "tunefulness" such that the most tuneful chord-progressions in a system will move by ratios more complex than those already approximated in 12-EDO, unless we are willing to use tuning systems that are actually less consonant than those of 12-EDO (i.e. those based on harmonies more complex than the 5-limit, and/or lacking some of the consonances of the 5-limit). And if we stick to 5-limit progressions, the net effect will be minimally xenharmonic, and most people probably won't notice the difference, because most listeners are not mentally tracking the movement of chords across the 5-limit lattice when they listen to music. Novel comma pumps give people like Paul Erlich and Mike Battaglia a thrill, because they're super-listeners who are able to track things like that, but even *I* couldn't tell you a Magic comma pump from a Hanson comma pump from an Augmented comma pump if you just played it for me out of nowhere. I bet you couldn't, either, now that I think about it.

>    Side question...what's a good scale 9 notes or under to find chained
> supermajor/minor chords?

Superpyth[7] is the best. Godzilla[9] (3 1 3 1 3 1 3 1 3 in 19-ED2) is also good. But good luck making those supermajor chords sound "tuneful".

>    Thing is, once we convince people xenharmony can be tuneful along with original,
> it's only a matter of time before the obvious patterns get taken up and artists start
> reaching for the more novel ones.  I figure, we have to convince them we have a good
> "car" for basic comfortable travel before we convince them to race it.

Man, would you quit acting like xenharmony is something we can wrap up in a nice shiny box and go out selling to people? "Convincing people" is a waste of time, and generally a fruitless endeavor. All those people out there making great music in 12-TET? They know their music is *already* great...and you think there's *any* argument that could convince them to either ditch or convert all their existing equipment, and re-learn how music works from the ground up all over again? It's like going up to an Olympian swimmer and saying, "hey, have you considered joining the National Made-Up Sports Association? I've created a new sport and I think you'd be great at playing it, even though it's nothing like swimming...."

The obvious patterns of behavior demonstrated by people entering the xenharmonic world for the first time indicate two main types: those who want to *re-write* the rules of music themselves, and those who want to *get rid of* musical rules all together. Anyone who wants to learn another pre-existing musical language is probably more interested in one that is already spoken in another culture, like Indian classical music, Persian/Arabic classical music, Indonesian gamelan music, African music, etc. Xenharmony is to "world music" as constructed languages (like Esperanto) are to natural languages. It is going to be a niche, forever, and that's fine. Get over it.

-Igs

🔗RR <djtrancendance@...>

11/19/2012 10:12:41 AM

>>"Er, a chord progression with a root that moves by a m6 isn't odd. Why
on earth do you think that's odd? Smells like Teen Spirit moves from
goes from Db back to Fm every time the cycle rolls around."

From http://en.wikipedia.org/wiki/Smells_Like_Teen_Spirit

   "The song's chord progression has been described as 'an ambiguous, harmonically dislocated sequence,'"
A bit like, well, almost anything from The Beatles -> http://beatlesite.blogspot.com/2008/05/what-are-all-those-flat-sevenths-doing.html

> even when they
> are original they are often not even vaguely "tuneful", as you'd find out if
> you tried to sing them.

   >Then they aren't advanced :)

Hehehe...

   Well, unless they are, say, the Beatles, Nirvana, Pearl Jam, Metallica, The Smashing Pumpkins...wait, those are all considered somewhat classics and people seem to have run out of ideas that fresh within 12EDO (at least, non-modulated) especially in the last 10 years (hence the problem) and IMO do some weird and cool things with chords while staying "tuneful".  Or what exactly qualifies to you as advanced?

>>You'll get better at it, it gets easier. Extended 12-EDO harmony is not rocket science; it's just (often) poorly taught.

  Agreed.  I'm just posting here what I understood from our last chat: you can resolve down by a 5th from a chord (perhaps any chord) in a "normal" progression back to a new root, pick a chord with all notes in common between two chords and build a melody on that to switch the feel between keys.  The problem along the way (at least for songwriting) seems to be having to force yourself to concentrate on breathing to breathe, so to speak: it just doesn't come naturally yet and only rears it's head "automatically" in maybe 15-20% of what I compose, and this indirectly seems to make the mood of the music feel more studious than uplifting. 

  Funny thing is, if I have it right, that's a huge reason why we switched to 12EDO from things like meantone in the first place beside easy transposition: "easy" modulation...and it also seems to be something that plagues higher EDOs unless there's some brilliant solution for finding large interval jumps without counting keys that someone has thought of (do isometric keyboards handle this issue?).

>>People do this all the time. You'd probably like Gene's or Petr Parizek's compositions. Petr has a quick improv in Sensi here:
http://dl.dropbox.com/u/8497979/pp_guess_what_this_is.mp3 - lots of motions by 9/7 in the last part

  Interesting, those the chords sound a bit dense for my ears...at the very least the melodic motion of the roots is pretty clear.  Mathematically very well done but, emotion-wise, not quite there.

>>"http://soundcloud.com/mikebattagliamusic/bach-fugue-in-c-major-bwv952-22-edo
    
Now here it is in "C major" in meantone
    
http://soundcloud.com/mikebattagliamusic/bach-fugue-in-c-major-bwv952-31-edo"

   I agree...it's simply not enough difference...almost sounds like the same thing, mood and all, slightly transposed for brightness: better than nothing but certainly not enough to really sound fresh.

     That seems to push me back in the direction of the Rast Modmos, at least for now: chords like 1/1 5/4 22/15 or 1/1 4/3 11/6 (6:8:11) at least have enough "tint" to them to sound new to me.  Then again, history already seems to show this works: both in Maqam music and the blue tones in blues, so you can argue it's not really all that fresh a concept.

  I really want to find somewhere unused (in 12EDO) ratios of 7 work a forms chords alien enough to sound fresh (perhaps not chained, who knows), but still tonal enough to sound coherent/not-arrived-at-by-accident.

  The problem in 12EDO already covers a bit of ratios of 7 (7/5, 10/7), a good chunk of 9 (16/9, 9/8, 10/9...only missing 14/9 AKA 9/7), and all of 2,3,5.  It looks like the two ways to get the most difference are to aim for dyads involving ratios of 7 and 11, since those are the ones 12 EDO misses, and it seems Rast does a better job at making 11 sound harmonic than anything else I've heard so far.

-----------------------------------------------------------------------

>>"On the other hand, try messing around with hedgehog in 22-EDO; the
scale is 3 3 2 3 3 3 2 3. Now it's like 6/5 is a "major third" and 7/6
is a "minor third", and 1/1 6/5 7/5 and 1/1 7/6 7/5 are somehow otonal
and utonal-sounding inverses, rather than just "different types of
diminished chord."

  Will do, and post the results, thank you for the tip.  Chained diminished chords sound very interesting...
  Are there any other systems that chain chords not available in 12EDO, but as or more relaxed-sounding than diminished chords (excluding BP)?

 

>>Or for you, specifically, maybe a xenharmonic Deadmau5 is in order.
>>It's just not an easy thing to actually figure out how to do.

   For now, sure...even if I don't like that artist I figure it's a necessary evil to have a figure like that around to jump-start things.  I agree on Mozart (or Handel) for simplicity, but the energy/groove/percussive-rhythm is simply missing for me (and, I'm pretty sure, most others who often end up stuck with pop music for the more percussive and often sophisticated rhythms alone). 

   I know I posted this before but...think it's a great example of balance between something simple/foundational/hummable (the chords, especially splitting up a m7 into triads a bit like Calvin Harris does), and complex (the vocals and all the rhythmic accents, perhaps some of the odd notes on top of the chords and the bass-line contrast). 

http://www.youtube.com/watch?v=kCr7mktOyBw
   Some type of xenharmonic funk (not the one we're in, the genre), I'm guessing, would cure a whole lot: think xenharmonic Daft Punk...at least for some nice xen basslines.
------------------------------------

    I think what many of us forget...is that many people don't listen or create music on a foundational level because if shows their sophistication/technical-prowess...but simply because it makes them feel good (or even smart, like they are uncovering a lot with very little effort) and can do so very efficiently.

  Begs the question...how does all this mumbo-jumbo tie into the emotions xenharmonic temperaments offer?  
  The obvious one to open the doors seem to be "happy" temperaments that evoke the relaxed, energized, groovy feelings most people seem to want to get from music...though there is much more that could eventually click, I'm sure, especially the sort of cool and confident melancholic-yet-upbeat feel that drove the grunge era and pops its head in some of the more popular metal (GNR and Metallica being obvious culprits) and "classier" hip-hop.

>>It's just not an easy thing to actually figure out how to do.
  Story of my life. :-)

 

________________________________
From: Mike Battaglia <battaglia01@...>
To: tuning@yahoogroups.com
Sent: Monday, November 19, 2012 12:54 AM
Subject: Re: [tuning] Re: Chord progression program (scale independent within subsets of EDOs)

 
On Sun, Nov 18, 2012 at 11:01 PM, RR <djtrancendance@...> wrote:
>
> Personally, I've found myself using things like pivot chords and
> modulations plus movement in the roots of chord progressions by even odd
> intervals like minor 6ths

Er, a chord progression with a root that moves by a m6 isn't odd. Why
on earth do you think that's odd? Smells like Teen Spirit moves from
goes from Db back to Fm every time the cycle rolls around.

> plus extensive use of odd inversions, diminished
> chords, 11th and even 13th chords...in my "basic" dance tracks just to keep
> them from sounding unoriginal in 12EDO...and boy it is not versatile; takes
> ages to find a melody or chord progression that's both mathematically
> elegant (all notes have simplified relations to all other notes played
> within the last few seconds or more so well as to be hummable) and not
> taken.

You'll get better at it, it gets easier. Extended 12-EDO harmony is
not rocket science; it's just (often) poorly taught.

> And most of the advanced progressions just plain old don't chain
> together efficiently and end up sounding academic/forced e.g. even when they
> are original they are often not even vaguely "tuneful", as you'd find out if
> you tried to sing them.

Then they aren't advanced :)

> Also, in 12EDO we are forced to move by only a fixed number
> of simple ratios like 3/2, 5/4, and 6/5...why not do a chord progression
> moving by something like 9/7 or, as you said, even just a basic comma pump
> by the usual ratios that doesn't exist in 12EDO?

People do this all the time. You'd probably like Gene's or Petr
Parizek's compositions. Petr has a quick improv in Sensi here:
http://dl.dropbox.com/u/8497979/pp_guess_what_this_is.mp3 - lots of
motions by 9/7 in the last part

> Side question...what's a good scale 9 notes or under to find chained
> supermajor/minor chords?

Look at superpyth[7] in 22-EDO, which is 4 4 1 4 4 4 1. Note that it's
just a diatonic scale, but where the fifths are a bit sharp so that
four of them makes 9/7 instead of 5/4, and three fourths makes 7/6
instead of 6/5, and two fourths is 7/4 instead of 9/5. In other words,
it's the most boring possible way to play with supermajor and subminor
chords.

What does it sound like? Well, here's Bach's Fugue in the key of "C
supermajor" in superpyth temperament

http://soundcloud.com/mikebattagliamusic/bach-fugue-in-c-major-bwv952-22-edo

Now here it is in "C major" in meantone

http://soundcloud.com/mikebattagliamusic/bach-fugue-in-c-major-bwv952-31-edo

...So, you may disagree, but I don't think that this is the pinnacle
of xenharmonics right here. Yeah, I hear the intonation is different,
but... meh.

On the other hand, try messing around with hedgehog in 22-EDO; the
scale is 3 3 2 3 3 3 2 3. Now it's like 6/5 is a "major third" and 7/6
is a "minor third", and 1/1 6/5 7/5 and 1/1 7/6 7/5 are somehow otonal
and utonal-sounding inverses, rather than just "different types of
diminished chord." The structure of the scale, in this case, somehow
adds an extra dimension of musical information beyond just what you
get from the ratios involved, and to my ears this extra dimension is
more related to all of this tonal mood/tension/happiness/etc stuff
that you talk about than the ratios themselves are.

> Thing is, once we convince people xenharmony can be tuneful along with
> original, it's only a matter of time before the obvious patterns get taken
> up and artists start reaching for the more novel ones. I figure, we have to
> convince them we have a good "car" for basic comfortable travel before we
> convince them to race it.

There are a lot of us trying to learn how to do this. What you want is
a xenharmonic Mozart, who can write brilliantly "simple" compositions
that outline the basics of functional harmony in some tuning system.
Or for you, specifically, maybe a xenharmonic Deadmau5 is in order.

It's just not an easy thing to actually figure out how to do.

-Mike

🔗RR <djtrancendance@...>

11/19/2012 12:02:38 PM

>>"Right, like I said: it's not specific chord progressions per se, but relationships between the notes, between the chords, etc."
  But don't said relationships between chords define the chord progression (e.g. resolving by going down a fifth to the tonic will virtually always work, but something like a 6th is a toss up...and so on)? 

>>"Most people who listen to music in our culture don't actually like music, they like singing (or rapping, as the case may be)."
  And yet, name one hit rap track, even, without at least a bassline counterpoint contrasting with the lyrics and hinting at the chords: it may be a minimal hint, but it's there.  One sad thing...everything in pop music, in many ways, is moving toward dyadic inversions...look at AVICII, for example.  The good news, if we're really just talking dyads, we have many more possibilities of only very slightly more complex dyads than in meantone under 12EDO that can be arrived at in countless other temperaments.

  I agree on singing though...and studies have shown even our basic diatonic system and many melodies basically rip off vocal inflections and pitches in everyday speech.  It's as if the Lord himself created the diatonic scale (at least, for Western speech)...through it would be interesting to see  if people in the Middle East actually use vocal intonations mirroring the Rast scale or if other animals use different systems, for example.

>>"If people aren't even interested in those temperaments--which, BTW, are very good temperaments"
   I just can't get around the uneven spacing in those...although something like augmented[6] might work if people actually knew about it or heard some works in it.  I'm betting most people don't know it exists...or understand that you can make chord progressions and fitting melodies in scales containing two consecutive semitones not done by accident.  When I asked my brother, a jazz guitarist, about Augmented temperament, he had no clue what it was...most people simply don't know it's there.

>>"And yet, musicians seemingly never tire of exploiting them...and
apparently never will."
  But, alas, their mood range, regardless of simplicity, is very limited by the underlying chords and, as we've discussed, the more notes you add on top of a chord, the less sensitive each note is to detuning and the less emotional change each additional note has on the sound of the chord. 

>> In fact, scientists have discovered that popular music is moving toward *simpler* progressions, *simpler* melodies, and
*simpler* orchestration. It's basically commercial suicide these days
to try to do something harmonically or melodically adventurous."
  Why not something simple, but that uses a different palette.  Not more complex just...different.  For one, a bet a simple chord progression in Rast would become accepted almost instantly, much like the once "alien" genre dubstep suddenly became huge once sampled by a major artist (Rihanna).  IMO, if you can do things like resolve by 5ths and make a handful of chords involving numbers less than 10 and spacing is comparably even compared to diatonic, you're basically there far as making an addictive chord progression.

>>It usually takes a few decades for a song to be deemed a "classic".
Nirvana, Metallica, Pearl Jam, for example, apparently took far less, for example...more like 5, if that. It's not just that people remember who the were (e.g. classic rock), but they had styles no other group truly matched since: it's not just about time, but uniqueness...which is why MC Hammer isn't a classic. 

>>"Because there is no sensible way to quantify "tunefulness" such that the most tuneful chord-progressions in a system will move by ratios more
complex than those already approximated in 12-EDO"
   IMO, you can cheat by tone classes a bit.  9/7 is fine as counting as "moving by 5/4"...as is 11/9...there's a bit of wiggle room.  The biggie seems to be 3/2: there seems to be no way around having it: 4:5:6, 5:6:8, 3:4:5, 2:3:4...just about any chord with ratios under ten or large movement between chords, in an arpeggio...and you end up needing a good 3:2 to pull it off and/or to move along it and/or resolve by moving by it.

  Mike B. suggested Hedgehog for its chained 5:6:7 1/(5:6:7) chords and it sounds like a good idea.  In fact, I think it would be a of great benefit to have a list of systems most saturated with chords that are either 5-limit, contain no prime factor higher than 7, or are a minor inversion e.g. 1/(x:x:x) of the above, for starters.  Chords like 6:7:8 or 7:8:9 or 5:7:9 simply don't exist in 12EDO, as does movement between chords along ratios involving 7 really not significantly more complex than anything in 12EDO, especially if you throw in things like the occasional diminished chord at the end of a measure...why not capitalize on this?

>>"Man, would you quit acting like xenharmony is something we can wrap up in a nice shiny box and go out selling to people?"
Well, it's not about selling, it's about relating to, trusting.

>>"It's like going up to an Olympian swimmer and saying, "hey, have you
considered joining the National Made-Up Sports Association? I've
created a new sport and I think you'd be great at playing it, even
though it's nothing like swimming...."
Well, fortunately, some people are like that e.g. Lance Armstrong doing marathons and even admitting, to him, it was more of a challenge than any bicycle race and felt, yes, refreshing (as a change).  

   The other thing is, I don't think it's that much harder if we get it into a few consistent terms e.g. find a scale where maybe 80% of the structures are the same as in 12EDO and the other 20% can be treated like 12EDO equivalents e.g. "yes, you can resolve by this new fangled 14/9 just like you would a fifth" or "yes, you can move chords/melodies by this 11/9 for the same melodic effect as your minor third or, occasionally, a major third".  You're going to hate me for this but...I think a lot of it comes down to phrasing things as extensions of the diatonic scale: things that ultimately act in a similar fashion when composing, but sound different.

>>"Indian classical music, Persian/Arabic classical music, Indonesian gamelan music, African music"
   Well, the Persian and African, not to mention blues, point to blue tones...and it still bugs me to tears no one has tried to use Rast in a hit track.  In fact, for grins, I'm going to retune a ton of my older/less-advanced tracks that use no modulation to Rast.

  You sound a bit like some of the guys on the trance scene who say "trance is not dead, it's underground, where it works best", instead of doing what they already do so well with textures/phrasing/blurring-sounds/deep-often-advanced-chords/crazy-arpeggios...but making the effort to throw a relate-able melody or two on top or and occasional drum line variation over the boom-click-boom so people could "get it".
  You shouldn't feel you have to shoot yourself in the foot to make something work...in fact your track Colorbars -> http://cityoftheasleep.bandcamp.com/album/transfinity-complex-2  has a downright killer hook and bass-line and, IMO, the whole track could be melded into something Marcus-Satellite-level appealing if a couple such hooks and rhythmic add-ins were added to those down/abstract ambient parts.  One obvious example of a group that did outright weird stuff in the background but had polished leads to hook you in regardless...the Beatles.

     I think there's a healthy balance between the two extremes of creative self-indulgence/"sophistication" and trying to rip past rules altogether and selling out trying to relate to people at all creative costs...a kind of relate-able-but-not-desperate music that both enlightens people to the new and draws them in with the old.  And, if we weren't so adamant about making something "special" often at the cost of virtually all relate-ability , I'm pretty sure at least a handful of us could pull it off. 

 

________________________________
From: cityoftheasleep <igliashon@...>
To: tuning@yahoogroups.com
Sent: Monday, November 19, 2012 11:42 AM
Subject: [tuning] Re: Chord progression program (scale independent within subsets of EDOs)

 
--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>   And you never said anything along the lines of their thinking there are just too many > possibilities and no easy way for them to quickly discover which system works for them?

That hasn't scared anyone away yet, at least not anyone interested enough to dip a toe in the pool. That's one reason the community exists: to help people figure out what a good system to play around with might be.

>I also remember you saying that a huge problem with many of my scale systems is they
> neglected the fact that musicians like to move along simple intervals, such as 3/2,
> 5/4...concerning chord progressions and I was neglecting "how musicians actually
> use/combine the chords, not just how many chords are available".

Right, like I said: it's not specific chord progressions per se, but relationships between the notes, between the chords, etc.

> >>"12-TET is plenty in-tune and plenty expressively versatile for most people."

>      Minus one thing: a vast majority of the most mathematically efficient chord
> progressions in it have been taken (and taken, and taken again) by musicians in the past.

That's not actually a problem, at least not for most people, because music--and especially popular music--runs on more than chord progressions. Most people who listen to music in our culture don't actually like music, they like singing (or rapping, as the case may be). Anyone who wants to make formulaic pop music--i.e. by utilizing "mathematically efficient" chord progressions that are "maximally tuneful" or whatever--is in all likelihood quite content to rely on using the old standbys of 12-TET over and over and over again. It's quite obvious, really, by the fact that almost no one writing pop music even bothers to exploit the myriad other temperaments compatible with 12-TET, like augmented, diminished, or pajara temperaments. If people aren't even interested in those temperaments--which, BTW, are very good temperaments, better than many xenharmonic temperaments, like Magic, Hanson, or Porcupine if the 5-limit error of 12-TET is considered
acceptable--they're certainly not going to care about xenharmony.

>   Look at the proportion of upbeat popular music that has a majority of its melodies
> based on a combination of scale runs and jumps by fourths, octaves, and fifths (and
> rarely anything else): it's huge...and there are only a fixed number of such efficient
> jumps in 12EDO.

And yet, musicians seemingly never tire of exploiting them...and apparently never will. In fact, scientists have discovered that popular music is moving toward *simpler* progressions, *simpler* melodies, and *simpler* orchestration. It's basically commercial suicide these days to try to do something harmonically or melodically adventurous.

>   Hence there are very few modern "classics" that are considered breakthroughs.  Even > in alternative genres and completely outside the major label scene...how hard is it to find > a modern jazz artist with a current (less than 10 years old) work considered a classic?

It usually takes a few decades for a song to be deemed a "classic". But I think you'll find that many "classic rock" stations are now playing hits from the '90s in heavy rotation. I can't think of any more definitive way to establish a song as a "classic". But in any case, the whole notion of a "classic" is a fiction of the commercial music industry, which feeds heavily on nostalgia. Over-play a song during someone's youth, and that person will think it's a classic a few decades later, and then you can hit them with the re-issue/re-master/box set/etc. If you think classics have anything to do with having adventurous or novel chord progressions, you better reconsider.

> >>"The most "tuneful" chord progression might also be the most boring/pedestrian/unremarkable."
>   Within 12EDO, sure.  But within Xenharmony, we have this profound advantage in
> that even the obvious mathematical progressions usually haven't been covered.  Also,
> in 12EDO we are forced to move by only a fixed number of simple ratios like 3/2, 5/4,
> and 6/5...why not do a chord progression moving by something like 9/7 or, as you said, > even just a basic comma pump by the usual ratios that doesn't exist in 12EDO?

Because there is no sensible way to quantify "tunefulness" such that the most tuneful chord-progressions in a system will move by ratios more complex than those already approximated in 12-EDO, unless we are willing to use tuning systems that are actually less consonant than those of 12-EDO (i.e. those based on harmonies more complex than the 5-limit, and/or lacking some of the consonances of the 5-limit). And if we stick to 5-limit progressions, the net effect will be minimally xenharmonic, and most people probably won't notice the difference, because most listeners are not mentally tracking the movement of chords across the 5-limit lattice when they listen to music. Novel comma pumps give people like Paul Erlich and Mike Battaglia a thrill, because they're super-listeners who are able to track things like that, but even *I* couldn't tell you a Magic comma pump from a Hanson comma pump from an Augmented comma pump if you just played it for me out of
nowhere. I bet you couldn't, either, now that I think about it.

>    Side question...what's a good scale 9 notes or under to find chained
> supermajor/minor chords?

Superpyth[7] is the best. Godzilla[9] (3 1 3 1 3 1 3 1 3 in 19-ED2) is also good. But good luck making those supermajor chords sound "tuneful".

>    Thing is, once we convince people xenharmony can be tuneful along with original,
> it's only a matter of time before the obvious patterns get taken up and artists start
> reaching for the more novel ones.  I figure, we have to convince them we have a good
> "car" for basic comfortable travel before we convince them to race it.

Man, would you quit acting like xenharmony is something we can wrap up in a nice shiny box and go out selling to people? "Convincing people" is a waste of time, and generally a fruitless endeavor. All those people out there making great music in 12-TET? They know their music is *already* great...and you think there's *any* argument that could convince them to either ditch or convert all their existing equipment, and re-learn how music works from the ground up all over again? It's like going up to an Olympian swimmer and saying, "hey, have you considered joining the National Made-Up Sports Association? I've created a new sport and I think you'd be great at playing it, even though it's nothing like swimming...."

The obvious patterns of behavior demonstrated by people entering the xenharmonic world for the first time indicate two main types: those who want to *re-write* the rules of music themselves, and those who want to *get rid of* musical rules all together. Anyone who wants to learn another pre-existing musical language is probably more interested in one that is already spoken in another culture, like Indian classical music, Persian/Arabic classical music, Indonesian gamelan music, African music, etc. Xenharmony is to "world music" as constructed languages (like Esperanto) are to natural languages. It is going to be a niche, forever, and that's fine. Get over it.

-Igs

🔗Mike Battaglia <battaglia01@...>

11/19/2012 2:22:28 PM

On Mon, Nov 19, 2012 at 1:12 PM, RR <djtrancendance@...> wrote:
>
> From http://en.wikipedia.org/wiki/Smells_Like_Teen_Spirit
> "The song's chord progression has been described as 'an ambiguous, harmonically dislocated sequence,'"
> A bit like, well, almost anything from The Beatles -> http://beatlesite.blogspot.com/2008/05/what-are-all-those-flat-sevenths-doing.html

Oh please, what nonsense. Smells Like Teen Spirit is in F minor and
the chords are i IV III VI. The bVII chord in the Beatles is IV/IV and
they use it when they're writing stuff in mixolydian mode. I can't
read anymore of the stuff on this Beatles page; this is exactly why I
say extended harmony is often taught so poorly. If you talk to Josh
these days I'm sure he'd also crack up at that page.

> Hehehe...
> Well, unless they are, say, the Beatles, Nirvana, Pearl Jam, Metallica, The Smashing Pumpkins...wait, those are all considered somewhat classics and people seem to have run out of ideas that fresh within 12EDO (at least, non-modulated) especially in the last 10 years (hence the problem) and IMO do some weird and cool things with chords while staying "tuneful". Or what exactly qualifies to you as advanced?

If you've come up with some arbitrary mathematical pattern for a chord
progression, and you play it and it sounds like crap, it's not
advanced. What's "advanced" is when you have a complex pattern that
actually sounds good.

> Agreed. I'm just posting here what I understood from our last chat: you can resolve down by a 5th from a chord (perhaps any chord) in a "normal" progression back to a new root, pick a chord with all notes in common between two chords and build a melody on that to switch the feel between keys.

I never said anything about this restriction where you can only
resolve by a fifth; that was something you came up with... never in my
life would subscribe to such a restrictive view of harmony. There's a
middle ground between "all root movements are equal" and "resolving by
fifth is the only thing you can do which doesn't sound weird." In my
view, more complex root movements just contain more information, and
sometimes that information can be overwhelming if you don't know how
to parse it, making the whole thing sound disconnected and not
functional in any clear sort of way. I don't think moving to the bVI
chord is over that line for the average person (see Stone Temple
Pilots' "Sour Girl").

> Funny thing is, if I have it right, that's a huge reason why we switched to 12EDO from things like meantone in the first place beside easy transposition: "easy" modulation...and it also seems to be something that plagues higher EDOs unless there's some brilliant solution for finding large interval jumps without counting keys that someone has thought of (do isometric keyboards handle this issue?).

Right, easy modulation. What plagues higher EDOs, that it's more
difficult to modulate?

Isometric keyboards do indeed make it easier to handle large EDOs, and
I'm speaking from experience on that.

> >>People do this all the time. You'd probably like Gene's or Petr Parizek's compositions. Petr has a quick improv in Sensi here:
> http://dl.dropbox.com/u/8497979/pp_guess_what_this_is.mp3 - lots of motions by 9/7 in the last part
>
> Interesting, those the chords sound a bit dense for my ears...at the very least the melodic motion of the roots is pretty clear. Mathematically very well done but, emotion-wise, not quite there.

Mike, the point isn't for you to give a thumbs up/thumbs down about
whether or not you "like" it. The point is to expose your ears to the
sound you asked for.

If you think you can do it better, then go do it. We need more
intelligent musicians who are capable of figuring out how to actually
DO things, not just critics who tell everyone they're doing it wrong
:)

> >>"http://soundcloud.com/mikebattagliamusic/bach-fugue-in-c-major-bwv952-22-edo
> Now here it is in "C major" in meantone
> http://soundcloud.com/mikebattagliamusic/bach-fugue-in-c-major-bwv952-31-edo"
>
> I agree...it's simply not enough difference...almost sounds like the same thing, mood and all, slightly transposed for brightness: better than nothing but certainly not enough to really sound fresh.

Right. So, this is why I don't care about ratios unless they're in the
context of some interesting scale system.

> That seems to push me back in the direction of the Rast Modmos, at least for now: chords like 1/1 5/4 22/15 or 1/1 4/3 11/6 (6:8:11) at least have enough "tint" to them to sound new to me. Then again, history already seems to show this works: both in Maqam music and the blue tones in blues, so you can argue it's not really all that fresh a concept.

What I suggest doing is messing around with MOS's. You should go on a
systematic review of MOS's with 9 notes or less, especially ones with
more "L" than "s" notes. Some of them are close enough to "locally"
sound like a diatonic scale, but then the whole thing fits together in
a very strange and exotic way. When you mix THAT with good intonation,
then the magic happens.

> I really want to find somewhere unused (in 12EDO) ratios of 7 work a forms chords alien enough to sound fresh (perhaps not chained, who knows), but still tonal enough to sound coherent/not-arrived-at-by-accident.

Try slendric temperament, which tempers out 1029/1024; it makes three
8/7's equal to a 3/2. There's a good 5, 6, and 11 note MOS. Try the
4:6:7 and 4:6:7:9 chords in it.

Another thing I think you should do is find 5-limit temperaments which
aren't present in 12-EDO. This gives you chords that you're familiar
with, but now they all "connect" in different ways, which changes
everything. Blackwood in 15-EDO is a good way to start if you don't
mind a bit more error (careful with the timbre).

> The problem in 12EDO already covers a bit of ratios of 7 (7/5, 10/7), a good chunk of 9 (16/9, 9/8, 10/9...only missing 14/9 AKA 9/7), and all of 2,3,5. It looks like the two ways to get the most difference are to aim for dyads involving ratios of 7 and 11, since those are the ones 12 EDO misses, and it seems Rast does a better job at making 11 sound harmonic than anything else I've heard so far.

Well, as you can see from the example above, you can get all of that
in superpyth and it's not all that interesting (although I think 4:6:7
chords in superpyth can be a lot of fun). I recommend taking a
complete break from thinking about ratios and just start worrying
about other scales for a little bit. The two need to work together;
7/6 might sound like two completely different intervals in two
completely different scales.

> Will do, and post the results, thank you for the tip. Chained diminished chords sound very interesting...
> Are there any other systems that chain chords not available in 12EDO, but as or more relaxed-sounding than diminished chords (excluding BP)?

Yes, there's 11-EDO and its 4:7:9:11 chords. I especially like machine
temperament, which I told you about before, which has good 4:7:9
chords and one or two 4:7:9:11 too. There's also porcupine
temperament, which has good 8:10:11:12 chords. You might like 8-EDO,
which has these really interesting 0-450-900 chords, which are like
two 9/7's that combine to make a 5/3. (Or you can try sensi[8] for
something more like that).

None of these scales are perfect and I'm sure that you'll be able to
find something to gripe about for each one. But I have to warn you
that I don't actually think like you do about scales, so you're asking
the wrong person - I almost never just pick a single 7 or 8 note scale
and exclusively use that. I like to expand my mental reach to a larger
chromatic scale and then use smaller diatonic-sized scales within it,
modulating as I damn well please. It's the modulations that give me
all of the color. I suggest learning to use chromaticism in a similar
way.

I think that learning to modulate is even more important for other
tunings than for meantone - in meantone you can more or less stick to
the diatonic scale and write something like Pachelbel's Canon. For
most other temperaments which contain a lot of chords in a small scale
size, the chords are usually inaccurately tuned (like mavila
temperament). It's rare to find a lot of chords in a small scale size
and which are also well-tuned. I've given you some above, but the hunt
will always continue. If you don't mind dealing with a bit higher
error, then there's a lot of good stuff - mavila temperament,
superpelog, etc. If you demand better intonation, then you're going to
have to learn to deal with more notes. And as it's hard to keep track
of, say, 15 notes in your head at once, you're going to have to learn
to use continuously modulating 7 or 8 note subsets in order to present
the listener with a manageable chunk of information that they can
actually grab onto. However, since you're continuously modulating, you
can slowly paint the listener's brain with all of the colors in the
larger chromatic scale in a manageable and comprehensible way.

Luckily, every rank-2 temperament comes with an MOS series which makes
it relatively easy to figure out how to do this.

> I know I posted this before but...think it's a great example of balance between something simple/foundational/hummable (the chords, especially splitting up a m7 into triads a bit like Calvin Harris does), and complex (the vocals and all the rhythmic accents, perhaps some of the odd notes on top of the chords and the bass-line contrast).
> http://www.youtube.com/watch?v=kCr7mktOyBw

I think you should check out Sevish's "Golden Hour" album, which is
awesome from start to finish. One of my favorite albums ever,
microtonal or not: http://split-notes.com/001/

The EP "Human Astronomy" is also really good - http://www.split-notes.com/005/

Also, this Calvin Harris song is a good example of what I'm talking
about wrt to the "tradeoff" that's there in other tunings than
meantone. This entire song uses nothing but the white keys on the
piano, at least the part of it I listened to. That's a lot of musical
mileage to be gained out of only 10 notes. If you want to find other
scales that do the same thing, you're going to have to do one of the
following

1) Accept more tuning error
2) Use a larger scale
3) Use smaller subsets that continually modulate within a larger scale
(my approach)
4) Keep looking at subgroup temperaments and hope that you hit the jackpot

> I think what many of us forget...is that many people don't listen or create music on a foundational level because if shows their sophistication/technical-prowess...but simply because it makes them feel good (or even smart, like they are uncovering a lot with very little effort) and can do so very efficiently.

I don't think anybody here forgets that

> Begs the question...how does all this mumbo-jumbo tie into the emotions xenharmonic temperaments offer?

I have no idea

-Mike

🔗RR <djtrancendance@...>

11/19/2012 3:42:35 PM

>>"The bVII chord in the Beatles is IV/IV and they use it when they're writing stuff in mixolydian mode."
   So, in other words, they aren't using B, at all, and the entire piece(s) are in c mixolydian?  If that's the case, wow, that is much ado about nothing. 

>>"If you've come up with some arbitrary mathematical pattern for a chord
progression, and you play it and it sounds like crap, it's not advanced. What's "advanced" is when you have a complex pattern that actually sounds good."

Such as?

>"I never said anything about this restriction where you can only resolve by a fifth; that was something you came up with... never in my life would subscribe to such a restrictive view of harmony

   You're right, you never did, I'm just saying that's one sure-fire way that virtually always works.  On a more optimistic note...some other ways to accomplish resolution that usually work are?  
I'm sure you can find an exception to just about everything e.g. even someone resolving by a tritone, for example...but what's the point of music theory if you can't at least give yourself a few options that almost always work to balance out the experimentation?

>"I don't think moving to the bVI chord is over that line for the average person (see Stone Temple Pilots' "Sour Girl").
Neither do I (hence why I mentioned the minor 6th resolution in that last youtube link in the vocals before)...but it seems like a more sensitive option that, like you said "just contain(s) more information...can be overwhelming if you don't know how
to parse it, making the whole thing sound disconnected".  I tried a few melodic lines after dropping the bass line on a 6th resolution...and there were much fewer options that worked than with a fifth...as if there had to be a predictable "calm" in the melodic pattern to balance the overload caused by the jump.  Not that it can't work really well (and it's d-mn amusing/entertaining when it does), but it apparently takes more care to pull off.

>>"Smells Like Teen Spirit is in F minor and the chords are i IV III VI."
   Never said it modulated but...the pattern seems to be it's decidedly tense (at least to my ears, even if the math behind it is "normal") and far less directed at the tonic to do that 7th jump.  And, to note, it's followed by a 5th-like relaxed movement to a fourth, which makes sense to balance out said "more information" and, it seems,push back the tonic.

>>"Right, easy modulation. What plagues higher EDOs, that it's more difficult to modulate?"
  Indirectly...or just to keep track of the notes, period: and having to remember where all the "new" notes are after the modulation in such a large set.

>>"If you think you can do it better, then go do it. We need more
intelligent musicians who are capable of figuring out how to actually
DO things, not just critics who tell everyone they're doing it wrong
:)"

    Right, which is why I'm taking your advice and digging into Hedgehog temperament.  Theory wise I don't actually think there's any formal right or wrong, just more or less likely to work most of the time.

>>"Try slendric temperament, which tempers out 1029/1024; it makes three 8/7's equal to a 3/2. There's a good 5, 6, and 11 note MOS. Try the 4:6:7 and 4:6:7:9 chords in it."
   Will do, after I finish up with Hedgehog...might even try the 11 and see of I can pull off some decent modulation.

>>"You should go on a systematic review of MOS's with 9 notes or less, especially ones with more "L" than "s" notes."

Gotcha...and I'm seeing that in the temperaments you're handing me, like Machine...these "diatonic-ish spaced, but not diatonic" scales tend to sound surprisingly natural regardless of the ratios involved.

>>"Blackwood in 15-EDO is a good way to start if you don't mind a bit more error (careful with the timbre)."
I tried that before but wasn't careful with the timbre...is this yet another odd-harmonic-centric system?

>"The two need to work together; 7/6 might sound like two completely different intervals in two completely different scales."
I get the picture...now that chord progressions and the like are becoming more a part of the picture I realize what all the fuss about different MOS spacing was/is about.  

>"I like to expand my mental reach to a larger chromatic scale and then use smaller diatonic-sized scales within it, modulating as I damn well please. It's the modulations that give me all of the color."
  Ah, if I only had the quasi-immortal mental flexibility to pull that off.  If I have that right though, even if you're stuck with a lousy 3-4 chords that really work for you, you can get 8,12,16...by modulating and achieve a fair degree of color regardless...correct?

>>It's rare to find a lot of chords in a small scale size and which are also well-tuned. I've given you some above, but the hunt will always continue. If you don't mind dealing with a bit higher error, then there's a lot of good stuff - mavila temperament,
superpelog, etc. If you demand better intonation, then you're going to have to learn to deal with more notes.

   I guess that's the thing...even ignoring issues with color variety, even Hedgehog was starting to push me so far as accuracy goes: I couldn't get the chords working in any coherent way without using an odd-harmonic flute to "normalize" it.  So I think my line of attack is to stick with not-so-high-error systems and, in cases where I can't get the chord-color-variety...teach myself xenharmonic modulation.  It's my main issue with Machine and Mavila temperament that I can't modulate around, the error.

>>"And as it's hard to keep track of, say, 15 notes in your head at once, you're going to have to learn to use continuously modulating 7 or 8 note subsets in order to present
the listener with a manageable chunk of information that they can actually grab onto."
  Got it...so that's how you make something like Hedgehog[14] work without sounding random or just iterating through notes until one fits.

>>I think you should check out Sevish's "Golden Hour" album
    Love his stuff, always have...and his whole "microtonal with a beat" project is right up my alley.

>"Also, this Calvin Harris song is a good example of what I'm talking about wrt to the "tradeoff" that's there in other tunings than meantone. This entire song uses nothing but the white keys on the piano, at least the part of it I listened to."
   Not only that...but the scary fact most of it only use parts of the same min7 chord (bassline included)...it's almost a parody of pop music he gets away with it and still shifts the VF enough to keep the feeling playful. 

   That's the elephant in the room: "having" to walk on a tight-rope of well over 10 notes to get the range of tonal color I'm used to getting from more like 7 to 8.

>"Luckily, every rank-2 temperament comes with an MOS series which makes it relatively easy to figure out how to do this."

  Any links for tips how to modulate through/between MOS series? 

🔗clearinsulation <gsn10@...>

11/19/2012 3:58:04 PM

I've been working on something that's maybe a little similar to what you're talking about. Basically the idea is to find all size-n subsets (i.e. scales) of k-EDO, eliminate some based on interval size (no very tiny intervals, no consecutive small intervals, etc.), then eliminate the scales where a joint error/complexity measure falls above a certain threshold. The remaining "good" scales can then be assembled into a network. Additional metrics can be used to navigate this in a (hopefully) musically useful manner.

I'm treating chords as a subset of the scale, and navigating those in a similar way, but it's actually completely general. You could just as easily search for 3 note triads or whatever.

So it's an automated search for useful subsets of any equal temperament. The idea is to use it for both algorithmic composition and as a general sort of exploratory aid.

The results I've gotten so far are promising, but it needs more work. I need to rewrite most of it, and I haven't found the time.

You'll probably want to see Dmitri Tymoczko's work. His paper "Scale Networks and Debussy" introduces scale networks. I was surprised when I found it, as it's almost exactly what I'd been doing (since I started by looking at 12-EDO). He later wrote the book A Geometry of Music, which looks at chord networks and ways to derive musically useful chord progressions.

--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>
> I wonder if any of you have an interest in working with me to design something like this.
>
> It will hopefully allow you to specify certain "tunefulness" criteria e.g.
>
> A) How many fourth/fifth/any-alternative-semi-equivalence-ratio are allowed in a row far as shifting the root of the chord
> B1) What kind of melodic progression is allowed e.g. no larger than a whole tone apart for each note unless shifting by something in A) above
> B2) Additionally, what's the maximum total melodic movement per chord switch e.g. if C E G shift to D E A, that's (C-D = 2) + (E-E = 0) + (G to A = 2) = 4 total steps
>
> C) What percentage of the chords must involve (as I understand them) comma pumps (e.g. in a three note chord, keep two of the same notes, but invoke a third that shifts the apparent VF)
> D) How many iterations of chords in the progression must return to the root e.g. 3,4,5...
> E) What counts as a chord e.g. either specify a list of define criteria such as minimum ratio between any two tones in the chord or average ratio/difference among all tones.
>
>
> One thing required is the ability to specify the scale and what ratio in the scale you are treating as a fifth and/or semitone...this is needed to make sure all random combinations calculated fit within the scale.

🔗cityoftheasleep <igliashon@...>

11/19/2012 4:26:23 PM

--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>
> >>"Right, like I said: it's not specific chord progressions per se, but relationships between the notes, between the chords, etc."
>   But don't said relationships between chords define the chord progression (e.g. resolving by going down a fifth to the tonic will virtually always work, but something like a 6th is a toss up...and so on)? 
>

A chord progression is a specific set of chord movements, progressing forward through time in a linear fashion. In any given scale, there is a humongous number of chord progressions that you can come up with, if you allow any combination of 3 notes to be called a "chord". Even if you stick to, say, major and minor triads, can you list all the possible chord progressions available in meantone[7]? Every note in the scale connects to every other note by a variety of harmonic relationships. One chord progression cannot exemplify all of those relationships. Get it? But knowing the relationships enables you to conceive of the various possible directions you can move harmonically from a given note or chord, i.e. the various steps you can take in a chord progression, and since every scale has a different set of harmonic relationships between its notes, it has a different set of possible chord progressions.

>   And yet, name one hit rap track, even, without at least a bassline counterpoint contrasting with the lyrics and hinting at the chords: it may be a minimal hint, but it's there.

You've somehow managed to miss the point completely: popular music is trending away from harmonic/melodic innovation, toward recycling old patterns ad nauseam.

> >>"If people aren't even interested in those temperaments--which, BTW, are very good temperaments"
>    I just can't get around the uneven spacing in those...

They are all as evenly-spaced as the diatonic scale, if not more; augmented[9] is 2 1 1 2 1 1 2 1 1; diminished[8] is 2 1 2 1 2 1 2 1; pajara[10] is 1 1 1 1 2 1 1 1 1 2.

> although something like augmented[6] might work if people actually knew about it or
> heard some works in it.

It's been known about for over a century. Ever hear of a guy by the name of Stravinsky? Try googling "Tcherpnin's scale"--that's augmented[9]. People learn about it in music school, they just don't learn about "augmented temperament"--because they also don't learn about "meantone temperament".

But the point is, it IS there--people already have the means to be "xenharmonic" right there in 12-TET. Tcherpnin's scale--augmented[9]--is just about the best scale for crazy 8:9:10:12:14:15:19 chords in the known universe--name ONE other nine-note scale that gets you three otonal heptads with this degree of accuracy. You also get six major and six minor 5-limit triads, oh, and three 8:10:12:15:17:19 hexads as well. That is some far-out crazy shit, right there. So if someone isn't interested in the xenharmonic possibilities dangling right in front of their faces, why would they be interested in something that's even further away and requires special equipment?

> >>"And yet, musicians seemingly never tire of exploiting them...and
> apparently never will."
>   But, alas, their mood range, regardless of simplicity, is very limited by the underlying chords and, as we've discussed, the more notes you add on top of a chord, the less sensitive each note is to detuning and the less emotional change each additional note has on the sound of the chord. 
>

Again, you've missed the point. The mood range only *seems* limited *TO YOU*. Most "regular people" don't see it that way at all. Heck, I reckon you could squeeze the entire range of human emotion out of arpeggiations of a single major triad. Limitation is in the mind of the craftsman, not in his set of tools.

>   Why not something simple, but that uses a different palette. 

Because that's not "simple". If all you need out of a car is to drive to the local grocery store and back, you sure as heck don't need a Ferrari. People who want to do simple stuff will stick with simple scales...and nothing's simpler than what they already have.

> >>It usually takes a few decades for a song to be deemed a "classic".
> Nirvana, Metallica, Pearl Jam, for example, apparently took far less, for example...

Well congratulations, you made my point for me. Not only is there no shortage of "modern classics", they were already classics a mere 5 years after their release.

> >>"Because there is no sensible way to quantify "tunefulness" such that the most tuneful chord-progressions in a system will move by ratios more
> complex than those already approximated in 12-EDO"
>    IMO, you can cheat by tone classes a bit.  9/7 is fine as counting as "moving by 5/4"...as is 11/9...there's a bit of wiggle room.  The biggie seems to be 3/2: there seems to be no way around having it: 4:5:6, 5:6:8, 3:4:5, 2:3:4...just about any chord with ratios under ten or large movement between chords, in an arpeggio...and you end up needing a good 3:2 to pull it off and/or to move along it and/or resolve by moving by it.
>

So now you're accepting that ratios don't have anything to do with "novelty", and that even something like 11/9 can get "rounded" into sounding "like 5/4". You have officially escaped the realm of the quantifiable, and there's no hope of proceeding from here to arrive an algorithm that picks out "tuneful" chord progressions.

  Chords like 6:7:8 or 7:8:9 or 5:7:9 simply don't exist in 12EDO, as does movement between chords along ratios involving 7 really not significantly more complex than anything in 12EDO, especially if you throw in things like the occasional diminished chord at the end of a measure...why not capitalize on this?
>

Didn't you JUST SAY that 9/7 can sound "like 5/4" in a chord progression? If so, then 12-TET can certainly imply ratios of 7. Or are you going to tell me that 0-400-1000-1400 cents sounds completely unlike a 4:5:7:9, and that no one in their right mind would ever notice a similarity between those chords?

> >>"It's like going up to an Olympian swimmer and saying, "hey, have you
> considered joining the National Made-Up Sports Association? I've
> created a new sport and I think you'd be great at playing it, even
> though it's nothing like swimming...."
> Well, fortunately, some people are like that e.g. Lance Armstrong doing marathons and even admitting, to him, it was more of a challenge than any bicycle race and felt, yes, refreshing (as a change).  
>

Not quite the right analogy. I know lots of Western-trained musicians who play a variety of world musical styles and instruments, but none of them are into xenharmony. A marathon is still a legitimate sport; if Lance Armstrong had started up a National Calvinball League, that'd be more appropriate....

>    The other thing is, I don't think it's that much harder if we get it into a few
> consistent terms e.g. find a scale where maybe 80% of the structures are the same as in > 12EDO and the other 20% can be treated like 12EDO equivalents

Nope, that's not the problem. The problem isn't that people aren't getting their hands held enough, it's that they don't want to walk in this direction in the first place. And it's not a "problem" that we need to solve; people will do what they love, and as long as they love what they do, they have no good reason to change, despite what *you* may think of what they are doing. Try it yourself: try to teach your brother, the accomplished jazz guitarist, about Tcherpnin's scale, and try to get him to write a few pieces of music in it. If you can't convince him to do that, what makes you think anything you can say will convince anyone that they should be interested in xenharmony?

>   You sound a bit like some of the guys on the trance scene who say "trance is not dead, it's underground, where it works best", instead of doing...

Okay, I'm cutting you off here. Everything you wrote after this point is complete nonsense and totally off-topic.

Michael, you're not interested in getting people to write xenharmonic music. You're interested in getting people to adopt your musical philosophy, so that they'll make the music you wish YOU could make. You have a vision in your head of what you want other peoples' music to sound like, and what you're really after are the tools and arguments to persuade people to make their music more like how *you* want it to be. That's what it always comes back to; you think that if we can find you the right scales, the right tunings, the right ways to describe the scales, you can go out and cajole people into adopting *your* approach, so that you don't have to create anything yourself. You already seem to have given up on creating your own music, which is a ridiculous thing to do. If you're giving up on yourself, then you should definitely give up on the rest of us, because we're sure as hell not going to do your bidding.

If, instead of wasting your time petitioning the empty sky, you actually tried to hone your compositional craft, and just stopped giving a fuck about what everyone else is doing, you might actually come up with something worthwhile. But all your little schemes to find or create the "perfect scale" to catapult xenharmony into the limelight are a waste of your time and everyone else's.

And please: I don't want to hear what you think about my music ever again, okay? Not EVER.

-Igs

🔗RR <djtrancendance@...>

11/19/2012 9:09:05 PM

>>"One chord progression cannot exemplify all of those relationships. Get it?"
    Right, but eliminate those which are simply transposed versions of other progressions, ones that only include minor/major chords (like you said) or inverted versions of other progressions, have no more than four chords, don't move root by complex intervals, sound a lot like each other in mood...and you get something much more limited.  And I'm not implying "hey, let's find every single possible chord progression", but rather "let's find a handful (maybe 7-10) for each scale that gives the musician a general feel for what the scale most naturally/easily sounds like" (e,g, without special rhythm, instrument usage, lead melodies, etc. attempting to pull it in another direction).

>>"But knowing the relationships enables you to conceive of the various
possible directions you can move harmonically from a given note or
chord, i.e. the various steps you can take in a chord progression, and
since every scale has a different set of harmonic relationships between
its notes, it has a different set of possible chord progressions."
  Sure, but how long will it honestly take you to test for these and get a feel for what the scale can do?    Or what's a quick way to go about finding that?  One obvious answer seems to be find a few good short chord progressions per scale.

>>"You've somehow managed to miss the point completely: popular music is
trending away from harmonic/melodic innovation, toward recycling old
patterns ad nauseam."
  You're saying this to me >after< I brought up examples like Calvin Harris and people like AVICII and Leona Lewis suing over remixes of tracks that are neither of theirs?!...if anything, I've pointing at said-above point all along. 

Also, you're missing my greater point on that: the >reason< it's become so g-d-awfully simple is because musicians have by and large exhausted the good complex combinations.  So they have two choices
A) Do a lot of extra work trying to find the very few, if any, remaining complex combinations that haven't been used.
B) Stick with a simple one they know works, often plain old evokes surefire upbeat emotions, and likely isn't any less original than A as the search for A) often fails to yield original results.
  Is it any wonder they are betting on A)?
  Of course, there is always the BS factor, which I hate

C) Recycling garbage "knowing" that the last generation buying most probably hasn't heard the originals and truly thinks it's fresh.

------------------
   IMO the general reason it's going this way is there's so little originality left to fight for in non-modulated diatonic scales in 12EDO.
--------------------------- 
>>"They are all as evenly-spaced as the diatonic scale, if not more;
augmented[9] is 2 1 1 2 1 1 2 1 1; diminished[8] is 2 1 2 1 2 1 2 1;
pajara[10] is 1 1 1 1 2 1 1 1 1 2."
  They are loaded with tiny steps...which is what I meant (perhaps a bit un-clearly) by uneven spacing.

>>"Heck, I reckon you could squeeze the entire range of human emotion out
of arpeggiations of a single major triad. Limitation is in the mind of
the craftsman, not in his set of tools."
  Considering most musicians aren't wizards...you have a problem here.  You can probably get happy/sad/angry/striving...just by virtue of things like timing: heck, you can do that with a single drum.  However, if you want the sense of freedom, depth...within each range, I'm sorry but a triad isn't going to cut it, not even in Hogwarts.  Also, if it were all down to the mind of a craftsmen, surely you'd find one man bands with one or two note instruments able to jam out a storm and a single musician could generate the same energy and polyrhythmic depth as a full 4+ man band...there are limits.

>>"Tcherpnin's scale--augmented[9]--is just about the best scale for crazy 8:9:10:12:14:15:19"
  Before I try this for grins...how on earth does he end up at 19?

>>"If all you need out of a car is to drive to the local grocery store and
back, you sure as heck don't need a Ferrari. People who want to do
simple stuff will stick with simple scales...and nothing's simpler than
what they already have."
  But who says they wanted simple?  Many would gladly have the Ferrari if it weren't for cost/maintenance/risk factors.  It's funny because the latest Ferrari's are built with all sorts of wizardry to do things like automatically limit acceleration/burnout on corners and keep wheels from spinning during hard acceleration: they actually went through pains to make sure the car didn't feel "advanced" and that anyone driving it could feel like an F1 hero and/or easily keep it under control for their supermarket run.  
   In music, all most people want, it seems, is something that makes them feel good/upbeat/smart/relaxed/in-control and (unrelated to actual music, but just lyrics wise) empathized with.  The "classic" songs/pieces...are often the ones that do so in a complex way that somehow alludes to simple patterns: they make the listen think, in some sense, he's heroic and brilliant for decoding it so easily.  That's why things like the song "Groove is in the Heart" samples Herbie Hancock's "Bring Down the Birds" for it's bassline...it's sophisticated yet dead easy to follow and uplifting.  

> Nirvana, Metallica, Pearl Jam, for example, apparently took far less, for example...
>Well congratulations, you made my point for me. Not only is there no
shortage of "modern classics", they were already classics a mere 5 years
after their release.

  And those pre-millenium groups are considered modern since when?  Where are the classics from the last 10 years, even though those only took 5 to achieve such status?

>>"So now you're accepting that ratios don't have anything to do with
"novelty", and that even something like 11/9 can get "rounded" into
sounding "like 5/4"."
  And blues or anything else that uses it to morph between major and minor is a form of heresy or quackery?  I was always under the impression they used it that way because it works.  And the more narrow-banded versions of harmonic entropy graphs show a slight minimum at 11/9, though still enough above those at 6/5 and 5/4 that it makes sense it can still act as either depending on the chord.  

>"Didn't you JUST SAY that 9/7 can sound "like 5/4" in a chord progression? If so, then 12-TET can certainly imply ratios of 7."
  Not that it sounds the same, but has a similar function e.g. amount of tension introduced: you can "get away" with using a 9/7 for most of the things you'd normally use a 5/4 for.

>>"Or are you going to tell me that 0-400-1000-1400 cents sounds completely unlike a 4:5:7:9, and that no one in their right mind would ever notice a similarity between those chords?"
  Similarity, sure...same impact and usability (who normally plays chords that spanning over an octave), no way: that would be like saying the square root of 2 tritone in 12EDO is virtually as clean as a 7/5 or that 3:4:5 and 4:5:6 sound "the same" because they are inversions.  Also, as we've discussed before, the more notes you have in a chord (and, especially, the more very simple ratios), the less adding an extra note on top like that 9/7 is going to matter.  Take a 4:5:6 chord in 12EDO and throw in an "illegal" note a semitone above it...it's still going to have the basic dominating character of a plain old 4:5:6.

>>"A marathon is still a legitimate sport; if Lance Armstrong had started
up a National Calvinball League, that'd be more appropriate...."
  And Xenharmony is not legitimate?  Here's an analogy: the actual act of using alternative systems is like training for a marathon with weights on your shoes: weird, but can get the job done and even understood and eventually admired by those training for other sports; ever heard of the Spartan Race series?  The way it's portrayed is more like running over burning coal out of pure stupidity to help "toughen up".  The latter seems to be your analogy for the circus-like how you think it has to be seen, by nature, kind of like "Calvinball".

>>"Try it yourself: try to teach your brother, the accomplished jazz
guitarist, about Tcherpnin's scale, and try to get him to write a few
pieces of music in it. If you can't convince him to do that, what makes you think anything you can say will convince anyone that they should be interested in xenharmony?"
  Ha, well, if I find it useful myself in such a way I can argue for it intelligently from experience, sure, I'll try it.

>>"Michael, you're not interested in getting people to write xenharmonic
music. You're interested in getting people to adopt your musical
philosophy, so that they'll make the music you wish YOU could make."
   Complete hogwash...and I've said this before.  The music I want to make and listen to is underground psytrance/liquid-d&b...some rather unpopular EDM genres I would highly >not< recommend trying to use to popularize xenharmony and never have recommended here.  The only thing I've seen here, essentially, that really matches that is Sevish's d&b work...and even then it's only a passing resemblance.

   Something like, shoot...Deadmau5 interests me about as much as Britney Spears...which is none.  I will say I personally don't like traditional classical/jazz/blues/funk...music, but I have repeatedly tipped my hat when I see someone composing blues/funk much as I would for an underground track because I see how it could work for other people.  Easy-to-follow melodies and harmonies (even ones I hate) work for most people...that's not me pushing my musical tastes or rocket science; that's historical fact, at least for the last 30 or so years.  I used to make nothing but weird acid-jazz...but then I took my head out of my and realized it might help to put some actual motifs in my tracks and not exclusively avoid major/minor chords and fifths (and believe me, for the most part I did) to forcibly sound "special" e.g. there's such a thing as overdoing "artistic license".

   On rare occasion, I've even tipped it about classical e.g. when Aaron K. Johnson dropped a beautiful piano improv he wrote that no one could believe was an improv, and I generally just don't get classical or any variation (soundtrack, ambient, new-age).  I just see the value in music with generally simple harmonic relations (or, better yet, tricks to allude to them yet add depth)...that's all: I'm not this self-style-worshipping purist you seem to make me out to be, at all.  

>>"and just stopped giving a fuck about what everyone else is doing, you
might actually come up with something worthwhile. But all your little
schemes to find or create the "perfect scale" to catapult xenharmony
into the limelight are a waste of your time and everyone else's.
And please: I don't want to hear what you think about my music ever again, okay? Not EVER."

   Well, at least I can say I can take musical criticism and realize that some of it is worth taking seriously just as some of it is worth neglecting and harmful to artistic license.  That attitude is toxic...just as bad as the flip-side attitude of the types of people who think everything has to be their genre, on a certain popular (or, on the flipside, academic) music top list, or what not.  Is it that difficult to understand or try the concept of balancing what other people say your music sounds like to what you think it sounds like and working on a clever way to, for the most part, satisfy both for at least a handful of people? 

  After all, how can you learn anything if you've come in making a choice to ignore people...

  

________________________________
From: cityoftheasleep <igliashon@sbcglobal.net>
To: tuning@yahoogroups.com
Sent: Monday, November 19, 2012 6:26 PM
Subject: [tuning] Re: Chord progression program (scale independent within subsets of EDOs)

 

--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>
> >>"Right, like I said: it's not specific chord progressions per se, but relationships between the notes, between the chords, etc."
>   But don't said relationships between chords define the chord progression (e.g. resolving by going down a fifth to the tonic will virtually always work, but something like a 6th is a toss up...and so on)? 
>

A chord progression is a specific set of chord movements, progressing forward through time in a linear fashion. In any given scale, there is a humongous number of chord progressions that you can come up with, if you allow any combination of 3 notes to be called a "chord". Even if you stick to, say, major and minor triads, can you list all the possible chord progressions available in meantone[7]? Every note in the scale connects to every other note by a variety of harmonic relationships. One chord progression cannot exemplify all of those relationships. Get it? But knowing the relationships enables you to conceive of the various possible directions you can move harmonically from a given note or chord, i.e. the various steps you can take in a chord progression, and since every scale has a different set of harmonic relationships between its notes, it has a different set of possible chord progressions.

>   And yet, name one hit rap track, even, without at least a bassline counterpoint contrasting with the lyrics and hinting at the chords: it may be a minimal hint, but it's there.

You've somehow managed to miss the point completely: popular music is trending away from harmonic/melodic innovation, toward recycling old patterns ad nauseam.

> >>"If people aren't even interested in those temperaments--which, BTW, are very good temperaments"
>    I just can't get around the uneven spacing in those...

They are all as evenly-spaced as the diatonic scale, if not more; augmented[9] is 2 1 1 2 1 1 2 1 1; diminished[8] is 2 1 2 1 2 1 2 1; pajara[10] is 1 1 1 1 2 1 1 1 1 2.

> although something like augmented[6] might work if people actually knew about it or
> heard some works in it.

It's been known about for over a century. Ever hear of a guy by the name of Stravinsky? Try googling "Tcherpnin's scale"--that's augmented[9]. People learn about it in music school, they just don't learn about "augmented temperament"--because they also don't learn about "meantone temperament".

But the point is, it IS there--people already have the means to be "xenharmonic" right there in 12-TET. Tcherpnin's scale--augmented[9]--is just about the best scale for crazy 8:9:10:12:14:15:19 chords in the known universe--name ONE other nine-note scale that gets you three otonal heptads with this degree of accuracy. You also get six major and six minor 5-limit triads, oh, and three 8:10:12:15:17:19 hexads as well. That is some far-out crazy shit, right there. So if someone isn't interested in the xenharmonic possibilities dangling right in front of their faces, why would they be interested in something that's even further away and requires special equipment?

> >>"And yet, musicians seemingly never tire of exploiting them...and
> apparently never will."
>   But, alas, their mood range, regardless of simplicity, is very limited by the underlying chords and, as we've discussed, the more notes you add on top of a chord, the less sensitive each note is to detuning and the less emotional change each additional note has on the sound of the chord. 
>

Again, you've missed the point. The mood range only *seems* limited *TO YOU*. Most "regular people" don't see it that way at all. Heck, I reckon you could squeeze the entire range of human emotion out of arpeggiations of a single major triad. Limitation is in the mind of the craftsman, not in his set of tools.

>   Why not something simple, but that uses a different palette. 

Because that's not "simple". If all you need out of a car is to drive to the local grocery store and back, you sure as heck don't need a Ferrari. People who want to do simple stuff will stick with simple scales...and nothing's simpler than what they already have.

> >>It usually takes a few decades for a song to be deemed a "classic".
> Nirvana, Metallica, Pearl Jam, for example, apparently took far less, for example...

Well congratulations, you made my point for me. Not only is there no shortage of "modern classics", they were already classics a mere 5 years after their release.

> >>"Because there is no sensible way to quantify "tunefulness" such that the most tuneful chord-progressions in a system will move by ratios more
> complex than those already approximated in 12-EDO"
>    IMO, you can cheat by tone classes a bit.  9/7 is fine as counting as "moving by 5/4"...as is 11/9...there's a bit of wiggle room.  The biggie seems to be 3/2: there seems to be no way around having it: 4:5:6, 5:6:8, 3:4:5, 2:3:4...just about any chord with ratios under ten or large movement between chords, in an arpeggio...and you end up needing a good 3:2 to pull it off and/or to move along it and/or resolve by moving by it.
>

So now you're accepting that ratios don't have anything to do with "novelty", and that even something like 11/9 can get "rounded" into sounding "like 5/4". You have officially escaped the realm of the quantifiable, and there's no hope of proceeding from here to arrive an algorithm that picks out "tuneful" chord progressions.

  Chords like 6:7:8 or 7:8:9 or 5:7:9 simply don't exist in 12EDO, as does movement between chords along ratios involving 7 really not significantly more complex than anything in 12EDO, especially if you throw in things like the occasional diminished chord at the end of a measure...why not capitalize on this?
>

Didn't you JUST SAY that 9/7 can sound "like 5/4" in a chord progression? If so, then 12-TET can certainly imply ratios of 7. Or are you going to tell me that 0-400-1000-1400 cents sounds completely unlike a 4:5:7:9, and that no one in their right mind would ever notice a similarity between those chords?

> >>"It's like going up to an Olympian swimmer and saying, "hey, have you
> considered joining the National Made-Up Sports Association? I've
> created a new sport and I think you'd be great at playing it, even
> though it's nothing like swimming...."
> Well, fortunately, some people are like that e.g. Lance Armstrong doing marathons and even admitting, to him, it was more of a challenge than any bicycle race and felt, yes, refreshing (as a change).  
>

Not quite the right analogy. I know lots of Western-trained musicians who play a variety of world musical styles and instruments, but none of them are into xenharmony. A marathon is still a legitimate sport; if Lance Armstrong had started up a National Calvinball League, that'd be more appropriate....

>    The other thing is, I don't think it's that much harder if we get it into a few
> consistent terms e.g. find a scale where maybe 80% of the structures are the same as in > 12EDO and the other 20% can be treated like 12EDO equivalents

Nope, that's not the problem. The problem isn't that people aren't getting their hands held enough, it's that they don't want to walk in this direction in the first place. And it's not a "problem" that we need to solve; people will do what they love, and as long as they love what they do, they have no good reason to change, despite what *you* may think of what they are doing. Try it yourself: try to teach your brother, the accomplished jazz guitarist, about Tcherpnin's scale, and try to get him to write a few pieces of music in it. If you can't convince him to do that, what makes you think anything you can say will convince anyone that they should be interested in xenharmony?

>   You sound a bit like some of the guys on the trance scene who say "trance is not dead, it's underground, where it works best", instead of doing...

Okay, I'm cutting you off here. Everything you wrote after this point is complete nonsense and totally off-topic.

Michael, you're not interested in getting people to write xenharmonic music. You're interested in getting people to adopt your musical philosophy, so that they'll make the music you wish YOU could make. You have a vision in your head of what you want other peoples' music to sound like, and what you're really after are the tools and arguments to persuade people to make their music more like how *you* want it to be. That's what it always comes back to; you think that if we can find you the right scales, the right tunings, the right ways to describe the scales, you can go out and cajole people into adopting *your* approach, so that you don't have to create anything yourself. You already seem to have given up on creating your own music, which is a ridiculous thing to do. If you're giving up on yourself, then you should definitely give up on the rest of us, because we're sure as hell not going to do your bidding.

If, instead of wasting your time petitioning the empty sky, you actually tried to hone your compositional craft, and just stopped giving a fuck about what everyone else is doing, you might actually come up with something worthwhile. But all your little schemes to find or create the "perfect scale" to catapult xenharmony into the limelight are a waste of your time and everyone else's.

And please: I don't want to hear what you think about my music ever again, okay? Not EVER.

-Igs

🔗Keenan Pepper <keenanpepper@...>

11/20/2012 4:58:14 PM

--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>   I agree on singing though...and studies have shown even our basic diatonic system and many melodies basically rip off vocal inflections and pitches in everyday speech.  It's as if the Lord himself created the diatonic scale (at least, for Western speech)...through it would be interesting to see  if people in the Middle East actually use vocal intonations mirroring the Rast scale or if other animals use different systems, for example.

What studies are you talking about? I'd be very interested in any that conclude speech intonation has anything to do with the diatonic scale, because that seems so unlikely to me.

>    Well, the Persian and African, not to mention blues, point to blue tones...and it still bugs me to tears no one has tried to use Rast in a hit track.

http://www.youtube.com/watch?v=Xu3FTEmN-eg ?

Keenan

🔗RR <djtrancendance@...>

11/20/2012 5:48:59 PM

>>"What studies are you talking about? I'd be very interested in any that
conclude speech intonation has anything to do with the diatonic scale,
because that seems so unlikely to me."
  Read it somewhere a few years ago (probably Psychology Today or something not-so-formally-reviewed)...but I did find this

  http://www2.hawaii.edu/~hunterh/Docs/JoshuaSteel.pdf

  Apparently, the notes speech stops at before/after its natural drifts/portamentos are virtually limited in accuracy to quarter-tones.

     "the difference between absolute frequency in Hertz and a quarter-tone value was never more than 3 Hertz."

>>    Well, the Persian and African, not to mention blues, point to
blue tones...and it still bugs me to tears no one has tried to use Rast
in a hit track.
>http://www.youtube.com/watch?v=Xu3FTEmN-eg ?
   Ha, I stand corrected...and even for the tiny motif I hear it in...I works beautifully.  The good news is...it stands as at least partial proof it can work over chords as polyphonic...and seems to hint the next step is to put Rast in the entire chord, not just a section over it (or, at least, that's what I'm hearing).

________________________________
From: Keenan Pepper <keenanpepper@...>
To: tuning@yahoogroups.com
Sent: Tuesday, November 20, 2012 6:58 PM
Subject: [tuning] Re: Chord progression program (scale independent within subsets of EDOs)

 
--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>   I agree on singing though...and studies have shown even our basic diatonic system and many melodies basically rip off vocal inflections and pitches in everyday speech.  It's as if the Lord himself created the diatonic scale (at least, for Western speech)...through it would be interesting to see  if people in the Middle East actually use vocal intonations mirroring the Rast scale or if other animals use different systems, for example.

What studies are you talking about? I'd be very interested in any that conclude speech intonation has anything to do with the diatonic scale, because that seems so unlikely to me.

>    Well, the Persian and African, not to mention blues, point to blue tones...and it still bugs me to tears no one has tried to use Rast in a hit track.

http://www.youtube.com/watch?v=Xu3FTEmN-eg ?

Keenan

🔗Keenan Pepper <keenanpepper@...>

11/20/2012 6:01:33 PM

--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>
> >>"What studies are you talking about? I'd be very interested in any that
> conclude speech intonation has anything to do with the diatonic scale,
> because that seems so unlikely to me."
>   Read it somewhere a few years ago (probably Psychology Today or something not-so-formally-reviewed)...but I did find this
>
>   http://www2.hawaii.edu/~hunterh/Docs/JoshuaSteel.pdf
>
>   Apparently, the notes speech stops at before/after its natural drifts/portamentos are virtually limited in accuracy to quarter-tones.

I don't see how "limited in accuracy to quarter-tones" has anything to do with being related to the diatonic scale, which is what you said originally, and what I asked about.

>      "the difference between absolute frequency in Hertz and a quarter-tone value was never more than 3 Hertz."

Here, the paper is not stating that speech tends to line up with 24edo quarter-tones based on A440; it's merely saying that in converting from Hz to quarter-tones no errors greater than 3 Hz were introduced. (Keep in mind that below about 200 Hz, quarter-tones are less than 6 Hz apart, so it's impossible for rounding to quarter-tones to produce errors greater than 3 Hz.)

So, I think I have to call BS on your original claim that speech intonation has anything to do with the diatonic scale whatsoever. Speech does not work that way.

Keenan

🔗Mike Battaglia <battaglia01@...>

11/20/2012 6:15:38 PM

On Mon, Nov 19, 2012 at 6:42 PM, RR <djtrancendance@...> wrote:
>
> >>"The bVII chord in the Beatles is IV/IV and they use it when they're
> >> writing stuff in mixolydian mode."
> So, in other words, they aren't using B, at all, and the entire
> piece(s) are in c mixolydian? If that's the case, wow, that is much ado
> about nothing.

Paperback Writer was the example given, and it's in G mixolydian. (I
don't remember the bridge right now but I think it modulates a bit.)

> >>"If you've come up with some arbitrary mathematical pattern for a chord
> progression, and you play it and it sounds like crap, it's not advanced.
> What's "advanced" is when you have a complex pattern that actually sounds
> good."
>
> Such as?

I'm a fan of the impressionists for being able to pull stuff like that off well.

> >"I never said anything about this restriction where you can only resolve
> > by a fifth; that was something you came up with... never in my life would
> > subscribe to such a restrictive view of harmony
>
> You're right, you never did, I'm just saying that's one sure-fire way
> that virtually always works. On a more optimistic note...some other ways to
> accomplish resolution that usually work are?

The immediately obvious example is the tritone substitution: instead
of G7 -> Cmaj, try Db7 -> Cmaj.

For something slightly more exotic there's the "backdoor progression,"
which is a ii-V as though you were doing to the bIII, but then you go
back to the I. Making the V lydian dominant is good. So in B, you can
do A7#11 -> B maj, for instance. Listen to the Beatles' "For No One"
and "Hello Goodbye" for an example of this, as well as the ending to
Eric Clapton's "Layla," and Joe Cocker's "You Are So Beautiful" and so
on.

There's a bunch of other random ways to resolve to I that can work in
various situations. bVI can resolve well to I sometimes. iim7 usually
resolves to I really nicely without needing to go to V first, as in
Fmaj7 Em7 Dm7 Cmaj7 (the Calvin Harris song you just played does
this).

> Neither do I (hence why I mentioned the minor 6th resolution in that last
> youtube link in the vocals before)...but it seems like a more sensitive
> option that, like you said "just contain(s) more information...can be
> overwhelming if you don't know how
> to parse it, making the whole thing sound disconnected".

I guess that makes sense. I suggest learning how to parse it though.
(I'm trying to go through this process with other tuning systems and I
see how difficult it is now.)

> I tried a few
> melodic lines after dropping the bass line on a 6th resolution...and there
> were much fewer options that worked than with a fifth...as if there had to
> be a predictable "calm" in the melodic pattern to balance the overload
> caused by the jump. Not that it can't work really well (and it's d-mn
> amusing/entertaining when it does), but it apparently takes more care to
> pull off.

Yup, sometimes things like that can be more sensitive. I have no idea
why, I just know that if you play it right, it can sound extremely
"colorful."

> Never said it modulated but...the pattern seems to be it's decidedly
> tense (at least to my ears, even if the math behind it is "normal") and far
> less directed at the tonic to do that 7th jump. And, to note, it's followed
> by a 5th-like relaxed movement to a fourth, which makes sense to balance out
> said "more information" and, it seems,push back the tonic.

Yeah, something like that. It explicitly constructs a bridge from this
far-out note back to the tonic, showing how the whole thing fits into
some larger "functional" thing. (Good exercise: play around in 19-EDO
and learn to do this with the extended meantone intervals there.)

> Indirectly...or just to keep track of the notes, period: and having to
> remember where all the "new" notes are after the modulation in such a large
> set.

Yes, I agree with this. Here's one solution: think about if you're in
19-EDO, for instance. Meantone[12] is still in it, so you can use that
as a subset. But if you just use one meantone[12] subset and never
change anything, you'll be limited in terms of what chords you can do.
For instance, here's one mode of meantone[12]:

C C# D Eb E F F# G Ab A Bb B C

Only 12 notes, easy to grab onto.

Now, say you want to play ||: Fmaj Abmaj | Cmaj | Emaj | Am Gmaj :||
(pay attention to the timing here). Note that you can't. Emaj requires
G#, and Abmaj requires Ab. So if you use only these notes, you're
screwed and you'll either have to have that Abmaj be some messed up
G#-C-Eb chord or you'll have to have the Emaj be E-Ab-B, which is a
supermajor chord. So what happens now? Is all hope lost forever?

No! Just modulate, damn it! So do this: for the Fmaj Abmaj | Cmaj
part, use this chromatic scale

C C# D Eb E F F# G Ab A Bb B C

Then for the Emaj | Am Gmaj part, use this chromatic scale:

C C# D Eb E F F# G G# A Bb B C

See how the Ab changed to a G#?

The secret is to still use meantone[12], but play what you feel and
then continuously change the mode of meantone[12] to match what you're
playing. The net effect is that you have 12 quasi-equal "regions" of
note in 19-EDO which sometimes adapt to match the current chord. This
is much more freeing than only using one 12-note subset and limiting
your choice of chords to only the subset you use: just continually
modulate through modes of meantone[12], and then within each
meantone[12], modulate further through the modes of meantone[7] to
play the chords you want.

So then the same principle applies to other large EDOs. Do the same
with porcupine[15] in 22-EDO and the like.

> Right, which is why I'm taking your advice and digging into Hedgehog
> temperament. Theory wise I don't actually think there's any formal right or
> wrong, just more or less likely to work most of the time.

I guess that's one way to think of it. I've never thought about the
relative probabilities that something will "work," but maybe that
might be a good paradigm to work within...

> >>"You should go on a systematic review of MOS's with 9 notes or less,
> >> especially ones with more "L" than "s" notes."
>
> Gotcha...and I'm seeing that in the temperaments you're handing me, like
> Machine...these "diatonic-ish spaced, but not diatonic" scales tend to sound
> surprisingly natural regardless of the ratios involved.

Exactly! That realization has changed the way I think about music. So
if you find "surprisingly natural" sounding scales, and then you ALSO
intone them with nice ratios so that the chords are concordant, you've
hit the jackpot.

> >>"Blackwood in 15-EDO is a good way to start if you don't mind a bit more
> >> error (careful with the timbre)."
> I tried that before but wasn't careful with the timbre...is this yet
> another odd-harmonic-centric system?

Not necessarily odd-harmonic centric; just less harsh timbres =
better. Think flutes and marimbas instead of a horn section.

Try Blackwood in 20-EDO as well to compare.

> >"The two need to work together; 7/6 might sound like two completely
> > different intervals in two completely different scales."
> I get the picture...now that chord progressions and the like are becoming
> more a part of the picture I realize what all the fuss about different MOS
> spacing was/is about.

Right.

> >"I like to expand my mental reach to a larger chromatic scale and then
> > use smaller diatonic-sized scales within it, modulating as I damn well
> > please. It's the modulations that give me all of the color."
> Ah, if I only had the quasi-immortal mental flexibility to pull that
> off. If I have that right though, even if you're stuck with a lousy 3-4
> chords that really work for you, you can get 8,12,16...by modulating and
> achieve a fair degree of color regardless...correct?

Yes, exactly. I don't think it requires quasi-immortal mental
flexibility if you do what I said above when working with large EDOs;
e.g. chunk them into smaller quasi-EDOs that you modulate within. For
instance, it's easy to make 19-EDO sound like 12-EDO by just
continually changing the mode of meantone[12]; it'd be interesting to
try to make 22-EDO sound like 15-EDO by just continually changing the
mode of porcupine[15]. That's what I'm toying with now.

> I guess that's the thing...even ignoring issues with color variety,
> even Hedgehog was starting to push me so far as accuracy goes: I couldn't
> get the chords working in any coherent way without using an odd-harmonic
> flute to "normalize" it. So I think my line of attack is to stick with
> not-so-high-error systems and, in cases where I can't get the
> chord-color-variety...teach myself xenharmonic modulation. It's my main
> issue with Machine and Mavila temperament that I can't modulate around, the
> error.

If hedgehog's not good for you, then you might not like porcupine too
much either; those 327 cent intervals are simultaneously 6/5 and 11/9
(but I kind of like that "feature" about it).

Hmm, what are some accurate, higher-limit temperaments you might like?
You might want to experiment with miracle[10] and tetracot[7]. Also
don't forget sensi; those 1/1 9/7 5/3 chords are pretty nuts (two
9/7's makes a 5/3). Huge stacks of 9/7 sound like deep space to me or
something.

> Got it...so that's how you make something like Hedgehog[14] work without
> sounding random or just iterating through notes until one fits.

That's my idea, anyway.

> Not only that...but the scary fact most of it only use parts of the
> same min7 chord (bassline included)...it's almost a parody of pop music he
> gets away with it and still shifts the VF enough to keep the feeling
> playful.

I don't hear any obvious VFs in this song. Are you talking about the bassline?

> That's the elephant in the room: "having" to walk on a tight-rope of
> well over 10 notes to get the range of tonal color I'm used to getting from
> more like 7 to 8.

You'll get the hang of it.

> >"Luckily, every rank-2 temperament comes with an MOS series which makes
> > it relatively easy to figure out how to do this."
>
> Any links for tips how to modulate through/between MOS series?

Pick an MOS which is "diatonic" sized, and then pick a larger one
which is "chromatic" sized. So porcupine, for instance, has MOS's of
size 7, 8, and 15. (The 7-note one is 1L6s and the 8 note one is
7L1s.) So you might say the 7-note one is diatonic (or "albitonic" is
the term Gene uses) and the 15-note one is chromatic.

Once you've done that, you will be successful if you follow this one simple rule

==SIMPLE RULE==
When you come up with a nice chord in a progression try to find a way
to build the scale around the chord, not the other way around.
==

Somedays I want to scream that off of the highest mountain. Of course,
this is just my idea, so I can't tell anyone that it's better than
anything else, but that's basically how extended harmony in 12-EDO
works and I really like the way it sounds in other tuning systems,
particularly porcupine.

So for instance, if you hear this amazing color chord, you'll have to
find a mode of your diatonic scale that fits it, and then modulate to
that mode. Ahh, but what if you can't find a mode of the diatonic
scale which fits it - for instance, say you want to play an augmented
maj7 chord in meantone? Then you have to use chromatic alterations!
Don't just stick to the MOS, but sharpen or flatten notes.

OK, what interval do you sharpen or flatten things by? I find the
results often work well if the interval you're sharpening or
flattening by is the difference between the large and small step,
called the "chroma" for that MOS. So for meantone[7] it's just the
interval L-s (in 19-EDO, this is 1 step out of 19).

Then shut your brain off and have fun. Now, how do you find the
awesome color chords? This is the fun part, go exploring and let us
know what you find.

Again, these are just my ideas and I don't claim they're the One True
Way to write music, but I think it's an interesting technique and I
like the way it sounds.

-Mike

🔗Mike Battaglia <battaglia01@...>

11/20/2012 6:16:30 PM

On Tue, Nov 20, 2012 at 9:01 PM, Keenan Pepper <keenanpepper@...>
wrote:
>
> So, I think I have to call BS on your original claim that speech
> intonation has anything to do with the diatonic scale whatsoever. Speech
> does not work that way.

The paper you're looking for is here:
http://ase.tufts.edu/psychology/music-cognition/pdfs/Curtis&Bharucha2010Emotion.pdf

-Mike

🔗RR <djtrancendance@...>

11/20/2012 6:25:47 PM

>>"I don't see how "limited in accuracy to quarter-tones" has anything to
do with being related to the diatonic scale, which is what you said
originally, and what I asked about."
  Turns out, after reading the above more formal articles, it apparently doesn't (isn't a complete answer to say it's 'just' diatonic, which is why I mentioned " not-so-formally-reviewed".  So I corrected my old view/mistake there.

  However the below seems to elaborate that non-impassioned speech is spoken in just simple diatonic whole tones:

http://books.google.com/books?id=jadDAAAAIAAJ&pg=PA585&lpg=PA585&dq=speech+diatonic+scale&source=bl&ots=KT3P9J-y_R&sig=7mVxgLhQ8dR27R3DSUntJCWiSZ0&hl=en&sa=X&ei=RDCsUL_XJJKtqAH1p4DACQ&ved=0CFIQ6AEwBg#v=onepage&q=speech%20diatonic%20scale&f=false ...and only "plaintave" and "passioned" speech involves the semitone, chromatic scales, and beyond.

  My guess is said article I read years before only focused on one type of speech...but my remaining question is if/when do intervals like 9/7, 13/8...work their way into speech, or is it just the quarter tone at 50 cents that appears?

   The inclusion of the quarter tone and not "just" the diatonic in speech seems to hint Middle Eastern scales may well have been indirectly derived by vocal tones and perhaps this connection makes them sound more "native/instinctual/relate-able".

>>"(Keep in mind that below about 200 Hz, quarter-tones are less than 6 Hz
apart, so it's impossible for rounding to quarter-tones to produce
errors greater than 3 Hz.)"
  Didn't think of that...and then questions arise such as if the range of vocals tested regularly went significantly over 200hz.  So there indeed may be the possibility for beyond quarter tone accuracy used in non-fluctuating notes in speech.

________________________________
From: Keenan Pepper <keenanpepper@...>
To: tuning@yahoogroups.com
Sent: Tuesday, November 20, 2012 8:01 PM
Subject: [tuning] Re: Chord progression program (scale independent within subsets of EDOs)

 

--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>
> >>"What studies are you talking about? I'd be very interested in any that
> conclude speech intonation has anything to do with the diatonic scale,
> because that seems so unlikely to me."
>   Read it somewhere a few years ago (probably Psychology Today or something not-so-formally-reviewed)...but I did find this
>
>   http://www2.hawaii.edu/~hunterh/Docs/JoshuaSteel.pdf
>
>   Apparently, the notes speech stops at before/after its natural drifts/portamentos are virtually limited in accuracy to quarter-tones.

I don't see how "limited in accuracy to quarter-tones" has anything to do with being related to the diatonic scale, which is what you said originally, and what I asked about.

>      "the difference between absolute frequency in Hertz and a quarter-tone value was never more than 3 Hertz."

Here, the paper is not stating that speech tends to line up with 24edo quarter-tones based on A440; it's merely saying that in converting from Hz to quarter-tones no errors greater than 3 Hz were introduced. (Keep in mind that below about 200 Hz, quarter-tones are less than 6 Hz apart, so it's impossible for rounding to quarter-tones to produce errors greater than 3 Hz.)

So, I think I have to call BS on your original claim that speech intonation has anything to do with the diatonic scale whatsoever. Speech does not work that way.

Keenan

🔗RR <djtrancendance@...>

11/20/2012 7:50:54 PM

>>"If hedgehog's not good for you, then you might not like porcupine too
much either; those 327 cent intervals are simultaneously 6/5 and 11/9
(but I kind of like that "feature" about it)."
  Quick note, Porcupine[7], in an only very slightly modified MODMOS form, does seem to work for me (check out my post on Xenharmonic Alliance).  This sounds mysteriously pure...almost "check this, I can fool my neighbor into thinking I'm in diatonic (under 12EDO)" pure ->

http://soundcloud.com/spectrafloor/eternalbrightness
    I don't think there's a problem with nearby intervals acting as multiple ratios either, in fact I get the feeling my above example leverages the near 11/8 interval being used as a nearby 18/11 along with 11/6 acting like 9/5 and also really wonder about systems where an interval can represent both 13/8 and 8/5 (any ideas?).  If you would have caught me a few months before I'd jump and say something like "but that's virtually 20/11, which sounds way to sour and nothing like 11/6 or 9/5"...but, in the context of larger chords (where you'd likely be using them much of the time), it seems snapping those not-so-huge errors shut isn't that hard.

>"You might want to experiment with miracle[10] and tetracot[7]. Also don't forget sensi; those 1/1 9/7 5/3 chords are pretty nuts (two 9/7's makes a 5/3). Huge stacks of 9/7 sound like deep space to me or something.
Will do.

>"I don't hear any obvious VFs in this song. Are you talking about the bassline?"
I think we're talking about different songs (even though they both use a minor 7th chord a lot).
The Calvin Harris song is -> http://www.youtube.com/watch?v=tg00YEETFzg ...literally breaking the minor 7th into d-minor and f major triads and, it seems, shifting the VF when doing so as opposed to the "static" VF of a non-split minor 7th.  Of course the bass-line helps things further: I hear something like A C F G and it really does seem to make those two chords feel like they are pointing at four VFs while being about as easy to follow as two, so it comes out as really efficient and clever to me in a bizarre way despite also being laughably simple, kind of like modular code and sub-classing to make very few items accomplish a lot through only minor customization in programming or something like that.  Not to say it's the best way to do somethings, but it seems both very useful and one advanced musicians too often end up frowning upon rather than seeing where it can/can't work.  I really wonder what kind of special "illusions" of massive tonal
movement from very few notes and/or very slight changes in chords can be accomplished outside 12EDO.

>>"Pick an MOS which is "diatonic" sized, and then pick a larger one which is "chromatic" sized."
So the "diatonic" sized scales overlap perfectly to form the chromatic?

>"==SIMPLE RULE==
When you come up with a nice chord in a progression try to find a way
to build the scale around the chord, not the other way around.
=="
Makes sense, that's kind of how I ran into that MODMOS above...although I still cheated a bit with my old ways: I started with a scale and tried chords I thought would sound best and, when they didn't work, I'd try to modify the scale to fit them until everything fits.  I suppose the real basis of your idea is the start with any chords you like you can find in the chromatic and then chain them together in a chord progression that fits into a diatonic-sized scale (if it fits)?  it just seems kind of hard to test a chord progression before you have a scale to test it in...

>>"So for meantone[7] it's just the interval L-s (in 19-EDO, this is 1 step out of 19)."
    Ok, so that's how to modify when something doesn't fit perfectly...makes sense.

 

  

________________________________
From: Mike Battaglia <battaglia01@gmail.com>
To: tuning@yahoogroups.com
Sent: Tuesday, November 20, 2012 8:15 PM
Subject: Re: [tuning] Re: Chord progression program (scale independent within subsets of EDOs)

 
On Mon, Nov 19, 2012 at 6:42 PM, RR <djtrancendance@...> wrote:
>
> >>"The bVII chord in the Beatles is IV/IV and they use it when they're
> >> writing stuff in mixolydian mode."
> So, in other words, they aren't using B, at all, and the entire
> piece(s) are in c mixolydian? If that's the case, wow, that is much ado
> about nothing.

Paperback Writer was the example given, and it's in G mixolydian. (I
don't remember the bridge right now but I think it modulates a bit.)

> >>"If you've come up with some arbitrary mathematical pattern for a chord
> progression, and you play it and it sounds like crap, it's not advanced.
> What's "advanced" is when you have a complex pattern that actually sounds
> good."
>
> Such as?

I'm a fan of the impressionists for being able to pull stuff like that off well.

> >"I never said anything about this restriction where you can only resolve
> > by a fifth; that was something you came up with... never in my life would
> > subscribe to such a restrictive view of harmony
>
> You're right, you never did, I'm just saying that's one sure-fire way
> that virtually always works. On a more optimistic note...some other ways to
> accomplish resolution that usually work are?

The immediately obvious example is the tritone substitution: instead
of G7 -> Cmaj, try Db7 -> Cmaj.

For something slightly more exotic there's the "backdoor progression,"
which is a ii-V as though you were doing to the bIII, but then you go
back to the I. Making the V lydian dominant is good. So in B, you can
do A7#11 -> B maj, for instance. Listen to the Beatles' "For No One"
and "Hello Goodbye" for an example of this, as well as the ending to
Eric Clapton's "Layla," and Joe Cocker's "You Are So Beautiful" and so
on.

There's a bunch of other random ways to resolve to I that can work in
various situations. bVI can resolve well to I sometimes. iim7 usually
resolves to I really nicely without needing to go to V first, as in
Fmaj7 Em7 Dm7 Cmaj7 (the Calvin Harris song you just played does
this).

> Neither do I (hence why I mentioned the minor 6th resolution in that last
> youtube link in the vocals before)...but it seems like a more sensitive
> option that, like you said "just contain(s) more information...can be
> overwhelming if you don't know how
> to parse it, making the whole thing sound disconnected".

I guess that makes sense. I suggest learning how to parse it though.
(I'm trying to go through this process with other tuning systems and I
see how difficult it is now.)

> I tried a few
> melodic lines after dropping the bass line on a 6th resolution...and there
> were much fewer options that worked than with a fifth...as if there had to
> be a predictable "calm" in the melodic pattern to balance the overload
> caused by the jump. Not that it can't work really well (and it's d-mn
> amusing/entertaining when it does), but it apparently takes more care to
> pull off.

Yup, sometimes things like that can be more sensitive. I have no idea
why, I just know that if you play it right, it can sound extremely
"colorful."

> Never said it modulated but...the pattern seems to be it's decidedly
> tense (at least to my ears, even if the math behind it is "normal") and far
> less directed at the tonic to do that 7th jump. And, to note, it's followed
> by a 5th-like relaxed movement to a fourth, which makes sense to balance out
> said "more information" and, it seems,push back the tonic.

Yeah, something like that. It explicitly constructs a bridge from this
far-out note back to the tonic, showing how the whole thing fits into
some larger "functional" thing. (Good exercise: play around in 19-EDO
and learn to do this with the extended meantone intervals there.)

> Indirectly...or just to keep track of the notes, period: and having to
> remember where all the "new" notes are after the modulation in such a large
> set.

Yes, I agree with this. Here's one solution: think about if you're in
19-EDO, for instance. Meantone[12] is still in it, so you can use that
as a subset. But if you just use one meantone[12] subset and never
change anything, you'll be limited in terms of what chords you can do.
For instance, here's one mode of meantone[12]:

C C# D Eb E F F# G Ab A Bb B C

Only 12 notes, easy to grab onto.

Now, say you want to play ||: Fmaj Abmaj | Cmaj | Emaj | Am Gmaj :||
(pay attention to the timing here). Note that you can't. Emaj requires
G#, and Abmaj requires Ab. So if you use only these notes, you're
screwed and you'll either have to have that Abmaj be some messed up
G#-C-Eb chord or you'll have to have the Emaj be E-Ab-B, which is a
supermajor chord. So what happens now? Is all hope lost forever?

No! Just modulate, damn it! So do this: for the Fmaj Abmaj | Cmaj
part, use this chromatic scale

C C# D Eb E F F# G Ab A Bb B C

Then for the Emaj | Am Gmaj part, use this chromatic scale:

C C# D Eb E F F# G G# A Bb B C

See how the Ab changed to a G#?

The secret is to still use meantone[12], but play what you feel and
then continuously change the mode of meantone[12] to match what you're
playing. The net effect is that you have 12 quasi-equal "regions" of
note in 19-EDO which sometimes adapt to match the current chord. This
is much more freeing than only using one 12-note subset and limiting
your choice of chords to only the subset you use: just continually
modulate through modes of meantone[12], and then within each
meantone[12], modulate further through the modes of meantone[7] to
play the chords you want.

So then the same principle applies to other large EDOs. Do the same
with porcupine[15] in 22-EDO and the like.

> Right, which is why I'm taking your advice and digging into Hedgehog
> temperament. Theory wise I don't actually think there's any formal right or
> wrong, just more or less likely to work most of the time.

I guess that's one way to think of it. I've never thought about the
relative probabilities that something will "work," but maybe that
might be a good paradigm to work within...

> >>"You should go on a systematic review of MOS's with 9 notes or less,
> >> especially ones with more "L" than "s" notes."
>
> Gotcha...and I'm seeing that in the temperaments you're handing me, like
> Machine...these "diatonic-ish spaced, but not diatonic" scales tend to sound
> surprisingly natural regardless of the ratios involved.

Exactly! That realization has changed the way I think about music. So
if you find "surprisingly natural" sounding scales, and then you ALSO
intone them with nice ratios so that the chords are concordant, you've
hit the jackpot.

> >>"Blackwood in 15-EDO is a good way to start if you don't mind a bit more
> >> error (careful with the timbre)."
> I tried that before but wasn't careful with the timbre...is this yet
> another odd-harmonic-centric system?

Not necessarily odd-harmonic centric; just less harsh timbres =
better. Think flutes and marimbas instead of a horn section.

Try Blackwood in 20-EDO as well to compare.

> >"The two need to work together; 7/6 might sound like two completely
> > different intervals in two completely different scales."
> I get the picture...now that chord progressions and the like are becoming
> more a part of the picture I realize what all the fuss about different MOS
> spacing was/is about.

Right.

> >"I like to expand my mental reach to a larger chromatic scale and then
> > use smaller diatonic-sized scales within it, modulating as I damn well
> > please. It's the modulations that give me all of the color."
> Ah, if I only had the quasi-immortal mental flexibility to pull that
> off. If I have that right though, even if you're stuck with a lousy 3-4
> chords that really work for you, you can get 8,12,16...by modulating and
> achieve a fair degree of color regardless...correct?

Yes, exactly. I don't think it requires quasi-immortal mental
flexibility if you do what I said above when working with large EDOs;
e.g. chunk them into smaller quasi-EDOs that you modulate within. For
instance, it's easy to make 19-EDO sound like 12-EDO by just
continually changing the mode of meantone[12]; it'd be interesting to
try to make 22-EDO sound like 15-EDO by just continually changing the
mode of porcupine[15]. That's what I'm toying with now.

> I guess that's the thing...even ignoring issues with color variety,
> even Hedgehog was starting to push me so far as accuracy goes: I couldn't
> get the chords working in any coherent way without using an odd-harmonic
> flute to "normalize" it. So I think my line of attack is to stick with
> not-so-high-error systems and, in cases where I can't get the
> chord-color-variety...teach myself xenharmonic modulation. It's my main
> issue with Machine and Mavila temperament that I can't modulate around, the
> error.

If hedgehog's not good for you, then you might not like porcupine too
much either; those 327 cent intervals are simultaneously 6/5 and 11/9
(but I kind of like that "feature" about it).

Hmm, what are some accurate, higher-limit temperaments you might like?
You might want to experiment with miracle[10] and tetracot[7]. Also
don't forget sensi; those 1/1 9/7 5/3 chords are pretty nuts (two
9/7's makes a 5/3). Huge stacks of 9/7 sound like deep space to me or
something.

> Got it...so that's how you make something like Hedgehog[14] work without
> sounding random or just iterating through notes until one fits.

That's my idea, anyway.

> Not only that...but the scary fact most of it only use parts of the
> same min7 chord (bassline included)...it's almost a parody of pop music he
> gets away with it and still shifts the VF enough to keep the feeling
> playful.

I don't hear any obvious VFs in this song. Are you talking about the bassline?

> That's the elephant in the room: "having" to walk on a tight-rope of
> well over 10 notes to get the range of tonal color I'm used to getting from
> more like 7 to 8.

You'll get the hang of it.

> >"Luckily, every rank-2 temperament comes with an MOS series which makes
> > it relatively easy to figure out how to do this."
>
> Any links for tips how to modulate through/between MOS series?

Pick an MOS which is "diatonic" sized, and then pick a larger one
which is "chromatic" sized. So porcupine, for instance, has MOS's of
size 7, 8, and 15. (The 7-note one is 1L6s and the 8 note one is
7L1s.) So you might say the 7-note one is diatonic (or "albitonic" is
the term Gene uses) and the 15-note one is chromatic.

Once you've done that, you will be successful if you follow this one simple rule

==SIMPLE RULE==
When you come up with a nice chord in a progression try to find a way
to build the scale around the chord, not the other way around.
==

Somedays I want to scream that off of the highest mountain. Of course,
this is just my idea, so I can't tell anyone that it's better than
anything else, but that's basically how extended harmony in 12-EDO
works and I really like the way it sounds in other tuning systems,
particularly porcupine.

So for instance, if you hear this amazing color chord, you'll have to
find a mode of your diatonic scale that fits it, and then modulate to
that mode. Ahh, but what if you can't find a mode of the diatonic
scale which fits it - for instance, say you want to play an augmented
maj7 chord in meantone? Then you have to use chromatic alterations!
Don't just stick to the MOS, but sharpen or flatten notes.

OK, what interval do you sharpen or flatten things by? I find the
results often work well if the interval you're sharpening or
flattening by is the difference between the large and small step,
called the "chroma" for that MOS. So for meantone[7] it's just the
interval L-s (in 19-EDO, this is 1 step out of 19).

Then shut your brain off and have fun. Now, how do you find the
awesome color chords? This is the fun part, go exploring and let us
know what you find.

Again, these are just my ideas and I don't claim they're the One True
Way to write music, but I think it's an interesting technique and I
like the way it sounds.

-Mike

🔗Mike Battaglia <battaglia01@...>

11/20/2012 9:07:08 PM

On Tue, Nov 20, 2012 at 10:50 PM, RR <djtrancendance@...> wrote:
>
> I don't think there's a problem with nearby intervals acting as
> multiple ratios either, in fact I get the feeling my above example leverages
> the near 11/8 interval being used as a nearby 18/11 along with 11/6 acting
> like 9/5 and also really wonder about systems where an interval can
> represent both 13/8 and 8/5 (any ideas?).

This means you want 65/64 to vanish. Flattone in 26-EDO is an obvious
example; the diatonic scale is 4 4 3 4 4 4 3 and C-Ab is 8/5 and 13/8.
You can also look here

http://x31eq.com/cgi-bin/uv.cgi?uvs=65/64

Looks like negri is a winner. (generator 2\19, 2 2 2 2 3 2 2 2 2 is a good MOS)

Also, if you don't know how to read every single temperament on that
page above, then now's the time to learn, because I think it's time
for you to "make the leap" so to speak.

> If you would have caught me a few
> months before I'd jump and say something like "but that's virtually 20/11,
> which sounds way to sour and nothing like 11/6 or 9/5"...but, in the context
> of larger chords (where you'd likely be using them much of the time), it
> seems snapping those not-so-huge errors shut isn't that hard.

Right. You can also learn to hear something like "20/11" as a compound
interval made up of simpler intervals.

> >"I don't hear any obvious VFs in this song. Are you talking about the
> > bassline?"
> I think we're talking about different songs (even though they both use a
> minor 7th chord a lot).
> The Calvin Harris song is -> http://www.youtube.com/watch?v=tg00YEETFzg
> ...literally breaking the minor 7th into d-minor and f major triads and, it
> seems, shifting the VF when doing so as opposed to the "static" VF of a
> non-split minor 7th.

What part are you talking about? First off, this is Eb minor and Gb
major triads, and the only part where I actually do hear notes fusing
into an explicit VF is in the beginning of the song where it's like
Bb-Gb -> Db-Gb dyads being played on a distorted organ patch, and
those have VFs which are an octave apart.

> Of course the bass-line helps things further: I hear
> something like A C F G and it really does seem to make those two chords feel
> like they are pointing at four VFs while being about as easy to follow as
> two, so it comes out as really efficient and clever to me in a bizarre way
> despite also being laughably simple, kind of like modular code and
> sub-classing to make very few items accomplish a lot through only minor
> customization in programming or something like that.

The bass line is Eb Cb Gb Ab (note that that first chord progression
moves down by a major third, aka moving up by a minor sixth, so so
much for the notion that this is really unnatural).

I don't hear any obvious timbral fusion effects. What thing are you
hearing that you're calling a "VF" here? Are you sure you're not just
imagining root movements and saying that those are VFs, when they're
not actually related?

> >>"Pick an MOS which is "diatonic" sized, and then pick a larger one which
> >> is "chromatic" sized."
> So the "diatonic" sized scales overlap perfectly to form the chromatic?

Right. For instance, you can think of the meantone chromatic scale as
being made up of six overlapping diatonic scales which are a fifth
apart. The same applies to other MOS's, except instead of being a
fifth apart, they'll be spaced apart by whatever the generator of the
MOS is.

> >"==SIMPLE RULE==
> When you come up with a nice chord in a progression try to find a way
> to build the scale around the chord, not the other way around.
> =="
> Makes sense, that's kind of how I ran into that MODMOS above...although I
> still cheated a bit with my old ways: I started with a scale and tried
> chords I thought would sound best and, when they didn't work, I'd try to
> modify the scale to fit them until everything fits. I suppose the real
> basis of your idea is the start with any chords you like you can find in the
> chromatic and then chain them together in a chord progression that fits into
> a diatonic-sized scale (if it fits)? it just seems kind of hard to test a
> chord progression before you have a scale to test it in...
>
> >>"So for meantone[7] it's just the interval L-s (in 19-EDO, this is 1
> >> step out of 19)."
> Ok, so that's how to modify when something doesn't fit
> perfectly...makes sense.

You can mess with other modifications too, of course. For instance,
porcupine is weird because it has two diatonic-sized scales: 1L6s and
7L1s. Of those, 1L6s is pretty magical because 4:5:6 and 10:12:15
share a pattern of interval steps; they're both root - some type of
three-step interval - fifth. The difference between these types of
thirds is the interval L-s, which is a tempered version of 25/24.

So in 22-EDO you have 4 3 3 3 3 3 3, which is one mode of porcupine
with a major chord. Now say you want to flat that 3 to make it a minor
chord over the tonic: now you have 4 2 4 3 3 3 3, the third is now
6/5. But say you want to play a subminor chord? Just flat it again!
Now you have 4 1 5 3 3 3 3. You can, of course, change other notes
too: say you want to play a minor chord, so you go to 4 2 4 3 3 3 3.
But, you note the whole thing would be a bit more "even" if that major
second (a 9/8) was flatter so that it's half of the 6/5. You can
flatten the 2 as well, giving you 3 3 4 3 3 3 3, which is now an MOS
again.

Mavila is really crazy with this if you use a flute timbre or
something really chilled out. You'll play some chord you're used to,
like 4:5:6, and then reveal that to be a part of the mavila[9] MOS,
and if you do it right it's like a steamroller plowing directly into
your brain to hear the whole thing break up into a series of large and
small steps that are "coherent" but something completely different
than you're used to. I'm still trying to learn to master what's going
on there.

Now, do you absolutely have to only modify things by L-s? No. For
instance, porcupine doesn't just have 4 3 3 3 3 3 3, which is
porcupine[7], but it also has 1 3 3 3 3 3 3 3, which is porcupine[8].
This scale is also pretty magical, especially if you're in 37-EDO,
where it becomes 2 5 5 5 5 5 5 5, and the small step becomes widened a
bit and sounds like a "leading tone." The mode 5 5 5 5 5 5 5 2 also
has that leading tone effect going on.

Unfortunately, 5/4 and 6/5 don't share a pattern of interval steps
here; 6/5 is a "large third" and 5/4 is a "small fourth." So this
means that if you play a root-third-fifth triad and move it up and
down the scale, it's not transforming between major and minor and
diminished chords anymore. So what if you're playing 2 5 5 5 5 5 5 5
and you just wish there were a 6/5 there instead of the 5/4? Are you
trapped because you can only modulate by 5-2=3 steps? No, you can just
modulate by something else, like just change the 5/4 to 6/5 even
though that's "cheating" because it sounds good. So in this specific
case, that would equate to flattening it by the "s" sized step, not
the "L-s" sized chroma; you can do that too, or anything you want, of
course.

The key thing here is to note that the "s" sized step in porcupine[8]
is the same as the L-s sized chroma in porcupine[7], which is a
mathematical trick that you can take advantage of in these situations.
For instance, if you're playing 2 5 5 5 5 5 5 5, aka porcupine[8],
that also contains 7 5 5 5 5 5 5, aka porcupine[7], within it. So if
you're playing in porcupine[8], you can always just mentally shift
back up one level in the MOS series to porcupine[7] and use the
porcupine[7] chroma, but still have that extra note from porcupine[8]
in there because it sounds good. Finding the most "natural" way to
balance all of this out is the trick, and I can't claim I'm an expert
at it yet.

-Mike

🔗RR <djtrancendance@...>

11/21/2012 11:14:53 AM

>"First off, this is Eb minor and Gb major triads,"
   Yep, as i figured, I don't have AP, and I was a half step off transposed from the chord roots.  
>"Also, if you don't know how to read every single temperament on that
page above, then now's the time to learn, because I think it's time
for you to "make the leap" so to speak."
  You mean the mapping of primes to scale steps...or what?
My main issue is once I get the Scala file the program I use to compose only accepts decimal values, so I'm stuck converting yet again from cents to decimal so I can actually use them with instruments.
It's all about getting to the point I can actually test the scale, and then mess with things like chromatic (and then arbitrary, if needed) alternations.

>"The bass line is Eb Cb Gb Ab (note that that first chord progression
moves down by a major third, aka moving up by a minor sixth, so so
much for the notion that this is really unnatural)."
  Well...isn't that if you count octave equivalence...I think this is an "odd" case where octave equivalence just doesn't work.

>"Are you sure you're not just imagining root movements and saying that those are VFs, when they're not actually related?"
   Not sure what it's called...VF is just the first related-sounding term I could think of.
  Put it this way...if I hear C E G I hear C coming out as the strongest...but if I hear E G B I hear G (not E) coming out as the strongest.  Not sure if that violates the rules for VF detection or qualifies as an "imaginary root movement" I made up...but that's what I hear...any formal name for that?
  Another thing is G B E (different order) looks like some sort of G dominant 7th chord with a missing note and seem to point to the same "imaginary root" as E G B...and I wonder if perhaps that plays into why that trick you showed before of sticking a power-of-two note on the bottom of a chord doesn't seem to apply to minor chords.

Looking at your other notes, will reply later...

________________________________
From: Mike Battaglia <battaglia01@...>
To: tuning@yahoogroups.com
Sent: Tuesday, November 20, 2012 11:07 PM
Subject: Re: [tuning] Re: Chord progression program (scale independent within subsets of EDOs)

 
On Tue, Nov 20, 2012 at 10:50 PM, RR <djtrancendance@...> wrote:
>
> I don't think there's a problem with nearby intervals acting as
> multiple ratios either, in fact I get the feeling my above example leverages
> the near 11/8 interval being used as a nearby 18/11 along with 11/6 acting
> like 9/5 and also really wonder about systems where an interval can
> represent both 13/8 and 8/5 (any ideas?).

This means you want 65/64 to vanish. Flattone in 26-EDO is an obvious
example; the diatonic scale is 4 4 3 4 4 4 3 and C-Ab is 8/5 and 13/8.
You can also look here

http://x31eq.com/cgi-bin/uv.cgi?uvs=65/64

Looks like negri is a winner. (generator 2\19, 2 2 2 2 3 2 2 2 2 is a good MOS)

Also, if you don't know how to read every single temperament on that
page above, then now's the time to learn, because I think it's time
for you to "make the leap" so to speak.

> If you would have caught me a few
> months before I'd jump and say something like "but that's virtually 20/11,
> which sounds way to sour and nothing like 11/6 or 9/5"...but, in the context
> of larger chords (where you'd likely be using them much of the time), it
> seems snapping those not-so-huge errors shut isn't that hard.

Right. You can also learn to hear something like "20/11" as a compound
interval made up of simpler intervals.

> >"I don't hear any obvious VFs in this song. Are you talking about the
> > bassline?"
> I think we're talking about different songs (even though they both use a
> minor 7th chord a lot).
> The Calvin Harris song is -> http://www.youtube.com/watch?v=tg00YEETFzg
> ...literally breaking the minor 7th into d-minor and f major triads and, it
> seems, shifting the VF when doing so as opposed to the "static" VF of a
> non-split minor 7th.

What part are you talking about? First off, this is Eb minor and Gb
major triads, and the only part where I actually do hear notes fusing
into an explicit VF is in the beginning of the song where it's like
Bb-Gb -> Db-Gb dyads being played on a distorted organ patch, and
those have VFs which are an octave apart.

> Of course the bass-line helps things further: I hear
> something like A C F G and it really does seem to make those two chords feel
> like they are pointing at four VFs while being about as easy to follow as
> two, so it comes out as really efficient and clever to me in a bizarre way
> despite also being laughably simple, kind of like modular code and
> sub-classing to make very few items accomplish a lot through only minor
> customization in programming or something like that.

The bass line is Eb Cb Gb Ab (note that that first chord progression
moves down by a major third, aka moving up by a minor sixth, so so
much for the notion that this is really unnatural).

I don't hear any obvious timbral fusion effects. What thing are you
hearing that you're calling a "VF" here? Are you sure you're not just
imagining root movements and saying that those are VFs, when they're
not actually related?

> >>"Pick an MOS which is "diatonic" sized, and then pick a larger one which
> >> is "chromatic" sized."
> So the "diatonic" sized scales overlap perfectly to form the chromatic?

Right. For instance, you can think of the meantone chromatic scale as
being made up of six overlapping diatonic scales which are a fifth
apart. The same applies to other MOS's, except instead of being a
fifth apart, they'll be spaced apart by whatever the generator of the
MOS is.

> >"==SIMPLE RULE==
> When you come up with a nice chord in a progression try to find a way
> to build the scale around the chord, not the other way around.
> =="
> Makes sense, that's kind of how I ran into that MODMOS above...although I
> still cheated a bit with my old ways: I started with a scale and tried
> chords I thought would sound best and, when they didn't work, I'd try to
> modify the scale to fit them until everything fits. I suppose the real
> basis of your idea is the start with any chords you like you can find in the
> chromatic and then chain them together in a chord progression that fits into
> a diatonic-sized scale (if it fits)? it just seems kind of hard to test a
> chord progression before you have a scale to test it in...
>
> >>"So for meantone[7] it's just the interval L-s (in 19-EDO, this is 1
> >> step out of 19)."
> Ok, so that's how to modify when something doesn't fit
> perfectly...makes sense.

You can mess with other modifications too, of course. For instance,
porcupine is weird because it has two diatonic-sized scales: 1L6s and
7L1s. Of those, 1L6s is pretty magical because 4:5:6 and 10:12:15
share a pattern of interval steps; they're both root - some type of
three-step interval - fifth. The difference between these types of
thirds is the interval L-s, which is a tempered version of 25/24.

So in 22-EDO you have 4 3 3 3 3 3 3, which is one mode of porcupine
with a major chord. Now say you want to flat that 3 to make it a minor
chord over the tonic: now you have 4 2 4 3 3 3 3, the third is now
6/5. But say you want to play a subminor chord? Just flat it again!
Now you have 4 1 5 3 3 3 3. You can, of course, change other notes
too: say you want to play a minor chord, so you go to 4 2 4 3 3 3 3.
But, you note the whole thing would be a bit more "even" if that major
second (a 9/8) was flatter so that it's half of the 6/5. You can
flatten the 2 as well, giving you 3 3 4 3 3 3 3, which is now an MOS
again.

Mavila is really crazy with this if you use a flute timbre or
something really chilled out. You'll play some chord you're used to,
like 4:5:6, and then reveal that to be a part of the mavila[9] MOS,
and if you do it right it's like a steamroller plowing directly into
your brain to hear the whole thing break up into a series of large and
small steps that are "coherent" but something completely different
than you're used to. I'm still trying to learn to master what's going
on there.

Now, do you absolutely have to only modify things by L-s? No. For
instance, porcupine doesn't just have 4 3 3 3 3 3 3, which is
porcupine[7], but it also has 1 3 3 3 3 3 3 3, which is porcupine[8].
This scale is also pretty magical, especially if you're in 37-EDO,
where it becomes 2 5 5 5 5 5 5 5, and the small step becomes widened a
bit and sounds like a "leading tone." The mode 5 5 5 5 5 5 5 2 also
has that leading tone effect going on.

Unfortunately, 5/4 and 6/5 don't share a pattern of interval steps
here; 6/5 is a "large third" and 5/4 is a "small fourth." So this
means that if you play a root-third-fifth triad and move it up and
down the scale, it's not transforming between major and minor and
diminished chords anymore. So what if you're playing 2 5 5 5 5 5 5 5
and you just wish there were a 6/5 there instead of the 5/4? Are you
trapped because you can only modulate by 5-2=3 steps? No, you can just
modulate by something else, like just change the 5/4 to 6/5 even
though that's "cheating" because it sounds good. So in this specific
case, that would equate to flattening it by the "s" sized step, not
the "L-s" sized chroma; you can do that too, or anything you want, of
course.

The key thing here is to note that the "s" sized step in porcupine[8]
is the same as the L-s sized chroma in porcupine[7], which is a
mathematical trick that you can take advantage of in these situations.
For instance, if you're playing 2 5 5 5 5 5 5 5, aka porcupine[8],
that also contains 7 5 5 5 5 5 5, aka porcupine[7], within it. So if
you're playing in porcupine[8], you can always just mentally shift
back up one level in the MOS series to porcupine[7] and use the
porcupine[7] chroma, but still have that extra note from porcupine[8]
in there because it sounds good. Finding the most "natural" way to
balance all of this out is the trick, and I can't claim I'm an expert
at it yet.

-Mike

🔗Keenan Pepper <keenanpepper@...>

11/21/2012 12:32:17 PM

--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>   You mean the mapping of primes to scale steps...or what?
> My main issue is once I get the Scala file the program I use to compose only accepts decimal values, so I'm stuck converting yet again from cents to decimal so I can actually use them with instruments.

First of all, the Scala files generated by x31eq.com/temper are only some arbitrary example scales for that temperament. They are sometimes silly, and they never include wonderful things like MODMOSes. The other information on those pages is much more important than the Scala files.

Second of all, converting from Scala to decimal frequencies is very easy. I was about to just fire off a Python program for you but I realized you might have no idea how to run it. It would also be easy to do in a spreadsheet or whatever. If you think of this simple conversion as a chore you have to do then you're doing it wrong. We live in the age of computers; let the computers do the work automatically. =)

Keenan

🔗RR <djtrancendance@...>

11/21/2012 12:57:02 PM

I usually use http://www.sengpielaudio.com/calculator-centsratio.htm ...but it still leaves me copying them one by one before I can "automatically" convert them.

   I really (you're right) need a program that reads Scala files (in the usual Scala cent format, not the rarely used  Scala decimal format).
I could probably do it with Python, but it's just a matter of time would need to install the SDK/toolkit to actually run it (since it's interpreted code, if I'm right).
Something like javascript/c++/vb.net/c# would be ideal as I really have the SDKs installed.
Or maybe I should just build/code the reader myself in something like vb.net rather than install Python...I've admittedly just been a bit impatient to sit down and do that.

  And, also, you're right...the Scala files, sadly, don't list the MODMOSes or anything like that...which usually leaves me on xenwiki looking for MOS step-size charts/lists.

>>The other information on those pages is much more important than the Scala files.
  How can (or can it) that information be used to calculate MOS's?  I assume, once you get the MOSs, you just bump various notes by L - s to get the MODMOS's, correct?
 

________________________________
From: Keenan Pepper <keenanpepper@...>
To: tuning@yahoogroups.com
Sent: Wednesday, November 21, 2012 2:32 PM
Subject: [tuning] Re: Chord progression program (scale independent within subsets of EDOs)

 
--- In tuning@yahoogroups.com, RR <djtrancendance@...> wrote:
>   You mean the mapping of primes to scale steps...or what?
> My main issue is once I get the Scala file the program I use to compose only accepts decimal values, so I'm stuck converting yet again from cents to decimal so I can actually use them with instruments.

First of all, the Scala files generated by x31eq.com/temper are only some arbitrary example scales for that temperament. They are sometimes silly, and they never include wonderful things like MODMOSes. The other information on those pages is much more important than the Scala files.

Second of all, converting from Scala to decimal frequencies is very easy. I was about to just fire off a Python program for you but I realized you might have no idea how to run it. It would also be easy to do in a spreadsheet or whatever. If you think of this simple conversion as a chore you have to do then you're doing it wrong. We live in the age of computers; let the computers do the work automatically. =)

Keenan

🔗Graham Breed <gbreed@...>

11/21/2012 1:16:51 PM

RR <djtrancendance@...> wrote:

> >>The other information on those pages is much more
> >>important than the Scala files.
>   How can (or can it) that information be used to
> calculate MOS's?  I assume, once you get the MOSs, you
> just bump various notes by L - s to get the MODMOS's,
> correct?

You could download the Python code behind the website …
and … oh.

Well, go to a rank 2 page, and you'll see something like
this (this is for 7-limit porcupine):

Generator Tunings (cents)
<1197.839, 162.587]

That gives you the period (or generalized octave) and
generator for the MOS scale. Scala itself will know what
to do with them. Or you can get the nth note on the chain
of generators as mod(g*n, p). Sort the results.

You may want pure octaves, so scale the generator as
162.587*1200/1197.839 = 162.880.

Sometimes you'll note that the period divides the octave,
so to get an octave scale, repeat the above results by
every period. The number of periods to the octave, if it
isn't obvious, is the first number under the bold "2" in
the "Reduced Mapping".

If you want an idea of how many notes will work as an MOS,
look at the equal temperaments listed after you click the
"Subsets" button. (I'm pleased with this, because it's a
feature I planned to add, and I found it was already
there. I like it when I leave presents for myself.)

Graham