This week marks the end of a three week unit of looking at how to implement the Common Core State Standards into our music classrooms. Last week, we focused on the implementation of the English Language Arts standards. This week, we are focusing on the implementation of the Standards for Mathematical Practice.
We use math skills and mathematical practices in the music classroom regularly. Now, we just need to document when and how we use them. If you need ideas, read pages 11 and 36-47 from the Arts and the Common Core document or read through the Crosswalk document. In the documents area, please find a link to Rhythms and Beyond by Timothy Loest (fjhmusic.com). This book may help you generate some ideas if you plan on using rhythms in your SLO.
You are not limited to using these resources in the creation of your assignment. The best lesson plans may come from the very music you are preparing for your next concert.
Create a lesson or an assignment where your students use math or mathematical practices to improve their knowledge and/or skills in the music classroom.
Our district’s Power Standards for K-12 Music divide into four categories: rhythm/beat/meter competency, tonal literacy, expression, and ensemble skills. The categories for rhythm/beat/meter competency and tonal literacy provide a structure for students to individually decode music. The Power Standards for students in 9-12 Instrumental or Vocal Music in those categories are:
- Rhythm/Beat/Meter Competency
- Dictate a performed rhythm (play or write)
- Perform a given rhythm with characteristic tone
- Identify a performed rhythm
- Identify meter
- Maintain a consistent pulse
- Breathe in time with proper technique and in musically appropriate places in performance
- Tonal Literacy
- Perform a major scale with characteristic tone
- Identify “do” through key signatures
- Identify tonal center
- Dictate a performed tonal sequence
- Perform a tonal sequence with characteristic tone
- Identify a performed tonal sequence
- Identify a harmonic sequence
- Perform a harmonic sequence with characteristic tone
The tools we use to teach and equip students with these skills are takadimi and solfege. Takadimi is a system of counting rhythms focused on the structure of the beat. Solfege is a system of teaching pitch focused on the tonal center of the music. Our district chose to use these two tools in all music classes K-12 so that teachers and students would have a common vocabulary when decoding music.
Takadimi and Solfege
Takadimi provides specific syllables for each division and subdivision of the beat. Regardless of time signature, the beat is always ta. In simple meter (beat divides into 2), the division of the beat is always di; the four subdivisions of the beat will be ta ka di mi. In compound meter (beat divides into 3), the three divisions of the beat are ta ki da, and the six subdivisions of the beat are ta va ki di da ma.
This system creates a rhythmic vocabulary, distinct words for nearly every possible rhythm in music. No two different rhythms will have the same “word” associated with it. Rhythms can be borrowed from simple meter into compound meter and vice-versa (triplets in simple meter are ta ki da, duplets in compound meter are ta di). If the division-subdivision does not fall into this 2-4 or 3-6 category, the syllable ti is added (ex: a quintuplet is ta ka di mi ti, a septuplet is ta va ki di da ma ti). There will be some rhythms that will not fit the mold, but the vast majority of rhythms our students will encounter in K-12 Music can be described using takadimi.
Our district chose to apply the solfege system using movable do and la-based minor. This decision was made because students will first learn the relationships of the syllables within a major scale. By allowing do to move throughout multiple key signatures and by allowing la to become the tonal center in minor key signatures, students maintain these relationships regardless of key signature or tonal center.
The solfege systems works well with transposing instruments. Because students know how to find do on their instrument, they are able to find concert pitch by continuing to use solfege. For Bb instruments, concert pitch is te. Eb instruments find me. F instruments find fa. The inverse could also be used with Bb instruments thinking of their do as re, Eb as la, and F as so, and then moving to the concert do.
Common Core State Standards for Mathematics
With both of the tools of takadimi and solfege, our students are able to independently decode music in lessons and ensemble settings. This ability to decode is a demonstration of several of the Common Core State Standards for Mathematics:
1. Makes sense of problems and persevere in solving them.
Students are able to read rhythms and pitches in a piece of music using takadimi and solfege to determine what the piece should sound like.
2. Reason abstractly and quantitatively.
Because the takadimi and solfege syllables limit rhythms and pitches to a very specific vocabulary, students are able to decontextualize phrases in order to decode them and contextualize phrases in the larger scheme of a piece of music.
4. Model with mathematics.
Students can apply takadimi and solfege to the music they hear every day outside of our music classrooms. These tools allow students to decode rhythm and tonal patterns as they occur in every day life.
5. Use appropriate tools strategically.
Takadimi and solfege are very specific tools for decoding rhythm and pitch. They provide a universal language across time signatures, key signatures, and instrument transpositions to help students better understand music.
6. Attend to precision.
The specific syllables used in takadimi and solfege allow for very specific “words” when decoding music. It is very clear what ta di mi or do mi so is in a given rhythm or tonal pattern.
7. Look for and make use of structure.
Because of the specificity of the takadimi and solfege syllables, students are able to discern rhythmic or tonal patterns due to repetition of “words.”
8. Look for and express regularity in repeated reasoning.
Students can expand this repeated reasoning to draw conclusions: “I see a lot of la and mi, so we must be in a minor tonality.” “This piece uses a lot of ta ki da rhythms, so it must be in compound meter.”
Every six weeks, students are expected to prepare and perform a short etude on their instrument from their lesson material. Each etude is in a different tonal center, and by the end of the school year, will have progressed through different divisions and subdivisions of simple and compound meter. During each of these summative performances, students are asked to:
- Identify meter (simple vs. compound).
- Find do.
- Identify the tonal center (major – do vs. minor – la)
- Perform the associated scale (major vs. harmonic minor)
- Patch and say the passage using takadimi syllables
- Perform the etude
By identifying and performing, the students are demonstrating the necessary skills detailed in the Power Standards which align with the Common Core State Standards for Mathematics.