Composing microtonal

(Please excuse me, the keyboards don't play very well so I made a few errors and some notes are left out)

Okay, I'm not so stupid as to fly against consensus and convention so I concede that my use of harmony is based wholly upon the strict mathematical meaning of the term than the laxer and purely musical meaning (which is actually closer to the colloquial meaning of the word as you all have described it). I have stressed this a number of times in all my posts in an attempt to avoid this confusion. 

If I further limit "any pitch" to actually mean "any pitch that is one of the 12 notes in the octave" (as opposed to the infinite number of pitches [frequencies] from 440Hz to 880Hz that are not), then each pitch [note] in the 12-note chromatic scale has a harmonic relationship to at least 5 other pitches [notes] that are also in that scale. And I'm happy with that.

If I adopt the convention that harmony is any two frequencies played together then obviously the maths is meaningless. Even if I then constrain that to harmony being any two notes played together irrespective of their harmonic relationship then I further concede that the determination of what is consonant and dissonant is wholly subjective (again, irrespective of the harmonic relationship between them).

And I'm fine with that since whatever "works" will inevitably work, but then it all reduced down to "whatever sounds good to you" and I don't believe that Music Theory (and thus the physics of sound) is that inexact or random. We would not have arrived at the word "harmony" if harmonics were not part of the equation.

However,

Well since all the notes on the musical scale are harmonically related by simple virtue of the interval between notes being a twelfth power of two then the relationship between any two of them will be harmonic to some extent. The relationships of 4ths and 7ths are not dissimilar in that they are both harmonics of C, so the ratio of the 4th is 4:3 and the 7th (B in the C-major scale) is 15:8 (15th harmonic), as opposed to the harmonic 7th of 7:4 (which is a 7th  harmonic), which is Bb in the following diagram:

The twelve pitches on the chromatic scale are not random and they were not arrived at by accident.

When music was developed back in prehistory it did not start out as a 12 note chromatic scale. There simply was no practical reason to say, "let's divide an octave into half-step intervals and see what we can do with it"... not withstanding for there to be a half-step interval means that prior to that there was only a whole-step interval which would result in a 6-note chromatic scale. The concept of steps and half-steps is an after the event 'invention'.

When those scales were transposed extra notes were needed to maintain that consonance, for example starting with a major pentatonic interval pattern: shift it by one note and the two more notes are needed giving a total of 7 to choose from (one of which is now the 7th); shifting it one more note uses one of the two new notes but two more are needed giving us a bag of 9 notes; shifting it once more uses 4 of the original 5 plus 1 of the 4 new notes and finally shifting it 4th time uses only 1 of the original 5 but all four of the new ones. But now there are 4 new notes to start that pentatonic pattern from so when the pentatonic pattern is transposed onto each of those 4 new root notes 3 more new notes are needed raising the total from 9 to 12 (which finally adds the elusive 4th to our bag). The same pentatonic pattern played starting from these three new notes all use notes from the bag of 12 so no further notes were required to play a major pentatonic from any starting note:

I illustrated this using a major pentatonic but I could have used any of the other pentatonic scales and derived these 12-notes by transposing their interval pattern sequence by one note each time. 

Now because each note in a pentatonic scale is harmonically consonant then each of the 12 notes from this derived bag of 12 notes will have at least 4 other notes that are consonant with it, but it was noticed that some of the remaining notes were almost consonant while others were not, so when these nearly consonant notes were incorporated into the original 5 then interesting things could happen, which resulted in the plethora of 7-note scales (but as I said earlier - only 14 of these are of practical use and only a few of those are in common use, and there is a good reason for that that is entirely down to harmony).

guilhermeafonso wrote: Finally, if we were to play by your rules, we'd only say there's harmony when there's tonality... And that's just not true

see above. (I agree btw but that is covered by the maths ["rules"] I have been using.)

The 12 note system we have, organised traditionally as a 7 note diatonic scale is not an objective truth sorry to say

Your comment reminded me of a MIDI interface called the The Samchillian Tip Tip Tip Cheeepeeeee (silly name, I know) that I read about probably a dozen years ago. It was developed by Leon Gruenbaum, a musician with a degree in mathematics, and is usable with a regular computer keyboard, though he uses a customized ergonomic Kinesis keyboard as his controller.

 

The Samchillian is based on intervals rather than pitches, so pressing one key repeatedly will increment the pitch by one step, while another key will decrement it by steps, for example.

 

From Leon's website: "Here's how it works: a user first selects a scale and a key (e.g. F# pentatonic), and then every key that is subsequently pressed will move the user up and down a certain amount within the selected set of notes, depending on the number of positive or negative number of steps assigned to that key. Also the user is able to select from a number of scales, including microtonal scales and key signatures. A pattern, or "harmonic contour", once learned, can then be played in any key or scale without needing to relearn fingering".

 

The Samchillian is available for $25 by contacting Leon Gruenbaum from his website, where there are few extra videos of the Samchillian in action. I remember there being a free version for non-commercial use, but can't find it anymore.

 

This article written by Leon includes a diagram of the keys' functions.

 

This is a demo video from 2002. Leon discusses microtonal scales between 4:24 and 5:48.

 

 

But that isn't wholly true is it? The 15 seconds judgement is a consequence of 15 years experience and there is no escaping that. 

Davesax1965 wrote: It's very difficult to describe what's going on in a musicians' head when soloing. You have point A, the start. You have point B, the end. There are bits in the middle. Now, you'll need a set of rules to get there, unless you're Ornette Coleman* but I think it's fair to say that there are two processes at work. There's a semi-automatic one where you're thinking "major triad, now, what note am I on ? OK, a descending major triad here..... " - you're referencing musical theory, subconsciously or not, but you're also working by intuition to the genre and reference to what other people are playing around you.

I still say that isn't intuition but a conditioned response born from experience. 

It isn't intuition as such, it's the application of learned experience. It appears intuitive because you don't have to think consciously about it but it's no different to tying shoe laces, driving a car or riding a bicycle - none of those actions are intuitive, they have to be taught but once mastered they become second-nature. 

If you have never learnt to play a musical instrument you cannot pick one up and intuitively play Beethoven's Moonlight Sonata, and the same is true of composition. 

You say that it isn't formulated but it is, you decide which key to begin in and which scale to use (and yes, I will say that both those are formula), you decide on the time signature (that is another formula) and you decide on the rhythm, phrasing, tempo and all the other elements that are necessary to play one note after the other (all of which are formulaic). Even the choice of which note to play next can be described as a formula, albeit an unspecified one because each successive note is not a wholly random choice - whether you call it instinctive or formulative, the next note you play will most likely have some harmonic relationship to the notes that preceded it and/or the underlying chord or bass line unless you deliberately want to create tension within that phrase before resolving that tension by returning back to harmonic relationship. You play a phrase and then repeat and/or progress it to produce a melody that can be considered to be formulated in some way or other (the most obvious is 12-bar blues, but even when Prog Rock dispenses with such simplistic music structure it is replaced by less obvious and more complex structure but it is still structured). As soon as you repeat a phrase you have defined a rule, it may be a rule that has never been used before but it is a rule just the same. The notes in that melody line will also determine the choice of chords and the chord progression that accompanies it (or vice versa depending on how you compose a tune), and once again that is not a wholly random choice.  Music created in this way will sound (for want of a better word) composed, whereas music that has been created that doesn't fit those prescribed and well-chosen formula (for example by throwing sets of 8 or 12 sided dice, or throwing a xylophone down a flight of stairs) will not.

Of course the taboo word here is "formulaic" because it implies some pretty negative connotations such as 'music by numbers' where the inference is that music composed to a formula lacks creativity and emotion, which is of course a complete nonsense, that would be like saying Shakespeare lacked creativity and emotion because he rigidly used Iambic Pentameter in his soliloquies and sonnets. {I don't believe for one minute that Bill sat there counting the syllables in each line, nor did he use 'intuition', he had learnt that each line in a verse fitted a ti-Dum ti-Dum ti-Dum ti-Dum ti-Dum rhythm with the stress on alternate 'beats' and he just ran with it without having to consciously think about it}.

It is because composers adhere to these musical constraints that we get 'music'. By your own admission, music that does not is not music to your ears.

Even atonal music sounds more (again for the want of a more appropriate word) composed when it follows some formulated process. Schoenberg devised some 'rules' for composing 12-tone music that was atonal (i.e., lacked a tonal-centre), these 'rules' ensured that no single note was more prominent than any other and so created Serialism. (Of course Riley then responded to that by devising a rule-set that contained a tonal centre and thus created Minimalism). The point being, while both these dispense with the traditional constraints of music theory, they merely replace them with new ones. With practice and experience these new rule-set also become 'intuitive' and second-nature. Just as composing music using Arabic maqam or Indian raga is second-nature to musicians who learnt their craft in those music systems.

Davesax1965 wrote: It's an excellent point that you don't have to "learn the rules first to know how to break them" and, to be honest, I'd never thought of that !  There has to be an element of cultural immersion in this otherwise it becomes an exercise in merely combining notes according to mathematical rules. As Dean says, "Experience is merely knowing the rules by heart regardless of how they were learnt." Jazz has rules and the rules vary, for, say, bebop as they are stylistically different from other forms of jazz. Referring back to the OP - "How do I compose microtonically ? " - the answer has to be "What are you trying to do or sound like ? ". You then have to refer to the rules pertinent to that style of music (if you want to fit in with. a style) and immerse yourself in it.

Yup, more or less.

Davesax1965 wrote: As Guilhermeafonso says there is always going to be music which doesn't suit our ears, and that's partially down to cultural heritage. Gamelan music might be structured, but I wouldn't know, as soon as I hear a snippet of it, I switch off (and switch over) after the first bar.

No comment.