17 tone notation

There are many approaches to 17tone notation.  I have finally found one that works for me (shown to me by Cam Taylor).   I believe my extension to be the same as his.  And I believe this to be analogous or directly mappable to Kite’s up & downs notation.

Principles of this system include:

  • naming conventions remain consistent, tuning changes; the major second/third/sixth/seventh namings are mapped to the largest of the 3 interval types within each category — this means that “majors” are tuned sharp, “minors” are tuned flat, and “neutrals/middles” are tuned middle — perfect fifths may be tuned slightly sharp or just, depending on performer/composer preferences — I feel that a non-exact 17equal approach is preferable
  • the sharp # symbol means 2 steps up, the flat b symbol means 2 steps down, the quarter sharp half sharp (or +) symbol means 1 step up, the quarter flat d symbol means 1 step down.

Chromatically we have:

1

C

2

C+ / Db

3

Dd / C#

4

D

5

D+ / Eb

6

Ed / D#

7

E / Fd

8

F / E+

9

F+ / Gb

10

Gd / F#

11

G

12

G+ / Ab

13

Ad / G#

14

A

15

A+ / Bb

16

Bd / A#

17

B

Some sample “major scales”

1

C C+ / Db D D+ / Eb

4

D D+ / Eb E E+ / F

7

E E+ / F F# F#+ / G

8

F F+ / Gb G G+ / Ab

11

G G+ / Ab A A+ / Bb

14

A A+ / Bb B B+ / C

17

B B+ / C C# C#+ / D

Sample modes of “neutral”, “dicot”, “suhajira”, or “beatles” ([7]s)

1

C D Eb G+

3

Dd Ed Fd A

6

Ed F+ Gd B

8

F G Ab C+

11

G A Bb D+

13

Ad Bd Cd E

16

Bd C+ Dd F#

Tunings and Tarot

I had thought recently about the solo piano albums I made in the past, The Moon, and the Devil, both named after the Tarot card which corresponds to the number of tones peroctave in those works, which are 18 and 15 respectively.

 

the moon tarot devil tarot

There are 22 major arcana / tarot trumps (including 0, which can be equated with 22 perhaps).  I was feeling slightly restricted because it would seem to me that the tunings more desirable to explore in this manner would be 12-24 and higher.  I realized upon pondering #1, the Magician / The Magus, how 1EDO could be conceived in this.  The root of concept is here: it is one division per octave.  On a piano, the detuning range seemed to be acceptable to drop an octave at any point, with a significant change of timbre.  The change in timbre is gradual between the conventionally tuned/tensioned string and the octave dropped one.  Dropping each octave on the piano to coincide with the root note/tuning note of the 1edo would be very practical and allow each of the 12 notes which will be in unison with each other to vary in timbre from one another.

the magician tarot

check out the Moon: https://noahdeanjordan.bandcamp.com/album/the-moon

Also, new 17-tone works on Patreon (for Rhodes and Tenor saxophone): https://patreon.com/noahjordansounds

 

November 13, 2018

“This is the next piece from the project, now titled: Formality vs Reality, with myself on 17-tone Rhodes and Dominic Conway on tenor saxophone.  This group name came from an early conversation between myself and Dominic about the deviances between notation, theory, and performance.  For example, in 12-tone systems, a notation will signify 12 different pitches (plus enharmonics), theory will describe how movements will function (when pitch is included, how enharmonics may be tuned differently, for instance, or how progressions which imply movements which utilize certain commas, or the removal thereof, could or should be tuned), and performance, which may differ in many ways to any of these aspects, and in which the aesthetic considerations of the intention of the music will determine how permissible these deviations.  In the setting of improvised music, as this is, these deviations and their relation to theory, and notational description, have a wonderful interplay; in the world of microtonality the instruments may be set to explore a certain pitch set and the theory may explore the patterns of the deviations from this structural basis heard by the performer and thus extend the theory to account for these patterns.

This piece is a free improvisation which has since been structured into a re-performable work which will be likely be recorded in presented again.”

repost from Patreon: (https://www.patreon.com/posts/22704575)

There is a growing backlog of recordings from the project, and many of solo Rhodes which will hopefully be editing or mixed and released.  Your Patreon support definitely encourages or helps guide this, or which endeavours are worth my or your time.  Regardless, many of these pieces and improvisations will be released over the coming months.

 

in-tune music and nomenclature

Since entering the world of microtonal music many years ago, I have found that there are many different perspectives on “what is microtonality”, “what is not microtonality”, and what other things we can this thing that some people are calling microtonality but hesitate because the word is not accurately describing the work they are doing.

On the wikipedia page for Xenharmonic music (another term used often synonymously with microtonal music, but implying “different” harmony rather than “micro” or small toned harmony, as often intervals in microtonal music are “bigger” than notes they would be compared to, such as the super-major third) it reads: “John Chalmers, author of Divisions of the Tetrachord, writes: “[sic] music which can be performed in 12-tone equal temperament without significant loss of its identity is not truly microtonal.””  While I do not fully disagree, this puts an air of subjectivity into this realm which from one point of view could combine the entire plethora of baroque tunings and 1/x-comma meantones as “not microtonal”, as well as diatonic 19 and 31 tone music, or even n-edo music which approximates diatonic progressions.  This is where the loss-of-identity element comes in, because one could argue that if the same piece was played in 12edo or 19edo, that both tunings have a very obvious and clear unique identity in relation to one another and that one could not switch tunings without an obvious loss of identity.  However, without careful listening, one might not know that an adjustment in tuning was made (as equal temperaments are in a sense artificial constructs anyways, and both 12 and 19 equal can be playing in a 5-limit meantone based system which has inherent functionality outside of the specifics of the tuning of a fixed pitch instrument).  So from this standpoint, these tunings are in fact the same because we are supposedly processing the information in the same functional manner.  But in the end, they are not, because the timbral aspects of the instrument and the technical aspects of the musician also affect the tuning and perception of the tunings of an instrument.  In addition, these ambiguous boundaries can be used as compositional devices to explore this fuzzy boundary.

This can be extended a step further when playing diatonic progressions in 15-equal for example, such as in the Bad Canada song: Hot Mary, which is essentially an A F#m E D progression, and can be played as such in 12 or 19 equal as well.  However, it really really does not sound that same.  I have had people argue to me that it is silly to play this song in this tuning because it is just an out-of-tune 12 progression.  And yes — it is possible to hear it as such, but it is also something else: it is a progression of triads with significantly sharp fifths, which have a beating near in sync with the sharp thirds (which are the same as in 12 equal), it also is a progression which share 3 roots which are a part of the 5 equal scale, and carry a certain odd symmetrical imbalance between the I IV and V chords, it also have a 160¢ step between the E and the F#, a xenharmonic or microtonal step by any accounts.  Neither 12 nor 19 equal can effectively replicate this combination of properties  — and yes this combination is somewhat arbitrary and definitely not an optimization of anything other than exactly itself, but it is not played in 12 without a loss of identity either.

So, while I agree that the pursuit of the integration and usage of higher complexity and higher limit harmonic structures in music is great and interesting goal, the usage of tuning as a compositional device for a variety of purposes and effects is at the heart of what I strive to do, as a mis-tuning, and alternate-tuning, or as an exploration of truly new tones and relations.

With this I propose to call this, as I have been doing so already, “intentionally tuned” music, or “int-tuned” music”, or “in-tune” music.  This last bit of word play will again bring some challenges with performance and it must avoid being used as an excuse for music play unintentionally out of tune.

In the end, however, the tuning of a piece is generally only part of the composition, as are all of the other factors, and so I hope we will soon get to a point where it is realized that 12-tone equal tuning is neither optimal nor unique in utility, and it really more of a colonial remnant which is not accurate in describing more current music and is a weak tool for creating more, and instead of relying on electronic tuners to make our instruments equal arbitrarily tuned so that we do not need to consider the sound of the tuning, we actually learn to tune our instrument how we would like to hear them, and continue to explore the beautiful patterns and alternate timbres that we can create, and just call it “music” which by nature should include intentional tuning.

But for now we will call things many things as we do.

Sonido 13

To whom may be concerned,

The pianos of Sonido 13 have long been unmaintained, and are currently in a state of (mild) disrepair and are not in-tune.  In 2014, I spent 2 months in an investigation of the pianos and the collection is really only in need of minor repairs.  To restore the collection to original tuning and performance condition, a small team of a piano technician, a specialist in microtonal tunings (I could volunteer myself), and someone acquainted with the restoration of historical / cultural artefacts.  In my city of Vancouver, old pianos are abundant and I have worked on retuning pianos (including to microtonal tunings) which are twice the age of the Sonido 13 pianos; there is no reason that these pianos should not able to be played, for the works of Carrillo, and new works.  There is a growing international interest in the possibilities for such a collection.  It is a great shame that after the beginning of world recognition of the work of Carrillo, he died, leaving a majority of the pianos having never been performed in a concert setting.
So, I propose to you all that I can begin a crowdfunding campaign to raise the funds needed to bring the pianos back to working condition.  I believe that $10,000 USD would be practical to raise, and also much much more than would actually be needed for this job.  What remains could be used as a call for scores, for works that use some of all of the pianos in the collection, and a performance / celebration / inauguration of the Sonido 13 collection.
I ask for your support, in writing of the restoration and reinauguration of the Sonido 13 pianos as a prequel to a fund-raising campaign.  I also ask for any advice or suggestions in this process, if differs from what I have proposed.  In the case in which you disagree that the pianos should be restored and played in the future, please leave me with reasons why.
All the best,
 Noah Jordan

two locrians

last week i posted a new tune on patreon called Cloud Rhyme featuring a locrian tuning (not that I stayed in that mode for a majority of the piece or anything)..  but you can hear it here: https://www.patreon.com/posts/cloud-rhyme-18940728

and the tuning is as follows to make things easy.

19/18 (93.6¢),

95/81 (276¢) __ 5/3 * 19/27

4/3 (498¢)

7/5 (582.5¢)

128/81 (792.2¢) __ 2*2*2*2*2*2/ 3*3*3*3

16/9 (996.1¢)

2/1 (1200¢)

 

anyways, I was asked by Cam Taylor for a version in Pythagorean Locrian:

1/1-256/243-32/27-4/3-1024/729-128/81-16/9-2/1,

which shares only the fourth, b6 and b7

do these 3 different notes make an impact?  In what way?  Which ones and where?

Listen to this one here:

 

or alternatively, both are here:

https://noahdeanjordan.bandcamp.com/album/in-some-loung

 

sooom, many options

many words

so, I mistakenly released an album which was already online “in some loung” by posting the photo/link to my portfolio on here, which made a notification to the Noah Jordan Music facebook page.  But it sold me a copy which was cool.   The album is here if you want to hear: https://noahdeanjordan.bandcamp.com/album/in-some-loung .  It is a solo piano exploration of a variety of tunings (and also a couple rhodes tracks).  It was not really meant to be an album per se, but more of an alternate place to store some files, since I was releasing tracks individually through Patreon.  –Which, if you would like to know more detailed information about the tunings of the tracks, they are on the Patreon posts (https://www.patreon.com/noahjordansounds), they are free to listen and such, but your support is always much appreciated.

Hopefully, I will start to write on here a bit more, the Patreon “blog” section took over my ideas flow because I was posting weekly, usually specifically about the piece that was being posted, but also would go on tangents.  I found it challenging to also write something here as I felt like I would be repeating myself.  But perhaps I can find their own identities moving forwards.

Last weekend was the Microtonal Adventures Fest in Bellingham, Washington.  Outside of it being a great time and being able to meet in person many who I’ve spoken with online, it provided a number of interesting ideas and concepts with which to address, and a number of them are connected.  For example, in the challenge of notation: do we base the “major third” name and notation on what is nearest to 12tone, what is nearest to 5:4, what is nearest to 81:64, or what is generated with 4 fifths and octave reduced.  This is challenging, for example, because in 15edo, 4 fifths is a fourth (and the 400¢ 3rd exists), in 22edo, it is the “large/supermajor” 3rd (and a near 5:4 third exists).  Tall Kite has been working on a notation scheme to be comprehensive (please check it out and bring feedback) (http://tallkite.com/).  Comprehensive and complete and generalizable might not be easy for musicians who have not already be trained to play microtonal music, but the easiest notation might not communicate the intuition and intention of the composer (for instance in systems written in 12tone notation with cent deviations marked).  It was discussed also the idea that simultaneous notations might be ideal, as a sort of key that can be used for general interpretations. — Personally, I am fond of the usage of an “adaptive” modular approach, as have used such in most “microtonal” projects I have been a part of.  This is based on knowing which tonic, scale degree, and chord tones are present at a given time and notating as such.  This mean in 15edo, for example, there can be two G’s, these would be the minor 3rd from E, and the perfect 5th from C, assuming this C is the minor 6th from E.  There are other ways to describe this, given a certain system, and these are generally easiest to comprehend when still in a tonal frame of mind, but somewhat familiar with the interval structure of the tuning system.  One of the great challenges in notation is that of familiarity — to which concepts will we be most familiar with and have the easiest time adapting to, and how does this change depending on the training of a musician. 

Another challenge that we are faced with, is that of the perception of microtones, tuning systems, and music in general.  I speak about this in relation to a new tune I have posted: Cloud Rhyme (https://www.patreon.com/posts/cloud-rhyme-18940728), if you are interested in a specific discussion.   Essentially, how to we hear comma pumps ((http://xenharmonic.wikispaces.com/comma+pump))?  Is this, as Aaron Wolf hypothesized, a syntax error when the commas are tempered / removed?  And especially, to which commas could we parse this as a syntax error?  The syntonic commas (https://en.wikipedia.org/wiki/Syntonic_comma) and pythagorean comma (https://en.wikipedia.org/wiki/Pythagorean_comma) are quite comfortable to western ears, would these be parsed as such?   What about to cultured of a different music tradition?  What about the difference between two 11/9s and 3/2, this is only a comma of 8 cents, but 11/9s are already a strange interval, so would we parse a comma as a syntax error anyways? 

For equal division tunings, especially of the octave, are we hearing perpetual approximations to just intonation?  Or are we hearing a symmetry instead?  Or a combination?  What about higher limits?  Do we hear 350¢ as a 5-limit, or 11-limit, or what is the range in which we are hearing something, and what is the function of context?  If we hear two subsequent 11/9s, can we hear 121/81 or the 19edo 5th, or 3/2?  or is 121/81 always “3/2” when one of the tones leading to it (or in the harmonic framework) is a 11/9?  Could a higher prime function differently, since, of course 11/9 and 11/9 is 11*11/9*9, is two 11s harder or easier to hear than a higher prime, but if they approach a lower prime (with less multiples), is it always approximated?  How does the 3 as the undertone function though in this situation?  Does 11/9 adapt more easily to 3/2 (as in temper to when in multiples) and 11/8 to 2/1 due to their subharmonics? 11/10 and 11/10 make 121/100 which is 121/120 higher than 6/5, but in this case the 5 is the utonality of both the 11/10 and the 6/5.  And for 7 — 11/7 * 11/7 = 121/49 which is the neutral third range, so this falls apart.  But these utones are all different forms, in 11/9 the utone is 3*3, in 11/8 it is 2*2*2, in 11/10 it is 2*5 and in 11/7 it is 7, these are all quite different types of composition.  In 5/4 * 5/4 = 25/16, it is near to 8/5 which would fit this pattern somewhat, but it is hard to analyze these patterns without going into multiples or much higher harmonics much quicker, and then it is a challenge to what the acceptable range of error is from an approximate harmonic.  IS 20¢ reasonable from anything?  But what if it is a superparticular distance?  These questions come into significance which dealing with EDOS as if we are stating that the interval’s nearest just approximation is 15¢ from the 11th or 13th harmonic, is it really possible to hear this in this way? 

I will hopefully test some of these questions more rigorously in pieces to come — and by that I mean compositionally – or through improvisation.  

Motivation for Scale Construction

Recently I finished a recording for the first piano piece I was commission to perform.  It was called Persian Glances by Jesse Maw.  Hear it here (https://www.patreon.com/posts/persian-glances-17963263).  And check out some of Jesse’s other music too (jessemaw.com).

The piece uses a scale generated by 3/2s and 7/4 (octave reduced 3rd and 7th harmonics).  On the Patreon page I give some examples of how to derive the scale, but here I will give a quick example of how this could create a scale before I go onto the main topic.

(( for reference:

“Persian Glances” JI tuning-

1:1 F @ 344 hz

567/512
9/8
5103/4096
81/64
21/16
729/512
189/128
3/2
1701/1024
27/16
7/4
15309/8192
243/128
63/32
2/1

))

Let’s start with the unison 1/1, this can be any note, as long as it is some note that we will use as the reference point for the scale.

Now let’s decide to make the scale repeat at the octave, so now we have pitch set 1/1, 2/1

Since, it is an octave repeating scale, it is convenient to express all notes between 1/1 and 2/1 (between one and two).

Let’s decide (as is the case for the Persian Glances scale) that we want to focus on combinations of the 3rd and 7th harmonics.

So lets triple our initial frequency and we get 3/1 (or 3).  Now, to put it within 1/1 and 2/1, we need to put some power of 2 on the bottom.  In this case it is just 2, so we have 3/2, which is 1.5 and is between one and two.  So now we have 1/1, 3/2, 2/1 (the root, P5 and octave).

Lets do the same for the 7th harmonic: multiply the initial frequency of vibration by 7, and divide by 4 (2 to the power of 2) to put it within the octave and we get 7/4.  Now we have: 1/1 3/2 7/4 2/1

Now lets combine these 3/2 * 7/4 = 3*7/2*4 = 21/8 … octave reduce by dividing another 2 we get 21/16.

We could combine two 7/4s to get 49/16 .. octave reduced to 49/32, but we see this scale doesn’t have it.  Instead we combine two 3/2s to get 9/4 = 9/8 which is in the scale, and then add a 7/4 to get 9*7/8*4 = 63/32 .. so on we can repeat this process.

Anywho, the central idea I wanted to discuss was that of motivation for scale design.  Persian Glances was both a good starting point for an example here, and also part of a conversation I had with Faras Almeer that inspired me to make this post.  We had been speaking recently about scale design and he had given me his specs for possible tunings for the Arabic Maqam of Rast and Hijaz.  He asked about the motivation for the Persian Glances tuning, and Jesse told me it was to explore the comma of 64/63 which is the interval between 63/32 (9/8 and 7/4 combined) and the octave, and this applied various times throughout.

Let’s show how this works:  If we apply another 3/2 to 9/8, following the Pythagorean method of scale construction, we get 3*9/2*8 = 27/16.  Let’s add the 7/4 again — 27/16 * 7/4 = 27*7/16*4 = 189/64 = 189/128.  This interval on the scale list is one step below 3/2.  This makes sense as 27/16 is a kind of major sixth and 7/4 is a kind of minor seventh, a flat one: the harmonic 7th.  So it is intuitive, as based on 12tone music that the 7th of the major 6th will be the 5th, and so a flat one would be flat of that.  And in just intonation, with the 7th harmonic, this does end up being true.  And lets test if this comma is there.  If it is then 189/128 * 64/63 should = 3/2.   We can see that 63*3 = 189 and 64*2= 128 and so this comma of 64/63 appears between 189/128 and 3/2 or between three perfect fifths + a harmonic 7th and a perfect 5th.  This pattern is repeated on each of the pythagorean fifths that are generated, essentially creating a 7/4 from each of these 5ths and then the respective 64/63 commas between each new part of the pattern.

Another perspective of how this works is to focus on the 3/2 and the 64/63 comma.  This was the method of interpretation of Faras Almeer.  You can take the octave and subtract the 64/63 comma and generate the tone of 63/32.  Then you can take the 3/2 and subtract the 64/63 to generate the 183/124 and so on.  This is an example of commas and generators being a different way to fundamentally express the same thing.  This is of music advantage to the composer and performer who can use these functions to their musical and creative advantage.

I have spoken with Faras Almeer a number of times recently about representations of maqam through just intonation.  What follows is not meant to be an accurate portrayal of maqam, not as historically or culturally accurate, but a framework in which some of the methods of scale construction may be analysed.

In Rast maqam, the third is often described as a neutral third (in just intonation, it is more simple to write this as 11/9 .. 347¢), or as sharp from a minor third, or flat from a major third.  These last two definitions both can describe a neutral third but also create an amount of flexibility or ambiguity.  In 12tone music, the minor third is 300¢ and the major third is 400¢, in 5-limit just intonation (ratios using up to the 5th harmonic), the minor third is 6/5 which is about 314¢ and the major third is 5/4 which is about 384¢ — sharp of the minor third or flat of the major third from the reference point of 12tone.

In addition, we can consider a pythagorean method or deriving the major or minor third: 32/27 (three 4/3s) for the minor third at 294¢ or the 81/64 (four 3/2s) for the major third at 404¢.  These don’t quite work for this definition.

Another approach is to approach this by melodic combinations of tones.  Two 3/2s will give us a 9/8 as a whole tone, and two of these will give us 81/64, which is expected as we just derived this interval as four of the 3/2s.  The minor whole tone of 10/9 combined with 9/8 will give us 5/4 which we already considered.  What about two 10/9s?  This gives us 100/81 at 365¢.  This could work.

What about a smaller representation of a tone?  The neutral third or neutral tone is often spoke of in Rast and the neutral sound often has correspondence with the 11th harmonic.  We have thus considered the 11/9 neutral third of 347¢,  what about the 11/10 neutral second (at 165¢)?  Two of these give us 121/100 which is 330¢, which could work.  With 11/10 and 10/9 we get 110/90 = 11/9, hey the neutral third (good to note that this is a way this interval can be generated).  What about 11/10 and 9/8, we get 99/80 which is 376¢.

We can also use another method of finding a note between a note.  Say between 6/5 and 5/4 we can calculate this mean as 6+5 / 5+ 4 = 11/9 which we already know to be between these.  We can continue the process with 6/5 and 11/9 as 6+11 / 5+9 = 17/14 which is 336¢, and another option.  We can also do this with 11/9 and 5/4 as 11+5 / 9+4 = 16/13 as 356¢, another option.

If you can imagine this many senses in which you can generate types of 3rds, you can imagine the spectrum of possibilities that exist in total.

For quick ratio to cent conversion, this place is great:

http://robertinventor.com/software/tunesmithy/help/cents_and_ratios.htm

Hope to write more on this soon.

Stay tuned ❤