Temari Balls, Spheres, SphereHarmonic: From Japanese Folkcraft to Music

Round 1

Reviewer 1 Report

The paper discusses Temari balls and  a new musical game SphereHarmonic is designed based on it. In general the paper is well-written. In Section 3.1, the worst case numbers of rotations of  upper hemisphere is given as (2n)!/n, which means the instrument could be complex. It would be good to have a complexity result, e.g., PSPACE-hard.

Line 55: "plane [3,6].".

Author Response

The authors would like to thank the reviewer for his/her critical reading of our manuscript and helpful comments. The followings are the one-to-one reply to the list of comments. We denoted the revised parts in blue. 

- Lines 258-263: We added the description about the computational difficulties to the manuscript. 
- We corrected the references. 

Reviewer 2 Report

I have some comments:

-        line 60: Articles [1,2] are not defined in the references. Please, give both articles. [15] is also not complete.

-        line 66: Could you give a web page if the reader would like to listen to the music with CubeHarmonic?

-        line 92: Sn: n is sometimes italic, sometimes not. Check it.

-        line 97 and 107: What is exactly the magic number? Can you define or cite? How did you calculate it?

-        line 153: article, not manuscript.

-        line 155-163: Please, write a little bit more about the stereographic projection, especially, about the lower sub-figures of Fig.7.   Line 150: I think you illustrated the further half hemisphere instead of upper one in Fig. 7. It would be better if you could give a figure about the methods of the projection. The centres of the projections are sometimes vertices, sometimes middle of segments. Am I right? Why has just one subfigure of C6 in Fig. 7?

-        in Fig.8.: L=lower, U=upper

-        line 215: Table 2?

-        line 280-281 ??

-        line 312: What is the name of the journal?

Author Response

The authors would like to thank the reviewer for his/her critical reading of our manuscript and helpful comments. The followings are the one-to-one reply to the list of comments. We denoted the revised part in blue. 

- References 1-2: We changed the references to the correct ones.
- Line 77-78: We added the URL of the movie of CubeHarmonic on YouTube.
- Throughout the text, we unified the representation of Sn with S$n$. 
- Lines 115-117: We added the description of the magic numbers. 
- Line 183: We replaced the word "manuscript" with "article".
- Lines 170-183: We added the description of the stereographic projection with a new figure. 
- Caption of Fig. 9 (Fig. 8, previously): We corrected the caption. 
- Line 241: We corrected the table number. 
- Description of "Reset": the description wasn't essential for our objectives; however, we added some explanations on lines 313-315.
- Reference 27 (Reference 13, previously): We corrected the name of the journal.