4 ms·

Musical Scale Generator

35 points by bozho 12y ago

mrcactu5 12y ago
Have you considered examining Jazz scales? https://en.wikipedia.org/wiki/Jazz_scale https://en.wikipedia.org/wiki/Jazz_scale They start with the modes - Ionian, Phrygian, Lydian... - and they were embellished with certain accent notes. * https://en.wikipedia.org/wiki/Bebop_scale https://en.wikipedia.org/wiki/Bebop_scale * https://en.wikipedia.org/wiki/Lydian_augmented_scale https://en.wikipedia.org/wiki/Lydian_augmented_scale * https://en.wikipedia.org/wiki/Aeolian_dominant_scale https://en.wikipedia.org/wiki/Aeolian_dominant_scale * https://en.wikipedia.org/wiki/Altered_scale https://en.wikipedia.org/wiki/Altered_scale Many examples in Jazz recording and later classical composers like Debussy and Ravel
- showman 12y ago
  Good call on these scales. For those who are new to music theory basics, the easy way to remember your Modes is to relate them to their first step. For example. C D E F G A B is a C major scale also known as the IONIAN MODE. Beginning this scale on the 2nd note: D E F G A B C is the Dorian mode. So continue in this ++ manner and get the rest: PHRYGIAN, LYDIAN, MIXOLYDIAN, AEOLIAN (The natural minor scale), and LOCRIAN. These are all "Natural Modes" The significant one here is the 6th Mode or AEOLIAN. That is the minor key enharmonic (using the same notes) as the 1st Mode, our Major Scale. Why is it significant? Because the minor was a target for early composers to modify. Primarily the Melodic Minor and Harmonic Minor are based on the Natural Minor by using accidentals ( sharp notes and flat notes (a modification up or down by a half step)). Once we take our Modified Minor scale and play it starting on each individual scale step, we get our Fancy Jazz Scales. Voila. New Scales. So easy it is criminal. But, for some, very pleasing to the ear.
baddox 12y ago
This looks neat. I wish I could try it on my iPad. There is a lot of interesting mathematics behind music. I particularly enjoy reading about different temperaments, which are our attempts to compromise between just intonation (the harmonic-based scales the article mentions, which ostensibly sound the most "natural" and "correct" in a given key), and physical instruments, which we usually want to be able to play in multiple keys without significant adjustment. Twelve-tone equal temperament is the most common temperament in Western music, where the frequency of each semitone is the frequency of the previous semitone multiplied by the twelfth root of two. With equal temperament instruments, the error between just intonation intervals is the same regardless of the key. There is a rich history of temperaments. A early attempt, attributed to Pythagoras, illustrates the impossibility of constructing a temperament perfectly from the simple ratios generates by harmonics: http://en.wikipedia.org/wiki/Pythagorean_tuning#Method http://en.wikipedia.org/wiki/Pythagorean_tuning#Method The Wikipedia article on the tuning of Bach's aptly-titled Well-Tempered Clavier is also fascinating: http://en.m.wikipedia.org/wiki/Well-Tempered_Clavier#Intended_tuning http://en.m.wikipedia.org/wiki/Well-Tempered_Clavier#Intende... http://en.wikipedia.org/wiki/Musical_temperament http://en.wikipedia.org/wiki/Musical_temperament Edit: this video is a great demonstration of the errors between just intonation intervals and our equal temperament compromise: http://youtu.be/6NlI4No3s0M http://youtu.be/6NlI4No3s0M.
- shemol 12y ago
  Constructing a perfect temperament is impossible if you require each logical tone to be mapped to a constant frequency. I've long been curious about what would happen if you allowed the specific frequencies to drift in order to keep the ratio between concurrently sounding tones perfect (well, closer to perfect, as you add more tones). No idea whether the shift would be perceptible, or to how many ears.
  - baddox 12y ago
    Do you mean shift the frequencies when the key changes, e.g. between songs or when a song modulates? That certainly works, at least with electronic or continuously variable instruments. But even within one diatonic scale in a single key, it's impossible to have a fixed set of frequencies such that the intervals are correct in all of the diatonic triads. I suppose you could shift individual frequencies based on the chord currently being played, but I'm not sure how that would sound.
    - shemol 12y ago
      Per-chord is what I meant, not per-key. 3:2 means you can't have a coherent set for all tones in a key, full stop. But you could slightly shift the frequencies of the notes in a given chord to make that chord perfectly tempered. There'd be a million details; making sure the melodic voice, bass, or both avoided wolf intervals; figuring out what to when some voices are moving over a sustained chord in others; keeping the main anchor frequency from drifting "too far" from the original (and probably determining "too far" in the first place); figuring out whether the resulting sound was going to be anywhere near distinguishable enough to be worth all the effort of hacking through all this rigamarole.
      - baddox 12y ago
        Yeah, it sounds complicated. I wonder what a cappella groups like barbershop quartets do, or if they even think about it.
pierrec 12y ago
The scale generation algorithm described here is really interesting - it starts from the natural core of harmony (using rational relationships between frequencies), and gives you the option to keep the resulting natural-tempered notes, or to adapt them to the modern-day 12-tone equal temperament (12TET) and its irratonal, twelvth-root frequencies. The question of whether 12TET is "natural" or not is an interesting one, and in my opinion, it was great for a few centuries, but at some point music will move beyond 12TET. Take a look at one of richest websites exploring this question [1], whose author has a different opinion from mine. As for skipping the 7th harmonic -- i'd say you shouldn't do it. If you scroll down [1] until you get to the "n-tone equal temperament" graph, you'll find one of the nicest ever justifications for 12TET. However, if you added more harmonics to that graph, you'd find that the 7th does not fall anywhere close the 12TET frequencies: that's why we're not used to hearing it, and it sounds the most alien to us. [1]: http://www.geocities.jp/imyfujita/wtcpage004.html http://www.geocities.jp/imyfujita/wtcpage004.html
- TheOtherHobbes 12y ago
  It's an oversimplification to suggest that scales are based on the harmonic series. Many instruments have slight non-linearities in their overtones, and intervals that sound consonant aren't usually mathematically perfect. E.g. pianos don't even have perfect octaves. The major and minor scales seem to be based on very specific ratio sets, not on the general overtone series. But 12TET has 12 tones for a very practical reason - instruments with more tones are difficult to build and damn near impossible to play, because human hands are only so wide and finger movements have limited precision. There were experiments with more tones per octave back in the middle ages, but the idea never caught on because the musical benefits aren't obvious. So 12TET is a 'good enough' compromise between flexibility and expressiveness. Performers on instruments with an infinite pitch range vary their pitches anyway. Intonation problems drive conductors insane, and the reality is that orchestral and choral pitches tend to drift slightly towards consonance and away from the nominal ET ratios. Of course, with a computer you can do what you like. Here's some recent microtonal music written with SuperCollider: http://composerprogrammer.com/pitchdeviations.html http://composerprogrammer.com/pitchdeviations.html
dharma1 12y ago
-soundcloud link or mp3s would be nice -how do i run the java app? -I grew up playing several instruments from age 5, and love the vocabulary of chords and harmonies 12-TET gives us. It has a strong internal logic. But something bothers me about the fact that it's a man made system, not aligned with natural overtones that are rooted in physics -This guy is nuts. But I really want one of these big pythagorean monochords https://www.youtube.com/watch?v=tbCZO6rPcY8 https://www.youtube.com/watch?v=tbCZO6rPcY8 -using an ipad as a playable instrument with harmonic tuning - https://www.youtube.com/watch?v=o965af7w6_o https://www.youtube.com/watch?v=o965af7w6_o
gtani 12y ago
That's interesting. I've always suspected that the rules/heuristics governing intonation for voice, wind and (unfretted) string instruments is free form, depending on whether they're carrying the melody or playing in the "corps" of small or large ensembles. This vid, by (I think) a respected violin prof addresses this: carrying melodies in Pythagorean, ensemble playing in Just intonation, and ET if you have to (playing with piano). https://www.youtube.com/watch?v=QaYOwIIvgHg https://www.youtube.com/watch?v=QaYOwIIvgHg

35 points by bozho 12y ago

Have you considered examining Jazz scales? https://en.wikipedia.org/wiki/Jazz_scale https://en.wikipedia.org/wiki/Jazz_scale They start with the modes - Ionian, Phrygian, Lydian... - and they were embellished with certain accent notes. * https://en.wikipedia.org/wiki/Bebop_scale https://en.wikipedia.org/wiki/Bebop_scale * https://en.wikipedia.org/wiki/Lydian_augmented_scale https://en.wikipedia.org/wiki/Lydian_augmented_scale * https://en.wikipedia.org/wiki/Aeolian_dominant_scale https://en.wikipedia.org/wiki/Aeolian_dominant_scale * https://en.wikipedia.org/wiki/Altered_scale https://en.wikipedia.org/wiki/Altered_scale Many examples in Jazz recording and later classical composers like Debussy and Ravel

showman 12y ago
Good call on these scales. For those who are new to music theory basics, the easy way to remember your Modes is to relate them to their first step. For example. C D E F G A B is a C major scale also known as the IONIAN MODE. Beginning this scale on the 2nd note: D E F G A B C is the Dorian mode. So continue in this ++ manner and get the rest: PHRYGIAN, LYDIAN, MIXOLYDIAN, AEOLIAN (The natural minor scale), and LOCRIAN. These are all "Natural Modes" The significant one here is the 6th Mode or AEOLIAN. That is the minor key enharmonic (using the same notes) as the 1st Mode, our Major Scale. Why is it significant? Because the minor was a target for early composers to modify. Primarily the Melodic Minor and Harmonic Minor are based on the Natural Minor by using accidentals ( sharp notes and flat notes (a modification up or down by a half step)). Once we take our Modified Minor scale and play it starting on each individual scale step, we get our Fancy Jazz Scales. Voila. New Scales. So easy it is criminal. But, for some, very pleasing to the ear.

baddox 12y ago

This looks neat. I wish I could try it on my iPad. There is a lot of interesting mathematics behind music. I particularly enjoy reading about different temperaments, which are our attempts to compromise between just intonation (the harmonic-based scales the article mentions, which ostensibly sound the most "natural" and "correct" in a given key), and physical instruments, which we usually want to be able to play in multiple keys without significant adjustment. Twelve-tone equal temperament is the most common temperament in Western music, where the frequency of each semitone is the frequency of the previous semitone multiplied by the twelfth root of two. With equal temperament instruments, the error between just intonation intervals is the same regardless of the key. There is a rich history of temperaments. A early attempt, attributed to Pythagoras, illustrates the impossibility of constructing a temperament perfectly from the simple ratios generates by harmonics: http://en.wikipedia.org/wiki/Pythagorean_tuning#Method http://en.wikipedia.org/wiki/Pythagorean_tuning#Method The Wikipedia article on the tuning of Bach's aptly-titled Well-Tempered Clavier is also fascinating: http://en.m.wikipedia.org/wiki/Well-Tempered_Clavier#Intended_tuning http://en.m.wikipedia.org/wiki/Well-Tempered_Clavier#Intende... http://en.wikipedia.org/wiki/Musical_temperament http://en.wikipedia.org/wiki/Musical_temperament Edit: this video is a great demonstration of the errors between just intonation intervals and our equal temperament compromise: http://youtu.be/6NlI4No3s0M http://youtu.be/6NlI4No3s0M.

shemol 12y ago
Constructing a perfect temperament is impossible if you require each logical tone to be mapped to a constant frequency. I've long been curious about what would happen if you allowed the specific frequencies to drift in order to keep the ratio between concurrently sounding tones perfect (well, closer to perfect, as you add more tones). No idea whether the shift would be perceptible, or to how many ears.
- baddox 12y ago
  Do you mean shift the frequencies when the key changes, e.g. between songs or when a song modulates? That certainly works, at least with electronic or continuously variable instruments. But even within one diatonic scale in a single key, it's impossible to have a fixed set of frequencies such that the intervals are correct in all of the diatonic triads. I suppose you could shift individual frequencies based on the chord currently being played, but I'm not sure how that would sound.
  - shemol 12y ago
    Per-chord is what I meant, not per-key. 3:2 means you can't have a coherent set for all tones in a key, full stop. But you could slightly shift the frequencies of the notes in a given chord to make that chord perfectly tempered. There'd be a million details; making sure the melodic voice, bass, or both avoided wolf intervals; figuring out what to when some voices are moving over a sustained chord in others; keeping the main anchor frequency from drifting "too far" from the original (and probably determining "too far" in the first place); figuring out whether the resulting sound was going to be anywhere near distinguishable enough to be worth all the effort of hacking through all this rigamarole.
    - baddox 12y ago
      Yeah, it sounds complicated. I wonder what a cappella groups like barbershop quartets do, or if they even think about it.

pierrec 12y ago

The scale generation algorithm described here is really interesting - it starts from the natural core of harmony (using rational relationships between frequencies), and gives you the option to keep the resulting natural-tempered notes, or to adapt them to the modern-day 12-tone equal temperament (12TET) and its irratonal, twelvth-root frequencies. The question of whether 12TET is "natural" or not is an interesting one, and in my opinion, it was great for a few centuries, but at some point music will move beyond 12TET. Take a look at one of richest websites exploring this question [1], whose author has a different opinion from mine. As for skipping the 7th harmonic -- i'd say you shouldn't do it. If you scroll down [1] until you get to the "n-tone equal temperament" graph, you'll find one of the nicest ever justifications for 12TET. However, if you added more harmonics to that graph, you'd find that the 7th does not fall anywhere close the 12TET frequencies: that's why we're not used to hearing it, and it sounds the most alien to us. [1]: http://www.geocities.jp/imyfujita/wtcpage004.html http://www.geocities.jp/imyfujita/wtcpage004.html

TheOtherHobbes 12y ago
It's an oversimplification to suggest that scales are based on the harmonic series. Many instruments have slight non-linearities in their overtones, and intervals that sound consonant aren't usually mathematically perfect. E.g. pianos don't even have perfect octaves. The major and minor scales seem to be based on very specific ratio sets, not on the general overtone series. But 12TET has 12 tones for a very practical reason - instruments with more tones are difficult to build and damn near impossible to play, because human hands are only so wide and finger movements have limited precision. There were experiments with more tones per octave back in the middle ages, but the idea never caught on because the musical benefits aren't obvious. So 12TET is a 'good enough' compromise between flexibility and expressiveness. Performers on instruments with an infinite pitch range vary their pitches anyway. Intonation problems drive conductors insane, and the reality is that orchestral and choral pitches tend to drift slightly towards consonance and away from the nominal ET ratios. Of course, with a computer you can do what you like. Here's some recent microtonal music written with SuperCollider: http://composerprogrammer.com/pitchdeviations.html http://composerprogrammer.com/pitchdeviations.html

dharma1 12y ago

-soundcloud link or mp3s would be nice -how do i run the java app? -I grew up playing several instruments from age 5, and love the vocabulary of chords and harmonies 12-TET gives us. It has a strong internal logic. But something bothers me about the fact that it's a man made system, not aligned with natural overtones that are rooted in physics -This guy is nuts. But I really want one of these big pythagorean monochords https://www.youtube.com/watch?v=tbCZO6rPcY8 https://www.youtube.com/watch?v=tbCZO6rPcY8 -using an ipad as a playable instrument with harmonic tuning - https://www.youtube.com/watch?v=o965af7w6_o https://www.youtube.com/watch?v=o965af7w6_o

gtani 12y ago

That's interesting. I've always suspected that the rules/heuristics governing intonation for voice, wind and (unfretted) string instruments is free form, depending on whether they're carrying the melody or playing in the "corps" of small or large ensembles. This vid, by (I think) a respected violin prof addresses this: carrying melodies in Pythagorean, ensemble playing in Just intonation, and ET if you have to (playing with piano). https://www.youtube.com/watch?v=QaYOwIIvgHg https://www.youtube.com/watch?v=QaYOwIIvgHg